diff --git "a/capability_index.json" "b/capability_index.json"
--- "a/capability_index.json"
+++ "b/capability_index.json"
@@ -1 +1 @@
-{"model":"ai999x-encoder-2","dim":256,"parameters":4715520,"domains":["algebra","mechanics","physics"],"entries":[{"domain":"physics","key":"uniform_motion","name":"Motion at constant 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potential of a point charge","package":"physics-ai999x","example":"What is the electric potential 0.5 m from a point charge of 3 nC?","v":[-0.0084,0.00452,0.10261,-0.05347,0.03797,-0.08261,-0.03166,0.08222,-0.09007,-0.1186,-0.09689,-0.03489,-0.05518,0.03232,0.00625,-0.06343,-0.04055,-0.06035,-0.0215,-0.00687,-0.02561,-0.04115,-0.05243,-0.04915,-0.05547,0.03793,-0.02001,-0.02536,0.02807,0.02528,-0.14692,0.06723,-0.00682,0.02081,-0.11652,0.09589,0.09353,-0.03669,0.03262,0.03964,0.12769,-0.02709,0.03547,-0.00137,-0.10033,0.04523,-0.10918,-0.07833,-0.09549,0.03553,-0.01143,0.036,-0.03475,-0.06635,-0.09692,-0.11087,-0.02441,0.05163,-0.02769,-0.01995,-0.01144,0.01342,-0.07632,-0.04285,0.06277,-0.00595,0.09347,0.01988,-0.03521,0.04848,0.0799,0.07221,-0.00657,0.00071,-0.03439,0.06593,-0.06641,-0.11109,0.07682,0.03871,0.05602,-0.031,0.01217,-0.04295,-0.00668,-0.01494,0.05441,0.00264,0.09374,-0.05728,0.11452,0.08533,-0.00837,0.01701,-0.05213,0.06383,-0.07626,-0.08108,0.00816,-0.07941,-0.02536,-0.17913,0.03153,-0.00534,-0.09167,0.00628,0.04491,-0.01471,-0.00758,-0.06555,0.07153,-0.01789,-0.00683,0.07342,0.07549,-0.01409,0.01245,-0.10544,0.00503,0.01335,-0.00979,0.01561,-0.03935,-0.02342,-0.06133,-0.06155,0.13851,0.10055,0.01949,0.11542,0.09079,0.09185,0.06164,-0.06356,0.04785,0.02215,0.02414,-0.0144,0.08041,-0.06273,0.05452,-0.08107,-0.00755,-0.07768,0.08912,-0.09825,0.09556,0.04173,0.04447,0.06266,-0.05119,-0.01191,0.08153,0.00688,-0.06511,0.0378,0.02831,-0.01776,0.01002,0.01032,-0.15084,-0.0827,0.06762,0.03754,0.08989,0.02754,-0.0147,-0.05068,-0.03037,-0.00494,-0.02571,-0.01572,0.05189,-0.05115,0.06231,-0.00461,-0.11598,0.02195,0.0545,0.02427,0.00543,0.00232,0.11017,0.00226,0.05705,0.01166,-0.07662,-0.05245,0.09326,-0.03545,-0.04191,0.00456,0.13303,0.07486,-0.05477,-0.05853,-0.07214,-0.08919,0.12814,-0.06261,0.00174,0.00982,0.11708,-0.10901,0.03391,-0.00348,-0.08922,-0.0546,0.08163,0.01671,0.00173,-0.00164,0.08024,-0.06939,0.00105,0.02173,-0.04184,-0.0131,0.07241,0.00972,-0.0403,0.02623,0.09861,0.08168,-0.01207,0.00442,-0.10736,0.02326,0.04544,-0.07322,0.04665,-0.00176,-0.00204,0.05269,0.04649,-0.00997,0.02732,0.09907,-0.00071,-0.10187,-0.01846,-0.00329,0.11656,-0.00883,-0.0146,-0.15423,-0.02996,0.04555,-0.05655,0.09295,0.12141,0.01266,0.08691,-0.03754,0.04688,0.04984]},{"domain":"physics","key":"uniform_field_potential","name":"Potential difference in a uniform field","package":"physics-ai999x","example":"Parallel plates are 5 mm apart with a uniform electric field of 2000 V/m between the plates. What is the potential difference?","v":[0.00587,0.02781,0.14997,-0.03324,-0.05069,-0.06848,-0.00434,0.01904,-0.03872,-0.09912,0.01798,0.00119,-0.00713,0.07853,0.03558,-0.0697,0.01021,0.05813,-0.0774,0.16146,0.00205,-0.01395,0.0074,-0.10649,-0.00493,0.02319,-0.0154,0.05336,0.01495,0.06351,-0.09213,0.04631,0.03118,-0.02138,-0.13725,0.0903,0.11753,-0.00471,0.00868,0.089,0.06515,0.0139,0.11819,-0.05042,-0.0221,-0.05217,-0.0023,0.0846,0.00576,0.07662,0.01298,0.05233,-0.06598,-0.04595,-0.11939,-0.01975,0.06804,0.07224,0.05808,-0.03234,0.02015,-0.01583,0.03116,-0.06518,0.04842,0.03113,0.03895,0.03245,-0.05122,0.08039,0.1016,0.10868,-0.0579,0.08955,-0.04024,0.19915,-0.08073,-0.10409,-0.02136,0.02795,-0.00494,-0.02199,-0.06745,-0.02361,-0.08675,0.01708,0.07974,-0.04226,0.02739,0.01696,-0.02313,0.06738,-0.04677,0.02948,-0.03391,-0.02922,-0.00985,-0.04426,-0.01292,-0.00699,-0.02596,0.00951,-0.02066,-0.01168,-0.04276,-0.03904,0.06202,-0.04264,-0.00816,-0.02264,-0.02707,-0.08204,-0.04295,0.09169,-0.09394,-0.05285,-0.01437,-0.01802,-0.02465,0.0255,-0.06395,7e-05,-0.06892,0.09508,-0.09089,0.01162,0.07803,0.11431,-0.00739,-0.0349,0.07912,0.12289,0.07574,-0.06379,-0.07096,-0.02349,0.03473,0.01612,0.07265,-0.00656,0.01284,-0.02031,-0.00685,0.04496,0.16166,-0.13253,-0.01452,-0.00838,0.13475,0.05372,-0.01492,-0.03485,-0.02192,-0.045,0.03357,-0.03432,-0.00641,-0.09188,-0.07759,-0.03402,-0.06444,-0.00173,0.05919,-0.01901,0.0545,0.00352,-0.12645,-0.034,0.00415,-0.11642,-0.07592,0.0245,0.08792,0.00029,0.12639,-0.08139,-0.06217,0.04927,0.00144,-0.12677,0.08187,-0.01806,-0.05256,-0.02187,-0.01999,0.02883,0.01371,-0.02924,0.10262,-0.08796,0.00259,-0.0123,0.01081,0.06515,-0.06329,-0.02886,-0.04829,-0.06301,0.08707,0.0185,0.00226,-0.02936,-0.01588,-0.16838,-0.04582,-0.03499,-0.07515,-0.07802,-0.0153,0.06413,-0.03674,0.04294,-0.00918,-0.03223,0.06106,-0.06944,0.08442,-0.0296,-0.04225,-0.07141,-0.05106,-0.00721,0.13404,0.03021,-0.00582,-0.00878,0.01613,0.01619,0.15179,-0.05691,-0.01541,-0.01001,-0.08909,0.04701,0.08041,0.00364,-0.03614,0.00797,0.0319,-0.06415,-0.02095,0.02739,0.1637,-0.04341,0.00227,0.05995,-0.10286,-0.02438,0.10266,-0.02921,0.08714,-0.00557,-0.05568,-0.03553,0.09604,0.02116]},{"domain":"physics","key":"capacitance_definition","name":"Charge on a capacitor","package":"physics-ai999x","example":"A 10 uF capacitor is charged to 12 V. How much charge does it hold?","v":[0.02104,0.09629,0.01602,-0.02149,-0.13996,-0.0762,0.08555,0.01431,-0.07415,0.0057,-0.04978,0.02791,0.0075,0.01744,0.03091,-0.02801,-0.01681,-0.05871,0.11549,0.02118,0.03895,0.00078,-0.03091,-0.01455,-0.12502,-0.00621,-0.02465,-0.00853,0.01952,0.0026,-0.07749,0.11403,0.02566,-0.02915,-0.0636,0.09907,0.04956,-0.16549,0.05117,0.05859,0.08705,0.03612,0.04872,-0.01603,-0.02033,-0.0436,-0.13711,-0.02088,0.00893,0.03887,-0.0749,-0.11393,0.10396,-0.02379,-0.08564,0.01105,-9e-05,0.01809,-0.08715,0.00547,-0.04073,-0.03998,-0.13692,0.06406,-0.01022,0.00936,0.07646,0.02365,-0.06962,0.00846,0.0098,0.06755,0.04918,0.03534,0.04701,0.0116,-0.06775,-0.08705,0.08157,0.06667,0.01508,-0.13913,0.05763,0.00094,-0.01172,-0.00773,0.09737,-0.00208,0.01883,-0.02269,0.08374,0.00671,0.0347,0.05779,-0.04943,-0.07587,-0.08003,-0.11009,0.02849,-0.00232,-0.04198,0.02461,0.0151,-0.0252,-0.01922,-0.02783,0.08707,0.01503,-0.02101,-0.00759,0.03349,-0.05817,-0.00896,0.09601,0.06873,-0.00066,0.08561,-0.0653,0.04452,0.12551,-0.07062,-0.00481,0.02804,0.06112,-0.04783,0.01625,0.00378,0.00382,-0.03832,0.02305,0.00883,0.05772,0.02062,-0.11892,0.02584,-0.10859,0.017,-0.01141,0.03353,-0.03164,0.02287,-0.07195,-0.01393,-0.01894,-0.02439,-0.03977,0.15432,0.11845,0.02174,0.02814,-0.04238,0.14044,0.08605,0.0021,-0.01982,-0.00701,0.00144,-0.10727,-0.00676,0.05591,-0.09719,-0.03047,0.10999,-0.02181,0.04999,0.07873,0.03054,0.01451,-0.07106,-0.04112,-0.07588,-0.03322,-0.0434,-0.0428,-0.0625,-0.00423,-0.12793,-0.02817,0.06578,0.10395,0.03637,0.11515,0.14994,-0.02609,-0.08957,0.03072,-0.09388,-0.05621,-0.04127,-0.02926,0.04796,-0.11677,-0.02647,0.01913,-0.02683,-0.05411,-0.08214,0.0302,0.14062,-0.05054,-0.00341,0.04713,0.06066,-0.06552,0.03136,0.01667,-0.11314,-0.09226,0.02419,-0.0013,0.01948,-0.2054,0.0479,-0.04891,-0.00915,-0.09254,-0.03366,-0.05526,-0.02792,0.04069,-0.00523,0.09754,0.05705,-0.03275,0.00508,0.03725,0.0149,-0.01848,-0.00074,-0.04037,0.05493,-0.02346,-0.04929,0.05498,0.03685,0.11592,0.06872,0.05617,0.03023,-0.10523,-0.07322,0.03639,0.06994,0.02128,0.10661,-0.07865,0.01802,-0.03922,0.02846,0.08146,0.03302,-0.0157,0.01491,0.08671,-0.02633,0.10599]},{"domain":"physics","key":"capacitor_energy","name":"Energy stored in a capacitor","package":"physics-ai999x","example":"A 100 uF capacitor is charged to 20 V. What is the energy stored in the capacitor?","v":[-0.01431,-0.03487,0.01752,-0.01827,-0.10815,0.08569,0.08715,-0.04763,-0.07841,0.08783,0.00152,0.03736,-0.05021,-0.02225,0.00132,-0.01244,0.04052,-0.03482,0.02958,-0.0151,0.02489,0.04568,0.06018,0.08012,-0.2058,-0.04489,0.06461,0.07192,-0.04526,0.02095,-0.04396,0.031,-0.02276,-0.01514,-0.00028,0.11004,0.03807,-0.12035,0.02523,-0.04496,0.02942,0.04041,0.01802,0.00594,-0.02207,-0.07325,-0.08757,-0.06832,-0.01381,-0.03903,0.03303,-0.04311,0.05253,0.08981,0.00192,0.06141,-0.03152,0.02823,-0.13524,0.03236,-0.00682,0.0387,-0.08758,0.06146,-0.03433,0.00583,-0.02601,0.01456,-0.07523,-0.00716,0.0078,0.0458,0.02379,0.0575,0.00594,0.14299,-0.05825,-0.03919,-0.01156,-0.00065,-0.00542,-0.03515,-0.03217,-0.07055,-0.07128,-0.12751,0.08581,0.03876,0.05198,-0.05057,0.06012,0.10333,0.05328,0.04146,-0.0239,-0.02072,0.00254,-0.09581,0.02705,-0.0001,-0.06703,0.04979,0.0576,-0.01397,-0.14048,-0.1353,0.0457,-0.02766,-0.02409,0.02641,0.0533,-0.01957,-0.04546,0.02623,-0.01119,-0.06408,0.03474,-0.00807,0.09552,0.08594,-0.03907,-0.06387,0.12801,0.02482,-0.09549,0.04264,-0.00256,-0.06006,-0.05088,0.05272,-0.01595,-0.01146,0.02414,-0.02906,0.0694,-0.05518,0.07426,-0.00406,0.11965,-0.02411,0.0346,-0.05899,-0.03333,0.09404,0.01913,-0.00659,-0.02962,0.04087,0.05677,-0.01643,-0.01976,0.09844,0.03927,-0.12655,-0.01046,0.01487,-0.04609,-0.0304,0.01898,0.03415,-0.00807,0.00122,0.10742,0.0109,-0.00835,0.01826,0.07494,0.07592,-0.03328,-0.03483,-0.0063,-0.0102,0.00677,-0.04273,-0.11257,-0.09998,-0.13508,-0.03308,0.14804,-0.14245,0.09398,0.10503,0.04073,0.06611,-0.02407,-0.04466,-0.02665,-0.01276,-0.00515,0.00542,0.03783,-0.11049,0.07707,0.03054,0.036,-0.05526,-0.01845,-0.05264,0.05665,-0.0869,-0.00347,0.04445,0.05975,-0.07448,0.05851,-0.04789,-0.02021,-0.18127,-0.06174,-0.02186,0.00706,-0.15602,0.01963,-0.03172,0.03346,-0.10367,0.03639,-0.13188,0.05597,-0.0172,-0.00387,0.03937,0.09898,0.04173,-0.04943,0.00774,0.09354,-0.02881,-0.00312,0.01861,0.01355,-0.03993,-0.08944,0.09781,-0.07216,0.09621,0.10332,0.0747,0.01155,-0.05806,-0.08156,0.00616,0.09393,0.09705,0.06007,-0.02691,-0.04436,-0.03156,0.14178,0.08473,-0.0189,-0.02815,-0.03319,0.07843,-0.01204,0.09271]},{"domain":"physics","key":"parallel_plate_capacitor","name":"Capacitance of parallel plates","package":"physics-ai999x","example":"A capacitor has parallel plates of area 0.01 m^2 with a plate separation of 1 mm. What is its capacitance?","v":[-0.0009,-0.05166,0.07439,0.00341,-0.10898,-0.04605,0.0679,-0.04289,0.01981,0.01831,-0.00133,0.04024,0.0481,0.05807,-0.04658,-0.0455,0.09332,0.01086,0.05799,0.11116,0.01076,-0.03181,0.10484,-0.1113,-0.14823,0.00699,0.0301,-0.02445,0.0609,-0.02077,-0.0023,0.04544,0.09054,-0.0413,0.01845,0.05197,0.02386,-0.0451,-0.03311,0.04082,0.08361,0.01887,-0.00338,-0.02959,-0.04204,-0.09377,-0.01235,0.03964,0.02415,0.00267,-0.01634,-0.04516,0.10725,0.01964,-0.05901,0.09732,0.00334,0.10874,-0.0175,0.00576,0.02781,-0.04683,-0.0721,0.04325,-0.06441,-0.01546,0.00232,0.0255,-0.04202,0.04643,0.05887,0.00851,-0.08009,0.07502,0.0483,0.05692,-0.08457,-0.10251,-0.00234,0.04409,-0.05232,-0.11986,0.05936,-0.04894,-0.04416,0.01826,0.13419,-0.01465,0.03062,-0.01383,-0.04522,0.06305,0.00024,0.13821,-0.04488,-0.04075,-0.04053,-0.09784,0.01667,-0.01738,-0.0193,0.14636,-0.03295,0.05357,-0.03845,0.03731,0.05965,-0.08055,-0.03628,0.0738,-0.02119,-0.0055,0.05713,0.05819,-0.03036,-0.07668,0.09866,0.05255,-0.02127,0.13445,-0.14059,0.08263,0.03863,0.0735,-0.09452,0.05299,-0.06286,0.02713,-0.07591,-0.07461,-0.04107,0.10051,0.02123,-0.14687,-0.02135,-0.03347,-0.00885,0.05335,0.01685,0.03007,0.05177,-0.13151,0.01212,0.02058,0.06542,-0.04571,0.03998,0.00078,0.04775,-0.01283,-0.03653,0.14304,0.05973,0.054,0.02022,-0.02356,0.00456,-0.08665,-0.01248,0.05827,-0.0539,0.01555,0.04506,-0.08244,-0.01861,0.07845,0.06075,0.15406,0.01084,-0.06623,-0.09747,-0.0484,0.01928,0.05658,0.021,-0.04203,-0.05004,0.03691,0.09256,-0.11826,0.05739,-0.00741,-0.05541,0.06141,-0.04315,0.07242,0.00697,-0.00663,-0.06737,-0.09204,0.08728,-0.05461,-0.02466,-0.00583,-0.08432,0.00149,-0.02764,0.0885,0.04141,-0.17845,0.0644,0.05938,0.00097,-0.11936,0.00413,-0.01542,-0.05991,-0.09214,-0.05828,0.06833,-0.04613,-0.17178,0.06065,-0.11259,-0.01918,-0.07714,0.06291,-0.10461,-0.03076,-0.02867,-0.02388,-0.04544,0.07473,-0.01462,0.0432,0.0134,-0.03185,-0.01173,0.09128,-0.04807,0.01819,0.00678,-0.01863,0.07967,-0.0124,0.11455,0.1019,-0.04322,-0.03442,-0.05349,-0.01889,-0.01747,0.04381,-0.0705,0.09817,0.05942,-0.05895,-0.01607,0.0292,-0.00014,-0.02729,0.01035,-0.0818,0.02545,-0.05294,-0.01536]},{"domain":"physics","key":"ohm_power_current","name":"Power from current and resistance","package":"physics-ai999x","example":"A current of 2 A flows through a 5 ohm resistor. What power does it dissipate?","v":[0.0164,-0.03561,-0.0404,-0.03956,0.04832,-0.01309,0.12568,-0.11964,0.04417,0.03511,-0.04682,-0.03079,0.01901,-0.00789,-0.09096,0.01552,-0.05615,-0.04536,0.00987,-0.00582,0.00831,-0.08068,0.0398,-0.00872,-0.05165,0.0228,-0.06677,-0.01627,0.02291,0.07087,0.04919,-0.03333,-0.1066,0.03337,0.01677,0.05726,0.02237,0.01189,0.08342,-0.02981,0.00128,0.02629,-0.01894,-0.09006,-0.07172,-0.09994,-0.02555,-0.01974,0.10683,-0.05296,0.04756,0.10753,0.03848,0.01213,0.05388,0.00066,0.03254,0.01681,-0.09948,-0.03262,-0.03074,-0.00237,0.07053,0.01006,-0.01189,0.02486,-0.03592,0.04283,0.02156,-0.04136,0.01413,-0.03628,-0.15074,-0.08497,-0.05229,0.0464,0.0156,0.0363,-0.05577,-0.00656,-0.11563,-0.05712,0.05383,0.07474,0.12187,0.05886,0.06774,-0.15758,-0.04544,-0.02795,-0.02607,0.00834,-0.02264,-0.03476,-0.02213,0.06233,-0.04258,0.05549,-0.05853,0.02983,0.04337,-0.02411,0.00099,0.04239,-0.04874,0.04951,0.07964,-0.03444,-0.15677,0.03514,0.01873,0.13653,-0.00303,0.01731,-0.03741,-0.00328,0.08177,-0.06872,-0.01908,-0.12902,0.01897,0.06832,0.06872,0.00728,0.01014,-0.05884,-0.08946,0.02212,-0.00321,-0.02558,-0.05801,-0.04704,0.02107,0.02246,-0.04699,0.04237,-0.05931,-0.05395,-0.00072,0.01647,-0.08207,-0.05874,0.04574,0.03186,0.11122,0.01865,-0.01205,-0.07865,-0.04424,-0.06716,-0.08942,0.12215,-0.05023,0.09897,-0.03169,-0.00826,-0.07899,0.08848,0.18795,-0.01333,-0.01784,-0.0048,0.00974,-0.02905,-0.15919,-0.05427,0.11816,0.003,-0.08796,-0.02044,-0.03012,-0.00821,-0.08081,0.08706,-0.14578,-0.00338,-0.01119,-0.07443,0.04481,-0.02083,0.01118,0.04029,-0.05401,0.13569,-0.03774,-0.05192,0.01265,0.08171,-0.12848,0.05589,0.01847,0.01149,-0.02214,0.03294,0.08415,-0.03085,-0.05715,0.02382,-0.04004,-0.06259,0.03771,0.1129,0.07241,-0.02842,-0.00392,0.10413,0.05506,0.049,-0.022,-0.02777,-0.04414,0.13324,0.09022,0.07989,-0.03569,0.01129,-0.03288,-0.00548,0.00753,0.01348,0.09514,-0.05575,-0.09987,0.05047,0.07707,-0.09998,-0.03918,0.14032,0.04762,0.11,0.08132,0.05774,0.03777,0.00098,-0.02144,-0.07265,0.03057,-0.04785,-0.05307,-0.02464,0.02924,-0.01883,-0.026,-0.04482,-0.01835,0.09524,0.07486,-0.04508,-0.02767,0.07679,-0.01817,-0.03358,0.17317,0.0759,-0.05087,0.09916]},{"domain":"physics","key":"ohm_power_voltage","name":"Power from voltage and resistance","package":"physics-ai999x","example":"A 6 ohm resistor is connected across 12 V. What power does it dissipate?","v":[-0.00395,-0.10534,-0.01982,-0.07287,-0.02701,0.08653,0.15281,-0.06664,0.13313,-0.03742,-0.0103,-0.01501,-0.05546,0.03428,-0.0785,-0.04584,-0.05036,-0.04506,-0.01559,0.09775,0.05017,-0.10221,0.02843,0.04253,-0.02142,0.00625,-0.07846,-0.03066,0.00981,0.11778,-0.10651,0.00622,-0.11567,0.03345,-0.08455,0.08677,0.15336,-0.04156,0.0434,0.03298,0.03706,0.11329,-0.03025,-0.07782,-0.06337,-0.11291,0.05425,0.01879,0.08574,-0.00986,0.0897,0.10352,-0.05434,-0.01889,-0.01443,-0.04662,0.06269,0.01888,0.03357,0.00553,0.00424,0.01101,-0.03027,0.00353,-0.0169,0.02805,-0.02329,0.00182,0.0093,-0.01723,0.03051,0.0033,-0.0446,-0.04417,-0.07784,0.14661,-0.00194,-0.04883,0.01043,0.01731,-0.12305,0.03869,-0.10069,0.02283,0.0353,0.05575,0.04857,-0.13589,0.02203,-0.02077,0.06436,0.10985,0.04055,-0.03706,-0.00828,-0.02896,0.02054,0.09501,-0.09843,0.00604,-0.09418,0.03877,0.04469,0.00557,-0.04421,-0.01507,0.02161,-0.07927,-0.06864,-0.02319,0.03875,0.00424,-0.14751,0.10768,-0.06855,-0.02402,-0.00979,-0.06062,0.04946,-0.07815,0.09266,-0.04765,-0.0193,-0.01902,0.02569,0.01995,-0.03064,-0.07207,-0.0842,0.08204,-0.00426,0.02199,0.03559,-0.04697,-0.05467,0.00575,-0.00705,-0.01567,0.029,-0.04441,-0.02003,0.05259,-0.00659,0.02394,0.11354,-0.04797,-0.13232,-0.05992,0.0822,-0.03087,-0.03094,0.12362,-0.11045,0.05256,0.0538,0.05615,-0.05521,0.00137,0.10746,0.03535,-0.14799,-0.04303,0.05298,0.00103,-0.0801,0.055,0.05211,0.00051,-0.03929,-0.12066,-0.00508,-0.0304,-0.06161,0.10729,-0.0723,0.00311,0.00564,-0.12288,0.03562,-0.07302,0.04856,0.06337,0.01827,0.06514,-0.15646,-0.10157,-0.03324,-0.02264,-0.10314,0.07715,-0.01455,0.01622,0.02345,0.01785,0.058,-0.04068,-0.03802,-0.07773,0.10637,0.03495,-0.07082,0.02646,0.02664,0.02376,0.00876,0.1404,-0.07781,-0.04904,-0.06216,-0.05559,0.00195,0.00069,-0.03589,0.05358,0.05578,-0.02674,0.00616,0.06785,0.02707,-0.01836,0.08298,0.04624,0.01292,0.00906,0.02523,-0.05464,0.01077,0.08818,0.08661,0.09018,0.02333,0.06167,-0.04624,0.04797,-0.0547,-0.07117,-0.03818,-0.02815,-0.06555,-0.03804,0.04661,0.03845,0.04326,0.00883,-0.00972,0.08597,-0.05762,0.05302,0.09378,0.08363,0.04145,-0.02773,0.10622,-0.00519,0.03801,0.08308]},{"domain":"physics","key":"resistivity","name":"Resistance of a uniform wire","package":"physics-ai999x","example":"A copper wire of resistivity 1.68e-8 ohm*m has a wire length of 10 m and a cross-sectional area of 1e-6 m^2. What is its resistance?","v":[0.0178,-0.03834,0.06292,-0.02261,-0.00436,0.06842,-0.00176,-0.02922,0.15092,0.03981,-0.01855,0.00313,0.13401,0.02165,-0.08965,-0.04172,-0.00648,0.06969,-0.08593,0.09059,-0.02714,0.03501,-0.01216,-0.07555,0.05398,0.07421,-0.07938,-0.1045,0.04924,0.12921,-0.10064,0.03912,0.06988,-0.00792,-0.00701,-0.03493,0.04745,0.07516,-0.02801,0.07845,0.12873,-0.01916,0.04822,-0.03008,-0.14374,-0.05043,0.0759,0.02666,-0.00645,-0.06039,-0.0793,0.05636,-0.01209,-0.01866,-0.01709,0.01532,0.05747,0.05495,0.01163,0.03061,-0.00632,-0.09232,-0.01415,0.0188,-0.03494,0.00948,0.09483,-0.01818,-0.05105,-0.05237,-0.04957,0.004,-0.14083,-0.01964,0.10765,0.03668,-0.09256,-0.05844,0.00884,0.00065,-0.01407,-0.00594,0.00288,0.01535,0.05313,0.13082,0.03668,-0.01941,-0.01824,-0.01407,-0.09385,0.092,-0.16173,0.08499,-0.08309,0.00341,-0.13878,0.06499,-0.00732,-0.03489,0.01604,-0.02189,0.01968,0.06742,0.00447,0.00925,-0.03305,-0.01077,-0.04383,0.11538,-0.07789,0.09627,-0.02503,0.05054,-0.13976,-0.10105,0.14335,-0.01485,-0.04195,-0.07383,-0.0009,0.06733,-0.02528,0.06296,0.00603,-0.02189,-0.02691,0.01852,-0.0245,-0.00406,-0.01913,0.15802,0.02449,0.03447,-0.08417,0.06055,-0.00322,-0.04212,-0.07656,-0.05488,-0.0,-0.06196,0.03792,0.03144,-0.01492,-0.09722,-0.01173,-0.02186,-0.01325,-0.08544,0.00278,0.06435,-0.04056,0.00141,0.09573,-0.08949,-0.0093,0.0115,0.06091,-0.05349,-0.08722,-0.00869,0.0143,-0.05425,-0.01243,-0.00929,0.11118,0.06347,-0.03603,-0.02296,-0.06916,-0.06538,0.09141,0.13805,0.02992,-0.02577,0.03777,0.00422,0.04996,-0.07158,0.02607,-0.07436,-0.05278,-0.0156,-0.0585,0.08108,0.05296,0.07557,-0.02874,0.1038,-0.00242,0.0321,0.02442,-0.04124,0.00107,-0.07321,0.01015,0.05555,0.04081,-0.00045,-0.02777,0.00585,0.0268,-0.09669,-0.09184,-0.07431,0.01461,0.09717,-0.12581,0.02937,-0.03242,0.09885,0.06322,-0.02571,-0.02698,-0.03745,0.06705,-0.02062,-0.00293,0.01871,-0.1299,-0.02093,-0.01084,-0.0246,0.16324,-0.04337,-0.00979,0.10538,0.08703,-0.02113,-0.04255,0.07327,0.0091,-0.03456,-0.07336,-0.05092,-0.02833,-0.0449,-0.06858,-0.05577,0.05159,0.02794,0.00379,-0.18288,0.00592,0.07721,0.06619,0.07956,-0.05537,0.06909,0.04834,0.02025,0.01515,-0.04221,-0.01656,0.07421]},{"domain":"physics","key":"magnetic_force_charge","name":"Magnetic force on a moving charge","package":"physics-ai999x","example":"A proton with charge 1.6e-19 C moves at 2e6 m/s perpendicular to the field of a 0.5 T magnetic field. What is the magnetic force on it?","v":[0.01412,-0.0377,0.01819,0.01549,-0.00461,-0.03844,-0.00199,-0.01327,0.02849,-0.00997,-0.06821,-0.0132,0.11123,-0.01952,0.05602,0.03086,-0.11568,0.00403,-0.02215,0.10786,-0.01923,0.09662,0.01328,-0.00822,0.00725,0.02203,0.00014,0.00264,-0.0325,0.0293,-0.03326,0.11021,0.05318,0.0587,-0.07621,0.03713,-0.013,-0.08453,-0.00814,0.06155,0.14091,0.05545,0.21142,-0.06957,0.03627,-0.01838,0.0407,0.12373,0.02601,-0.07399,-0.10125,-0.12476,-0.06297,-0.01921,0.03762,0.03803,-0.08952,0.02128,0.03068,-0.05695,-0.00185,0.03723,-0.04089,-0.17428,0.00547,0.02662,0.12363,0.10234,-0.12622,0.04341,0.05943,0.05968,0.00648,-0.12714,-0.07079,-0.15261,0.08074,0.06711,-0.0204,0.01262,0.03532,-0.06379,0.01087,-0.01651,-0.00029,-0.05189,0.00166,-0.06289,-0.02264,0.03686,0.07687,-0.03429,-0.03162,-0.04668,-0.05607,-0.0027,0.00516,-0.0072,0.07427,0.02775,0.04827,-0.03533,0.0652,-0.03752,0.02259,-0.03054,-0.0154,0.07772,0.05113,0.04163,-0.0919,-0.01454,0.0471,0.01131,0.00457,-0.03039,0.01969,0.03667,-0.00934,-0.01189,-0.10155,0.07802,-0.00227,-0.05166,0.01213,-0.0344,0.02194,0.1165,0.00583,-0.05255,0.01526,-0.05426,0.00823,0.04241,-0.06261,-0.03418,0.01896,-0.062,-0.08993,-0.09534,0.00389,-0.03688,0.02424,-0.03771,-0.01104,-0.09223,0.0718,0.09755,-0.04274,-0.047,0.07039,0.0088,0.0051,-0.02704,-0.17452,-0.00755,-0.02558,-0.0146,-0.07148,-0.09499,0.14082,-0.05613,-0.01482,0.01832,-0.0094,0.00122,-0.00481,-0.05703,-0.11481,-0.06129,-0.04754,-0.04757,0.00973,0.02514,0.10355,0.04967,0.05187,0.1137,-0.05927,0.0172,0.01765,0.01974,0.069,-0.06994,0.07121,0.0069,-0.07636,0.01202,-0.0435,-0.07927,0.00582,-0.00524,-0.00627,0.04712,-0.01906,0.01377,-0.08304,0.00109,-0.04594,0.14346,0.02606,-0.04832,0.01713,-0.02306,0.02323,0.05251,0.01373,0.14554,0.00722,0.01408,0.01698,0.10824,0.08298,0.0449,0.03099,-0.09773,-0.173,0.00116,-0.01898,0.04297,-0.08775,-0.01476,-0.00407,0.07256,-0.0146,0.04175,0.00032,-0.01415,0.17481,0.05352,-0.0701,-0.13801,0.03153,0.05906,-0.03615,-0.04973,0.12807,0.02213,0.06222,-0.04403,-0.06964,0.02166,0.00117,0.02162,0.00957,-0.06553,0.03097,0.01134,-0.08371,-0.03779,-0.028,0.05782,0.00468,0.13794,-0.0987,0.03807]},{"domain":"physics","key":"magnetic_force_wire","name":"Magnetic force on a current-carrying wire","package":"physics-ai999x","example":"A wire carrying 5 A has a wire length of 0.2 m perpendicular to the field of a 0.4 T magnetic field. What is the magnetic force on the wire?","v":[0.00388,0.03376,0.02272,-0.02577,0.0414,0.01356,-0.028,-0.05839,0.04772,0.09578,-0.0805,-0.01069,0.12721,-0.02036,0.02985,0.01464,-0.09336,0.05495,-0.01129,0.02539,-0.06433,0.11966,-0.01549,-0.04676,0.04952,0.01724,-0.00761,0.06818,-0.03913,0.05924,0.02042,0.04455,-0.00346,0.09192,-0.01255,0.0065,-0.08209,0.032,0.00488,0.04712,0.009,0.01195,0.20342,-0.02066,0.01769,-0.02443,-0.00865,0.104,0.03509,-0.04775,-0.10943,-0.04209,-0.05867,0.00967,0.00688,0.04734,-0.11544,0.00411,-0.05335,-0.07664,-0.03985,0.02477,-0.00226,-0.16513,0.01066,0.0432,0.05243,0.07163,-0.13652,-0.05339,0.02962,0.0148,-0.00724,-0.07129,-0.05749,-0.15763,-0.03085,0.0255,-0.08952,-0.06999,-0.0101,-0.02622,0.08753,-0.02979,-0.00085,0.00284,-0.02007,-0.04321,-0.07408,0.0017,0.00343,-0.06124,-0.1517,-0.04694,-0.04929,0.02964,-0.06015,0.00874,0.02842,0.06734,0.06915,-0.09057,-0.00804,-0.00479,0.07236,-0.03337,-0.05843,-0.00924,0.00313,-0.00044,-0.11547,0.03306,0.04929,0.01953,-0.0324,0.02297,0.07479,0.06613,-0.02324,-0.06657,-0.06267,0.11207,0.04833,-0.02957,-0.02177,0.01128,-0.003,0.01743,0.11482,-0.12418,0.00246,-0.01312,0.06129,0.12622,-0.09268,0.03982,-0.02499,-0.08807,-0.10463,-0.0693,-0.02163,-0.02463,-0.02368,0.02205,0.1011,-0.02979,0.01722,0.03596,-0.02268,-0.11189,0.03192,0.00874,0.00377,-0.05459,-0.02678,-0.0469,-0.01111,0.04348,0.01733,-0.09789,0.15393,-0.01094,-0.03298,-0.03241,-0.03577,-0.11387,0.04748,-0.02961,-0.13105,-0.05554,-0.07319,-0.01974,0.00889,0.09739,0.05224,-0.03233,0.01983,0.03846,0.02524,-0.01834,-0.00284,-0.04925,-0.03506,-0.01851,0.0902,0.01258,0.02433,0.1103,-0.02713,-0.05769,0.03548,-0.03251,0.01271,0.0026,0.03872,-0.00015,-0.03603,0.06312,-0.1507,0.10029,0.03878,-0.00197,-0.00975,-0.09112,-0.00791,-0.03679,0.05871,0.12601,-0.0072,0.06434,-0.02294,0.23891,0.06273,0.08623,0.07493,-0.04446,-0.06311,0.01478,-0.01063,-0.02399,-0.05791,-0.00044,-0.01791,0.06601,0.0865,-0.01499,0.1275,0.03091,0.15145,0.05447,-0.03106,-0.0731,0.04088,0.01931,-0.05097,-0.00692,0.11555,-0.0072,0.08563,-0.01719,-0.01635,0.02882,-0.03551,-0.01879,-0.04816,0.03101,0.05955,0.05083,-0.11291,-0.07097,0.00488,0.02286,0.04469,0.09406,-0.06041,0.07819]},{"domain":"physics","key":"long_wire_field","name":"Magnetic field of a long straight wire","package":"physics-ai999x","example":"What is the magnetic field 5 cm from a long straight wire carrying 10 A?","v":[0.04311,0.01529,0.05795,0.00142,0.08994,-0.0523,-0.04757,0.00141,0.10402,0.10804,-0.08366,-0.03331,0.159,-0.02986,0.00047,0.00747,-0.01505,0.02399,0.02593,0.02709,-0.09286,0.05598,-0.05072,-0.11814,0.05471,0.02199,0.02266,-0.02623,0.01761,0.03424,0.0549,0.01765,0.02647,0.07508,-0.03566,0.0175,-0.0092,0.108,-0.00632,0.03167,-0.01489,-0.04175,0.17938,-0.02677,-0.08967,-0.03177,-0.04791,0.06931,-0.03709,-0.05473,-0.09595,0.03776,0.00378,-0.0262,-0.01833,0.05173,-0.05627,0.05132,-0.08237,-0.07755,-0.07438,-0.00038,0.01909,-0.12955,-0.00986,0.07743,0.06484,0.08001,-0.10421,0.0114,0.04666,0.04736,-0.13275,-0.01195,-0.04677,-0.15306,-0.08639,-0.06471,-0.05515,-0.03364,0.02138,-0.03777,0.05922,-0.05793,-0.00262,0.0271,0.02364,-0.06153,-0.06664,-0.03909,0.02214,-0.0202,-0.12506,0.02756,0.0118,0.05017,-0.04019,-0.00884,-0.00194,0.04996,0.05236,-0.15953,0.00501,0.02337,0.00024,-0.00087,-0.05072,-0.03852,0.04398,0.0013,-0.11827,0.06355,0.07133,0.02464,-0.05816,-0.0223,0.07522,0.01482,-0.07336,-0.07338,-0.06225,0.0712,0.03774,-0.01218,-0.05912,-0.00813,0.08726,0.11194,0.13461,-0.08077,0.01244,0.01422,0.04486,0.10602,-0.0206,0.04817,-0.03026,-0.06196,-0.03776,-0.02812,-0.03704,-0.03262,-0.00979,-0.00396,0.06794,-0.00494,0.05777,-0.01562,-0.023,-0.0845,0.04149,0.00219,0.09874,-0.0062,-0.01939,-0.05123,0.01994,0.09167,0.01553,-0.10021,0.1138,0.01073,-0.01897,-0.12491,-0.03252,-0.1219,0.03093,-0.00418,-0.02897,-0.03421,-0.07575,0.00311,0.0182,0.06235,0.03646,-0.07885,-0.03596,0.04202,0.09095,-0.04739,0.02816,-0.0432,-0.05021,0.05968,0.11734,0.07465,0.09218,0.09057,0.01942,-0.03718,-0.04797,-0.0806,0.0527,0.01882,0.02316,-0.04943,-0.00965,0.09547,-0.12596,0.01251,0.08428,-0.01358,0.03811,-0.15608,0.01837,-0.13896,0.09263,0.06153,0.0067,0.08863,-0.08629,0.21454,0.07051,0.00837,-0.00387,-0.0472,-0.06079,-0.02619,0.02679,-0.02132,-0.07845,-0.05337,0.00682,0.06683,0.07367,-0.03252,0.10336,0.01942,0.09535,-0.03535,-0.03267,-0.00035,0.07271,-0.00248,-0.00933,0.03182,0.05736,0.041,0.01949,-0.04117,0.05142,0.013,-0.0176,-0.08316,-0.04559,-0.0051,0.0734,-0.03669,-0.10413,0.01598,0.06001,-0.0532,0.02694,0.0557,-0.05726,-0.00366]},{"domain":"physics","key":"solenoid_field","name":"Magnetic field inside a long solenoid","package":"physics-ai999x","example":"A solenoid has 1000 turns per meter and carries 2 A. What is the magnetic field inside it?","v":[-0.005,-0.03567,0.0098,-0.00825,0.05278,-0.01223,-0.00378,0.04607,0.12404,0.08484,-0.09293,-0.08484,0.0968,0.04913,0.00034,0.02276,-0.01931,0.03591,0.06836,0.06877,-0.01381,0.03295,-0.02744,-0.05589,0.08836,-0.02517,0.11024,0.01644,0.04186,0.0397,0.07338,-0.04755,0.01739,0.02343,-0.02907,-0.06038,0.02054,0.05145,0.00602,0.07394,0.02116,0.00169,0.11259,-0.02133,0.06072,-0.07313,0.00475,0.14907,0.02472,-0.0968,-0.03851,-0.01935,0.01742,-0.11094,-0.02328,0.05417,-0.0666,0.01827,-0.07114,-0.04926,-0.08314,0.03406,0.03758,-0.12528,0.05843,0.09245,0.00798,0.0274,-0.0304,-0.01809,0.08381,0.03867,-0.12757,0.0,-0.07608,-0.05239,-0.09007,0.00054,-0.01993,0.02294,-0.01964,0.07372,0.02416,-0.04235,0.03027,-0.00866,-0.0053,-0.07715,-0.00249,-0.00445,0.06317,-0.02876,-0.10959,-0.04382,-0.02591,0.0245,-0.06432,-0.06056,0.0099,0.10059,0.09295,-0.06494,0.03346,-0.02382,0.07794,-0.00741,-0.064,-0.03003,0.07255,0.07049,-0.11492,-0.00879,-0.00243,0.02834,-0.08861,-0.05291,0.09869,0.03126,-0.0434,-0.09852,-0.04433,0.03996,0.08095,0.00083,-0.08767,0.02979,0.14639,0.10481,0.01337,-0.11538,-0.01556,-0.05615,-0.02499,0.08626,-0.00707,0.04085,-0.06459,0.03268,-0.0277,0.03459,0.01981,-0.04564,0.06647,0.08684,0.10729,-0.08338,0.01311,-0.00569,-0.00643,-0.02612,0.03323,-0.02897,-0.02474,-0.0764,-0.04771,-0.0994,-0.06908,0.09469,-0.07502,-0.10546,0.10084,-0.06592,-0.04336,-0.07745,-0.09493,-0.09762,0.03265,-0.07274,-0.13905,0.01574,-0.01986,0.00306,0.01449,0.04382,0.08874,-0.04374,-0.00465,0.03665,-0.00028,-0.05711,0.00143,-0.02688,-0.10538,0.10011,0.16027,0.0132,0.07985,0.10541,-0.01277,-0.00354,-0.02325,0.02631,0.06018,0.01502,0.01039,-0.02489,0.07736,0.05842,-0.19282,0.02898,0.0968,-0.00848,-0.00781,-0.05687,0.07043,-0.16702,0.06009,0.02482,-0.08192,0.0448,-0.04997,0.05067,0.17345,0.00274,-0.00594,-0.07366,-0.07082,-0.03835,-0.04998,-0.03427,-0.07164,-0.07358,0.03382,0.1,0.02947,-0.01461,0.05846,0.05839,-0.00976,-0.04392,0.04745,-0.0625,-0.01082,-0.01029,-0.0162,0.00941,0.013,0.05071,-0.00993,0.01995,0.05512,-0.02902,0.06905,-0.03018,-0.0178,-0.01673,0.14104,-0.05814,-0.12018,0.00911,0.06497,-0.01191,-0.02099,0.02982,-0.01076,-0.0322]},{"domain":"physics","key":"surface_gravity","name":"Gravitational acceleration at a distance from a mass","package":"physics-ai999x","example":"A planet has a mass of 5.97e24 kg and a radius of 6.37e6 m. What is the acceleration due to gravity at its surface?","v":[-0.02013,-0.05708,-0.01186,0.03846,0.02411,-0.03853,0.05183,-0.05068,0.11838,0.00204,-0.01854,-0.02314,0.05084,-0.01394,-0.13622,-0.04568,0.01055,0.07247,0.08051,-0.05052,0.03248,-0.05863,0.0286,-0.04218,-0.00671,-0.05269,0.03767,-0.0636,-0.01662,-0.06768,-0.03944,-0.00018,0.00145,-0.014,-0.03793,-0.0849,-0.01993,0.09145,-0.06128,-0.07343,0.06321,0.03075,-0.10544,0.02537,-0.05163,-0.02592,-0.03159,0.00942,0.0542,0.01651,-0.04587,0.13271,0.11179,0.07833,-0.08843,0.04802,-0.05628,-0.07628,-0.01237,0.03964,-0.00373,-0.10315,-0.02141,0.07229,0.05306,-0.02369,0.05051,0.05894,0.03431,-0.01823,0.06727,-0.07446,-0.02718,-0.05598,-0.00817,0.21615,-0.08983,-0.14616,-0.07256,-0.00803,-0.05845,0.0619,-0.00476,-0.08752,-0.07177,0.08542,0.15645,-0.08038,0.09742,-0.04059,0.0435,0.01791,0.01273,0.03737,-0.05642,0.14924,-0.04761,-0.09533,0.0319,-0.05602,0.04177,-0.12976,0.05231,0.05459,-0.05833,-0.08899,0.02191,-0.09158,0.05981,0.07174,0.02587,0.15312,-0.04809,0.0116,-0.01369,-0.05737,0.04429,-0.02163,0.00547,0.08511,0.0007,0.07904,0.04068,-0.06691,-0.03858,0.05752,0.01806,0.01157,-0.04007,-0.03669,-0.03512,0.0486,0.01929,-0.03357,-0.02141,0.06497,-0.02657,0.03711,0.06783,0.01777,0.04815,-0.05994,0.02442,0.01915,0.09453,0.04249,0.12109,-0.03426,-0.04354,0.00073,-0.02698,-0.00168,-0.01943,0.02634,-0.02758,0.02586,-0.00182,0.01543,-0.06276,0.07322,-0.13246,0.0187,0.01428,-0.11181,-0.08855,0.06,0.113,0.09284,-0.0044,-0.01109,-0.04653,0.06858,-0.04519,0.00821,-0.02114,0.00923,-0.01741,-0.05288,0.06399,-0.07357,0.0388,0.07961,0.02224,0.04524,0.0269,0.04405,0.01737,0.07964,0.0518,-0.16408,-0.00849,0.083,0.09583,-0.02513,-0.04355,-0.0185,0.03986,-0.02468,-0.10939,-0.17973,-0.07393,0.01036,-0.10156,-0.04153,-0.00192,-0.05508,-0.08831,-0.01472,-0.02044,0.02481,-0.07191,-0.00799,0.07824,-0.09606,0.02913,-0.05739,0.02227,-0.00829,0.07473,0.09536,-0.07023,-0.06267,0.04339,0.11277,0.04275,-0.10315,-0.07992,-0.03125,0.06143,0.01007,0.02119,0.11553,0.01498,-0.00205,-0.01516,0.02056,-0.01179,-0.0098,-0.05912,0.04684,0.09253,-0.03008,0.02893,-0.00907,0.00445,0.06325,0.09661,0.10887,0.00716,-0.00668,-0.0258,-0.04902,-0.05792,0.06834,-0.04965,-0.00947]},{"domain":"physics","key":"orbital_speed","name":"Speed in a circular orbit","package":"physics-ai999x","example":"A satellite is in a circular orbit of radius 6.77e6 m around a planet of mass 5.97e24 kg. What is its orbital speed?","v":[0.03773,-0.08084,0.01862,0.01202,-0.04073,-0.18484,0.07734,-0.00815,0.19475,-0.00417,-0.00379,-0.08002,0.07809,-0.0463,-0.08539,0.0026,-0.05136,-0.02906,0.0139,-0.02142,0.03357,0.05612,0.05115,-0.06054,-0.04107,-0.03739,0.04353,-0.08024,0.04354,-0.038,0.0224,0.04312,0.09322,-0.00889,-0.01975,-0.09223,-0.01764,0.12156,-0.06654,0.08028,0.11817,0.06285,-0.00883,0.00854,0.00243,-0.05232,-0.02927,0.04618,0.03006,-0.06881,-0.02677,0.0553,0.0229,0.03298,0.00451,0.03921,0.02057,-0.00049,-0.03245,0.05919,-0.00098,-0.00467,-0.06447,0.07871,0.00949,-0.05634,0.05784,-0.00036,0.00678,0.09966,-0.00436,-0.09769,-0.01667,0.01683,-0.00096,0.12473,-0.08922,-0.02938,-0.04281,0.07962,-0.03941,-0.04677,-0.01714,-0.00454,0.02682,-0.03656,0.07599,-0.0021,0.04123,-0.04841,-0.00825,0.01108,0.06753,0.06193,-0.04436,0.1577,-0.03029,0.03342,-0.02412,-0.05872,-0.02256,-0.00921,0.10243,-0.01408,-0.06323,-0.03885,-0.01317,-0.01311,-0.03623,0.04216,-0.0506,0.03191,-0.00391,0.02788,0.03522,0.00568,0.05382,0.01827,0.0132,0.00587,-0.04228,0.03036,-0.03174,0.03265,0.03254,-0.06574,-0.01476,0.18426,-0.11952,0.08028,-0.08625,0.04351,-0.07264,-0.00867,-0.03208,0.05735,0.04568,0.09607,0.05456,-0.03436,-0.00856,0.01543,0.0781,-0.02625,0.02005,0.05893,-0.09647,-0.10834,-0.12812,0.03986,-0.01395,0.08137,0.03246,0.01091,-0.16591,-0.01762,0.1178,-0.0639,0.03882,-0.05912,-0.05725,0.05868,-0.04346,-0.17474,-0.06253,0.07217,0.05077,0.09846,0.0764,0.06256,-0.04746,0.00032,0.03289,-0.03521,0.05221,0.01476,-0.05039,0.12228,0.04205,-0.11952,0.06607,0.03095,0.04501,0.09912,0.00202,-0.01208,-0.01379,-0.05092,-0.04058,-0.14723,-0.06097,0.01299,0.01752,-0.00955,-0.02382,0.00077,-0.06004,0.03678,0.01287,-0.04469,-0.00379,-0.01078,-0.12928,-0.02565,-0.07368,-0.02356,0.02206,0.06968,-0.11763,-0.0607,0.01027,0.02322,0.17933,-0.08543,0.01087,-0.07104,-0.07154,-0.01845,0.08232,0.06257,-0.15388,-0.05055,-0.00513,0.05744,0.0488,0.01895,-0.07184,0.10102,0.03051,0.04838,-0.02068,0.05045,0.01975,-0.07272,0.01544,-0.07293,-0.02469,-0.03512,-0.10769,-0.05413,0.02305,-0.04431,0.10921,-0.01589,-0.0105,-0.01276,0.09397,-0.00562,0.02477,0.04349,-0.07841,0.03344,-0.0876,0.09614,-0.02961,0.02924]},{"domain":"physics","key":"orbital_period","name":"Period of a circular orbit","package":"physics-ai999x","example":"A satellite orbits a planet of mass 5.97e24 kg at an orbital radius of 4.22e7 m. What is its orbital period?","v":[0.07313,-0.02206,-0.09008,0.03822,0.03071,-0.12288,0.04442,-0.03941,0.18615,0.0555,-0.00133,-0.03312,0.09641,-0.0253,-0.05617,0.0015,0.03359,0.03308,0.04618,-0.06342,0.03439,0.07793,-0.03722,-0.01573,0.01876,-0.03717,0.00927,0.01934,0.07342,-0.03198,0.0603,0.0438,-0.02929,0.02827,0.03151,-0.1168,-0.06476,0.20245,-0.04475,0.05371,0.08829,0.09143,-0.01406,0.03928,-0.12511,-0.03592,-0.03474,0.12053,0.06001,0.00343,-0.14028,0.15029,0.00585,0.08223,-0.00824,-0.02319,-0.06347,-0.02961,-0.06442,0.05166,0.00477,-0.03095,-0.03907,0.10671,0.12641,-0.00902,0.00063,-0.05371,0.04202,-0.01648,-0.03247,-0.15065,-0.01742,-0.08188,-0.02417,0.0916,-0.0393,0.06892,0.00053,-0.01953,-0.03718,-0.06429,0.09298,-0.01691,0.03247,-0.01945,0.02352,-0.04238,0.04948,-0.04819,-0.02031,-0.06307,0.00116,-0.04662,-0.05213,0.12347,0.06305,0.07511,-0.04744,-0.02376,0.0042,-0.03088,0.04674,0.06735,-0.00704,0.04555,-0.0134,-0.10199,0.03693,-0.06064,-0.0354,0.04183,-0.06832,-0.03406,0.04787,0.01532,-0.01245,0.0069,-0.00521,0.09891,-0.08078,0.01695,-0.02381,0.00723,-0.03433,-0.00393,0.02502,-0.00584,-0.06275,0.04679,-0.03312,-0.00654,0.01683,0.05545,-0.00119,0.03489,-0.00782,0.10134,0.18822,0.03886,-0.03336,-0.07321,0.02999,-0.05959,0.00534,0.05971,-0.12162,-0.02981,-0.02651,0.02821,-0.03841,0.0033,0.01682,-0.07229,-0.0936,0.05941,0.08781,0.06967,0.06155,-0.00627,-0.06167,0.12586,-0.02246,-0.16275,-0.01783,0.04298,0.02977,0.12006,-0.07331,0.00151,-0.06669,0.02494,0.07438,0.0441,-0.03959,0.0483,-0.03373,0.04146,0.03062,-0.06822,-0.0086,0.02562,0.09282,-0.02141,0.04647,0.03493,0.04493,0.00886,-0.0172,-0.16771,-0.01524,0.06397,0.05591,-0.06173,-0.00468,0.04854,0.06526,0.04934,-0.01351,-0.12252,0.008,0.01495,-0.15627,-0.01034,-0.11202,-0.01878,0.04387,0.01663,-0.08976,-0.06205,0.05477,-0.11343,0.18567,-0.08173,0.05365,-0.03328,-0.04034,0.00142,0.10192,-0.00599,-0.0635,0.01938,0.00157,0.01353,0.00292,-0.06344,0.01905,-0.02244,-0.03268,0.04946,-0.00834,0.00468,-0.01101,-0.04582,-0.07928,-0.05502,-0.05268,-0.07583,-0.07002,-0.03325,-0.01226,-0.07803,0.02673,-0.06349,-0.01802,-0.01681,0.07515,-0.06853,-0.01516,0.03908,-0.00704,-0.01482,0.02164,0.09942,-0.05995,0.01897]},{"domain":"physics","key":"ideal_gas_moles","name":"Ideal gas law","package":"physics-ai999x","example":"2 moles of an ideal gas are held at 300 K in a volume of 0.05 m^3. 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The coefficient of linear expansion is 12e-6 1/K. 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nm?","v":[-0.13198,-0.05927,-0.0097,0.0825,0.11839,-0.03845,0.13173,0.02327,0.02352,-0.06484,0.0408,-0.00236,-0.04705,0.0614,-0.03779,-0.03685,-0.02939,0.10704,0.00474,-0.03269,0.06491,0.03929,-0.10442,0.06438,0.04229,-0.05678,-0.06223,-0.03542,-0.01815,0.03306,0.01505,0.02547,-0.03873,0.02189,-0.01987,0.10151,-0.05371,0.08903,0.02936,0.03389,0.02909,-0.12902,0.05949,0.0399,0.02905,0.04709,-0.0463,-0.04919,0.03514,0.01546,-0.00013,-0.04367,-0.03914,-0.01938,-0.06861,-0.00587,0.00744,0.03387,0.01577,-0.0465,0.00485,-0.01984,0.05859,-0.02206,-0.01624,0.02305,-0.01087,-0.0513,-0.05937,-0.08734,0.00454,-0.0021,0.1191,-0.00405,0.09293,-0.06453,0.06738,0.01514,0.0264,-0.03591,-0.04619,0.0664,0.06037,-0.02236,0.06588,0.04259,0.00723,0.01872,0.03713,-0.0538,-0.02417,0.0171,-0.03102,-0.04081,-0.03646,-0.08494,0.00527,-0.0336,0.09601,0.04256,0.02757,0.10161,-0.09531,0.12499,0.07371,0.03036,-0.10583,-0.06461,0.01448,-0.03246,-0.03254,-0.00798,-0.03002,-0.0012,0.02934,-0.01385,-0.04162,0.01627,0.05331,-0.05196,-0.04222,0.09975,-0.05971,0.02622,0.03581,-0.06267,0.07806,-0.0319,0.07495,0.01626,-0.04348,0.05141,0.13502,-0.04645,0.05187,0.03327,-0.09254,-0.0137,0.07156,-0.01256,0.03941,0.01177,0.02782,-0.1439,-0.12533,-0.03351,-0.00862,-0.077,-0.06484,-0.09615,0.03405,0.04478,-0.07564,0.01618,0.03656,-0.01787,0.01913,0.01435,0.11076,-0.05641,0.00314,0.02503,0.02433,-0.00648,-0.05691,0.06377,0.00949,0.00377,-0.22128,-0.02303,0.0512,0.02038,-0.0355,-0.03255,-0.00305,0.03515,0.0146,0.0283,0.00171,0.00926,0.0664,0.0325,0.00166,0.10737,-0.09204,-0.19835,0.02169,0.00327,0.02051,-0.05558,-0.08971,-0.03701,0.07638,-0.04598,-0.0093,-0.00622,-0.06565,-0.00381,0.04691,-0.11339,-0.06619,0.01329,0.06255,-0.01863,0.04043,0.02212,0.0325,0.12992,-0.11544,0.05693,-0.00859,0.09785,-0.08611,-0.04129,0.10021,-0.01843,-0.04644,0.07287,0.10811,-0.02589,-0.07343,-0.09323,0.08611,0.04035,0.00342,0.04425,-0.07126,-0.04539,0.12349,-0.14009,-0.00167,0.07998,0.0765,0.01051,0.08398,0.0192,0.01533,-0.03656,-0.02596,-0.07945,0.04298,0.11921,-0.06213,-0.01992,-0.00868,-0.09658,0.10241,0.15169,-0.05245,0.12681,-0.01458,-0.00233,-0.01833,-0.11119,-0.10278,-0.09692]},{"domain":"physics","key":"de_broglie","name":"De Broglie wavelength","package":"physics-ai999x","example":"An electron has a momentum of 1e-24 kg*m/s. What is its de Broglie wavelength?","v":[-0.10104,-0.05631,-0.00301,0.07873,0.08722,0.01225,0.08334,0.01022,0.07413,-0.09034,0.0029,0.015,-0.00147,0.0883,0.02087,-0.02413,-0.06313,0.07973,-0.1045,0.04766,0.09316,0.05485,-0.11094,0.06543,-0.02272,-0.06477,-0.01956,-0.0674,0.00175,0.04744,-0.04186,-0.01783,-0.04155,-0.02003,-0.0257,-0.00769,-0.05193,0.02371,-0.00731,0.05573,0.03729,-0.05407,0.08314,0.02098,0.00921,-0.00203,0.05497,0.0674,0.02274,-0.04523,0.00284,-0.06332,-0.01343,-0.1094,0.02212,-0.10488,-0.00814,0.01246,0.02722,-0.02734,0.00167,-0.02734,0.06118,0.03168,0.04504,0.068,0.00926,-0.05382,0.00024,-0.04929,-0.03422,-0.01892,0.05267,-0.0765,0.05238,-0.00123,0.16423,0.00392,0.10138,-0.01965,0.0094,0.02253,0.00724,0.03563,-0.01498,-0.01247,0.05698,0.00674,0.05727,0.02533,0.01684,0.01425,0.02051,0.08566,-0.03834,-0.00525,0.01687,-0.04595,-0.00461,0.07027,-0.04322,0.11161,-0.03783,0.05579,0.03521,0.00977,-0.01904,-0.0357,0.01252,0.0016,-0.01548,-0.05244,-0.04844,0.02613,-0.11839,-0.07665,-0.08364,0.0672,0.07053,-0.04011,-0.0444,0.11244,-0.03135,0.0635,-0.02662,-0.07225,0.10028,-0.03018,0.02138,0.0457,0.02069,0.01044,0.18099,-0.06967,0.04212,-0.04481,-0.05549,0.06397,0.04286,-0.01947,-0.01615,-0.00603,0.05613,0.01716,-0.11535,0.00451,-0.03099,-0.0178,-0.03472,-0.08591,0.04164,0.06677,-0.08919,-0.00885,-0.00764,-0.052,0.16032,0.04487,0.0363,-0.00155,-0.03073,0.01153,0.021,0.02303,-0.01503,0.07199,-0.03238,-0.06337,-0.2053,-0.05066,0.04008,0.09012,-0.00672,0.00938,0.06689,0.05493,0.01558,-0.01284,-0.03138,-0.01061,0.06726,-0.00131,0.07866,0.09828,-0.05012,-0.13328,-0.03826,-0.02639,0.12857,-0.04719,-0.06094,0.00683,0.06648,-0.03714,-0.00426,0.00797,-0.03331,-0.01664,0.03212,-0.05152,-0.06506,-0.07965,-0.00178,-0.10668,-0.01087,-0.02846,0.09274,0.03257,-0.07948,-0.08791,0.07804,0.06821,-0.00169,-0.08529,0.09176,0.01128,-0.17543,0.07752,0.0494,0.02513,-0.1611,-0.08044,0.04975,0.03827,-0.00566,0.07127,-0.00573,0.05852,0.05477,-0.1868,-0.00826,0.04751,0.09457,-0.04826,0.11131,-0.07947,-0.05909,-0.03757,-0.04912,-0.11859,0.05032,0.07833,0.02209,0.0326,-0.03739,-0.08097,0.04111,0.13177,-0.05777,0.09763,-0.05366,-0.00506,-0.08002,0.01888,-0.04307,-0.17036]},{"domain":"physics","key":"rest_energy","name":"Rest energy","package":"physics-ai999x","example":"What is the rest energy of a 1 g mass?","v":[-0.043,0.03877,0.02366,-0.02885,0.05988,0.0182,0.02715,-0.05255,0.00579,0.08887,0.03599,0.04074,-0.11492,-0.10375,-0.02232,-0.04155,0.04485,0.00335,-0.07013,-0.00342,0.05364,0.03562,0.00028,0.08536,-0.12255,0.02905,0.12377,0.00031,0.00404,0.03855,-0.06384,-0.0708,-0.00022,-0.0427,0.06137,0.00978,-0.0276,-0.03719,-0.02006,-0.15222,0.11416,0.0031,-0.01259,0.05946,0.05441,0.02836,-0.06787,-0.06175,-0.06446,-0.04968,-0.02255,-0.01938,0.01746,0.06308,0.05404,0.0607,0.03877,-0.01159,-0.02215,0.02793,-0.03772,0.01954,0.12543,0.00224,0.00392,0.00669,-0.09822,0.06705,0.02636,0.03663,-0.00944,-0.10333,0.02359,-0.0203,0.06671,0.1301,0.06043,-0.03858,-0.03679,0.07455,0.1014,-0.03207,-0.04289,-0.01316,-0.01991,-0.08988,-0.01899,0.0647,0.03259,-0.07182,0.02352,0.04494,0.12375,0.04489,0.02155,0.159,0.00788,-0.06328,0.03808,0.00545,0.04556,-0.13856,-0.00801,-0.03118,-0.10728,-0.17731,0.03338,-0.13506,0.022,-0.00147,-0.03116,0.14073,0.03809,-0.0849,-0.05665,-0.05402,0.01356,-0.07471,0.09094,0.01867,-0.10699,0.01395,0.08061,0.01627,-0.00686,0.00417,-0.0212,0.06691,0.06186,0.05452,-0.00257,0.01294,-0.04874,0.01446,0.01899,-0.03294,0.02248,-0.04429,-0.00613,0.03705,-0.00421,-0.00064,0.00481,0.10834,-0.09332,0.03468,0.03797,0.03676,-0.06107,-0.02949,0.00327,0.01856,0.03322,-0.05244,-0.13075,-0.03077,-0.00257,0.11795,0.0629,0.06092,0.03997,0.10613,0.02472,0.03561,-0.06551,0.05632,0.01024,0.08101,0.01471,-0.04546,0.02955,-0.0213,0.03277,-0.00512,-0.06259,-0.03463,-0.06405,0.04667,0.04126,-0.089,0.07053,0.12058,-0.0488,-0.00184,0.04557,-0.01982,-0.08158,0.01276,0.10931,0.06448,-0.12436,0.00315,0.13001,0.01886,0.05078,-0.02201,-0.07441,-0.10446,-0.03668,-0.12443,-0.00871,-0.00098,0.06896,-0.04014,-0.08135,-0.09685,0.12216,-0.03112,-0.12762,-0.02486,0.00218,-0.01361,0.0373,-0.0958,0.04319,-0.03952,-0.0278,-0.13479,0.00964,0.0183,-0.0655,-0.07164,0.04782,0.046,-0.01761,-0.01624,0.03887,-0.06765,-0.00496,0.02139,0.04545,0.03664,-0.06576,0.03601,0.01322,-0.15222,-0.01869,-0.04917,-0.06238,-0.05402,0.00575,-0.04776,0.04434,0.15823,0.0099,-0.04599,0.03643,0.00759,0.07521,0.11435,-0.04799,-0.00098,-0.02115,0.12719,-0.01133,-0.08151]},{"domain":"physics","key":"pendulum_period","name":"Period of a simple pendulum","package":"physics-ai999x","example":"What is the period of a pendulum with a pendulum length of 1 m?","v":[-0.02749,0.03816,-0.10337,0.09969,0.03496,0.00287,0.08624,0.06841,0.15667,0.0724,0.01833,0.04418,0.07521,-0.01594,-0.02316,-0.00582,0.10222,0.03211,0.10842,-0.08803,-0.03712,-0.00257,-0.05759,-0.01407,0.0691,0.02782,-0.07472,-0.01246,0.03798,0.05311,0.01952,0.06441,-0.06108,-0.00071,0.00139,-0.02964,-0.06173,0.10029,-0.02462,0.13397,-0.00884,-0.1358,0.0371,0.09739,-0.0485,-0.00759,0.03939,0.11631,0.03153,0.07234,-0.17642,0.14843,-0.0396,0.02489,-0.08636,0.00647,-0.10632,-0.01356,-0.06745,-0.05983,-0.06274,-0.01822,-0.11886,0.01044,0.1026,-0.01212,-0.00059,-0.09332,0.04168,-0.04648,0.00991,-0.07261,-0.00484,-0.13985,0.05521,0.0015,0.12499,0.01764,0.08514,-0.02781,-0.0786,-0.02095,0.07472,-0.04369,0.04825,0.03897,0.02558,-0.0536,0.07121,-0.03053,-0.06525,-0.10392,-0.08334,0.04566,-0.0525,-0.02554,0.05039,-0.03001,0.0014,0.00383,-0.01386,0.06993,-0.08309,0.08307,0.06514,0.1229,-0.01164,-0.1033,-0.00792,0.01038,-0.0955,-0.05761,-0.01401,0.01548,0.05028,-0.0364,-0.08236,-0.03017,3e-05,0.0822,-0.07452,-0.03972,-0.03773,0.01878,-0.01849,0.07723,0.0541,-0.00396,0.06624,0.05044,0.10117,-0.05628,0.14027,-0.09796,0.01992,0.08632,0.0013,0.12142,0.07013,0.08831,-0.04632,-0.09882,0.0347,-0.00611,-0.0331,0.04656,-0.03003,0.03089,-0.01077,0.052,-0.08525,-0.00295,-0.0513,-0.03818,0.10187,0.07387,0.05307,0.05898,-0.04631,-0.04755,0.01962,0.02861,-0.03919,0.0288,-0.04958,0.05043,-0.01806,0.05254,-0.08882,0.02974,-0.05228,0.12089,0.13613,0.05303,0.02936,0.03544,0.01498,-0.01736,0.00566,-0.04755,-0.08634,-0.05843,0.00265,-0.0305,0.07643,0.09987,-0.00818,-0.01115,-0.00247,-0.06268,0.02414,0.01498,0.09634,-0.0514,-0.02619,-0.01824,0.00519,-0.03976,0.1124,0.08311,-0.0118,0.01053,-0.09779,0.02692,-0.05775,0.02786,-0.00546,-0.10441,-0.04001,0.0031,0.03381,-0.12986,-0.03955,-0.00124,0.07063,-0.01608,-0.07801,-0.01439,0.08172,-0.10553,0.00147,0.00015,0.06895,-0.03276,-0.00995,-0.00021,-0.00337,-0.08418,-0.09714,0.00478,0.04084,-0.02485,-0.07227,-0.06198,-0.08995,-0.01797,-0.09269,0.0275,-0.02128,-0.05441,0.08822,0.02619,-0.02936,-0.05688,0.02491,-0.00017,-0.00983,-0.00834,-0.10427,-0.03959,0.00529,-0.06253,0.06461,-0.06424,0.03671,-0.02932]},{"domain":"physics","key":"spring_oscillation_period","name":"Period of a mass on a spring","package":"physics-ai999x","example":"A 0.5 kg mass oscillates on a spring with a spring constant of 200 N/m. What is the period?","v":[-0.04136,0.12995,-0.09815,0.07149,-0.00649,-0.01232,-0.00874,0.00927,0.11091,-0.01412,-0.01732,0.08426,0.03839,0.10679,0.04967,-0.02726,0.06373,0.04267,0.01454,-0.03479,0.02039,0.01565,-0.08887,-0.01223,0.02534,-0.01113,-0.0138,0.11301,0.12283,-0.06694,0.14739,0.02858,-0.07,0.02282,0.02056,-0.19693,-0.04126,0.12371,0.02985,-0.02604,-0.04675,-0.02081,0.00505,0.07737,-0.08261,-0.00098,-0.05305,0.22571,0.03263,0.01056,-0.08088,0.03987,-0.05981,-0.03156,0.00901,-0.0211,-0.04641,0.0356,0.03777,0.04012,-0.02292,-0.06533,-0.00593,0.00394,0.1895,0.07102,-0.01687,-0.05706,0.10214,-0.05471,0.01116,-0.04931,0.02259,-0.03893,0.02388,0.01499,-0.01987,0.02653,0.09363,0.06066,0.01711,0.02525,0.02905,0.04032,0.04349,0.00829,0.00655,-0.02319,-0.01453,0.0372,-0.01838,-0.05691,0.03833,-0.05282,-0.00235,0.01597,0.00542,0.01197,0.03755,0.07768,0.03665,0.01536,-0.05641,0.05726,0.01238,0.10666,0.01852,-0.08328,-0.04598,-0.03732,-0.0323,-0.05769,-0.07546,-0.00365,-0.05774,0.01825,-0.01438,0.00558,0.03534,-0.00039,-0.02626,0.01489,-0.00382,-0.00902,-0.11457,-0.03986,-0.00208,-0.10533,-0.03886,-0.04338,0.0149,0.01885,0.11776,0.00957,0.00072,0.0508,-0.05435,0.08738,0.09872,0.09047,-0.03595,-0.0024,-0.00147,-0.01431,-0.02189,0.03442,-0.03755,0.06305,-0.07322,-0.03756,-0.02283,-0.04257,-0.0473,-0.08806,-0.03701,0.00401,0.12839,0.05846,0.02677,-0.05936,-0.06972,0.07778,-0.05392,0.02061,-0.02966,0.01892,0.02008,0.0102,-0.07735,0.07763,-0.07882,0.0434,0.09797,0.08236,0.06144,0.03742,-0.04375,-0.0592,-0.07929,-0.09699,-0.0155,0.04307,0.08324,-0.05386,0.0044,0.01633,0.03924,-0.00718,-0.06372,-0.02036,-0.0542,-0.01015,-0.00709,-0.07234,0.04055,0.02439,0.06539,0.01124,-0.05765,0.03172,0.10318,-0.00292,-0.21525,0.01594,-0.07773,0.06737,0.03152,-0.02416,-0.0959,-0.09693,0.08509,-0.1636,0.117,0.08513,0.13201,-0.0515,-0.11466,0.00358,0.02084,-0.10109,-0.01003,0.06195,0.04033,0.04649,-0.03584,0.02813,0.02165,-0.09223,-0.14277,0.04964,0.02664,-0.05026,-0.04144,-0.01192,-0.06455,0.03613,-0.13241,-0.00554,-0.05834,-0.03373,-0.01929,-0.01176,-0.01478,0.00812,-0.02177,-0.0976,0.05182,-0.10716,-0.0209,0.08876,0.01851,0.01706,0.05227,-0.06394,-0.08097,0.02972]},{"domain":"physics","key":"torque_lever","name":"Torque of a force","package":"physics-ai999x","example":"A wrench applies an applied force of 50 N at a lever arm of 0.3 m, at an angle of 90 degrees. What is the torque?","v":[-0.0046,-0.00697,0.01556,-0.00732,-0.02844,0.00868,0.03987,-0.02233,0.0632,-0.03518,-0.03305,0.0384,-0.04325,0.06936,0.01122,-0.03389,0.00114,0.04986,-0.08645,0.01474,-0.09994,0.02842,0.00143,-0.02699,0.09195,-0.00893,-0.09128,0.08996,-0.01267,0.09734,0.02946,0.07871,-0.01618,-0.01109,-0.0557,0.10601,-0.00177,0.0887,-0.05315,0.13694,0.11306,-0.04605,0.08184,-0.03485,0.02748,-0.04281,0.01053,-0.02001,0.02153,-0.02809,-0.09112,-0.06081,-0.16024,0.00464,-0.04397,0.02141,-0.15359,0.00782,-0.01183,-0.07899,0.04258,0.07522,-0.07353,-0.11502,0.04835,-0.0381,0.01581,0.00972,-0.15029,-0.05791,0.00746,-0.0522,-0.0233,-0.06262,-0.06126,-0.00391,0.00053,0.07676,-0.04685,-0.01103,-0.08842,-0.0153,0.08825,-0.10636,0.0249,-0.09068,-0.05424,0.02972,-0.01292,0.00184,-0.11211,0.00785,-0.0473,-0.11421,-0.03735,-0.06863,0.00493,0.0255,-0.05111,-0.00033,0.0701,0.0049,0.02203,-0.00107,0.07604,-0.02683,-0.14123,-0.13608,-0.07062,-0.0274,-0.00475,-0.00772,0.05195,0.04698,0.09786,0.03164,-0.00155,0.00981,0.05223,-0.01484,-0.047,0.01857,0.00762,-0.00953,0.05924,0.10357,-0.04254,-0.03571,0.08001,-0.03898,0.05638,0.01552,-0.01161,0.01915,-0.05864,0.08864,0.02139,-0.00622,0.06014,-0.02006,0.01,-0.01518,0.02555,-0.0628,0.1144,0.08176,-0.06819,0.06053,0.06606,-0.09962,-0.02864,-0.00461,-0.11009,-0.07355,-0.00247,0.06933,-0.07625,0.03602,0.10011,-0.06153,0.0515,-0.0512,-0.02732,0.12162,0.02489,-0.01627,-0.03151,-0.02088,-0.07934,0.05096,-0.01724,-0.00151,0.00238,0.10822,0.00513,-0.04122,0.05468,0.00997,5e-05,0.07076,0.00477,-0.04677,0.02437,-0.0202,0.07172,-0.08272,-0.0359,0.02207,-0.09009,-0.12844,0.10088,-0.04373,0.00011,-0.0035,0.04909,0.1005,-0.02763,0.00056,-0.03849,0.0911,-0.00968,0.0223,-0.08803,0.02794,-0.02221,0.04873,0.01789,-0.00121,-0.05872,0.07977,0.05366,0.01514,-0.0718,0.02474,0.04674,-0.01345,-0.02204,0.02922,0.12925,-0.13653,0.00462,-0.01488,0.07302,-0.04446,0.0569,-0.00693,0.11372,0.04071,0.07504,0.14654,0.0558,-0.04869,-0.04296,-0.03956,-0.1643,0.06414,0.1277,-0.04001,0.06191,-0.01748,-0.05019,-0.00519,0.09255,-0.04274,-0.00804,0.13381,-0.01522,0.16355,-0.06841,-0.08259,0.07035,0.0627,0.0457,-0.06728,-0.02709,0.0934]},{"domain":"physics","key":"rotational_kinetic_energy","name":"Rotational kinetic energy","package":"physics-ai999x","example":"A flywheel with a moment of inertia of 2 kg*m^2 rotates at 10 rad/s. What is its rotational kinetic energy?","v":[0.13533,-0.04925,-0.06231,0.02997,0.04953,0.03999,0.00255,-0.09299,0.02777,0.03114,0.01441,0.00482,-0.05054,0.05626,-0.01144,-0.11497,-0.03786,-0.06753,-0.16812,-0.0245,0.01739,0.06306,-0.05658,0.0493,-0.04511,0.0343,0.09649,0.11939,0.01448,0.02551,0.00807,0.01356,-0.05512,-0.0501,0.05949,-0.00092,0.01162,0.11689,-0.02844,-0.07234,0.08448,-0.00817,-0.00216,0.04439,-0.07997,-0.06623,0.01802,-0.06524,0.06756,-0.08403,0.06048,-0.01816,-0.01142,0.07654,-0.02683,-0.00523,0.00509,0.11128,-0.17225,0.02767,0.06667,0.10748,0.00597,-0.08147,0.02495,0.01582,-0.05034,0.01776,-0.09005,0.01621,-0.03321,0.00102,-0.13331,-0.03796,0.01059,0.03082,0.05821,0.12517,0.01827,0.00153,-0.00827,0.09166,0.01423,0.03617,-0.03723,-0.1016,0.01874,-0.03614,-0.014,0.01397,-0.02174,0.01202,6e-05,-0.11651,-0.06784,0.08863,-0.00746,0.03437,-0.07386,0.01084,-0.03154,-0.04975,0.06216,0.08691,-0.11841,-0.00574,0.01131,-0.01608,-0.07242,0.04698,0.00981,0.00702,-0.00669,-0.04706,-0.03645,-0.02911,0.07719,-0.06294,0.02564,0.02774,-0.04434,-0.02247,0.05231,-0.00891,-0.03792,0.04541,-0.00283,-0.02124,-0.015,-0.04414,0.02938,-0.05238,0.01134,0.05017,0.03035,0.02369,0.03923,-0.00672,0.06721,0.07061,0.01536,0.0237,-0.05284,0.02636,-0.06789,0.00338,-0.21799,0.02839,0.10878,-0.16346,-0.00567,0.0403,-0.13143,-0.07644,-0.01228,0.04888,-0.03063,0.13968,0.06991,0.01871,0.02861,-0.01505,0.03399,0.023,0.11982,-0.00271,-0.01178,0.07987,0.03168,0.10198,-0.00765,0.02033,0.00931,-0.02455,-0.09556,-0.04365,0.00644,0.03594,0.01305,-0.19656,0.02474,0.02631,-0.03305,-0.01122,0.10497,-0.04486,-0.04073,-0.00396,0.0587,0.02481,0.01032,0.03299,0.0928,-0.005,0.03002,-0.06662,-0.00934,-0.01986,0.00494,-0.0716,-0.02244,-0.02157,-0.00062,0.04432,0.01914,-0.01054,0.06065,-0.10097,-0.10761,-0.02178,0.10575,0.0683,0.04578,0.06646,-0.02745,-0.0482,0.05513,-0.09517,0.08117,-0.04021,-0.05124,-0.02397,0.06898,0.14082,-0.07323,-0.05604,0.05396,-0.10368,-0.05131,0.08846,0.02343,0.06163,-0.03104,0.04045,-0.12613,0.02919,-0.05827,-0.05843,-0.01824,-0.02164,0.00977,-0.06872,0.10242,0.0964,-0.10305,0.04332,-0.01368,0.04419,0.0925,0.08886,-0.10317,0.05316,0.07273,-0.03255,-0.09706,0.06143]},{"domain":"physics","key":"angular_momentum","name":"Angular momentum of a rotating body","package":"physics-ai999x","example":"A turntable with a moment of inertia of 0.5 kg*m^2 rotates at 8 rad/s. What is its angular momentum?","v":[0.05589,0.01088,-0.12663,0.05074,0.06944,-0.08748,0.03343,-0.0507,0.07182,-0.0006,-0.02399,-0.01393,0.00771,0.16528,0.03124,-0.07574,-0.08444,0.00458,-0.1375,-0.05725,0.07623,0.07055,-0.13916,0.02639,0.02838,-0.06562,0.00843,0.13535,0.00209,0.07111,0.02505,0.09883,-0.03196,-0.01524,0.01312,0.0486,-0.06579,0.10447,-0.03453,0.06327,0.05184,-0.0861,0.04736,0.08831,0.0223,-0.05298,-0.0248,-0.03405,0.04629,-0.04273,-0.07806,-0.08584,0.03892,0.01451,-0.09394,0.03094,-0.03028,0.08974,-0.11125,-0.0167,0.07586,0.08006,-0.01555,-0.14242,0.02675,-0.02233,0.02564,-0.01577,-0.09408,-0.02092,-0.03799,-0.00687,-0.00321,-0.01564,0.04513,-0.11953,0.05912,0.12937,0.00991,-0.04017,-0.07021,0.07163,0.13271,0.02011,0.04688,-0.02949,-0.02938,-0.04352,-0.00599,0.02166,-0.01372,-0.02006,-0.04751,-0.10985,-0.05086,0.08222,-0.01346,0.05481,-0.00046,-0.00154,-0.01795,0.00845,-0.00928,0.05618,0.09434,0.01706,-0.04294,-0.01846,-0.06217,-0.00643,-0.01009,-0.01396,-0.05162,0.01421,0.0393,-0.03323,0.05189,-0.01768,0.02582,-0.04801,-0.06477,0.02317,-0.05616,0.05361,-0.00405,-0.05177,0.05338,-0.07195,0.08914,-0.0361,0.08858,-0.04418,0.06425,0.02974,0.05438,0.02414,-0.07069,-0.03793,-0.01166,0.04247,0.02285,0.05782,0.00323,-0.11083,-0.1278,-0.04543,-0.13968,-0.00037,0.04815,-0.0535,-0.00161,0.06765,-0.14689,-0.0927,-0.00148,-0.01939,-0.0206,0.10239,0.06205,-0.02305,0.06984,-0.01918,0.02111,-0.00953,0.13347,-0.02202,-0.04777,0.02812,-0.14881,0.08368,-0.00996,0.04783,-0.06021,-0.08455,-0.08738,0.02705,0.00198,0.07053,-0.05753,0.01324,0.0691,-0.03182,0.02183,-0.01569,0.02001,-0.15921,-0.02302,0.01896,0.05827,-0.09202,-0.00467,0.04654,-0.01388,-0.06711,-0.0208,-0.03748,-0.0454,0.04723,0.05182,-0.02131,-0.08908,-0.05696,-0.03731,0.02108,0.02186,0.01619,0.08971,0.03429,-0.0553,0.00882,0.12996,0.04087,0.04512,0.04582,-0.04261,-0.06016,0.04369,0.05183,0.02765,-0.05268,0.00108,-0.0344,0.05839,0.08686,-0.03695,0.04234,0.02717,-0.08194,-0.01544,0.01404,0.08652,0.06879,0.07972,0.00127,0.00608,0.06787,-0.04109,-0.03324,-0.00324,-0.07362,-0.03687,0.05748,0.07179,0.05955,-0.09122,-0.03926,0.10885,0.13031,0.0837,0.0088,-0.02583,-0.00946,0.17753,-0.0778,-0.1274,0.02941]},{"domain":"physics","key":"tangential_acceleration","name":"Tangential acceleration of a point on a rotating body","package":"physics-ai999x","example":"A point on a rotating wheel is at a radius of 0.5 m. The wheel has an angular acceleration of 4 rad/s^2. What is the tangential acceleration of the point?","v":[-0.02194,-0.15484,0.03428,0.05759,-0.09728,0.1062,-0.02892,-0.04802,0.13451,0.0099,0.04309,0.03773,0.0009,0.00056,-0.09057,-0.04208,0.01905,-0.1159,-0.00274,-0.04178,0.02224,-0.04422,-0.09896,-0.09751,0.00318,-0.00971,0.02389,0.01278,0.00614,-0.03082,0.06477,0.03444,-0.01626,-0.03566,0.00199,-0.01728,0.10328,0.06931,-0.06831,0.02428,0.02301,-0.04635,0.01659,-0.05259,-0.08701,-0.03156,-0.05014,-0.03385,-0.07796,-0.02805,0.07252,0.01349,0.05138,0.07163,-0.07175,0.07856,0.02922,0.04766,-0.05345,0.00095,0.00593,0.11551,-0.03769,0.05688,-0.01963,0.045,0.0128,0.07621,-0.06828,-0.07531,-0.12805,-0.02263,-0.00834,-0.00399,-0.06607,-0.02905,0.02108,0.05689,-0.06681,0.01825,-0.06648,-0.00658,0.03984,-0.07457,-0.02254,0.02026,0.05174,-0.12743,0.05511,-0.01197,-0.0142,-0.07146,0.01775,-0.09942,-0.10137,0.01302,-0.014,-0.03934,0.10689,-0.0232,-0.0609,-0.03641,0.03992,0.01299,-0.02792,0.08566,0.01363,0.00872,0.0434,0.12699,-0.00036,0.03687,-0.03573,-0.03197,0.08473,0.01308,0.13327,-0.09684,0.04789,0.03761,-0.0543,-0.02684,0.01548,-0.02901,-0.03273,0.10855,-0.02669,-0.05135,0.00446,-0.11538,-0.08855,-0.02587,0.02885,-0.01646,-0.02293,0.07769,-0.07885,0.00155,0.01812,0.04499,-0.01913,-0.04505,-0.02195,-0.0315,0.0314,0.03818,0.0134,0.06414,-0.01272,0.01994,0.03061,-0.02191,-0.0017,0.06496,-0.00679,0.08382,-0.09869,0.10294,-0.09386,-0.01494,-0.04146,-0.08804,-0.01525,0.12361,0.01656,-0.0216,0.08318,0.02372,0.13138,0.0683,-0.08966,0.02599,-0.09065,0.04172,-0.00064,0.05761,0.03594,-0.02313,0.04511,-0.01738,0.0296,0.0107,-0.01085,-0.06543,-0.00771,0.05575,-0.00767,0.00836,-0.07833,-0.12579,0.04444,0.08076,0.04306,0.0773,-0.00038,0.01726,0.01021,0.07298,0.07296,0.00525,-0.02117,-0.01006,-0.09052,0.0527,0.09216,-0.01157,-0.05518,0.01179,0.09885,0.03125,-0.0195,-0.07011,-0.07538,0.00454,-0.11197,-0.09102,0.02302,-0.17351,-0.06175,0.04268,0.03442,-0.11329,0.07388,0.16986,0.04389,-0.13129,0.07431,-0.04168,0.07595,0.10286,-0.06854,0.07427,0.02624,0.08022,-0.06223,0.10335,0.08734,-0.04373,0.07941,0.02828,0.12988,0.08311,0.05637,0.00598,-0.09827,0.09272,-0.12277,0.03291,0.02127,-0.07947,-0.06617,0.05228,0.00845,-0.08741,0.00493,-0.01114]},{"domain":"physics","key":"centripetal_acceleration_omega","name":"Centripetal acceleration from angular velocity","package":"physics-ai999x","example":"A centrifuge rotates at an angular velocity of 3 rad/s. What is the centripetal acceleration at a radius of 2 m?","v":[0.08079,-0.0731,0.00477,0.0172,-0.00127,0.02327,-0.02126,-0.06692,0.15315,0.03803,-0.00395,0.02618,0.04701,0.02695,-0.12734,-0.04695,-0.08964,-0.06022,-0.09106,-0.1306,0.09364,0.01155,-0.11736,-0.03352,-0.04337,-0.04188,0.06571,0.05724,-0.05183,0.0013,-0.01053,0.14597,-0.06676,-0.042,-0.00988,-0.08075,0.02476,0.022,-0.01375,0.07933,0.06581,-0.04962,-0.01969,0.07102,-0.01669,-0.02754,0.03369,-0.06196,-0.01531,-0.04653,-0.0169,-0.04801,0.05526,0.02388,-0.11688,0.01428,-0.00788,-0.0141,-0.13593,-0.02428,0.06589,0.00846,-0.06114,-0.04487,0.03509,0.00925,-0.02415,0.03471,-0.03424,-0.04802,0.02849,0.04969,0.09721,-0.04113,-0.00138,-0.04664,-0.0879,0.03179,-0.01204,0.03641,0.02836,0.06223,0.06448,0.00179,-0.04561,-0.05194,0.03233,-0.01839,0.11964,-0.03565,0.16197,-0.03272,-0.00017,-0.06141,-0.08139,0.13134,0.02372,0.05991,0.04249,-0.05329,-0.069,-0.086,0.19341,-0.01614,0.07174,0.01834,0.00782,-0.01939,0.01902,0.04789,0.01184,0.05624,-0.05447,-0.03527,0.12472,0.04117,0.09826,-0.0996,-0.01089,0.06833,-0.03084,-0.13307,-0.00517,0.00134,-0.05981,0.07385,0.09722,0.06754,0.0117,-0.05683,0.01241,-0.14467,-0.02923,-0.00337,-0.04848,0.06192,0.00538,0.00327,0.05284,0.01636,-0.04734,0.00263,-0.10902,-0.12917,0.08649,0.06271,-0.01619,-0.00643,-0.04109,0.05121,0.06908,0.08769,0.02476,0.02068,0.03071,0.01092,0.04999,-0.00312,-0.09046,-0.00567,-0.16925,-0.07468,0.04167,-0.07453,-0.02861,-0.08006,0.04423,-0.03051,0.07447,0.04798,0.05107,0.0256,-0.01638,-0.07005,-0.10724,0.09546,-0.06346,0.0196,0.02238,-0.0156,-0.00657,-0.02832,0.05767,-0.03027,0.0254,0.0465,-0.03539,-0.00026,0.09795,-0.10478,0.01658,0.06708,0.0591,-0.05278,-0.03359,-0.09809,-0.00204,0.05742,0.07157,0.08637,-0.06202,-0.0525,0.00106,0.02285,0.05246,0.05099,-0.0421,0.04726,-0.03782,0.03191,0.03674,-0.05795,0.02449,0.07263,-0.13878,-0.02624,0.02661,0.02334,0.06314,0.06936,-0.08376,-0.02583,0.10056,0.07058,-0.01707,-0.05252,-0.01392,-0.02427,0.0533,0.12592,-0.0169,0.05768,-0.04122,0.14668,-0.06429,0.0519,0.04738,-0.02176,-0.00341,-0.01842,0.04278,0.00619,-0.01493,-0.04889,-0.06334,-0.04361,-0.14165,0.06967,-0.03045,-0.00033,-0.06701,0.06393,0.11132,-0.02061,-0.04327,-0.05251]},{"domain":"physics","key":"angular_momentum_point_mass","name":"Angular momentum of a point mass on a circle","package":"physics-ai999x","example":"A 2 kg satellite moves at 3 m/s in a circular orbit of radius 4 m. What is its angular momentum?","v":[-0.00281,-0.04136,-0.04911,0.05646,0.04729,-0.21983,0.08592,-0.02891,0.13744,0.01151,-0.00502,-0.05942,0.03797,0.08286,0.02484,0.011,-0.05609,-0.01308,-0.07653,-0.04195,0.06959,0.13345,-0.03901,-0.03445,-0.00815,-0.04849,-0.01159,0.018,0.02227,-0.00332,0.03768,0.08318,0.02578,0.02571,0.0084,-0.01184,-0.06738,0.10294,-0.02363,0.13535,0.07732,-0.03181,0.03448,0.07368,0.0219,-0.05157,-0.04539,0.02965,-0.00362,-0.06255,-0.04831,-0.02949,0.03446,-0.00901,-0.0086,0.05339,-0.03089,0.05346,-0.06152,-0.00496,0.06089,0.09348,-0.08493,0.00648,-0.02207,-0.05828,0.04831,-0.00887,-0.03379,0.0349,-0.07052,-0.07919,0.05927,0.03619,0.0157,-0.05919,0.00089,0.07216,-0.04201,0.03472,-0.13159,-0.05063,0.12089,0.02294,0.08893,-0.07328,0.02816,0.00714,0.02757,-0.0336,-0.01881,-0.03004,0.00061,9e-05,-0.03351,0.09569,0.02165,0.04459,-0.04385,0.01941,-0.05648,-0.00325,-0.02657,-0.00756,0.05535,-0.00894,-0.07437,0.03268,-0.13393,-0.02738,-0.04676,-0.01201,-0.05787,0.04673,0.05116,0.01422,0.03618,0.03244,0.06787,-0.06193,-0.05892,0.0134,-0.0486,0.05879,0.04744,-0.09438,0.05752,0.06841,0.07018,0.085,-0.03356,-0.0115,0.06,-0.05631,0.05433,0.05845,-0.03522,0.06169,0.00841,-0.02356,-0.01094,0.00759,0.06169,-0.10831,-0.03364,0.00818,-0.15616,-0.04833,-0.06256,0.007,-0.04895,0.09341,-0.00575,-0.11189,-0.10584,-0.03007,0.08557,-0.01903,0.07675,-0.0606,0.07373,0.04832,-0.0077,-0.11645,0.04802,0.02198,-0.03571,0.05396,-0.09151,0.05039,-0.0443,0.03157,-0.00257,-0.05484,0.01433,-0.02383,-0.07318,0.14803,-0.02418,-0.04796,0.13035,-0.01102,0.0499,0.10183,0.01632,-0.11976,-0.04932,-0.0827,0.04416,-0.17748,-0.09255,0.03686,0.01163,-0.03259,-0.05238,-0.01329,-0.12126,0.03286,0.05759,-0.00852,-0.04009,-0.01882,-0.10498,-0.01741,-0.04029,-0.01339,0.12802,0.09139,-0.10046,-0.04117,0.10934,0.05934,0.11404,-0.00425,-0.00565,-0.05112,-0.03884,0.06312,0.05542,-0.01034,-0.07789,-0.04279,0.01375,0.09708,0.01539,0.05356,-0.04315,0.06032,0.00788,0.01804,0.04292,0.0437,0.09772,-0.06684,0.02803,-0.05875,-0.0091,-0.05666,-0.07072,-0.16228,0.02409,0.06232,0.12047,0.01738,-0.07535,-0.08554,0.13097,0.09019,0.03531,0.02432,-0.04707,0.01215,0.06248,-0.0078,-0.06262,0.0119]},{"domain":"physics","key":"absolute_pressure_depth","name":"Absolute pressure at a depth in a fluid","package":"physics-ai999x","example":"The atmospheric pressure is 101325 Pa. What is the absolute pressure 10 m below the surface of water of density 1000 kg/m^3?","v":[0.02377,-0.06632,-0.02985,0.01929,0.11349,0.11199,-0.01127,0.08032,-0.12645,0.00159,0.01801,0.09224,-0.06113,0.00483,0.03974,-0.05735,0.12631,0.04139,0.08487,-0.02347,0.00179,-0.08523,-0.02051,-0.01151,0.01726,-0.06037,0.07214,0.03604,-0.05584,0.06946,0.07251,0.00922,0.07369,-0.0389,-0.06553,0.10247,0.03563,-0.05864,-0.04466,0.10824,-0.0142,-0.04539,-0.03852,-0.03232,0.02815,-0.04205,-0.11063,-0.23031,-0.02553,0.05204,0.05759,-0.05961,0.01626,0.02274,-0.06947,-0.0582,0.01213,0.0182,0.14396,-0.02152,-0.09366,0.01109,-0.06201,-0.08858,0.03982,-0.05774,0.04176,0.05264,0.03261,-0.03709,-0.08178,0.00937,0.07014,0.03097,-0.05926,0.01454,0.0175,-0.05036,-0.05679,0.04021,0.06109,0.02196,-0.0561,-0.03623,0.05573,0.04593,0.014,-0.00187,0.0206,0.0236,0.03702,0.07297,-0.11504,0.02067,-0.03827,0.08901,0.05668,-0.08685,0.03652,-0.01815,-0.04994,-0.03116,-0.0908,-0.02171,0.04259,0.024,0.03326,0.03616,0.06548,-0.03954,-0.0502,-0.09358,0.02831,0.03543,0.01307,-0.11007,0.05372,0.00606,0.00958,-0.06823,0.05792,0.03009,-0.03696,-0.01573,0.015,0.01738,-0.06412,0.10746,0.19095,-0.04535,-0.01727,-0.02559,0.13259,-0.07149,-0.07659,0.01075,-0.08106,-0.01975,0.03111,-0.0403,-0.07136,-0.01555,0.00552,-0.04478,0.09999,-0.05656,0.03242,0.07393,-0.08796,-0.01813,-0.03745,-0.04738,0.04905,0.11712,-0.03592,0.0583,0.01843,-0.05486,-0.0507,0.03583,-0.04219,0.04847,0.06579,-0.00464,-0.15292,0.09245,-0.0087,-0.12766,0.10956,-0.01299,-0.01818,0.01048,-0.05956,-0.02214,0.06329,-0.0989,-0.04242,0.0089,0.11336,0.11084,-0.00772,0.05892,-0.09556,0.07614,-0.01086,0.03885,0.06748,-0.00267,-0.03035,-0.06951,-0.04949,0.06195,0.05033,0.05744,-0.07622,-0.02014,-0.00568,0.05078,0.02549,-0.00848,2e-05,0.04024,-0.03851,-0.05654,0.0535,-0.01418,-0.1334,0.02747,-0.01895,0.07851,-0.01868,0.06096,-0.08642,-0.07553,-0.05257,-0.03577,-0.05536,-0.1173,0.07034,-0.01154,0.0514,0.0115,0.04498,0.01288,-0.0564,-0.02219,-0.09618,-0.02623,0.05617,0.08352,0.0273,-0.09784,0.0649,-0.00351,0.08475,0.0926,-0.07659,0.05223,0.04461,-0.025,0.07713,-0.00249,0.05813,-0.0026,0.12758,-0.07847,0.03236,-0.01429,-0.09054,-0.09465,-0.00073,0.00953,0.10949,0.0208,-0.02301,-0.06205]},{"domain":"physics","key":"flow_rate_volume_time","name":"Flow rate as volume per time","package":"physics-ai999x","example":"A hose fills a 2 L bucket in 10 s with water. What is the flow rate?","v":[0.00369,-0.01755,-0.12201,0.04579,0.01983,-0.04685,0.05755,-0.03003,0.06216,-0.05837,-0.04033,0.08323,0.19758,-0.02479,0.01973,0.00252,0.03372,0.13662,0.08699,0.0251,0.05098,-0.02083,-0.02766,-0.03694,0.02279,-0.03239,-0.08335,0.17321,-0.01542,0.06975,0.09655,-0.01276,0.03743,0.00071,-0.05761,-0.03722,-0.00528,0.05565,0.03105,0.04744,0.09107,0.04079,-0.05048,-0.0735,-0.03283,-0.00084,0.02189,-0.00568,0.07292,-0.00347,-0.13549,0.04896,-0.1511,-0.04355,0.03607,0.00078,-0.06607,-0.02963,-0.12653,0.00098,0.07985,0.01279,-0.00776,0.05207,0.00802,-0.06142,0.07716,-0.09052,-0.01805,-0.03422,0.01,-0.04998,-0.04566,-0.05283,0.04524,-0.03551,0.09195,0.07648,0.05356,-0.05149,0.02789,-0.09349,0.07622,0.04588,0.02256,0.01936,-0.07432,0.0333,-0.01033,0.04983,-0.0594,-0.0359,-0.08426,-0.01961,-0.02828,0.06955,0.03129,0.00566,-0.01661,-0.00346,0.00862,0.00198,-0.01876,0.03708,0.0826,0.10274,-0.01807,0.00382,0.00938,-0.0535,-0.03233,-0.0957,0.02436,0.02032,0.05533,-0.05121,-0.03896,0.05125,0.04337,-0.02838,-0.01074,0.06355,0.00945,-0.00714,-0.03832,-0.01597,0.03975,0.01352,-0.01712,-0.00991,-0.04142,-0.07297,0.0378,0.08259,0.03137,-0.02482,-0.04021,0.08135,0.0715,-0.09791,-0.11167,0.02776,0.02031,-0.12709,-0.08501,-0.06304,-0.10376,0.10922,0.03864,-0.01962,-0.05371,-0.05638,-0.0197,-0.06263,-0.04853,0.06392,-0.10614,-0.03402,0.06359,-0.03962,0.13245,-0.01162,-0.0224,-0.04052,0.06686,0.0154,-0.02108,0.00229,-0.06345,-0.06793,-0.02626,0.03039,-0.04563,-0.02764,0.02898,0.04716,0.0163,-0.04189,-0.02128,0.09834,-0.10247,0.07542,0.08789,-0.06768,-0.00763,0.06787,0.04306,0.00448,-0.10378,0.02362,-0.08563,-0.07314,-0.06819,0.04651,0.02271,0.15569,0.11832,0.11117,0.07016,-0.05905,-0.00029,0.02406,-0.03737,-0.06019,0.0254,-0.02211,-0.02544,0.0312,0.00312,-0.02276,0.08036,0.01099,0.07494,0.04663,-0.04311,-0.05828,-0.10906,-0.00618,0.07148,0.00663,0.09948,-0.05489,-0.08923,-0.15296,0.00583,-0.0037,-0.01043,0.06842,-0.05249,0.01958,-0.09082,-0.06917,0.02084,0.01521,-0.00678,0.09007,-0.04185,-0.04094,-0.0257,-0.05348,-0.06266,-0.07593,0.04271,-0.10207,0.0548,0.02367,0.12653,-0.09582,0.14029,0.14248,0.0375,-0.0916,0.05415,0.0053,-0.06685,0.1202]},{"domain":"physics","key":"flow_rate_area_speed","name":"Flow rate through a cross section","package":"physics-ai999x","example":"Water flows through a pipe with a cross-sectional area of 3e-4 m^2 at a speed of 2 m/s. What is the flow rate?","v":[-0.01945,-0.11698,0.0157,0.01984,-0.02099,-0.02067,0.03578,-0.04374,-0.02108,-0.11133,-0.00674,0.04745,0.17192,-0.05246,-0.02807,0.04856,-0.01419,0.08522,0.00511,0.12015,0.03939,-0.06115,0.11744,-0.06321,-0.05092,0.02288,-0.07137,0.05938,-0.02199,0.09473,0.02967,-0.04636,0.09652,-0.0379,-0.05939,-0.03536,0.0412,-0.04765,0.02498,0.08796,0.12054,0.00898,-0.05515,-0.05465,0.04693,-0.00719,0.14245,-0.00996,0.07032,-0.04879,-0.00359,0.00684,-0.04717,-0.07993,0.06302,0.06372,0.02244,0.01928,-0.05391,0.01433,0.07526,0.00383,-0.06465,0.09284,-0.11225,-0.07905,0.1229,0.00719,0.01035,0.02067,0.0067,-0.04746,-0.08314,0.01867,0.02128,0.02834,0.03491,-0.04156,-0.01082,0.05576,0.01333,-0.08956,0.02329,0.03313,0.022,0.02435,0.05172,0.0503,-0.03764,0.04666,-0.0963,0.03968,-0.05487,0.09443,-0.09139,0.12888,-0.007,-0.06695,0.09946,-0.00961,-0.01563,0.07576,0.00514,-0.007,0.03542,0.03565,-0.00039,0.10841,-0.11467,0.0682,-0.06408,-0.07326,0.04944,0.06919,-0.04642,-0.0873,0.04983,0.05536,0.01428,-0.09949,-0.0265,0.08056,0.00963,0.02843,-0.00601,-0.02873,-0.07406,0.10164,-0.09391,-0.0262,-0.13002,0.03272,0.01625,-0.04038,-0.04259,0.03291,0.00715,0.10796,-0.02975,-0.07242,-0.08268,0.01247,0.06403,-0.0609,-0.03869,-0.09335,-0.08321,0.02865,-0.04654,-0.03759,-0.0172,0.02994,-0.02784,0.00067,-0.00884,0.01165,-0.15938,-0.09482,0.01515,-0.0231,0.09612,-0.04699,0.00275,-0.05238,-0.00788,0.00605,-0.00363,0.04705,0.06768,-0.01347,-0.05136,-0.02295,0.01093,-0.02605,0.14332,-0.00532,0.01952,0.00959,-0.00702,-0.04768,-0.0073,0.03327,-0.05112,0.02186,-0.03811,0.08032,0.00633,0.03196,-0.14469,-0.00071,-0.07624,-0.0329,-0.0619,0.0632,0.00433,0.0786,0.03785,0.06407,0.061,-0.02686,0.02263,0.0086,-0.06183,-0.08811,0.04543,0.00707,-0.06794,0.03351,-0.07128,0.00336,0.02025,0.06956,0.09034,0.05573,-0.07064,-0.12718,-0.09139,-0.06514,0.07428,0.04359,0.01827,-0.12017,-0.09101,-0.08978,0.08661,0.02271,-0.1242,0.17601,0.056,0.01806,-0.09068,-0.00738,0.03842,0.01978,0.03361,0.05048,-0.00871,-0.03544,-0.03083,-0.06938,0.00981,-0.02344,0.09099,-0.0973,0.115,0.06333,0.08271,-0.02021,0.07665,0.06468,-0.0573,-0.03445,-0.08221,-0.01168,-0.05324,0.08912]},{"domain":"physics","key":"volume_expansion","name":"Thermal expansion of volume","package":"physics-ai999x","example":"Water with an original volume of 1 L and a coefficient of volume expansion of 2.1e-4 1/K is heated by 50 K. What is the change in volume as it expands?","v":[-0.03872,-0.1119,-0.07433,0.01655,-0.03176,0.15324,-0.06105,0.01932,0.14109,0.0265,0.01841,0.0195,-0.09153,0.02908,0.02129,-0.08056,0.07827,0.06534,0.0796,0.05352,0.10738,-0.00945,-0.14143,-0.03598,0.00212,-0.09417,0.05484,-0.0129,-0.04397,-0.02322,-0.03111,0.00233,-0.00666,0.00328,-0.05242,-0.06394,0.10038,-0.10551,-0.01773,-0.02913,0.04917,0.05581,0.01016,-0.05846,-0.00432,-0.13468,0.01913,0.07359,-0.066,-0.06155,0.00495,0.05159,0.03576,-0.04809,-0.04823,-0.03414,0.04216,0.01956,0.01399,-0.00237,-0.02384,0.01356,-0.04512,0.06261,0.01107,-0.02274,0.07308,-0.06091,-0.01046,0.01938,0.04739,0.00734,0.0276,0.009,-0.04595,0.08521,-0.04428,-0.09514,0.08298,-0.03956,-0.04763,0.00288,-0.07681,-0.04297,-0.03771,0.22188,-0.00261,0.00424,0.06095,0.00536,0.137,0.04326,0.01127,0.0331,-0.01286,-0.02509,0.00095,-0.02336,0.10042,-0.07325,0.0214,0.03002,-0.02791,-0.02001,-0.09015,-0.00284,-0.02525,0.05719,0.047,0.04658,0.05829,-0.03574,0.04211,0.03627,-0.06892,-0.11116,-0.03325,0.01244,0.05992,-0.00584,-0.00043,0.05612,0.07446,-0.06298,0.02632,0.007,0.0664,-0.13007,0.01268,-0.09111,-0.02882,-0.01254,0.06208,0.05677,-0.00514,-0.05186,-0.03629,0.02117,0.02895,-0.0614,-0.03779,0.00143,-0.04326,0.07509,0.024,0.06248,-0.02136,0.03901,-0.03356,0.02608,-0.06556,-0.08073,-0.01651,-0.07999,0.05271,0.01886,-0.05911,-0.15455,0.05823,-0.06099,-0.13591,-0.11615,-0.01126,-0.02524,0.11367,-0.02407,0.03848,-0.05934,-0.06756,-0.0323,-0.03229,0.04686,-0.18821,0.05605,0.02602,-0.01544,-0.01843,-0.03407,0.00027,-0.02854,-0.04684,0.00474,-0.024,0.01079,-0.02519,-0.0527,-0.01374,-0.08596,-0.07368,0.05317,-0.06619,0.03086,0.08227,0.02811,0.12956,0.11127,0.08845,0.01526,0.00683,-0.07816,-0.01725,-0.04467,0.08911,0.02996,0.06662,-0.01622,-0.06811,0.01045,0.09837,-0.07596,0.08399,-0.19798,0.05328,0.07497,0.10806,0.04282,0.04301,-0.06296,0.01836,-0.02882,-0.05636,-0.04629,0.08328,-0.07518,-0.00637,0.03916,0.03959,0.10196,-0.03993,0.05624,0.00706,-0.06918,-0.02165,-0.09933,0.05686,0.14779,0.05939,0.01789,-0.02697,0.00855,0.11555,0.00613,0.09378,0.04008,0.06344,-0.05533,-0.00782,0.11508,0.06589,-0.01969,-0.01143,-0.00968,-0.08902,0.01863,-0.00154,0.0141]},{"domain":"physics","key":"engine_efficiency","name":"Efficiency of a heat engine","package":"physics-ai999x","example":"A heat engine takes in a heat input of 1000 J and produces a work output of 300 J. What is its efficiency?","v":[0.04962,0.0334,-0.23266,-0.03435,0.0284,-0.04188,0.03626,-0.03147,-0.00299,-0.03179,0.06004,0.02589,-0.04136,-0.03004,-0.0067,0.06517,0.00326,0.0107,0.1133,-0.00604,0.00259,0.08933,0.09912,0.01182,-0.00779,0.06645,-0.10542,0.00985,0.00696,0.133,-0.00929,-0.0218,0.02807,0.02327,0.03803,0.07811,-0.09586,0.03611,0.00738,-0.00551,0.01463,0.07579,-0.04976,-0.02153,0.01227,-0.06999,0.02761,-0.07251,-0.01096,-0.06188,0.02079,-0.01629,-0.12752,-0.03144,-0.00657,0.10744,-0.03113,-0.0443,-0.04112,0.00304,-0.04152,-0.12754,0.07737,-0.02766,0.11069,0.02231,-0.0539,-0.03554,0.02122,0.0473,0.01741,0.0471,-0.04946,-0.094,0.02925,0.01758,0.03594,0.21451,-0.07081,0.01158,-0.02076,-0.0215,-0.0261,0.03494,-0.03226,-0.09698,0.04653,-0.01638,0.01578,0.02007,-0.00354,0.08321,0.02389,-0.00829,-0.07875,0.05809,0.04238,0.04087,0.02187,0.0093,0.01322,0.11199,0.02125,-0.00728,-0.09153,-0.09489,0.04117,0.02727,-0.13853,0.0316,-0.0249,-0.01965,-0.043,-0.0464,0.02454,0.03632,-0.04968,0.0265,0.04991,-9e-05,-0.11967,-0.09399,0.05548,0.00187,-0.0958,0.03451,0.07717,0.01747,0.0072,-0.03664,-0.04118,0.03354,-0.01151,0.06581,-0.07971,0.03927,-0.01783,0.02114,-0.04798,0.00067,-0.00102,-0.03121,-0.11786,0.03625,0.20391,-0.02332,-0.12736,-0.02786,0.00081,-0.0346,0.01143,-0.01741,-0.06866,-0.03438,0.07028,0.05739,-0.11778,0.04962,0.01732,-0.03043,0.03507,-0.03614,-0.04496,-0.06078,0.01284,-0.0949,0.00671,0.0867,-0.04015,-0.0027,0.05414,-0.06985,0.01248,0.06704,-0.00909,0.04217,0.05418,0.00929,0.0531,-0.07522,-0.03134,-0.04157,0.01004,-0.07975,-0.09417,-0.05039,-0.04461,0.05074,-0.13642,0.07394,-0.03056,0.01807,0.0098,0.07273,0.011,0.07749,-0.02885,-0.01754,0.01944,-0.14175,-0.12719,-0.00266,-0.02833,0.09196,0.07273,-0.01876,0.00824,0.07323,-0.04685,-0.05887,0.03322,-0.08453,-0.06923,0.17489,0.16549,-0.01648,0.03519,-0.03936,0.13283,-0.07313,-0.00888,-0.0591,0.04411,-0.07062,0.03677,0.08623,0.0738,0.09169,0.02796,0.10722,0.048,0.06846,-0.05603,0.0267,0.02124,-0.05985,-0.00309,-0.02078,0.01724,0.04615,-0.00818,-0.0508,0.05343,0.04798,-0.0329,0.05156,-0.0756,-0.05973,0.03026,-0.04159,-0.01959,0.04422,-0.00941,0.15867,-0.06996,-0.03065]},{"domain":"physics","key":"carnot_efficiency","name":"Carnot (maximum) efficiency","package":"physics-ai999x","example":"A heat engine works between a hot reservoir temperature of 600 K and a cold reservoir temperature of 300 K. What is its maximum efficiency?","v":[0.02492,0.02841,-0.07787,-0.00416,-0.0053,-0.03872,0.04798,0.04145,0.07112,-0.02433,0.04948,0.03366,-0.05415,0.00895,0.04936,0.03322,0.01727,0.01016,0.1432,-0.02871,0.00067,0.03608,0.03373,-0.08566,0.01878,0.04282,-0.03388,-0.0476,0.01274,0.06259,-0.0349,0.00926,0.04794,-0.00041,-0.06365,0.08221,-0.12971,-0.03916,-0.04572,0.04704,0.0561,-0.01654,-0.00813,0.04082,0.08459,-0.15201,0.05256,-0.12672,-0.0225,0.02014,-0.00352,-0.0655,-0.07747,-0.09046,-0.01743,0.01975,0.02808,-0.03027,0.03184,0.02908,-0.13786,-0.11863,0.03978,-0.08841,0.15252,-0.05524,-0.00301,0.00568,-0.00655,0.02424,-0.02943,0.03967,0.02238,-0.06178,0.04352,0.05148,-0.06494,0.04259,-0.01761,0.05938,0.11787,-0.01929,-0.09631,0.00229,0.01221,-0.00876,0.05339,0.04505,0.0344,-0.03745,0.09234,0.18679,0.02086,0.00771,-0.08145,0.09115,0.02234,-0.08113,-0.03314,-0.03818,0.0273,0.05692,0.02092,0.00909,-0.08107,-0.1248,-0.02488,0.00799,-0.10521,0.00523,-0.0148,-0.01919,0.03408,-0.02571,0.08494,-0.03354,0.00901,-0.00271,0.01458,-0.0534,-0.02477,0.00203,0.04081,0.0552,-0.05206,0.00758,0.0561,0.05473,0.01504,-0.05813,-0.01424,0.02203,-0.07125,-0.04325,-0.09634,-0.00943,0.00593,-0.0,-0.09942,0.00268,0.0228,0.02121,-0.08173,0.01639,0.18563,-0.10184,-0.08802,-0.02734,-0.10945,-0.01355,0.01207,-0.03613,-0.08429,0.01263,-0.00805,0.06974,-0.02925,0.03915,-0.08901,0.02213,-0.053,-0.00064,-0.11937,-0.06784,-0.0122,0.03549,0.05387,0.04107,0.05084,-0.01544,0.02965,-0.03949,-0.05696,0.01179,0.00672,0.02418,0.01313,0.00637,0.04936,-0.03426,-0.00052,-0.05051,0.0201,0.06286,-0.12748,0.04844,-0.07651,0.05923,-0.13378,0.16354,0.03929,0.02722,0.0168,0.03247,0.00402,0.04901,-0.02105,-0.0313,0.12551,-0.03173,-0.07738,-0.02662,0.03336,0.09114,0.02859,0.04914,-0.08038,0.119,-0.02791,-0.04686,-0.04595,-0.06673,-0.09004,0.13639,0.17218,0.02521,-0.04282,-0.04462,0.05416,-0.01334,-0.08581,-0.05147,0.09513,-0.11395,-0.04142,0.10508,0.01407,0.02145,0.00582,0.11143,0.10194,-0.00179,-0.02353,-0.02258,0.08707,0.0165,-0.00157,0.06099,-0.00831,0.01066,0.05796,0.00772,0.04042,0.09251,-0.04229,0.01218,-0.03511,-0.01329,-0.0832,-0.11,0.02062,0.15751,0.03776,0.09214,-0.09594,-0.10145]},{"domain":"physics","key":"shm_max_speed","name":"Maximum speed of a mass on a spring","package":"physics-ai999x","example":"A 1 kg mass oscillates in simple harmonic motion on a spring with a spring constant of 100 N/m and an amplitude of 0.1 m. What is its maximum speed?","v":[-0.10399,0.08291,-0.01084,0.06939,-0.06171,-0.01558,0.01223,0.01994,0.02832,-0.07091,-0.05389,0.10356,-0.01495,0.07431,0.05616,0.01067,-0.05614,0.00889,-0.03064,-0.06205,0.016,-0.02253,-0.01315,-0.02764,-0.03517,-0.02284,0.00256,0.0088,0.0839,-0.02428,0.05519,-0.01258,0.0301,0.0136,-0.03155,-0.11941,-0.05299,-0.01304,-0.00513,0.01802,-0.05055,-0.08258,-0.03156,0.06142,0.05922,-0.04228,-0.02029,0.14794,-0.00999,-0.04832,-0.00205,-0.05171,-0.0079,-0.09791,0.03957,0.02275,-0.03783,0.03755,0.098,0.00803,-0.02084,-0.07273,-0.03855,-0.00061,0.06936,-0.00164,-0.00361,-0.01617,0.11525,0.01663,0.07836,0.06092,0.11686,0.00119,-0.02489,0.03424,-0.09441,-0.09075,0.05409,0.14603,0.03266,0.0663,-0.10885,0.01788,0.0351,-0.01405,0.06903,0.07237,0.00586,0.03601,0.08027,0.08298,0.10719,0.06681,-0.01544,0.04167,-0.094,-0.03994,0.05031,0.01737,-0.01068,0.10068,-0.0117,-0.05499,-0.04793,-0.01565,0.00138,0.07367,-0.14063,0.04744,-0.01288,-0.0097,0.0173,0.09524,-0.08414,-0.0275,-0.01718,0.01478,0.0592,-0.07494,0.09703,0.02543,-0.02834,-0.00726,-0.10113,-0.03437,-0.02478,0.02484,-0.07298,0.01208,-0.05722,0.04887,0.02408,-0.08758,-0.04872,0.06228,0.01416,0.11212,-0.02967,0.03348,0.01145,0.05815,0.02668,0.02318,0.04916,-0.01845,0.01132,0.0017,-0.16329,-0.00977,-0.07505,0.03132,-0.03983,-0.05876,-0.05777,-0.01409,0.12059,-0.02042,-0.06655,-0.09139,-0.07622,-0.0235,-0.03484,0.04138,-0.1265,0.04928,0.02146,-0.05135,0.1091,0.10726,-0.00264,0.00173,0.07021,-0.0091,0.14612,-0.03894,-0.01811,-0.06044,-0.08836,-0.09196,0.07282,0.03301,0.08333,0.12772,-0.02564,-0.04283,-0.0428,-0.02557,-0.04378,-0.04099,-0.09781,-0.01517,0.00392,-0.04058,0.05702,-0.02694,-0.00277,-0.0417,-0.02672,0.10192,0.04855,0.00104,-0.15403,0.03215,0.01949,0.06345,-0.05198,0.00241,-0.10108,-0.10486,0.00878,-0.07901,0.04987,0.12834,0.09249,-0.00774,-0.17748,0.03557,0.0176,-0.06061,-0.12495,-0.02748,0.05206,0.06994,-0.02742,0.12812,-0.08729,0.02597,-0.05383,0.04665,0.03495,-0.06051,-0.02132,0.04388,0.03328,0.04041,-0.11277,0.03114,-0.07131,-0.04658,0.01374,0.06494,0.04133,0.07281,0.02768,-0.13811,0.10148,0.04231,-0.01096,0.03322,-0.0024,0.11488,-0.02363,-0.09749,-0.05473,0.02508]},{"domain":"physics","key":"intensity_power_area","name":"Intensity as power per area","package":"physics-ai999x","example":"A power of 100 W falls uniformly on an area of 2 m^2. What is the intensity?","v":[-0.04714,-0.14827,0.07389,-0.00914,0.04512,-0.04353,0.04484,-0.04801,-0.04869,0.03931,0.03168,0.03649,-0.00815,0.00179,-0.09029,0.04394,0.05103,0.02854,0.08831,0.08962,0.03073,-0.07625,0.22069,0.00718,-0.04548,0.02722,-0.0162,0.03195,-0.00418,0.07037,0.04851,-0.04098,-0.03825,0.02828,0.0002,0.13815,-0.01508,0.04313,-0.02812,0.02087,0.03148,0.02599,-0.07111,-0.02419,-0.03763,-0.02344,0.00455,-0.06051,-0.02083,0.04544,-0.00926,0.12229,0.04175,-0.01477,-0.05712,0.03006,0.04041,-0.04369,-0.09354,0.03612,0.00151,0.0893,0.06013,0.05517,-0.01277,-0.02102,-0.05216,0.09533,0.07254,-0.01604,0.07302,-0.0715,-0.07309,0.06708,-0.07952,-0.01217,-0.0419,-0.08332,-0.13734,0.05003,-0.05428,-0.09825,0.05721,-0.05224,0.00441,0.0113,0.04264,-0.07947,0.02327,-0.06668,-0.06065,0.02186,0.02382,-0.02989,-0.0209,-0.00402,0.04438,0.03624,0.09691,0.04223,-0.00616,-0.01585,-0.04035,0.01297,-0.00169,0.02057,0.0154,-0.04066,0.00673,-0.01677,-0.01925,0.0241,0.03038,-0.01407,-0.04493,-0.05322,-0.01108,-0.06051,-0.00147,-0.01423,-0.09413,-0.04716,0.07719,-0.04297,-0.05039,0.01579,-0.10227,0.00293,-0.06836,-0.03011,-0.04547,0.06321,0.03461,-0.0159,0.00754,0.06354,0.00952,0.00447,0.0055,0.08121,0.01979,0.00801,-0.02157,-0.0208,0.05256,-0.03104,-0.08033,-0.03097,0.00918,-0.06842,-0.05517,0.04947,0.02402,0.10751,-0.00714,-0.00236,-0.19905,0.01634,0.13856,0.03364,0.09477,0.02805,0.0475,-0.02448,-0.03635,0.01514,0.08669,0.08353,-0.00777,0.01604,-0.01328,-0.0642,-0.00878,0.0453,0.05641,-0.03803,0.01854,0.004,0.02302,-0.27147,0.02931,0.05149,-0.16862,0.00888,-0.04217,-0.03523,0.05832,0.0912,-0.04574,-0.10351,-0.09134,-0.06733,0.04451,0.07021,-0.03344,0.0457,-0.05451,-0.07733,-0.0331,-0.09487,0.06148,0.0332,0.07688,-0.07328,0.0633,0.00783,0.00652,-0.03982,-0.09806,0.13189,-0.05344,0.0002,0.06797,0.01629,-0.03059,-0.01203,0.04358,-0.06598,0.09667,-0.1443,0.04166,-0.10746,-0.11643,0.02888,0.02449,-0.05319,-0.02563,-0.05391,0.11405,0.00734,0.01561,0.15752,-0.01288,0.05359,0.07082,0.12151,0.11077,-0.13372,-0.08531,-0.0119,0.05584,-0.00185,0.00072,0.05622,-0.00214,0.05955,0.10824,0.01571,0.03775,-0.0215,-0.06275,-0.00936,0.04754,-0.00093,-0.0238,-0.01272]},{"domain":"physics","key":"wavelength_in_medium","name":"Wavelength of light in a medium","package":"physics-ai999x","example":"Light with a wavelength in vacuum of 600 nm enters glass with an index of refraction of 1.5. What is the wavelength in the medium?","v":[-0.10626,0.0067,0.08939,0.03598,0.03936,0.08403,-0.00675,-0.04003,0.15319,-0.10996,-0.01898,-0.03641,0.05579,0.06141,-0.0822,-0.02226,0.02196,0.02853,0.04116,0.04111,-0.05654,-0.02958,-0.05133,-0.02518,0.06217,-0.02168,0.00961,0.05592,0.00405,0.02732,-0.00664,0.04177,0.00544,-0.00581,0.0469,-0.09801,0.08192,-0.07319,-0.0049,-0.02142,0.06227,-0.05352,0.05606,-0.09219,-0.00028,-0.09144,-0.03869,-0.09619,-0.04854,-0.00884,0.04118,0.05428,0.0255,-0.03183,-0.05391,-0.07667,0.04608,-0.06011,0.03162,-0.04978,0.0353,-0.05118,0.09914,-0.06619,0.08547,0.03685,0.03063,0.01239,-0.00391,-0.0032,0.0245,0.05304,0.09905,0.07321,0.06456,-0.05621,-0.10176,-0.14561,0.10048,0.06614,0.03304,0.06218,-0.04823,0.00334,0.03592,0.00092,-0.00016,-0.09189,-0.01904,0.0539,-0.03339,0.07897,-0.06063,0.02521,0.03378,-0.06944,-0.06137,0.02669,0.04842,0.00992,0.06445,0.13176,-0.04891,0.01843,0.11278,-0.00763,-0.02825,-0.06598,0.11595,0.00112,-0.07916,-0.12425,0.00463,-0.03616,-0.08667,0.00631,-0.02175,-0.02845,0.00429,0.06897,0.02581,0.08367,-0.00922,0.03888,0.05252,0.00038,0.06487,0.07089,-0.09414,0.02875,-0.04995,-0.01899,0.04325,-0.07626,0.00595,0.01973,0.02541,0.04427,0.01863,-0.04815,-0.02472,0.02343,0.01845,0.1051,-0.01556,-0.00385,0.09706,-0.07465,-0.1248,-0.10188,0.02452,0.06412,-0.02686,-0.00782,0.02167,-0.03062,0.12044,-0.14209,-0.0519,0.00382,-0.12182,0.02101,-0.01182,-0.02561,-0.02258,0.07307,0.05383,-0.1071,0.1144,0.0272,-0.00473,0.03252,-0.132,-0.00467,0.12607,-0.00922,0.0378,-0.10861,0.01222,-0.04823,0.04378,0.02472,-0.03594,0.11749,-0.07451,-0.00212,0.0259,0.00733,-0.05683,0.06597,-0.0528,-0.02677,0.11573,-0.00201,0.06919,-0.00968,-0.02507,0.02745,0.00516,-0.0095,0.00802,0.0145,0.1339,-0.00595,-0.02578,0.01278,0.04829,0.06047,-0.09525,0.08661,-0.07504,0.02493,-0.13996,-0.01883,0.01679,-0.02864,-0.08451,-0.04757,0.13267,0.02131,-0.07957,-0.09994,0.06798,0.05966,0.02759,-0.05651,-0.03143,-0.00819,0.13415,-0.13878,0.03299,0.02791,-0.03253,0.0287,0.14295,-0.00819,0.04663,-0.04308,-0.03744,0.00181,0.05932,0.01611,-2e-05,-0.04821,-0.01212,0.02835,-0.06133,-0.04578,-0.0863,0.10553,0.00276,0.03071,-0.10082,-0.09711,-0.09748,-0.12381]},{"domain":"physics","key":"index_of_refraction","name":"Index of refraction","package":"physics-ai999x","example":"The speed of light in the medium is 2e8 m/s for a certain glass. What is the index of refraction of the glass?","v":[0.03031,0.03657,0.1,-0.02644,0.01402,-0.02355,0.00975,0.00623,0.14438,-0.09452,-0.02509,-0.04088,0.05263,-0.01624,-0.07405,0.03538,-0.01875,-0.02381,0.04504,0.06974,-0.05212,-0.05814,0.04515,-0.03418,0.04242,0.06943,0.03235,0.05604,0.04056,0.01176,-0.00489,0.03591,0.0536,-0.04227,0.05402,-0.07341,0.03125,-0.11412,-0.02358,-0.02722,0.07039,-0.05726,0.03891,-0.14742,0.0696,-0.06483,-0.02267,-0.1066,-0.03144,-0.02639,0.01636,0.00165,-0.02171,-0.05813,-0.05446,-0.00291,0.05999,-0.08116,-0.01428,-0.01255,0.04937,-0.01808,0.07956,-0.13335,0.01416,-0.03404,0.08915,-0.0081,0.02162,0.11396,0.00879,0.00287,0.0333,0.01763,0.10677,-0.06742,-0.05382,-0.10234,0.10506,0.12775,0.02633,0.02572,-0.03825,0.0423,0.07134,-0.01223,-0.02357,-0.08211,-0.04622,0.01656,-0.04111,0.07496,-0.06051,0.05203,0.04385,-0.01551,-0.08917,0.01118,0.09792,-0.02686,0.11424,0.09636,-0.00908,-0.04354,0.0932,0.00773,-0.00254,0.02575,0.09442,0.03984,-0.04112,-0.08692,0.06583,-0.06107,-0.05493,-0.03352,0.02314,-0.03368,-0.0646,0.04202,-0.02227,0.07001,0.01286,0.08245,0.09348,-0.04528,0.00342,0.18639,-0.12747,0.05687,0.01923,0.00081,-0.12173,-0.03392,-0.02393,0.03553,0.04929,0.079,-0.07223,-0.01787,-0.0293,0.06277,0.09076,0.084,-0.08477,-0.02502,0.12669,-0.02269,-0.15175,-0.02021,-0.01273,0.05433,0.00926,-0.02959,-0.06863,-0.06659,0.02233,-0.12921,-0.08659,-0.01329,-0.03746,0.04739,-0.00192,-0.06999,0.01854,0.05292,0.01684,-0.0953,0.13535,0.05321,-0.06391,-0.03841,-0.10548,-0.02846,0.13878,0.02083,0.01584,0.0034,-0.01358,-0.01681,-0.00624,-0.00748,-0.06411,0.07582,-0.00472,0.05852,0.00574,0.00406,-0.12185,0.13811,-0.08059,-0.03816,-0.03558,-0.00438,0.02733,0.02632,-0.0639,0.03283,0.04443,0.06073,0.0599,0.00209,0.13427,0.02629,-0.03308,0.02208,0.06514,0.0872,-0.06519,0.09287,-0.03252,-0.03269,-0.02773,-0.05057,-0.04122,-0.05939,-0.08196,-0.10447,0.04329,0.04709,-0.01308,-0.16092,-0.00081,-0.02128,-0.00368,-0.00501,-0.0804,0.01672,0.02703,-0.0394,0.02813,-0.05147,-0.01763,0.0021,0.12399,-0.01919,0.03257,-0.01692,-0.07563,0.0416,0.01591,0.00608,-0.00411,-0.00459,0.06486,0.00465,0.05058,-0.1269,-0.07053,0.11668,-0.0225,0.07843,-0.11877,-0.04114,-0.04117,-0.05211]},{"domain":"physics","key":"mirror_focal_length","name":"Focal length of a spherical mirror","package":"physics-ai999x","example":"A concave mirror has a radius of curvature of 0.4 m. What is its focal length?","v":[0.07781,-0.06856,0.13393,0.01957,-0.00532,-0.05037,0.06536,-0.02646,0.16135,-0.06593,-0.02849,-0.11687,-0.04398,0.02563,-0.07354,0.04494,0.10201,0.08977,0.12709,-0.02673,-0.07438,-0.01258,0.04591,-0.10274,0.02185,-0.02393,-0.05882,-0.09374,0.04914,-0.0304,0.03275,0.04761,0.02166,-0.00592,-0.04504,-0.1453,0.06156,0.05109,0.02096,0.06865,-0.01736,-0.05033,0.06072,-0.01396,0.03117,0.06599,-0.06034,-0.04976,0.05008,-0.04413,0.04591,0.04033,0.00562,-0.01335,-0.18702,0.06317,0.00836,-0.09492,-0.03438,-0.03826,0.01628,-0.09142,-0.06595,0.05528,0.04387,0.08793,-0.03608,-0.05882,-0.07999,-0.02843,0.15593,-0.00235,-0.02666,0.01653,-0.04223,-0.06138,-0.02297,-0.02486,0.04994,0.01842,-0.0706,-0.06562,0.03231,-0.07645,0.20942,0.01082,0.09424,-0.03401,0.07961,0.04478,0.02688,-0.0028,-0.03003,0.14532,-0.00589,-0.02353,-0.13039,-0.02061,-0.00138,0.05846,0.04716,-0.02072,-0.08709,0.04946,-0.07839,-0.0268,-0.05216,-0.01284,0.10324,-0.01939,-0.0308,-0.01797,0.0479,0.00952,0.04791,-0.0199,0.05845,0.0152,-0.01113,-0.00153,-0.05647,0.01244,0.02857,-0.01182,-0.02786,0.01163,0.03413,0.1066,-0.00595,0.04002,-0.06371,-0.00288,-0.05578,-0.08137,-0.00072,0.04386,-0.12104,0.11321,-0.00096,-0.01255,0.00808,-0.08225,-0.01641,-0.05043,0.04857,0.08686,0.11292,0.0079,-0.05829,0.07074,0.003,0.11364,0.03506,-0.01755,0.09706,-0.06775,-0.05696,-0.01076,-0.05221,0.04072,-0.04809,0.04814,-0.05175,-0.04789,-0.06392,0.08892,-0.04113,-0.03507,0.05751,0.03913,-0.086,0.02235,0.04567,0.02007,0.04912,-0.09193,-0.0206,0.05945,0.02747,-0.07246,0.03535,-0.02405,0.0201,0.03393,0.0093,0.05577,0.03181,0.07655,-0.05995,-0.10847,-0.03791,0.00259,0.04135,-0.04655,0.02196,0.05475,-0.05183,-0.052,-0.01084,-0.09012,-0.0563,0.09304,0.0863,-0.00017,0.01332,-0.0295,0.00778,0.02223,-0.12958,-0.04719,-0.03501,-0.03032,-0.01662,-0.08132,-0.08104,-0.02966,-0.01774,-0.04157,0.18295,-0.0531,0.0582,-0.12391,0.04701,0.02929,0.06848,-0.0103,-0.09745,0.04278,-0.04504,-0.01483,0.06149,0.01065,-0.00274,-0.01935,-0.03979,0.00463,0.03982,-0.0893,-0.09588,-0.01356,0.12651,0.05148,-0.06706,0.06412,0.09143,-0.00955,-0.02058,0.08313,-0.08044,-0.07208,0.03679,0.09716,0.05591,0.04676,0.03238,-0.02302]},{"domain":"physics","key":"rms_voltage","name":"Rms voltage of a sinusoidal supply","package":"physics-ai999x","example":"An AC supply has a peak voltage of 170 V. What is the rms voltage?","v":[0.09735,-0.08829,0.06914,0.01753,-0.09086,0.0182,-0.07905,0.05152,0.01473,-0.00736,0.0019,0.03004,-0.06497,0.01318,-0.00381,0.04375,0.05844,-0.03238,-0.10762,0.06843,0.01845,-0.15679,-0.04442,0.07905,-0.05156,0.05471,0.07521,-0.03318,-0.07332,0.00535,-0.16473,0.00911,-0.00517,0.02265,-0.02035,-0.03614,0.02528,-0.08036,0.08331,0.04373,-0.0158,0.01545,0.07309,0.05073,0.05647,-0.10552,-0.01845,-0.04529,-0.0544,0.00325,-0.03244,0.0935,-0.08586,-0.04181,-0.02549,-0.01844,0.06972,0.01195,0.00181,-0.01704,0.04166,0.02022,-0.05499,-0.02337,-0.0067,0.01406,0.06588,0.10847,-0.07503,-0.08484,0.05555,0.00482,0.14038,0.0312,-0.07862,0.09943,-0.05333,-0.05045,-0.03172,0.01697,0.04189,0.14612,-0.12593,-0.05417,0.03788,-0.01798,0.04803,0.05255,0.02953,-0.04017,0.14581,0.12813,0.01389,0.07514,-0.01761,0.02465,-0.00993,-0.10049,0.03208,-0.02243,-0.10205,-0.01101,0.04185,-0.12067,-0.00146,-0.05737,-0.0515,0.12027,0.01253,-0.00344,0.00057,-0.08384,-0.05312,0.05742,-0.0294,0.04237,-0.00066,-0.08895,-0.00371,-0.09022,0.07187,0.00022,-0.01292,-0.09027,-0.05172,0.02957,-0.06921,-0.04394,-0.02969,0.1143,-0.00012,-0.05246,0.00228,-0.05776,-0.04196,0.03494,-0.02296,0.09077,-0.01419,0.00047,0.00603,0.07136,0.01818,0.04773,0.08499,-0.06807,0.02715,0.07202,0.06347,-0.01073,0.03767,0.06527,-0.01828,0.00126,0.0061,0.03642,-0.03904,0.00699,-0.0557,0.04179,-0.04965,-0.02953,0.04799,0.00701,-0.00318,-0.00437,-0.11242,0.00711,0.10483,-0.0593,-0.05302,0.04799,-0.00978,-0.09907,-0.04263,-0.02605,-0.07644,-0.02493,-0.00557,-0.0307,0.02906,0.0232,0.05882,0.12699,-0.04454,0.03306,-0.01525,0.01973,0.01369,-0.01548,-0.03583,0.03713,0.0763,0.01699,0.04706,-0.04219,0.01854,0.01594,0.21232,0.10759,0.01891,-0.07495,-0.04688,-0.00901,0.03947,-0.04604,-0.15951,-0.05754,0.01013,-0.03734,0.00959,-0.06857,-0.07635,0.06355,0.1148,0.00016,-0.14204,0.06946,-0.00795,-0.09064,-0.02621,0.05317,0.08754,0.03659,-0.03297,-0.05273,-0.05436,-0.10801,0.0669,-0.06731,-0.02455,-0.04472,0.03262,0.09545,0.08397,-0.05922,-0.06618,-0.0111,0.07377,0.02009,0.11185,0.0382,0.05317,0.08926,0.08549,-0.07191,-0.05438,0.09874,0.0495,-0.0016,-0.00175,0.08363,-0.11095,-0.00554,-0.07051,-0.09073]},{"domain":"physics","key":"rms_current","name":"Rms current of a sinusoidal supply","package":"physics-ai999x","example":"An AC circuit has a peak current of 10 A. What is the rms current?","v":[0.1255,-0.01489,0.02937,0.02798,-0.00762,-0.08906,-0.09021,-0.01787,-0.01024,0.08731,-0.05994,0.01051,0.028,-0.01821,-0.01789,0.09812,0.08548,-0.07512,-0.0491,-0.03364,-0.02722,-0.11708,-0.03477,-0.00214,-0.05148,0.08598,0.06737,0.02564,-0.00554,-0.05423,-0.00294,-0.00892,-0.00731,0.02741,0.078,-0.06495,-0.10219,-0.03836,0.1051,-0.02859,-0.06245,-0.0489,0.07303,0.07025,0.06369,-0.08496,-0.09979,-0.10315,-0.04574,-0.03597,-0.08639,0.0697,-0.00774,0.02825,0.04463,0.05137,0.01595,0.02749,-0.12056,-0.06579,-0.01304,0.03507,0.02381,-0.01605,0.01286,-0.0086,-0.01363,0.13188,-0.07312,-0.11894,0.00814,-0.06027,0.04995,0.00182,-0.03508,0.0308,-0.0641,0.01075,-0.09678,-0.00878,0.04459,0.04783,0.02325,-0.00535,0.13094,-0.01949,0.04396,0.0483,-0.01552,-0.04995,0.07002,0.04796,-0.04303,0.03218,-0.01857,0.09403,-0.03488,-0.08968,0.07385,-0.01902,0.0075,-0.10223,0.00635,-0.08564,0.00729,0.00992,-0.03021,0.08349,-0.02624,0.03289,-0.00708,0.02297,0.08727,-0.01587,0.01755,0.06967,0.10078,-0.08453,-0.07345,-0.09344,-0.00837,0.07591,0.06284,-0.09275,-0.09068,-0.01822,-0.14022,0.02497,0.0482,0.02593,-0.02851,-0.10297,-0.04722,0.02239,-0.03699,0.0953,-0.08138,0.07535,-0.07656,0.0628,0.00866,-0.03968,0.02666,0.02748,0.11608,-0.01429,0.13256,0.06115,-0.05035,-0.02637,-0.02124,0.06919,0.08127,0.05364,-0.05751,-0.00548,-0.03904,0.1519,0.01691,0.03309,0.07259,0.0292,-0.01641,-0.00191,-0.09698,-0.09181,-0.04319,0.01969,0.08336,0.08496,-0.05721,0.05963,-0.00216,-0.09241,-0.09585,-0.0266,-0.08781,0.02886,-0.01177,0.01322,-0.01299,0.04424,-0.04085,0.1606,0.08847,0.07167,0.02414,0.11557,0.01981,-0.06936,0.00331,0.02243,0.0173,0.0062,0.02635,-0.05218,0.01489,0.09277,0.11595,-0.01598,0.11888,0.00874,-0.00564,-0.07728,0.01138,-0.07472,-0.04586,0.05035,0.05371,0.00942,-0.06733,0.02195,0.03007,0.08549,-0.01886,0.04803,-0.16802,-0.00715,-0.05704,-0.0643,-0.00124,-0.01681,-0.06145,0.07224,0.00905,-0.06142,-0.06201,-0.1004,0.01021,-0.03566,0.01747,-0.05953,0.10618,0.03403,0.11654,-0.04493,-0.02124,-0.01587,0.06273,0.0444,0.10057,-0.01757,-0.05939,0.02497,0.06666,-0.06952,0.07439,-0.02671,-0.07493,0.00464,-0.0261,0.09372,-0.05034,0.03965,-0.12155,-0.09441]},{"domain":"physics","key":"loop_center_field","name":"Magnetic field at the centre of a circular loop","package":"physics-ai999x","example":"A circular loop of wire with a radius of 0.1 m carries a current of 5 A. What is the magnetic field at its centre?","v":[0.02765,-0.06709,0.01196,-0.01501,0.02639,-0.0848,-0.02071,0.01929,0.17342,0.12284,-0.07104,-0.10276,0.11643,-0.03946,-0.03096,0.01011,-0.03995,-0.01161,0.09116,-0.00327,-0.05102,0.04206,0.02005,-0.06237,0.00661,-0.00992,0.02357,-0.0447,0.04691,-0.01391,0.12804,-0.01859,0.00128,0.0298,-0.05531,-0.09469,0.02792,0.06063,-0.00511,0.04621,0.03456,0.01962,0.08132,0.00444,-0.01592,-0.02443,-0.04647,0.0496,-0.02159,-0.06763,-0.04722,-0.0456,0.05253,-0.04034,-0.0532,0.03789,-0.01655,-0.03152,-0.0545,-0.04847,-0.07278,0.0212,0.00885,-0.01911,0.04282,0.05775,0.02631,0.09049,-0.07044,0.02669,0.08439,-0.01775,-0.11042,-0.01559,-0.12532,-0.08459,-0.1628,0.01156,-0.06891,0.01621,-0.01756,-0.05858,0.07061,-0.05374,0.03293,0.02267,0.07076,-0.05397,0.00544,-0.07081,0.03028,-0.02023,-0.09304,-0.00908,0.01254,0.08093,-0.03204,0.03629,-0.01053,0.03304,-0.01215,-0.15855,0.05731,-0.0221,0.02945,0.03059,-0.03816,-0.06567,0.02629,0.02213,-0.11416,0.03909,0.09282,0.02049,-0.0022,-0.01389,0.12709,0.00354,-0.0435,-0.08615,-0.08411,-0.00151,0.02131,0.02041,-0.117,-0.00502,0.09931,0.15439,0.09427,-0.08099,-0.03648,-0.00929,0.03599,0.06376,-0.02702,0.0812,-0.09305,0.0447,-0.00784,-0.02442,-0.03695,-0.03492,0.04503,-0.04809,0.16443,0.03633,0.04841,-0.04473,-0.02772,-0.04839,0.04661,0.1024,0.12472,0.04491,-0.02274,-0.05771,-0.00729,0.08284,-0.01665,-0.0369,0.05785,-0.00777,-0.03,-0.1564,-0.04016,-0.10372,0.08237,-0.00154,-0.05972,0.02006,-0.01843,0.00697,0.01388,-0.00601,0.07073,-0.0834,-0.09413,0.12985,0.06891,-0.04953,-0.02527,0.01005,-0.02909,0.0697,0.11924,0.03789,0.04228,0.0553,-0.03322,-0.11323,-0.04106,0.03057,0.02324,0.03159,0.04278,-0.03779,0.00892,0.07949,-0.10616,0.00063,0.07956,0.00176,0.01835,-0.0407,0.02186,-0.16894,0.08178,0.10628,0.00617,0.06967,-0.03886,0.14884,0.17434,0.05477,-0.03646,-0.06755,-0.07956,-0.08036,0.0364,0.00173,-0.08776,-0.01137,0.00307,0.09095,0.045,0.02049,0.01626,0.05915,0.07258,0.035,-0.03197,-0.01217,0.04841,-0.00156,-0.02107,-0.0575,0.03696,-0.00422,-0.02119,-0.00876,0.05575,-0.03485,-0.00809,-0.06682,-0.00714,-0.03568,0.07068,-0.05182,-0.1427,0.0323,-0.00846,-0.0601,-0.01319,0.07968,-0.05211,-0.06415]},{"domain":"physics","key":"rl_time_constant","name":"Time constant of an RL circuit","package":"physics-ai999x","example":"An inductor of inductance 0.5 H is connected in series with a 100 ohm resistor. What is the time constant?","v":[0.02554,0.04564,-0.09905,0.0565,-0.04285,-0.00965,0.10461,0.01474,0.23053,0.14379,0.04822,0.016,0.023,0.15258,-0.00878,-0.06533,-0.04254,0.00435,0.04544,0.077,-0.05581,-0.0025,0.00604,0.0101,0.11978,-0.05773,-0.00384,0.06091,0.11784,0.02885,0.06755,0.0672,-0.02306,-0.04387,0.07097,-0.03348,0.05709,0.1642,-0.01004,0.07136,-0.0361,0.00224,0.0006,-0.06758,-0.02422,-0.0518,0.02364,0.14142,0.05367,-0.09161,0.01288,-0.00144,-0.0696,-0.05262,-0.02848,-0.03504,-0.00409,0.03094,-0.04111,0.04055,0.00287,0.10021,0.0191,-0.09981,0.03263,0.00781,-0.00174,-0.06124,0.00301,-0.04462,-0.03952,-0.03421,-0.16537,-0.03499,0.01775,-0.08925,0.06324,0.08859,0.05388,-0.09186,-0.04838,0.03105,-0.00294,0.04985,0.03224,-0.0074,-0.05303,-0.07941,-0.06584,-0.01282,-0.11278,-0.00836,-0.02185,-0.11712,0.04329,-0.0449,-0.00849,0.03191,-0.04591,0.07403,0.03325,0.03068,-0.02908,0.03054,0.02959,0.09146,-0.12453,-0.15339,0.063,0.04264,-0.06832,0.00148,-0.09104,0.02885,-0.03824,-0.048,0.07624,0.11171,-0.00847,0.01953,0.0133,0.0072,0.09393,-0.00702,-0.09616,-0.02044,-0.01059,-0.03154,-0.02396,-0.04101,0.07555,-0.02155,0.00348,0.04713,0.05044,0.05093,-0.12648,0.05559,0.02999,0.00112,-0.0207,-0.03006,0.08198,0.00304,-0.02267,-0.07565,-0.04619,0.00229,0.1794,-0.05171,0.00104,-0.01173,-0.08615,-0.13756,-0.03739,-0.06279,-0.02094,0.13284,0.04639,-0.12059,0.05627,0.04379,-0.06569,0.00273,-0.04448,-0.04642,0.03983,-0.05331,-0.13795,-0.04361,-0.01791,0.02873,-0.00806,0.04871,0.00301,-0.01583,-0.00592,0.04395,0.01199,0.04853,-0.04674,-0.02597,-0.02785,-0.01221,0.06146,-0.05518,0.05863,-0.02898,-0.10055,0.06457,0.02136,0.07042,0.03624,-0.01697,-0.03291,0.02128,-0.01502,0.02622,-0.02887,-0.02111,0.03433,8e-05,-0.03969,0.10623,-0.06679,-0.06201,0.14018,0.02844,-0.07804,-0.01518,0.07937,0.00588,0.09964,0.01474,-0.00524,0.00634,-0.01585,-0.04699,-0.09769,-0.10937,0.01014,0.00665,0.01959,0.01502,0.03934,-0.00351,0.09144,0.03822,-0.04569,-0.0909,0.02518,-0.07805,-0.00185,-0.05989,-0.03609,-0.09224,-0.03619,-0.02554,-0.05061,0.01852,0.00638,0.0483,-0.01458,-0.03365,-0.05422,-0.01486,0.11245,-0.13782,0.04067,0.12059,0.059,0.04672,-0.00079,0.03756,-0.06274,0.03739]},{"domain":"physics","key":"inductive_reactance","name":"Reactance of an inductor","package":"physics-ai999x","example":"An inductor of inductance 0.03 H is in an AC circuit at a frequency of 60 Hz. What is its reactance?","v":[-0.01609,0.03814,-0.09991,0.07624,-0.0255,0.11893,0.05447,0.04455,0.23052,0.05384,0.0518,-0.03127,-0.0129,0.10418,-0.04248,-0.0378,-0.0405,-0.03539,-0.09939,0.05235,-0.04153,-0.04505,-0.05781,0.05299,0.05425,-0.09475,0.02447,-0.1077,-0.0142,0.04729,-0.1684,0.10283,-0.04305,-0.00812,0.03581,-0.0259,0.03789,0.06233,-0.04319,0.08984,-0.08575,-0.0438,0.06817,0.0396,0.00943,-0.06291,-0.06491,0.07675,0.05404,-0.12705,0.02593,0.00274,-0.03819,-0.01949,-0.11771,0.02048,0.0351,0.05661,0.02424,-0.01053,-0.04928,-0.00856,-0.08006,-0.11871,0.06256,0.02178,-0.01024,-0.02566,-0.02288,-0.09185,0.02696,0.02024,-0.14639,-0.09362,-0.02596,0.00068,0.03463,0.05823,0.03118,-0.1084,-0.02167,0.10294,-0.05654,0.04643,0.01458,-0.00111,-0.0243,-0.03665,-0.05993,0.04258,0.03196,0.04737,-0.06112,-0.03624,0.01958,-0.04622,-0.10259,-0.03051,0.01095,0.00906,-0.03886,0.09855,0.00432,0.00724,0.13269,0.05353,-0.19216,-0.00131,-0.01257,0.03699,-0.11313,-0.0864,-0.05099,-0.02552,-0.02175,-0.10254,0.13385,0.01705,0.02258,0.02353,0.043,0.03021,0.05843,-0.03097,-0.0682,-0.02411,0.05437,-0.00589,0.00266,-0.05409,0.01782,-0.04652,0.04993,0.02977,-0.04211,0.06949,-0.14255,0.0545,-0.11558,0.05979,-0.03267,-0.02799,-0.01796,0.04409,0.0361,-0.11011,-0.02097,-0.05134,0.1549,-0.11838,0.12444,0.05243,0.00444,-0.01834,0.00017,-0.04182,0.01937,0.02128,-0.03184,-0.03149,0.02288,-0.08021,0.04794,0.04142,-0.05646,-0.09115,0.08487,-0.06779,-0.02471,-0.02445,0.08429,-0.0086,0.10942,0.0085,0.04855,-0.0007,0.04548,0.02723,-0.04676,0.0917,0.0372,-0.02596,-0.04303,0.09032,0.03914,-0.01812,-0.00735,0.00786,-0.04709,0.04795,0.02207,0.08718,0.04551,-0.03598,-0.08401,-0.05617,-0.03168,0.0286,-0.08379,0.05134,-0.0336,-0.04383,-0.00601,0.0838,-0.05588,-0.01311,0.03486,0.02028,-0.09334,0.05005,0.13233,-0.00752,0.12027,0.04727,-0.02297,-0.00217,0.06746,0.04629,-0.0154,-0.12526,-0.01291,0.06433,0.04407,0.02873,0.00925,0.0235,-0.01804,-0.04407,0.04043,-0.05649,0.01176,-0.09667,0.03823,0.04131,-0.06495,-0.06047,0.00035,0.02563,0.02883,0.02807,0.07708,0.11251,0.01646,-0.00403,0.02404,-0.0808,0.0375,-0.00466,0.1189,0.00576,-0.00412,0.08161,0.03378,0.01189,-0.07067,0.02212]},{"domain":"physics","key":"capacitive_reactance","name":"Reactance of a capacitor","package":"physics-ai999x","example":"A capacitor with a capacitance of 1 uF is in an AC circuit at a frequency of 60 Hz. What is its reactance?","v":[0.03691,0.06434,-0.00787,0.06142,-0.10149,0.11145,0.07421,0.02055,0.16584,-0.00344,0.05424,0.0522,0.02711,0.02618,-0.03638,-0.04979,0.03307,-0.05238,0.00601,-0.00407,0.02927,-0.08781,0.01528,-0.01812,-0.09359,-0.07067,0.02532,-0.15032,0.01874,0.01057,-0.11303,0.13956,0.01126,-0.01126,0.03036,0.03297,0.003,-0.06512,-0.05292,0.0527,-0.01972,-0.02086,0.05001,0.04938,-0.04472,-0.0803,-0.09196,-0.0139,0.11012,-0.05553,-0.05347,-0.10197,0.0718,0.03219,-0.08248,0.06518,0.01801,0.09096,-0.00776,-0.0092,-0.04383,-0.10622,-0.06622,-0.00327,0.02481,-0.02924,-0.03324,-0.01951,-0.05832,-0.0796,0.02121,0.06052,-0.03889,-0.12042,0.03317,0.0863,-0.04599,-0.04876,0.04513,-0.03962,0.02781,-0.01869,0.00455,0.03824,0.02,0.01107,0.07534,0.00705,0.017,0.01209,0.0569,0.09063,0.01293,0.02641,-0.05663,-0.04706,-0.1061,-0.10615,-0.00476,-0.04955,-0.05846,0.1599,-0.00843,0.03708,0.04641,-0.01778,-0.09556,0.01125,-0.02863,0.07953,-0.01845,-0.01246,0.02476,5e-05,0.06489,-0.04887,0.11595,-0.00158,0.00651,0.12132,-0.03392,0.01785,0.05501,0.02273,-0.07051,0.03686,-0.02318,-0.05795,-0.08269,-0.09165,-0.02562,-0.00327,0.02121,-0.06696,-0.08698,-0.01876,-0.07697,0.00379,-0.09746,0.05562,-0.03375,-0.04286,-0.07313,0.02573,0.01094,-0.09598,0.07229,0.00654,0.10401,-0.05161,0.05955,0.14837,0.05733,0.08067,0.00132,-0.03037,0.04982,-0.01385,-0.07595,0.08469,-0.13845,-0.02174,0.12064,0.02176,-0.00908,0.02505,0.14456,0.04198,0.04176,-0.07122,0.04137,-0.0768,0.14004,0.04286,-0.08049,0.01971,-0.01865,-0.05607,-0.00701,0.0835,0.0485,0.01868,0.06587,0.05261,-0.09426,0.01187,-0.05535,-0.0142,-0.08615,0.01864,0.09427,0.00665,-0.00228,-0.07162,-0.10595,-0.07482,-0.05642,0.06824,-0.0002,-0.04728,-0.06512,0.02104,0.01585,-0.01187,-0.03337,0.05984,-0.06041,-0.05871,-0.08198,0.07129,0.03772,-0.15856,0.07449,-0.00221,-0.02078,-0.03577,0.06807,0.06603,0.00241,-0.03746,-0.0034,0.09352,0.07901,-0.02395,-0.02784,0.03866,-0.07507,-0.04639,0.10266,0.03393,0.02863,-0.09028,0.01571,0.11998,-0.11348,0.0932,0.0518,-0.00667,-0.01094,0.01931,-0.02045,0.05016,-0.06266,-0.03173,0.1592,-0.01158,-0.06186,-0.02815,0.07615,0.05316,-0.0458,0.04229,0.01849,0.01642,-0.06196,0.00165]},{"domain":"physics","key":"lc_resonance","name":"Resonant frequency of an LC circuit","package":"physics-ai999x","example":"A resonant circuit has an inductance of 0.01 H and a capacitance of 1 uF. What is the resonant frequency?","v":[-0.0196,0.08982,-0.0561,0.04136,-0.12663,-0.03403,0.11097,0.07414,0.10252,0.15817,-0.01483,0.01084,-0.01645,0.12422,-0.09899,0.00164,0.07174,0.01262,0.00515,-0.03703,-0.07216,-0.04555,0.08245,-0.03786,0.00528,-0.09455,-0.06123,-0.08545,0.07745,0.04604,-0.04765,0.02029,0.05871,-0.05636,0.04427,0.01843,0.07103,0.03064,0.00137,0.1283,-0.03986,-0.05997,-0.00504,-0.05784,0.00156,0.01143,-0.14445,0.11889,-0.02287,-0.07953,-0.06127,-0.07377,-0.00966,-0.01921,-0.07832,0.06438,-0.09192,0.12768,-0.03207,0.01992,-0.01134,0.00356,0.00024,-0.0888,0.06056,-0.02246,-0.0299,-0.0415,-0.00931,-0.10797,0.03673,0.05859,-0.02351,0.0204,0.01577,-0.0679,-0.10918,0.00866,0.00548,-0.04952,0.01685,-0.0094,-0.00794,-0.00038,-0.00996,-0.05206,0.0376,0.00871,-0.01089,0.01063,-0.02161,0.05744,-0.02094,-0.01634,0.08516,-0.00159,-0.11948,0.05456,-0.01978,-0.00276,-0.03342,0.12939,-0.05441,-0.02632,0.05766,-0.10842,-0.0085,-0.02342,-0.05364,0.12533,-0.05879,-0.10465,-0.02757,0.0064,0.0208,-0.03791,0.1186,0.07498,0.02625,-0.01739,-0.02239,-0.07389,0.08782,0.074,-0.14026,0.00929,-0.05274,0.0186,-0.03194,-0.08413,0.10335,0.02463,0.03048,-0.06413,0.05299,0.08744,-0.13449,0.05417,0.02468,-0.02846,-4e-05,-0.02132,0.00668,0.00648,0.10191,-0.078,0.04451,0.01562,0.04046,-0.11619,0.04886,0.14146,-0.01176,-0.0,-0.0147,-0.12096,0.07343,0.04457,-0.06565,0.02437,0.01548,-0.05171,0.01629,0.09082,-0.03586,-0.00981,0.06772,0.03173,-0.02853,0.04104,0.08433,-0.05483,0.11274,0.05294,0.05466,-0.07727,-0.05076,0.08152,0.02355,-0.01596,0.01789,-0.00394,0.08593,0.03838,0.04583,-0.06666,-0.01388,0.02305,-0.00343,0.02921,0.04791,0.01161,0.00748,0.03103,0.01017,-0.11198,-0.0638,-0.04495,-0.07352,-0.11059,0.03239,0.01388,-0.07316,0.08373,-0.07829,-0.00736,0.08486,0.0261,-0.15769,0.03654,0.0502,-0.11811,0.10709,0.00228,0.00669,-0.05834,0.04662,-0.0044,0.0415,-0.23147,-0.05992,0.03636,0.06226,0.0284,-0.0025,0.08461,0.03429,0.03973,-0.03463,-0.01865,0.07133,-0.09302,-0.00756,0.00943,-0.0567,0.04636,0.02173,-0.04137,-0.01198,0.04799,-0.0123,-0.02275,-0.02706,-0.08753,-0.02535,-0.00364,0.02082,-0.05878,0.10224,0.05588,0.03799,0.0374,0.02172,0.05552,-0.01503,0.04636]},{"domain":"physics","key":"angular_velocity_time","name":"Angular velocity under constant angular acceleration","package":"physics-ai999x","example":"A flywheel rotating at an initial angular velocity of 2 rad/s has an angular acceleration of 3 rad/s^2 for 4 s. What is its final angular velocity?","v":[0.12861,0.01289,-0.11672,0.00378,0.0286,0.0925,-0.10211,-0.08398,0.03747,0.07733,0.07505,0.08052,0.0412,0.03852,-0.01261,-0.06467,-0.01721,-0.08542,-0.03955,-0.0577,0.05907,0.03253,-0.14854,0.02766,0.06284,-0.06302,0.07499,0.17219,0.03174,0.0841,0.05536,0.07061,-0.13147,-0.02187,0.04464,-0.01652,-0.01071,0.04233,-0.03038,-0.01342,0.01822,-0.01224,-0.0074,-0.04884,-0.11429,-0.04396,-0.00537,0.04774,0.02349,-0.01808,-0.01121,-0.043,0.01017,0.0896,-0.04595,-0.01475,0.05286,0.05543,-0.11333,0.00699,0.05059,0.05892,0.00553,-0.07927,0.09572,0.01659,-0.0073,-0.02222,-0.00505,-0.10499,-0.04566,0.01603,0.04177,-0.09004,0.01129,-0.12527,0.05141,0.08544,-0.0127,-0.05274,0.09345,0.04742,0.01205,0.04478,-0.01243,-0.01677,-0.00889,-0.07188,0.0273,0.04748,0.04778,-0.03769,0.00194,-0.12759,-0.05811,0.08185,0.06231,0.08535,-0.03678,-0.0514,-0.01315,-0.01278,0.07208,-0.01101,0.02163,0.04178,0.0189,-0.042,0.16297,0.01617,0.05704,0.03677,-0.07225,-0.07671,0.02196,0.00143,-0.00364,-0.09087,0.00624,0.05737,-0.05015,-0.07977,0.00275,-0.01353,-0.03277,0.01924,0.0878,-0.11491,-0.02204,-0.09527,0.08362,-0.10566,-0.00951,0.14382,-0.031,-0.0366,0.049,-0.01727,0.15034,0.05684,-0.03277,0.02044,-0.11789,-0.09895,-0.05247,0.01739,-0.09904,0.08265,0.01561,0.0287,0.05286,-0.10207,-0.10844,-0.05321,0.01956,0.04865,-0.05089,0.09037,-0.0745,0.02776,-0.04805,-0.05431,0.00905,0.06096,0.00849,-0.08877,0.01053,-0.04591,0.01079,0.01007,0.07253,0.05602,-0.04145,-0.0446,-0.09815,0.06416,0.01366,-0.02359,0.04556,0.00317,-0.0569,-0.01805,0.10968,-0.21096,-0.00029,0.03173,-0.04316,0.04173,0.06643,-0.02815,0.01787,0.07564,0.03794,-0.04265,0.0161,0.00334,0.11099,0.02284,0.09726,0.00387,-0.05948,-0.04919,0.00702,0.00137,0.04334,0.07331,-0.00595,-0.01675,0.05726,-0.03202,0.06151,-0.10893,-0.0194,0.0447,-0.08785,-0.0641,0.04259,-0.02304,-0.04786,0.0174,0.00611,-0.00228,0.01788,0.04414,-0.0549,-0.07234,0.08062,-0.14166,0.04061,0.06788,0.0103,-0.0058,-0.02994,0.11068,-0.05874,0.06955,-0.07009,-0.05398,0.04385,0.04107,-0.01612,-0.0193,-0.0285,0.0331,-0.05585,0.04362,-0.11166,-0.08755,0.07504,0.03244,0.00041,0.03041,0.10685,-0.04902,-0.01111,0.05269]},{"domain":"physics","key":"angular_velocity_angle","name":"Angular velocity and angle turned under constant angular acceleration","package":"physics-ai999x","example":"A flywheel starts from rest and spins up with an angular acceleration of 2 rad/s^2 through an angular displacement of 25 rad. What is its final angular velocity?","v":[0.05553,-0.03719,-0.04423,0.01872,-0.00583,0.08564,-0.10232,-0.07619,-0.03526,0.09235,0.04503,0.01822,-0.03855,0.09985,-0.02135,-0.03462,-0.01807,-0.14959,-0.11123,-0.12548,-0.00902,0.03748,-0.08915,0.00861,-0.04517,-0.07153,0.07825,0.12959,-0.02444,0.07344,-0.05866,0.07205,-0.08029,-0.03932,0.06145,0.01709,0.0597,-0.01925,-0.0443,0.0483,0.08551,-0.03947,0.01355,0.00379,-0.02906,-0.0574,-0.02994,-0.02566,-0.07664,-0.08038,0.07037,-0.05789,0.10074,0.05387,0.00816,0.0379,0.03956,0.09905,-0.08885,-0.0171,0.04346,0.09065,-0.03557,-0.1251,0.04731,-0.01403,-0.00026,0.06977,-0.07923,-0.13926,-0.01913,0.03314,0.12632,0.05795,-0.02871,-0.09648,-0.06554,0.01077,-0.07524,0.01786,0.07038,0.08735,0.01842,-0.00444,0.03498,-0.08156,0.01066,0.01123,0.05422,0.06759,0.08929,0.00361,0.05692,-0.1027,-0.07134,0.10973,-0.04866,0.03786,-0.02886,-0.05542,-0.04881,-0.08755,0.08481,-0.06589,0.00288,-0.03675,-0.03608,-0.02422,0.06168,0.07879,0.07226,0.05547,-0.03154,0.01101,-0.04383,-0.01582,0.05682,-0.11811,0.03391,-0.02031,0.02185,-0.05722,0.05471,-0.02666,-0.01741,0.03201,0.02006,-0.02693,0.00054,-0.06085,0.06923,-0.0388,-0.00132,0.06017,-0.06621,0.05519,0.02394,-0.03916,0.04403,0.00917,0.00982,-0.01689,-0.13787,-0.0476,0.06312,-0.01465,-0.07815,0.07303,-0.07172,-0.03081,0.02654,-0.08226,-0.07763,-0.03283,-0.00424,0.01441,-0.05246,0.06655,-0.04029,0.02531,-0.05053,-0.09662,0.01554,0.13204,0.0027,-0.10533,0.05304,-0.05592,0.09534,0.06898,0.13972,0.0911,0.00257,-0.08718,-0.037,-0.05406,-0.02868,0.00089,0.02843,-0.09577,0.00717,0.01935,0.06145,-0.08653,0.08016,-0.01956,-0.09403,0.04256,0.15439,-0.03361,0.00999,0.08988,0.13147,-0.01867,0.06926,-0.03375,0.02579,-0.07611,0.0565,-0.01469,-0.01677,-0.00388,0.03177,-0.01911,0.06999,0.05158,0.00504,0.03586,0.01797,-0.01916,0.01087,0.01194,-0.03351,0.06877,-0.1186,-0.09106,0.0432,-0.06271,-0.04479,-0.0215,-0.02629,-0.01723,0.05327,0.13267,0.01342,-0.04882,-0.01969,-0.07996,0.0722,0.07815,0.01928,0.02953,-0.05102,0.0865,-0.04224,0.05196,0.02006,-0.02429,0.05945,-0.00427,0.00884,0.00222,0.07001,0.10656,-0.10727,0.03479,-0.15267,0.03203,0.02579,-0.0957,-0.01774,0.08226,0.10029,-0.07815,-0.01775,0.03517]},{"domain":"physics","key":"engine_energy_balance","name":"Energy balance of a cyclic heat engine","package":"physics-ai999x","example":"A heat engine takes in a heat input of 1000 J and has 700 J of heat rejected per cycle. What is its work output?","v":[0.01281,-0.00344,-0.17956,-0.03459,0.01782,-0.00473,0.05872,0.00796,-0.11045,0.11106,0.07553,-0.05353,-0.05046,-0.03729,0.01117,-0.03022,-0.00478,-0.05033,0.03263,-0.12583,-0.04719,0.06284,0.00691,0.00452,-0.07967,0.01796,-0.08648,0.0319,-0.06358,0.11121,-0.01136,0.03006,-0.00523,0.05225,0.004,0.04741,-0.03313,-0.06311,0.01462,-0.0144,0.11096,0.05675,-0.01535,0.0507,-0.04791,-0.03462,-0.02511,-0.18605,-0.14167,0.04955,-0.05158,0.08116,-0.01984,0.06499,0.07506,0.0005,-0.03878,0.03659,0.01,-0.02269,-0.12402,-0.06334,0.03011,0.10853,0.15503,0.03721,-0.05104,0.00209,-0.04873,-0.01804,0.00465,0.01329,-0.03023,0.02802,-0.01145,-0.03477,-0.06698,0.15837,-0.0391,0.00961,-0.00654,-0.06378,0.06418,0.00012,-0.03508,-0.0328,-0.02952,0.0247,0.04765,-0.02493,0.02435,-0.01166,0.06343,0.08397,-0.0188,0.08544,0.01735,0.02042,0.03163,-0.06623,-0.03218,-0.07979,-0.00691,-0.04333,-0.08603,0.01469,0.06097,-0.11648,-0.06828,-0.02775,-0.04039,0.01142,-0.02648,-0.0382,0.07417,0.02357,0.00643,-0.05717,0.06143,0.04563,-0.08682,-0.07144,0.04591,-0.0744,-0.0399,-0.02498,0.08618,0.03309,0.07488,0.03886,-0.0195,-0.01273,0.02073,0.03828,-0.03221,-0.00011,-0.09067,0.02835,0.06352,-0.05196,0.00242,-0.00928,-0.13784,-0.09684,0.15809,0.11219,-0.1301,0.0006,-0.01125,-0.06753,0.05064,-0.07594,0.04504,0.07219,0.00992,0.13221,-0.09148,-0.00055,0.09459,0.02277,-0.01907,-0.00703,-0.06503,-0.06159,0.05328,-0.06514,0.05783,0.04391,0.06789,0.00628,0.04777,0.01764,0.02257,-0.0304,-0.03941,-0.05615,-0.04078,0.06219,0.08145,-0.06237,0.01288,-0.01125,0.05485,-0.04075,-0.01889,-0.01876,0.04871,-0.03073,-0.01308,-0.00891,-0.10659,-0.00333,0.13486,0.14359,0.07127,-0.06996,-0.08807,0.0417,0.08466,-0.11619,0.011,0.05095,0.00972,0.00747,0.02415,-0.05092,0.04075,-0.00012,0.00871,-0.09588,0.00246,-0.05807,-0.03589,0.12933,0.07445,0.01351,0.08468,-0.06647,0.13766,-0.06358,0.06164,0.0397,-0.03331,-0.01724,0.04371,0.04932,-0.01073,0.10009,-0.00593,0.07267,-0.01676,0.01266,-0.00829,0.05047,0.0775,-0.08494,0.01112,0.02019,0.02089,-0.02988,0.0303,-0.05281,-0.01762,0.02014,-0.03974,-0.03911,-0.08086,-0.03389,0.00435,-0.08198,0.00299,-0.0034,0.13801,0.18075,-0.11644,-0.01101]},{"domain":"physics","key":"cop_refrigerator","name":"Coefficient of performance of a refrigerator","package":"physics-ai999x","example":"A refrigerator has 1200 J of heat removed using a work input of 400 J. What is its coefficient of performance?","v":[0.08405,-0.05651,-0.19352,0.06275,-0.02801,0.03986,-0.02276,0.00882,-0.01221,0.02702,0.02123,0.0556,-0.03694,-0.04503,0.01329,-0.08983,0.09597,-0.16682,0.00413,-0.00039,-0.12856,0.07524,-0.0134,-0.07004,-0.04743,-0.02417,0.03599,-0.06704,0.02178,-0.02153,0.11936,0.01718,-0.02221,0.01093,-0.07775,0.07016,0.00961,-0.089,0.00525,0.02724,-0.05315,0.01535,0.00913,-0.01098,0.01306,-0.08121,-0.03196,-0.14536,-0.08074,-0.00137,0.06539,0.10559,0.12099,0.02085,0.04344,-0.02688,0.02105,-0.02927,-0.06108,-0.0307,-0.06398,-0.07005,-0.02622,0.04071,0.09253,0.00122,-0.01264,0.01655,-0.06586,-0.00546,0.0781,0.03906,-0.06627,0.03552,0.07966,-0.05049,-0.00609,-0.10679,0.13462,0.0337,-0.06005,0.06951,0.02724,0.00754,0.00643,0.03607,0.03062,-0.03817,0.07983,-0.00583,0.01867,-0.02388,0.07316,-0.00138,-0.04811,0.05437,0.04243,-0.06325,-0.00852,-0.06359,-0.03005,-0.06209,-0.06004,-0.05949,-0.08224,-0.04223,0.05847,0.07318,0.11025,-0.0339,0.02121,0.04535,0.02997,-0.00221,0.09904,0.06987,0.06381,-0.08665,0.01674,0.01995,-0.09115,-0.01877,0.11476,0.00314,-0.04814,0.01119,-0.03643,0.04573,-0.12154,0.07405,0.05679,-0.1142,0.0492,-0.00889,0.02628,-0.03758,-0.0133,-0.02801,-0.0734,0.02014,0.03891,-0.18141,-0.04721,0.07626,0.02953,0.04162,0.07656,0.08789,-0.01134,-0.06267,-0.03214,-0.10904,0.07085,0.03169,-0.08867,0.06742,0.05138,0.00963,-0.02016,0.07724,-0.02125,-0.05893,-0.00828,0.08845,0.03368,-0.06722,-0.01253,0.00222,0.07149,0.08521,0.10148,0.05827,-0.12581,0.036,-0.01341,-0.06087,-0.08316,0.06859,0.09464,-0.08093,-0.02693,0.11622,-0.00567,0.0246,-0.04236,0.12434,-0.06575,0.04485,-0.03225,0.01923,-0.09707,0.04249,0.11371,0.0626,-0.05201,-0.05069,-0.0302,0.06046,0.00989,-0.02104,0.10722,0.05055,0.16593,-0.02097,-0.00513,0.11122,-0.11292,-0.02375,-0.03587,-0.09818,0.01633,-0.09545,-0.09623,0.00484,0.07903,-0.03635,0.04838,-0.11126,0.02031,-0.06171,0.02561,0.03341,-0.02294,0.14319,-0.02514,-0.02855,0.0207,0.032,-0.06156,0.00764,-0.02341,-0.01616,-0.03759,0.0179,0.04513,0.00259,0.09564,0.0411,-0.00452,-0.026,-0.00525,-0.03861,0.02235,0.05654,0.07744,0.0084,-0.00473,0.0282,-0.08804,-0.04902,-0.06439,0.00058,0.03276,-0.00841,-0.06802,-0.02921]},{"domain":"physics","key":"cop_heat_pump","name":"Coefficient of performance of a heat pump","package":"physics-ai999x","example":"A heat pump delivers 1500 J of heat delivered for a work input of 500 J. What is its coefficient of performance?","v":[0.04388,-0.10652,-0.24579,-0.00863,-0.01763,0.00808,0.08497,-0.08332,0.02872,-0.06932,-0.01242,0.06854,0.0297,0.06805,-0.06078,-0.01526,0.00816,0.00091,0.04608,0.02387,-0.03016,0.08798,0.016,-0.00321,0.03491,-0.02634,-0.06897,-0.04695,0.0025,0.03124,0.04981,0.00428,0.02125,0.07945,-0.0275,0.07489,-0.02669,0.02077,0.01858,0.00099,0.02145,0.00862,-0.06837,-0.01024,-0.00337,-0.1216,0.06333,-0.05681,0.01967,-0.08977,0.03272,0.11215,0.00888,-0.01899,0.00663,-0.0317,-0.00234,0.04714,-0.05384,-0.03364,-0.05178,-0.09933,0.01448,0.08191,0.1276,0.01026,-0.02876,-0.08677,0.02077,0.00762,0.05868,0.03156,-0.16851,0.02062,0.01678,0.0311,-0.04763,0.01622,0.13604,-0.00803,-0.12588,0.08435,0.02966,0.00894,-0.00152,0.04913,0.02991,-0.10347,0.11491,0.03357,0.02494,0.00597,0.03704,-0.0522,-0.09201,0.01415,0.08421,-0.00579,0.07354,-0.08327,-0.00182,0.05671,0.06688,0.02923,-0.06002,0.03502,0.0493,0.04838,-0.01745,0.0012,-0.02371,0.04775,0.02032,0.02504,0.14321,-0.00478,0.00719,-0.1304,-0.03896,-0.00435,-0.05089,-0.03383,-0.01416,-0.08035,-0.07849,-0.0514,0.02075,0.04118,-0.07018,-0.03024,-0.02649,-0.0616,0.00877,0.05931,0.03037,-0.00923,0.05453,-0.06183,-0.03469,-0.01154,0.05699,-0.14129,0.02144,0.00458,0.14375,-0.01135,0.00847,-0.07022,0.04584,0.00887,-0.08147,-0.02777,-0.02289,0.04558,-0.13007,0.06139,-0.06274,-0.03694,0.02344,-0.03581,0.01745,-0.1674,-0.00792,0.06126,-0.03956,-0.08859,0.07134,0.02798,-0.09475,0.11992,0.0883,0.03902,-0.12561,0.00078,0.01196,-0.00748,0.00468,0.06222,0.06466,0.00986,0.0055,0.03201,-0.05263,0.00648,-0.03944,0.00976,0.01255,0.0125,-0.14571,0.01799,-0.04818,0.05617,0.01814,0.04791,-0.0827,0.01145,0.00771,0.10788,-0.08636,-0.18478,-0.0236,0.04918,0.07704,-0.02055,0.07948,-0.00138,-0.0869,0.05437,-0.03786,-0.00438,-0.01824,-0.08934,0.08114,0.12881,0.10361,0.01865,0.10113,-0.07184,0.09561,0.0246,0.05221,-0.04476,0.00503,0.03558,0.00092,0.01037,-0.05047,0.07717,0.02802,0.06903,0.00652,0.08338,-0.00574,0.0368,-0.10108,0.02289,0.12381,0.03537,-0.08647,0.04199,-0.09315,-0.04446,-0.02634,-0.08719,0.03308,0.01312,-0.01671,0.09699,-0.0203,0.04039,-0.01762,-0.09379,0.0198,-0.07351,-0.02906,0.08356]},{"domain":"physics","key":"cyclotron_radius","name":"Radius of a charged particle's circle in a magnetic field","package":"physics-ai999x","example":"A proton of mass 1.67e-27 kg and charge 1.6e-19 C moves at 1e6 m/s perpendicular to a magnetic field of 0.5 T. What is the radius of the circular path?","v":[-0.03827,-0.03095,-0.00546,0.03196,-0.01497,-0.1454,0.00817,-0.00127,0.17869,-0.0234,0.01243,-0.02863,0.09913,-0.00788,0.01563,0.03584,-0.08801,0.01601,0.00445,0.08827,0.03181,0.12241,-0.02803,-0.04556,-0.05711,0.00723,-0.02958,-0.0486,0.00936,-0.02212,-0.00707,0.05052,0.07481,0.01836,-0.00404,-0.02588,0.05635,0.02676,-0.03039,0.1168,0.13379,0.04108,0.14977,-0.00211,0.02388,0.01444,0.00071,0.12096,-0.04242,-0.0976,-0.04345,-0.06487,0.0524,-0.01045,-0.00509,0.04083,-0.03569,-0.00227,0.0376,-0.04675,0.00958,0.04662,-0.02854,-0.02229,0.04298,0.01406,0.06496,0.08801,-0.10597,0.03766,0.04779,0.0355,0.01835,-0.04346,-0.02729,-0.10318,-0.00403,0.03491,-0.02901,0.11066,-0.00763,-0.13804,0.04224,0.00761,0.02233,-0.10716,0.0625,-0.05255,0.06789,-0.00078,0.04765,-0.08715,0.04959,-0.0097,-0.00889,0.03098,-0.0259,0.04666,0.01217,0.0558,0.01622,-0.10175,0.035,0.0016,-0.01496,-0.02832,0.02208,0.04008,-0.01036,0.00847,-0.09925,0.06562,0.02141,0.06785,-0.03476,-0.04599,0.02639,-0.01868,-0.00825,-0.05963,-0.14846,0.03009,-0.03558,-0.00118,-0.04337,-0.04696,0.06291,0.13649,0.03598,0.02314,-0.0348,-0.01217,0.03214,-0.02732,-0.02892,0.05608,-0.00943,0.0169,0.00122,-0.04762,-0.02962,-0.1529,0.06975,-0.02375,0.02914,-0.047,0.07149,0.06785,-0.06056,-0.05927,0.00628,0.07319,0.07203,-0.0544,-0.13102,-0.01342,0.00449,-0.04108,-0.03356,-0.04794,0.05767,0.01449,-0.01742,0.00654,0.00798,0.03719,-0.02301,-0.00301,-0.06855,-0.04736,-0.04677,0.00913,0.05516,0.01561,0.12163,-0.00084,-0.04525,0.1698,-0.06042,-0.04356,0.01564,0.08868,0.09572,-0.0155,0.10606,0.02924,-0.0692,-0.07215,0.02728,-0.17137,-0.07817,0.06534,0.09677,0.05547,0.05695,0.02132,-0.09393,-0.03538,-0.00185,0.05444,0.03378,-0.02379,-0.04339,-0.04682,-0.0522,-0.05501,0.04686,0.10755,-0.06937,-0.07138,0.05974,0.07661,0.17807,0.02512,-0.0034,-0.10635,-0.15569,-0.0839,0.00371,0.04413,-0.17069,-0.06179,0.03342,0.0955,0.02063,0.03786,-0.09274,-0.01213,0.10352,0.02901,-0.09702,-0.01313,-0.01544,0.00104,-0.04633,-0.14457,0.03955,-0.04354,-0.02876,-0.08479,-0.01446,0.01923,0.12044,-0.01615,-0.06331,-0.04839,-0.02007,0.03481,-0.07038,0.03636,-0.04711,0.03198,-0.04297,0.10916,-0.0596,0.0149]},{"domain":"physics","key":"rc_time_constant","name":"Time constant of an RC circuit","package":"physics-ai999x","example":"An RC circuit has a resistor of 1000 ohm and a capacitor of 8 uF. What is the time constant?","v":[0.02534,0.14505,-0.02866,0.06786,-0.1352,-0.01621,0.10991,-0.01255,0.12932,0.0444,0.07116,0.09874,0.03109,0.02669,0.00347,-0.06256,0.08223,-0.03978,0.10019,0.00536,-0.03021,-0.06957,0.02335,-0.03726,-0.03996,-0.03632,-0.03692,0.08063,0.14399,0.00792,0.10887,0.10905,0.0237,-0.08809,0.04182,-0.00339,0.0329,0.05894,0.01582,0.04025,0.08479,0.02644,0.00604,-0.09663,-0.1233,-0.06122,-0.0235,0.00143,0.08145,0.00968,-0.07587,-0.08434,0.04588,-0.0162,0.00714,-0.01286,-0.02513,0.05444,-0.07529,0.03662,-0.00339,0.01056,0.0458,0.02438,0.03251,-0.01132,0.0002,-0.03661,-0.08888,-0.03188,-0.04033,0.01808,-0.06368,-0.06225,0.10659,-0.01086,-0.00896,0.00973,0.05151,0.00685,0.04322,-0.12451,0.0425,0.02911,0.04344,0.04393,0.04775,-0.03743,0.01299,-0.05653,-0.13378,0.03916,-0.00025,-0.03352,-0.01586,-0.04952,-0.0335,-0.01868,-0.08063,0.03602,0.04556,0.04854,-0.0599,0.05404,-0.06985,0.04124,-0.00933,-0.09764,0.02269,0.04626,0.04094,0.07306,0.01947,0.07455,0.06217,0.03415,0.05429,0.04865,-0.00732,0.14755,-0.05207,-0.01921,0.08431,0.04594,-0.06094,0.01869,-0.09412,-0.04007,-0.09107,-0.02607,0.04138,0.01274,-0.03023,-0.05852,-0.00592,-0.0613,-0.02243,-0.01448,0.11402,-0.01722,-0.0448,-0.11972,0.04834,-0.056,-0.12126,6e-05,0.07459,0.11058,0.08694,-0.01917,-0.08951,0.03832,-0.04686,-0.04176,-0.01315,-0.02177,0.00891,0.08537,0.04943,-0.01155,-0.10202,0.11323,-0.0294,0.02988,-0.01265,0.08743,0.08,0.03788,-0.0921,-0.03291,-0.06597,-0.03753,0.0303,0.06797,-0.14184,0.00125,-0.07421,-0.03076,0.06528,0.10128,-0.06201,0.04847,0.12347,-0.09489,-0.09725,0.01465,0.00154,-0.02317,-0.15788,0.04021,0.09107,-0.04167,-0.02038,-0.031,0.01072,0.01567,-0.01526,0.0495,0.07549,-0.09192,0.03211,0.083,0.02787,0.05403,-0.07468,0.03219,0.00877,-0.03526,-0.01949,-0.04116,0.02624,-0.16776,0.0448,-0.05736,-0.01004,-0.02775,-0.04216,-0.07906,-0.07524,-0.01915,0.0287,0.08333,0.03264,-0.02949,-0.01919,0.00543,0.02775,-0.01294,-0.02564,-0.00367,0.04005,-0.08449,-0.06001,0.00771,-0.09239,-0.02702,0.01408,-0.03547,-0.05087,-0.01462,-0.06192,-0.01225,-0.06595,-0.0763,0.07211,0.05825,0.0046,-0.14457,-0.02702,0.19997,0.07998,0.02553,0.00316,0.0723,-0.08493,0.04542]},{"domain":"physics","key":"rc_discharging","name":"Voltage of a discharging capacitor","package":"physics-ai999x","example":"A capacitor of 8 uF with an initial voltage of 12 V discharges through a 1000 ohm resistor. What is the voltage across the capacitor after 8 ms?","v":[-0.01255,0.08126,-0.03,0.03247,-0.14574,0.07439,0.0615,0.00425,0.03007,0.0203,0.0334,0.11362,-0.03162,0.01277,0.06309,-0.02518,-0.00275,-0.06941,0.13009,0.02613,0.01377,-0.05268,0.03155,0.0398,-0.07467,-0.0721,-0.04115,0.10767,0.03453,0.02862,0.0186,0.10687,-0.01707,-0.01716,-0.01632,0.07232,0.03953,-0.07766,0.02874,0.08107,0.03924,0.07949,0.0154,-0.092,-0.13897,-0.07692,-0.02353,0.04669,0.05195,0.03471,-0.04003,-0.09084,0.01579,-0.03129,-0.01462,-0.02456,0.00236,0.03976,-0.06413,0.03362,0.02355,0.02944,0.00745,0.03384,0.01979,-0.00542,0.04734,-0.01767,-0.04889,0.00665,-0.01573,0.06414,0.10061,-0.06304,0.04182,0.01363,-0.05305,-0.03471,0.03213,0.03494,0.03371,-0.06109,0.01828,0.00778,-0.01113,-0.01333,0.05958,-0.01986,-0.01811,-0.04538,-0.02373,0.06927,0.0026,-0.01609,-0.03435,-0.05201,0.01443,-0.07042,-0.09893,0.02906,-0.01511,0.04543,-0.01912,-0.0259,-0.09017,-0.01424,0.00078,-0.03472,0.061,-0.02814,0.09713,0.02368,-0.05741,0.12173,-0.03077,0.05114,-0.06544,0.04495,0.05573,0.11909,0.04136,-0.01447,0.0706,0.01888,-0.08116,0.06536,-0.04428,-0.10863,-0.08121,0.00623,-0.00186,0.01982,0.02618,-0.0657,0.00198,-0.13945,0.02274,0.02942,0.13323,-0.06268,-0.03923,-0.07345,-0.01698,-0.04893,-0.08821,-0.02569,-0.01582,0.12041,0.10743,0.03264,-0.08719,0.01184,-0.07957,-0.09886,0.04253,0.02352,-0.07233,0.02142,-0.03319,0.03246,-0.15405,0.05976,0.04505,0.02348,0.00413,0.07315,0.01899,0.01819,-0.10121,-0.1471,-0.0256,-0.00234,-0.00663,0.00625,-0.07379,-0.02753,-0.10836,-0.10291,0.08787,0.0569,-0.03123,0.0524,0.19366,-0.0611,-0.12545,0.01039,-0.00291,-0.06733,-0.09605,0.0768,0.10242,-0.04648,0.01662,-0.02717,0.03652,0.03411,0.03692,-0.01175,0.14787,0.01243,-0.0253,0.06895,0.05926,0.01017,0.03826,0.02092,-0.06777,-0.1122,0.01948,-0.07894,0.06015,-0.19419,-0.02974,-0.01603,0.03931,-0.11298,-0.06405,-0.02418,-0.06502,-0.006,0.07718,0.11058,0.08232,-0.0501,-0.05663,-0.0253,0.02545,0.00323,0.02539,-0.01862,0.03891,-0.11668,-0.09305,0.07518,-0.04151,0.02123,-0.01321,0.01695,0.02005,-0.04088,-0.04259,0.06539,0.02845,0.02552,0.12639,-0.01138,-0.04754,-0.11857,0.06079,0.14261,0.08035,-0.00297,0.0197,0.05037,-0.03187,0.07029]},{"domain":"physics","key":"rc_charging","name":"Voltage of a charging capacitor","package":"physics-ai999x","example":"An uncharged 8 uF capacitor starts charging through a 1000 ohm resistor from a 9 V emf. What is the voltage across the capacitor after 8 ms?","v":[-0.01021,0.09335,-0.0464,0.02366,-0.15076,0.10071,0.07044,0.00389,0.05841,0.01509,0.01558,0.07079,-0.00695,0.05093,0.04267,-0.02805,0.00094,-0.03482,0.14808,0.00237,0.03371,-0.01555,0.03421,0.0504,-0.07339,-0.03655,-0.04304,0.12139,0.03036,0.0567,0.01207,0.14166,-0.02338,-0.02169,-0.03336,0.07469,0.02444,-0.08934,0.01841,0.0816,0.0683,0.071,0.01655,-0.08687,-0.16324,-0.06903,-0.02799,0.06562,0.07176,0.05507,-0.07331,-0.09573,-0.01541,-0.0109,-0.02571,-0.0303,-0.01349,0.02375,-0.03805,0.05156,0.03161,0.01902,0.01109,-0.00277,0.01905,-0.01304,0.05224,-0.03059,-0.03576,-0.00053,-0.03321,0.07899,0.07355,-0.10281,0.04799,0.00547,-0.03899,-0.00939,0.02478,0.03109,0.06028,-0.05171,0.01016,0.00847,-0.02763,-0.00263,0.05906,-0.0307,-0.01043,-0.05274,-0.01634,0.07082,-0.0208,-0.06977,-0.0542,-0.02852,0.02223,-0.07616,-0.08409,0.02186,-0.0018,0.04598,0.00364,-0.01985,-0.06981,-0.03547,-0.02863,-0.05464,0.04994,0.00767,0.0769,0.01524,-0.04296,0.1394,-0.01761,0.02992,-0.07947,0.067,0.02456,0.10946,0.02787,0.00543,0.02333,0.02147,-0.08682,0.06388,-0.00412,-0.0993,-0.09874,0.0214,-0.00151,0.03881,0.01767,-0.02348,-0.00168,-0.10922,0.00917,0.01863,0.08621,-0.04146,-0.04549,-0.0594,-0.03745,-0.05213,-0.03904,-0.06888,-0.03696,0.11817,0.12381,0.05068,-0.05282,0.03452,-0.0919,-0.14351,0.0545,0.02133,-0.05571,0.06161,-0.06665,-0.00451,-0.15684,0.04954,0.02255,0.01327,0.02429,0.06985,0.00061,0.00786,-0.14439,-0.12513,-0.03579,-0.00133,-0.00971,0.01008,-0.06216,-0.00765,-0.10016,-0.07398,0.06323,0.07808,-0.05348,0.01305,0.17171,-0.08688,-0.11502,0.02837,-0.01249,-0.04431,-0.10246,0.06381,0.10876,-0.02788,0.02158,-0.02159,0.00837,0.04316,0.02276,-0.01244,0.15503,0.02924,-0.01103,0.04016,0.08439,0.06021,0.02497,0.0113,-0.06111,-0.07558,0.01669,-0.07873,0.05761,-0.1711,-0.04025,-0.00082,0.03522,-0.10235,-0.05866,-0.02399,-0.05515,-0.01574,0.06352,0.11334,0.08817,-0.04259,-0.05143,-0.0383,0.00406,0.01751,0.05294,-0.01867,0.03873,-0.12824,-0.09373,0.07654,-0.04204,-0.01978,-0.00719,-0.01112,0.01459,-0.02696,-0.05369,0.05715,0.0291,0.02448,0.11747,-0.02393,-0.06608,-0.13061,0.06226,0.13711,0.08802,0.03674,0.00521,0.07478,-0.04645,0.07681]},{"domain":"physics","key":"area_expansion","name":"Thermal expansion of an area","package":"physics-ai999x","example":"A steel plate with an original area of 2.0 m^2 and a coefficient of linear expansion of 12e-6 1/K is heated by 50 K. What is the change in area?","v":[0.00365,-0.07449,0.03511,0.01971,-0.04788,0.00266,-0.08121,-0.10573,0.07562,0.04883,0.06726,-0.04271,-0.04625,0.04662,-0.01814,-0.00663,0.19006,-0.01282,0.03102,0.12079,0.0296,-0.04774,0.02837,-0.07573,-0.02101,0.06242,0.04034,-0.05605,0.04414,-0.0396,0.00699,0.0647,0.01666,-0.00091,-0.0046,-0.07334,0.0592,-0.01378,-0.05104,-0.03689,0.01357,0.05173,-0.01038,0.00328,-0.0002,-0.0917,0.0665,0.07927,-0.06234,-0.03022,0.07855,0.06716,0.0665,0.01299,-0.00068,0.04618,0.1121,0.0824,-0.01427,-0.00025,-0.04857,0.03411,-0.03634,0.1024,0.0104,-0.01166,-0.03558,0.03901,0.08784,0.02519,-0.01676,-0.10921,-0.12651,0.0314,0.00448,0.03569,0.02074,-0.07309,-0.07298,-0.01933,-0.11045,-0.06852,0.01801,0.0005,-0.02246,0.19763,0.07983,0.00629,-0.07401,0.02033,-0.04134,0.03149,0.0104,-0.00683,-0.05112,-0.05194,0.06646,-0.04717,0.11063,-0.01845,-0.03516,0.11961,-0.06776,0.02364,-0.06214,0.08507,0.00838,-0.02027,-0.02527,0.05936,-0.04644,0.02764,0.02932,-0.01937,-0.08055,-0.04755,0.08116,0.04408,0.01786,0.0135,-0.09679,0.14035,0.05958,-0.01616,0.01734,0.0119,-0.12333,-0.07246,-0.04239,-0.16947,-0.08698,0.07296,0.07168,-0.01263,-0.10041,-0.02905,-0.02322,0.01057,-0.02668,0.06221,0.00703,-0.10815,0.03735,0.04053,0.03021,0.01836,0.02967,-0.01908,-0.0418,0.02841,0.01353,-0.00801,0.02171,0.01795,-0.01845,-0.00186,-0.10758,-0.01287,0.08084,-0.05235,-0.00766,-0.02252,-0.01096,0.00633,0.05122,-0.05112,0.06699,0.08425,0.00088,0.03284,-0.08245,-0.00855,-0.03651,0.13461,0.122,-0.04691,0.00264,0.0179,-0.02366,-0.1522,0.02861,-0.03009,-0.24808,-0.06409,0.00954,0.0339,0.04291,-0.02453,-0.09994,-0.07272,0.00926,0.08746,-0.00499,-0.0088,-0.03224,0.08452,0.01703,0.06053,0.07179,-0.16585,0.08353,0.01365,0.0407,-0.05433,0.02488,-0.05981,0.01089,0.06371,-0.00147,0.05477,0.06684,-0.13212,0.08746,0.04112,0.06436,-0.01352,0.05948,-0.14497,-0.05729,-0.03278,-0.01638,-0.12082,0.00334,-0.03407,0.02692,-0.03588,0.0273,0.00934,0.07239,0.05252,0.01901,0.02047,0.01119,-0.09924,-0.00016,0.05997,0.08342,-0.00283,-0.06898,-0.00144,0.11533,-0.00531,-0.00887,-0.01907,0.05627,-6e-05,-0.00586,0.02494,-0.0077,-0.11057,-0.0876,0.026,-0.09452,0.01223,-0.00832,0.02407]},{"domain":"physics","key":"motional_emf","name":"Emf of a rod moving through a magnetic field","package":"physics-ai999x","example":"A rod of length 0.2 m slides along rails at 3 m/s through a magnetic field of 0.5 T. What is the motional emf?","v":[-0.03157,0.02852,0.03626,0.07326,-0.07409,0.07192,-0.04728,0.07331,0.04827,0.03884,0.0404,-0.00991,0.0535,0.02122,0.00133,-0.00444,-0.01902,0.02186,-0.01054,0.05116,-0.01243,0.04175,0.01541,-0.00788,-0.00412,0.05588,0.03402,0.00936,-0.02202,0.13712,-0.05299,0.04041,0.00228,-0.01419,-0.08183,0.04393,0.05882,-0.05988,-0.03305,0.05594,0.02074,-0.02012,0.16477,-0.09034,-0.02198,-0.03756,0.04331,0.05912,0.00141,0.00215,-0.02044,-0.03022,-0.16349,-0.0583,-0.00696,0.00309,-0.04549,0.00828,0.07629,-0.03214,-0.01521,0.0312,-0.02805,-0.13102,-0.0934,0.01205,0.11135,0.06035,0.00282,0.12114,0.0344,0.10778,-0.06098,-0.01542,-0.01971,-0.0775,0.05336,-0.04735,-0.06209,0.03654,0.08696,0.03966,-0.07243,-0.00947,-0.08946,0.01825,0.02201,-0.02864,-0.0966,-0.02116,-0.0607,-0.01432,-0.11282,0.06923,0.00107,0.08116,0.00118,-0.03684,0.02829,0.06698,0.04399,-0.00539,0.03738,-0.02036,-0.00385,-0.05601,-0.0967,0.01719,-0.02779,0.12232,-0.1045,-0.07644,-0.01562,0.12174,-0.0995,0.01177,-0.05099,0.06266,-0.04207,-0.03172,0.02457,0.00097,-0.05255,0.03177,0.00624,0.03017,0.10323,0.16532,0.01621,-0.01533,0.02122,0.02997,-0.01979,0.02062,-0.05109,0.06551,0.00777,-0.0065,-0.057,-0.03444,-0.08044,0.0595,0.00641,0.05953,0.02846,-0.14626,-0.05762,0.04815,0.01868,0.03682,0.0959,0.04035,-0.03309,-0.15378,0.04779,-0.0584,-0.00598,0.03867,-0.12861,-0.18131,0.04227,-0.03486,-0.03105,0.00287,0.02869,-0.05678,-0.10813,-0.06472,-0.05721,-0.0331,-0.10451,0.01789,0.03265,-0.01314,0.15049,-0.04341,-0.02683,0.07809,-0.00923,-0.05725,-0.00913,-0.11536,-0.00218,-0.00318,-0.00623,0.02944,-0.01797,-9e-05,-0.04195,0.02908,-0.03269,-0.09781,0.03159,0.02128,-0.01916,-0.02998,-0.03378,0.03546,0.0046,0.19205,0.05597,-0.08438,0.06989,0.02203,0.04175,0.00212,0.00258,0.03839,-0.06869,-0.03545,0.00607,0.13084,-0.1415,0.08001,0.07285,-0.13608,-0.08246,-0.01831,-0.01794,-0.06792,-0.11338,-0.03157,0.00579,0.06151,0.09177,0.06327,-0.02052,0.10861,0.13899,-0.091,-0.04258,-0.07198,-0.01583,-0.03522,0.04026,-0.05984,-0.01255,0.00693,0.02044,-0.01754,-0.01876,0.09415,0.11746,0.00036,0.07287,0.02714,0.03956,-0.01776,0.02562,-0.0068,0.04742,0.05914,-0.08621,0.09617,0.01979,-0.02877]},{"domain":"physics","key":"rl_current_decay","name":"Current dying away in an RL circuit","package":"physics-ai999x","example":"In an RL circuit with an inductor and a time constant of 2.5 ms, an initial current of 10 A is switched off. What is the current after 2.5 ms?","v":[0.0196,0.06433,-0.08265,0.0505,0.03967,-0.06905,-0.03544,0.00031,0.03666,0.12448,0.05668,0.06354,-0.06463,0.0089,0.07515,0.00353,-0.04394,-0.15884,0.08787,-0.01218,-0.07427,-0.01155,-0.01428,0.01459,0.06177,-0.03151,0.05531,0.12396,0.02851,-0.07595,0.14323,0.0493,-0.06265,-0.02134,0.14936,-0.03274,-0.06353,0.06864,0.02319,0.00866,-0.06728,-0.01758,0.0542,-0.05963,0.02837,-0.02963,-0.05159,0.01018,-0.06285,-0.02547,-0.00991,-0.06041,0.07657,-0.08999,0.01464,0.00692,0.02306,-0.02452,-0.16131,-0.04682,-0.04312,0.14242,0.08279,-0.08995,0.07443,0.00724,-0.02481,0.0651,0.02106,-0.01419,-0.01873,-0.03104,0.0118,-0.04893,0.02116,-0.14767,-0.01201,0.02186,0.00795,-0.08159,0.05513,-0.02964,0.05461,0.02255,0.04179,-0.02277,0.02975,0.00406,-0.06928,-0.0946,-0.05298,-0.03876,-0.01506,-0.07692,0.00462,0.07734,-0.0281,-0.08975,-0.02526,0.0597,0.06817,-0.10305,-0.08876,-0.05663,-0.04132,0.03315,-0.05731,-0.08574,0.08564,-0.03278,0.01893,0.06101,0.01058,0.00303,-0.04496,0.06766,0.05086,0.09086,-0.01703,-0.00247,0.02483,0.07857,0.16744,0.01534,-0.10129,0.01839,-0.04248,0.03671,0.04262,-0.04268,-0.00604,-0.04036,-0.04542,0.04298,0.00908,-0.01729,-0.08943,0.06901,-0.00508,0.02804,-0.02725,-0.08082,0.04661,-0.0366,-0.03578,0.03184,0.05699,0.04482,0.07854,0.02335,-0.08709,-0.11688,0.04369,-0.04265,-0.01655,-0.06047,-0.01888,0.18272,0.00075,-0.06424,0.06488,0.09583,-0.05394,-0.01522,-0.05276,-0.15138,0.04026,-0.04224,-0.02752,-0.0097,0.01804,0.06695,-0.03327,-0.08027,-0.02856,-0.03422,-0.03975,0.04234,0.07504,0.02628,-0.1038,0.0009,-0.00038,0.01011,0.08748,-0.00157,0.03824,0.03598,0.0365,0.0859,0.05022,0.02554,0.03164,-0.01408,0.03581,0.03076,-0.01696,0.03962,-0.01147,-0.07351,0.06597,0.03517,0.09327,-0.03855,0.03059,-0.13352,0.08331,0.0459,0.06637,-0.00218,0.02292,0.07253,0.07021,0.01008,-0.00866,-0.00373,-0.13643,-0.04076,-0.17203,-0.03263,0.05609,-0.06841,-0.02834,0.04156,0.01757,-0.03836,0.04473,-0.0056,-0.06888,-0.06267,0.05741,-0.08622,0.03828,-0.05143,0.11656,-0.09172,-0.04571,-0.00982,0.03529,0.00762,0.03199,0.07323,-0.00806,0.06611,0.03374,-0.06872,0.09955,-0.17334,-0.05508,0.10369,0.03514,0.02458,0.00544,0.11365,-0.04797,-0.03737]},{"domain":"physics","key":"two_resistors_series_parallel","name":"Two resistors in series and in parallel","package":"physics-ai999x","example":"What are the series and parallel equivalents of 6 ohm and 3 ohm resistors?","v":[0.0774,-0.04173,-0.0585,-0.01418,-0.08022,-0.06478,0.06408,-0.01972,0.15047,0.02311,0.00278,0.02004,0.02478,0.08841,-0.05608,-0.12068,0.04556,0.10349,-0.01476,0.1291,-0.02517,-0.025,0.04676,-0.0804,-0.00368,0.02409,-0.05993,-0.01224,0.0579,0.04232,-0.09441,0.01231,-0.01708,-0.06004,-0.01273,-0.01973,0.06646,0.15514,-0.03142,0.08375,0.03603,0.11715,-0.00421,-0.16971,-0.09593,-0.07695,-0.00669,0.08309,0.0493,0.00526,-0.1552,0.10614,-0.06198,-0.03719,-0.02873,0.00159,0.04206,-0.0053,0.02075,0.03161,0.06216,-0.0718,0.0328,-0.05543,-0.02178,-0.00554,0.03907,-0.00957,-0.00474,0.00546,0.03822,0.04779,-0.07546,-0.03558,-0.03916,0.00196,-0.01274,0.03058,0.07114,-0.00875,0.01535,-0.08232,0.01187,0.09452,0.01262,-0.01778,0.03976,-0.10018,-0.03092,0.03916,-0.10232,0.04262,-0.02189,0.00707,-0.00342,-0.05869,-0.02989,0.16201,-0.12922,0.04842,0.02707,0.09106,-0.02041,0.03307,-0.00801,-0.0595,-0.00138,-0.08108,-0.09089,0.0684,0.01346,-0.05003,-0.03325,0.03552,-0.02629,-0.0412,0.05893,0.00809,0.01023,0.03839,-0.04013,0.05428,-0.03673,0.12031,0.01183,0.02777,0.02581,0.04636,0.00957,-0.01402,0.00185,0.00478,-0.0827,-0.03417,-0.02979,-0.09363,-0.00408,0.03546,0.00187,0.00569,-0.06029,0.00958,-0.00011,0.03802,0.20303,-0.00184,-0.01904,0.076,0.09241,-0.07461,-0.15058,0.12867,-0.07932,0.01324,0.10278,-0.00984,-0.00442,-0.00918,0.03809,-0.03417,0.02608,0.0745,0.02501,-0.07619,0.02627,0.08336,-0.06692,0.04009,-0.09323,-0.09082,-0.02831,-0.01792,0.13152,0.1627,-0.12507,-0.0491,0.08066,-0.00686,-0.01875,-0.02608,-0.07978,0.02327,0.00166,-0.04905,-0.12558,0.07076,0.00161,-0.03829,-0.05307,0.08024,0.00945,0.02008,-0.1008,0.02596,-0.00374,-0.04634,-0.01945,-0.00156,0.06571,-0.05741,-0.0317,-0.01044,-0.03057,0.07604,-0.08205,0.08765,-0.08048,0.05112,-0.0193,0.02841,0.01408,-0.01352,-0.0637,-0.05593,-0.03646,-0.05067,0.05055,0.02796,-0.11905,0.04407,0.04442,0.02416,0.04669,-0.02381,0.06212,0.01094,0.10332,0.04859,0.10767,0.06314,-0.01697,0.03682,-0.02531,-0.01419,-0.03914,0.00113,-0.05689,-0.08013,-0.05847,-0.01324,0.03652,-0.0091,0.01887,-0.1685,-0.03262,0.05614,-0.0039,-0.08214,0.02604,0.07496,0.07487,0.0744,-0.09513,-0.03791,-0.04381,0.06099]},{"domain":"physics","key":"uniform_acceleration_state","name":"Velocity and displacement after constant acceleration","package":"physics-ai999x","example":"A body moving at 4 m/s accelerates uniformly at 2 m/s^2 for 5 s. What are its final velocity and displacement?","v":[0.03663,-0.05055,-0.05642,0.09967,0.00975,0.12012,0.05922,-0.00616,-0.01475,-0.00111,0.05012,0.06624,-0.02513,-0.04594,0.04377,0.05587,0.00134,-0.02437,0.05881,0.01575,-0.01991,-0.05396,-0.02902,0.04825,0.02068,0.01194,0.0789,0.00695,-0.01627,0.07333,0.09653,-0.11536,0.01388,0.0104,0.00177,-0.00093,0.05612,-0.00574,0.0002,-0.01403,-0.06875,-0.06147,-0.01946,-0.19945,-0.17478,0.03735,-0.04391,0.03354,-0.00291,0.02924,0.07761,-0.00302,-0.0486,0.01199,0.05854,-0.02526,0.0893,0.10445,-0.00403,-0.05359,-0.07107,-0.00466,0.04481,0.02594,-0.01662,0.08799,0.06701,-0.02174,0.07765,0.06636,-0.04623,0.00843,0.01894,-0.06911,-0.06118,-0.09486,0.06672,-0.03247,-0.06055,0.00204,0.00497,0.02265,-0.03827,0.03711,-0.04775,0.05355,-0.03351,-0.06273,-0.03033,0.03107,-0.00232,0.02959,0.03993,0.06702,-0.02166,-0.04075,0.05474,0.05716,-0.02217,-0.0695,-0.00974,0.06919,-0.0181,-0.07313,-0.04554,0.07079,0.00893,-0.00224,0.16493,-0.00198,-0.02939,0.07694,-0.05509,0.03797,-0.01394,-0.00706,-0.08133,-0.07839,0.02042,0.1061,0.07199,-0.05107,0.03863,0.00764,-0.01121,-0.02879,0.07793,0.02992,0.09896,-0.03325,0.02411,-0.05936,-0.01492,-0.02188,-0.09489,-0.05266,0.0287,0.04732,0.17728,-0.05848,-0.07967,0.07371,-0.0076,0.01559,-0.05148,0.0217,0.01526,0.11114,0.01183,0.02821,-0.09624,-0.15905,-0.0865,-0.0666,0.08765,0.04467,-0.05456,0.01179,-0.06449,-0.07104,-0.0269,-0.10456,0.08236,0.11913,-0.12202,-0.02645,-0.00786,-0.20434,0.08079,-0.01392,0.00518,0.05513,-0.01583,-0.04213,-0.02008,-0.06291,0.02174,-0.04601,0.05137,0.06157,0.08648,-0.04289,0.14496,-0.06851,-0.08368,0.01978,0.09999,-0.07949,0.03602,-0.10661,-0.09282,-0.02969,0.0248,0.0762,-0.01369,0.01273,0.03257,0.08263,0.05232,0.07453,0.00836,0.06718,0.08323,-0.09913,0.03846,0.07428,-0.02117,-0.07237,0.13076,-0.04082,0.0188,-0.12415,-0.0492,-0.02785,0.03779,-0.0032,0.08254,-0.02837,-0.11183,0.04833,-0.00026,-0.02242,-0.07699,0.01954,-0.01625,0.01443,-0.04272,0.02239,-0.00925,-0.02256,-0.07327,-0.0734,0.03313,0.00516,0.0709,0.05381,0.01238,0.00421,0.01518,0.01137,0.02036,-0.00048,-0.10157,-0.00344,0.1604,-0.00872,-0.01569,-0.12682,0.07148,-0.01988,-0.00241,0.00169,-0.08221,-0.11578,-0.00938,-0.01821]},{"domain":"mechanics","key":"damped_angular_frequency","name":"Angular frequency of a damped oscillator","package":"mechanics-ai999x","example":"A 2 kg mass on a spring with a spring constant of 50 N/m has a damping coefficient of 4 kg/s. What is the damped angular frequency?","v":[0.00471,0.05677,-0.15978,0.05599,0.00887,0.00472,-0.11346,-0.0266,-0.03098,-0.05837,0.055,0.11444,-0.07159,0.13513,0.0196,-0.08106,0.00664,-0.00802,-0.04558,-0.02319,0.01618,0.05326,-0.04266,0.02028,0.05029,-0.14995,0.02667,0.05248,0.10127,-0.0597,0.1291,0.05972,-0.08444,0.05846,0.06534,-0.08809,0.02067,0.05169,0.04207,0.02486,0.00221,-0.02255,-0.04967,0.05212,-0.07276,-0.08247,-0.07801,0.13665,-0.01732,-0.0384,0.02576,0.02997,0.07912,-0.05466,-0.00575,0.02139,-0.06773,0.12143,0.03659,0.05428,0.07774,-0.02483,-0.00732,-0.07174,0.11586,-0.00288,-0.02697,0.01977,0.03107,-0.09134,0.07176,0.04184,0.07988,0.01454,0.01187,-0.06193,-0.03928,-0.04254,0.02009,0.02942,-0.01786,0.05455,-0.05457,-0.01863,0.05967,-0.06458,0.09263,0.0239,-0.01195,0.0914,-0.02448,0.00303,0.05749,-0.11529,0.02713,-0.0119,-0.06077,-0.02767,0.04167,0.07385,-0.00849,0.0032,-0.12274,0.01779,0.03171,0.0383,0.02718,-0.03625,-0.13517,-0.01849,-0.00579,-0.02867,-0.0658,0.04974,-0.07658,-0.07193,-0.02594,-0.01857,0.07445,-0.07677,-0.03864,0.01077,0.03911,-0.03729,-0.07325,-0.02534,-0.08755,-0.08004,-0.00274,-0.06397,0.06425,-0.03429,0.07725,-0.05945,-0.04254,0.10029,-0.03001,0.01069,0.05134,0.11267,-0.02015,-0.05006,-0.03006,0.03568,0.06651,-0.02213,0.03264,-0.04623,-0.1386,-0.07645,-0.06374,-0.01818,-0.07895,-0.07414,0.00348,-0.0438,0.09751,0.03027,-0.01578,0.04887,0.01867,0.00154,-0.02031,0.06989,-0.06144,-0.04768,0.13642,-0.07413,-0.05035,0.10768,-0.03502,0.03397,-0.05505,0.0534,0.08639,-0.04109,-0.00556,-0.05751,0.00946,-0.09154,0.073,0.04818,0.05308,-0.00932,0.04728,-0.03911,-0.04238,0.04332,-0.00229,0.04672,-0.09624,-0.01919,0.03566,-0.10994,0.00018,-0.02367,-0.02219,-0.09004,-0.06391,-0.04779,0.03182,0.03303,-0.13702,0.03082,-0.0148,0.04363,0.02448,-0.02978,-0.03987,-0.05863,0.02875,-0.04982,0.02345,0.18703,0.02287,-0.0154,-0.07056,0.03858,0.06145,-0.07089,0.02719,0.01555,0.09218,0.10063,-0.04178,0.00182,-0.02907,-0.12714,-0.03342,0.13864,0.10989,0.05284,0.03676,-0.0321,-0.03913,0.04765,-0.07507,0.05014,0.03492,-0.01808,0.01232,0.04674,0.05699,0.02047,-0.03665,-0.05124,0.009,-0.02551,0.08944,0.06825,0.01962,0.06787,0.16246,-0.14732,-0.04587,0.06404]},{"domain":"mechanics","key":"damping_ratio","name":"Damping ratio","package":"mechanics-ai999x","example":"A damped oscillator has a 2 kg mass, a spring constant of 50 N/m and a damping coefficient of 4 kg/s. What is the damping ratio?","v":[0.00461,0.04919,-0.16432,0.05402,-0.01307,-0.01002,-0.08298,-0.00855,-0.02941,-0.08151,0.05247,0.13112,-0.08792,0.12044,0.01251,-0.06046,0.00396,0.01077,-0.00239,0.04265,0.01741,0.01267,0.01429,0.0344,0.0492,-0.12008,0.00167,-0.02306,0.13154,-0.07853,0.12969,0.0684,-0.0571,0.06124,0.09929,-0.09166,0.02786,0.07611,0.05853,0.01303,0.00885,-0.00778,-0.08097,-0.00642,-0.03596,-0.06847,-0.04879,0.11611,-0.01449,-0.03694,0.02446,0.04492,0.0931,-0.1155,-0.0025,0.03054,-0.07239,0.07447,0.04951,0.03101,0.05789,-0.08461,0.02824,-0.07347,0.06723,-0.00426,0.00439,0.0139,0.06474,-0.02862,0.10438,0.04643,0.05137,0.00665,0.01205,-0.02976,-0.0362,-0.05269,0.04723,0.02779,-0.06289,0.04358,-0.09047,-0.04057,0.0383,-0.06604,0.10264,0.02239,-0.04164,0.05317,-0.07233,-0.02886,0.09003,-0.09067,0.06568,-0.04888,-0.06511,-0.05012,0.03937,0.09492,0.00909,0.04998,-0.13859,0.02362,0.00064,0.05205,0.03489,-0.02066,-0.12071,0.02422,-0.03002,0.00235,-0.06252,0.05446,-0.10661,-0.07354,-0.01156,0.00971,0.05756,-0.05838,-0.04316,0.02075,0.07039,-0.03089,-0.10462,0.00695,-0.11421,-0.04308,-0.00834,-0.09444,0.04112,-0.00553,0.03144,-0.07336,-0.04672,0.08677,-0.00502,0.03362,0.00322,0.10642,-0.01112,-0.05804,0.02726,0.083,0.05535,-0.03708,0.13156,-0.06595,-0.08106,-0.06324,-0.0921,0.00504,-0.05353,-0.04778,0.02624,-0.08008,0.10405,0.04984,-0.04348,0.04608,0.02196,-0.00358,-0.02857,0.03722,-0.05979,-0.03108,0.16886,-0.06922,-0.07124,0.09045,-0.06246,0.00419,-0.0801,0.09216,0.11788,-0.02858,0.03487,-0.04995,0.0136,-0.05946,0.05816,0.04934,0.04129,-0.02525,0.02045,-0.05451,-0.03446,0.03776,-0.04107,0.09128,-0.09122,-0.02604,0.01083,-0.11662,-0.03722,0.00062,-0.06557,-0.09235,-0.09393,-0.04603,0.04267,0.05381,-0.08412,0.02175,0.00721,-0.00445,0.00447,-0.02438,-0.03112,-0.05269,-0.01362,-0.0347,0.00675,0.17354,0.06368,-0.00318,-0.09329,0.04913,-0.01492,-0.01971,0.04277,-0.04313,0.10023,0.05415,-0.02243,0.00206,-0.03567,-0.1164,-0.04364,0.13492,0.10388,0.07417,0.04693,-0.08866,-0.02321,0.03787,-0.05422,0.04052,0.02821,0.0049,-0.00069,0.06494,0.02557,0.01438,0.02816,-0.03167,0.0273,-0.02077,0.07462,0.0991,-0.02317,0.04657,0.07961,-0.13604,-0.03467,0.00794]},{"domain":"mechanics","key":"quality_factor","name":"Quality factor of a damped oscillator","package":"mechanics-ai999x","example":"What is the quality factor of a damped oscillator with mass 2 kg, spring constant 50 N/m and damping coefficient 4 kg/s?","v":[0.02074,0.07477,-0.18081,0.04085,-0.00427,-0.05235,-0.06517,-0.01186,-0.03898,-0.08297,0.06373,0.12255,-0.07237,0.10854,0.01396,-0.06466,0.03476,-0.03192,0.04165,0.06231,0.03573,0.02669,-0.00492,0.01668,0.03669,-0.12233,0.02493,-0.03668,0.14413,-0.06987,0.14456,0.08513,-0.04898,0.06497,0.04812,-0.06697,0.01879,0.04733,0.049,0.005,-0.00162,-0.01228,-0.05417,-1e-05,-0.05629,-0.07617,-0.0708,0.08948,0.00116,-0.02571,0.0093,0.0428,0.08996,-0.1193,0.00707,0.02149,-0.05122,0.08598,0.05743,0.0331,0.03118,-0.10993,0.00605,-0.04672,0.10242,0.0004,0.0081,0.00293,0.04249,-0.01782,0.11395,0.04234,0.02879,0.00473,0.04446,-0.08229,0.00052,-0.04663,0.06936,0.03521,-0.03287,0.00917,-0.08002,-0.0058,0.06189,-0.01871,0.10638,-0.02613,-0.02356,0.05512,-0.08858,-0.03339,0.0727,-0.08688,0.04875,-0.02762,-0.06703,-0.04001,0.05994,0.06969,-0.00408,0.01575,-0.14605,0.0432,0.00781,0.05989,0.03678,-0.03541,-0.07509,-0.0107,-0.03058,0.01118,-0.03271,0.03449,-0.04866,-0.06685,-0.02945,-0.03069,0.06462,-0.06358,-0.07984,0.0592,0.07563,-0.0102,-0.10734,-0.03247,-0.10079,-0.01076,-0.02514,-0.05858,0.03552,-0.01096,0.02696,-0.0655,-0.0227,0.05085,-0.02616,0.01063,0.04618,0.11315,-0.00938,-0.08948,0.03777,0.08893,0.00485,-0.03818,0.14538,-0.05065,-0.0896,-0.05291,-0.08364,0.01007,-0.0262,-0.03388,-0.00803,-0.04517,0.12345,0.01399,-0.05136,0.04645,0.02265,-0.01336,-0.04757,0.04618,-0.05186,-0.00042,0.19253,-0.07107,-0.06263,0.09864,-0.09571,-0.00815,-0.13323,0.07353,0.11852,0.01169,0.00012,-0.05318,-0.00735,-0.06463,0.05388,0.08181,0.04008,-0.03512,-0.00808,-0.03714,-0.05781,0.0256,-0.06198,0.07619,-0.10296,-0.0476,0.00026,-0.11413,-0.03376,0.00749,-0.05634,-0.07464,-0.07119,-0.05418,0.04153,0.06601,-0.08229,0.04487,-0.00399,0.01922,-0.0264,-0.04445,0.00579,-0.07388,0.00929,-0.04657,0.02638,0.15078,0.07513,0.00619,-0.12281,0.02891,0.02298,0.00829,0.0372,-0.03095,0.05013,0.06892,-0.03857,0.01487,-0.04338,-0.11206,-0.07668,0.09512,0.09976,0.07869,0.06398,-0.09558,-0.00221,0.05398,-0.03651,0.03431,0.02632,-0.01049,-0.01684,0.04559,0.0402,0.00485,0.03364,-0.05915,0.04502,-0.01502,0.06732,0.12259,-0.01229,0.01908,0.14667,-0.10387,-0.0542,0.00963]},{"domain":"mechanics","key":"driven_amplitude","name":"Steady-state amplitude of a driven damped oscillator","package":"mechanics-ai999x","example":"A 2 kg mass on a spring with spring constant 50 N/m and damping coefficient 4 kg/s is driven by a periodic force of amplitude 10 N at a driving frequency of 3 rad/s. What is the steady-state amplitude?","v":[-0.09247,0.06733,-0.13123,0.04209,0.00507,-0.01378,-0.0885,-0.02832,-0.06399,-0.06749,-0.01148,0.11878,-0.06596,0.1374,0.03344,-0.04475,-0.04515,0.0055,-0.08141,-0.04588,-0.00387,0.03778,0.01346,0.06294,0.06525,-0.15853,-0.0244,0.03964,0.09504,-0.01356,0.14958,0.02659,-0.09314,0.09881,0.07793,-0.05856,-0.07902,-0.00797,0.01922,0.03934,0.00412,-0.00911,-0.05774,0.02764,-0.03685,-0.03869,-0.0549,0.11371,0.00114,-0.04584,-0.06191,-0.04133,-0.00626,-0.02501,0.01835,-0.00653,-0.10081,0.07863,0.09233,0.02387,0.06202,-0.04908,0.04346,-0.09869,0.06539,0.00814,-0.03587,-0.02387,0.08248,-0.13703,0.07886,0.07381,0.11066,-0.02098,-0.00873,-0.05591,-0.09985,-0.03561,-0.0182,0.01685,-0.021,0.08971,-0.04398,-0.00337,0.08788,-0.02092,0.06207,0.0574,-0.02606,0.06308,0.0049,-0.02804,0.03078,-0.05433,0.00752,-0.01587,-0.10626,-0.01057,0.10853,0.01468,0.03515,0.00519,-0.07936,-0.02537,0.06568,0.0048,0.00259,0.02921,-0.08559,-0.0233,0.00176,-0.018,-0.00047,0.04706,-0.01823,-0.07352,-0.04682,0.00203,0.0306,-0.08205,-0.01489,0.0025,0.03715,-0.05836,-0.09252,0.00029,-0.07757,-0.03609,-0.02316,-0.08784,0.02256,-0.00941,0.04838,-0.00534,-0.11321,0.08018,-0.02404,-0.02044,0.00863,0.04715,0.01709,-0.01152,-0.03394,0.0205,0.11921,0.02842,0.05356,0.00654,-0.16334,-0.07554,-0.07856,0.00492,-0.07345,-0.05388,-0.07835,-0.03909,0.09291,0.0317,-0.03201,-0.01451,-0.01408,-0.01192,-0.02377,0.08218,-0.09234,-0.04628,0.12544,-0.09556,-0.07492,0.09551,-0.04307,-0.0208,-0.06546,0.07112,0.12276,-0.04626,0.02339,-0.12235,-0.00805,-0.00463,0.0604,0.03256,0.06742,-0.00858,0.03443,-0.09636,-0.03967,0.08887,-0.05732,-0.02365,-0.05038,-0.01963,-0.00602,-0.08257,0.02104,0.04927,-0.00308,-0.06085,-0.11934,0.01544,0.03464,0.06231,-0.14728,0.046,0.01853,0.0674,0.0162,0.07148,-0.01203,-0.04285,0.04018,-0.02526,0.02353,0.15321,0.08262,0.04934,-0.0964,0.07016,0.05691,-0.09712,0.04515,0.01267,0.0101,0.07949,-0.03586,0.02428,-0.05324,-0.05033,-0.00949,0.15598,0.10152,-0.04084,0.08954,0.02461,-0.04573,0.10991,-0.03795,0.01998,0.04823,0.03274,-0.02488,0.06674,0.00143,0.03812,0.02028,-0.05889,0.04562,0.09064,0.03626,0.05116,0.01419,0.09373,0.10426,-0.07898,-0.06353,0.06375]},{"domain":"mechanics","key":"amplitude_resonance_frequency","name":"Amplitude-resonance frequency of a driven damped oscillator","package":"mechanics-ai999x","example":"A driven oscillator has mass 2 kg, spring constant 50 N/m and damping coefficient 4 kg/s. What is its amplitude resonance frequency?","v":[-0.09411,0.0538,-0.11946,0.0436,-0.05768,0.01301,-0.02986,-0.02415,0.00254,-0.03301,-0.03003,0.13314,-0.07148,0.12832,0.00026,-0.02368,-0.05331,0.04017,-0.04969,-0.05417,0.00029,0.01313,0.02943,0.01495,0.05998,-0.1199,-0.06894,0.02803,0.10774,-0.02497,0.10907,-0.00962,-0.065,0.07522,0.06152,-0.07455,-0.0548,0.01423,-0.007,0.04205,0.02127,-0.00166,-0.04119,-0.00512,-0.0484,-0.04926,-0.03833,0.14322,0.01102,-0.0517,-0.09967,-0.02009,-0.04991,-0.02014,0.01906,0.01939,-0.10834,0.0685,0.1182,0.01283,0.0653,-0.07921,0.07354,-0.09965,0.08865,-0.01262,-0.03078,-0.02962,0.08516,-0.10423,0.09524,0.0776,0.12921,-0.05628,-0.02179,-0.03486,-0.13764,-0.02111,0.00979,0.05631,0.00055,0.06476,-0.07813,-0.04462,0.05774,-0.01239,0.0552,0.0071,0.00678,0.04152,-0.02099,-0.00295,0.06327,-0.05444,0.01779,-0.01105,-0.10571,0.05721,0.07098,-0.01078,0.02291,0.04185,-0.0688,0.00467,0.05435,-0.00176,0.00131,0.02061,-0.10262,0.00682,-0.00705,-0.00869,0.00275,0.06368,-0.02776,-0.08985,-0.03332,-0.00895,0.01565,-0.08887,-0.00956,0.00225,-0.00646,-0.02825,-0.09477,0.00149,-0.10835,-0.04202,-0.00765,-0.08376,0.00397,0.00176,0.03786,-0.02118,-0.09695,0.09923,-0.04187,-0.00677,0.04788,0.04072,0.01347,0.01144,-0.03037,0.00614,0.14904,0.01467,0.06027,-0.03174,-0.1192,-0.09172,-0.08263,0.02397,-0.086,-0.02864,-0.03175,-0.01214,0.06953,0.03898,-0.03712,0.01093,-0.05169,-0.02487,-0.0193,0.08271,-0.07557,-0.01552,0.15113,-0.06019,-0.05087,0.08184,-0.05459,-0.05964,-0.03746,0.08439,0.10448,-0.052,0.07894,-0.09174,-0.02885,0.01928,0.04657,-0.00065,0.09925,0.00099,-9e-05,-0.08065,-0.05553,0.05663,-0.07886,0.00126,-0.03071,-0.01741,-0.0202,-0.07403,0.0445,0.03381,-0.00544,-0.08832,-0.10504,-0.00018,0.0483,0.05144,-0.14612,0.11826,0.00292,0.09504,-0.02716,0.05995,-0.02986,-0.03723,0.02194,-0.10881,0.02255,0.16127,0.07892,0.02967,-0.06455,0.0812,0.07641,-0.13057,0.03951,0.0101,0.03671,0.05275,-0.07169,0.07499,-0.06814,-0.0454,0.02594,0.16248,0.09435,-0.06601,0.03895,0.05303,-0.07172,0.1096,-0.05158,-0.01349,0.03408,0.0526,-0.00773,0.04738,0.01333,-0.00145,0.02338,-0.03177,0.01402,0.06965,0.01874,0.03209,0.00949,0.12583,0.09879,-0.05567,-0.05017,0.04724]},{"domain":"mechanics","key":"coupled_fast_mode","name":"Higher normal-mode frequency of two coupled oscillators","package":"mechanics-ai999x","example":"Two identical masses of 2 kg are each attached to a wall by a spring of spring constant 40 N/m and joined by a coupling spring of 10 N/m. What is the higher normal mode frequency?","v":[-0.04629,0.06103,-0.04603,-0.02513,-0.07525,-0.1528,-0.0287,-0.00075,-0.026,-0.04542,0.0113,0.08695,-0.01976,0.13652,-0.00781,-0.08493,0.03471,-0.00275,-0.08174,0.00375,-0.00846,0.07059,-0.01008,0.00052,-0.00138,-0.01281,-0.00286,0.06658,-0.03137,-0.09163,0.06896,0.03154,0.01482,0.02019,0.0336,-0.18131,-0.02286,0.06802,-0.00487,-0.02238,0.03644,-0.05061,-0.00201,0.07189,-0.03626,-0.05587,-0.13829,0.12645,-0.06457,-0.04718,-0.13785,0.04105,-0.06145,-0.00268,-0.01648,0.06181,-0.01784,0.12764,-0.02116,0.03848,0.00413,0.00829,0.013,-0.1387,0.14895,0.02372,0.02794,0.03489,0.02524,0.00378,0.03842,0.03579,0.03301,0.14016,-0.0037,0.01417,-0.22471,-0.03806,0.10382,0.11061,0.07693,-0.00016,-0.05373,0.03099,0.01486,-0.02143,0.03455,0.06513,-0.035,0.04675,0.07874,0.09528,0.02191,-0.07106,0.02763,0.08931,-0.03306,0.03554,0.00927,0.03598,0.01293,-0.03702,-0.03707,0.07635,0.06189,-0.04593,-0.03008,-0.05127,-0.15917,-0.00689,0.03099,-0.08598,0.03289,0.00788,-0.00353,-0.05622,0.06861,0.00028,0.03291,-0.10044,-0.04422,0.05233,0.05798,-0.02857,-0.04842,-0.02126,-0.06847,-0.0095,0.03081,0.00413,0.05286,0.05776,-0.0215,-0.01275,-0.0046,-0.0013,-0.04694,0.02091,0.05042,0.07379,0.04311,0.02791,-0.06129,-0.06341,0.09139,0.03695,0.00687,0.06929,-0.12507,-0.04664,-0.01152,-0.01154,-0.04229,0.04962,-0.03721,-0.03856,0.09492,-0.02696,-0.01103,-0.03687,-0.00924,0.03429,-0.00892,-0.00653,0.01757,0.01248,-0.00199,0.10478,0.03164,0.10361,-0.05537,0.08341,0.05877,-0.02138,0.02481,0.00338,-0.04504,0.06813,-0.11689,-0.20708,-0.05714,0.05811,-0.05309,-0.1077,-0.02398,0.03035,0.01917,0.041,0.02175,0.11376,-0.00607,3e-05,-0.04089,-0.01792,0.02306,-0.09043,0.04927,-0.09465,-0.05271,-0.08335,0.1216,-0.01922,-0.17054,0.06343,-0.0404,0.08113,-0.00669,0.06908,-0.06262,0.02422,-0.01591,-0.09528,0.07634,0.00362,-0.02225,-0.01011,-0.00124,-0.01244,0.03413,-0.06778,0.0136,0.00429,0.06552,0.0951,-0.03309,0.03517,0.0042,-0.12736,-0.08533,0.06077,0.03881,0.03874,-0.0074,0.06095,-0.01838,0.07198,-0.0788,0.0457,-0.0375,-0.00748,0.06357,-0.01104,0.04775,0.04042,-0.0834,-0.14099,-0.0042,-0.0339,0.0546,0.0757,0.03661,0.06721,0.02379,-0.06238,-0.0457,0.05546]},{"domain":"mechanics","key":"physical_pendulum_period","name":"Period of a physical pendulum","package":"mechanics-ai999x","example":"A physical pendulum of mass 2 kg has a moment of inertia of 0.5 kg*m^2 about its pivot, and the distance from the pivot to the center of mass is 0.3 m. What is its period?","v":[-0.04216,0.04051,-0.1386,0.1245,0.04133,-0.00351,0.10484,0.07084,0.1383,0.02599,0.01444,0.05164,0.03294,-0.00816,-0.00697,-0.00546,0.05413,0.02687,0.06597,-0.09649,0.00593,-0.00341,-0.0579,-0.00367,0.03416,0.00556,-0.08957,-0.01834,0.0288,0.00464,0.04146,0.01784,-0.06854,0.01035,0.03539,-0.03129,-0.01645,0.10968,-0.05448,0.09325,-0.00866,-0.13993,-0.02077,0.10939,-0.06227,-0.00357,0.00997,0.09076,0.0364,0.05922,-0.14368,0.12612,-0.00788,0.02311,-0.07594,0.02044,-0.12349,0.0227,-0.03517,-0.08315,-0.03984,-0.00986,-0.10414,0.02612,0.08653,-0.01788,0.01111,-0.07794,0.03742,-0.03256,0.00996,-0.05606,0.01984,-0.12765,0.01406,0.03102,0.10716,0.03901,0.06646,0.01914,-0.10976,-0.0077,0.09802,-0.03884,0.02349,0.01075,0.03743,-0.04103,0.03309,-0.0341,-0.08117,-0.11224,-0.04175,0.03068,-0.0598,-0.01258,0.03431,-0.00329,-0.03161,0.01126,0.00458,0.05693,-0.10582,0.0652,0.0303,0.07693,-0.03304,-0.12623,-0.06083,-0.00484,-0.07453,0.00137,-0.00357,0.07952,0.00687,-0.05327,-0.06749,0.00491,0.0105,0.10286,-0.06218,-0.00812,-0.01938,0.01349,-0.01869,0.12041,0.01303,-0.05225,0.1063,0.03034,0.05903,-0.02376,0.11529,-0.12918,0.01656,0.10278,-0.03327,0.13408,0.05912,0.0825,-0.03419,-0.14285,0.06407,0.00066,0.0155,0.05213,-0.0476,0.05235,0.0023,0.01856,-0.14792,0.02937,-0.07906,-0.05952,0.12139,0.10279,0.05299,0.09078,-0.02979,0.01758,-0.007,0.00149,-0.01323,0.05342,-0.02293,0.06071,-0.0435,0.0483,-0.10389,0.05378,-0.05309,0.07623,0.1109,0.04322,0.01616,-0.01314,0.02998,-0.0542,-0.02665,-0.05685,-0.01032,-0.0124,0.02629,0.01013,0.13301,0.05329,-0.00727,-0.02208,0.00176,-0.10867,0.02556,-0.00168,0.0953,-0.05256,0.02348,-0.0278,0.0213,-0.04032,0.07866,0.05071,-0.00293,0.01868,-0.137,0.03479,-0.06511,0.01581,0.00114,-0.1405,-0.03399,-0.02535,0.05875,-0.13376,-0.04246,-0.00856,0.09962,-0.02425,-0.06653,-0.01445,0.10314,-0.11445,-0.01493,-0.01031,0.08177,0.00749,-0.01941,-0.00154,-0.02721,-0.03573,-0.12892,0.01651,0.0645,-0.0103,-0.04414,-0.07422,-0.08788,0.00419,-0.10837,0.02691,0.00859,-0.05348,0.07034,0.01556,0.03508,-0.00977,0.0514,-0.01144,-0.00407,0.06362,-0.07829,-0.01611,-0.02031,-0.05623,0.1024,-0.07934,-0.01569,-0.00346]},{"domain":"mechanics","key":"double_pendulum_slow_mode","name":"Lower normal mode of a double pendulum","package":"mechanics-ai999x","example":"A double pendulum has equal masses and a length of each arm of 1 m. What is the lower normal mode frequency?","v":[-0.0406,0.02641,-0.02398,0.02135,-0.03665,-0.12398,0.00599,0.04554,0.02542,0.01486,0.02882,0.07174,-0.01464,0.06234,-0.05535,-0.04776,0.06583,-0.01447,-0.07935,-0.06091,-0.06227,0.02849,-0.05661,0.01798,0.0394,-0.01974,-0.02037,-0.01208,-0.11097,-0.02484,-0.01966,0.08172,-0.02068,-0.01577,0.03661,-0.05344,-0.02099,0.05808,-0.05256,0.10539,0.07603,-0.17532,0.02694,0.13317,-0.00762,-0.07077,-0.03995,0.10136,-0.06681,0.03204,-0.13433,0.09662,-0.0533,0.00427,-0.09007,0.04507,-0.03204,0.10615,-0.06477,-0.05585,-0.0407,0.05964,-0.09729,-0.14311,0.12773,-0.01498,0.00431,-0.00586,0.0249,0.01972,0.00211,0.01422,0.06458,-0.00758,0.07349,-0.00766,-0.09902,-0.06545,0.08958,0.01572,-0.03801,0.06496,-0.04569,-0.02813,0.0372,0.01494,0.05318,0.06657,0.03979,0.00252,0.07348,0.00642,-0.07151,-0.01144,-0.00192,0.07447,0.01576,-0.03605,0.0586,-0.0056,-0.04858,-0.00567,-0.06554,0.0355,0.06142,-0.06051,-0.04854,-0.06083,-0.09226,0.02514,-0.02133,-0.11491,0.05458,0.02159,0.06976,-0.09956,-0.05177,-0.04747,0.02703,-0.05347,0.00045,0.01431,-0.00061,-0.03708,-0.02345,0.04327,-0.08082,0.05372,0.095,0.06673,0.16457,0.00901,0.05662,-0.10564,0.00076,0.08762,0.01456,0.04985,0.04218,0.1347,0.00201,-0.01112,-0.02592,0.00679,0.04171,0.0272,0.01088,-0.00242,-0.11147,0.02796,-0.05696,-0.01517,-0.05158,0.07771,0.05543,0.01358,0.10805,-0.01148,-0.12338,-0.02707,-0.01714,0.03405,-0.0084,0.01204,0.01314,0.01283,-0.05532,0.10174,0.0242,0.03939,-0.01203,0.1743,0.11566,-0.05104,0.07132,-0.00489,-0.03976,0.03346,-0.05477,-0.20247,-0.07197,0.0024,-0.05467,-0.02244,0.07991,0.1031,-0.07338,0.04598,0.10079,0.11873,0.05552,-0.01228,0.0206,-0.06167,-0.00144,-0.09157,0.00374,-0.1438,0.07604,-0.00642,0.02835,-0.06236,-0.09638,0.01657,-0.01763,0.05078,0.02772,0.04138,-0.07971,0.05849,-0.05918,-0.01726,-0.05223,-0.03699,-0.00167,-0.03896,-0.04065,0.0094,0.11635,-0.11093,0.02321,0.01566,0.08948,0.06563,0.00733,0.00241,-0.06092,-0.11592,-0.10528,-0.02203,0.07888,0.03617,-0.02692,0.02434,-0.00465,0.01379,-0.07878,0.0821,0.00591,-0.07226,0.1111,0.04008,0.08207,0.01679,-0.04896,-0.03795,-0.02354,0.02995,-0.02885,-0.02595,0.05722,-0.03614,0.04062,-0.05642,0.10493,-0.04545]},{"domain":"mechanics","key":"double_pendulum_fast_mode","name":"Higher normal mode of a double pendulum","package":"mechanics-ai999x","example":"A double pendulum has equal masses and a length of each arm of 1 m. What is the higher normal mode frequency?","v":[-0.06212,0.03083,-0.0374,0.02581,-0.05321,-0.13735,0.00841,0.03887,0.01202,0.01419,0.03253,0.085,-0.02914,0.09149,-0.05849,-0.04322,0.05467,-0.00093,-0.07007,-0.05446,-0.04261,0.03296,-0.04719,0.024,0.02651,-0.01293,-0.02048,-0.01722,-0.11788,-0.02845,-0.00363,0.065,-0.00355,0.00319,0.05219,-0.05192,-0.01665,0.0567,-0.04667,0.08845,0.08206,-0.17111,0.01609,0.12271,-0.02996,-0.07369,-0.04456,0.09575,-0.08397,0.01707,-0.15063,0.09201,-0.04251,0.01591,-0.08589,0.05302,-0.0439,0.12174,-0.08255,-0.05538,-0.03417,0.06653,-0.09711,-0.16553,0.11945,-0.01987,0.01539,-0.00253,0.02706,0.02042,0.01935,0.02739,0.04866,0.01429,0.05425,-0.00343,-0.10778,-0.05785,0.08094,0.02378,-0.04621,0.04743,-0.06094,-0.019,0.03842,-0.00496,0.03845,0.06326,0.0197,0.00849,0.0607,0.0188,-0.05238,-0.01539,0.00286,0.06026,0.01712,-0.03411,0.06251,-0.00019,-0.03409,-0.00707,-0.06409,0.04201,0.07902,-0.04973,-0.04823,-0.05143,-0.1043,0.02454,-0.01857,-0.09805,0.05051,0.03148,0.07386,-0.11068,-0.05534,-0.0405,0.01873,-0.05884,-0.00062,0.0257,-0.0033,-0.04963,-0.00504,0.05293,-0.08512,0.04093,0.1099,0.06464,0.14651,0.0207,0.03551,-0.11036,-3e-05,0.08744,0.0156,0.03039,0.04363,0.13202,0.00765,-0.01722,-0.02792,-0.00446,0.06191,0.02339,0.00923,0.00909,-0.11807,0.05172,-0.07482,-0.02175,-0.05897,0.06857,0.05106,0.01641,0.07381,-0.00381,-0.12026,-0.04759,-0.00595,0.02583,0.00431,0.01161,0.02384,0.01412,-0.05733,0.11089,0.01628,0.05198,-0.0135,0.15935,0.10712,-0.06286,0.05281,0.01113,-0.04148,0.02925,-0.06402,-0.19074,-0.07057,-0.00013,-0.07808,-0.04009,0.06975,0.07449,-0.06701,0.041,0.07662,0.11345,0.0536,-0.00321,0.02602,-0.0571,0.00765,-0.08844,-0.00116,-0.15627,0.05642,-0.02903,0.04917,-0.04856,-0.10457,0.05507,-0.00251,0.06446,0.03724,0.04441,-0.05886,0.05802,-0.06029,-0.02493,-0.04792,-0.01606,-0.02218,-0.02591,-0.02857,-0.00547,0.12103,-0.11961,0.02997,-0.00137,0.09392,0.07619,0.01078,0.00228,-0.07507,-0.11651,-0.10831,-0.02327,0.08166,0.05383,-0.03358,0.0237,-0.00487,0.03222,-0.05102,0.09636,0.01016,-0.07825,0.11696,0.03784,0.09443,0.02247,-0.04643,-0.05111,-0.01819,0.04617,-0.01245,-0.02766,0.05037,-0.02793,0.04398,-0.05057,0.0976,-0.01942]},{"domain":"mechanics","key":"vis_viva","name":"Orbital speed on an elliptical orbit (vis-viva)","package":"mechanics-ai999x","example":"A satellite on an elliptical orbit around a planet of mass 5.972e24 kg has a semi-major axis of 8.0e6 m. What is its orbital speed at a distance from the center of 7.0e6 m?","v":[0.02355,-0.11752,0.0786,-0.00987,-0.03875,-0.16211,0.08357,0.04209,0.13392,-0.02754,0.00553,-0.05189,0.02422,-0.02702,-0.09108,-0.00574,-0.05513,-0.00271,-0.00324,-0.06138,0.01423,0.03632,0.07651,-0.05264,-0.04806,-0.03683,0.01559,-0.11118,-0.00542,-0.06012,0.01042,0.01759,0.10821,0.00311,-0.02717,-0.10175,0.01181,0.09606,-0.08389,0.076,0.11444,0.00717,-0.05884,0.00251,-0.02301,-0.06421,-0.05111,-0.03709,-0.02663,-0.08315,0.0113,0.08748,0.0096,0.01608,-0.01828,0.0588,-0.00769,0.04598,0.01126,0.03489,0.00437,-0.01565,-0.05058,0.03685,-0.01601,-0.07806,0.0711,0.02036,0.04099,0.14039,0.01127,-0.02416,0.05181,0.04872,-0.03623,0.11534,-0.14862,-0.10043,-0.05867,0.08095,-0.02897,-0.02993,-0.06786,-0.02962,0.03626,-0.02803,0.09035,0.02427,0.05323,-0.04943,0.03405,0.05944,0.0701,0.0741,-0.03548,0.15603,-0.03433,0.02261,-0.00456,-0.06995,-0.02255,-0.04423,0.10873,-0.02277,-0.07224,-0.09897,-0.06335,-0.00854,-0.09943,0.02712,-0.02997,0.04071,-0.00092,0.04517,0.03164,-0.02631,0.04014,0.03871,0.03259,-0.0007,-0.0046,0.01862,-0.01291,-0.00144,0.00618,-0.04856,-0.01534,0.17605,-0.05018,0.0987,-0.08275,0.05057,-0.09591,-0.0408,-0.03769,0.10867,0.08094,0.10037,0.00892,-0.0382,0.02106,-0.02686,0.0397,-0.02131,0.06593,0.03702,-0.0769,-0.12565,-0.09976,0.08913,-0.03044,0.04656,0.05969,-0.03285,-0.10998,-0.03782,0.07481,-0.0746,-0.00428,-0.06149,-0.1127,0.02004,-0.02962,-0.12201,-0.0819,0.07315,0.03236,0.06186,0.12273,0.04091,-0.05659,0.00689,0.02054,-0.04292,0.0712,-0.05812,-0.05292,0.09096,0.03048,-0.13297,0.07745,0.01628,0.00484,0.16142,0.05812,-0.03363,0.01003,-0.02141,0.00059,-0.12848,-0.07732,0.00362,0.07309,0.01203,0.01423,-0.00103,-0.04119,-0.04895,-0.00946,-0.06674,0.00397,0.0193,-0.0886,-0.0565,-0.011,-0.02704,0.00206,0.03141,-0.0866,-0.01798,-0.01607,0.01686,0.10716,-0.04542,0.01882,-0.04633,-0.04006,-0.02552,0.14995,0.06068,-0.09004,-0.09121,0.0371,0.10329,0.04478,-0.05142,-0.10457,0.14273,0.03286,0.02002,-0.00096,0.01973,0.05191,-0.04058,0.02321,-0.01957,-0.00201,0.03973,-0.06098,-0.03749,0.05738,-0.03847,0.11605,0.00201,0.02928,-0.04059,0.03835,0.05916,0.0827,0.01971,-0.05152,0.0263,-0.08718,0.05966,0.00934,0.02013]},{"domain":"mechanics","key":"escape_speed","name":"Escape speed","package":"mechanics-ai999x","example":"What is the escape speed from a planet of mass 5.972e24 kg and radius 6.371e6 m?","v":[-0.06351,-0.0561,0.06765,0.02732,0.01554,-0.08115,0.01899,0.03171,0.06401,-0.02953,0.02792,-0.06109,-0.03037,-0.04712,-0.06475,-0.00057,-0.06088,-0.01369,0.02362,-0.02327,-0.0204,-0.04457,0.05035,-0.05151,-0.07592,-0.01438,0.09317,-0.08012,-0.04988,-0.01473,-9e-05,0.02055,0.08262,-0.02616,-0.04026,-0.04313,0.00229,0.05823,-0.08723,0.00102,0.12066,-0.01617,-0.03436,0.02738,0.05092,-0.04095,-0.0418,-0.08155,-0.06115,-0.02788,0.08252,0.051,0.00365,-0.01509,0.01336,-0.0084,0.00549,0.0065,-0.02682,0.03348,-0.01296,0.01964,-0.0277,-0.05537,0.02482,-0.07244,0.03965,0.05635,-0.03226,0.09018,0.04853,0.0121,0.01956,0.05459,0.00652,0.11761,-0.14266,-0.1904,-0.07902,0.05933,-0.01866,-0.00994,-0.11133,-0.06947,-0.0479,-0.03087,0.08195,0.04716,0.03393,-0.06492,0.05987,0.10831,0.08927,0.05837,0.04196,0.13141,-0.08852,-0.12843,0.0067,-0.09073,0.03094,-0.13421,0.06539,-0.04184,-0.101,-0.06607,-0.04977,-0.0548,0.01647,0.01947,0.0245,0.0928,0.01352,0.02806,0.0088,-0.04659,-0.00374,0.0041,0.02015,-0.01236,0.08563,0.07604,-0.00473,-0.03032,-0.00324,-0.04831,0.00918,0.17199,-0.0337,0.119,-0.02397,0.06765,-0.10096,-0.05406,-0.03906,0.03417,0.06942,0.02552,0.01327,-0.06537,0.05224,0.01021,0.02861,-0.00778,0.04324,0.01356,0.0614,-0.09581,-0.13748,0.0328,0.0256,-0.02953,-0.00102,0.04153,-0.11215,-0.00274,-0.00625,-0.04741,-0.01479,-0.03024,-0.11647,-0.01048,-0.03626,-0.02135,-0.15123,0.09282,0.0898,0.0507,0.1557,0.01817,0.04899,0.07955,-0.06758,-0.10298,0.09418,-0.07166,-0.05468,0.03447,0.0088,-0.08082,0.07369,0.01854,-0.02554,0.15637,0.03324,0.02188,-0.01912,-0.03539,0.08224,-0.03548,-0.07047,-0.00736,0.09714,0.01872,-0.06589,0.00761,-0.05947,-0.07079,0.00757,-0.07841,0.04589,0.02253,0.00706,-0.0672,0.00201,0.01146,0.02686,0.08729,-0.04292,-0.03592,-0.0969,0.12536,0.10152,-0.0734,0.00021,-0.05349,-0.06011,-0.06627,0.14479,0.0703,-0.0807,-0.04888,0.03376,0.11358,0.05542,-0.01927,-0.15088,0.05567,0.01976,-0.01775,0.05756,0.03213,0.04163,-0.07415,0.04875,-0.00768,0.05862,0.07446,-0.06157,-0.04896,0.03227,0.02085,0.11572,0.03252,0.03693,0.03432,0.05312,0.06523,0.04503,0.00478,-0.02242,0.05871,-0.06217,0.04303,-0.01021,-0.04975]},{"domain":"mechanics","key":"kepler_period_semi_major","name":"Orbital period from the semi-major axis (Kepler's third law)","package":"mechanics-ai999x","example":"A planet orbits a star of mass 1.989e30 kg on an elliptical orbit with a semi-major axis of 1.496e11 m. What is its orbital period?","v":[0.06757,-0.04921,-0.06421,0.04022,0.03252,-0.13226,0.04012,-0.04244,0.18566,0.06535,0.01973,-0.01919,0.0777,-0.01263,-0.05695,0.0043,0.05711,0.02474,0.06703,-0.06779,0.02769,0.08552,-0.01843,-0.00838,0.02458,-0.04552,-0.00857,0.01534,0.07135,-0.00816,0.06661,0.04761,-0.01428,0.04247,0.03654,-0.13223,-0.07935,0.22643,-0.0471,0.04654,0.07968,0.07432,-0.02299,0.00542,-0.14823,-0.05932,-0.04981,0.0903,0.06307,0.00626,-0.12471,0.158,-0.01526,0.06821,-0.02732,-0.03772,-0.06825,-0.02406,-0.06489,0.04102,0.00672,-0.02642,-0.03485,0.11032,0.12236,-0.02207,0.01113,-0.06499,0.05643,-0.00056,-0.04366,-0.13811,-0.02208,-0.09242,-0.0601,0.06845,-0.04301,0.09115,0.00655,-0.02441,-0.04618,-0.09243,0.08861,-0.00774,0.06871,-0.003,0.02173,-0.06403,0.04859,-0.04618,-0.03205,-0.06971,-0.00935,-0.02954,-0.07656,0.13073,0.06475,0.06411,-0.05774,-0.00884,0.02594,0.00211,0.04712,0.0744,0.00177,0.04402,-0.03277,-0.08869,0.00893,-0.07974,-0.03027,0.03039,-0.04016,-0.05908,0.06461,0.01249,-0.03284,0.03232,-0.01375,0.11162,-0.09506,0.04302,0.00093,0.00499,-0.03461,0.00835,0.05242,-0.00943,-0.044,0.05498,-0.06046,-0.025,0.00595,0.03289,0.01412,0.044,0.0013,0.11809,0.19367,0.03681,-0.03406,-0.11333,0.00898,-0.07464,0.0146,0.04851,-0.13356,-0.03405,-0.02496,0.05665,-0.0384,-0.00655,0.0245,-0.08179,-0.08757,0.05644,0.06324,0.06456,0.05736,-0.04551,-0.04902,0.12189,-0.02343,-0.15647,-0.01403,0.05953,0.03062,0.11115,-0.06641,0.02196,-0.05645,0.02602,0.06142,0.04583,-0.03844,0.03166,-0.03775,0.04895,0.0287,-0.07873,-0.02134,-0.01298,0.08772,-0.00419,0.0465,0.01949,0.04056,0.01716,-0.03744,-0.15014,0.01638,0.07008,0.04343,-0.05828,0.00125,0.06596,0.06344,0.01254,-0.03763,-0.12146,0.009,0.03711,-0.1344,0.0108,-0.06783,0.00754,0.04428,0.01705,-0.06589,-0.05574,0.05896,-0.13694,0.14216,-0.06728,0.03923,-0.00362,-0.05243,-0.00806,0.1158,0.00854,-0.05543,-0.00035,-0.01338,0.01717,0.01096,-0.0691,0.02602,-0.01824,-0.04589,0.03528,0.01022,-0.01901,0.0004,-0.04208,-0.06291,-0.03273,-0.04418,-0.05237,-0.06575,-0.02789,0.00717,-0.05761,0.02407,-0.0509,-0.00348,-0.02287,0.04594,-0.07359,-0.0018,0.02939,-0.00468,-0.00187,0.01752,0.09827,-0.04553,0.01043]},{"domain":"mechanics","key":"inertia_solid_sphere","name":"Moment of inertia of a solid sphere","package":"mechanics-ai999x","example":"A uniform solid sphere has a mass of 2 kg and a radius of 0.5 m. What is its moment of inertia about its center?","v":[0.05888,-0.0853,-0.0499,0.04796,0.04017,-0.03481,0.0479,0.01749,0.10297,-0.06096,-0.04581,-0.06217,0.04031,0.00774,-0.07433,-0.03524,-0.03647,-0.02058,0.01954,-0.11049,0.08719,-0.10276,0.02028,-0.02612,-0.04111,-0.06823,-0.00638,-0.03322,0.0993,-0.01193,0.07865,-0.05133,0.03061,0.00414,0.04053,-0.12045,0.09133,0.11202,-0.09057,-0.04358,0.0625,0.01998,-0.02735,0.14446,-0.02643,-0.02119,-0.03003,-0.0084,0.05169,-0.04686,0.00182,0.00618,0.08426,0.0355,-0.01187,0.04355,0.05288,0.0607,-0.01719,0.00377,-0.01588,-0.04621,-0.01628,0.05658,0.04498,-0.00866,0.00091,0.01236,-0.09608,0.03375,0.06064,-0.03372,-0.08835,0.0857,-0.026,0.08858,-0.11299,0.0151,-0.0355,0.06068,-0.03801,-0.01201,0.07568,-0.02038,0.05588,0.07019,0.03585,-0.01185,-0.01737,0.00264,0.00359,0.05908,0.0154,-0.03397,0.02078,0.11934,-0.12202,0.09802,-0.03898,-0.05071,0.06505,-0.05374,0.03405,0.059,-0.1117,0.05495,-0.02174,-0.06812,0.02151,0.0615,0.01773,0.05375,0.00584,0.0535,-0.09708,-0.12168,0.11898,-0.00981,-0.07068,0.04841,-0.06092,0.07375,-0.00518,-0.024,-0.01136,0.02975,-0.00584,0.0523,0.04609,-0.04749,0.03485,0.05775,0.00167,0.00878,-0.02318,0.03724,-0.05617,-0.00563,0.00119,0.03386,0.00931,-0.07469,0.09389,0.03195,0.00968,-0.00954,-0.00896,-0.00326,-0.05629,-0.01689,-0.10848,0.13412,-0.0513,-0.04545,0.00545,0.03921,-0.11534,0.00171,0.04087,0.08656,-0.07778,-0.02878,0.00538,-0.03633,0.12747,0.05233,0.00637,0.0307,0.01353,0.09484,0.01047,0.03392,0.01998,-0.05418,-0.04229,-0.08226,-0.01113,0.00856,-0.07138,-0.08273,0.05881,0.10663,0.06106,0.10445,0.06129,0.01105,0.03043,0.03619,-0.02781,-0.0772,-0.05319,0.06155,0.01158,0.00666,0.06157,-0.02575,0.05251,0.01466,-0.01423,-0.14402,-0.07087,0.00273,-0.08859,0.02425,-0.02049,-0.03446,-0.01156,0.0064,-0.03458,0.00614,-0.00954,0.01697,0.2006,-0.08246,-0.05184,-0.09047,0.00455,-0.04614,0.06264,-0.04691,-0.09424,-0.07735,0.04264,0.004,0.03083,0.04149,-0.14179,-0.04805,-0.09288,0.01036,0.02715,0.08618,-0.05584,-0.09457,0.02773,-0.02463,-0.11451,-0.01152,-0.1473,0.06622,0.0361,-0.09267,0.10901,0.07826,0.07233,-0.0472,0.15141,0.08106,-0.00045,0.05804,-0.0225,-0.04526,0.03062,-0.04362,-0.23938,0.03119]},{"domain":"mechanics","key":"inertia_hollow_sphere","name":"Moment of inertia of a thin spherical shell","package":"mechanics-ai999x","example":"A uniform hollow sphere has a mass of 2 kg and a radius of 0.5 m. What is its moment of inertia about its center?","v":[-0.03001,-0.15432,-0.03657,0.07507,0.04796,0.03001,0.05474,-0.01385,0.12571,-0.07872,-0.04148,-0.08335,-0.01819,0.02602,-0.08702,-0.01288,-0.0103,0.01531,0.07904,-0.09687,0.1207,-0.0877,-0.00116,0.00012,-0.02915,-0.1709,0.00336,-0.03393,0.04317,-0.02338,0.06749,-0.01945,0.00738,0.03849,0.02825,-0.1444,0.06532,0.08241,-0.05645,-0.03012,0.03846,0.02069,-0.11154,0.14205,-0.00642,0.00198,-0.00961,-0.01302,0.00196,-0.07432,0.02327,-0.03629,0.11355,-0.0228,-0.05349,0.00382,0.00154,0.00955,-0.03594,-0.00675,-0.03894,-0.02184,0.01867,0.06142,0.03915,0.03733,0.003,-0.04133,-0.02323,-0.05876,0.07258,-0.02619,-0.0662,0.06596,-0.0501,0.03021,-0.10543,0.0325,-0.05833,0.02199,-0.05216,-0.0143,0.08226,-0.03119,0.02629,0.01413,0.00905,-0.01328,0.00888,0.00734,0.04912,0.06533,0.02397,-0.0254,0.00319,0.10008,-0.11555,0.01651,-0.0453,-0.00546,0.06841,-0.01498,0.05466,0.03398,-0.07496,0.01026,-0.03858,-0.04835,0.0485,0.0289,0.01859,0.03586,-0.0352,0.04691,-0.10333,-0.1253,0.06878,0.09788,-0.0513,0.01997,-0.02974,0.08732,0.03539,-0.03447,-0.03799,0.05313,0.01558,0.01341,0.0542,-0.05552,-0.04404,-0.00467,0.05769,-0.04443,-0.03401,-0.02419,-0.10058,0.02711,-0.00134,0.02223,0.03847,-0.09086,0.07224,0.0284,0.09291,0.012,0.03718,0.01214,-0.06549,-0.00603,-0.0615,0.10076,-0.04304,-0.06836,-0.00653,0.03367,-0.11972,-0.01624,-0.00526,0.05882,-0.09725,-0.00452,0.01633,-0.05304,0.08193,0.0732,-0.02479,-0.0109,-0.03852,0.00408,0.04693,0.02682,0.03461,-0.03653,-0.03948,-0.07705,-0.01929,-0.06332,-0.03453,-0.0431,0.09888,0.08611,0.08829,0.13726,0.05882,-0.04578,-0.01482,0.04033,-0.02313,-0.06712,-0.01524,0.12622,0.06389,-0.02662,0.06767,0.03964,0.0842,-0.00152,-0.04003,-0.15436,-0.12391,0.04098,-0.12167,0.06251,0.01305,-0.03643,0.02386,0.04811,-0.05937,-0.01042,0.03733,-0.03075,0.16899,-0.06022,-0.0521,-0.05984,-0.06221,-0.03264,0.06685,-0.04895,-0.07558,-0.04621,0.09633,-0.01326,0.05971,0.04985,-0.06963,-0.01747,-0.05701,0.00022,0.0645,-0.00585,-0.0135,-0.01474,0.05243,0.04385,-0.06228,-0.00968,-0.12577,0.01843,0.11421,-0.01487,0.09835,0.14202,0.06631,-0.07867,0.14973,0.14925,0.00148,0.0968,-0.05638,0.00974,0.0246,0.02699,-0.18942,-0.03634]},{"domain":"mechanics","key":"inertia_solid_disk","name":"Moment of inertia of a solid disk about its axis","package":"mechanics-ai999x","example":"A uniform solid disk has a mass of 2 kg and a radius of 0.5 m. What is its moment of inertia about its center?","v":[0.04783,-0.03969,-0.07186,0.08195,-0.01019,-0.03554,0.07398,-0.03444,0.03483,-0.02476,0.03181,-0.02632,-0.03041,0.04885,-0.01349,-0.03346,-0.00029,-0.09621,-0.05184,-0.06989,-0.02826,-0.05144,-0.02796,-0.05459,-0.06111,0.02926,-0.01143,0.02037,0.06605,-0.04408,0.08392,-0.0757,0.0578,-0.03394,0.05519,-0.02025,0.13799,0.12969,-0.05876,-0.036,0.03352,-0.04705,0.01489,0.07014,-0.08486,-0.04475,-0.08069,-0.05272,-0.00905,0.00345,0.01246,0.0643,0.0254,0.07757,-0.04182,0.08843,0.07984,0.12714,-0.01532,-0.01674,-0.00529,0.04481,-0.03044,0.08243,0.04352,0.01048,0.03986,0.04615,-0.08544,0.09779,0.03087,-0.00556,-0.09083,0.12873,-0.01185,0.05545,-0.06369,0.0681,-0.04146,0.11901,-0.04191,-0.01444,0.04017,-0.02159,0.03564,0.02855,-0.00929,0.01146,-0.05859,0.02115,-0.15071,-0.02797,0.03202,0.00614,0.01801,0.03217,-0.06774,0.12294,-0.03814,0.0018,-0.00144,-0.03996,-0.054,0.05353,-0.06598,0.1074,0.01243,-0.12267,-0.05742,-0.0125,-0.10717,0.04853,0.05921,0.10572,-0.09947,-0.02768,0.10399,-0.09257,-0.02858,0.0558,-0.06282,0.08305,0.00195,-0.01827,-0.02036,0.03334,-0.06106,0.08959,0.09625,-0.0372,-0.03042,0.10929,0.00626,-0.04862,-0.01117,0.09284,-0.09592,-0.0022,0.05612,0.01902,-0.00526,-0.06395,0.04473,-0.00691,-0.04959,0.03584,-0.06961,-0.0688,0.02232,-0.04832,-0.15986,0.05903,-0.08446,-0.00851,0.07111,0.03468,-0.03873,0.04765,0.07431,-0.00508,-0.02466,-0.02405,0.00573,-0.00259,0.16514,0.00145,-0.02505,0.05525,0.10691,0.12534,-0.04472,0.02702,-0.01328,-0.07735,0.01284,-0.11348,-0.02433,0.08644,-0.03635,-0.07491,0.04906,0.0757,-0.01976,0.04698,0.0331,0.01845,0.08577,-0.05093,-0.00911,-0.13848,-0.05033,0.01004,0.03146,0.03481,0.06893,-0.05449,-0.05841,0.07695,0.00511,-0.13547,0.03732,0.03005,-0.06245,-0.00426,0.00031,-0.06979,0.02157,-0.05121,-0.03345,-0.00245,0.06387,0.07418,0.13505,-0.04764,-0.0641,-0.06942,0.07178,-0.09479,0.05802,-0.051,-0.08106,-0.05777,0.00576,0.02679,0.06049,0.00542,-0.14384,-0.0202,-0.02995,-0.00138,-0.003,0.10692,-0.04107,-0.05852,0.07132,-0.02933,-0.08211,-0.01751,-0.01623,0.0059,-0.01537,-0.07898,0.15467,0.00553,0.0534,0.03275,0.02159,0.05986,-0.00289,-0.01792,-0.018,-0.04749,0.0972,-0.0757,-0.17803,0.01714]},{"domain":"mechanics","key":"inertia_rod_center","name":"Moment of inertia of a thin rod about its center","package":"mechanics-ai999x","example":"A uniform rod of mass 3 kg and length 2 m rotates about its center. What is its moment of inertia?","v":[-0.037,0.02411,0.01651,0.05009,0.01679,-0.03737,0.01251,0.08694,0.12438,0.01572,-0.01198,-0.06847,0.02627,0.02833,-0.07177,-0.00462,0.06649,0.01963,-0.07419,-0.14153,0.01724,-0.05485,-0.07948,-0.08667,0.04552,-0.02373,-0.07492,-0.05838,0.00633,0.02953,0.04448,0.02684,-0.0163,-0.02808,-0.01499,-0.06219,0.10435,0.09845,-0.09728,0.04069,0.04135,-0.06096,-0.00285,0.09302,-0.04222,0.00155,-0.04376,-0.13779,-0.01661,-0.03131,-0.08518,0.03458,-0.04449,-0.02294,-0.04032,0.02309,-0.08013,0.01579,0.00174,-0.10281,-0.07524,-0.03936,-0.07353,-0.04746,-0.03494,0.03412,0.0087,0.02355,-0.0859,0.07141,0.01455,-0.00638,-0.06663,0.07755,-0.07924,0.04773,-0.03383,0.02247,-0.02025,0.03709,-0.01999,-0.05405,0.12856,-0.05198,0.0053,0.0081,0.03451,0.04877,-0.08747,-0.08788,-0.0484,0.07664,-0.10296,0.13799,0.01893,0.07009,-0.08649,0.07463,-0.10095,-0.02343,0.05544,-0.07987,-0.00632,0.03979,-0.03417,-0.06648,-0.08204,-0.15332,-0.10997,0.01373,-0.05007,0.07586,0.05119,0.06105,-0.06642,-0.05234,0.10318,0.04781,-0.02901,0.0095,0.00026,-0.02572,0.07551,0.00325,0.01756,0.11719,0.03739,0.08182,0.16989,-0.02508,0.03943,0.03113,-0.02036,-0.0542,-0.05303,0.0905,-0.04349,0.07283,-0.05529,-0.02345,0.03367,-0.05966,0.10382,-0.01347,-0.04828,0.03114,0.05439,0.0388,-0.02162,0.0119,-0.0971,0.10605,0.00585,-0.06366,0.11735,-0.03237,-0.00227,0.08843,0.06424,-0.01997,-0.07216,-0.02211,0.03706,0.05559,0.09553,-0.01439,-0.01434,0.01148,-0.0548,0.15444,-0.04273,-0.00699,0.10404,-0.03134,-0.03225,-0.12301,-0.01718,0.02836,-0.0734,-0.05235,0.05849,0.05309,0.05967,0.03914,0.06743,-0.05668,0.06452,0.06715,0.09128,-0.05209,-0.04166,-0.00626,0.03625,-0.0087,0.03954,-0.11501,-0.01531,0.04891,0.05561,-0.02524,-0.01286,0.04001,-0.05016,0.01964,-0.05425,-0.01584,0.01253,-0.02416,-0.06755,0.00502,0.04069,0.10439,-0.02332,0.03017,0.02496,-0.03297,-0.02368,0.05634,0.05899,-0.04045,-0.13141,-0.08783,0.03105,0.00364,0.02806,0.03068,-0.03595,0.04486,-0.11924,0.01752,0.04625,-0.02072,-0.02168,-0.10259,0.02375,0.00858,-0.02961,0.08789,-0.06539,0.0155,0.04824,-0.00603,0.09932,-0.02468,0.09049,-0.07803,0.14697,0.20183,-0.02076,0.01891,0.05905,0.02438,0.07087,-0.05398,-0.08608,-0.05932]},{"domain":"mechanics","key":"inertia_rod_end","name":"Moment of inertia of a thin rod about one end","package":"mechanics-ai999x","example":"A uniform rod of mass 3 kg and length 2 m rotates about one end. What is its moment of inertia?","v":[-0.02995,0.0628,-0.04606,0.05876,-0.00504,-0.02255,-0.02668,0.05376,0.06798,-0.00514,0.03395,-0.02017,0.01253,0.04936,-0.01664,-0.01453,0.10759,0.05255,-0.07806,-0.06702,0.03392,-0.03255,-0.08492,-0.03427,0.06451,-0.02326,-0.0561,0.03443,0.02569,0.08706,0.00349,0.03255,-0.05022,-0.02281,0.02601,0.00559,0.08521,0.13135,-0.04007,0.03968,0.04404,-0.06993,0.06919,0.05117,-0.06321,-0.002,-0.00383,-0.06439,0.0422,-0.01786,-0.13324,0.06318,-0.10835,-0.0081,-0.03934,0.04931,-0.02619,0.03852,0.02661,-0.05308,-0.07732,-0.00863,-0.02832,-0.12196,-0.06626,0.07272,0.06854,-0.01162,-0.04768,0.04916,-0.00802,0.01692,-0.11769,0.05779,-0.00645,-0.00649,0.09682,0.02108,-0.07024,0.03027,-0.02521,4e-05,0.07864,-0.02744,-0.02824,0.02178,-0.03485,0.00316,-0.14122,-0.03723,-0.12403,0.03445,-0.07256,0.10532,0.03165,0.05408,-0.09883,0.06638,-0.10421,0.03608,0.12459,-0.01039,-0.08737,0.09121,0.00127,-0.05498,-0.09393,-0.09179,-0.01133,0.02575,-0.03555,-0.0206,0.01516,0.06394,-0.17628,-0.06854,0.03641,0.03841,-0.0406,0.0367,-0.02461,0.00224,0.02913,0.04312,0.05075,0.16062,0.03569,0.02194,0.13342,-0.03719,0.07079,0.06549,-0.01354,-0.00744,-0.00392,0.02896,-0.03847,0.01304,-0.01745,0.05893,-0.01265,-0.03455,0.10061,0.03011,-0.13404,-0.00995,0.02854,0.0603,0.0331,-0.01454,-0.09461,0.02348,-0.10092,-0.11944,0.16495,-0.02321,-0.06805,0.11996,0.09489,-0.08713,-0.04543,0.01656,0.02189,0.09895,0.15841,-0.02515,-0.0646,0.01849,-0.14572,0.1057,-0.0802,-0.00863,0.07385,0.02289,-0.01984,-0.05841,0.01559,-0.03659,-0.04663,-0.08111,-0.01626,0.01464,0.08137,-0.04853,-0.02836,-0.0477,0.02576,0.03907,0.02577,0.00237,-0.02086,-0.0003,0.00811,-0.02038,0.0706,-0.03536,-0.02412,0.01329,0.07267,-0.0085,-0.00293,-0.03636,-0.07776,0.05618,-0.06438,0.04233,-0.01053,-0.0576,-0.06565,-0.04084,0.09493,0.03849,-0.09789,0.0213,0.03158,-0.08972,0.00605,0.05189,-0.03018,-0.07453,-0.09754,-0.05943,0.01193,-0.06391,0.00096,0.06828,0.05624,-0.02826,-0.07143,-0.00875,0.06191,-0.00537,-0.05453,-0.10518,0.00436,0.03477,-0.05954,0.03129,-0.07648,0.03884,0.01089,0.00124,0.11975,-0.02056,0.07149,0.01646,0.15592,0.1506,0.00073,0.02547,0.09681,0.03285,0.06995,-0.05234,-0.09411,0.00374]},{"domain":"mechanics","key":"rolling_incline_acceleration","name":"Acceleration of a body rolling without slipping down an incline","package":"mechanics-ai999x","example":"A cylinder of mass 2 kg and radius 0.2 m with a moment of inertia of 0.04 kg*m^2 rolls without slipping down an incline. The angle of the incline is 30 degrees. What is its acceleration?","v":[-0.04662,-0.08388,-0.08892,0.0684,-0.10765,0.03552,0.07064,0.03009,0.02886,-0.00442,0.00981,-0.09895,0.02456,-0.07491,-0.09532,-0.00791,-0.07249,-0.08531,-0.0149,-0.15476,0.01304,-0.06666,0.00195,-0.01371,-0.06394,-0.07677,-0.01334,-0.11507,-0.02835,-0.06405,0.03568,0.00683,-0.00338,0.02855,0.02981,-0.02748,0.08947,7e-05,-0.04511,0.00939,0.08746,-0.1117,0.031,0.09149,-0.02469,0.04192,0.04789,-0.066,0.01068,-0.05381,0.07626,-0.02147,0.06886,0.04111,0.06449,0.05734,-0.00759,-0.02793,0.01888,-0.06634,-0.01718,0.04843,-0.04736,0.02605,0.05305,0.05815,-0.00253,0.0454,-0.05799,-0.06359,-0.02302,0.04328,0.10316,-0.0282,-0.06156,0.02789,-0.03189,0.07055,-0.0421,0.07579,-0.01842,-0.01906,0.07581,-0.02019,0.02522,0.00709,0.07605,-0.00756,0.02172,0.01324,0.05214,0.04254,0.02805,0.01397,-0.0275,0.10834,-0.05558,0.01002,0.02791,-0.06237,-0.04521,-0.05565,-0.00673,-0.07938,-0.06148,-0.02498,-0.02312,0.01193,0.03066,0.15634,0.0129,0.17848,0.05544,0.04121,-0.04451,-0.07726,0.08171,-0.02099,0.01367,0.00318,-0.04255,0.07511,0.09849,-0.0957,-0.0104,0.11854,-0.03254,-0.04404,0.03381,-0.05178,-0.02338,0.00765,-0.01394,-0.0452,-0.05131,0.095,-0.04312,0.08044,-0.06725,-0.01135,-0.05622,-0.14035,-0.01711,0.04342,0.06487,-0.06853,0.04375,0.07889,-0.0732,-0.02728,-0.1973,0.08187,0.00972,0.00493,0.01586,0.04841,-0.10399,0.04963,-0.03295,0.07001,-0.07341,-0.07029,0.00654,0.14791,0.00321,0.0146,0.02969,-0.00067,0.05815,0.08401,0.07436,0.0444,0.01979,-0.05951,-0.06657,-0.07578,0.0322,0.01431,-0.04434,-0.08845,0.00273,0.06311,0.046,0.05105,0.1016,0.02896,-0.04349,0.0078,0.07992,-0.03714,0.03971,0.09617,0.11652,0.02063,0.10415,-0.05068,-0.00589,0.00605,0.07198,0.00945,-0.06265,0.03128,-0.07325,0.0347,-0.00341,-0.05099,-0.04254,0.07037,0.09113,0.0072,1e-05,-0.02686,-0.04369,-0.05551,-0.04025,-0.07065,0.00931,0.00405,-0.0127,0.03739,-0.0634,-0.11651,0.02465,0.18459,-0.02666,-0.06164,-0.12579,0.09023,-0.05573,0.02716,-0.08366,0.03165,-0.07503,-0.02,-0.02912,-0.01555,0.05872,0.00271,-0.04389,0.04403,0.10203,0.02671,0.09467,0.0027,0.14647,-0.10304,-0.06382,0.09088,-0.10765,-0.08499,-0.05161,0.09068,-0.00241,-0.05647,-0.08092,0.03173]},{"domain":"mechanics","key":"atwood_massive_pulley","name":"Acceleration of an Atwood machine with a massive pulley","package":"mechanics-ai999x","example":"In an Atwood machine the heavier mass is 3 kg and the lighter mass is 2 kg. They hang over a pulley with a moment of inertia of 0.02 kg*m^2 and a radius of 0.1 m. What is the acceleration of the masses?","v":[-0.03115,-0.03905,-0.17409,0.0558,0.02946,-0.00369,0.04322,0.00221,0.00172,0.0286,0.03398,-0.0047,-0.00734,-0.04668,-0.071,-0.04721,-0.03868,-0.08046,0.11447,-0.0785,0.07666,-0.05561,0.02243,0.01884,-0.06682,-0.02335,-0.04097,-0.00574,0.05357,-0.02715,0.02772,-0.06041,-0.07793,-0.02379,0.0289,-0.02542,0.00943,0.01409,0.02167,-0.02442,-0.0388,-0.06315,-0.07518,0.00986,0.04648,0.09981,0.04343,-0.00022,0.07363,-0.0342,-0.02484,0.03604,0.04052,0.05132,-0.00175,0.07456,-0.03287,-0.06179,-0.01434,-0.06607,-0.04231,-0.02054,0.03124,0.03809,-0.04509,0.07502,-0.0216,-0.03261,0.09778,-0.09016,-0.00473,0.01446,0.0465,-0.07342,-0.02106,0.0205,0.01695,0.05748,-0.01129,0.09909,-0.09498,0.02083,0.03513,0.04318,-0.05853,0.03713,0.09938,-0.09572,0.01141,0.03869,-0.04559,-0.08834,0.0148,0.04961,-0.06883,0.06914,-0.07038,0.0352,0.01387,0.01647,0.00146,0.03479,-0.03356,0.04339,0.00446,-0.04728,-0.04608,-0.05854,0.01396,0.13573,0.03317,0.11178,-0.00925,0.05333,-0.04478,-0.03347,0.04325,0.02331,0.04591,0.02742,-0.07341,0.0892,0.11023,0.0245,-0.02611,0.17222,0.0121,-0.05455,0.05862,-0.1025,-0.01872,0.00336,-0.00872,-0.07376,-0.05216,0.05244,-0.07753,0.02256,0.00409,0.046,-0.00687,-0.13102,0.06751,0.08492,0.1153,0.03549,0.08911,0.14736,0.00194,-0.06843,-0.17693,0.03383,-0.1145,0.02145,0.0568,0.091,-0.09551,0.10722,-0.06696,0.06215,-0.06054,-0.05186,0.08828,0.04221,-0.00338,0.03529,0.01387,0.07568,-0.08283,0.00218,-0.02078,-0.02996,-0.05464,0.09724,-0.02721,0.03998,0.07848,-0.11152,-0.03528,-0.00708,0.00298,0.04745,0.02024,0.00956,-0.03318,0.05183,-0.0371,-0.02112,-0.01388,-0.165,0.03042,0.2191,0.03991,-0.02427,0.04716,-0.05033,-0.0141,0.03289,-0.02582,-0.02107,0.00931,0.0159,-0.20639,0.12522,0.03128,0.00267,-0.10816,0.00256,0.0397,-0.06329,0.06524,-0.09688,-0.10539,-0.13304,-0.03001,-0.01077,-0.01217,0.00311,-0.06609,0.04275,-0.02353,-0.04383,-0.01943,0.08018,-0.03187,-0.04451,-0.03281,0.02521,-0.03028,0.08185,-0.02414,0.04905,-0.05196,0.00923,0.06013,-0.00571,-0.12786,-0.07785,-0.03057,0.01677,0.13991,0.03782,0.04474,0.00636,0.08528,-0.03274,-0.05282,0.04765,-0.07252,-0.0056,-0.06164,0.06218,0.00259,0.01054,-0.03062,0.09866]},{"domain":"mechanics","key":"torque_free_precession","name":"Body-frame precession rate of a torque-free symmetric body","package":"mechanics-ai999x","example":"A torque-free symmetric body spins with a spin angular velocity of 10 rad/s. Its transverse moment of inertia is 2 kg*m^2 and its moment of inertia about the symmetry axis is 3 kg*m^2. What is the precession rate?","v":[0.08027,0.09402,-0.01659,0.015,-0.01311,0.00224,-0.03812,0.03734,0.06938,0.00764,-0.02365,-0.01505,-0.09218,0.04612,-0.00499,-0.04137,-0.04156,-0.074,-0.05063,-0.13569,0.05627,0.0112,-0.06794,-0.03191,0.04179,-0.09389,-0.03765,-0.00962,0.01161,0.05162,0.02985,0.00381,0.0034,-0.01627,0.0529,-0.06731,-0.02808,-0.02681,-0.05447,0.08808,0.14361,-0.08553,-0.03465,0.11803,0.01778,-0.13382,-0.04264,-0.04901,0.06391,-0.03936,-0.04795,-0.08284,0.06405,0.00853,-0.05236,-0.00657,-0.02792,0.10115,-0.08381,-0.0765,-0.0473,0.00958,-0.03275,-0.08453,0.07113,-0.06009,0.01242,0.00722,-0.05171,0.00135,-0.03825,0.056,0.05601,-0.09853,-0.05519,-0.06885,-0.09496,0.06128,0.06618,0.02581,0.02756,-0.00334,0.06583,-0.06055,0.1236,-0.0004,-0.01829,-0.02944,0.03811,-0.04463,0.09434,0.03745,-0.05149,-0.073,-0.09252,0.17802,-0.02832,0.00296,0.01334,-0.0346,0.01419,-0.03367,0.03702,0.02819,0.04977,-0.06056,-0.04867,-0.06735,-0.03416,0.05404,0.08912,0.09034,0.08054,0.05852,0.06312,-0.10851,0.01635,-0.03865,-0.03356,-0.07928,-0.06331,0.05479,-0.03445,0.01371,0.04824,0.09297,-0.07551,0.01013,0.01651,-0.0953,0.08925,-0.04757,-0.00542,0.02825,-0.03998,-0.01363,0.01696,-0.00608,-0.04808,0.09104,0.06299,-0.03475,-0.00426,-0.10522,-0.038,0.00179,-0.09625,-0.03164,-0.10748,0.10323,-0.04698,-0.06597,-0.02234,0.08054,-0.02411,0.01938,-0.01588,0.04623,-0.06818,-0.08247,0.08247,-0.07698,-0.01255,0.05754,0.00863,0.00331,-0.10061,0.07909,-0.02005,0.11154,0.03275,0.04893,0.02418,-0.10458,-0.02017,0.12023,0.0335,0.02058,-0.07232,-0.10779,-0.04192,-0.01694,0.06129,-0.02903,0.09767,-0.09707,-0.03623,0.15559,0.00702,0.07461,0.10354,0.10507,-0.04112,-0.07009,-0.01989,-0.03789,0.07329,0.01761,-0.04679,-0.04046,0.028,0.01704,-0.08699,0.06033,0.05986,0.08911,0.01211,0.08854,-0.11615,0.05955,-0.02199,-0.00092,0.07483,-0.01942,-0.07475,-0.15017,-0.06731,-0.03815,0.0285,-0.0479,-0.01367,-0.02587,0.0752,0.04848,0.02095,0.02321,-0.03489,-0.09366,-0.01297,0.06402,0.12993,-0.03675,-0.10444,0.01542,0.01542,0.12506,-0.05215,0.02891,-0.0307,0.00684,0.06965,-0.00126,0.03602,0.10277,0.10199,0.00028,0.12747,0.03787,-0.0093,-0.01446,0.02703,0.05097,0.09312,0.03211,-0.03868,0.01136]},{"domain":"mechanics","key":"foucault_precession_period","name":"Precession period of a Foucault pendulum","package":"mechanics-ai999x","example":"A Foucault pendulum swings in Paris at a latitude of 48.85 degrees. What is its precession period?","v":[0.02564,0.11503,-0.03435,0.09072,0.05686,0.03887,-0.04442,0.04005,0.15817,0.07573,0.03284,0.02796,0.04312,0.01622,-0.01452,-0.01212,0.05312,0.01024,0.07641,-0.05707,-0.05329,0.01559,-0.03979,-0.04494,0.0807,-0.03648,-0.05655,-0.06519,0.00385,0.06615,0.0323,0.04358,-0.07009,0.01321,0.05317,0.00529,-0.09279,0.05488,-0.03581,0.15963,0.01771,-0.08792,0.02429,0.08558,-0.07773,-0.04526,-0.02185,0.07511,0.05377,-0.00889,-0.12031,0.01572,-0.02093,0.0205,-0.10281,-0.08212,-0.07341,0.02101,-0.08013,-0.06446,0.03194,-0.00834,-0.08481,-0.09153,0.15477,-0.00011,-0.05075,-0.0484,0.01911,-0.08006,-0.02822,-0.06136,0.05777,-0.14335,0.03157,-0.0924,0.08451,0.0199,0.04891,-0.03307,0.03976,-0.01543,0.02537,-0.05508,0.12106,-0.01565,-0.02444,-0.06025,0.13149,-0.02877,0.02388,-0.04206,-0.0959,-0.10889,-0.09124,0.04265,0.05457,0.01393,-0.05059,-0.00212,-0.0454,0.02279,-0.01497,0.06362,0.08668,0.06383,-0.05576,-0.09626,0.05667,-0.02701,0.02782,0.03792,0.0512,-0.02126,0.13002,-0.03972,-0.06999,-0.03264,0.00659,0.04375,-0.08762,-0.07824,-0.04354,0.00337,0.01909,0.06047,-0.03412,-0.00628,0.03084,-0.00265,0.10765,-0.10968,0.12283,-0.04499,-0.03697,0.04464,0.03438,0.04582,0.04864,0.07572,0.01738,0.01136,-0.02211,-0.12046,-0.04203,0.02291,-0.09329,-0.02833,-0.02866,0.12632,0.04401,-0.05991,0.00117,0.05869,0.04999,0.06919,0.04824,0.01027,-0.10378,-0.03878,0.07821,0.02481,0.0057,-0.00153,-0.00208,0.01564,-0.04531,0.07724,-0.11793,0.02748,0.01688,0.11283,0.15824,-0.03083,-0.00147,0.11003,0.03699,0.04043,-0.02232,-0.06398,-0.07283,-0.07444,0.07192,-0.10515,0.07219,0.00745,-0.07114,0.09592,0.03623,0.04793,0.05072,0.08974,0.05214,-0.07873,-0.07294,0.00867,0.04918,-0.0574,0.08476,0.02543,0.01569,0.00977,-0.02011,0.01075,-0.05228,0.08276,-0.01817,0.01676,-0.08712,0.03741,0.00372,-0.09664,0.00033,0.00318,0.0058,-0.05121,-0.11474,0.0173,0.07811,-0.0382,-0.08949,0.04283,0.09448,-0.02424,0.00886,-0.0697,-0.00729,-0.17567,-0.04277,0.04847,0.02132,-0.00819,-0.06713,0.02337,-0.11826,0.01059,-0.00559,-0.01885,0.02932,-0.04943,0.04247,-0.00198,-0.09846,-0.02044,0.04917,-0.00175,-0.01366,-0.04908,-0.09186,-0.05052,0.04797,-0.03073,0.12896,0.00894,0.00635,0.01515]},{"domain":"mechanics","key":"bead_hoop_equilibrium","name":"Off-axis equilibrium of a bead on a rotating hoop","package":"mechanics-ai999x","example":"A bead slides without friction on a rotating hoop of radius 0.2 m. The hoop rotates at 10 rad/s about its vertical diameter. What is the equilibrium angle of the bead?","v":[-0.11209,-0.05474,-0.03679,0.09167,-0.03063,-0.05269,0.06336,-0.02695,0.10106,0.07,0.01594,-0.04077,-0.0441,0.07505,-0.15185,-0.02857,-0.0069,-0.16361,0.01762,-0.14124,-0.01514,0.00796,-0.05872,-0.08226,0.02864,-0.08337,-0.09345,-0.06304,-0.01142,-0.00335,0.09112,0.11526,-0.00503,-0.00936,-0.01334,-0.03708,0.1231,0.07443,-0.03498,0.11539,0.14586,-0.07042,-0.01298,0.03803,-0.04685,-0.01729,-0.02675,-0.04323,-0.07068,-0.0187,0.02328,-0.03934,0.08899,-0.03424,-0.11079,-0.04005,-0.07188,-0.02752,-0.03215,-0.05874,-0.03944,0.07477,0.01087,0.01851,0.04005,0.02981,-0.05621,-0.02921,0.01075,-0.12433,0.01168,0.02048,0.06777,0.02479,-0.10155,-0.03146,-0.10581,0.11277,0.01019,0.06366,-0.01695,-0.05603,-0.01795,-0.0678,0.017,0.01622,0.0684,-0.02896,0.12185,0.10183,0.0574,-0.00792,0.01949,-0.07187,-0.04896,0.04449,-0.09343,-0.02403,-0.04781,-0.01303,-0.10752,-0.05153,0.05776,0.04716,0.08681,0.02032,0.03799,-0.01751,-0.06063,0.04195,-0.02275,0.07546,0.07472,0.07507,0.06661,-0.02973,0.06943,-0.05476,0.00848,0.05953,0.01249,-0.06143,-0.0398,-0.03655,0.00699,0.04376,0.05931,0.05448,0.0711,-0.07143,-0.00267,-0.09027,0.0801,-0.13048,-0.06113,0.0481,0.00565,0.09361,-0.0671,0.00726,-0.03266,-0.04273,-0.01629,-0.09237,0.10991,0.04665,0.03848,0.01984,-0.03499,0.028,-0.04395,0.08127,0.0473,0.07419,-0.07177,-0.00315,0.01601,-0.00479,-0.08881,-0.08028,0.03532,-0.09451,0.0581,0.03587,-0.04958,-0.02424,-0.03322,-0.03963,0.08016,0.13951,0.0464,0.06695,0.0033,-0.07833,0.02517,-0.07232,-0.0043,0.03161,-0.06803,-0.0478,0.02279,0.00425,0.02722,0.03317,0.08847,-0.03148,-0.05105,-0.02026,0.04,-0.06274,-0.02145,0.14573,0.09376,-0.02737,0.04196,-0.1159,-0.02759,-0.03124,0.04397,0.01449,-0.05098,0.04547,-0.11575,0.04544,0.03294,0.02315,0.0146,0.14243,-0.01452,-0.00142,0.02406,-0.02304,-0.02943,0.11263,-0.12475,0.00814,-0.02881,-0.07906,0.08349,-0.00058,-0.07938,0.0192,-0.00699,0.06264,0.0595,0.05858,-0.0165,0.01901,0.02651,0.10978,0.02074,0.03529,0.01149,-0.0735,-0.07456,0.01805,0.02157,0.04146,-0.05124,-0.0368,0.08405,0.04803,0.00846,0.06016,0.03399,-0.08198,-0.02914,0.10009,-0.05988,-0.03708,-0.0186,-0.01938,0.1591,-0.09087,0.03472,0.06309]},{"domain":"mechanics","key":"elastic_collision_first_final","name":"Final velocity of the first body in a one-dimensional elastic collision","package":"mechanics-ai999x","example":"In an elastic collision the first mass is 2 kg with a velocity of the first of 3 m/s, and the second mass is 1 kg with a velocity of the second of 0 m/s. What is the final velocity of the first?","v":[0.10261,-0.04558,0.02568,-0.04665,0.02433,-0.00736,0.00433,0.0219,-0.04961,-0.05959,0.06033,0.01039,-0.06768,-0.07643,0.07243,-0.0724,-0.05789,-0.04065,0.01216,0.04301,0.13608,0.07488,0.02136,0.14223,-0.04612,-0.02302,0.05543,-0.05188,-0.06818,0.03871,0.00999,-0.01351,0.05056,0.02884,-0.03072,-0.08795,-0.05394,0.02058,0.06905,-0.01635,0.01028,-0.07534,-0.00467,-0.0432,-0.0383,-0.00831,0.01043,0.10361,-0.03789,0.01363,-0.10072,-0.02031,-0.01232,-0.06112,0.08527,0.11239,0.04184,0.04463,0.08566,0.05242,-0.05977,-0.03316,0.0293,-0.09949,-0.02734,-0.00437,0.10945,0.0309,0.04901,0.04852,-0.00474,-0.00974,0.1444,-0.02196,0.02601,-0.04553,0.059,-0.13039,-0.04593,0.0553,0.07181,-0.0598,-0.07043,0.08898,-0.00172,-0.03635,-0.03356,0.0734,-0.09376,0.04063,0.03574,0.0059,0.06943,0.00964,0.03876,0.09252,0.00823,0.02416,-0.14594,0.02529,0.01476,0.10289,-0.01996,-0.02836,-0.03398,-0.11057,-0.08183,0.1018,0.05794,0.01088,0.0228,-0.01642,-0.02893,0.01262,-0.14043,-0.06408,-0.00408,0.05206,0.10179,0.00765,-0.0851,0.08383,0.0402,0.08,0.0027,-0.02908,0.07631,0.06391,0.08428,0.07678,0.04156,-0.0186,-0.12326,-0.0322,-0.00901,-0.06764,0.12895,0.0531,0.01258,0.06003,-0.00326,0.04104,0.09714,0.0302,-0.00926,-0.02576,-0.04176,0.05593,-0.05443,-0.03035,-0.05397,0.05682,-0.06403,-0.14641,0.02071,-0.03744,-0.01134,-0.00344,-0.03127,0.001,-0.10892,-0.01905,0.01295,0.01421,0.03029,0.04539,-0.10484,-0.05947,0.0004,-0.04827,-0.00071,0.0631,-0.01097,-0.07571,0.04663,-0.02296,-0.01872,0.05662,-0.03391,-0.07238,0.0172,-0.00337,0.0796,-0.04272,-0.03285,0.00413,-0.05101,-0.09615,0.12255,0.11391,-0.12533,0.10438,0.01907,0.04071,0.091,-0.03178,0.01614,-0.08313,0.08087,0.06776,-0.02737,-0.01267,-0.05625,0.04347,-0.06847,0.02475,-0.06994,0.06476,-0.03103,-0.05554,0.05699,-0.12787,-0.12586,-0.01753,-0.01294,-0.10319,-0.07042,-0.00728,-0.0857,0.02829,-0.08369,-0.09386,0.06014,0.04307,-0.03796,0.00588,0.02637,0.03985,0.0124,0.00161,-0.04866,-0.05693,0.03872,-0.0127,0.09147,-0.08198,-0.12702,-0.00773,-0.02843,-0.0453,0.10889,-0.01672,-0.01601,0.08505,0.10613,-0.13961,0.10685,0.02232,0.08203,0.07134,-0.02379,0.04116,-0.07272,-0.06973,-0.01276,0.0477]},{"domain":"mechanics","key":"elastic_collision_second_final","name":"Final velocity of the second body in a one-dimensional elastic collision","package":"mechanics-ai999x","example":"In an elastic collision the first mass is 2 kg with a velocity of the first of 3 m/s, and the second mass is 1 kg with a velocity of the second of 0 m/s. What is the final velocity of the second?","v":[0.09789,-0.02733,0.02557,-0.04304,0.0134,-0.00716,-0.0078,0.02252,-0.04354,-0.08373,0.06733,0.01819,-0.0521,-0.07595,0.0694,-0.05673,-0.06619,-0.01869,0.01385,0.05823,0.14248,0.0701,0.02472,0.13591,-0.05107,-0.02235,0.05515,-0.05,-0.06544,0.04246,-0.00286,-0.0153,0.04386,0.01433,-0.02738,-0.07734,-0.05769,0.02518,0.06168,-0.01094,0.01561,-0.0657,-0.0104,-0.03308,-0.02445,-0.00695,0.03512,0.11917,-0.01793,0.00765,-0.08938,-0.02393,-0.0259,-0.07205,0.08415,0.11701,0.03769,0.04499,0.07087,0.06442,-0.05254,-0.04778,0.0401,-0.1028,-0.03605,-0.00952,0.10439,0.02247,0.05086,0.05352,-0.00527,-0.00611,0.14803,-0.03532,0.04688,-0.04028,0.05113,-0.1488,-0.02613,0.0647,0.08035,-0.05821,-0.07709,0.09793,-0.009,-0.05034,-0.01774,0.06491,-0.0862,0.04475,0.02618,0.01865,0.06817,0.03055,0.03678,0.10228,0.00101,0.01433,-0.13431,0.02942,0.01678,0.10905,-0.01343,-0.03468,-0.02633,-0.12134,-0.07826,0.09764,0.03839,0.03661,0.03237,-0.01107,-0.02897,0.00115,-0.13716,-0.06724,-0.00447,0.05495,0.09836,0.00516,-0.08237,0.07651,0.03044,0.08846,-0.00726,-0.01842,0.06731,0.07709,0.06144,0.06892,0.04048,-0.01482,-0.12743,-0.03217,-0.00912,-0.06642,0.1409,0.05031,0.00862,0.06413,-0.00088,0.02686,0.11391,0.0445,-0.02371,-0.03237,-0.0369,0.04905,-0.06537,-0.00737,-0.0408,0.0726,-0.07062,-0.14063,0.01009,-0.04709,-0.00217,0.00335,-0.05403,0.0059,-0.10178,-0.02311,0.01431,0.01903,0.02134,0.04888,-0.11015,-0.04241,-0.00708,-0.05796,-0.00462,0.06315,-0.01262,-0.06284,0.05377,0.00503,-0.00899,0.04365,-0.05091,-0.08638,0.00449,-0.00572,0.07434,-0.05202,-0.03903,0.01725,-0.06304,-0.08549,0.11648,0.12948,-0.11011,0.10182,0.00194,0.01676,0.07936,-0.02934,0.014,-0.08435,0.07849,0.08294,-0.02132,-0.02369,-0.05511,0.0317,-0.07087,0.02357,-0.07896,0.06096,-0.0414,-0.06067,0.03966,-0.13386,-0.10455,-0.02823,0.00974,-0.10423,-0.1022,-0.00379,-0.08641,0.03072,-0.08743,-0.10574,0.04644,0.04219,-0.03187,0.00529,0.02816,0.03522,0.00618,-0.00265,-0.04423,-0.04375,0.03172,-0.01478,0.08699,-0.06845,-0.13134,-0.0139,-0.04265,-0.04159,0.09422,-0.01251,-0.00566,0.07959,0.09712,-0.12134,0.11487,0.02361,0.07463,0.08309,-0.02973,0.0443,-0.08774,-0.06869,-0.01212,0.04497]},{"domain":"mechanics","key":"rocket_delta_v","name":"Velocity change of a rocket (Tsiolkovsky)","package":"mechanics-ai999x","example":"A rocket with an exhaust velocity of 3000 m/s has an initial mass of 1000 kg and a final mass of 400 kg after the burn. What is its change in velocity?","v":[-0.03404,0.05585,-0.0151,0.02482,0.03025,-0.01929,-0.00084,0.08151,-0.08407,-0.01904,0.087,0.03522,-0.12288,-0.13882,0.1241,0.00509,-0.01167,-0.03219,0.03425,0.00072,0.08517,-0.01513,0.00646,0.01095,-0.08543,-0.04668,0.04383,-0.05204,-0.03303,0.02275,-0.07553,-0.07318,0.02375,-0.04018,0.00073,0.02197,-0.04084,-0.02368,0.01725,0.03709,0.07451,-0.01892,0.06891,-0.0675,0.14184,-0.07922,-0.03173,-0.05048,-0.06203,-0.04777,0.00236,-0.01111,0.03864,-0.02812,0.06244,0.05417,0.03394,-0.0,-0.00295,-0.05938,-0.0472,-0.07053,0.04543,-0.05293,-0.03972,0.00405,0.05633,0.05876,-0.0212,0.09458,-0.04515,0.06542,0.15419,0.02647,-0.02291,0.06709,0.01118,-0.07118,-0.13135,-0.00301,-0.04816,-0.02325,-0.04709,0.02371,-0.04943,-0.07892,0.04446,0.09135,-0.06132,0.00903,0.02789,-0.01661,0.06129,0.10947,0.00843,0.06842,-0.04155,-0.08854,0.01177,-0.02451,0.0246,0.05752,-0.11759,-0.04189,-0.01112,-0.12167,-0.09314,0.08026,0.03961,0.11279,0.0382,-0.0197,-0.06343,-0.00463,-0.11389,0.00096,-0.0542,0.04475,0.07089,-0.0766,0.01485,0.06413,0.0175,0.08359,-0.02632,0.05758,0.07434,0.10078,0.05543,0.07821,-0.06309,0.06596,-0.03216,-0.07991,0.00807,-0.09653,0.02065,0.07875,-0.02481,-0.015,-0.02043,0.04994,-0.00355,0.07368,-0.04648,-0.02574,-0.04399,-0.02515,-0.10356,-0.02298,-0.07857,-0.1115,-0.00335,-0.08888,-0.00774,-0.07524,-0.082,-0.04252,-0.04291,-0.0197,-0.04768,-0.00529,0.00264,0.03388,-0.07751,0.10243,0.086,-0.02083,0.06372,-0.03386,0.04275,0.03379,-0.06599,-0.03879,0.11808,0.00495,0.02715,-0.09021,-0.01269,-0.01402,0.05508,0.03194,0.05141,0.10139,-0.05398,0.02081,-0.07853,-0.09126,0.13382,0.01116,-0.1685,0.04304,0.07164,0.04743,0.01137,0.02711,-0.14024,-0.06618,-0.02358,0.02271,-0.05116,0.00407,0.05445,0.03343,0.0324,0.0328,0.0036,0.0426,0.01349,-0.06019,0.01303,0.08871,-0.01136,-0.02496,0.12853,-0.13422,-0.04023,0.03791,-0.12063,-0.00154,-0.033,-0.07971,0.01157,0.02837,-0.00747,-0.04789,-0.04774,0.0224,0.01,-0.02718,0.05307,-0.10059,0.02643,-0.04,0.1316,0.04071,-0.01972,-0.02554,0.02583,-0.05841,0.09668,0.08278,0.13124,0.0819,0.1433,0.08598,0.00091,0.11326,0.09261,-0.04667,-0.02457,0.10231,-0.04301,0.00187,0.00979,-0.09598]},{"domain":"algebra","key":"abs_value_inequality_lower_bound","name":"Solution set of |x - c| > d","package":"algebra-ai999x","example":"Solve |x - 1| > 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0).","v":[-0.00938,0.07373,0.08881,-0.00528,0.0221,0.01119,-0.12761,0.03464,0.04271,-0.04836,-0.00327,0.04856,0.05211,0.00939,0.09388,-0.02809,0.10523,-0.08868,-0.14837,-0.02798,-0.05199,-0.10195,-0.00665,-0.11105,-0.01849,0.08851,-0.03252,0.04875,-0.01437,-0.01256,0.01751,0.0605,-0.05477,-0.02714,-0.0507,0.0852,0.03064,-0.05795,0.00527,0.00178,-0.12064,0.09082,-0.06691,0.09509,0.06945,0.0184,0.04077,0.03121,-0.01499,-0.07079,0.01576,0.03164,-0.07935,0.04997,0.09922,0.06689,0.07449,0.05575,-0.06785,-0.0767,0.00668,-0.04377,-0.05477,-0.04562,-0.04315,0.00986,-0.08221,0.05122,0.0184,0.04554,-0.03717,0.00812,0.05029,0.00105,0.02913,0.08321,0.03956,-0.10566,0.00345,-0.09476,0.06209,0.04244,0.08412,-0.0178,0.08589,-0.02907,0.07217,0.02532,-0.00575,0.06703,0.07261,0.11221,0.0541,0.02039,0.01793,-0.04242,-0.03735,0.03852,0.00901,-0.05897,-0.06791,-0.05941,-0.01102,-0.04322,-0.06879,-0.06745,0.00534,-0.05441,0.14908,0.07868,0.08924,-0.05732,-0.05498,0.02028,-0.02491,-0.02751,0.05398,-0.03928,0.06394,-0.00041,0.07139,-0.04394,0.01899,0.10618,-0.06389,-0.04041,-0.03066,-0.03723,-0.04402,-0.02451,0.06191,0.01804,0.02132,0.04814,-0.0829,-0.0403,0.00108,0.06779,-0.08363,-0.00501,-0.0613,0.08541,-0.02788,-0.00673,-0.04343,0.01368,-0.11802,-0.00375,0.03045,0.07528,0.06064,-0.21078,0.01524,-0.09523,0.06105,0.02577,0.12798,0.03781,0.0483,0.08771,0.01897,-0.04881,0.01374,0.09811,0.02388,-0.04542,-0.12375,-0.00572,0.07968,-0.15104,0.10456,0.00633,0.11507,-0.04939,-0.0033,-0.02444,0.084,-0.03631,-0.01689,0.07971,-0.00976,0.04029,0.09405,-0.01672,-0.03731,0.07877,-0.07585,0.04442,0.06132,0.02496,-0.08396,0.13459,0.00963,0.04372,-0.04033,0.01315,0.0141,-0.01186,0.15482,-0.11853,-0.02769,-0.01096,0.01248,-0.12724,-0.01842,-0.05056,-0.0403,-0.01113,-0.07062,0.04847,-0.02279,0.06259,-0.06293,0.00093,0.00096,-0.09529,-0.04618,0.02149,-0.08298,0.03354,0.04864,-0.01221,0.03721,0.00599,0.02637,-0.12188,-0.0267,0.0603,-0.02978,-0.03353,-0.08084,-0.11506,-0.04465,-0.02051,0.13689,-0.01759,0.04355,0.02538,0.06806,-0.01892,-0.02187,-0.07246,0.00052,0.04835,0.02292,-0.02754,-0.03466,-0.09487,0.05826,-0.05202,0.08704,-0.06764,-0.08862,-0.04112,-0.06707,0.02268]},{"domain":"algebra","key":"binomial_product","name":"Product 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2?","v":[-0.00319,0.01799,0.06527,-0.01076,0.003,-0.13112,0.08593,0.00702,0.0106,0.08252,0.0213,0.08375,-0.00062,0.07877,-0.04284,-0.03766,0.12231,0.07615,-0.07941,0.04698,-0.15235,-0.0856,-0.00107,-0.06015,-0.03303,0.07431,0.02048,-0.11388,0.0138,0.09162,-0.03559,0.09476,0.06815,-0.00762,-0.09363,-0.00446,0.03357,0.07789,0.01509,0.09228,0.03864,-0.04336,0.04295,-0.02828,0.00059,0.0118,-0.06654,-0.14656,-0.08011,0.06895,0.0112,0.06223,0.01786,-0.00964,0.02834,0.01907,0.00821,0.1002,-0.01406,-0.05762,-0.048,-0.03297,-0.01246,0.02016,0.05853,-0.00591,0.06587,-0.0178,-0.07347,-0.02448,0.00118,0.02453,-0.06358,0.05494,-0.04948,-0.12656,0.07796,-0.04385,-0.05606,-0.07381,-0.04305,-0.07364,0.00403,-0.07706,0.00162,0.05561,-0.02984,0.02115,0.05071,-0.00137,-0.00613,0.01116,-0.07366,0.09351,0.06331,-0.01719,0.02573,0.06713,0.00065,0.0276,-0.06838,0.03256,-0.09056,0.06491,0.04807,0.07357,-0.01847,-0.09849,-0.07223,-0.05342,-0.14474,-0.02075,-0.03183,0.0852,0.03885,0.00457,0.06213,0.02138,0.01702,0.01113,-0.06194,0.07604,0.0031,0.04616,-0.01481,0.00878,-0.04162,0.08592,0.0581,0.01044,0.08025,-0.04782,0.02832,-0.10717,-0.03554,0.03575,-0.0015,-0.01781,0.0276,-0.00058,-0.04691,0.00843,0.03103,-0.00024,0.0607,0.05979,-0.11604,-0.03401,0.01584,-0.06563,-0.08362,-0.00026,-0.00841,0.06445,0.13585,-0.00942,0.14625,-0.0414,0.11018,-0.03224,0.04831,-0.07439,-0.05674,0.02286,-0.02888,-0.00269,-0.01906,-0.01125,0.03824,0.05477,-0.02356,0.09566,0.10056,0.00128,-0.07427,-0.05617,-0.01615,0.06977,0.06743,0.04487,0.08118,-0.01465,0.0002,0.01808,-0.00788,0.03518,0.05382,-0.07308,0.05991,-0.22149,-0.11498,-0.09123,0.07499,0.07028,-0.05147,-0.05271,-0.0493,0.00313,0.10907,-0.03239,0.11541,-0.0209,0.01421,-9e-05,-0.05287,0.01851,0.07274,-0.03539,-0.14615,0.01064,-0.09621,0.0068,0.03766,0.06119,0.00599,0.07466,0.03974,-0.03685,0.04286,-0.14455,0.02868,-0.00045,-0.07555,-0.06738,0.09351,0.00059,-0.08076,-0.02343,-0.02216,-0.07678,0.00209,0.01798,0.00711,-0.0804,0.07938,-0.15277,0.07639,0.04002,-0.00094,-0.02632,0.04827,-0.03308,-0.00365,-0.12922,-0.10213,0.00927,0.09311,0.14508,-0.02196,-0.02116,0.06853,-0.03057,-0.01683,0.03451,0.04523,-0.05638]},{"domain":"algebra","key":"perpendicular_lines_slope_product","name":"Slope 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What is the slope of a line perpendicular to it?","v":[-0.01473,-0.06379,0.08781,0.01352,-0.07788,-0.06356,-0.04506,-0.0247,0.08703,-0.09112,-0.01339,-0.00858,-0.01449,0.06879,0.03124,0.05846,0.03562,0.04757,-0.04286,0.07249,-0.06877,-0.04403,-0.04593,-0.08392,-0.01757,-0.02036,-0.06543,-0.10011,-0.02844,-0.0658,-0.06426,0.09448,0.05998,0.06546,0.07443,0.08154,-0.05424,-0.00159,0.04049,0.14389,0.00574,-0.11592,0.12121,0.00244,0.06688,-0.03627,0.01269,-0.03484,0.0003,-0.03028,0.00666,0.00085,0.05536,-0.11311,0.00455,0.02077,-0.07646,0.02608,0.05178,-0.05332,-0.00686,-0.04771,-0.05739,-0.05225,0.10805,0.01794,0.08472,-0.00793,-0.04233,0.01732,0.0451,0.08728,0.02143,-0.08493,0.09254,-0.1093,0.02491,-0.04437,0.10924,-0.02843,-0.06059,-0.01251,0.09673,-0.02466,0.13839,-0.19202,-0.08838,0.08241,0.00678,0.06788,0.01519,-0.01945,0.01518,0.0334,0.00878,-0.06134,0.04574,-0.08904,0.05514,0.11916,0.01893,-0.00606,-0.00792,0.03753,0.01581,-0.00501,-0.03251,0.00141,0.02561,-0.0021,-0.06452,0.05239,-0.03832,0.05435,-0.01781,-0.05793,-0.05875,-0.00198,-0.03713,-0.01312,-0.05436,0.08184,-0.00663,-0.01007,0.04241,-0.00783,0.05443,0.05344,0.05895,0.03392,0.02131,0.05484,-0.05281,-0.13769,0.04607,0.02353,0.01772,0.01997,-0.01893,-0.00145,-0.03052,-0.0329,0.0832,0.11756,0.08317,-0.06847,-0.07573,-0.05147,0.05436,0.02523,-0.01314,0.00768,-0.01626,-0.01908,-0.06587,-0.05038,0.08164,-0.01544,0.07516,-0.07305,0.03185,-0.00475,-0.04053,0.05792,0.02576,-0.03401,-0.1049,-0.03083,0.00528,-0.03904,-0.00715,0.04483,0.12317,0.07284,0.05038,-0.01494,-0.00624,0.0342,0.00908,0.01269,-0.02279,-0.04564,0.06258,0.08743,0.12083,0.05353,-0.02878,-0.01428,0.01888,0.0186,0.07878,-0.0043,0.0299,-0.04333,-0.01858,0.03042,-0.04996,0.02503,0.03351,0.05139,0.09312,0.02844,-0.04523,-0.00079,-0.02109,-0.06522,0.10359,-0.01691,-0.14697,0.09539,-0.03145,0.04113,-0.02655,0.02023,-0.08734,-0.03958,-0.05898,-0.0026,-0.04901,0.13628,-0.06096,-0.06158,0.17499,0.02057,0.10481,0.04707,-0.09089,0.05633,-0.05372,-0.04837,-0.09705,0.0025,-0.063,-0.14441,-0.0481,-0.04819,0.03369,-0.00191,-0.1013,-0.09198,0.03005,0.07689,0.1155,-0.08334,0.09116,-0.08093,0.01585,-0.02731,-0.18384,-0.05836,-0.00469,0.07098,-0.08291,-0.05687,0.05279,-0.0937]},{"domain":"algebra","key":"quadratic_discriminant","name":"Discriminant of a quadratic","package":"algebra-ai999x","example":"What is the discriminant of x^2 + 4x + 4?","v":[-0.01192,-0.01809,-0.08018,0.0843,-0.02918,-0.04186,0.01653,-0.10197,-0.0492,0.01275,0.0956,0.00261,-0.10167,0.07001,-0.0338,0.01902,0.11182,-0.19529,0.03998,0.02464,-0.10022,-0.03053,0.12041,0.02342,-0.03304,0.05971,0.05918,-0.03601,0.07474,0.06126,-0.09169,-0.04655,-0.02841,0.01615,0.02878,-0.11012,0.01931,-0.00314,0.0816,-0.01487,0.07541,-0.02329,-0.0409,-0.01732,-0.07009,-0.05917,-0.0792,-0.11548,0.02721,0.09096,0.11108,0.15034,0.05312,0.00867,-0.07787,-0.05907,-0.06726,0.15907,0.04289,-0.03229,-0.01686,-0.08068,-0.04542,0.06698,0.03321,-0.04129,0.04554,-0.01739,0.00997,-0.04965,0.04343,-0.02062,-0.05979,0.05187,0.05456,0.02867,-0.03202,-0.02185,0.01559,0.00302,-0.06962,-0.0783,0.00349,-0.0276,0.07505,0.09199,0.02274,-0.05075,0.00722,0.04405,-0.05281,-0.03957,0.02015,-0.04559,0.01562,-0.06528,-0.04924,-0.02717,0.04472,0.03485,-0.06181,0.0049,-0.06071,-0.01937,0.07393,0.11786,0.03143,-0.08295,-0.09472,-0.04557,-0.05879,0.01574,0.00478,0.03057,0.04794,-0.01669,0.02534,-0.07268,-0.05901,0.07979,0.01513,0.11211,0.00597,-0.06538,0.06381,0.03228,-0.02171,0.00803,0.0358,-0.00537,-0.06245,0.04204,0.05831,-0.11689,-0.04729,0.00274,-0.14085,-0.02663,0.06957,0.00577,0.03736,-0.04524,-0.03188,0.03333,0.05015,0.00755,-0.02291,0.02189,-0.00827,-0.0622,0.01384,0.02142,0.02628,0.08347,0.02329,0.01959,-0.11689,0.02069,-0.13036,0.11462,0.08618,-0.06419,-0.01145,-0.01917,-0.03512,0.0627,0.08795,0.00834,0.08096,0.04216,-0.04991,0.0582,-0.0735,-0.02955,0.09713,-0.16,-0.07971,0.02457,-0.04177,0.00011,0.04137,0.01763,-0.15213,-0.04587,0.07369,-0.02763,0.00922,0.03179,-0.10737,-0.12247,0.07005,-0.08368,0.03155,-0.03725,-0.02905,-0.05711,-0.10961,-0.05238,0.00624,-0.06476,0.04408,0.1279,0.00562,0.10277,0.01467,0.03413,0.00109,-0.02497,-0.01898,0.02124,-0.00767,0.01169,0.06939,0.02196,0.01721,0.11582,-0.03618,-0.10097,0.09487,0.08117,0.09429,0.03122,-0.10736,-0.00249,0.08938,0.02635,-0.08063,-0.04617,0.00067,0.11012,0.07177,0.08992,-0.00768,-0.06905,0.00469,0.00448,0.04228,0.06567,0.01848,-0.01482,0.08331,0.0509,-0.04916,0.06793,0.06552,0.04448,-0.07787,0.07054,-0.01448,-0.01485,-0.1224,-0.00577,0.04518,-0.01118,0.02248,-0.04472]},{"domain":"algebra","key":"quadratic_roots","name":"Roots of a quadratic equation","package":"algebra-ai999x","example":"Solve x^2 - 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Minimum expected 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0.5?","v":[0.02966,-0.05672,0.07434,0.03264,-0.00714,-0.02202,0.09354,0.07189,-0.05223,0.1064,-0.10021,0.07092,-0.07206,0.06111,-0.04169,0.03263,0.08241,-0.07513,0.10627,-0.0279,-0.02793,0.02601,0.04106,0.07935,-0.08691,-0.02479,-0.08543,0.03269,0.05479,0.03636,-0.06552,-0.00273,-0.00126,0.00311,-0.0791,0.05908,-0.09203,-0.00651,-0.00332,0.03964,0.05175,-0.05054,0.08007,0.03021,-0.00852,0.00398,-0.00135,-0.09582,-0.01018,0.06169,0.07735,0.01383,0.04008,-0.02274,-0.11528,0.12394,-0.05238,-0.07745,-0.0083,-0.13251,-0.03788,-0.10831,0.06435,-0.04052,0.0094,0.02671,0.12578,-0.0305,0.00228,-0.13179,0.01754,-0.04543,0.06071,-0.05874,0.01432,-0.02285,0.06323,-0.02899,0.18912,0.05767,-0.08577,0.00446,0.01626,-0.07518,-0.06077,0.04368,0.05185,0.02529,0.01198,-0.10726,0.00729,0.08115,-0.00012,0.08672,0.02601,-0.12448,0.00462,0.11709,0.08318,-0.06103,0.02101,-0.04455,0.03879,0.08165,-0.00389,0.03198,-0.16098,0.04463,0.09176,0.03908,0.03378,0.11977,-0.08309,0.04962,-0.01,-0.02403,0.07005,-0.09499,-0.07644,0.03642,-0.10247,0.0444,0.01984,0.07727,0.01973,0.12283,-0.05828,-0.11997,0.02953,0.02441,0.01294,-0.04821,-0.08651,-0.02884,-0.10705,-0.02781,-0.01517,-0.06271,-0.12319,-0.10507,-0.01305,0.04581,-0.0454,-0.08371,-0.01104,0.02199,0.03139,-0.0092,-0.02402,0.05682,-0.00162,0.0111,0.1491,0.04347,-0.05957,0.01159,-0.10963,-0.14789,-0.03528,-0.06799,-0.00873,0.01882,-0.0567,-0.08195,-0.06497,-0.03284,-0.02402,0.0006,-0.03591,-0.03845,-0.03156,0.07146,0.0132,0.00137,0.04303,0.05463,0.01104,0.05299,0.08562,0.04657,-0.06751,0.03326,0.10869,0.00701,0.05831,-0.02349,-0.02188,0.01106,-0.00785,-0.06203,0.02042,0.01674,-0.00151,-0.02737,-0.08241,0.10153,-0.03444,-0.00734,0.10469,-0.00072,0.04304,-0.01139,0.03205,0.05396,0.06524,-0.0553,-0.06566,0.04888,-0.0029,-0.05334,-0.00554,-0.05084,0.05187,-0.01987,-0.00088,0.07642,0.02419,0.04169,-0.03388,0.06904,0.13919,-0.02037,-0.07266,0.01678,-0.06988,0.05651,0.00118,-0.03084,0.09853,0.06617,-0.04914,0.04871,-0.01946,-0.00873,-0.12186,-0.0218,-0.00774,0.04501,0.06621,-0.02566,0.01007,0.10732,0.01987,0.07972,-0.07844,0.0442,-0.01724,-0.01568,-0.00459,0.03582,-0.11234,8e-05,0.07057,-0.03912,0.07857,-0.10061]},{"domain":"bayesian_statistics","key":"beta_prior_from_mean_sd","name":"Beta prior from a mean and standard deviation","package":"bayesian-statistics-ai999x","example":"Find the beta prior with mean = 0.3 and standard deviation = 0.1.","v":[0.03021,0.07799,0.11319,0.06467,-0.03414,-0.03977,-0.00759,0.09178,-0.0621,0.03276,-0.01683,0.03217,0.0038,0.04121,-0.04044,0.0506,0.03785,-0.04498,0.02709,-0.04088,0.0057,0.03802,0.07526,0.10695,-0.06253,-0.06509,0.10245,-0.01286,0.04013,0.01945,0.00398,-0.01538,-0.01964,-0.00755,0.0288,0.01793,-0.00861,0.06105,-0.00288,-0.06704,-0.04281,0.02109,-0.06838,-0.01199,0.09368,0.09279,-0.02315,-0.11177,-0.02819,0.01581,-0.00807,0.01679,0.01397,0.03926,0.04264,0.09882,-0.10489,-0.10019,-0.03343,-0.10698,-0.13898,-0.0035,-0.04578,-0.05365,0.1204,0.1056,-0.02952,-0.05004,0.00701,-0.01796,-0.0733,0.00858,0.0018,-0.14221,0.06009,0.01206,-0.00691,0.02152,0.0468,0.13376,-0.04566,0.14898,-0.10246,-0.01539,0.09342,0.05321,-0.02237,0.1136,0.06093,-0.0095,0.04496,-0.05555,0.04002,0.01296,0.00575,-0.05671,-0.13222,-0.01752,-0.03945,-0.08,-0.06812,-0.03579,0.03775,0.03844,-0.0165,0.02491,-0.01243,-0.01203,0.14782,-0.00697,0.06303,0.09379,-0.08395,-0.08028,-0.04293,-0.0104,0.03187,-0.01603,0.00194,-0.10002,0.05346,0.00068,0.03313,0.11106,-0.028,0.03159,-0.07289,-0.06712,0.0483,0.00668,-0.04935,0.08754,0.01754,-0.00084,-0.02782,-0.11673,-0.06528,-0.08512,-0.11746,-0.09673,-0.01991,-0.0415,-0.01712,-0.00696,-0.0033,0.02439,-0.08052,0.04479,-0.05464,-0.03281,0.03056,0.11642,0.07755,-0.00811,0.04628,-0.06731,-0.01446,-0.04348,-0.01281,0.03327,0.00592,0.00015,-0.06336,0.08622,-0.09494,0.03009,0.0079,-0.0661,-0.12589,-0.08661,0.02007,0.13169,0.11575,-0.0243,-0.0133,-0.02975,0.02336,0.0366,-0.08855,-0.00992,0.00565,0.09958,0.04848,0.02045,0.08162,0.03906,0.01911,0.01908,0.00054,-0.07802,0.01967,0.00143,0.08178,-0.01852,0.11096,0.06609,0.0919,0.02334,-0.02673,0.06952,-0.08341,-0.00584,0.04253,-0.05231,0.18357,-0.05116,0.00815,0.0618,-0.07728,-0.09018,-0.03402,0.08866,0.04777,0.03008,0.01703,0.05523,-0.08931,-0.10957,0.082,0.12633,-0.02646,-0.04081,-0.02891,0.04295,-0.0589,-0.02234,0.05108,-0.04243,0.14467,0.08983,-0.02185,0.0244,-0.0387,-0.00244,-0.09156,0.01075,-0.00396,-0.01528,0.02918,-0.01719,0.03065,0.00716,-0.0405,0.03474,-0.05362,0.00976,0.01483,0.0289,-0.04944,0.0252,-0.00872,-0.03044,-0.05151,-0.16675,-0.11091,-0.09411]},{"domain":"bayesian_statistics","key":"break_even_probability","name":"Break-even (indifference) probability of two actions","package":"bayesian-statistics-ai999x","example":"Break-even probability for payoffs = [[100, -20], [40, 30]].","v":[-0.07584,-0.10741,0.05585,0.02809,0.1101,-0.00282,-0.00405,-0.05734,0.03497,-0.00214,0.04145,0.12933,-0.10352,0.04677,0.01881,-0.07917,-0.11397,-0.00387,-0.07656,-0.0671,0.03176,0.0654,0.09663,0.01434,-0.03685,0.04845,-0.09154,0.05104,0.11569,-0.04836,0.08487,0.14081,-0.11021,-0.03192,0.00379,0.08389,-0.06101,-0.01129,-0.01826,0.01525,0.10161,-0.03724,0.03089,0.10548,-0.01226,-0.09311,0.07137,0.04065,-0.01889,0.06463,-0.03647,0.03201,-0.02465,-0.03366,0.00173,0.12171,0.02122,-0.03644,-0.0389,0.02213,-0.10417,-0.00479,-0.00816,-0.07984,-0.02848,-0.12248,0.06004,0.03435,0.05018,-0.10647,0.05436,-0.02799,0.01988,0.05592,-0.0311,-0.01381,-0.06371,-0.03491,0.00119,0.06143,-0.04126,-0.01659,-5e-05,0.04192,-0.10178,-0.11937,0.06361,0.04574,-0.01697,0.06192,-0.0481,-0.03227,-0.04474,-0.01237,0.04682,-0.07036,-0.03942,-0.00644,-0.07722,0.07288,-0.02396,0.10601,-0.01142,0.00692,-0.00053,-0.02977,-0.07567,-0.00802,0.08,-0.09504,0.11621,0.06271,-0.07303,0.02722,0.08752,-0.1983,0.09097,-0.07525,-0.0032,0.02268,0.00975,-0.01762,-0.06899,-0.03882,0.02591,0.03946,-0.01333,0.04134,0.04681,0.15474,-0.02033,-0.01588,-0.02848,-0.05478,-0.05834,-0.00047,-0.02284,0.04279,0.042,-0.08261,0.12293,-0.06036,0.06491,-0.04412,0.06278,0.11156,-0.02647,0.02435,0.00672,0.03902,-0.00052,-0.01164,0.09337,0.03399,0.00363,0.04473,0.12703,-0.04443,0.02438,-0.00378,0.00796,0.00142,-0.01057,-0.11726,0.03742,-0.11928,-0.02879,-0.01467,-0.05165,-0.05745,0.01467,0.08965,-0.02019,0.0126,0.07753,0.03821,0.01549,-0.01672,-0.00479,-0.01268,-0.02735,0.04632,-0.03812,0.07393,-0.0366,-0.00105,-0.00552,0.07057,0.00101,0.05657,0.04227,0.16852,-0.06907,0.02861,0.01478,0.01771,-0.05068,-0.07617,-0.02789,0.0628,-0.02976,0.06909,0.09266,0.06381,0.03835,-0.09173,-0.0895,0.15119,0.03081,0.05864,-0.11146,0.02857,-0.08102,0.05605,-0.08237,0.02039,-0.02567,-0.02905,0.03891,-0.00533,0.07073,0.04783,-0.09522,-0.03139,-0.06009,-0.01461,-0.09126,0.03329,0.05461,0.02411,-0.04286,0.00199,0.07775,0.0359,0.01395,-0.03631,0.03713,-0.0816,-0.02103,-0.00036,0.12213,0.06261,-0.00824,0.01953,-0.03531,-0.15305,0.01946,-0.10554,-0.07812,-0.07719,-0.05259,0.06814,-0.04825,-0.0113,0.06572,-0.01481]},{"domain":"bayesian_statistics","key":"certainty_equivalent_exponential_utility","name":"Expected utility and certainty equivalent (exponential utility)","package":"bayesian-statistics-ai999x","example":"Exponential utility with risk tolerance = 500: outcomes = [1000, 0], probabilities = [0.5, 0.5]. Certainty equivalent?","v":[0.03024,-0.06562,-0.04022,0.13305,0.11107,0.08107,0.04512,-0.08657,0.06831,-0.01037,0.13661,0.05403,-0.08415,0.05613,0.00735,-0.15708,-0.02782,-0.08564,0.02683,-0.00807,0.08018,0.09118,0.01107,-0.03609,0.03082,0.07899,0.08545,0.02925,0.07639,-0.06987,-0.06993,0.16102,-0.06615,-0.10247,0.0055,0.02643,-0.02481,0.0259,0.03544,-0.00158,0.05173,-0.05495,-0.02053,0.07957,0.04816,-0.01907,0.05965,-0.09943,0.00469,-0.09012,-0.03406,-0.02825,-0.03942,0.00954,0.10039,-0.01932,-0.05344,-0.07461,-0.08211,-0.05454,-0.089,-0.0352,0.04184,0.00579,-0.14611,-0.13241,0.04034,-0.00268,0.02091,-0.00645,0.04572,0.02322,0.0332,0.02631,0.07889,0.16679,0.04555,-0.10353,0.08005,-0.02645,-0.03476,0.03196,-0.02319,-0.03264,-0.07777,-0.07816,0.02252,0.02356,0.02663,-0.12341,-0.05752,0.03197,0.03624,-0.01265,-0.01197,0.0448,-0.05354,-0.02357,-0.00226,0.02068,0.00017,-0.00494,-0.00586,-0.00211,0.10179,-0.01565,-0.06661,-0.02485,0.04945,0.08817,0.12566,-0.00296,-0.01674,0.04378,0.09507,-0.07148,-0.00525,-0.13529,0.05451,-0.00908,-0.08089,0.0022,-0.02583,0.02996,0.12698,-0.10281,0.07391,-0.0056,-0.06109,0.11547,-0.03493,-0.06157,-0.0806,-0.09631,-0.13782,0.02742,0.05195,-0.00016,-0.01733,-0.0199,0.04223,-0.11717,-0.04746,0.0698,0.00819,0.10786,0.00167,-0.00449,0.05531,0.02356,-0.01181,0.00881,0.03562,0.00466,0.00306,0.02175,0.0751,0.06147,-0.0164,0.01082,-0.02918,0.0089,-0.03373,0.02218,0.09622,-0.00099,-0.05468,-0.01967,0.00285,-0.05657,-0.03204,0.00312,0.04299,0.05855,-0.04182,-0.00586,0.02083,0.00929,0.09455,0.02372,-0.02838,-0.07222,-0.03723,-0.03813,0.08869,0.07792,-0.04794,0.07735,0.12995,0.06268,0.0722,-0.0853,-0.06486,-0.05242,0.06695,-0.00306,0.0429,-0.00084,-0.02291,-0.00364,-0.14158,-0.00965,0.20009,0.10323,-0.00486,-0.07848,0.00078,0.02186,0.00105,0.00044,-0.03002,0.11573,0.04973,0.03527,0.02121,-0.06666,-0.03503,-0.0559,0.00656,-0.02515,-0.1308,-0.00036,0.00468,0.02213,0.04092,-0.05436,-0.09383,0.03556,-0.02403,-0.02434,-0.00646,-0.0037,0.11141,0.12533,-0.05036,0.02948,-0.05351,-0.06268,-0.05502,-0.02457,0.05152,0.02978,-0.01225,-0.02505,0.00621,-0.03789,-0.04611,-0.03654,0.02883,-0.028,0.08338,0.02239,0.08029,-0.0963,0.03062,-0.02074]},{"domain":"bayesian_statistics","key":"certainty_equivalent_log_utility","name":"Certainty equivalent with logarithmic utility","package":"bayesian-statistics-ai999x","example":"Logarithmic utility: outcomes = [100, 400], probabilities = [0.5, 0.5]. Certainty 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mean with known variance: posterior from data","package":"bayesian-statistics-ai999x","example":"Normal-normal posterior: prior mean = 10, prior sd = 2, known sigma = 3, data = [12, 9, 14]. Posterior mean?","v":[0.08156,0.09285,0.13404,-0.06536,0.00795,0.03497,-0.03397,0.08947,0.0194,-0.03784,0.01005,0.0817,0.03169,0.06907,0.04884,0.00386,0.00236,-0.02155,0.06217,-0.04719,-0.03369,-0.05485,0.01103,0.08515,-0.08907,-0.0959,0.01056,-0.04353,0.02647,0.00796,0.06986,-0.02941,0.09854,-0.01949,-0.00177,-0.05198,0.05302,-0.02732,0.05814,-0.05329,0.01438,-0.02583,-0.07841,-0.03629,0.05117,0.00368,0.0355,-0.06889,-0.06499,0.05575,-0.08591,-0.05703,0.05726,0.02218,0.00467,0.01099,-0.07162,-0.04005,-0.03621,-0.10788,-0.10117,0.03077,-0.02482,0.00397,0.13555,0.08844,-0.05348,0.02301,0.1337,0.01441,-0.04979,-0.08516,-0.02712,-0.01847,0.04972,-0.01555,-0.07703,-0.01394,-0.054,0.12604,-0.0212,0.13246,-0.12358,0.03117,0.08826,0.07133,-0.08331,-0.00528,0.08506,-0.08024,0.05265,0.04482,0.00491,0.06721,0.01475,-0.02116,-0.05412,-0.00086,0.04104,-0.14281,-0.03351,0.02625,0.01947,0.08288,-0.01667,-0.0398,0.02074,0.00397,0.12344,-0.11696,0.06431,0.14186,0.00091,-0.02033,-0.08106,0.04101,0.03596,-0.06714,0.07736,-0.05746,0.01032,-0.02542,0.01017,-0.00179,0.05273,-0.06698,-0.0178,-0.04196,0.03947,0.05867,-0.02687,0.01939,-0.00439,-0.04454,0.09917,0.00604,-0.01344,-0.0237,-0.06706,-0.07456,0.00779,0.02666,-0.03999,-0.01716,0.0531,0.0383,-0.14883,0.00345,-0.04068,-0.11314,0.00613,0.07032,0.08578,0.03964,-0.02335,-0.08687,0.02103,-0.00851,0.01459,0.05039,-0.07071,0.11939,-0.01821,-0.03168,-0.0749,0.01651,-0.00952,-0.04725,-0.10085,-0.16342,0.00963,0.02037,0.03913,-0.00907,-0.05041,0.02055,-0.03414,0.0568,-0.09035,0.01027,0.01466,0.0666,-0.0134,-0.04073,0.0392,-0.00909,-0.02217,0.06101,-0.00484,-0.121,0.10311,0.07075,0.04526,-0.02649,0.21063,0.07757,0.05357,0.13449,-0.06363,0.11298,-0.00331,-0.01084,-0.00558,-0.07291,0.13704,-0.02638,-0.04161,0.0665,-0.04529,-0.12745,-0.01706,0.08138,0.11051,-0.09759,0.00569,0.00908,-0.06258,-0.02594,0.04525,0.03298,-0.03092,-0.05565,-0.03292,-0.04687,-0.01656,-0.03296,0.03317,-0.10682,0.05871,-0.01808,0.0022,-0.00525,-0.01958,0.0115,-0.0344,0.01204,0.06631,0.02653,0.04294,0.0484,0.00866,0.15189,-0.04561,0.04095,-0.0406,-0.00482,-0.03667,0.05553,0.01439,0.01603,0.04609,-0.00425,-0.08465,-0.16034,-0.07508,-0.02337]},{"domain":"bayesian_statistics","key":"normal_normal_summary","name":"Normal mean with known variance: posterior and credible interval from a sample mean","package":"bayesian-statistics-ai999x","example":"Normal prior with prior mean = 0, prior sd = 1; sample mean = 1 from n = 4 with known sigma = 2. Posterior mean and 95% credible interval?","v":[0.04097,0.11742,0.18928,-0.04908,0.02967,0.03443,-0.02668,0.06368,0.00234,-0.03053,0.03494,0.05557,0.05425,0.01007,0.0442,-0.0353,0.04547,0.01489,0.00396,-0.03659,0.00406,-0.06017,0.03231,0.0674,-0.01226,-0.03347,0.08052,-0.06997,0.05272,-0.01484,0.06004,-0.07436,0.03701,-0.02786,-0.0385,-0.02318,0.04105,-0.03024,0.05161,-0.04731,0.06975,0.03811,-0.12027,0.0275,0.13364,-0.0053,0.04137,-0.02518,-0.0087,-0.00816,-0.02211,-0.06049,0.03495,-0.01091,0.01754,-0.00766,-0.03522,0.02908,-0.01186,-0.12593,-0.1147,0.06581,-0.10213,0.02066,0.12715,0.15557,-0.02576,-0.06185,0.11521,0.01428,-0.07545,-0.02015,0.02422,0.03166,0.01231,0.00432,-0.12012,0.0329,-0.04473,0.1047,0.02088,0.10506,-0.12129,0.00495,0.09769,0.0578,-0.04337,0.00983,0.103,-0.0574,0.08384,0.07032,0.02346,0.05893,0.0033,-0.03153,-0.02397,0.04394,0.04547,-0.08504,-0.05863,0.06728,-0.02807,0.04589,-0.00059,-0.0389,-0.02526,-0.03084,0.2088,-0.07426,-0.00774,0.13885,0.03036,-0.03782,-0.09076,-0.00013,0.04687,-0.08457,0.03894,-0.02904,0.02741,0.00271,0.00558,0.00948,0.04703,-0.03986,-0.09177,-0.04605,0.01781,0.08907,-0.01602,0.00478,-0.03893,-0.06797,0.08059,-0.02934,-0.01879,0.0073,-0.03934,-0.04219,-0.0301,0.03596,-0.01226,0.02237,-0.02314,0.02657,-0.08859,0.00111,-0.07658,-0.09326,0.08464,0.09763,0.1271,-0.00077,0.03324,-0.06626,0.09309,-0.04398,-0.02189,0.03842,-0.03447,0.14244,-0.03213,-0.05403,-0.059,-0.02011,0.04749,-0.04068,-0.05313,-0.16236,-0.1283,0.05067,0.01267,0.03646,-0.03856,-0.01461,-0.11981,0.01186,-0.05526,-0.06019,0.0403,0.01997,-0.00315,-0.08747,0.04338,0.03139,-0.04272,0.02997,0.05771,-0.0629,0.08639,-0.03431,0.02669,-0.00881,0.16707,0.06963,0.04794,0.09048,-0.0451,0.10379,0.027,-0.01003,-0.05432,-0.05717,0.07868,-0.04014,0.00788,-0.00908,-0.08712,-0.14677,0.02249,0.07266,0.10169,-0.05849,0.05919,0.05859,-0.01991,0.00042,-0.005,0.04116,-0.09797,-0.08904,-0.02355,-0.10775,-0.05633,-0.05883,0.03168,-0.10742,0.06352,0.03071,-0.04391,-0.01507,-0.03006,0.03306,-0.01594,0.03915,0.01151,-0.03062,0.01886,-0.00068,0.02818,0.08108,-0.08248,0.02612,-0.05607,0.00143,-0.00475,0.05027,0.01867,0.00568,0.04441,0.04963,-0.02908,-0.09995,-0.10236,-0.09203]},{"domain":"bayesian_statistics","key":"normal_posterior_predictive","name":"Posterior predictive distribution of a new observation","package":"bayesian-statistics-ai999x","example":"Posterior predictive: prior mean = 0, prior sd = 1, known sigma = 2, sample mean = 1, n = 4. Probability that the next observation exceeds 0.5?","v":[0.10207,0.08846,0.18638,-0.03383,0.04915,0.01681,0.00431,0.06588,0.01721,-0.03592,0.02999,0.13025,0.0209,0.05678,0.0474,0.05339,0.09262,0.00664,0.04396,-0.026,-0.05188,-0.01649,0.01088,0.11171,-0.03933,-0.08327,-0.04113,-0.03514,0.10075,0.0052,0.00838,-0.01435,0.07741,-0.01238,-0.07124,-0.0145,0.05082,-0.06668,0.04048,-0.03175,0.0504,-0.03531,-0.02193,0.01311,0.07312,-0.01703,0.08984,-0.05351,-0.04248,0.01639,-0.03563,-0.09524,0.05211,0.02283,0.00223,-0.02746,-0.06384,-0.02391,-0.04304,-0.12025,-0.12081,0.01286,-0.06593,-0.04225,0.12083,0.05136,-0.03501,0.00436,0.14048,-0.00377,-0.01283,-0.07083,-0.03059,0.01888,-0.00146,-0.02547,-0.04871,0.00205,-0.09162,0.1608,-0.02331,0.08022,-0.02351,-0.01629,-0.0142,0.06979,-0.06263,0.00182,0.13311,-0.1021,0.05364,0.02977,0.00899,0.07463,0.00239,0.04095,-0.07241,0.06787,0.07807,-0.11759,0.00242,0.00275,0.06878,0.03765,-0.03999,-0.01503,-0.01369,0.04399,0.22807,-0.07097,-0.01594,0.12945,-0.01051,-0.0278,-0.043,0.02515,-0.00527,-0.04656,0.06522,-0.11368,0.00224,0.01809,-0.00298,-0.01203,0.00273,-0.0283,-0.02812,-0.04603,0.02459,0.03334,0.01118,-0.03822,0.00548,-0.1035,0.0925,0.04044,-0.00125,-0.03067,-0.11181,-0.08332,0.02442,0.05232,0.0226,-0.01551,0.02301,0.08545,-0.14985,-0.03368,-0.10657,-0.09198,-0.01038,0.03531,0.11951,0.05124,-0.07539,-0.06771,0.01214,-0.06572,-0.02944,-0.00357,-0.08891,0.17048,0.04003,-0.05702,-0.05413,-0.00105,-0.04129,-0.04399,-0.0947,-0.14913,-0.03054,0.03672,0.0031,0.024,0.04529,0.01122,-0.06517,0.05644,-0.03434,0.0231,0.01546,0.03707,-0.01065,-0.01619,0.0519,-0.00723,-0.02714,0.0378,-0.03637,-0.10414,0.10795,-0.01361,0.00522,-0.02642,0.14196,0.00838,0.0741,0.08827,-0.05021,0.112,-0.00166,-0.00715,-0.02679,-0.00918,0.13326,-0.06235,-0.03798,0.04597,-0.01081,-0.12135,-0.00318,0.09211,0.11364,-0.12692,0.02672,0.00105,-0.02596,0.04735,0.02454,0.08705,-0.00202,-0.02359,-0.05099,-0.06588,-0.07223,-0.05247,0.02535,-0.07081,0.07555,-0.0142,0.01231,0.01039,0.01404,-0.00597,0.00844,0.01827,0.01276,0.01529,0.05866,0.03171,0.01934,0.11597,-0.07962,0.0952,-0.03063,-0.06118,-0.02057,0.02867,0.00617,-0.01275,-0.01869,0.00985,-0.01523,-0.1095,-0.06003,-0.01507]},{"domain":"bayesian_statistics","key":"odds_to_probability","name":"Probability 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of a sum or linear combination (independent inputs)","package":"bayesian-statistics-ai999x","example":"Uncertainty of a sum: values = [12.3, 4.5, 7.1], uncertainties = [0.2, 0.1, 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degrees of freedom and expanded uncertainty (Welch-Satterthwaite)","package":"bayesian-statistics-ai999x","example":"Welch-Satterthwaite: uncertainties = [1], degrees of freedom = [10]. Expanded uncertainty at 95% coverage?","v":[0.06323,0.11718,0.05387,0.07218,0.03425,0.14409,0.00011,-0.03654,-0.01268,-0.06827,0.07436,0.07093,0.00144,0.02303,0.02127,-0.14945,0.00281,-0.06661,0.0531,0.00783,0.00594,0.11581,0.01932,-0.0085,0.03491,-0.00399,0.08263,-0.10039,0.04542,0.07024,-0.02331,0.06297,0.02576,-0.05099,-0.0371,0.015,-0.03348,-0.02566,-0.0444,0.02164,0.00041,0.06631,-0.01993,-0.06659,-0.00928,-0.06022,0.06121,0.0781,0.04615,-0.10703,0.01356,-0.04749,-0.01503,-0.02938,0.03769,-0.00895,0.10977,0.08009,-0.0501,-0.04818,-0.10528,0.14454,-0.01515,-0.02849,-0.04058,-0.05219,0.13448,-0.07801,0.04832,-0.05004,-0.00228,0.03003,0.02721,0.07063,-0.0799,0.06471,-0.06896,-0.02862,-0.00747,0.06917,-0.04164,-0.02738,0.05959,-0.0559,-0.0374,-0.0482,0.03826,0.03937,0.0142,-0.05208,-0.05587,0.10144,0.01801,0.01921,-0.07229,-0.09978,-0.11299,0.09035,-0.02468,-0.0274,-0.007,0.0402,0.01961,0.0649,0.10414,0.00266,-0.05032,0.00402,-0.01749,0.04569,0.0789,0.04628,0.0895,-0.00025,-0.05199,0.02994,-0.03497,-0.1295,0.07427,-0.02456,-0.0899,0.03789,-0.0461,0.12795,0.11256,0.03603,-0.02032,-0.06827,0.04257,0.02976,-0.06322,0.02839,-0.10242,-0.11296,-0.07477,-0.01429,-0.00223,0.11159,0.10209,-0.08388,-0.00279,-0.08444,-0.0726,0.1233,0.01778,-0.04086,0.10809,-0.05736,0.0198,0.09602,-0.0625,0.04612,-0.0121,0.02637,0.09224,-0.01296,0.03871,-0.09052,0.02684,0.06282,0.01769,-0.06743,-0.0539,0.09092,0.08747,0.07928,0.10518,0.06209,0.0281,-0.08461,-0.00224,0.13263,-0.03061,0.00891,-0.00097,0.05484,-0.11717,-0.0244,0.05148,0.01543,-0.06564,-0.09759,-0.04449,-0.14717,-0.02833,0.03769,0.00926,-0.07849,0.0524,0.05354,-0.03017,-0.13741,-0.04242,0.03367,0.00328,-0.0179,0.04674,0.02304,0.01839,0.08725,-0.02323,0.01515,-0.03694,-0.0254,-0.07683,-0.04279,-0.02574,0.02966,-0.01871,0.02646,0.09405,0.05114,0.03587,0.02511,-0.01395,0.01908,-0.03201,-0.03606,-0.02678,0.01278,-0.16024,-0.02333,0.03074,-0.05591,-0.00828,-0.05595,0.04302,-0.08281,-0.00266,0.03409,-0.00761,0.0019,0.00649,-0.02722,-0.03852,0.09958,-0.00478,-0.12487,-0.07472,0.02023,0.12167,0.00882,-0.0024,0.08238,-0.0449,0.078,-0.04127,-0.02533,0.11019,-0.1386,-0.01868,-0.03189,0.07387,-0.03754,-0.05032,0.02732]},{"domain":"calculus","key":"arc_length","name":"Arc length of a graph","package":"calculus-ai999x","example":"Find the arc length of y = x^2 from x = 0 to x = 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between two curves","package":"calculus-ai999x","example":"Find the area between y = x^2 and y = x from x = 0 to x = 2.","v":[0.00407,-0.21112,0.07549,0.00782,0.02265,-0.02238,0.03203,0.04599,0.01715,0.07874,0.05623,0.15101,-0.02143,0.01658,0.03271,0.01316,0.04738,-0.11345,-0.0248,0.09976,0.00298,0.00948,0.20617,-0.03129,0.00095,0.04451,0.01374,0.01987,-0.04772,-0.01251,-0.08739,0.05931,-0.08123,-0.00864,-0.08223,0.05979,0.04794,0.00299,0.03612,0.02754,-0.04551,0.1209,0.00921,0.03022,0.03627,0.00864,0.04201,0.06594,0.07373,0.03301,0.03027,0.08101,0.06961,0.02558,-0.01351,0.00683,-0.02237,-0.03026,0.079,0.01724,-0.01179,-0.08345,-0.01197,-0.03356,-0.01061,0.00126,0.05559,0.08161,0.04921,-0.03569,0.02172,0.01596,0.01641,-0.08743,0.08225,0.01704,-0.04175,-0.05371,0.00175,0.06436,0.0566,-0.09141,-0.0342,0.01641,0.04281,0.10543,0.02697,0.00445,0.02945,0.07174,-0.10246,-0.02583,0.03919,0.03554,-0.03895,-0.0841,0.19439,0.00519,-0.08424,0.05023,-0.04099,0.07088,-0.09382,0.0702,0.03051,-0.05427,-0.03058,-0.09148,-0.0062,0.01345,-0.02296,0.01258,-0.02483,0.06681,0.04251,-0.01824,-0.01794,-0.05209,0.0016,0.09498,0.00597,-0.02321,-0.0112,0.01478,-0.07015,-0.04661,-0.10993,-0.02294,-0.05793,0.02544,0.02245,-0.00437,0.02132,-0.03795,-0.12665,0.01865,0.09292,0.07225,0.05586,-0.0112,-0.03389,-0.12856,-0.00595,0.02744,-0.08725,-0.07389,-0.00918,-0.07917,0.1351,0.05508,0.0792,-0.01239,-0.05608,-0.07163,0.01329,0.03512,0.03043,-0.09829,0.05175,-0.04009,0.03017,-0.02322,0.07262,-0.00712,-0.01109,0.0408,-0.05154,0.03588,-0.00487,-0.00323,-0.08324,0.0307,0.08798,0.00134,0.06506,0.02476,0.03146,0.00202,-0.09294,-0.06881,0.01483,-0.08346,-0.09028,-0.02045,-0.03446,0.04133,0.00842,-0.05765,-0.003,-0.10765,-0.01315,0.17727,0.03837,0.08281,0.00227,-0.10243,-0.03445,-0.09031,0.07057,-0.04884,0.095,-0.00777,0.04149,-0.01192,0.04288,0.03915,-0.22151,-0.0418,-0.08253,0.01368,-0.02329,-0.03282,0.04855,0.07452,-0.04563,0.04242,-0.00265,-0.05301,0.01584,-0.00584,0.08812,0.04482,-0.07197,-0.13459,-0.11015,-0.01973,-0.03097,-0.00908,-0.03785,-0.0769,-0.03907,-0.0898,0.03645,-0.01227,0.07343,0.02325,0.08136,-0.11757,-0.01074,-0.07202,0.03124,-0.00213,0.0125,0.08902,0.03482,-0.15142,0.0065,0.04951,0.10486,0.05121,-0.02626,-0.05644,-0.08402,0.02884,-0.02319,0.05167]},{"domain":"calculus","key":"area_enclosed_curves","name":"Area enclosed by two curves","package":"calculus-ai999x","example":"Find the area enclosed by y = x^2 and y = 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of an arithmetic series","package":"calculus-ai999x","example":"Find the sum of the first 10 terms of the arithmetic series with first term 2 and common difference 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rate of change","package":"calculus-ai999x","example":"Find the average rate of change of f(x) = x^2 from x = 1 to x = 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value of a function","package":"calculus-ai999x","example":"Find the average value of f(x) = x^2 on [0, 3].","v":[-0.04358,-0.12459,0.07347,-0.03751,0.01407,-0.00175,-0.00895,0.07506,-0.07361,0.06082,0.07351,0.00279,0.04439,-0.01759,0.0699,0.01659,-0.03208,-0.00954,-0.12312,0.08462,0.03274,-0.07102,0.02219,-0.00697,0.01783,0.01806,0.04018,-0.0025,0.03239,-0.09761,-0.0442,0.08892,0.021,0.01093,0.00583,0.00038,0.08722,-0.1317,0.05533,0.11813,-0.09697,0.08067,-0.06258,0.03034,0.15579,-0.07573,0.01937,0.02727,-0.01684,0.01984,-0.02539,-0.03253,-0.02908,-0.03005,0.07604,-0.16378,0.09093,0.00235,0.01943,-0.02498,0.02523,-0.04915,-0.04149,0.0439,-0.07974,0.0567,-0.05613,0.06224,0.06254,-0.02087,0.01412,0.03644,-0.04122,-0.09355,0.09466,0.09687,-0.01599,0.0168,-0.04803,0.01484,0.05005,0.00244,-0.0631,-0.11285,0.02543,-0.10883,0.04954,-0.03733,0.0116,0.03274,-0.01482,0.03491,-0.02685,-0.04718,-0.07239,0.01318,0.0835,-0.03679,-0.0233,0.14477,-0.03497,0.04987,0.04882,0.02823,0.11234,-0.07222,0.03342,-0.0312,0.12077,0.01826,-0.08457,-0.02988,0.02166,-0.00612,0.03073,0.0035,-0.03128,0.0212,-0.0486,0.10221,-0.01751,-0.01149,0.01681,-0.00128,-0.06745,-0.06106,-0.09585,-0.0504,-0.08356,0.05888,0.026,0.06574,0.08203,-0.07289,-0.16852,-0.04512,0.08314,0.05641,-0.01562,0.14253,-0.07489,-0.04374,0.08381,-0.01284,-0.13009,-0.00467,0.01894,0.06254,0.05651,0.03395,0.00912,-0.10089,0.07411,-0.1473,0.07568,0.03835,0.06804,-0.13447,0.09355,0.01293,0.03024,0.01782,0.0443,0.04542,0.0121,0.00891,-0.04173,-0.07646,-0.03401,-0.05284,-0.03016,-0.0039,0.08955,0.00599,-0.06815,0.00944,-0.00379,-0.0473,-0.05354,0.07094,0.00767,-0.00828,0.01571,-0.03437,-0.05524,0.07391,-0.10454,0.08249,0.0921,-0.10668,-0.09998,0.04783,0.05727,0.02824,0.00011,0.03191,-0.03078,-0.01351,0.01018,0.00046,0.07578,-0.06086,-0.0788,0.02586,0.05782,-0.03339,-0.04909,-0.00716,0.03693,-0.01682,0.04989,0.05668,-0.07155,0.04827,-0.05866,0.04539,0.0276,-0.00497,0.04846,0.10097,0.1257,0.05209,0.00959,0.07286,0.05975,-0.09589,-0.02104,-0.01092,0.01325,-0.06102,-0.00064,-0.03534,-0.0982,0.04281,0.04013,0.06564,0.0994,-0.13453,0.02727,-0.00193,0.05735,-0.00923,-0.01128,-0.01455,0.08575,-0.12807,0.00354,0.01076,0.01609,-0.03942,0.0756,0.01857,-0.09606,0.01588,-0.1597,-0.05368]},{"domain":"calculus","key":"bessel_j","name":"Bessel 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J_0(1).","v":[0.0498,-0.06699,0.06429,-0.0185,-0.03366,-0.0879,0.06278,0.02672,0.04346,0.10843,-0.06903,0.05704,-0.01445,-0.08147,-0.00411,-0.08567,-0.00429,0.04113,0.03962,0.06265,0.0542,0.02104,0.02565,0.02199,-0.07169,0.04688,0.03714,0.0725,-0.01227,-0.08128,-0.08043,0.01911,0.08339,0.11429,0.10132,-0.08315,-0.04215,-0.06722,0.02012,0.07408,0.03584,0.09842,-0.09872,-0.01055,0.16527,-0.06499,-0.0706,0.0241,-0.00987,0.07675,-0.12022,-0.05056,-0.07043,-0.01785,-0.04114,0.01206,0.08302,-0.00202,-0.01131,-0.06765,-0.06295,-0.02986,0.01549,-0.03469,-0.03162,-0.05261,0.08034,-0.02183,-0.07339,-0.00861,-0.08809,-0.01833,0.01124,-0.02023,-0.00439,-0.02087,0.10514,-0.10032,0.14107,-0.12515,0.12621,0.01965,-0.01509,-0.12343,-0.01888,-0.08778,-0.05663,-0.03424,0.00194,0.06781,0.0567,-0.13091,-0.01233,0.05285,-0.02595,0.05897,0.00091,-0.12125,0.04763,0.09403,0.01221,-0.03184,0.09238,-0.10532,0.04067,0.08291,0.01128,-0.01726,-0.00714,0.06196,-0.08522,0.03396,-0.00838,-0.13906,0.02066,-0.01377,0.02914,0.03942,-0.07484,0.05633,-0.0256,0.00422,-0.05067,-0.02077,0.01811,-0.03485,-0.0007,0.01694,0.0444,0.04562,0.11636,-0.03958,0.06346,-0.00221,-0.00532,-0.00822,0.05766,0.033,-0.01046,0.04788,-0.09775,-0.00104,0.00103,0.01093,0.0243,-0.05761,0.13487,-0.00281,-0.0054,-0.03914,-0.04382,-0.01533,-0.04121,0.02579,0.05643,0.00688,0.0391,0.04744,0.04522,0.02191,0.14533,-0.10468,-0.11122,0.00565,-0.0138,0.05978,-0.00225,-0.15668,0.03953,0.10487,-0.00667,0.06492,-0.03253,-0.12656,-0.02441,0.04998,-0.11105,-0.0679,-0.09439,0.00684,-0.01351,-0.04899,0.08195,-0.06221,-0.06842,-0.00736,-0.03614,-0.00133,-0.00061,0.03713,0.01915,0.03505,0.10735,0.05825,-0.04343,-0.03723,0.02414,-0.07344,-0.01643,0.00834,0.01345,-0.06087,-0.03142,-0.0313,0.15752,-0.01249,0.0299,0.01764,-0.02976,0.09008,-0.09901,0.00476,-0.11163,0.06015,0.0452,0.0045,0.07337,-0.12183,0.16404,0.08226,-0.0103,-0.00323,0.02045,0.05216,-0.05001,0.05433,0.06498,-0.03123,0.03583,0.1088,0.02173,0.09721,-0.0111,-0.05653,-0.04468,-0.00585,-0.12626,0.02142,0.05933,0.06094,-0.07164,0.0177,-0.03908,0.04822,-0.04673,-0.08193,-0.02808,-0.05308,0.05274,0.0695,0.00494,-0.02502,-0.0189,-0.02408,-0.03476,0.02966]},{"domain":"calculus","key":"beta_function","name":"Beta 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3).","v":[-0.01154,-0.15647,0.06191,0.06163,-0.03332,-0.05011,0.047,0.05222,-0.08569,0.11915,-0.01569,0.11744,-0.06091,0.08732,0.02905,-0.01482,-0.00727,-0.02037,0.03188,-0.01037,0.03255,-0.0613,0.04733,0.03221,0.01952,-0.10966,0.08622,0.10575,0.03848,-0.00547,-0.05195,0.03066,0.0182,0.00347,0.04729,0.03041,-0.04942,-0.0616,-0.08032,0.01137,-0.02046,0.14354,-0.03702,0.00239,0.11542,-0.0091,-0.10551,-0.01256,-0.03333,0.07366,-0.05449,-0.0295,-0.05443,-0.02709,-0.03521,0.06847,0.01201,-0.04031,-0.01913,-0.00254,-0.00655,0.01053,0.06973,-0.10927,-0.05433,-0.00236,0.05924,-0.0274,-0.02868,-0.07346,-0.01826,0.00631,0.03447,-0.1551,0.02045,-0.10082,0.05368,-0.08848,0.12892,0.0181,0.0444,0.00972,-0.0465,-0.082,-0.00584,-0.05484,0.07998,0.13222,-0.03804,0.07158,0.00655,-0.12052,0.03424,-0.02169,0.00311,-0.00572,-0.0019,-0.06145,-0.10209,0.0146,0.01723,-0.0544,0.0575,0.00134,-0.00571,-0.03046,-0.01223,0.01601,0.05848,-0.00483,0.00661,0.03107,-0.04353,-0.05702,0.06397,-0.03147,0.05826,-0.0062,-0.05911,0.04851,-0.0308,0.04639,-0.00173,0.06239,-0.05117,0.06607,-0.0691,0.00313,0.03407,0.03999,0.0193,0.05737,0.07434,-0.03934,-0.15723,-0.09466,0.01705,-0.02707,-0.10613,0.03431,-0.07121,-0.03995,0.00447,0.02948,-0.04998,-0.05123,0.1087,0.05874,-0.07225,0.03564,0.01914,0.00698,0.04773,-0.06579,0.09464,-0.03358,0.03944,-0.14332,0.02548,-0.06883,0.10871,-0.07703,-0.05072,0.05334,0.00399,0.03315,-0.00308,-0.0408,-0.04755,0.00017,-0.03667,0.18196,0.02238,-0.02068,-0.02191,0.04234,-0.02439,-0.11596,-0.10004,0.07285,-0.04346,-0.02689,0.12531,0.00157,0.01632,-0.01094,-0.02026,-0.02229,-0.04255,-0.01918,-0.01867,0.04502,0.07262,0.01487,-0.05632,0.01997,-0.03867,-0.01023,0.00273,0.01709,-0.02804,0.01844,-0.00308,-0.00936,0.21505,-0.03213,-0.00227,0.06852,-0.00343,0.04869,-0.06816,0.04126,-0.13036,0.11582,0.01791,0.09625,-0.01664,-0.12158,0.09706,0.20586,0.06419,-0.05972,-0.02748,0.10224,-0.08378,0.07559,0.0756,-0.01532,0.08386,0.09997,-0.01524,0.08624,-0.08922,-0.035,-0.06169,0.05555,0.04596,-0.02838,0.04159,-0.03766,-0.04194,-0.0646,-0.00932,0.03656,-0.01626,-0.05193,0.03133,0.04686,0.0183,0.03399,0.01942,-0.07195,-0.06549,0.0696,-0.08248,0.0085]},{"domain":"calculus","key":"centroid_region","name":"Centroid 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3).","v":[0.02043,-0.05442,0.01109,-0.1092,-0.14674,-0.04973,-0.20047,0.03717,0.06469,7e-05,-0.10858,-0.01905,0.02797,0.00303,-0.02338,-0.07803,-0.13212,0.05651,0.01139,-0.05448,0.03284,0.02471,-0.02351,-0.00873,0.07462,0.03837,-0.03502,0.04138,0.02226,0.08722,-0.02742,0.00346,0.01537,-0.02878,-0.02258,-0.06169,0.00991,0.01374,0.0334,-0.00468,0.03779,0.01071,0.02504,0.00439,0.03801,0.06369,0.17034,-0.00082,-0.02598,-0.23468,0.06356,-0.07132,-0.1039,-0.10325,-0.10484,0.0018,-0.05125,0.02379,-0.02008,-0.05452,0.04643,-0.02909,0.03142,-0.05365,-0.07221,-0.04489,-0.0556,0.03552,-0.10357,0.01853,0.06253,0.06916,0.03516,-0.03313,0.04155,0.06915,0.1177,-0.04775,0.14383,-0.08469,-0.04867,0.02504,-0.10267,-0.16236,0.00886,0.11281,-0.06563,-0.09126,-0.01487,-0.12429,-0.00791,-0.04267,0.01065,0.10492,-0.0027,0.05792,0.00121,-0.01181,0.03016,0.04402,-0.02034,-0.09276,-0.03708,0.00536,0.02368,0.09718,-0.05733,-0.02767,-0.02744,0.05976,-0.01534,-0.0274,0.15801,0.00762,0.00599,0.04886,-0.02475,0.03678,-0.03324,-0.03119,-0.01207,-0.04028,-0.05287,0.0394,-0.04573,-0.02106,0.09926,0.01384,0.08413,0.02719,0.05995,-0.12104,0.00786,0.03455,0.01873,-0.05744,0.02828,0.01967,0.00546,-0.02722,0.10091,-0.06256,-0.03955,-0.07444,0.06354,-0.08784,0.01861,-0.04559,0.09278,0.124,0.02328,-0.11685,-0.07083,0.07601,0.06539,0.01876,-0.05354,-0.01499,0.04723,-0.02656,0.01556,-0.09708,0.06594,-0.02676,0.03517,0.01991,0.03812,0.05485,0.00447,-0.02146,0.05805,-0.05929,-0.0499,-0.01965,0.02258,0.03888,-0.00845,0.10367,0.04508,0.05592,0.00258,-0.03282,0.02524,-0.00886,0.09481,-0.01921,-0.05717,-0.01068,0.00049,0.04141,0.07127,0.00892,-0.00728,-0.00449,0.03503,-0.03424,-0.06915,-0.01118,0.0193,-0.02666,-0.02855,-0.04589,0.07085,0.02265,-0.04472,-0.01656,-0.01649,0.04939,0.12296,0.00889,0.00596,0.1718,0.04762,0.00673,-0.0244,-0.13817,-0.00621,0.04643,0.0592,0.10098,-0.02737,0.01295,0.05142,0.10967,0.0219,0.04885,0.04306,-0.02635,-0.00782,0.0111,-0.02319,-0.09007,0.04391,0.01391,-0.12876,-0.04601,0.09978,-0.04866,0.03327,0.02234,0.06625,-0.01499,0.11612,-0.00924,-0.05479,0.0054,-0.04135,0.04163,0.03592,0.03291,-0.00576,0.02892,0.01751,0.0178,-0.18014,-0.05483]},{"domain":"calculus","key":"curvature","name":"Curvature 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integral","package":"calculus-ai999x","example":"Evaluate the integral of x^2 from 0 to 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at a point","package":"calculus-ai999x","example":"Find the derivative of f(x) = x^3 - 2x at x = 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derivative","package":"calculus-ai999x","example":"Find the directional derivative of x^2*y at (1, 2) in the direction (3, 4).","v":[-0.06867,-0.06479,-0.03824,-0.1108,-0.09789,-0.02915,-0.11084,0.01844,-0.00383,0.00577,0.04264,0.0179,0.05771,0.04113,0.10686,0.03711,-0.05266,0.04677,-0.04275,0.0318,-0.03361,-0.08105,-0.0562,-0.02671,-0.0028,-0.04822,-0.07723,0.06369,-0.05457,0.03967,0.00135,-0.02003,0.0809,0.04894,0.10614,0.0241,0.04152,0.04807,0.085,0.02101,0.14849,-0.00388,0.10189,-0.04294,0.09709,0.04461,0.12399,0.05295,0.06019,-0.07831,0.03841,0.05725,-0.18691,-0.03917,-0.07833,-0.06564,-0.02956,-0.05417,-0.12599,-0.04605,-0.05528,-0.02542,0.06821,-0.06877,0.02109,0.04704,-0.11062,0.01229,-0.11138,0.0464,-0.02157,-0.03509,0.05816,0.15549,0.08165,-0.07423,0.05301,-0.11181,-0.00356,-0.13787,0.02445,0.04929,-0.13215,-0.06307,-0.0277,0.04116,-0.06985,-0.03436,-0.15359,-0.05225,-0.03558,-0.12727,0.06625,0.02391,-0.07635,0.05829,-0.04228,0.0,0.13909,0.02049,0.04174,-0.00192,-0.05303,-0.03398,-0.01525,0.06692,0.0847,0.07392,0.0139,0.05549,-0.01444,0.04521,0.07561,0.03608,-0.00412,0.02321,-0.05607,0.08555,-0.05475,0.04592,0.08019,0.05445,-0.04323,0.02554,-0.00059,-0.07165,-0.00377,0.01554,0.07235,-0.04792,-0.03737,-0.0393,0.04741,-0.03346,-0.00112,0.099,0.0381,-0.04518,-0.03385,0.03056,0.01793,-0.04125,-0.01197,-0.12172,0.15698,0.00107,-0.00167,-0.02328,0.01201,0.1006,-0.00392,-0.07344,0.05648,0.05507,-0.00059,-0.01706,-0.00543,-0.05714,-0.0065,-0.08158,0.04417,-0.0412,0.09126,0.02406,0.00438,0.03378,-0.02076,0.03408,0.03922,-0.06609,-0.01803,-0.0461,0.00618,0.03018,-0.00815,0.04038,0.09775,0.07441,0.0032,-0.00398,-0.00121,-0.05628,0.0368,0.01127,-0.06398,-0.04155,0.03477,0.07789,-0.00448,-0.06184,0.06508,0.05787,-0.02079,-0.12979,-0.04202,-0.06975,-0.10931,-0.01122,-0.00951,-0.02312,-0.00443,-0.04375,0.02369,-0.02003,0.05616,-0.01458,0.05868,0.10991,0.03732,0.01753,0.02654,0.20179,-0.01348,-0.00689,-0.0396,-0.08268,0.03825,0.0906,0.05323,0.0681,-0.02325,-0.03059,-0.01525,0.09748,0.04166,-0.01926,0.01481,-0.02231,-0.02427,-0.0739,-0.06302,-0.02426,-0.061,-0.03883,0.03532,0.07141,0.05427,-0.01181,-0.04173,0.09169,-0.05276,0.00953,0.08479,-0.00047,0.05864,-0.02549,-0.02952,0.08639,0.07222,-0.08029,0.05825,-0.06986,-0.03575,-0.14966,0.02211,-0.02277]},{"domain":"calculus","key":"disk_volume","name":"Volume of revolution (disk method)","package":"calculus-ai999x","example":"Find the volume when y = x^2 from x = 0 to x = 1 is rotated about the 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the divergence of F = (x*y, y*z, x*z) at (1, 2, 3).","v":[0.05064,-0.03454,0.05234,-0.05965,-0.11167,-0.06525,-0.22063,-0.04478,-0.02361,-0.14583,-0.058,0.00438,-0.04427,-0.05163,0.02427,-0.07682,-0.17068,0.05293,-0.08864,-0.00032,-0.00491,0.03125,-0.04182,-0.00256,0.07431,0.04392,-0.10323,0.01967,0.06169,0.06761,-0.02119,-0.00837,0.01464,-0.01285,0.00473,0.00904,-0.04642,-0.02185,0.00641,-0.03825,-0.03314,0.03473,-0.01655,-0.01869,0.02511,0.03678,0.08912,-0.00659,-0.05985,-0.07614,0.04971,-0.06507,-0.07942,-0.02581,-0.09971,0.00468,0.03198,0.0408,-0.04403,-0.0769,0.04994,0.05877,0.01927,-0.07632,0.05053,-0.09758,0.02036,-0.03133,-0.02874,0.07305,0.08579,0.05233,0.05611,0.01396,-0.07707,0.05532,0.05276,-0.01981,0.0868,-0.06423,0.0384,0.0358,-0.10421,-0.03254,0.00113,0.07687,0.02848,-0.09244,-0.09501,-0.0827,-0.04978,-0.09021,-0.01179,0.07939,0.03058,-0.02704,-0.02694,-0.0038,0.06397,-0.01523,0.04192,-0.11769,-0.01635,0.00183,-0.03724,0.14207,0.01334,0.00969,0.07708,0.08488,-0.06604,0.02491,0.08135,0.04079,-0.00948,-0.03135,-0.05178,0.07007,-0.01404,-0.06499,-0.06137,-0.00851,-0.20618,0.00179,0.09272,-0.02979,0.06791,0.02637,0.17371,0.02451,-0.0047,-0.11599,0.08251,-0.01743,-0.02152,-0.05147,0.02822,-0.01326,-0.01953,-0.06681,0.01061,-0.00126,-0.02494,-0.10019,0.10171,-0.05212,0.07088,-0.04109,0.12504,0.13221,0.04539,-0.05513,0.03992,0.07686,0.11623,-0.03844,0.00825,0.01874,0.07169,0.00078,0.06884,-0.07634,-0.00713,-0.04877,-0.06707,0.00848,0.1607,0.0606,0.02271,-0.06214,0.08352,-0.0644,-0.08948,0.03905,0.0743,0.04693,-0.02171,0.11073,0.0355,0.00541,0.07835,0.03916,-0.09045,-0.0262,0.07573,0.00838,0.01555,0.02075,0.13164,-0.04462,0.00591,0.01855,0.00845,0.01725,-0.02163,-0.05162,0.00716,0.03628,-0.02174,-0.02805,-0.07316,-0.03045,0.0567,-0.0224,0.03968,-0.01842,0.0059,0.0435,0.03244,-0.0034,0.00429,0.0863,0.08194,-0.01126,-0.02525,-0.09909,-0.02118,0.03135,0.01427,0.01092,0.00467,0.04489,-0.00259,0.07108,0.016,-0.00987,0.03043,-0.06672,0.0065,0.08908,0.00574,-0.0535,-0.01389,-0.05936,-0.08892,-0.04222,0.09412,0.01243,-0.04903,0.03895,0.17916,0.0093,0.11775,-0.02548,0.11115,0.03953,-0.07934,0.02063,0.10084,-0.03567,-0.02855,-0.00118,-0.03669,-0.01579,-0.06207,-0.04353]},{"domain":"calculus","key":"divergence_theorem_box","name":"Outward flux through a box (divergence theorem)","package":"calculus-ai999x","example":"Find the outward flux of F = (x^2, y^2, z^2) through the box [0, 1] x [0, 1] x [0, 1].","v":[0.03536,-0.04943,0.0533,0.00297,-0.12235,0.00397,-0.15792,-0.13885,-0.0412,-0.04174,-0.03239,-0.01449,-0.09485,0.01647,0.04643,-0.00182,-0.12261,0.10191,-0.07075,0.03453,0.05059,0.07385,-0.02225,0.08547,-0.0092,0.02422,-0.07995,0.1036,-0.01368,0.06791,0.08557,-0.02835,0.02656,-0.05897,-0.09967,0.02569,-0.02896,-0.06069,-0.04701,0.01124,-0.03589,-0.01604,-0.06964,0.03555,-0.02271,0.00208,0.10037,-0.05574,-0.00177,0.00743,-0.02383,-0.13714,0.02434,0.01483,-0.03649,0.02756,0.0896,0.06407,-0.05504,-0.04368,0.00501,0.02561,-0.04095,0.00401,0.053,-0.04143,0.11161,-0.05106,0.00394,0.00955,0.04246,-0.05568,0.0585,0.03238,-0.03052,0.0937,0.07953,-0.05175,0.03099,-0.05471,0.05965,0.05376,-0.0755,-0.01723,-0.0453,0.09744,-0.03865,-0.01752,-0.05316,-0.04202,-0.04222,-0.0485,0.01051,0.10589,0.07458,0.04676,-0.00544,-0.0306,0.1597,0.01752,0.07536,-0.02857,0.00723,-0.08539,0.02147,0.0177,-0.00369,-0.00967,0.10043,0.05227,-0.0697,0.02159,0.11888,0.0054,0.09038,-0.09124,0.03515,0.06404,-0.04515,-0.05744,-0.11632,0.03436,-0.15233,0.03628,-0.01432,0.03438,0.04568,0.02128,-0.00702,0.07464,0.03538,-0.08269,0.12939,-0.00884,-0.00292,-0.06938,-0.00038,0.03415,0.01582,-0.09201,-0.10364,-0.09301,-0.13538,-0.08629,0.06143,-0.11424,0.0839,0.01361,0.14964,0.07473,-0.05175,-0.05301,0.03795,0.0322,-0.00128,-0.04034,-0.04433,0.00361,0.11925,0.0162,0.05863,-0.08847,-0.00347,-0.06529,-0.04765,-0.01961,0.19579,-0.00386,0.00378,-0.06709,0.0379,-0.0029,-0.06283,0.0407,0.01977,0.04472,0.02794,0.03435,-0.04359,0.03668,0.04805,-0.02858,-0.06309,-0.02684,-0.00094,0.0413,-0.05542,0.00164,0.14407,-0.08326,0.0116,0.00278,-0.01847,-0.03717,-0.0407,-0.02975,0.04299,0.08033,-0.09095,0.01325,-0.07141,-0.02572,0.04191,-0.0189,0.06022,0.01198,-0.00691,0.05914,0.0205,0.01728,-0.0341,0.04644,0.16283,0.04778,-0.03844,-0.05863,-0.03449,0.01781,0.07387,0.00843,0.05888,0.0638,-0.08792,-0.01709,0.03633,-0.07049,-0.07228,-0.05144,0.0293,0.06705,-0.01116,-0.05037,-0.09649,0.04476,-8e-05,-0.04767,0.07712,0.00824,-0.10055,-0.01735,0.01061,0.0299,0.15229,-0.01378,0.10073,-0.04248,-0.03873,0.03351,0.15439,0.00926,0.01585,-0.05565,-0.02002,0.00768,-0.0671,-0.03458]},{"domain":"calculus","key":"double_integral_rectangle","name":"Double integral over a rectangle","package":"calculus-ai999x","example":"Find the double integral of x*y over [0, 2] x [0, 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integral over a region","package":"calculus-ai999x","example":"Find the double integral of x*y over the region 0 <= x <= 1, x^2 <= y <= 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extrema on a closed interval","package":"calculus-ai999x","example":"Find the absolute maximum and minimum of x^3 - 3x on [0, 2].","v":[-0.06424,-0.11979,-0.05526,0.05617,-0.01476,0.07433,-0.00939,0.01758,-0.0289,-0.03435,-0.08778,0.1323,0.00038,-0.01446,0.06157,0.01105,0.0913,-0.08628,0.05718,-0.01695,0.00482,-0.05236,0.05077,-0.06911,0.10768,0.05322,0.04489,0.09075,0.08384,0.02267,-0.00483,0.0091,-0.03555,0.06527,-0.08695,-0.06134,-0.00846,-0.04125,0.08809,-0.05885,-0.07505,-0.01668,-0.00017,0.03613,0.10664,0.00915,0.02155,-0.04284,0.12586,0.03789,0.14592,0.01285,-0.04823,0.03246,-0.06063,-0.1264,-0.02464,-0.05333,0.09005,-0.03529,-0.05157,-0.05985,-0.01454,0.02063,-0.02159,-0.038,-0.05359,0.0071,-0.01678,-0.00665,-0.03528,0.09181,0.05603,-0.01657,0.05839,-0.00427,0.01396,-0.04802,0.1057,0.09882,0.13416,0.03956,-0.11321,-0.01303,0.03145,0.09968,-0.04473,-0.03,-0.03575,-0.0523,-0.00139,0.04989,-0.02136,-0.00956,-0.01516,-0.08565,0.11902,-0.04132,-0.07436,0.18618,-0.07467,0.05313,-0.08397,-0.03124,-0.02289,0.03221,-0.11821,-0.10455,-0.11888,0.00948,-0.04654,0.07178,0.02251,0.05206,0.06801,-0.02069,-0.00627,-0.00995,-0.0348,0.13782,0.15653,0.07326,0.04092,-0.06807,-0.09688,0.01737,0.05658,-0.08245,0.04829,-0.02088,-0.06678,-0.00727,0.02644,-0.04565,-0.08463,0.01818,0.02011,0.01931,0.1268,0.05707,-0.00576,-0.09749,0.07906,0.02714,-0.14736,-0.0445,0.05395,-0.07274,0.0936,-0.04218,-0.01826,-0.08025,-0.0446,-0.11052,0.01094,0.08123,-0.01149,-0.00934,-0.10182,0.02513,0.00997,0.001,-0.02452,0.01449,-0.01404,0.05709,0.06809,-0.05583,0.05129,0.00071,-0.07407,-0.04259,0.05922,0.00594,-0.0416,0.0124,0.00964,-0.0338,-0.00687,-0.01901,0.00248,-0.05973,-0.07552,0.05998,-0.03705,-0.01644,-0.05394,0.113,0.07881,0.01131,-0.07185,-0.05116,0.05285,0.05898,-0.01236,-0.00234,-0.04997,-0.0745,0.0995,-0.02866,0.06029,0.07487,-0.01151,0.08597,0.0145,0.02561,-0.05382,-0.02178,-0.13274,-0.04665,-0.04656,0.0317,0.05976,0.02262,-0.08646,0.18002,-0.07421,0.0432,0.00976,0.03102,0.01944,0.05721,-0.08416,-0.09275,0.00783,0.07658,-0.00193,-0.0055,-0.11355,-0.08506,0.07726,-0.0196,-0.02855,-0.0075,0.06093,0.09762,-0.00524,-0.03209,0.01172,-0.04336,-0.00671,0.04972,-0.00616,0.05364,0.01291,-0.0285,-0.05163,0.00148,-0.08519,-0.03449,0.05045,0.05807,0.09092,0.02809,0.02515,0.00792]},{"domain":"calculus","key":"fourier_coefficients","name":"Fourier coefficients","package":"calculus-ai999x","example":"Find the Fourier coefficients of order 2 of f(x) = x on [-pi, pi].","v":[-0.0115,-0.05436,-0.0502,0.0075,0.06291,0.01506,-0.00438,0.06494,-0.08694,0.05406,-0.01248,0.01139,-0.05849,-0.03065,0.06284,-0.04409,-0.02602,0.05046,-0.03149,-0.02016,-0.00236,-0.00025,0.0317,-0.052,0.02834,-0.13507,0.05575,0.01521,-0.0125,-0.08352,-0.02902,0.06522,0.07098,0.02025,0.12649,-0.10262,0.09102,-0.01517,-0.0168,0.14705,-0.02591,-0.05182,0.08951,0.03779,0.01336,0.02441,-0.10748,0.16909,-0.018,-0.05737,-0.09732,0.05268,-0.01289,-0.07675,-0.06826,-0.08367,0.09949,-0.02418,0.11694,0.0487,0.05894,-0.01879,-0.00106,-0.01692,-0.00857,0.11249,0.05553,0.00366,0.00672,-0.02892,-0.00691,-0.06889,-0.13576,-0.09226,-0.00045,0.05335,-0.0104,-0.05712,0.08444,-0.07009,0.09581,0.0311,0.05454,-0.06678,0.12033,-0.12874,-0.01264,0.03634,0.00713,-0.04341,0.06878,-0.03191,-0.01942,-0.06494,-0.01981,-0.02685,0.0095,-0.10168,0.04123,-0.05823,-0.00836,0.05878,-0.05473,-0.0033,0.01832,0.03904,-0.02794,0.01066,0.08097,-0.07772,0.04308,-0.06994,0.17459,0.00572,0.01327,-0.07853,0.02492,0.00235,-0.01709,0.01333,-0.10926,-0.00825,-0.03352,-0.0786,0.00569,0.03779,-0.02861,-0.05732,0.06352,0.0374,0.08918,0.01391,0.07297,-0.03856,-0.1155,-0.04102,0.04396,0.08727,0.03836,-0.0209,-0.03735,-0.13758,0.07178,0.01288,-0.01166,-0.02154,0.08049,-0.01111,-0.06547,-0.0161,-0.05652,-0.00846,0.04842,-0.06851,0.05335,-0.12205,0.12389,0.02012,-0.06403,-0.02806,0.00563,-0.07545,-0.09791,0.04775,0.06623,0.01609,0.00513,-0.06859,-0.03894,0.10365,-0.00741,0.03427,-0.01868,0.08499,-0.0423,0.07464,-0.08295,-0.04944,-0.0367,-0.06266,-0.04823,0.02279,-0.09345,-0.02486,-0.07443,-0.0627,-0.02481,0.04738,0.04027,0.06015,0.06402,0.12138,0.01098,-0.0148,-0.01481,-0.04627,0.06464,0.00423,0.03988,-0.01197,0.12964,0.01998,-0.13298,0.03635,0.02076,-0.04107,0.07661,0.02869,0.01397,-0.01526,-0.02363,-0.07247,0.00321,0.09635,0.11276,0.11289,-0.0249,0.04363,0.11943,-0.01713,-0.07611,0.03069,0.01336,0.07217,-0.03632,0.01553,0.08467,0.0566,0.07297,-0.03436,-0.0679,-0.02484,-0.14355,-0.04241,-0.07961,-0.01865,0.07384,-0.08494,0.00055,0.03401,0.12152,-0.00244,-0.00311,0.00907,0.04166,-0.02186,0.01566,-0.09832,0.08861,0.06275,0.05524,0.07752,-0.04978,-0.02501,-0.10721,-0.0051]},{"domain":"calculus","key":"ftc_derivative","name":"Derivative of an integral (fundamental theorem)","package":"calculus-ai999x","example":"Find the derivative of the integral from 0 to x^2 of sin(t) dt at x = 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quadrature","package":"calculus-ai999x","example":"Use 2-point Gauss-Legendre quadrature to approximate the integral of x^3 + x^2 from 0 to 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sum of a geometric series","package":"calculus-ai999x","example":"Find the sum of the first 4 terms of the geometric series with first term 2 and ratio 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of an infinite geometric series","package":"calculus-ai999x","example":"Find the sum of the geometric series with first term 3 and ratio 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the gradient of x^2 + y^2 at (1, 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2].","v":[-0.03456,-0.07259,0.12149,-0.03409,-0.06612,-0.11574,-0.01294,0.03317,-0.10097,0.00364,0.00278,0.03144,-0.08877,-0.02112,-0.06845,-0.04973,-0.09844,-0.05108,-0.07553,0.11485,-0.00547,-0.02257,0.08059,0.06065,-0.00033,0.06616,-0.07602,0.03976,-0.06377,0.05237,0.10651,0.05462,-0.00307,-0.03676,-0.04169,0.07898,-0.05987,-0.06883,-0.02454,-0.01068,0.05887,0.05502,0.06219,0.01988,0.06922,0.06014,0.10854,0.12242,-0.00672,0.04226,-0.03061,-0.02614,0.04966,-0.00402,-0.00584,0.0316,0.07524,0.09959,0.05353,0.04411,-0.06684,-0.04177,0.00234,-0.0304,-0.06647,-0.08986,-0.01056,0.02955,-0.06458,0.00621,0.01615,-0.03931,0.03925,-0.08998,0.05573,0.03977,0.0198,0.08223,-0.0163,-0.033,0.03054,-0.04745,-0.02948,-0.03551,-0.07458,0.12816,0.09617,0.02916,0.04955,0.00767,-0.0663,0.0081,0.00709,0.13412,0.03422,-0.00158,0.13629,0.02488,0.00972,-0.00413,-0.00059,0.0393,-0.07513,0.03684,0.09018,-1e-05,-0.09348,-0.04462,0.05092,0.03265,-0.13456,-0.10476,0.11306,0.01134,0.0095,0.00222,0.012,0.05545,-0.04727,-0.01028,-0.18629,0.02119,-0.07859,-0.01667,-0.01092,0.05056,-0.02143,0.10324,0.02365,0.11222,0.10534,-0.06651,0.01884,0.00753,-0.08205,0.02956,0.05819,0.07758,-0.00525,-0.06571,-0.02504,-0.18813,-0.00582,-0.13601,0.07314,-0.12875,0.08826,-0.06066,0.11465,0.07722,0.02418,-0.04107,0.08948,0.02822,0.13948,-0.03657,0.02307,-0.05678,0.03379,0.0695,0.03783,-0.02887,0.03731,-0.07779,0.03125,-0.12252,0.05567,-0.0429,-0.07694,0.05907,-0.08675,0.00434,0.02202,-0.0583,-0.06009,0.03799,0.03496,0.03586,-0.04489,-0.02343,-0.01523,0.05432,-0.04985,-0.08023,-0.04029,0.0475,-0.03655,-0.06661,0.01173,-0.10806,0.0043,0.07807,0.02691,0.07792,0.01413,-0.13036,-0.02744,-0.00628,-0.00869,-0.01661,0.08246,0.00096,0.03749,0.0734,-0.01767,-0.01133,-0.04305,-0.00658,-0.0147,-0.02893,-0.00289,-0.04393,0.09482,0.10561,0.081,0.04215,0.0031,-0.02193,0.00467,-0.0175,0.06301,0.03238,-0.05888,0.0641,0.02478,-0.0066,-0.1047,-0.0368,0.00626,0.01803,0.01228,-0.04258,-0.0108,0.03399,-0.00984,-0.13266,0.10886,-0.05915,-0.02987,-0.03882,0.04657,-0.04659,0.06737,0.00249,-0.01708,-0.15309,-0.01013,-0.07663,0.01798,0.04993,-0.05635,0.03769,-0.01617,0.04053,-0.10707,-0.0355]},{"domain":"calculus","key":"hessian_classification","name":"Second 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0).","v":[-0.05536,-0.03207,-0.03238,-0.01601,-0.01613,0.06258,-0.03911,-0.0104,0.08299,-0.03822,-0.15145,0.00856,-0.03964,-0.13368,0.02618,0.04403,-0.00617,0.06246,0.08395,0.01026,-0.12018,-0.01356,0.03172,-0.04572,-0.10429,-0.00583,0.01756,0.05521,-0.00639,0.00414,-0.09597,-0.04982,-0.00236,-0.00694,0.1211,-0.02898,-0.06784,-0.00106,0.0619,-0.09266,0.08729,-0.02242,-0.1147,-0.01925,0.04701,0.00289,0.03759,0.00127,0.07055,0.07805,0.15835,0.00413,-0.10117,0.00848,-0.02895,0.0328,-0.02958,-0.00155,-0.01943,-0.02037,0.00052,-0.03583,0.09643,0.01802,-0.04372,0.02796,-0.12068,0.04248,0.03866,0.05074,-0.00628,-0.06892,0.03808,0.0363,0.02485,-0.07579,-0.00087,-0.09461,0.08219,-0.02784,0.06706,0.04298,-0.1249,0.03335,-0.01559,0.00764,-0.10205,-0.02201,-0.17052,0.08252,-0.04632,-0.03783,0.00789,0.16916,-0.04551,-0.02575,-0.00431,0.00678,-0.11005,-0.00719,-0.05266,0.05653,0.01528,-0.07687,-0.07077,0.13842,-0.00892,-0.00874,-0.1688,-0.00544,0.05891,0.00128,0.02887,0.00266,0.03228,-0.08289,0.03033,0.04575,-0.07281,0.0536,0.04394,0.0629,0.00371,-0.00559,-0.03639,-0.03204,-0.06755,-0.01511,0.12375,-0.02937,-0.00693,-0.03001,-0.0148,0.02053,-0.0592,0.14906,-0.11639,0.06022,0.08935,0.00049,-0.01675,-0.10438,0.01259,-0.0661,0.07785,-0.0022,0.09458,0.00147,0.03336,0.01682,0.01477,-0.04581,-0.07349,0.03161,0.12949,0.03016,0.09241,0.04393,-0.11272,0.04872,0.09243,-0.03383,-0.08422,0.02025,0.02073,0.00953,-0.01795,0.07732,0.02056,0.00953,-0.05639,-0.0451,0.04549,-0.09759,0.04757,-0.03875,0.01011,0.0258,0.0753,-0.07314,-0.02311,0.0179,-0.06705,0.05161,-0.0416,0.00656,-0.03976,0.01027,-0.0225,0.03512,0.07833,0.04987,-0.08197,0.05832,0.00684,-0.04974,-0.06715,-0.05889,0.07409,-0.14831,0.0316,0.07523,0.0286,-0.05222,-0.05335,-0.06222,0.04181,0.13028,-0.06636,-0.01163,0.01477,0.05295,0.10528,-0.04484,-0.06232,0.07596,0.01543,0.07315,0.00761,0.01991,-0.06897,-0.00332,-0.07544,0.07853,0.08658,0.10755,0.00413,-0.0577,-0.08626,-0.03778,0.05505,0.03905,-0.0106,-0.04956,0.01045,0.01691,0.04721,0.09322,0.07433,0.10039,0.06068,-0.05956,0.06383,-0.00186,-0.0757,0.0374,-0.06635,0.04244,0.08106,-0.10894,-0.07173,0.04172,-0.05761,-0.00113,0.05063,-0.00801]},{"domain":"calculus","key":"implicit_derivative","name":"Implicit 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infinity.","v":[0.05671,-0.07603,0.01332,0.02026,0.00098,-0.05793,-0.04168,0.006,-0.09298,0.02786,-0.01704,0.15132,-0.06069,0.00836,0.03175,-0.00592,-0.10956,0.03941,-0.11771,0.09772,-0.03316,0.09612,-0.0027,-0.04984,0.03628,-0.03867,-0.08932,0.08078,0.00059,-0.06423,-0.05617,0.07715,0.00372,-0.04639,-0.01619,0.03033,-0.0295,-0.05719,0.0258,0.05718,0.0313,0.07875,-0.02659,0.09037,0.18214,-0.04281,0.03578,-0.01852,-0.03695,0.06832,0.02308,-0.06394,0.03361,0.07391,-0.0124,-0.11013,0.04446,0.03214,-0.01891,-0.03695,0.02977,0.02574,-0.02731,-0.01304,-0.1379,-0.05879,-0.00889,-0.05305,0.08799,0.00821,0.10136,-0.04579,-0.03748,-0.04756,0.12417,0.01398,-0.0022,0.03833,-0.0722,0.01216,0.02905,0.0557,-0.08215,-0.09029,0.00252,-0.00266,-0.03062,0.04104,0.07114,0.02625,-0.02201,0.15619,-0.08135,0.07551,0.14174,0.01809,-0.01561,-0.1156,0.02967,0.04588,0.04923,0.03412,-0.05802,0.11249,0.0428,-0.08425,-0.0118,-0.02726,0.06822,-0.05023,-0.12606,0.03162,0.02426,0.09344,0.08983,-0.0591,-0.02043,0.05354,0.03595,-0.00896,-0.01014,0.01407,0.00147,-0.01359,-0.01825,0.09253,-0.07159,0.00853,-0.07572,0.06438,-0.03181,-0.0328,0.08659,-0.05142,-0.0001,0.02367,0.05812,-0.00611,0.05616,0.0448,-0.07138,0.02726,-0.08603,-0.00519,-0.06207,-0.02819,0.02872,-0.05371,0.1434,0.07933,0.05811,0.05245,0.06168,0.01098,-0.01455,-0.00971,0.00108,-0.07456,0.05475,0.06412,-0.11623,0.06484,0.01344,-0.01162,-0.05746,-0.0502,0.08556,-0.06798,-0.05164,-0.01943,0.03001,0.0364,0.00657,0.07763,-0.02154,-0.02541,0.04218,0.09911,-0.03677,0.03894,-0.0192,-0.10859,-0.03356,-0.17627,-0.04095,0.07835,-0.08319,-0.00414,0.10192,-0.10633,-0.13351,-0.13131,0.02264,-0.09983,-0.00404,-0.02724,-0.12506,-0.03856,0.05612,0.0072,0.01231,-0.04405,-0.10433,-0.08174,0.07907,-0.01352,-0.04391,0.00326,-0.03588,0.01585,-0.0021,0.0212,0.03169,0.01441,0.01061,0.06513,-0.02313,-0.00744,0.01842,0.09522,0.07306,0.01722,-0.07429,0.08332,0.05941,0.01647,-0.03657,-0.11397,0.01285,-0.07336,-0.00953,-0.12493,-0.02465,-0.00197,0.05126,0.04428,-0.04918,-0.05634,-0.02222,-0.02423,0.0796,0.07129,0.00445,0.00042,0.0797,-0.09873,-0.04137,0.03193,0.05091,-0.02345,0.10519,0.13434,-0.03917,0.08073,0.03581,0.01776]},{"domain":"calculus","key":"inflection_points","name":"Inflection points","package":"calculus-ai999x","example":"Find the inflection points of x^3 - 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determinant","package":"calculus-ai999x","example":"Find the Jacobian of x = u*cos(v), y = u*sin(v) at (2, 0.5).","v":[0.06271,-0.04086,0.00317,0.06222,-0.05433,0.00681,-0.06717,0.02144,0.06553,-0.01869,-0.07713,-0.09089,-0.04405,-0.10593,-0.0416,0.02191,-0.01978,-0.10596,-0.0199,0.06831,0.01138,0.04037,0.01983,-0.01036,-0.04712,0.07062,0.01262,-0.01877,-0.08019,0.00608,0.03898,-0.0755,-0.0562,0.01795,0.04057,-0.08122,-0.02812,-0.0664,-0.00527,0.02016,0.10658,-0.0045,0.04766,-0.13783,0.0505,-0.07872,-0.05391,0.0994,0.01592,0.04405,0.06409,-0.03128,-0.20583,0.02112,0.08892,0.05479,0.03582,-0.04548,-0.09827,0.00127,-0.04266,-0.06334,0.03062,-0.11098,-0.04151,-0.09824,-0.05392,0.09138,0.02706,0.14526,-0.05324,-0.03061,0.1867,-0.00509,0.00729,-0.01299,0.00812,-0.02266,0.04505,-0.03935,0.06667,-0.06833,-0.07679,-0.03527,0.00724,-0.06576,-0.0804,-0.08708,-0.06799,0.07432,-0.02218,-0.07709,0.08923,0.07647,-0.0241,0.10591,0.05306,-0.03018,0.13006,-0.05701,0.02475,-0.05231,0.02583,-0.12492,-0.02204,0.09357,0.00145,0.04631,-0.0136,0.09279,-0.01061,0.03396,0.04678,-0.0677,-0.07137,-0.01344,0.00396,-0.00353,-0.0616,-0.05161,-0.02127,-0.05995,-0.05559,-0.09588,0.06677,-0.04277,0.00498,-0.00703,0.00841,0.08534,0.01037,-0.07079,0.06009,-0.02469,-0.07265,0.08441,-0.01539,0.05587,0.07341,0.00701,0.07437,-0.16629,0.03244,-0.10557,0.01597,0.0455,-0.07419,-0.08133,0.07256,0.01027,-0.00968,-0.13282,0.09988,-0.00718,0.05964,0.06638,0.06774,0.01583,0.04615,0.02523,0.12654,0.00183,0.01048,0.04105,0.11168,-0.03434,0.03908,-0.03597,-0.08829,0.04643,0.01569,0.0407,0.05641,-0.17196,-0.00316,0.01816,-0.02371,0.11352,0.09132,-0.041,0.00366,0.01133,0.10386,-0.01255,-0.00122,-0.02878,0.05202,-0.00674,0.03108,0.04549,0.10329,0.05272,0.00136,0.0755,0.00594,-0.09425,0.07292,-0.00865,-0.07123,0.0779,-0.00774,-0.0718,0.04054,-0.0379,0.07543,-0.12311,0.02984,0.03166,0.02465,0.08089,0.01457,0.0358,0.01921,-0.03053,0.07543,-0.02448,0.03626,-0.03981,-0.02746,0.02838,0.02025,0.04678,-0.05428,0.0562,-0.0733,0.05802,-0.01648,0.00668,0.04928,-0.06863,0.09538,0.11252,-0.11905,-0.06168,-0.01135,0.00982,-0.02785,0.0151,-0.00938,0.05697,-0.06721,0.01658,0.10807,0.02589,0.04259,-0.02637,-0.0548,0.06053,-0.02021,-0.04989,-0.07076,0.06431,0.00662,-0.038,0.00137,0.02431]},{"domain":"calculus","key":"laplacian","name":"Laplacian","package":"calculus-ai999x","example":"Find the Laplacian of x^2*y + z^3 at (1, 2, 3).","v":[-0.1019,-0.02486,-0.01649,-0.0546,-0.07916,-0.05968,-0.07702,0.00135,0.01326,0.0494,-0.06052,-0.09346,0.00809,-0.03229,-0.03034,0.03122,-0.05784,0.10638,-0.00401,0.0311,0.00261,-0.05612,-0.04329,0.00143,-0.03301,-0.05605,-0.10837,-0.05083,0.02819,0.06066,-0.07148,-0.0037,0.04507,-0.07273,0.1098,0.0105,0.06134,-0.0578,0.01423,-0.11023,0.03185,-0.02574,-0.01183,-0.05489,0.02751,0.0533,0.04283,0.00357,0.03788,-0.02683,0.04883,-0.05905,-0.07739,-0.04924,-0.06474,-0.0025,-0.01235,-0.07113,0.00086,0.01987,0.12199,-0.0642,0.09086,-0.02232,-0.06123,0.03976,-0.09231,0.0066,-0.00846,0.04073,-0.01675,0.00161,-0.00095,-0.0576,-0.00938,-0.00707,0.00276,-0.1142,0.05005,-0.13544,0.01563,0.03719,-0.07076,0.03134,-0.04262,-0.04553,-0.01806,-0.10787,-0.10053,0.00592,0.01078,0.01297,-0.01234,0.16379,-0.06868,0.01558,0.00328,0.04068,0.06446,-0.02706,-0.04053,0.08907,0.03797,-0.15271,0.01046,0.21562,-0.02792,0.04525,-0.05502,-0.01272,0.02576,-0.10323,0.04683,0.00807,0.09321,-0.02752,0.06681,0.1057,-0.03125,0.02914,0.05433,-0.01583,0.00268,-0.01447,0.03463,0.08685,-0.01575,0.0298,0.14365,-0.01737,0.04524,-0.04233,0.09486,-0.00671,-0.05247,0.12482,-0.04749,0.02873,0.06532,-0.03181,0.02372,-0.07078,0.04558,-0.13306,0.03229,-0.00023,0.05412,-0.08819,0.01921,0.10899,0.0003,-0.05135,0.03775,0.02493,0.05742,-0.01818,0.07175,0.05683,-0.05878,-0.01363,-0.03676,-0.00087,-0.0522,0.06547,0.03511,0.00568,0.10123,0.05337,0.06649,0.00683,-0.03545,-0.04666,0.0063,-0.13728,0.06842,0.03875,0.04474,0.07273,0.01192,-0.09356,-0.01536,0.01704,-0.0299,-0.00706,0.03962,-0.08931,-0.02355,0.07162,-0.04013,0.04949,0.17876,0.15536,0.09623,0.07136,-0.01176,-0.07579,-0.03442,-0.08683,0.00612,-0.1095,0.06742,0.00219,0.02603,-0.00325,-0.00928,-0.09117,0.08196,0.11137,0.07248,0.03434,-0.04827,0.03504,0.05203,-0.13977,-0.02511,0.04503,0.14335,0.04472,0.01928,-0.01265,-0.03625,0.01296,-0.01039,0.12462,0.03306,-0.00361,0.08484,-0.02397,0.01721,-0.08371,0.07846,-0.00364,-0.04266,-0.09637,-0.02288,-0.00817,0.03561,0.09881,-0.05548,0.04034,0.00645,-0.07112,0.06141,-0.02194,-0.04543,-0.02718,-0.03477,-0.04496,0.11849,0.00067,-0.04936,-0.05241,-0.1128,-0.02055,-0.08795,0.02212]},{"domain":"calculus","key":"left_riemann_sum","name":"Left Riemann sum","package":"calculus-ai999x","example":"Find the left Riemann sum of x^2 on [0, 2] with n = 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polynomial","package":"calculus-ai999x","example":"Evaluate the Legendre polynomial P_3(0.5).","v":[-0.04402,-0.05693,-0.00789,-0.02937,0.08909,-0.03334,0.01928,0.03039,-0.05338,0.10453,-0.09502,-0.00774,-0.01928,0.03212,-0.06523,0.02449,-0.02568,-0.01681,-0.12156,-0.00854,-0.00078,-0.05334,0.01954,-0.09803,-0.02509,-0.01372,-0.0865,0.03938,0.03416,0.05217,-0.02453,-0.04718,0.13808,0.05486,0.0922,-0.06359,0.03029,-0.03975,0.01416,0.03627,0.02066,0.04255,0.07794,0.05796,-0.01121,-0.01664,-0.01267,-0.01309,0.04872,-0.08143,-0.0259,-0.00346,0.00286,-0.01414,0.0217,-0.05357,0.00806,-0.07938,0.05898,-0.02841,0.06082,-0.01918,-0.06752,-0.06915,-0.05404,0.0238,0.00965,-0.0522,-0.03203,0.05557,-0.03588,0.08219,-0.02958,-0.04487,0.1234,0.01758,0.1217,-0.05022,0.04652,-0.08499,-0.01057,0.0534,0.06649,-0.04385,0.04232,-0.02119,-0.0505,-0.00189,0.01826,0.03259,-0.02149,0.00753,-0.05187,-0.01476,0.00943,0.1142,-0.00214,0.07217,0.0815,0.00034,0.02319,0.08836,0.04097,-0.05742,-0.0043,-0.0255,-0.1418,-0.09294,0.00129,0.0445,-0.0124,-0.03809,0.01072,0.03925,0.0217,-0.03124,0.05473,-0.02417,-0.04681,-0.05083,0.07575,0.04063,-0.08479,-0.06043,-0.01027,0.00409,0.04564,0.09211,0.06638,0.03049,0.15932,-0.11058,0.13379,-0.03607,-0.07046,0.12275,0.01067,-0.00277,0.0426,-0.01938,0.04296,-0.05334,0.22166,-0.02744,0.04249,-0.10002,0.06932,-0.05071,-0.03946,0.00897,-0.0894,0.0169,0.04638,0.0438,0.07954,-0.06827,0.02972,-0.01613,-0.02391,-0.04111,-0.0838,-0.02043,0.00688,0.05282,-0.00526,0.05468,0.03318,-0.07058,-0.03882,-0.00529,-0.18513,0.09483,-0.05787,-0.10771,0.01142,0.13733,-0.04807,0.0117,-0.01266,0.05187,-0.01752,0.01979,-0.04947,0.02491,0.04984,-0.05964,-0.04068,-0.07169,-0.07159,0.08764,0.00589,0.05656,0.09061,0.15951,-0.07083,-0.03934,0.04877,-0.10355,-0.00088,-0.06478,0.05698,-0.08165,-0.00894,0.09653,-0.06274,-0.06005,0.06754,-0.01092,-0.0382,0.08808,0.03071,-0.0457,-0.00311,-0.10839,0.01382,-0.00658,0.07304,0.16103,0.01724,-0.0666,0.07899,-0.00782,-0.06173,0.09498,-0.01949,0.02903,0.20075,-0.0486,-0.04018,-0.03201,-0.10885,0.05033,-0.04262,-0.06848,-0.01369,0.02275,-0.0296,0.02153,0.02455,-0.0907,0.05688,0.01325,-0.05737,0.09313,-0.07777,-0.12857,0.06604,-0.05255,-0.00387,0.08045,0.02171,0.04239,-0.0445,-0.01174,-0.009,-0.03545]},{"domain":"calculus","key":"limit_at_infinity","name":"Limit at infinity","package":"calculus-ai999x","example":"Find the limit of (3x^2 + 1)/(x^2 - 5) as x approaches 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at a point","package":"calculus-ai999x","example":"Find the limit of (x^2 - 4)/(x - 2) as x approaches 2.","v":[-0.10461,-0.03086,0.06472,-0.15063,0.01873,-0.00905,-0.10869,0.01366,0.0171,0.07237,-0.06982,0.03685,0.00179,0.01559,0.12096,0.01536,-0.09321,-0.03453,-0.07919,-0.01864,-0.14061,-0.03461,-0.03936,-0.11654,0.02171,-0.08135,-0.02939,0.04001,0.03649,-0.03535,-0.0696,-0.01029,-0.00875,-0.02038,-0.00578,0.01868,0.03674,-0.04305,0.05116,0.06262,0.06403,0.03997,0.04373,0.03882,0.17593,-0.01012,0.03909,0.07319,-0.06678,0.00749,0.07932,0.02896,-0.07776,-0.08078,-0.00181,-0.03795,0.0268,0.01376,-0.05142,0.02376,0.06201,-0.05701,0.05669,-0.0653,-0.11795,-0.00591,-0.00624,0.00919,-0.04114,0.03106,0.07156,-0.08102,0.05048,0.0229,0.06182,-0.04498,0.02728,-0.01605,-0.10648,0.01945,-0.03503,0.04033,-0.10668,0.00167,0.10598,-0.07669,0.00043,-0.05023,0.02732,-0.12182,0.07578,0.06915,-0.01028,0.07655,0.00673,0.02748,0.01505,-0.02242,0.05041,-0.008,0.03476,0.03857,-0.01491,0.04583,-0.07785,0.06537,0.11698,-0.03257,-0.04491,-0.06437,-0.10824,-0.00309,0.07124,-0.0364,0.08861,0.05709,-0.04058,0.1253,-0.07351,0.03344,0.0223,0.01986,-0.02219,-0.01668,-0.00761,0.10592,-0.00687,-0.06441,0.03116,0.00761,-0.02057,0.0623,0.06897,-0.06261,-0.14662,-0.00122,0.0918,-0.05194,-0.07338,-0.00636,0.04296,-0.00131,0.04165,-0.02166,-0.10636,0.02251,0.05863,0.04173,-0.12397,0.09245,-0.03568,-0.00378,0.04637,-0.07631,-0.00921,0.00332,0.04124,0.04075,-0.02805,-0.00144,-0.05815,-0.01243,-0.02327,0.00573,-0.00747,0.02119,0.01959,-0.10987,0.13241,-0.11458,0.03898,0.03199,-0.05892,0.04655,-0.00098,-0.06451,-0.02984,-0.04432,0.14318,0.09597,0.02013,-0.07358,0.03505,-0.02242,0.04012,-0.08675,-0.13558,0.14871,0.0397,-0.04567,0.00228,-0.07861,0.02478,0.01097,0.0191,0.03235,-0.00301,-0.03615,0.11615,0.07407,0.08011,-0.04688,-0.17817,-0.02687,0.02995,0.07407,-0.09357,0.05923,0.02901,-0.03121,0.00588,0.06359,-0.04238,0.04471,-0.04473,0.08661,-0.03195,0.17939,0.01328,-0.01831,0.06673,0.06614,-0.01644,0.08838,0.11122,0.07088,0.06817,-0.08623,0.02639,-0.03957,-0.0682,-0.04192,-0.07975,-0.00944,0.04722,-0.0467,0.0144,-0.02129,0.00349,0.02343,0.11906,0.05024,-0.01752,-0.05689,0.0931,-0.06911,0.00979,0.07222,-0.0067,-0.07487,0.04799,0.00861,-0.0405,0.02144,0.03806,-0.02473]},{"domain":"calculus","key":"line_integral_scalar","name":"Line integral with respect to arc length","package":"calculus-ai999x","example":"Find the line integral of x + y ds along x = t, y = t from t = 0 to t = 1.","v":[-0.11926,-0.12129,0.06042,-0.08661,-0.01466,-0.04665,0.03002,0.01373,0.09031,-0.00464,0.00807,0.00088,0.06902,-0.07006,0.0251,0.08892,-0.09346,0.00366,-0.0971,-0.01703,0.0695,0.01809,-0.02963,0.01046,0.00151,0.04425,-0.07534,-0.02334,0.01985,-0.03191,0.01467,-0.07242,0.0203,0.02067,0.10662,0.03285,0.00275,-0.03439,0.00996,0.08689,-0.01206,0.04885,-0.06251,0.0039,0.03655,0.05056,0.09864,0.11028,0.03479,-0.12091,-0.11099,0.00027,-0.06571,-0.07881,0.04586,-0.09558,0.07276,0.06897,0.00416,0.02169,0.08147,0.03627,0.04789,0.05333,-0.06912,0.0217,0.00378,-0.03358,-0.01801,-0.03467,-0.052,-0.06328,0.02949,-0.09334,0.10658,0.03992,0.03378,0.04436,-0.08942,0.00922,0.04048,-0.01856,0.01354,-0.06914,0.11094,-0.00126,-0.03309,0.05393,0.07093,0.07491,-0.01009,-0.05438,-0.02777,0.08567,0.05604,-0.00163,-0.03568,0.00122,-0.02917,0.0488,-0.00778,-0.01622,-0.021,0.08159,0.07718,-0.11807,-0.10506,0.01387,0.05253,0.03112,-0.10134,0.06302,0.04536,-0.05053,0.03485,-0.04535,-0.08238,-0.05764,0.01804,0.06509,-0.13284,0.07061,0.01217,-0.06264,-0.00109,-0.00757,-0.07136,-0.0225,-0.09425,0.05736,0.11776,0.09737,0.04034,-0.00281,-0.04651,0.10414,0.04104,-0.00894,-0.07898,0.05041,0.04005,-0.13136,0.05161,-0.05549,0.09091,-0.04847,0.07968,0.017,0.08837,0.00149,0.02073,-0.03976,0.03607,0.01763,0.01345,-0.0475,0.02038,-0.09965,0.09118,0.00566,0.02476,0.04772,0.07259,0.09576,-0.01946,0.02386,0.06683,-0.03039,-0.07516,0.00148,0.02538,-0.03339,0.00121,-0.00323,-0.09436,-0.03713,0.00193,-0.01586,-0.03718,0.06687,0.05095,-0.02874,0.06147,-0.07222,-0.16985,0.18809,0.02624,-0.0415,-0.01946,-0.06326,-0.02088,0.09437,-0.03039,0.06777,0.07326,-0.10666,-0.08116,-0.11822,0.03439,-0.01716,0.12283,-0.02361,-0.06893,-0.0311,0.05555,-0.04649,0.05641,-0.00657,-0.03976,-0.02388,0.07726,0.10555,0.07507,0.03438,0.06429,-0.04993,-0.03058,-0.02656,-0.02773,0.13975,0.0063,-0.00813,0.00516,0.05105,0.07371,-0.08639,-0.09452,0.0006,-0.04958,-0.01903,-0.07843,-0.0899,-0.07786,-0.02698,-0.00616,-0.04922,0.10873,-0.12398,0.02149,-0.04112,-0.00013,-0.04397,0.1614,-0.06294,-0.03138,-0.08015,-0.02726,0.03809,0.04471,0.04193,0.0239,-0.00382,-0.04743,-0.02133,-0.13004,0.00458]},{"domain":"calculus","key":"line_integral_vector","name":"Line integral of a vector field","package":"calculus-ai999x","example":"Find the line integral of F = (-y, x) along x = cos(t), y = sin(t) from t = 0 to t = 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approximation","package":"calculus-ai999x","example":"Use the linear approximation of f(x) = sqrt(x) at x = 4 to estimate 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value theorem","package":"calculus-ai999x","example":"Find the value of c guaranteed by the mean value theorem for x^3 on [0, 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derivative","package":"calculus-ai999x","example":"Estimate the derivative of x^2 at x = 1 using a central difference with h = 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and concavity of a parametric curve","package":"calculus-ai999x","example":"Find dy/dx for x = t^2, y = t^3 at t = 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derivative","package":"calculus-ai999x","example":"Find the partial derivative of x^2*y + y^3 with respect to x at (1, 2).","v":[-0.09352,0.00767,-0.01581,-0.10659,0.05347,0.04655,-0.12554,-0.00477,0.04954,-0.00702,-0.00208,-0.0348,-0.0251,-0.10264,0.05858,-0.01151,-0.02677,-0.00559,0.01853,0.06058,-0.06822,-0.04227,-0.04081,-0.00753,-0.07087,0.01574,-0.04837,-0.01343,0.04659,0.0856,-0.04635,-0.0759,-0.05182,-0.00705,0.11454,0.01382,0.05178,-0.10371,-0.05062,0.03103,0.12591,-0.0207,-0.08177,-0.09011,0.07294,0.01615,0.02388,0.0297,0.02121,-0.04373,0.0395,0.03386,-0.20529,-0.10945,-0.02428,0.03165,0.02334,-0.09617,-0.02372,-0.06208,-0.042,-0.07556,0.0103,-0.04462,-0.01435,-0.01635,-0.08567,0.01449,-0.00746,0.0624,-0.0032,-0.05438,0.06874,0.0115,-0.00952,-0.09131,0.07746,-0.08992,0.10561,-0.13558,0.06981,0.03023,-0.05183,0.02921,0.00763,0.02521,-0.05035,0.0571,-0.11823,0.01708,0.08372,-0.16638,-0.05783,0.07622,-0.06828,0.06294,-0.02968,0.01054,-0.02322,-0.00144,0.00097,0.00565,0.10127,-0.07615,-0.09525,0.16367,0.10786,0.07853,0.02139,0.05037,0.03641,0.00937,-0.01929,0.03069,0.02755,0.02108,0.00573,0.05832,-0.04156,0.00445,0.04626,0.02345,-0.09991,0.06519,0.11789,0.08016,-0.07561,0.02397,0.07444,-0.04917,0.00249,0.06173,0.12541,0.02583,-0.09059,0.07172,-0.01906,-0.03418,-0.04341,0.09371,0.01016,-0.08705,0.03903,-0.09797,0.0218,-0.06393,0.0645,-0.02281,0.02812,0.07767,9e-05,-0.03631,-0.05045,0.03264,0.15457,-0.01844,0.16223,0.01191,-0.01984,0.01972,-0.01123,-0.05355,-0.06667,0.06946,0.0469,0.00484,-0.02978,0.08103,-0.00381,0.05235,-0.00741,-0.06055,-0.04742,-0.02376,0.04046,0.06964,0.0123,-0.02524,0.04143,0.04421,-0.03827,-0.02134,0.12273,0.06834,-0.05766,-0.02765,0.05497,-0.04111,-0.02542,-0.08377,0.0186,0.12531,-0.05131,0.06114,-0.05755,-0.05899,-0.03999,-0.01085,-0.00526,-0.00198,-0.01447,-0.03827,-0.01806,0.02578,0.05511,-0.03712,0.00585,0.08001,0.06288,0.03193,-0.04392,0.11149,-0.04962,-0.04102,-0.06142,-0.05179,0.04888,0.06045,-0.01212,0.0736,0.0197,0.08346,-0.09605,0.03244,-0.07133,-0.00361,0.09295,0.0139,0.02157,-0.01031,0.01276,-0.03793,-0.10611,-0.03589,-0.0232,-0.07726,0.14571,0.05553,-0.00292,0.09502,0.01148,-0.07453,0.07914,0.02708,0.00119,-0.0376,-0.04496,0.10406,0.0881,-0.01763,-0.07287,-0.06264,-0.09878,-0.11608,-0.01586,-0.0034]},{"domain":"calculus","key":"polar_area","name":"Area in polar coordinates","package":"calculus-ai999x","example":"Find the area enclosed by the polar curve r = 1 + cos(theta) from theta = 0 to theta = 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area of a graph","package":"calculus-ai999x","example":"Find the surface area of z = x + y over [0, 1] x [0, 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integral over a box","package":"calculus-ai999x","example":"Find the triple integral of x*y*z over [0, 1] x [0, 2] x [0, 3].","v":[-0.04125,-0.06348,0.03232,-0.07517,-0.0418,-0.03673,-0.06689,-0.01998,0.03334,-0.00628,0.04088,-0.0069,-0.04242,-0.03564,-0.02705,0.06201,-0.01677,0.04215,-0.12155,0.07538,0.06667,-0.00799,-0.04438,0.06614,0.02332,0.05445,-0.03381,0.15593,-0.03191,-0.03067,-0.00098,-0.06767,-0.06771,-0.10603,-0.03542,0.0141,0.03466,-0.0626,-0.01695,0.01363,0.01134,0.065,-0.10859,0.0449,0.00543,-0.09826,0.08504,0.05027,-0.04079,-0.06063,-0.01063,-0.0956,0.00575,-0.08197,0.06839,-0.02483,0.0893,0.01764,-0.08,0.00344,-0.0053,-0.07205,0.00707,0.01909,-0.02867,0.01159,0.06563,-0.01907,0.0265,0.00601,0.07804,-0.07177,0.02888,-0.01295,-0.00176,0.16029,-0.00222,-0.04989,0.07973,-0.05096,0.12634,0.03676,-0.06934,-0.02898,-0.01466,0.06962,-0.04711,-0.00735,0.04528,-0.0167,-0.02836,0.03854,-0.07547,0.09337,0.06653,0.0875,0.00776,0.0309,0.08323,0.01832,-0.01301,-0.01594,0.00803,-0.02036,0.03805,0.00202,-0.05932,0.03203,0.12313,0.03656,-0.12191,-0.00097,0.04206,-0.00745,0.05385,-0.03363,0.02227,0.0367,-0.04753,-0.01338,-0.0756,0.00707,-0.01042,0.04105,0.06561,0.04679,-0.02821,-0.01798,-0.03245,0.02215,0.10963,-0.03596,0.0972,0.04999,-0.0869,0.00396,0.02628,-0.01107,0.07107,0.05006,-0.054,-0.10015,-0.12036,0.00779,-0.07654,-0.08565,0.02884,0.09192,0.16107,0.047,0.0079,0.01229,-0.03005,-0.05163,-0.00252,0.01758,-0.02932,-0.04126,0.13032,-0.03196,0.07432,0.00527,0.07211,0.02422,0.03714,-0.02455,0.11531,0.02961,0.01286,0.00188,0.07758,-0.09103,0.01187,-0.01362,-0.05535,0.0748,0.0314,-0.01896,-0.02521,0.1123,0.0366,-0.01334,0.0625,-0.06354,-0.07164,0.02736,-0.07225,-0.0048,0.07092,-0.07136,-0.04878,0.02102,0.00705,0.07557,-0.03353,-0.09146,-0.03735,-0.01905,-0.13455,-0.05152,-0.08095,-0.07928,0.04181,0.00445,0.07516,0.03496,-0.07267,0.02586,0.0471,-0.08835,-0.04949,0.03774,0.05812,-0.03801,-0.07172,0.03496,-0.0311,0.00719,-0.0182,0.04321,-0.02686,0.11484,-0.07254,-0.01846,-0.02344,0.01309,-0.06797,-0.08401,-0.05672,0.00685,0.07744,-0.18476,-0.16266,-0.03607,0.10596,-0.00116,0.12027,-0.04418,-0.06084,0.07174,-0.00448,0.01919,0.21935,-0.01812,0.00455,-0.11433,-0.02595,0.0852,0.1039,0.05491,0.07011,-0.08344,-0.01902,-0.03531,-0.13448,-0.10428]},{"domain":"calculus","key":"velocity_acceleration","name":"Velocity and acceleration from position","package":"calculus-ai999x","example":"A particle has position s(t) = t^3 - 6t^2 + 9t. Find its velocity and acceleration at t = 2.","v":[-0.07623,-0.00037,0.00053,0.0161,-0.07849,-0.03965,0.08851,0.02449,0.07605,-0.04522,-0.06343,0.08576,0.00539,-0.04989,0.01628,0.02785,-0.04521,0.06096,0.06602,-0.04388,0.10333,-0.10385,-0.11812,-0.06505,-0.00736,0.02589,0.02806,-0.00801,0.06439,-0.04613,-0.03905,0.03682,0.05114,-0.06296,-0.01903,-0.10111,0.06512,-0.02507,-0.01309,0.03745,-0.00429,-0.05065,-0.05611,-0.00163,-0.11287,0.01305,-0.02783,0.05312,0.07144,-0.0039,0.02964,-0.10587,-0.12033,-0.01953,0.02999,-0.03576,0.03664,0.04422,0.00755,-0.02661,-0.0321,-0.01456,0.01146,0.0984,-0.11273,0.00811,0.08638,0.01431,0.06023,0.05179,-0.13419,-0.05441,0.10099,-0.08616,0.02383,-0.11102,0.06551,0.02011,-0.08477,0.02482,0.07144,0.08728,-0.02157,0.02696,0.0265,0.06812,-0.00439,-0.1297,-0.00108,-0.03105,0.08875,-0.10307,0.00662,0.06419,-0.03582,-0.01656,0.09807,0.04778,0.10954,0.07858,-0.0595,-0.03334,0.0951,-0.03489,-0.00947,-0.02483,0.06211,0.04885,0.02708,0.08076,-0.01575,0.06424,-0.10184,-0.00771,0.07868,0.04533,-0.11936,0.01973,-0.00918,0.12006,0.06524,0.0015,0.03285,0.00221,0.00576,0.04037,0.06691,-0.06843,-0.03237,-0.01788,-0.01548,0.03668,-0.02972,-0.09041,0.05022,0.0372,0.01247,0.01524,0.02521,-0.01122,0.02652,0.03428,0.03975,0.00948,0.06679,-0.00874,-0.033,0.07008,-0.10289,0.07128,-0.09763,-0.12249,0.00406,-0.12343,-0.0749,0.16861,0.00822,0.0074,-0.09532,-0.02885,0.02867,-0.1055,0.00071,0.08082,-0.01587,0.04142,-0.02473,-0.02278,0.10349,-0.09539,0.01738,-0.03311,-0.08322,0.0578,-0.00643,-0.01185,0.06702,-0.11943,0.05187,0.03009,0.08385,-0.01894,0.0433,-0.01669,-0.02868,-0.03072,0.00191,0.02068,-0.03186,-0.08233,0.07712,0.01194,-0.11016,0.06841,0.02553,-0.02768,0.03634,0.05463,0.10377,0.11715,-0.04479,-0.01419,-0.13612,-0.08871,-0.01454,0.09245,-0.03015,-0.0339,0.12192,0.05489,0.00968,0.05368,0.01176,-0.06849,0.07264,-0.03571,-0.00701,-0.00841,-0.05597,-0.05618,0.05344,-0.00485,0.05213,0.029,-0.04598,-0.07113,-0.03689,-0.00388,0.01611,-0.00211,-0.0147,-0.00368,-0.01868,-0.06718,0.04934,0.04616,0.06051,0.06279,0.13028,0.06801,0.06236,0.04796,-0.04107,0.0937,0.04963,-0.11534,0.04511,-0.03135,0.14518,0.00639,-0.02016,0.00449,-0.09538,-0.19822,0.02207,-0.02908]},{"domain":"calculus","key":"washer_volume","name":"Volume of revolution (washer method)","package":"calculus-ai999x","example":"Find the volume when the region between y = x + 2 and y = 1 on [0, 1] is rotated about the x-axis using washers.","v":[-0.01186,-0.11867,-0.03706,-0.03438,0.02404,0.03516,0.00281,-0.01417,0.04925,0.13736,0.09401,0.02262,-0.07455,-0.06112,-0.04896,-0.00357,-0.03689,-0.06106,-0.07535,0.05144,0.01178,-0.0087,-0.02485,0.02655,-0.0739,-0.03105,0.01237,0.02381,-0.0401,-0.06806,0.02603,-0.11636,-0.00464,-0.06178,-0.0604,0.02102,-0.01896,-0.11077,0.02284,0.1524,0.02697,0.03077,-0.06989,0.01686,0.00593,-0.02398,0.07653,-0.02329,0.04609,-0.04719,0.07997,0.00462,-0.01511,0.01752,-0.03729,0.09645,0.08239,-0.02067,-0.04191,0.05918,0.04086,0.00719,0.05462,0.06118,0.02796,-0.02217,0.14249,-0.03766,-0.0064,0.00638,0.08336,-0.06582,0.0513,-0.07632,0.02131,0.05426,-0.0857,-0.00996,-0.04333,0.06837,0.06744,0.00501,-0.04482,-0.0166,0.03826,0.11603,-0.01174,-0.04262,0.06839,0.00058,-0.02989,0.05313,-0.01349,0.14404,0.0261,-0.01452,0.05573,-0.04534,-0.01591,0.00872,0.01348,-0.04238,0.09217,-0.04668,0.00351,-0.06121,-0.03511,-0.03647,0.08198,0.03752,0.00426,-0.01533,0.01463,0.02737,0.07588,-0.05045,0.04047,-0.08565,-0.04192,-0.04476,-0.05883,-0.07138,-0.1157,-0.02988,-0.05719,0.02353,-0.04275,-0.01011,-0.03196,-0.04365,-0.02704,-0.03129,0.07665,-0.01577,0.00564,0.1084,0.08759,0.03128,0.05489,-0.01553,-0.03169,-0.07958,-0.00165,-0.09507,-0.04666,-0.04391,0.01549,-0.17769,0.07751,0.07193,0.072,0.12513,0.09964,0.01313,0.01599,0.04462,0.08893,0.04389,0.0244,0.02253,0.04079,-0.05642,-0.00011,-0.01479,-0.02693,0.09294,0.06029,-0.04966,0.01181,0.02492,0.01172,0.09812,-0.07296,-0.06579,-0.05059,0.06448,0.01599,0.00642,-0.0556,-0.10129,-0.02085,-0.02141,-0.00802,-0.0604,0.06265,0.06249,0.00761,-0.02769,-0.00515,-0.15957,-0.03309,0.16062,0.03113,0.04224,0.06675,-0.116,0.00456,-0.06125,-0.06717,0.07535,0.0291,-0.02861,-0.01703,0.07969,0.03719,-0.02203,-0.14492,-0.01932,-0.05497,-0.01256,-0.03004,-0.01479,0.12275,0.08511,-0.04188,0.06249,-0.0203,-0.10368,0.11833,0.02513,0.10412,0.14838,-0.04099,-0.12357,-0.04389,-0.04551,0.00446,0.07398,-0.02294,0.00193,0.02483,-0.02123,-0.10031,-0.03137,-0.01908,-0.09819,-0.00621,-0.0247,-0.02361,-0.06673,-0.06386,-0.11613,0.08565,0.05585,0.08417,-0.11925,-0.06478,0.10861,0.08945,0.04937,-0.06034,-0.1302,0.01288,0.0952,-0.03721,0.10024]},{"domain":"differential_equations","key":"amplification_factor","name":"Stability function (amplification factor) of a one-step method","package":"differential-equations-ai999x","example":"Find the amplification factor of the rk4 method for lam = -10, h = 0.2.","v":[0.00787,0.04623,-0.03402,0.01832,0.00841,0.01594,0.04517,0.03195,-0.0448,-0.04096,0.11318,-0.05598,-0.02864,0.06736,0.0968,0.09113,0.00983,0.03975,-0.0103,0.03368,-0.00589,0.00744,-0.00934,0.00741,0.07403,0.06105,0.03466,-0.02257,0.04347,0.06329,-0.03696,0.0047,-0.10246,-0.00329,-0.05076,0.0417,-0.02931,0.06838,-0.07416,0.05479,0.03721,0.01044,-0.02972,0.09951,0.05753,-0.02852,0.01503,0.07299,0.02272,-0.0113,-0.03073,-0.08265,-0.06738,0.10511,0.10223,-0.02954,-0.1091,-0.03418,-0.00598,-0.03678,0.01363,-0.14841,0.085,-0.07315,-0.03434,0.0012,-0.00747,0.07623,0.11361,-0.03471,0.06055,0.1395,0.08713,0.00472,0.04342,0.04002,-0.07294,0.0041,0.04064,-0.05605,2e-05,0.01327,-0.04454,-0.03928,0.11528,0.00237,0.06142,-0.01113,-0.02056,0.00901,-0.14704,-0.00153,0.01129,-0.1183,0.03677,0.11843,-0.00055,-0.07251,0.09736,-0.01541,0.01198,-0.01271,-0.11248,-0.003,0.00663,0.01877,0.01672,0.02343,0.03778,0.06019,0.05303,-0.01843,0.05035,-0.03519,-0.057,0.02864,-0.14591,0.06067,-0.03846,-0.02052,0.04861,-0.03416,-0.02842,-0.01026,-0.09127,-0.03421,-0.03799,0.00352,-0.0402,0.03647,-0.07582,0.07253,0.12923,-0.051,-0.09582,-0.01497,0.0371,-0.08892,0.06513,0.02418,0.09122,-0.01793,0.01835,0.09536,0.06638,0.02613,0.0052,-0.09471,-0.12663,-0.0005,0.03068,-0.03926,0.00429,0.02961,0.06039,-0.01774,0.00728,0.11901,-0.0443,-0.11048,-0.07297,0.02127,-0.04493,-0.04034,-0.04665,-0.04934,0.04332,-0.00858,0.02353,0.01083,0.05217,0.00367,-0.03484,0.01397,0.06554,0.06658,0.01239,0.01579,0.05892,-0.02904,-0.01967,0.08604,0.15602,-0.0787,0.12297,-0.10689,0.03038,-0.00289,-0.03939,0.03825,-0.00509,-0.07066,0.06912,-0.06689,0.03652,0.0176,-0.14553,0.00719,-0.09104,-0.02123,0.13072,-0.01264,0.04183,0.06107,-0.01686,0.00859,0.03569,0.04317,-0.04396,-0.05656,-0.07707,0.10437,0.00973,-0.0121,-0.13857,-0.02958,-0.12481,-0.1143,0.01581,0.10374,0.11109,0.00616,-0.05425,0.10738,-0.03587,0.00366,0.06065,0.06241,-0.0555,-0.07498,0.02194,-0.02731,-0.04392,0.04976,-0.02323,0.05895,-0.0624,-0.06596,-0.14399,-0.1205,-0.0288,0.02459,-0.03675,-0.13157,-0.00926,0.04805,0.10991,0.04585,-0.12674,0.0,0.00237,-0.09206,0.02266,0.05995,0.05066,-0.06884]},{"domain":"differential_equations","key":"autonomous_equilibria","name":"Equilibria of y' = f(y) and their stability (phase line)","package":"differential-equations-ai999x","example":"Find the equilibria of dy/dt = y*(1 - y) and their stability.","v":[-0.02393,-0.09166,-0.05622,0.07082,0.10437,0.02915,0.0986,-0.01523,0.00165,-0.09579,0.02152,-0.00092,-0.10471,-0.07032,-0.02207,0.0254,0.01833,-0.05198,0.01864,-0.06177,-0.10765,-0.0437,0.01292,0.00861,0.03575,-0.06282,0.04218,-0.0388,-0.00946,-0.00369,-0.00364,-0.07134,0.00882,-0.02864,0.04716,-0.02954,0.03512,-0.00461,0.09491,-0.07008,0.08507,-0.0171,0.10545,0.00211,0.0037,0.01754,-0.08953,-0.02795,0.12632,0.07802,0.0644,0.10184,-0.08572,0.05092,0.04173,-0.03663,-0.16884,-0.01755,0.02841,0.01178,-0.06443,0.01289,-0.08942,0.0196,0.10291,0.0499,-0.09893,-0.19649,0.08216,-0.07044,0.02615,0.09909,0.01437,0.1095,0.07651,-0.0645,-0.06174,0.00108,0.12453,0.00226,-0.07559,-0.13212,-0.08826,0.00874,-0.01362,-0.01621,-0.01044,-0.01753,-0.03241,0.03323,0.00292,-0.05748,-0.02057,0.06438,-0.04368,0.10044,-0.0653,0.02663,-0.01725,0.04973,-0.02181,-0.0064,-0.00406,0.01811,0.04114,0.03893,0.07798,-0.04565,-0.02565,0.05047,0.04392,0.03415,0.03187,-0.0308,0.03731,0.05364,0.0143,0.07262,-0.12488,0.09242,0.04107,0.06294,0.03448,-0.07615,0.03348,0.0735,0.11702,0.03157,-0.03536,-0.03622,0.09833,0.03139,-0.01117,-0.04147,-0.08716,0.06239,0.00252,0.0275,0.0557,0.02843,0.04687,0.04527,-0.03438,-0.04054,-0.02253,0.03647,-0.0583,0.03617,0.0723,-0.066,0.133,0.13891,-0.04832,0.00438,0.07034,0.06808,-0.00641,0.06711,-0.06816,-0.05742,-0.00786,-0.07274,-0.08849,0.02391,0.00099,0.02554,-0.03384,0.10029,0.07006,0.0465,0.01722,-0.07275,-0.0847,-0.05291,0.01999,-0.00833,-0.00191,0.00569,0.05935,0.01599,0.05363,0.02625,0.00711,0.07634,-0.05029,0.00357,0.09986,0.11087,0.04008,0.01783,-0.04209,0.09078,0.01783,-0.02786,-0.06435,-0.07602,-0.02413,-0.09391,-0.07851,-0.07861,0.05168,-0.03348,0.08181,0.07511,-0.04566,-0.0523,-0.03842,-0.00087,-0.12947,0.01459,-0.01501,0.04468,0.0285,0.063,-0.06624,0.02986,-0.00455,-0.02284,-0.13696,-0.00301,0.0183,0.01185,-0.13348,0.01663,0.0243,0.02511,-0.0727,-0.14147,-0.11702,0.06854,-0.02649,-0.08107,0.02732,0.00342,-0.11727,0.06107,-0.06618,0.02943,0.03851,-0.0408,-0.01463,-0.00433,0.11169,-0.05612,0.16,-0.05932,0.09459,-0.08936,-0.04331,0.01654,0.01377,-0.0028,-0.03015,-0.02285,0.06479,0.0112]},{"domain":"differential_equations","key":"backward_euler_method","name":"Backward (implicit) Euler method","package":"differential-equations-ai999x","example":"Use the backward Euler method for dy/dt = -2*y + t, y(0) = 1, h = 0.1, n = 2.","v":[0.08122,0.07077,0.06332,-0.07855,0.07508,0.02931,-0.0326,0.09031,-0.04548,-0.0365,0.00359,-0.04461,-0.10634,0.06904,0.10586,0.06445,-0.08634,-0.04576,0.06571,-0.00491,-0.0744,-0.09941,-0.10352,0.04498,0.03216,0.00866,0.0555,0.02025,0.10858,0.08686,0.03885,-0.04769,-0.04499,-0.07576,0.10174,0.03938,-0.05551,0.0139,-0.06508,-0.08757,0.10397,-0.06625,-0.02393,-0.09831,0.06643,0.04606,-0.02667,-0.12647,0.02046,0.02087,0.04404,-0.06985,-0.11199,-0.05285,-0.05727,-0.01938,0.0326,-0.06026,-0.00467,-0.05372,0.03349,-0.00664,0.08283,-0.02463,0.02125,0.09385,0.14059,-0.10081,-0.01833,0.06133,-0.01684,0.00126,0.08905,-0.06403,-0.00985,-0.07408,-0.02346,0.02256,-0.06321,0.0005,-0.09123,0.0865,-0.00909,0.06821,0.02103,0.01729,-0.02344,-0.14389,0.02153,-0.00673,0.05577,-0.05219,0.14348,0.02347,-0.05738,0.09112,-0.09467,-0.15926,0.04819,0.02752,0.07913,-0.00713,-0.03511,0.04139,-0.07216,0.01454,0.05396,0.10914,-0.02609,0.00912,0.08142,-0.04052,-0.05584,0.08761,0.12483,0.03892,-0.05518,0.05115,0.03679,0.05884,-0.07067,-0.04612,0.00989,-0.04608,0.06978,-0.06096,-0.02726,-0.03198,0.0409,-0.03652,0.03461,0.1124,-0.05355,-0.10365,-0.00862,0.00903,0.06048,-0.03326,0.07838,-0.06708,0.00245,-0.03747,-0.03809,-0.01197,0.10501,0.01331,-0.04987,-0.0741,-0.12808,-0.08219,0.06405,0.0186,0.02641,0.05994,0.05351,-0.01998,0.00737,0.09518,0.04821,-0.07873,0.00167,0.00828,0.01583,0.03292,-0.07965,0.0097,0.02082,0.13691,-0.05075,0.11811,0.01846,-0.04283,0.02972,-0.02837,0.07882,0.06814,0.00563,0.0257,0.0051,-0.10144,-0.08904,0.00732,0.09582,-0.01126,-0.04683,0.00748,0.1214,0.05551,-0.0137,0.00095,0.12517,0.05363,-0.01595,-0.0877,0.02188,0.03934,-0.05398,-0.02989,-0.05638,-0.03447,0.02423,0.00892,0.0171,0.03284,0.00756,-0.04723,0.02908,0.08799,-0.02193,-0.03568,0.05177,-0.02807,0.01797,0.06365,-0.02157,-0.09122,0.10601,-0.01357,0.01931,0.07349,0.10029,0.02204,-0.12039,0.04638,-0.06634,0.04463,0.05101,0.00105,-0.05683,0.01096,0.0445,-0.10117,-0.1314,0.00871,-0.00927,-0.05043,-0.00714,-0.0328,0.01354,0.01977,-0.01856,0.10713,-0.07266,0.01451,0.02567,-0.09422,0.00454,-0.0117,0.06345,0.03517,0.018,-0.1497,-0.00586,-0.0481,0.04634,0.04128]},{"domain":"differential_equations","key":"bernoulli_equation","name":"Bernoulli equation y' + p y = q y^n","package":"differential-equations-ai999x","example":"Solve the Bernoulli equation y' + p y = q y^n with p = 1, q = 1, n = 2, y(0) = 0.5; find y(1).","v":[0.01176,-0.01058,-0.07093,0.00717,0.08185,-0.04781,0.02588,0.02832,-0.05012,-0.05288,-0.05038,-0.0391,-0.08595,-0.10307,-0.00036,0.05687,0.10352,-0.14977,0.0185,0.0708,0.01241,-0.0524,0.03321,0.00565,0.0533,0.03507,0.05579,0.05221,-0.01174,0.07168,0.04564,0.05287,0.01855,-0.0313,0.00118,-0.02117,0.00661,-0.04175,0.0421,-0.02558,0.04578,0.00568,-0.03899,-0.13207,0.02187,0.01882,0.00084,-0.12892,0.08118,-0.03879,0.05368,-0.04512,-0.04615,-0.107,0.01395,0.03385,0.01472,0.10842,-0.01479,-0.02259,0.04267,0.01597,-0.02083,-0.06812,0.01942,0.02873,0.08333,-0.12589,0.03399,0.10359,-0.01506,-0.072,0.05461,0.1044,0.00187,-0.11759,0.03054,0.00115,-0.03834,-0.09034,-0.0677,-0.06808,0.0614,-0.03232,-0.08859,-0.01954,0.0839,-0.10123,0.16428,-0.01956,0.04963,-0.09959,0.11235,-0.0876,-0.01785,0.06413,0.03922,0.00207,0.10098,0.01332,-0.04158,-0.03014,0.02793,0.07923,0.01415,0.0131,-0.00887,-0.0052,0.12657,0.01738,0.02186,0.02114,-0.01953,-0.01877,0.02168,0.00792,-0.02617,-0.04497,0.04971,-0.01149,-0.13321,0.03119,0.01259,-0.06314,0.04221,-0.02636,-0.01341,0.04274,0.0098,-0.00191,0.04935,0.0387,-0.02205,0.01621,-0.04996,-0.03238,0.15763,-0.0288,-0.08383,-0.02058,-0.02557,0.07172,0.04032,0.04233,-0.00318,-0.02288,-0.03872,-0.02728,0.02856,0.00677,0.02244,-0.02985,-0.11779,0.07645,0.03817,-0.11216,-0.16004,0.04664,0.04807,0.04394,-0.03766,-0.03189,0.06103,0.02963,0.04602,-0.07196,0.02671,0.07208,-0.10945,-0.01267,-0.07413,0.02087,-0.0646,-0.11456,0.13716,-0.00559,-0.08396,0.08519,0.00484,-0.02155,-0.03884,0.09212,0.04387,0.00678,-0.02503,-0.02998,-0.07045,-0.06961,-0.12769,0.07378,-0.00742,-0.06689,0.00125,-0.01084,0.05649,-0.07934,-0.0562,-0.15903,-0.09281,-0.1233,-0.04931,-0.01324,-0.05578,0.0114,0.12023,-0.01528,-0.05341,-0.02209,0.12993,0.07,0.08906,-0.08608,0.11963,-0.05075,0.03262,-0.05387,0.08282,-0.03655,-0.05541,0.088,0.09602,-0.04056,-0.05578,0.00508,-0.03563,-0.03245,0.10603,0.08882,-0.04551,0.07357,0.03226,0.01147,0.01075,0.00457,-0.07204,0.06309,0.02463,0.02174,0.1059,0.03192,-0.0513,0.00402,0.00354,0.05678,-0.02077,-0.11235,-0.02474,0.02942,-0.00517,0.13529,0.03042,-0.0168,0.06033,0.04707,0.07801,0.01204]},{"domain":"differential_equations","key":"boundary_value_problem","name":"Linear two-point boundary value problem (constant coefficients)","package":"differential-equations-ai999x","example":"Solve the boundary value problem y'' + p y' + q y = r with p = 0, q = -1, r = 0, xa = 0, xb = 1, ya = 0, yb = 1, x = 0.5.","v":[-0.02588,0.03837,0.07224,-0.02672,-0.05668,-0.06346,0.02133,-0.00711,-0.07957,-0.11441,0.02211,-0.01877,-0.03387,-0.0304,0.01973,0.04487,0.0377,-0.10925,-0.08911,0.00706,0.03608,-0.05681,0.06427,0.06161,0.10033,0.03832,0.0919,0.03728,0.03356,-0.01155,0.08881,0.04812,-0.06636,0.06418,0.01575,0.03967,0.02536,0.05059,-0.043,0.0489,-0.07505,-0.00524,0.06551,0.03714,-0.06592,0.00401,0.00172,-0.01291,0.04175,0.0078,0.00959,-0.00041,-0.02193,-0.07513,0.01037,0.00467,0.07483,0.07213,0.05055,0.05658,0.00925,3e-05,-0.00346,-0.13626,0.01668,0.00897,-0.0364,-0.0668,0.0689,-0.01157,-0.09374,-0.00363,0.04148,-0.0181,0.05548,-0.04734,-0.03177,-0.00841,0.08963,-0.03231,-0.0009,-0.05026,-0.03158,0.03554,0.05072,0.02863,0.03455,-0.01604,0.11856,0.05183,-0.03582,-0.04455,0.04232,-0.00246,-0.03724,-0.00616,0.07571,-0.09099,0.03638,0.00134,0.03106,-0.09819,-0.0302,0.00911,0.06507,-0.01301,-0.0369,0.0371,0.07633,0.07448,-0.03503,-0.07115,0.0365,0.00696,0.02375,-0.03349,0.03518,0.02377,-0.02746,0.02869,-0.07421,-0.02089,-0.07276,-0.07343,0.00119,0.04565,-0.00937,0.12196,0.05957,0.02046,0.07885,-0.00961,0.08501,-0.039,-0.0873,-0.05601,0.06943,-0.0698,-0.03072,-0.03652,-0.09656,-0.13915,0.07069,-0.00846,0.024,0.01993,0.04003,-0.10576,-0.02128,-0.01699,-0.02665,-0.13514,0.10608,0.07713,0.06362,-0.08392,0.0605,-0.0514,0.05321,0.02905,-0.07619,-0.04417,-0.03851,0.02356,0.03973,-0.11999,0.05173,-0.08552,-0.12047,0.18234,-0.05333,-0.0254,0.0047,-0.18465,0.01529,0.10457,-0.096,-0.0473,0.03532,-0.07124,0.02747,0.04032,0.02629,0.0035,-0.08524,0.00891,0.0755,0.06385,0.05788,0.04958,-0.02165,0.05778,0.04729,0.09073,0.02345,-0.15717,-0.08101,-0.13378,0.03404,-0.12298,0.17497,0.0354,-0.03519,0.11815,0.09075,-0.02867,-0.09254,0.1187,-0.03,0.02421,-0.01817,-0.01813,0.10344,-0.04138,0.00681,-0.00266,0.08842,-0.02381,-0.06009,0.03798,0.13402,0.07374,-0.1292,0.03976,-0.08588,-0.00302,0.00089,0.09951,-0.00327,0.00465,0.05307,-0.10659,-0.06085,-0.04859,0.00447,-0.00114,0.02908,0.01387,-0.06358,0.03696,0.00676,0.0555,0.03656,-0.03312,-0.01366,-0.05062,0.00781,0.01341,-0.0373,0.16169,-0.04305,-0.00906,-0.05238,0.02583,0.04402,-0.11917]},{"domain":"differential_equations","key":"brusselator_hopf","name":"Brusselator: equilibrium, its type, and the Hopf value b = 1 + a^2","package":"differential-equations-ai999x","example":"Analyse the Brusselator with a = 1, b = 3.","v":[-0.10815,-0.10673,-0.03279,0.07206,-0.0148,0.08237,0.01144,-0.13066,-0.02449,0.03645,0.0099,-0.03971,-0.11641,0.03932,0.04432,-0.03345,0.01353,-0.06507,0.07342,-0.02148,-0.06278,-0.06425,-0.05624,0.01454,0.05704,-0.12446,0.04924,0.02013,0.04183,0.06158,-0.01869,-0.05045,-0.06691,-0.04435,0.0471,-0.04313,-0.05832,-0.02617,-0.00999,-0.1029,0.0875,-0.03433,-0.06213,0.00699,0.07506,0.00323,-0.05807,0.01933,0.02334,0.02849,0.0256,-0.09939,-0.11023,-0.06449,0.04289,0.07991,-0.00412,-0.01832,-0.01805,0.03774,-0.05102,0.00264,0.01032,0.03448,-0.06683,-0.08699,-0.05042,-0.09814,-0.02169,-0.05024,0.015,0.01954,0.01506,-0.11282,-0.03544,-0.04216,-0.09145,-0.0437,0.09986,0.13453,-0.02635,-0.08863,-0.09052,-0.11651,-0.03156,-0.03922,0.00903,-0.0483,0.00882,0.05843,-0.08924,-0.00894,0.09822,0.11606,0.08696,0.0705,0.01568,-0.06073,-0.08278,0.04686,-0.05676,-0.06288,-0.01471,0.05048,0.08084,-0.00728,0.00309,-0.0424,0.02093,-0.04572,0.07924,0.06239,0.12916,-0.04098,0.03661,-0.06417,-0.00021,0.06436,-0.13007,0.09452,-0.04245,0.00409,0.01903,-0.01101,-0.09302,0.03773,0.05603,-0.05785,0.02478,0.02175,0.10139,0.02225,0.04927,-0.10494,-0.11322,-0.01108,-0.02113,0.05681,0.02807,0.00028,0.03972,0.00307,0.04617,-0.03599,-0.02324,-0.0674,0.04776,-0.03667,0.04816,0.0022,0.09999,0.11026,0.08677,0.00713,0.06689,0.06023,0.07602,0.09323,-0.1078,-0.0229,0.02784,-0.02769,-0.01494,-0.04437,0.0262,-0.02462,0.04209,0.0279,0.00333,0.0224,0.12358,0.07578,-0.08929,-0.05684,-0.01077,-0.0551,-0.00983,-0.01523,0.00341,0.03453,-0.00397,0.0168,0.01276,-0.03156,-0.0215,-0.01295,0.09503,0.11267,0.03581,0.03126,0.01408,0.04356,-0.0683,-0.01962,0.08264,-0.09966,-0.09914,0.03857,0.00469,0.06859,0.10736,0.13428,-0.08002,0.04177,-0.02376,-0.046,0.02516,0.07004,-0.08053,0.02743,-0.16818,-0.05141,-0.01887,0.11633,-0.04868,0.14148,-0.01363,-0.01136,0.08041,0.08521,0.02604,-0.05768,-0.04136,0.05121,0.12612,0.05541,-0.05065,-0.0677,0.01465,0.14733,0.05279,-0.03488,0.06314,0.09077,-0.00091,0.0233,-0.0107,0.08224,0.03978,0.01292,-0.02955,-0.0104,0.11675,-0.03814,0.06647,-0.02131,0.04532,-0.06283,0.04808,-0.03618,-0.07714,0.07993,0.06557,0.0607,-0.02154,0.00437]},{"domain":"differential_equations","key":"cauchy_euler_ivp","name":"Cauchy-Euler (equidimensional) equation: initial value problem","package":"differential-equations-ai999x","example":"Solve the Cauchy-Euler equation t^2 y'' + 2t y' - 6y = 0 with y(1) = 1, y'(1) = 0; find y(2).","v":[-0.02803,0.02687,0.04253,0.09011,-0.07663,-0.07597,0.04961,0.00412,-0.06777,-0.09621,0.09661,0.04466,-0.02164,-0.02532,0.00388,0.05382,0.05406,-0.12645,0.00011,-0.07098,0.06744,0.01211,0.06806,0.05882,0.1165,0.02226,0.00821,0.15557,0.03538,0.02747,0.04714,0.0805,0.02572,-0.05483,-0.00568,-0.02342,-0.00195,0.04864,0.09105,-0.12631,0.05456,0.00728,0.06451,-0.00565,-0.11702,-0.05152,-0.01634,-0.04368,0.09479,0.03346,-0.02748,0.00761,-0.07667,-0.04722,-0.07424,0.05776,-0.01656,0.09158,-0.04986,0.02718,0.06233,0.01313,0.01804,0.01893,0.04281,0.0193,-0.00503,-0.16711,0.09835,0.02796,-0.10914,0.01359,0.06841,0.03545,-0.01496,-0.18182,-0.01808,-0.00617,0.02128,-0.05114,-0.01414,-0.04721,0.00745,-0.02507,-0.10066,0.01942,-0.03117,-0.10359,0.07665,0.01632,-0.00768,-0.00626,0.02353,0.04375,-0.01714,0.01435,-0.04446,-0.09893,0.05513,0.03092,-0.04356,-0.04628,-0.0195,0.05488,0.06362,0.00935,0.00905,0.1041,0.0996,0.15326,0.00845,-0.02478,0.03816,0.02843,-0.0196,0.01604,0.00704,-0.06437,0.01977,0.08422,0.02341,0.05658,0.0324,-0.08429,-0.01595,0.07428,0.04847,0.04948,0.01056,-0.03124,0.10907,0.05034,-0.00283,-0.0635,-0.0472,-0.02323,0.04058,-0.05208,-0.03184,-0.01409,0.03699,0.00889,-0.00579,0.04911,0.06615,0.00938,0.01627,-0.02759,0.0638,-0.02077,0.02812,-0.01276,-0.0197,0.02086,-0.01089,-0.05509,-0.03203,0.09611,-0.05672,0.08035,0.0324,-0.02963,-0.08257,0.06785,-0.07876,-0.00222,-0.11175,0.10728,-0.01713,0.10301,0.02387,0.11557,-0.05702,-0.09084,0.06627,-0.07557,-0.023,-0.01426,0.0111,-0.02624,0.05709,-0.043,0.0259,0.0012,-0.15605,-0.02779,0.0724,0.02482,-0.0094,0.13105,-0.0207,-0.00256,-0.00338,0.02981,0.06622,-0.11466,-0.18253,-0.21217,0.00884,-0.05841,0.11317,-0.02622,-0.14524,0.06919,0.04756,-0.04159,-0.04965,-0.02699,0.01485,-0.04279,0.11348,0.02076,0.09433,0.04305,0.07227,-0.09265,0.00268,-0.08788,-0.00476,0.06017,0.02973,0.00275,-0.07491,-0.00116,-0.09413,-0.05672,-0.02082,-0.07863,-0.10952,0.03716,0.0481,-0.00437,0.00166,-0.00473,0.01733,0.06223,-0.09125,0.01589,0.11022,0.03584,0.10982,0.03776,0.06865,0.02257,-0.05686,-0.0455,-0.00563,-0.05611,-0.01354,0.04868,-0.03616,-0.02852,-0.0889,-0.03595,0.01173,0.00211]},{"domain":"differential_equations","key":"cfl_condition","name":"CFL condition for the advection equation (upwind scheme)","package":"differential-equations-ai999x","example":"Check the CFL condition for c = 2, dt = 0.01, dx = 0.05.","v":[0.09881,0.06954,0.06746,0.16285,-0.0494,0.09172,0.008,0.05686,0.00497,-0.00216,0.04895,0.06602,-0.04089,0.05458,0.02441,-0.01616,-0.111,0.11675,0.06439,-0.06337,0.0267,-0.00728,0.00488,-0.04793,0.07186,0.02345,0.00013,0.015,-0.08022,0.08909,0.0603,-0.00087,-0.01684,-0.00757,-0.03093,0.0281,-0.0914,-0.03317,-0.00422,0.01856,0.02061,-0.14133,0.15284,0.05407,-0.05561,-0.07723,0.06267,-0.09987,0.06539,-0.03009,0.06093,-0.1407,-0.05365,0.01894,0.05858,0.01433,0.08028,0.02309,-0.08563,-0.00675,-0.03283,-0.06596,0.11463,0.04919,-0.11358,-0.03079,0.11137,-0.05177,-0.04304,-0.02893,-0.09374,0.04631,0.0158,0.11331,0.00634,0.01953,-0.018,-0.01461,0.09972,0.0689,0.03119,0.03625,-0.09851,-0.05012,0.04935,0.00849,0.02149,-0.00565,0.02298,-0.06123,-0.01964,0.02235,0.11111,-0.00427,-0.0163,0.05369,-0.04952,-0.08029,-0.02705,0.01083,0.00519,0.01596,-0.16736,-0.06433,0.10654,0.02621,-0.00422,-0.04199,-0.0435,0.01602,0.10462,-0.04768,-0.00666,0.06036,0.0693,-0.00421,-0.07997,0.00041,-0.02861,0.15114,-0.00207,-0.02209,0.00318,0.09169,0.03613,0.00425,0.03365,-0.04682,-0.02928,-0.05964,0.06386,-0.03261,0.04343,-0.11187,-0.01203,0.03064,0.09133,0.03704,0.13082,0.01823,0.10503,-0.04002,0.07695,-0.07642,-0.00457,-0.00262,-0.10754,-0.08541,-0.00854,4e-05,0.07219,-0.18374,-0.07123,0.04037,-0.11344,-0.01243,0.04912,-0.03678,-0.02596,-0.05826,-0.03815,0.0527,-0.05155,-0.0366,0.02272,0.06429,0.14401,0.05729,0.03064,-0.03948,0.03116,-0.04509,-0.05182,0.02981,-0.07129,0.03273,-0.01319,0.1118,0.03352,-0.05475,-0.06129,0.0079,0.08136,-0.02177,0.03446,-0.03507,0.0544,0.16225,0.03154,0.0228,0.05075,-0.17352,-0.03974,-0.14193,-0.07098,-0.11235,0.00805,0.04206,-0.01374,-0.00053,0.09058,0.01999,0.07882,0.03445,0.01696,0.00088,-0.02435,0.02591,0.03336,0.02522,-0.06419,0.05288,0.09729,-0.0404,-0.00587,0.00504,-0.04156,-0.05749,-0.04584,0.01916,-0.06567,0.00779,-0.07755,-0.03884,-0.00358,-0.09184,-0.01678,0.05286,0.03431,-0.07371,-0.02918,-0.09038,-0.05648,0.00924,0.10385,0.03112,-0.07782,-0.0123,0.01229,-0.01685,-0.00839,0.08735,-0.04392,0.00182,0.04594,-0.01086,-0.03679,-0.03264,-0.08042,0.01376,0.04413,0.00128,0.04159,0.03063,0.00586,0.03032]},{"domain":"differential_equations","key":"characteristic_roots","name":"Second-order constant-coefficient ODE: characteristic roots","package":"differential-equations-ai999x","example":"Find the characteristic roots of y'' + 3y' + 2y = 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species: coexistence equilibrium and its stability","package":"differential-equations-ai999x","example":"Competing species with a1 = 3, b11 = 1, b12 = 1, a2 = 2, b21 = 0.5, b22 = 1: find the coexistence 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integral (f * g)(t)","package":"differential-equations-ai999x","example":"Find the convolution of f(t) = exp(-t) and g(t) = sin(t) at t = 2.","v":[0.04391,0.03078,0.09057,0.02286,-0.11788,-0.0181,0.08168,-0.08755,-0.05514,0.01379,0.03754,0.09357,-0.0578,-0.00871,0.04085,-0.07192,-0.05477,0.00345,-0.02693,0.09349,0.01183,-0.01928,0.01009,-0.05115,0.03706,0.05693,-0.04949,0.02503,0.0146,-0.03613,-0.01689,0.03078,0.00558,-0.07226,0.0034,0.02147,-0.05128,-0.01654,0.02047,0.01698,-0.0125,0.01253,-0.05611,0.05383,0.04721,-0.03024,0.10884,0.1155,0.02203,-0.07107,-0.13339,-0.05509,-0.00774,-0.061,0.01906,-0.05652,-0.0626,0.00484,-0.04843,0.01405,0.01427,0.01557,0.01101,-0.06941,-0.13119,0.04271,-0.02938,-0.0116,0.02126,-0.01007,0.00566,-0.10104,-0.09408,-0.02839,0.16502,-0.02303,-0.03041,0.02577,-0.14723,0.0228,0.14694,0.05186,0.01514,0.04661,0.02203,-0.04142,-0.02264,0.03624,0.06278,0.01793,-0.04804,0.04432,0.002,0.07961,-0.01203,-0.07268,0.05591,-0.02013,-0.01465,-0.04711,0.05968,-0.01174,0.01398,0.11015,0.02047,-0.06163,0.02318,0.00782,0.07969,-0.03147,-0.01638,0.04986,0.04871,0.07237,0.06186,0.14175,0.00209,-0.04308,0.08418,0.0453,-0.11164,0.00402,0.02236,0.01234,0.01396,-0.03682,-0.08416,-0.0483,-0.03099,0.03253,0.09456,-0.13165,-0.06186,-0.02368,-0.06425,0.02523,0.03393,0.05514,0.01098,0.03115,-0.01506,-0.06046,-0.01011,-0.0589,-0.01583,-0.07093,-0.06642,-0.0906,0.04737,0.08397,-0.00564,-0.14804,-0.00991,-0.03675,-0.04078,-0.0596,0.13811,-0.09404,-0.04807,-0.09065,0.05941,0.0177,0.06054,0.11463,0.01298,0.01427,0.01015,0.05647,-0.06839,0.0422,0.0796,0.15916,0.01748,0.05211,-0.02469,0.02487,-0.00902,-0.06591,0.06075,0.01302,0.04381,0.00864,0.03879,-0.14034,-0.05027,-0.03265,0.07791,-0.05408,0.0038,0.09966,-0.03357,0.00144,-0.04469,-0.00228,0.03591,0.00016,0.01926,-0.05439,0.02348,0.08753,-0.10703,-0.03022,-0.08972,-0.06998,0.01901,-0.07263,0.03611,-0.08825,0.07799,-0.02353,0.24938,0.0149,0.09826,-0.04356,0.03638,-0.07312,-0.06359,-0.08336,0.1142,0.00965,0.06542,-0.05124,-0.02512,-0.03566,-0.04896,-0.077,0.10807,-0.04742,0.04182,-0.09981,0.01254,-0.02127,-0.00349,-0.02331,0.0481,0.0725,0.01933,-0.07861,-0.01778,0.02206,0.21206,-0.04345,-0.02662,0.04682,0.0326,-0.01055,-0.03369,0.03533,0.06615,-0.0181,0.08152,0.0066,-0.10375,0.031,-0.06946,0.03487]},{"domain":"differential_equations","key":"crank_nicolson_steps","name":"Crank-Nicolson steps for the heat equation","package":"differential-equations-ai999x","example":"Apply Crank-Nicolson to u = [0, 50, 100, 50, 0] with r = 1, n = 1.","v":[0.01848,0.08916,0.04881,0.01261,-0.07668,-0.00092,-0.00797,0.04582,0.0048,0.02393,0.05085,-0.06281,-0.05327,0.01434,-0.03837,0.06655,-0.02246,0.05005,0.09612,-0.0478,0.03555,-0.06351,-0.01112,0.0324,0.04212,0.03391,-0.03825,0.02098,-0.0409,-0.10602,0.0029,-0.07673,-0.11419,-0.01046,0.07175,0.14045,0.01332,0.03636,0.01035,-0.11143,0.03744,-0.07405,0.07477,0.03137,-0.13019,0.00303,0.04444,0.00155,-0.08699,0.05278,-0.09282,-0.02573,-0.0474,-0.01279,0.00411,0.01905,0.08998,0.01202,0.00153,-0.11376,-0.0336,-0.07357,0.05063,-0.03093,-0.03247,0.01408,0.13249,-0.13017,-0.12976,-0.00645,-0.07617,0.04901,0.0113,0.13078,-0.09282,0.05251,-0.08757,0.10948,0.14329,0.15864,-0.07987,0.03707,-0.10083,-0.04255,0.03218,-0.00066,0.02845,0.06179,0.00166,-0.03882,0.03828,0.0326,0.15288,-0.0042,-0.01221,0.0475,0.01554,-0.10741,-0.00311,-0.07277,0.07419,-0.04066,-0.06651,0.01287,0.06606,0.06686,-0.00663,-0.00078,-0.04806,-0.02255,-0.01762,-0.0754,-0.13265,0.036,0.00749,0.01174,0.15604,-0.03687,-0.05777,0.03975,-0.12728,-0.07827,-0.0241,-0.01216,0.03101,-0.02231,-0.00109,0.00337,0.04519,-0.04899,0.08169,-0.00836,-0.07466,0.00458,-0.15748,0.02095,0.1521,0.0462,0.13576,-0.0704,-0.06071,-0.0573,0.01546,-0.06688,-0.00751,-0.01961,-0.05853,0.01022,-0.02485,-0.00213,0.03373,-0.1977,-0.04601,0.04741,-0.02921,-0.09764,-0.02181,-0.05612,0.00884,-0.02662,-0.01498,0.0268,0.02707,0.06739,0.03118,-0.02445,0.03661,0.01877,0.00404,-0.0193,0.02891,0.01179,0.0464,-0.09721,0.00845,0.05125,-0.0636,0.01276,-0.001,-0.14979,-0.0877,0.08444,0.11626,-0.02263,-0.01822,-0.04086,0.06354,0.13471,-0.00815,0.06585,0.06483,-0.04935,-0.02944,-0.01903,0.02978,7e-05,0.01207,-0.02748,-0.00527,-0.01726,0.12581,-0.05943,0.03762,-0.01683,0.04022,-0.02875,0.02449,0.09601,0.02505,0.0317,0.0341,-0.0189,-0.02154,0.08687,-0.0644,0.02869,0.11949,-0.06263,-0.06588,-0.03138,0.05687,-0.02557,0.01742,0.04727,0.03487,0.00824,0.07023,-0.03517,0.03873,0.04056,0.04822,-0.04846,-0.06774,0.02782,-0.01428,-0.06528,-0.0449,0.10694,0.03343,0.05022,0.11458,0.00316,-0.09704,0.01008,-0.07502,-0.0064,0.00414,-0.03108,-0.00378,0.03813,0.0222,0.01418,-0.09011,0.0357,0.05728,0.01559]},{"domain":"differential_equations","key":"dalembert_solution","name":"Wave equation on the whole line: d'Alembert's formula","package":"differential-equations-ai999x","example":"Use d'Alembert's formula with f(x) = sin(x), g(x) = 0, c = 2, x = 1, t = 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natural frequency, damping ratio, damped frequency","package":"differential-equations-ai999x","example":"Find the damping ratio of a mass-spring-damper with m = 2, c = 1, k = 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0.05?","v":[0.09908,0.05636,0.01578,0.18901,-0.0735,0.06804,-0.01819,0.08698,0.00357,-0.00528,0.00262,-0.0442,0.00596,0.06683,-0.02747,0.08211,-0.01268,0.13596,0.06498,-0.05503,0.03921,0.02408,0.00334,0.01157,0.05582,-0.01653,0.0466,0.01621,-0.05022,0.14308,0.01173,0.03895,-0.05395,0.00933,0.04573,0.02929,-0.03343,0.03401,-0.02944,-0.01611,0.01779,-0.04076,0.12745,0.0614,-0.10444,-0.00108,0.08406,-0.10148,0.04742,0.00885,0.05693,-0.04408,-0.0447,0.10613,0.05314,0.05497,0.13375,-0.03495,-0.0342,-0.04478,-0.02348,-0.10368,0.1425,0.106,-0.07713,0.00692,0.04603,-0.0687,-0.03496,-0.02243,-0.06193,0.01024,0.00992,0.05121,0.00794,-0.00609,-0.04672,0.04727,0.02065,0.00828,-0.03954,0.04211,-0.11698,-0.04994,0.03322,-0.0132,-0.03067,0.03719,0.0191,-0.05488,-0.04425,0.00152,0.1358,-0.05699,-0.03446,0.03711,-0.08761,-0.05356,-0.0084,-0.04133,-0.02374,0.1014,-0.11534,-0.06745,0.00585,0.0037,0.0716,0.01827,-0.09587,-0.01689,0.09073,-0.038,-0.05868,0.08074,0.02221,-0.08229,-0.07655,0.03804,-0.01943,0.12173,-0.0448,-0.0222,0.0107,0.0414,-0.0267,0.03558,-0.0566,-0.05251,-0.01713,-0.06744,0.00482,0.02021,-0.03783,-0.04847,-0.03883,0.00919,0.08136,-0.0272,0.16283,0.01274,0.1535,-0.04258,0.04201,-0.07267,0.04115,0.00561,-0.05921,-0.04523,-0.00798,0.0465,0.02621,-0.10447,-0.13292,0.03034,-0.06252,-0.10205,-0.00288,-0.00271,-0.00166,-0.05083,0.04817,-0.05058,-0.06193,-0.01174,0.05585,0.0972,0.00594,0.05739,0.05313,-0.09303,0.04182,-0.02188,-0.02152,0.1519,-0.00055,0.00956,-0.00384,0.0794,-0.01205,-0.08702,-0.13215,0.0833,0.06037,-0.01669,-0.00014,-0.03331,0.03188,0.13549,0.01676,-0.02779,-0.0445,-0.09895,0.02647,-0.07978,0.02875,-0.14128,-0.05963,0.00665,-0.00128,0.0124,0.07437,-0.05152,0.09072,0.00473,-0.01649,-0.08852,0.08751,0.10022,-0.00829,0.02232,-0.05244,0.02445,0.0215,-0.02922,-0.07431,0.01603,-0.07971,-0.1262,-0.0148,0.00807,-0.05312,-0.01096,-0.13865,-0.01524,0.08388,-0.0752,-0.03639,-0.05231,0.06148,-0.06346,0.03566,-0.04732,-0.03876,-0.05556,0.0209,0.015,-0.04081,0.07398,-0.0022,0.10177,0.03547,0.12156,-0.01174,0.02376,0.00517,0.02858,0.00605,-0.11467,-0.03041,-0.07565,0.01311,-0.10481,0.02355,-0.00995,0.0626,0.08503]},{"domain":"differential_equations","key":"explicit_step_limit","name":"Largest stable step of an explicit method for y' = lambda y","package":"differential-equations-ai999x","example":"Largest stable step of the rk4 method for lam = 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model through two measurements","package":"differential-equations-ai999x","example":"Exponential model through two measurements: y1 = 100 at t1 = 2 and y2 = 300 at t2 = 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for exponential growth or decay to reach a value","package":"differential-equations-ai999x","example":"Exponential growth from y0 = 100 at k = 0.05: how long to reach y1 = 300?","v":[0.00484,-0.00306,-0.07646,0.0696,0.02789,-0.02134,-0.00142,-0.00198,-0.04057,0.02291,-0.00634,0.06365,0.04842,-0.01717,0.00286,-0.02468,-0.01726,-0.11066,-0.01973,0.10605,-0.11489,-0.0437,0.02898,-0.02132,0.07017,0.03606,0.06093,0.11399,0.07251,0.02062,0.02156,-0.00957,-0.01577,-0.03229,0.02226,-0.057,-0.03842,0.08882,-0.07787,0.08139,0.15178,0.02822,-0.00301,-0.09374,-0.00488,0.08159,-0.0318,-0.07334,0.16171,0.03196,0.03115,0.01401,0.00261,-0.06872,-0.01853,-0.02258,0.11859,0.00599,-0.14465,-0.00799,-0.03655,0.01333,0.01284,0.01701,0.05085,0.03295,-0.13333,0.03948,0.06998,0.04938,0.08651,-0.04779,-0.00427,-0.07926,-0.00132,-0.12148,-0.01668,-0.0636,-0.02765,-0.07603,0.11646,0.0061,0.02425,0.07509,-0.10605,-0.0007,0.09141,0.04816,0.06913,0.05187,0.0372,0.02071,0.11009,-0.11854,-0.05088,0.06672,-0.02407,0.00874,0.02647,-0.02846,-0.01553,-0.03627,0.01625,0.01154,-0.04751,0.09278,0.10029,-0.0361,0.13004,0.00357,0.0404,-0.02781,-0.11104,-0.02994,0.02488,0.06352,-0.06439,0.11967,0.026,0.04284,0.04044,0.03138,0.05113,-0.0559,0.01295,0.01064,-0.02363,-0.03343,-0.08426,-0.05016,-0.00679,-0.06241,0.02313,0.05484,0.01201,-0.10611,0.06317,0.0206,0.1301,0.05365,0.01911,0.11315,-0.03765,0.02748,-0.13963,0.01551,0.00937,-0.04415,0.07508,0.03344,0.01544,-0.0984,0.00979,-0.03217,0.05789,-0.18383,-0.02493,0.04646,0.08991,-0.14115,-0.05431,0.09737,0.02769,0.05266,-0.07394,-0.08242,0.09362,-0.00543,-0.08262,0.07946,-0.07511,-0.10373,-0.03181,-0.01053,0.0534,-0.06562,-0.05545,-0.01012,0.01462,-0.06443,-0.08682,-0.03544,0.0995,-0.01743,-0.01979,-0.02137,0.05463,-0.08887,-0.10437,0.02338,-0.04934,-0.00168,-0.01009,-0.0963,0.00533,0.04989,-0.01444,-0.05649,-0.05969,-0.08009,-0.007,0.05847,-0.03152,0.03606,0.06229,-0.07646,0.10026,0.00156,0.03608,0.04162,0.02647,0.00898,0.04412,-0.03353,0.0642,0.01987,0.04025,-0.02995,-0.19776,0.13692,-0.04001,-0.09686,-0.04354,0.0197,-0.04965,0.05943,0.02553,0.01086,-0.07315,-0.03039,-0.06998,-0.00049,0.03864,-0.03051,-0.0447,0.02594,0.06711,0.01613,-0.11448,-0.0527,-0.105,0.04292,-0.0281,0.0412,0.05772,-0.01679,0.0109,-0.02722,-0.03308,0.02573,0.0201,-0.00076,0.0125,-0.04083,0.07738,-0.04433]},{"domain":"differential_equations","key":"forced_oscillator_ivp","name":"Sinusoidally forced linear oscillator: initial value problem","package":"differential-equations-ai999x","example":"A forced oscillator a y'' + b y' + c y = F0 cos(w t) with a = 1, b = 0, c = 4, F0 = 1, w = 2, y0 = 0, v0 = 0, t = 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growth: value at a time","package":"differential-equations-ai999x","example":"Gompertz growth with y0 = 10, r = 0.3, K = 1000; find 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equation on a rod with ends at zero: Fourier series value","package":"differential-equations-ai999x","example":"Heat equation series with f(x) = x*(1 - x), L = 1, alpha = 1, N = 10, x = 0.5, t = 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equation on a rectangle: series value","package":"differential-equations-ai999x","example":"Solve Laplace's equation on a rectangle with top edge f(x) = 100, a = 1, b = 1, N = 50, x = 0.5, y = 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transform of a delayed function u(t - c) f(t - c)","package":"differential-equations-ai999x","example":"Find the Laplace transform of the delayed function u(t - c) f(t - c) with f(t) = t, c = 2, s = 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body with linear drag: velocity","package":"differential-equations-ai999x","example":"A falling body with linear drag: m = 2, c = 0.5, g = 9.81, v0 = 0; find v(3).","v":[-0.09453,0.04727,0.08281,0.06295,-0.00505,-0.03084,0.11436,-0.00782,0.00666,-0.06356,0.03962,-0.00432,-0.05022,-0.14847,0.02765,-0.06094,-0.03969,-0.09576,0.00756,-0.01216,0.01442,0.0051,0.03603,0.02437,0.02811,0.06891,0.02877,0.02263,-0.04994,-0.05822,-0.01803,0.01413,-0.03796,0.07521,-0.0112,-0.02613,0.01342,-0.04129,-0.05175,-0.00011,0.01807,-0.01896,-0.01017,-0.13374,-0.11442,0.04062,0.02422,0.02443,0.00799,0.02361,-0.03332,-0.05087,0.0249,-0.09558,0.06031,0.06467,0.02296,0.04789,-0.0321,0.03381,-0.06587,-0.00147,0.03053,0.01235,-0.05399,-0.07769,0.09775,-0.06434,0.08593,0.04469,0.01749,0.07012,0.08795,-0.15088,0.06091,-0.07392,-0.06695,0.02586,-0.01723,-0.05441,0.01694,0.06017,0.00157,-0.01352,-0.07245,0.11743,-0.00423,-0.01531,0.00294,0.09653,0.05746,0.0278,-0.11636,-0.00887,0.04823,0.04886,0.1047,-0.09235,-0.03004,0.02963,-0.00344,-0.13501,-0.01474,-0.03935,0.09106,0.04279,0.08155,0.05836,0.03073,0.04071,-0.06462,0.02188,-0.08387,-0.00386,-0.07341,0.00985,-0.03089,-0.09095,-0.00117,0.09547,-0.01927,0.00598,-0.02687,0.01722,0.04398,0.02384,0.00666,0.08823,-0.04987,0.0068,0.13919,0.02084,0.02424,-0.02638,-0.02986,-0.10412,0.12244,0.00494,0.0936,-0.04827,-0.02749,0.08169,0.08231,-0.03123,-0.03766,-0.03515,-0.013,0.03044,-0.02477,0.02627,0.06505,-0.03692,0.08865,-0.09979,-0.10562,-0.01838,-0.0594,-0.04755,-0.02515,0.00243,-0.02956,0.05967,0.01182,0.02306,-0.09149,-0.00042,0.04249,-0.03494,-0.04583,-0.00866,-0.03411,0.06128,-0.13933,-0.06638,0.03211,-0.0083,-0.09489,-0.05171,0.02275,-0.0725,0.08086,-0.02784,0.10726,0.02865,0.05466,0.03144,0.06428,0.07847,0.07283,-0.00142,-0.02855,0.06102,-0.03352,-0.01657,-0.02965,-0.05208,-0.06657,-0.04321,0.00046,0.03089,-0.04421,0.05857,-0.1414,-0.0591,0.04804,0.1226,-0.06486,-0.0809,0.04421,-0.07083,0.05021,0.0964,0.03411,0.01641,0.00052,-0.11461,0.16506,0.18089,-0.05175,0.02635,-0.04683,-0.00488,-0.00042,0.01412,-0.09166,-0.0373,0.05546,0.0642,-0.01717,0.02555,0.01431,-0.01766,-0.12817,-0.05158,0.04173,-0.12893,0.00279,-0.00964,0.00972,0.0549,0.05064,0.04323,0.02908,0.06309,0.12602,-0.03242,0.09884,-0.03602,0.10267,0.11442,-0.07853,-0.06364,0.02673,-0.07518,0.1568,-0.09698]},{"domain":"differential_equations","key":"linear_first_order","name":"First-order linear ODE with constant coefficients (integrating factor)","package":"differential-equations-ai999x","example":"Solve y' + a y = b with a = 2, b = 6, y(0) = 1; find y(1).","v":[0.02156,0.03701,-0.05983,0.00346,0.03419,0.00616,0.04008,-0.02099,-0.0077,0.0153,-0.00135,0.01123,-0.03292,-0.04237,-0.00811,0.00192,0.04383,-0.08967,-0.01414,-0.03166,0.01262,-0.07209,0.00101,0.05772,0.09519,-0.04104,0.0637,0.08027,0.0584,-0.06938,0.12235,0.05891,0.06505,-0.01897,0.00922,0.00914,0.02298,-0.0121,-0.07998,0.011,0.04432,-0.04923,-0.07811,-0.01749,-0.00616,-0.05105,-0.06036,-0.06566,0.1626,0.0664,-0.07041,-0.01347,-0.03884,-0.0735,0.0974,-0.03104,0.01227,0.03041,-0.03266,0.0232,0.0061,0.02478,0.04467,0.03954,0.08205,0.02193,-0.07935,-0.13015,0.15517,-0.04583,0.0137,-0.03861,-0.00036,-0.05983,-0.00883,-0.09424,0.0547,-0.05134,0.01873,0.00566,0.03993,-0.0403,0.07106,0.02165,-0.03532,-0.01155,0.05958,0.00743,0.06549,0.06058,0.03212,-0.0488,0.00362,-0.0242,-0.03671,0.06366,-0.0767,-0.09663,0.03423,-0.01011,-0.0647,-0.13568,0.04736,0.02604,0.06102,0.03655,0.10418,-0.02448,0.18928,0.03643,0.00954,0.0102,-0.05625,-0.0231,0.06748,0.0468,-0.0377,0.08361,-0.01285,0.09126,-0.02144,0.02587,0.02963,-0.09484,-0.00982,0.01411,-0.03741,0.11331,-0.031,-0.07398,0.04668,0.07279,0.0656,-0.0277,-0.06301,-0.14304,0.05495,-0.09566,0.01811,0.03128,-0.00092,0.03222,-0.03274,0.01839,0.01479,0.04755,0.00723,-0.04795,0.04208,-0.05496,0.00753,0.01464,-0.01696,0.02726,-0.00061,-0.1383,0.00482,0.03905,0.06455,0.00629,-0.00015,0.01986,-0.04524,0.11714,-0.02359,-0.07841,0.03706,-0.01754,-0.12337,0.07329,0.01764,0.00704,-0.08927,-0.04098,0.06929,-0.0291,-0.08203,-0.09888,0.07699,-0.03473,0.06131,0.03679,0.14195,0.03854,-0.1657,-0.08257,0.03447,-0.01723,-0.07937,-0.01702,-0.07844,0.06376,0.00151,0.03237,-0.02113,-0.01973,-0.00684,-0.01395,-0.05724,-0.12915,0.03322,0.07241,-0.19986,0.11622,0.10155,-0.05169,0.00926,0.04431,0.03531,0.02488,0.071,0.01329,0.08679,0.07575,0.01041,0.0192,0.07977,-0.10763,-0.20028,0.09149,-0.01617,0.0727,-0.10417,0.06361,-0.10294,0.03498,0.03471,-0.03807,-0.02289,0.1177,-0.0529,-0.06542,0.01291,-0.04098,-0.08336,0.0754,0.03944,0.01049,-0.05307,0.02703,-0.06132,-0.00776,-0.02408,-0.00235,0.06923,-0.07827,0.11262,-0.01706,-0.07074,0.09404,0.03305,-0.01361,-0.082,0.00868,-0.0123,-0.01957]},{"domain":"differential_equations","key":"linear_first_order_exponential_forcing","name":"First-order linear ODE with exponential forcing","package":"differential-equations-ai999x","example":"Solve y' + a y = b e^(c t) with a = 1, b = 2, c = 0.5, y(0) = 0; find y(2).","v":[-0.00807,0.03165,-0.10034,0.03749,0.03624,0.03654,-0.01717,-0.00104,0.0199,0.04059,-0.04655,-0.00724,-0.02395,0.01107,0.03983,-0.01548,0.06985,-0.02015,0.07525,0.00092,0.0339,-0.05749,0.01948,0.05544,0.02936,0.04745,0.00012,0.17249,-0.02654,0.07527,0.0514,0.03734,0.08648,0.0026,-0.00267,0.04313,-0.06138,-0.04427,-0.04223,0.04822,0.07539,-0.02371,-0.08076,-0.03646,-0.04657,-0.02128,-0.06041,-0.02772,0.0567,-0.04858,-0.09714,-0.02603,-0.02295,-0.01727,0.02483,0.02121,0.05391,0.06083,-0.06567,-0.04883,0.05851,0.03408,0.05097,0.0331,0.02323,-0.02084,0.00412,-0.15586,0.06281,0.0065,0.04457,-0.04329,0.0271,-0.04606,-0.02236,-0.08257,0.13143,-0.03651,-0.05334,-0.06195,0.00493,-0.02635,0.00627,-0.10377,-0.08436,-0.02044,0.02201,0.00523,0.09784,-0.03301,0.01701,0.01576,0.09612,-0.04101,-0.04557,0.00574,-0.05142,-0.00164,0.09572,-0.05888,-0.05045,-0.08411,0.03838,0.02472,0.06882,0.00489,0.0174,-0.01641,0.18935,0.1198,0.06432,0.08364,-0.05731,-0.05169,0.07567,0.074,-0.1601,-0.01442,0.059,0.05151,-0.0104,0.03897,-0.02556,0.04006,0.00023,-0.02435,-0.0534,-0.01573,-0.07311,-0.0628,0.00305,0.06685,-0.01507,-0.07266,0.03162,-0.06607,0.03705,-0.1024,-0.02503,-0.0049,0.10453,0.01946,-0.07791,0.06308,0.06372,0.02198,0.02431,-0.02687,0.00996,-0.00902,-0.02286,0.0705,-0.11147,0.04028,-0.03422,-0.06818,-0.06096,0.10158,0.16575,0.06972,-0.01658,-0.08838,-0.06252,0.10588,-0.06398,0.03224,-0.00414,0.11027,-0.08671,0.00362,-0.09159,0.04565,-0.01563,0.07346,0.10915,-0.01691,-0.08153,-0.02181,0.03393,0.07037,0.01317,-0.03877,0.12316,-0.04787,-0.12085,-0.0218,-0.00233,-0.00956,-0.08232,0.01166,0.05718,-0.04992,-0.06376,-0.08417,0.07033,0.00031,-0.09579,-0.10029,-0.05679,-0.10834,-0.0552,0.03038,-0.11407,0.09931,0.0446,0.07203,0.03406,-0.01467,0.06436,0.02781,0.04269,0.03854,0.12483,0.04723,0.00967,-0.1353,0.01264,-0.10493,-0.05384,0.10448,0.02534,-0.06876,0.02893,0.02175,-0.11876,-0.08741,0.04421,-0.07007,-0.04849,0.12231,-0.02365,-0.07662,0.05632,0.12494,-0.03149,0.0663,0.10757,-0.1113,-0.01472,0.05853,-0.04779,-0.00722,0.02985,-0.02526,0.01373,-0.05577,0.01112,-0.00036,0.00283,0.09892,-0.00159,-0.07697,0.10548,-0.00326,0.01848,0.01056]},{"domain":"differential_equations","key":"linear_system_solution","name":"Linear system x' = A x: solution at a time","package":"differential-equations-ai999x","example":"Solve the linear system x' = A x with A = [[0, 1], [-2, -3]], x0 = [1, 0] at t = 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of x' = A x (n x n) from the characteristic polynomial","package":"differential-equations-ai999x","example":"Is the linear system x' = A x stable for A = [[-1, 2, 0], [0, -3, 1], [1, 0, -2]]?","v":[-0.01221,-0.05997,-0.06328,0.05031,-0.04045,0.00058,0.03816,-0.03007,0.0216,-0.05588,0.03289,0.11313,-0.02583,-0.02203,0.05609,0.06423,-0.05247,-0.03386,-0.03032,-0.08959,-0.12795,0.08029,-0.03927,0.01756,0.05112,-0.1326,0.08579,-0.01613,-0.03205,0.00516,0.04829,-0.00817,0.05966,-0.01058,0.11959,-0.13378,0.03566,-0.02021,0.06638,0.00136,0.01409,-0.07612,0.10274,0.08651,-0.01648,-0.0509,-0.11236,-0.00042,0.03315,0.11856,0.06271,-0.07941,0.04338,0.06774,0.02586,-0.00928,-0.12143,0.04966,-0.00466,0.06381,-0.01851,-0.0407,0.04502,0.06196,0.03694,-0.05501,-0.01893,-0.0736,0.20812,-0.03074,-0.02185,0.14437,-0.00727,0.06865,0.04074,-0.02219,-0.02383,0.03584,0.16119,0.02378,0.05089,-0.1031,-0.0527,-0.03246,0.09345,-0.04176,0.01865,0.016,-0.01257,0.0005,-0.11453,-0.12214,-0.13861,0.06408,0.04619,0.10205,-0.04624,0.00306,0.04373,0.06678,-0.02194,-0.0302,-0.03262,-0.11051,0.11006,0.07274,0.04869,-0.10118,0.04266,-0.00419,0.02695,0.06182,0.01021,0.04296,-0.05058,-0.01586,0.00294,0.02718,-0.0068,-0.01788,0.05133,-0.05097,-0.00603,-0.06088,0.04061,0.1189,0.12437,0.0528,-0.06077,-0.00949,-0.04679,-0.07744,0.10502,-0.05486,-0.04179,-0.00094,0.05248,-0.02252,0.08841,-0.09485,0.05615,0.01132,-0.02713,-0.02091,-0.09268,0.05517,0.0095,-0.0375,0.02899,-0.05638,0.05612,0.05988,0.0736,-0.05117,0.01435,-0.024,0.01881,0.06943,-0.08009,0.06585,0.00481,-0.08352,-0.14117,-0.00645,-0.02825,0.08462,-0.00297,-0.00269,-0.00662,0.08179,0.13411,-0.06634,-0.08815,0.04035,-0.06697,0.00269,-0.03777,-0.07979,0.04676,-0.02191,0.00257,0.03784,0.02547,-0.00418,0.01696,0.0348,0.06417,0.0119,0.0177,0.06917,0.04442,-0.01513,0.02648,-0.04534,-0.07526,-0.09327,-0.03063,0.01717,0.03709,-0.06082,0.09264,0.03751,0.08141,0.07658,-0.00998,-0.03162,0.07286,-0.02817,-0.06497,0.0118,-0.03873,0.03157,0.02023,0.0282,0.04939,-0.01343,-0.09652,-0.01256,0.05293,-0.00422,0.00125,0.05048,-0.11367,0.06985,-0.06782,0.01574,-0.08428,-0.13872,-0.05946,-0.06746,0.03824,-0.0306,0.00495,-0.03531,-0.11738,-0.02799,-0.08693,0.05652,-0.06168,-0.00942,0.0471,-0.01565,0.03731,0.01339,0.0379,0.01018,0.15511,-0.12538,-0.06093,0.02239,-0.0635,0.03258,-0.05136,0.03446,0.03453,-0.05736]},{"domain":"differential_equations","key":"logistic_harvesting","name":"Logistic growth with constant harvesting: equilibria","package":"differential-equations-ai999x","example":"Logistic harvesting with r = 0.5, K = 1000, H = 100: find the 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growth: inflection time and maximum growth rate","package":"differential-equations-ai999x","example":"Logistic growth with P0 = 10, r = 0.5, K = 1000: when is the inflection 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map: fixed points and their stability","package":"differential-equations-ai999x","example":"Find the fixed points of the logistic map with r = 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1000.","v":[-0.13984,-0.13697,-0.01543,0.04943,-0.03282,-0.02142,-0.0394,-0.06438,-0.04306,0.15475,-0.06691,-0.18759,0.0457,-0.08189,0.12008,0.01298,-0.01142,-0.1567,-0.0779,0.04818,-0.01601,0.04854,-0.05138,-0.00934,0.07008,-0.04483,-0.02004,-0.01447,-0.01709,0.09531,0.00936,-0.04336,0.091,-0.04623,0.01917,-0.00652,-0.009,0.02565,0.00185,0.09302,0.09731,-0.04935,-0.11224,-0.02478,-0.0807,0.03187,-0.07298,0.1068,-0.05998,-0.05951,-0.14622,-0.04743,-0.06918,0.00475,0.09247,-0.01586,0.07965,0.00362,0.0183,0.00395,0.03193,-0.04159,-0.00121,-0.01188,0.03431,-0.0041,-0.00743,-0.05157,0.11998,-0.01168,0.03469,0.08008,-0.00515,-0.08715,0.0291,0.05169,-0.02929,0.07743,-0.02379,-0.08667,-0.03249,-0.00632,0.07129,-0.08998,-0.00338,-0.08334,0.01287,0.06375,0.03656,-0.00267,-0.11835,-0.02224,0.0398,-0.00154,0.06582,0.10246,-0.01948,0.07637,0.11856,-0.12052,-0.04322,-0.01912,-0.0422,0.01139,0.11863,0.00404,-0.03216,-0.08985,0.14576,0.02058,0.01284,-0.0418,0.0115,-0.07553,0.03138,0.0315,-0.02572,-0.04103,-0.0085,-0.09625,0.02552,-0.04361,-0.06498,0.08161,-0.10898,-0.03454,-0.00176,-0.08158,-0.07485,0.1543,-0.00219,0.01409,0.04103,-0.04741,-0.048,-0.02703,-0.00041,0.0553,0.02304,-0.13798,0.04663,0.07548,0.01604,0.02655,-0.0738,-0.00213,-0.02013,-0.02207,0.06507,0.02879,0.07998,-0.01277,0.06763,-0.08575,0.00232,-0.0075,-0.00148,0.0318,-0.05053,0.01439,-0.05176,-0.00289,-0.02597,0.03115,0.00866,0.01346,0.01137,-0.03302,-0.0021,-0.02328,0.09632,-0.0988,-0.02996,-0.02211,0.03528,0.00751,-0.01089,0.06092,0.03917,0.00622,-0.11136,0.05438,0.01644,-0.06361,0.1172,-0.05312,-0.04807,0.08303,0.09812,0.04039,-0.0445,0.02757,0.02995,0.00481,0.07352,0.05931,-0.10396,-0.05231,-0.01546,0.02085,0.04342,-0.01268,-0.00535,0.05809,0.02657,0.03874,0.07346,0.07548,-0.0582,0.04208,-0.09556,0.02433,0.02002,-0.00794,-0.08698,-0.06433,0.07275,0.07538,0.08944,0.04677,0.03416,0.00927,0.01476,0.11263,0.07181,-0.04697,0.01207,-0.0194,-0.08533,-0.02088,-0.03367,-0.14713,-0.0611,0.0969,-0.03628,0.03885,0.07054,-0.06993,-0.0213,0.05866,0.04016,-0.02875,0.11562,0.07172,0.01049,0.01853,0.14442,-0.02096,-0.02051,-0.00852,0.07983,0.02889,0.08833,0.03388,0.07289,-0.03464]},{"domain":"differential_equations","key":"logistic_map_two_cycle","name":"Logistic 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system: Hopf threshold rho_H (loss of stability of C+-)","package":"differential-equations-ai999x","example":"Find the Hopf threshold of the Lorenz system with sigma = 10, beta = 8/3.","v":[0.03022,-0.05419,-0.04367,0.17104,-0.01258,0.11439,0.02128,-0.05719,0.00328,0.07465,-0.06659,-0.08652,-0.02365,0.12209,0.02832,0.00961,-0.00943,0.06558,0.01136,0.03998,-0.04273,0.1108,-0.10815,-0.03242,0.13887,-0.01956,0.02443,0.00702,0.00281,0.02092,-0.11016,-0.06157,-0.03043,-0.00606,-0.04397,0.02176,-0.10478,0.0234,-0.05177,-0.0329,0.07939,-0.10005,-0.06109,-0.00239,0.01179,-0.0234,-0.01036,-0.02156,-0.03766,-0.07231,-0.00943,-0.18644,-0.05739,-0.03178,0.03601,0.03109,-0.03307,0.02321,-0.05202,-0.00588,0.04828,-0.0675,0.12241,0.12036,0.04174,-0.02318,0.04298,-0.00616,-0.04043,-0.067,-0.04645,0.10647,-0.05619,-0.08533,-0.01787,-0.05864,-0.00035,0.07233,0.05952,0.0527,0.04578,-0.00922,-0.0971,-0.05158,0.01415,-0.08783,-0.09894,7e-05,-0.03955,-0.0412,-0.10486,-0.07024,0.00431,-0.05835,0.03323,0.04406,0.02875,-0.03259,-0.05795,0.00042,-0.05983,-0.11162,-0.04624,0.01198,0.11068,0.01521,-0.05595,-0.016,0.0465,-0.00126,0.119,0.1029,0.16086,-0.06952,0.02693,-0.00769,-0.0238,0.00522,-0.09111,-0.0074,-0.03448,-0.05952,0.03998,0.03722,-0.07336,0.04656,-0.00161,0.00348,0.01703,0.02574,0.10362,-0.02567,0.00723,-0.06753,-0.00711,-0.05685,-0.06067,0.02185,0.04074,-0.0188,0.06396,0.06528,0.09967,0.03505,0.02561,-0.075,0.03407,-0.08626,-0.00637,0.00197,0.08635,0.06209,0.07223,-0.02342,0.00137,-0.00038,0.12046,0.04975,-0.10763,-0.07417,-0.05307,-0.04769,-0.03288,0.02919,0.04149,0.06093,0.04322,0.03634,-0.08055,-0.0268,0.0853,-0.01489,-0.10752,-0.0123,0.01884,-0.04132,0.01192,0.09681,0.05015,-0.025,-0.04863,0.04328,0.01802,-0.01413,0.07419,-0.06894,0.06371,0.12991,0.00367,0.1191,-0.0514,-0.05533,-0.07385,-0.01083,0.07258,-0.11331,-0.06049,0.03814,-0.07695,0.06492,0.11938,-0.02868,0.01341,0.06989,0.03362,0.01117,0.03723,0.11894,-0.15113,-0.02691,-0.09629,0.03219,0.10414,0.03558,-0.05599,0.05465,0.0107,0.03757,0.00643,0.06558,0.01787,-0.10082,0.00194,-0.06311,-0.09275,-0.00842,-0.01769,-0.05001,0.04021,0.05776,0.03668,-0.02037,-0.04916,0.02137,-0.03803,0.03802,-0.07142,0.00638,-0.04592,-0.10168,0.05889,0.04454,0.12721,0.00954,0.04579,0.03659,0.08769,0.05517,-0.03602,0.00012,0.00194,0.09632,0.14719,0.03389,0.03673,0.03719]},{"domain":"differential_equations","key":"lotka_volterra_equilibrium","name":"Lotka-Volterra predator-prey: coexistence equilibrium and oscillation period","package":"differential-equations-ai999x","example":"Lotka-Volterra predator-prey model with a = 1, b = 0.1, c = 1.5, d = 0.075: find the equilibrium and 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midpoint method (RK2)","package":"differential-equations-ai999x","example":"Apply the midpoint method to dy/dt = t + y, y(0) = 1, h = 0.1, n = 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tank (brine): amount of salt at a time","package":"differential-equations-ai999x","example":"A brine mixing tank has V = 100, r = 5, c_in = 0.2, A0 = 0; find A(10).","v":[-0.04548,0.08292,-0.06478,-0.03095,-0.02463,-0.02152,0.04604,-0.05336,0.04415,-0.00337,0.05717,0.02762,0.06185,-0.01481,0.08315,-0.12606,-0.09083,0.05883,-0.01774,0.07274,-0.02764,-0.01308,-0.07759,0.07228,-0.01144,-0.06729,0.04219,0.06167,0.10841,0.00711,-0.00551,-0.11784,0.02061,-0.07065,0.07801,0.01298,0.02173,-0.02524,0.02016,0.04815,0.04558,-0.05151,-0.03072,0.04576,0.0245,-0.00123,0.03679,-0.09633,0.01225,0.02791,-0.05385,-0.01894,-0.00884,-0.02525,0.05846,0.0453,0.01088,0.0225,-0.1109,6e-05,0.03269,0.11452,0.04388,0.0505,-0.00587,0.07415,-0.039,-0.10857,0.03375,-0.00787,0.01561,-0.08529,0.02098,0.0728,0.00695,0.02112,0.04071,-0.01313,-0.06708,0.05168,0.0679,-0.06785,0.05457,-0.08163,-0.07117,0.04574,0.02999,0.09475,0.07307,0.07976,-0.0488,0.01537,-0.00018,-0.0132,-0.04843,0.05938,0.0068,-0.03826,0.00358,-0.05113,0.04614,-0.11458,-0.0304,-0.00926,0.07844,0.00445,-0.00327,-0.04222,0.05494,0.01776,-0.00584,0.01671,-0.0611,0.03815,0.12581,-0.11485,0.04234,0.04899,0.0042,0.15056,0.01797,0.00307,0.0428,0.03111,0.0277,0.08966,0.07557,0.01424,0.02156,-0.10419,-0.09596,-0.08855,0.01596,-0.09955,-0.01198,-0.09305,0.03471,-0.02836,-0.05224,-0.02699,-0.06977,0.09806,-0.0694,-0.06342,-0.058,-0.08541,-0.07486,0.11571,-0.00748,-0.02064,-0.06231,-0.03023,0.00271,0.03004,-0.07345,-0.09923,-0.03607,-0.01644,0.11224,-0.10334,-0.02421,0.10262,-0.147,0.09751,-0.02537,0.03582,0.03873,0.01313,-0.07285,0.02164,-0.02902,0.05031,-0.06585,-0.0065,0.03135,-0.02104,-0.09174,-0.15812,-0.04121,0.09604,0.09291,0.04473,0.06853,-0.04114,-0.0302,0.0427,0.11581,0.01009,0.02642,-0.1011,-0.02001,0.02836,0.00432,0.04842,0.06251,0.05484,-0.00075,0.04099,-0.02763,-0.03603,0.008,0.12839,-0.18979,0.12641,0.08144,-0.10274,-0.02027,0.05118,0.0064,0.0396,-0.00594,-0.09646,0.11674,0.06097,0.03069,-0.1088,-0.03432,-0.05691,-0.04471,-0.02441,0.0953,-0.03962,0.00495,-0.07879,0.03523,0.04558,-0.08084,-0.00963,0.05125,0.11205,0.00297,-0.07844,0.09313,0.05523,-0.0431,0.03785,0.04321,-0.00643,-0.05099,-0.0799,0.01984,-0.09729,-0.10413,0.0559,0.03613,0.08383,0.07436,0.02433,0.03398,0.10136,-0.02469,0.08,0.06183,-0.06164,-0.05614,0.03287]},{"domain":"differential_equations","key":"newton_cooling_constant","name":"Newton's law of cooling: cooling constant from a measurement","package":"differential-equations-ai999x","example":"Newton's law of cooling: find the cooling constant if T0 = 90, Ta = 20 and T1 = 60 at t1 = 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law of cooling: temperature at a time","package":"differential-equations-ai999x","example":"Newton's law of cooling: T0 = 90, Ta = 20, k = 0.1; find T(5).","v":[0.00493,-0.05559,-0.08094,0.00627,-0.08788,-0.00923,0.05305,0.02803,0.05314,0.00425,-0.03367,-0.02322,0.0544,-0.11522,-0.03551,-0.0466,0.04647,-0.11122,0.02674,0.02617,-0.02161,-0.10537,-0.04049,-0.02694,0.05833,-0.04822,0.08258,0.03241,0.09986,-0.10508,0.12519,0.0974,0.04923,0.03299,-0.09688,0.0567,0.06651,-0.05046,-0.02065,0.01745,0.03723,-0.09967,-0.12214,0.03504,-0.06771,-0.04804,0.05898,-0.03366,0.12175,0.10158,-0.0539,-0.05346,0.05743,-0.1231,0.06762,-0.1163,0.0692,0.04196,-0.09152,-0.022,-0.06444,0.03655,0.06009,0.03591,-0.00819,0.11813,-0.00095,-0.01696,0.03152,0.04848,0.00323,-0.09303,0.01423,-0.06967,-0.01568,-0.0642,0.08103,-0.02756,-0.07651,-0.02264,0.15077,0.00181,0.14015,0.07503,0.01736,0.03236,0.07162,0.01351,0.0228,0.06869,0.06268,-0.00442,-0.02505,-0.05541,-0.10078,0.04167,0.01098,-0.02049,0.05741,-0.01612,-0.03525,-0.01105,-0.023,0.04117,-0.03904,0.07418,0.05789,-0.02976,0.06545,-0.04946,0.10606,-0.00867,-0.05379,0.03308,0.10175,0.06699,0.05509,0.06925,-0.0805,0.11118,-0.06677,-0.01022,0.09168,-0.08862,0.04963,-0.02069,0.07491,-0.01019,-0.07695,-0.00831,0.00086,-0.00916,0.03118,-0.00308,0.0582,-0.13562,0.10374,0.01031,0.0234,-0.03424,-0.0331,0.01259,0.01694,-0.0297,-0.07828,0.03068,-0.00284,0.06357,-0.03933,-0.09394,0.08275,-0.0331,-0.03097,0.07228,-0.04158,-0.05117,-0.0508,0.00173,-0.03711,-0.07386,-0.08425,0.08083,-0.06765,0.15148,-0.04111,-0.03019,0.06692,-0.10191,-0.05046,0.01056,0.09016,-0.06876,-0.00936,0.03662,0.02198,-0.08287,-0.08724,-0.08745,0.00596,0.01968,0.02333,0.01477,0.07428,0.01412,-0.11213,-0.0272,-0.06713,-0.03649,-0.10179,0.03063,0.03835,0.03919,-0.01968,-0.03313,0.02456,0.08593,0.12743,0.05427,-0.02548,0.04757,-0.00084,-0.04052,-0.12198,-0.05119,0.02821,-0.01818,0.10247,0.03537,0.02513,-0.03082,0.12827,-0.01454,-0.01503,0.01548,0.09751,0.03838,0.03667,-0.0841,-0.10118,-0.00635,-0.02788,0.00936,-0.05273,-0.04988,-0.03369,0.05783,0.09506,-0.1164,-0.0746,0.1139,0.01192,0.00771,0.04057,-0.04755,-0.03644,0.06848,-0.04621,0.01676,-0.11653,0.03212,-0.01809,-0.05201,-0.05437,0.10215,0.01992,0.03051,0.10452,-0.02223,-0.00298,-0.01257,-0.01707,0.06782,-0.03477,-0.06314,0.02993,-0.07272]},{"domain":"differential_equations","key":"newton_cooling_time","name":"Newton's law of cooling: time to reach a temperature","package":"differential-equations-ai999x","example":"Newton's law of cooling: how long until T1 = 40 if T0 = 90, Ta = 20, k = 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fractions of a rational function (simple poles)","package":"differential-equations-ai999x","example":"Find the partial fractions of (s + 3)/(s^2 + 3s + 2).","v":[-0.03199,-0.10003,-0.01616,0.02647,0.05011,-0.04331,-0.03643,-0.06028,-0.07678,-0.0721,-0.06118,0.17659,-0.0583,0.09706,-0.02142,0.04203,-0.10244,0.06008,0.0606,0.01159,-0.022,-0.12645,-0.02478,-0.06006,0.00553,-0.01042,-0.05317,-0.03158,0.13232,0.01236,-0.06755,0.02354,-0.00851,-0.04792,-0.03433,-0.07592,0.06099,-0.04953,0.04479,0.01531,0.00965,0.0023,0.09394,0.00829,-0.0012,-0.02694,0.00773,0.06273,0.0018,0.04166,-0.01422,-0.00617,-0.08342,0.08898,0.06667,-0.01427,-0.1479,0.07888,0.06802,-0.05746,0.036,0.08554,-0.03077,-0.06337,0.0684,-0.05136,-0.00168,-0.1369,0.01344,-0.03432,0.069,0.04283,-0.09268,0.0325,0.03778,0.06055,0.03684,0.0359,0.08035,-0.03029,0.11427,-0.12151,-0.0907,0.00323,0.12736,-0.02972,0.08818,0.01801,-0.0341,-0.07309,0.05405,-0.03071,-0.1176,-0.00779,-0.03743,0.04987,-0.01543,0.03429,-0.06027,0.04846,0.03964,-0.02048,0.03294,0.08788,-0.09327,0.03156,0.15534,0.00325,-0.09814,0.16372,-0.01437,0.03007,-0.01765,-0.00183,0.0108,0.05707,-0.01068,0.01368,0.07275,0.06562,0.04265,0.0195,0.05521,0.00405,-0.02083,0.08943,0.06989,0.06739,0.02268,0.02456,-0.03984,-0.01974,0.06395,-0.11195,-0.06656,0.04833,0.0293,-0.08756,-0.08609,0.05674,0.13397,0.05001,-0.05637,-0.01118,0.08048,0.01509,0.04968,0.03578,-0.01453,0.04743,-0.07026,0.01928,0.00783,0.02142,0.09621,0.02497,-0.04837,0.04123,-0.06011,-0.00674,0.06918,-0.12859,-0.04116,0.00416,0.03574,0.10563,-0.08165,0.10701,0.08739,-0.02347,-0.05045,0.06961,0.0113,0.01214,0.00435,0.052,0.02332,-0.10458,-0.05208,0.20399,-0.06436,-0.01746,0.09607,-0.06365,-0.0022,0.00499,-0.00433,-0.02704,0.02622,0.011,0.01632,0.08515,0.08703,0.00449,0.01271,-0.03852,-0.05404,-0.0249,0.01892,-0.01923,-0.03291,-0.00879,-0.07912,0.09911,0.0404,-0.05059,-0.00187,-0.0624,0.00931,-0.03235,0.08422,0.08811,0.04169,0.03748,0.02359,0.02788,0.03624,0.01714,-0.00311,-0.05239,0.00328,0.07031,-0.02666,-0.02325,-0.04548,0.0481,0.01503,-0.2039,-0.01761,-0.07231,0.00271,-0.03246,-0.01098,-0.08948,-0.15662,-0.00032,-0.02636,-0.13628,-0.00221,-0.01957,0.06667,-0.01674,-0.0286,0.03866,0.03727,0.02507,-0.00939,-0.14308,0.00664,0.0492,-0.02253,-0.00166,-0.07445,-0.03683,-0.01279,0.01032]},{"domain":"differential_equations","key":"phase_portrait_2x2","name":"Linear 2x2 system: equilibrium type and stability (trace-determinant plane)","package":"differential-equations-ai999x","example":"Classify the equilibrium of the linear system x' = A x with A = [[0, 1], [-2, 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oscillator: resonance frequency and peak amplitude","package":"differential-equations-ai999x","example":"Find the practical resonance frequency for m = 1, c = 0.4, k = 4, F0 = 2.","v":[-0.04658,0.07132,-0.05879,0.03136,-0.0508,0.01337,-0.0508,-0.01631,0.0362,0.02625,0.00295,0.04518,-0.01402,0.09262,-0.01937,-0.0377,0.02538,0.01361,0.02004,-0.01372,-0.04291,-0.02603,0.03769,0.03385,0.05816,0.04287,-0.03668,0.10327,0.07377,-0.04958,0.0901,0.00562,0.02359,0.04761,0.02587,0.0013,-0.05498,-0.02176,-0.00931,-0.04405,0.01562,-0.0414,0.00622,0.08159,-0.06449,-0.04061,-0.06783,-0.02234,0.088,0.00854,-0.02265,0.02193,0.02195,0.04207,-0.00197,-0.00264,-0.10243,0.05525,0.0225,-0.01451,0.08799,-0.07077,0.07272,0.09019,0.16125,-0.02157,-0.06084,-0.00796,0.08792,-0.10228,0.09051,0.07907,0.02509,-0.11656,-0.09694,-0.06287,-0.00247,-0.09709,0.04541,0.04596,0.08851,0.00495,-0.01134,-0.08563,0.04608,0.02362,0.01357,0.05628,-0.01792,-0.07124,0.02239,0.0938,0.04284,0.08668,0.02429,-0.04276,-0.00556,-0.02194,0.04916,0.01281,-0.14201,-0.09378,-0.07353,-0.07434,0.07388,0.13658,0.02599,0.06318,-0.14575,0.05774,-0.02197,0.07394,0.06897,-0.01634,0.00725,-0.00016,0.02906,-0.04364,-0.05988,0.06132,0.07379,-0.01875,0.00466,-0.11807,-0.13634,-0.01227,-0.05479,-0.09132,-0.00015,-0.07454,-0.04279,0.08848,-0.00868,0.0207,-0.05714,-0.00487,-0.06303,-0.06532,0.03595,0.10703,0.03421,0.08738,-0.06433,-0.01836,0.12665,0.05049,0.10611,-0.14362,-0.03547,-0.01648,-0.03459,0.09778,-0.0662,0.02613,-0.0638,0.05422,0.02215,0.06801,-0.05564,0.04669,0.0509,0.04808,-0.00993,0.08098,-0.11241,0.02526,0.07676,-0.02249,-0.05092,0.04068,-0.0676,0.04142,-0.0789,-0.02348,0.01828,-0.00314,0.06181,-0.07581,0.08299,-0.0003,0.07422,0.03524,0.00723,0.05919,-0.10789,-0.01735,-0.09444,-0.03061,-0.02646,0.03138,-0.13167,0.03289,-0.07931,-0.05807,-0.00299,-0.00657,-0.09819,-0.00051,-0.12714,-0.13169,0.07498,0.08426,-0.14682,0.16098,-0.0142,-0.00441,-0.01065,0.09711,-0.01425,-0.09037,-0.01784,-0.07016,0.0673,0.06868,0.00042,0.08794,-0.088,0.04714,-0.01884,0.00431,-0.05871,0.09987,-0.06943,0.01626,-0.13336,0.07034,-0.05032,-0.05679,-0.0778,0.03554,0.00684,0.05383,0.06848,0.0604,-0.03406,0.0207,-0.00727,0.0906,0.01332,-0.05279,-0.09746,0.03116,-0.02457,-0.02593,0.00414,-0.04316,0.04297,-0.01169,-0.05504,0.05032,-0.01624,0.03313,0.06177,-0.0213,-0.05809,-0.02561]},{"domain":"differential_equations","key":"quadratic_drag_velocity","name":"Falling body with quadratic drag: velocity","package":"differential-equations-ai999x","example":"A falling body with quadratic drag: m = 80, c = 0.25, g = 9.81, v0 = 0; find v(5).","v":[-0.06564,0.0215,0.10466,0.0904,0.00996,-0.05245,0.11019,-0.03871,0.01517,-0.12243,0.06099,0.00451,-0.01387,-0.148,0.01752,-0.07605,-0.01363,-0.05521,0.02698,0.04435,0.01573,0.00556,0.1023,0.02097,0.00597,0.05479,0.00477,0.05144,-0.07587,0.02363,-0.01573,0.05878,-0.06364,0.0463,-0.01217,-0.01997,-0.0181,-0.06572,0.0338,-0.10531,0.04575,0.04526,-0.06926,-0.12818,-0.12464,0.04494,0.04518,0.00635,0.04252,0.01295,-0.01098,-0.00745,0.05054,-0.07573,6e-05,0.08696,0.00829,0.13989,-0.01118,-0.00876,-0.05555,-0.037,-0.01417,0.06802,-0.0837,-0.06259,0.14806,-0.08659,0.01253,0.07203,0.00749,0.00552,0.02855,-0.13265,0.0381,-0.08404,-0.07044,0.05683,-0.06805,-0.05608,-0.0326,0.06439,-0.02573,-0.00186,-0.08172,0.13654,-0.00121,-0.08757,0.03316,0.083,0.01597,0.06219,-0.01024,0.00269,0.06073,0.00133,0.12781,0.01618,-0.05733,0.05268,0.00997,-0.08509,-0.03266,0.02403,0.02455,-0.00839,0.04341,0.10076,-0.01074,0.01979,-0.05835,0.01078,-0.029,-0.0218,-0.02511,-0.03943,-0.00451,-0.09609,-0.04065,0.09854,-0.03226,0.02707,0.01501,0.01382,0.01543,-0.01055,-0.00529,0.06034,-0.01149,0.04344,0.15656,0.02427,-0.04792,-0.02109,-0.02913,-0.08845,0.13441,0.0188,0.05426,-0.01011,-0.00852,0.07888,0.08842,-0.00748,-0.06305,-0.04154,-0.0218,0.05676,-0.00091,0.05994,0.09009,-0.03845,-0.00831,-0.12329,-0.09129,-0.01702,-0.07305,-0.08163,-0.06939,0.01339,-0.00747,0.0361,-0.00553,-0.00435,-0.15737,0.04614,0.07043,0.0734,-0.02594,-0.08778,-0.05123,0.14674,-0.14324,-0.08695,0.02142,-0.05679,-0.04228,0.01456,-0.03431,-0.05169,0.12142,0.01089,0.02854,-0.03176,0.10347,0.00624,0.01934,0.07774,0.0823,0.02944,0.00642,-0.0131,-0.0103,-0.0376,0.01795,-0.06069,-0.08516,-0.0754,-0.0309,-0.02423,-0.03712,0.06302,-0.09821,-0.07577,-0.02126,0.10311,-0.0914,-0.07573,0.06629,-0.10076,0.01219,0.04195,0.1128,-0.00924,0.04463,-0.04613,0.03509,0.15219,-0.00441,0.04,-0.01784,-0.03608,0.0214,-0.01234,-0.05764,-0.03729,0.01071,0.02478,-0.03537,0.03782,0.05881,0.02525,-0.07407,-0.05202,0.07567,-0.03788,-0.0206,0.03782,0.11903,0.03309,0.03241,0.03058,0.00087,0.07467,0.05339,-0.01224,0.01953,-0.03763,0.09251,0.06906,-0.14671,-0.07276,0.05518,-0.0537,0.14414,-0.04633]},{"domain":"differential_equations","key":"quadratic_ode_blowup","name":"Equation y' = k y^2: solution and blow-up time","package":"differential-equations-ai999x","example":"Solve y' = k y^2 with k = 1, y(0) = 0.5; find y(1).","v":[0.04332,0.04154,-0.03166,0.04733,0.04888,-0.09837,0.02264,-0.00465,0.00617,-0.13963,0.01318,-0.08965,-0.0073,-0.08526,0.08469,0.03836,0.01402,-0.07521,-0.03533,0.06034,-0.04134,-0.01102,0.06696,0.03488,0.06658,0.01462,0.08755,0.12144,0.07742,0.03851,0.05275,-0.00413,-0.05052,-0.01366,0.06065,-0.13389,-0.04529,-0.005,-0.00308,-0.07881,0.06466,-0.01005,-0.00436,-0.00271,-0.00499,0.02721,-0.00947,-0.05089,0.10795,-0.07585,0.0376,-0.00945,-0.00194,-0.06526,-0.01586,0.05252,0.02772,-0.00905,-0.04972,-0.04138,0.02707,0.03461,0.00788,0.01089,0.04238,-0.00022,-0.03104,-0.12599,0.04883,0.06421,0.04345,-0.15144,0.00819,0.05459,0.06841,-0.09505,-0.02238,0.00073,-0.0703,-0.05486,-0.04143,0.0126,0.00114,-0.007,-0.03907,0.04773,0.04492,-0.09584,0.16289,-0.00529,0.05062,-0.02868,0.07908,0.0186,0.01372,0.03346,0.03644,-0.02734,0.0383,0.01527,0.00271,-0.09124,-0.06706,0.09265,-0.08423,-0.05288,-0.01922,0.08371,0.12781,0.06162,0.04561,-0.04027,-0.06548,0.00886,0.05027,-0.02095,-0.03471,0.03407,0.04766,0.04686,0.00764,0.01861,0.03352,-0.06449,0.04025,0.00771,0.0584,-0.00656,0.11456,0.00452,0.06402,0.06796,-0.03916,0.01403,-0.08554,-0.14665,0.17977,-0.03727,0.06265,0.06217,-0.05005,0.02753,0.02145,0.05404,-0.09883,-0.01453,-0.08967,0.04083,0.04344,0.03492,0.07732,-0.00837,-0.06579,0.02626,-0.09337,-0.06587,-0.08463,0.0013,0.05351,0.00401,-0.01287,0.02869,-0.10881,0.05111,-0.05937,-0.02553,0.07132,0.12328,-0.07106,-0.02374,0.08501,-0.00387,-0.11355,-0.00454,0.08145,-0.07489,-0.13708,0.00447,0.09076,-0.07588,0.06871,0.02485,0.06872,-0.01578,-0.10392,-0.06405,-0.02873,0.09465,-0.04212,0.06468,-0.0152,-0.06383,0.03324,-0.02865,0.0118,-0.07247,-0.039,-0.18544,-0.04846,-0.04846,0.06027,0.04144,-0.03506,0.05775,0.06907,-0.01525,-0.09367,-0.05091,0.04374,-0.05995,0.12306,-0.02916,0.17506,-0.01921,-0.05563,-0.05321,-0.01042,-0.09024,-0.09514,0.07775,0.01805,-0.01401,-0.09726,0.02187,-0.09495,-0.01389,0.0251,-0.0458,-0.03243,0.11306,-0.07249,-0.00819,0.00803,-0.08123,-0.01487,0.10527,-0.06076,0.06835,0.113,0.05103,0.0902,0.03682,0.03463,0.10276,-0.00738,-0.04904,-0.04763,0.00131,-0.02083,-0.00597,0.00577,-0.07749,-0.00174,0.01485,-0.02749,0.00771]},{"domain":"differential_equations","key":"radiometric_age","name":"Age from the fraction remaining (radioactive dating)","package":"differential-equations-ai999x","example":"Radiocarbon dating: half-life T = 5730 and fraction remaining p = 0.25. What is the age?","v":[0.00953,0.07758,-0.14808,0.06003,0.12299,0.00871,-0.00927,0.05251,0.02303,-0.00451,0.01878,0.08413,-0.04169,-0.03497,-0.10172,-0.01793,0.01969,0.00154,-0.00839,0.05138,-0.11117,0.01932,-0.07335,0.02991,-0.00023,-0.0125,0.04065,0.03732,0.08454,0.05613,-0.07137,0.13989,-0.00864,-0.00444,-0.09315,-0.10953,0.0121,-0.07226,-0.04713,-0.01139,0.01822,-0.05872,0.15752,-0.08845,-0.03374,0.01484,0.04258,-0.02927,-0.10972,-0.05294,0.07088,0.0034,-0.05678,-0.07399,-0.03535,0.10011,0.06306,-0.0615,-0.06224,-0.03534,0.07468,-0.04204,0.08425,0.15998,0.02087,0.02301,0.05671,0.05534,0.07986,0.00675,-0.06189,-0.12135,-0.0169,0.01499,0.05261,-0.10851,-0.00803,0.01858,-0.06972,-0.05414,0.03553,0.0062,0.01442,0.13657,0.08527,-0.0573,0.04345,-0.13432,0.07324,-0.00059,-0.05501,-0.08413,-0.00779,-0.04098,-0.02557,0.08787,0.06592,-0.00381,-0.03308,0.05393,-0.07072,-0.07603,0.07596,-0.02472,-0.0744,-0.00242,-0.02765,-0.05915,-0.04786,-0.12218,0.00948,-0.0467,0.01374,-0.04013,-0.01727,0.01697,0.07392,0.0009,-0.03504,0.06624,0.00272,0.05707,0.01517,0.04026,-0.11205,0.02973,-0.04582,-0.00888,-0.01232,0.0459,0.08299,0.04416,0.04959,0.01668,-0.04224,0.0095,0.07818,0.02479,0.02065,0.11652,0.04913,0.01481,0.01777,-0.04429,-0.15661,0.04902,0.05175,0.08658,-0.01595,0.03215,-0.03767,-0.07026,-0.04029,-0.05653,0.0795,-0.05111,0.02855,-0.03091,0.00543,-0.13352,-0.07016,0.07695,-0.07518,-0.07437,-0.00401,-0.02237,0.11372,0.04536,0.00682,0.01204,-0.04309,-0.06099,0.06009,-0.01357,-0.01006,-0.04013,-0.03179,-0.01029,0.12542,-0.01904,0.0182,0.0073,0.01106,-0.01135,0.09227,0.01336,0.02956,-0.04851,0.06167,0.07344,0.00481,-0.04162,-0.01335,-0.07687,0.02812,0.03175,0.02424,0.00717,0.07307,0.10336,-0.05025,-0.01055,0.01259,-0.02926,-0.00265,-0.07935,0.12244,-0.03197,0.03509,-0.0065,0.05188,-0.02993,0.08442,-0.02551,0.14255,-0.01191,0.05505,0.02846,-0.15309,0.06019,0.04848,-0.00438,-0.02779,-0.19799,0.0675,-0.00906,0.15191,-0.0288,0.02622,-0.02187,0.0609,0.06815,0.04097,0.07473,-0.02216,-0.02778,-0.03239,-0.03425,-0.01145,-0.09185,-0.05873,0.00631,-0.07186,0.05529,0.05137,-0.04093,-0.12382,-0.05535,0.00202,-0.09713,-0.05994,-0.04634,0.10103,-0.00076,-0.04606,0.02915]},{"domain":"differential_equations","key":"robin_eigenvalues","name":"Eigenvalues with a Robin (convective) end condition","package":"differential-equations-ai999x","example":"Find the Robin eigenvalue with L = 1, h = 1, n = 1.","v":[-0.09583,-0.0439,0.03777,-0.00997,-0.08969,-0.06872,0.09098,0.04107,-0.04981,-0.10711,0.11659,0.01735,0.05155,0.01691,0.00755,0.09199,0.0717,-0.07965,0.00204,-0.07655,-0.00825,0.02998,-0.05449,-0.03053,0.2474,-0.00056,-0.05447,0.07083,0.03458,0.01044,-0.02826,0.04448,-0.02739,-0.0169,0.09037,-0.01314,0.09668,0.05887,0.07749,-0.05143,0.10696,-0.06641,0.03813,0.00732,-0.06436,0.04906,0.11547,-0.05301,-0.04705,-0.01604,-0.09248,-0.0258,-0.00733,-0.02138,-0.09137,-0.12517,0.04541,0.04985,0.11391,0.02164,0.03042,-0.02367,0.07967,0.06277,0.08167,0.07463,-0.05526,-0.07049,0.05929,0.01224,-0.05914,-0.00944,-0.05958,0.02471,0.01943,-0.11323,-0.03001,0.03457,-0.00244,-0.04559,0.03749,0.07754,0.01347,-0.05887,0.00584,-0.0655,-0.02414,-0.0429,0.01965,0.03519,-0.11656,-0.05449,0.05315,-0.00549,0.03694,0.02098,0.02105,-0.03784,0.02045,-0.04046,0.0473,-0.07895,0.00629,-0.0503,0.06245,-0.09303,-0.0232,0.10761,0.07369,-0.01546,-0.06941,-0.07856,0.02582,0.12065,-0.06531,-0.02268,0.06113,-0.07751,0.10754,-0.06845,0.03634,-0.00704,0.02389,-0.0775,-0.01471,0.02795,0.03255,0.05158,0.06976,0.00607,0.07522,0.12576,0.10748,-0.02788,-0.07358,-0.04981,-0.01563,0.00732,-0.02324,-0.01911,-0.00764,-5e-05,0.06182,0.01143,0.03377,-0.02083,0.00543,-0.0878,0.00262,-0.04833,0.08211,0.04112,-0.00235,-0.06892,0.04609,-0.06792,0.02037,0.01584,-0.00983,0.04361,-0.08583,0.02515,-0.11403,0.07404,-0.02423,-0.04698,-0.05337,-0.0209,-0.00418,0.09404,-0.00468,0.04596,-0.02719,-0.0434,-0.01242,-0.04191,6e-05,-0.01413,-0.03486,-0.17168,0.0021,-0.00931,-0.07144,-0.07115,-0.06918,-0.0294,0.06717,-0.03959,0.00092,0.06556,-0.03269,0.04551,0.01896,0.07195,0.00782,-0.09257,-0.17242,-0.06541,0.11278,-0.08522,0.22717,0.02923,0.02702,0.13234,0.03639,-0.11033,0.0559,0.08814,-0.04259,-0.054,0.04605,-0.01841,0.02221,0.06963,0.0225,0.02343,-0.07524,-0.06342,0.0679,-0.0105,-0.12727,0.07454,-0.01435,-0.02974,-0.00267,-0.05392,0.01193,0.02108,-0.01505,-0.12141,0.04582,0.01802,-0.02428,-0.0646,-0.01068,-0.02497,-0.03884,0.07961,-0.03312,0.046,0.15618,-0.01496,-0.02533,-0.03798,0.00402,0.00568,0.07209,0.00556,0.02341,0.0823,0.04357,-0.02159,-0.01609,-0.00029,-0.00667,-0.01802]},{"domain":"differential_equations","key":"routh_hurwitz","name":"Routh-Hurwitz stability test of a characteristic polynomial","package":"differential-equations-ai999x","example":"Apply the Routh-Hurwitz test to coeffs = [1, 6, 11, 6].","v":[0.04399,-0.08578,-0.04439,0.12397,-0.022,-0.02125,-0.00545,-0.01759,-0.02994,-0.04369,0.00165,0.1309,-0.05677,0.06579,0.02869,0.03119,0.00352,-0.08633,0.02428,-0.04495,-0.01263,0.02914,0.02908,-0.00761,0.07093,-0.06917,0.01208,-0.01506,0.04183,0.04985,-0.01869,0.10033,0.0311,-0.04764,-0.04709,-0.02602,0.09935,0.10466,0.07128,0.01432,0.03151,0.02566,0.16343,0.02177,-0.04301,-0.0262,-0.00536,-0.06092,0.03729,0.07951,0.06788,0.01761,0.06627,0.05138,-0.01618,-0.00378,-0.07972,0.11893,0.05218,0.00963,-0.05033,-0.02977,0.01735,-0.05226,0.15467,-0.03691,-0.0311,-0.0898,0.09657,-0.07577,-0.05242,0.12278,-0.0895,0.10989,0.10885,-0.00916,-0.04397,0.04246,0.09177,0.02951,-0.02204,-0.10852,0.01064,-0.03316,0.08014,0.00547,-0.02114,-0.01443,-0.11287,-0.04868,-0.10403,-0.00916,-0.01548,-0.06439,0.04306,0.02391,0.05113,0.07354,-0.08574,0.10292,-0.00528,-0.07049,-0.00282,0.03787,0.01558,0.07801,0.04243,-0.01955,-0.04013,0.01346,-0.0402,0.03634,0.04092,0.05255,-0.03885,0.06569,0.01518,-0.09181,-0.08499,0.01252,0.10504,-0.03812,0.02129,-0.03036,-0.09235,0.04799,0.07564,0.06072,-0.04644,-0.03823,-0.10239,-0.10716,0.10024,-0.10332,-0.0332,0.04262,-0.02851,-0.059,0.08012,-0.07086,0.00925,0.00167,0.0202,-0.01156,0.03022,-0.00961,0.01561,-0.00915,0.05761,-0.0443,0.0488,-0.01185,0.00699,-0.04305,-0.01586,-0.03199,-0.01142,0.08732,-0.12413,-0.02039,-0.00158,0.02144,-0.10526,-0.01126,-0.06767,0.02557,-0.07564,-0.01309,0.16873,0.02909,-0.0179,-0.04368,-0.07366,-0.00874,-0.01217,0.0156,-0.00335,-0.04423,-0.09245,0.05971,-0.00413,-0.03945,0.00539,-0.00872,0.1074,-0.03557,0.09883,-0.03051,0.01078,0.0836,-0.08282,-0.00334,0.03378,-0.05859,-0.0768,-0.05101,-0.10339,0.03239,-0.01234,-0.03888,0.00507,0.06654,-0.01687,0.088,0.07431,-0.00624,-0.00034,0.02117,-0.1426,-0.06003,-0.00433,0.06489,0.07008,0.08496,0.09981,0.02237,-0.14434,-0.00317,0.00387,0.05702,0.08497,0.07061,-0.01465,-0.05105,-0.09079,0.07647,-0.00976,-0.04479,-0.06145,-0.07348,-0.02245,-0.01205,0.00638,0.01168,-0.09395,0.0602,-0.14611,-0.09885,0.0157,0.00644,-0.02118,0.00433,0.03314,-0.0415,0.07099,0.05081,0.17923,-0.02532,-0.12286,0.1621,-0.04743,0.03552,-0.04561,0.01953,0.07915,0.00768]},{"domain":"differential_equations","key":"runge_kutta_4","name":"Classical Runge-Kutta method (RK4)","package":"differential-equations-ai999x","example":"Use RK4 for dy/dt = t + y, y(0) = 1, h = 0.1, n = 2.","v":[0.01518,0.04657,0.15217,-0.07074,0.06075,-0.0489,-0.0132,0.08072,0.07847,-0.05607,0.03589,-0.0088,-0.04762,-0.00507,0.14427,-0.0084,0.04684,0.01068,0.00185,-0.00973,-0.07892,-0.04513,-0.03576,-0.0854,0.00709,0.02611,0.04175,-0.00831,0.10677,0.00233,-0.05503,0.046,-0.05427,-0.13536,-0.06455,-0.08263,0.06558,0.07546,-0.01179,-0.13715,0.04643,-0.01899,-0.01255,0.03567,-0.01912,0.03488,-0.04388,0.05046,0.08841,-0.08164,-0.06099,-0.0003,-0.06891,-0.13953,-0.03227,-0.16904,0.03518,0.00412,0.10014,-0.16638,0.08612,0.02312,0.10786,-0.05786,0.01675,0.08071,0.10085,-0.03457,-0.03064,0.09959,-0.06955,-0.04157,-0.0208,0.0665,0.01657,0.01153,-0.05292,0.04387,-0.11602,0.03499,-0.03989,0.0129,0.06199,0.06437,0.05738,0.06044,0.03163,-0.07552,0.06756,-0.0603,0.00161,0.01639,0.09249,-0.05683,-0.08378,0.0819,-0.00807,-0.08431,-0.04878,0.06589,0.02932,-0.02556,-0.10286,0.00981,-0.07471,-0.0525,-0.01261,0.10639,0.10369,0.05314,-0.0062,-0.01244,0.04796,0.07389,0.01478,0.02597,-0.05307,0.03994,0.08905,0.00673,-0.04564,0.01663,-0.07957,0.00976,-0.04201,-0.15682,0.00164,-0.08636,0.06718,0.04961,-0.00662,0.04616,-0.11403,0.00124,-0.03747,-0.15469,0.1424,-0.0106,0.07078,0.07422,0.03736,-0.06395,0.0031,0.07057,-0.02608,0.0243,-0.06715,0.04533,-0.09219,-0.13502,-0.05331,-0.0666,-0.13375,0.08848,-0.05336,0.0331,0.00182,0.02875,-0.02405,-0.12207,-0.0009,-0.08844,-0.02957,0.04497,-0.03862,0.02981,-0.02809,0.05931,0.03719,0.06368,-0.05154,-0.09363,-0.00712,0.01755,0.07324,0.0675,-0.0663,0.06703,0.04343,-0.08881,-0.0039,0.08702,0.08493,0.00244,-0.02157,-0.09821,-0.03604,0.03642,0.03759,0.06527,0.03872,0.00085,0.03673,0.01093,0.0395,0.00016,0.00223,-0.06242,-0.07015,-0.06639,0.0419,0.0492,-0.11352,0.06276,-0.04358,-0.01531,-0.03113,0.06418,0.03585,-0.0453,0.09884,0.06661,0.04579,0.0156,-0.0176,-0.07056,-0.02198,-0.02626,0.02726,-0.04083,0.11476,0.03304,0.02686,-0.00453,-0.03462,-0.04847,0.00024,-0.0054,-0.08412,-0.06563,0.06296,0.01805,-0.06194,0.00738,-0.01781,0.08142,0.05177,-0.08542,0.02809,0.05591,0.10749,2e-05,-0.03559,0.07313,-0.01505,0.0147,-0.00538,0.00578,-0.00157,0.02558,0.09482,0.03022,0.02187,0.03855,-0.01044,0.01664]},{"domain":"differential_equations","key":"runge_kutta_4_system","name":"RK4 for a system of two first-order equations","package":"differential-equations-ai999x","example":"Use RK4 on the system dx/dt = y, dy/dt = -x with x(0) = 1, y(0) = 0, t0 = 0, h = 0.1, n = 10.","v":[-0.02489,0.01328,0.12324,-0.01149,-0.02839,-0.07454,0.02434,0.01945,0.10831,-0.09606,0.01337,0.00158,-0.10943,-0.02877,0.1578,-0.00346,0.01881,-0.06682,0.01337,-0.03136,-0.10617,-0.00599,0.01942,-0.0155,-0.07147,0.06491,-0.05635,-0.0077,-0.03134,-0.03217,0.00245,-0.02735,-0.07423,-0.06611,0.03933,0.02047,0.00494,0.12003,0.00226,-0.06173,0.0481,0.05529,-0.04836,0.04426,-0.04581,0.02715,-0.08137,0.13844,0.02191,0.00797,-0.13715,0.13136,-0.10027,-0.05797,-0.00137,-0.03058,0.04824,-0.01257,0.02067,-0.0518,-0.0303,-0.02852,0.09492,-0.05084,0.00229,0.02575,0.10963,-0.01402,0.0101,0.08035,-0.10834,-0.05483,0.00816,0.01721,-0.00711,-0.00262,-0.01137,0.01672,-0.09825,0.02943,0.00453,-0.00494,-0.02793,0.01128,0.03611,0.06339,-0.06411,0.05112,0.05179,0.0099,-0.03311,-0.08525,0.10308,-0.02698,-0.029,0.06562,-0.02456,-0.09126,-0.02528,0.03274,-0.03938,-0.01804,-0.09375,0.02859,-0.01216,-0.05648,0.00563,0.1004,0.12439,-0.02193,-0.03396,-0.00583,0.02326,0.07739,-0.01584,0.02458,-0.0127,0.05222,0.16378,0.00636,-0.04451,-0.00061,-0.0793,0.04084,-0.01564,-0.11183,-0.0325,-0.07092,0.05114,0.00949,-0.00973,0.00711,-0.05747,-0.04546,-0.02618,-0.03973,0.08446,0.01852,0.14697,-0.04994,0.00332,-0.04283,-0.075,0.01455,0.005,-0.00487,-0.01978,0.06891,0.0112,-0.0797,-0.02286,-0.07232,-0.08493,0.11547,-0.00644,-0.04425,0.07432,0.09036,-0.03012,-0.07876,0.06483,-0.08428,-0.0905,0.03446,-0.00716,0.03971,-0.0679,0.08239,-0.01072,0.14045,0.07474,-0.11952,-0.06021,0.01551,0.10571,0.01902,-0.05074,0.06143,0.03907,-0.05628,0.02364,0.06188,0.09974,-0.01544,-0.0604,-0.01764,0.07898,0.03405,0.02831,0.06611,0.04489,0.06162,0.01929,0.10564,0.06522,-0.03534,0.01794,-0.1037,-0.0817,-0.08491,0.11034,-0.03081,-0.0796,0.06887,0.00807,-5e-05,-0.03325,0.07794,-0.0082,-0.00644,0.06745,0.04806,0.0594,0.03524,-0.1356,-0.14009,-0.00455,-0.05646,-0.00638,-0.00403,0.20532,-0.01477,-0.03066,0.05916,-0.0445,-0.07024,0.05016,-0.02386,-0.06535,-0.02111,-0.0158,-0.09178,-0.09728,0.04047,-0.00218,-0.00769,0.12006,-0.00542,-0.03991,0.09317,0.20987,-0.01524,-0.01999,0.00592,-0.0325,0.01911,0.0381,0.05858,0.0014,0.02965,-0.03992,0.02259,-0.06842,-0.04472,0.02562,0.01501]},{"domain":"differential_equations","key":"second_order_homogeneous_ivp","name":"Second-order homogeneous linear ODE: initial value problem","package":"differential-equations-ai999x","example":"Solve y'' + 3y' + 2y = 0 with y(0) = 1, y'(0) = 0; find y(1).","v":[-0.04771,0.10186,-0.01735,0.00367,0.02009,-0.05091,0.01447,-0.00689,0.00748,-0.065,-0.03086,0.03801,0.01009,-0.06888,0.02939,0.01357,0.01992,-0.05876,0.00814,-0.00449,0.02093,0.00632,0.05579,0.09323,0.07929,0.0435,0.06953,0.15772,0.02199,-0.01025,-0.00571,0.06663,0.01182,0.03381,0.05073,-0.02665,-0.02698,-0.00674,0.0127,-0.08521,-0.027,-0.06118,-0.0947,-0.01951,-0.11018,-0.05777,-0.09318,0.04394,0.06413,0.04001,-0.01676,-0.02364,-0.04306,-0.12881,-0.00123,0.06418,0.02883,0.10926,-0.03195,-0.0158,0.0641,0.06126,0.09637,0.02684,-0.02722,0.06693,0.04146,-0.16542,0.10315,-0.02314,-0.07485,-0.02571,0.06077,-0.03653,-0.00539,-0.12401,0.01865,0.0191,0.01584,-0.02679,0.0736,0.04568,0.04071,0.00487,-0.03515,0.04407,-0.03863,-0.05454,0.06176,0.09365,0.01147,0.01263,0.02647,0.07876,-0.01194,-0.00541,-0.00595,-0.09104,-0.02393,-0.02099,-0.05933,-0.04017,0.05358,0.00629,0.06742,-0.04138,0.04006,0.08387,0.09547,0.12479,0.01417,-0.00394,-0.07124,0.00717,-0.02417,0.00018,-0.00991,-0.06013,0.05921,0.06501,-0.04531,0.04311,-0.03997,-0.03792,-0.01569,0.00338,-0.01001,0.03948,0.05238,-0.01733,0.12711,0.04328,-0.04508,-0.00292,-0.06483,-0.07073,0.03165,0.01909,-0.01138,-0.0034,-0.01482,-0.05384,-0.00209,0.04372,0.11736,0.06238,0.01811,-0.00427,0.03749,0.00788,-0.03417,-0.03428,-0.01034,0.03841,-0.01719,-0.05822,-0.01224,-0.0264,0.03104,0.1358,0.06515,-0.10628,-0.05467,0.02832,-0.00143,-0.02557,-0.04001,0.04599,-0.11011,0.07109,0.02949,0.0882,-0.06659,-0.09466,0.05036,-0.0313,-0.08926,-0.09556,0.15446,-0.1642,0.07006,0.00484,0.04537,0.02094,-0.20034,-0.05398,0.00588,0.06706,0.01006,0.08304,0.00159,0.0177,-0.02825,0.0663,0.07024,-0.15278,-0.11818,-0.18505,0.0255,-0.15519,0.01414,-0.00384,-0.14621,0.03209,0.01666,0.02522,-0.00631,0.00605,-0.01518,-0.05799,0.06053,-0.03576,0.13517,0.00456,0.03728,-0.04174,0.07027,-0.0339,-0.07251,0.06001,-0.04035,0.03776,-0.02825,0.07514,-0.17516,-0.03647,-0.0221,-0.00632,-0.05356,0.11899,0.04524,0.04572,0.01771,-0.09612,0.01254,0.0314,-0.0229,0.10705,0.05439,0.05131,0.06606,-0.00931,0.04956,0.06537,-0.06359,-0.07137,0.03425,-0.02697,0.01992,-0.03485,-0.15628,-0.04178,-0.006,-0.06884,0.01322,0.01654]},{"domain":"differential_equations","key":"separable_power","name":"Separable equation y' = a t^n y","package":"differential-equations-ai999x","example":"Solve the separable equation y' = a t^n y with a = 2, n = 1, y(0) = 3; find y(1).","v":[-0.0153,0.00148,-0.10756,0.00179,0.05732,-0.02684,-0.00328,0.03349,-0.00321,-0.07913,-0.02655,-0.0244,0.00616,-0.08928,0.01269,0.0156,0.0722,-0.11525,0.06637,0.02167,-0.08081,-0.00262,0.05878,0.01309,0.0061,0.0425,0.04966,0.09313,-0.00368,0.04839,0.01517,0.02685,-0.02755,0.00132,-0.00079,-0.07368,-0.04519,-0.02224,0.0153,-0.03917,0.02373,-0.01642,-0.04287,-0.09474,-0.0834,0.00563,-0.01706,-0.06201,0.1044,-0.08231,0.06279,0.05776,-0.04537,-0.10363,0.01513,-0.01514,0.04125,-0.00932,-0.0519,-0.07369,0.05415,0.00503,0.01746,-0.00064,0.01389,0.00932,-0.00067,-0.1194,0.11867,0.10886,0.02903,-0.11119,-0.03593,0.10779,0.00708,-0.11524,-0.02963,0.02221,-0.14986,0.00925,-0.02788,-0.04381,0.05829,-0.02156,-0.07072,-0.03664,0.08687,-0.11128,0.17304,-0.05824,0.10455,-0.0763,0.01276,0.00916,-0.05245,0.01884,-0.01586,0.05698,0.04164,0.02527,-0.04696,-0.08689,0.0708,0.02646,-0.04208,-0.02519,0.08879,0.01131,0.1584,0.05519,0.04722,0.02757,-0.13286,-0.02491,0.09511,0.00804,-0.08429,0.0146,0.04686,-0.0083,-0.01288,0.0782,0.05855,-0.0506,0.054,0.01752,0.00665,-0.00169,0.00082,-0.01174,0.00082,0.04102,0.00081,-0.02549,-0.0667,-0.01403,0.10817,-0.04475,-0.05374,0.07417,-0.04535,0.01001,0.00225,0.0631,-0.02038,-0.01227,-0.08091,0.07227,0.01121,0.02097,-0.00057,0.05203,-0.11936,0.08015,-0.03272,-0.01517,-0.10221,-0.00842,0.07467,0.07757,7e-05,0.02515,-0.07597,0.12482,-0.0285,0.01272,0.03251,0.12761,-0.07597,-0.04001,0.03594,0.0127,-0.08568,-0.00388,0.08885,-0.05261,-0.07674,-0.02358,0.02899,-0.00193,0.07106,0.05698,0.05815,0.02777,-0.11804,-0.05872,-0.01947,-0.0076,-0.12427,0.07575,-0.01641,-0.0878,-0.043,0.05235,0.07608,0.07232,-0.03053,-0.16384,-0.03088,-0.01117,0.02281,0.05388,-0.09755,-0.02512,0.09171,0.07972,-0.07779,-0.07934,0.10781,-0.03736,0.13046,-0.04606,0.10954,-0.04664,0.06494,-0.03359,0.00159,-0.1142,-0.04811,0.05203,0.09115,-0.05097,-0.0536,0.00543,-0.04737,-0.08021,0.13086,-0.02262,-0.03723,0.12298,-0.05971,0.03379,0.05348,0.0161,-0.06915,0.17274,0.02476,-0.04049,0.08886,0.01421,0.03027,0.01968,0.02613,0.11231,-0.04115,-0.06194,0.03831,0.02721,-0.02251,0.02568,0.02329,-0.09044,-0.01634,0.01726,-0.01044,0.03138]},{"domain":"differential_equations","key":"simple_harmonic_motion","name":"Simple harmonic motion: position, amplitude, period","package":"differential-equations-ai999x","example":"Simple harmonic motion with m = 0.5, k = 8, x(0) = 0.1, x'(0) = 0; find x(1).","v":[-0.06724,0.04714,-0.05156,-0.01519,-0.05971,-0.05066,-0.01027,-0.01284,0.04806,-0.06276,-0.11407,0.05637,0.00741,-0.00023,0.07249,-0.06503,-0.01684,-0.07179,-0.00557,-0.00768,-0.04983,-0.00714,1e-05,0.07326,-0.03173,0.05447,0.05059,0.06844,0.04748,-0.04307,0.00817,0.03893,-0.00273,0.00602,-0.01861,-0.07429,-0.00425,0.0831,-0.04302,-0.00439,-0.06902,-0.12586,-0.06849,0.09375,-0.093,-0.03765,-0.11609,0.1832,0.04199,0.01914,-0.12649,0.02229,0.02015,-0.04644,0.01267,0.03051,-0.00687,0.01961,0.0048,-0.00799,-0.02989,-0.02728,-0.01312,0.07768,0.05722,-0.033,-0.04497,-0.09788,0.07215,0.00619,-0.04518,-0.02088,0.10399,-0.12034,-0.0368,0.05687,-0.08077,0.09533,0.01288,0.04005,0.09329,0.10596,0.08906,-0.06387,0.04475,-0.00316,-0.03438,0.02364,0.0549,0.07446,0.05613,-0.08886,0.04648,0.00365,-0.05207,-0.0007,0.04256,0.01114,0.05528,-0.01527,-0.03866,0.01451,-0.03913,-0.04736,0.02468,0.01484,0.03274,0.07931,0.00184,0.03438,-0.00777,0.00138,-0.02484,-0.01764,-0.02346,0.01897,0.01983,-0.09318,0.0374,0.09186,-0.01258,-0.10913,-0.07608,-0.04135,-0.05526,-0.08881,0.07365,-0.13756,0.03784,0.02458,0.02476,0.04903,0.03736,0.02173,0.07728,0.05125,0.04747,0.11057,0.16767,-0.03856,-0.05461,0.02504,-0.11381,-0.09269,0.02875,0.00984,0.0108,0.00461,-0.05321,-0.04504,-0.04036,-0.07001,-0.02169,-0.02901,-0.04604,0.09937,0.06158,0.02311,-0.01665,-0.03452,-0.01937,-0.05727,-0.07529,0.12443,-0.0716,-0.07918,0.04414,-0.06734,-0.06186,0.12593,0.06376,0.03383,5e-05,0.06505,0.02142,-0.02129,-0.03758,-0.15524,0.06412,-0.08843,0.10275,0.06926,-0.00385,-0.04342,-0.11851,-0.02398,-0.00618,0.01817,0.01608,-0.11519,-0.03395,-0.06504,-0.01639,-0.00944,0.07497,-0.03866,-0.00924,-0.02507,-0.06236,0.04911,-0.00145,-0.07931,-0.22955,0.07484,0.02379,0.06855,0.02074,0.06774,0.00916,-0.0266,0.04761,-0.06169,0.01464,0.02362,0.03904,-0.0234,0.0295,-0.07934,0.0074,-0.1118,-0.04302,0.07866,-0.02327,0.11765,-0.04231,-0.02061,0.02055,0.01943,0.02411,0.09025,0.06238,0.04828,0.00781,0.12005,-0.01607,0.01289,0.02814,0.11862,0.00267,-0.03747,0.03705,-0.02746,-0.00041,0.05891,-0.00588,-0.09203,0.1013,0.02482,0.11049,0.1095,-0.04165,0.01982,0.06009,-0.18259,0.04351,-0.00988]},{"domain":"differential_equations","key":"sir_epidemic","name":"SIR epidemic: R0, peak infections and final size","package":"differential-equations-ai999x","example":"SIR epidemic model with beta = 0.3, gamma = 0.1, S0 = 0.99, I0 = 0.01: find the peak and final 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(direction) field value","package":"differential-equations-ai999x","example":"Slope field of dy/dt = t + y at t = 1, y = 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damped oscillator: steady-state amplitude and phase","package":"differential-equations-ai999x","example":"Find the steady-state amplitude of y'' + b y' + c y = F0 cos(w t) with a = 1, b = 0.5, c = 4, F0 = 2, w = 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of y'' + lambda y = 0 with Dirichlet/Neumann ends","package":"differential-equations-ai999x","example":"Find the eigenvalue of y'' + lambda y = 0 with dirichlet-dirichlet conditions, L = 1, n = 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tank (Torricelli's law): height and emptying time","package":"differential-equations-ai999x","example":"A draining tank obeys Torricelli's law with h0 = 4, k = 0.2; find h(5) and the emptying 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resonance: growing response","package":"differential-equations-ai999x","example":"Undamped resonance with m = 1, k = 4, F0 = 2: find y(3).","v":[0.0481,0.00018,-0.02268,-0.00876,-0.03506,0.05375,0.06249,-0.01734,0.0752,0.04162,-0.0237,0.08746,-0.01284,0.09546,0.03463,-0.03011,-0.00542,-0.01623,-0.0003,-0.00221,-0.06898,-0.04163,-0.00252,0.02845,0.00477,0.00465,-0.02718,0.08754,0.11597,-0.15809,0.14316,0.00453,0.03007,0.00316,0.04037,0.03388,-0.05256,0.08001,-0.02554,0.01557,0.00335,-0.04722,-0.11203,-0.01194,-0.04899,0.01923,-0.01279,0.02778,0.05712,0.01206,-0.16033,-0.0188,-0.00993,-0.03567,0.00777,-0.00925,-0.02647,0.11965,0.01001,0.0073,0.04558,0.01161,0.03021,0.03484,0.10196,0.02035,-0.06264,-0.08208,0.02546,-0.15401,0.09186,-0.03504,0.06174,-0.03583,-0.00747,-0.03674,0.00561,-0.0169,-0.03807,0.02194,0.11174,0.03241,0.00557,-0.01613,-0.02151,0.02585,0.06234,0.09008,0.00258,-0.07867,0.02216,0.03447,0.10233,0.03739,0.01951,-0.04535,-0.0632,0.03532,0.01891,0.00716,0.01455,-0.13463,-0.0712,-0.08078,0.03415,0.09494,0.13192,0.06419,-0.02988,0.07387,-0.05474,-0.0234,-0.02838,-0.04702,0.00028,0.06135,-0.04148,-0.0609,0.02236,0.12153,-0.00729,-0.0608,-0.00154,-0.09005,-0.00371,-0.07342,0.00676,-0.0514,-0.03958,-0.04625,0.00164,0.04838,-0.05323,-0.02292,-0.04833,-0.06971,0.07227,-0.03307,0.02158,0.01769,0.03123,0.04984,-0.13777,-0.08761,0.09459,-0.00182,0.08825,-0.15348,-0.05239,-0.09555,0.03743,-0.02258,0.01213,0.03382,-0.03125,-0.0317,0.08294,-0.00182,0.04091,0.03057,0.02184,-0.07879,0.02214,0.1445,-0.11221,0.05344,0.05569,0.08215,-0.06418,0.07804,-0.04269,0.04375,-0.02616,0.04013,0.00593,0.01149,0.05389,-0.11331,0.08708,-0.05649,0.10964,-0.00752,0.00954,-0.03952,-0.09878,-0.00418,-0.02414,-0.04144,-0.04602,0.01306,-0.02322,-0.03099,0.01221,-0.08761,0.05126,-0.01027,-0.09021,-0.02737,-0.13547,-0.07832,-0.01143,0.07887,-0.23328,0.04246,0.04507,0.00855,0.08462,0.08306,-0.01589,-0.11927,0.09202,-0.04775,0.10365,0.08273,0.08627,-0.01504,-0.01009,-0.05203,-0.05659,-0.03659,-0.06013,0.09197,0.00102,0.06623,-0.13697,0.04365,-0.09031,-0.10082,-0.08115,0.14131,0.02895,0.02251,0.0624,0.09124,-0.03944,0.05529,0.05069,0.01368,-0.06102,0.01018,-0.00385,-0.06853,0.00315,0.01075,0.02119,-0.06368,0.0519,0.03535,0.0686,0.04014,0.06173,-0.09086,-0.00177,0.01649,0.01157,0.00506]},{"domain":"differential_equations","key":"undetermined_coefficients_exponential","name":"Undetermined coefficients: exponential forcing","package":"differential-equations-ai999x","example":"Solve y'' + 3y' + 2y = 4e^(3t) with y(0) = 0, y'(0) = 0; find y(1).","v":[-0.04037,0.04261,-0.06122,0.05233,0.01383,0.09955,-0.0116,-0.02353,-0.02797,-0.016,-0.04579,-0.01596,0.00643,-0.03131,0.05244,-0.07733,0.07122,-0.0149,0.08644,0.02224,0.06227,0.01401,0.07277,0.05983,0.09318,0.00602,0.03314,0.15055,-0.03848,0.06565,0.01707,0.0344,0.07778,-0.00867,0.05966,0.00403,-0.01447,-0.01578,-0.01347,0.0603,0.04183,-0.04685,-0.05857,-0.06347,-0.02804,0.00311,-0.07186,-0.00992,0.05798,0.00706,-0.02854,-0.02436,-0.02787,0.00262,-0.00317,0.06675,0.06428,0.05222,-0.03963,0.00923,0.07565,0.05931,0.03168,0.00867,0.04165,0.02685,0.03823,-0.09118,0.11096,-0.01712,0.06076,-0.04588,-0.00435,-0.07936,-0.06643,-0.08798,0.05152,-0.05563,-0.03399,-0.0744,0.04572,-0.08454,0.03207,-0.11641,-0.07464,-0.03098,-0.00441,-0.00899,0.08495,-0.05622,-0.00634,0.03304,0.06308,-0.05999,-0.05769,-0.05637,-0.0563,-0.03973,0.11855,-0.12227,-0.05195,-0.05693,0.04817,0.0256,0.07696,0.05125,0.03819,-0.01676,0.12372,0.1255,0.08391,0.05199,0.00086,-0.01975,0.04835,0.00616,-0.06883,-0.03851,0.06751,0.02124,-0.07039,0.03116,-0.0212,-0.07283,0.0034,0.05401,-0.04778,0.02253,-0.00789,-0.11654,0.02542,0.05897,-0.04391,0.00472,-0.05554,-0.04626,0.03039,-0.08216,-0.00179,-0.01547,0.07787,0.00192,-0.09339,0.06128,0.14001,0.05213,0.07945,-0.07456,0.02913,-0.00495,-0.05342,0.02952,-0.09199,0.05495,-0.00791,-0.11438,-0.06658,0.09655,0.0979,0.11883,0.00869,-0.10766,-0.05839,0.09936,0.00463,-0.03115,-0.04303,0.07859,-0.1383,0.0985,-0.06597,0.10636,-0.05623,0.04716,0.07073,-0.00358,-0.06331,-0.09785,0.06532,0.05019,0.01233,-0.04979,0.00472,-0.07355,-0.17062,-0.05424,0.02968,-0.05999,-0.05079,0.05959,-0.00754,0.01246,-0.1223,-0.09242,0.05297,-0.04042,-0.14927,-0.16151,-0.04396,-0.11037,0.0121,-0.02746,-0.09791,0.12592,-0.00021,0.02912,-0.02589,0.03729,0.04984,0.02141,0.01878,0.01941,0.088,0.00606,0.06196,-0.06786,0.04909,-0.06126,-0.01991,0.14613,-0.02687,-0.01522,0.01916,0.02899,-0.16782,-0.07238,-0.03379,-0.05459,-0.08165,0.05716,0.03969,-0.02984,0.01285,0.1202,-0.03733,0.04785,0.12987,-0.05344,0.02901,0.06335,-0.02845,0.0009,-0.00084,-0.01991,0.00111,-0.03436,0.02185,-0.02186,0.01716,0.08148,-0.06994,-0.04896,0.04934,-0.00947,0.02584,0.03817]},{"domain":"differential_equations","key":"undetermined_coefficients_polynomial","name":"Undetermined coefficients: polynomial forcing","package":"differential-equations-ai999x","example":"Undetermined coefficients with polynomial forcing: a = 1, b = 0, c = 4, p = [0, 8], y0 = 1, v0 = 0, t = 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string with fixed ends: Fourier series value","package":"differential-equations-ai999x","example":"Vibrating string with f(x) = x*(1 - x), L = 1, c = 2, N = 20, x = 0.25, t = 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cipher","package":"discrete-math-ai999x","example":"Encrypt \"AFFINE CIPHER\" with the affine cipher a = 5, b = 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points (cut vertices)","package":"discrete-math-ai999x","example":"Find the articulation points of the graph with edges A-B, B-C, C-A, C-D, 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3)^5?","v":[-0.02496,-0.07499,-0.05265,0.00583,0.10109,0.13698,0.04894,0.02185,-0.01428,0.01102,0.07967,-0.03725,-0.08431,-0.06572,0.04388,-0.0311,0.12131,-0.03054,0.00264,-0.00618,0.00771,-0.07415,0.08875,-0.02784,0.03828,-0.07223,0.02353,-0.03131,-0.03875,-0.02605,0.01535,-0.02199,-0.0207,-0.02446,-0.00406,-0.05068,-0.0545,0.03732,0.10546,-0.02766,-0.13472,-0.00358,1e-05,-0.11154,-0.01339,-0.06489,-0.05495,-0.07413,0.01609,-0.05616,0.02705,0.1025,0.01338,-0.00428,0.04404,-0.0299,-0.08572,0.11861,0.11185,0.07917,-0.05912,0.01198,0.01019,-0.09329,-0.06699,-0.03834,0.08032,-0.00483,-0.03892,0.01011,0.0522,-0.04872,-0.02839,0.14332,-0.06811,0.01908,-0.06138,-0.0766,-0.02823,0.03842,-0.03609,-0.12249,0.03444,-0.05301,-0.05365,0.00215,0.11718,-0.02479,0.00171,-0.07075,0.04595,-0.00421,-0.00974,-0.00924,-0.01736,-0.0117,0.0055,0.01467,-0.00088,-0.04423,-0.06855,0.0074,0.05922,0.00337,0.01876,0.07195,0.03153,-0.11882,0.04254,-0.02306,-0.00322,0.03724,0.01285,0.04644,0.11164,-0.07976,0.07436,-0.0895,-0.04609,-0.05018,-0.10578,0.05121,0.07579,-0.12991,0.04384,-0.04072,0.06181,0.01283,-0.05113,-0.0523,-0.01348,-0.03299,0.08233,-0.03105,-0.06157,0.05096,0.0766,-0.08906,0.07219,-0.05802,-0.09726,-0.07006,0.07397,0.06043,-0.09603,-0.07488,0.04583,0.05159,-0.04911,-0.10388,-0.00388,0.0637,0.05305,0.01986,0.00564,0.04242,-0.11272,0.00776,0.02922,0.08656,-0.03457,0.01681,0.06862,0.05858,0.10752,-0.02892,0.04647,-0.06546,-0.02939,0.01639,0.0235,0.00442,0.00709,0.03657,-0.02927,-0.02524,-0.05902,0.04729,-0.08561,-0.02048,-0.08947,0.02324,-0.14489,-0.01513,0.03918,0.00048,-0.11089,-0.0579,-0.15065,-0.0254,0.02241,-0.00816,-0.01943,-0.00775,-0.00569,-0.06511,0.01982,-0.04692,-0.03761,-0.01638,0.06974,0.11065,-0.03713,0.04321,0.11646,0.03197,-0.03353,0.03126,0.09017,0.00067,-0.00776,-0.08209,0.04999,0.00924,0.11003,0.17746,0.02828,0.00375,0.06642,0.07624,0.04933,-0.05066,-0.0797,0.03666,0.0768,-0.02482,0.1665,0.07074,-0.07698,0.03414,0.00412,-0.03613,-0.05885,-0.00628,-0.02346,-0.00879,0.06221,0.12078,0.10164,0.10747,0.00257,-0.05913,-0.06468,0.02806,0.00552,0.02789,0.00402,-0.03509,0.09199,0.17361,0.03879,0.0875,-0.04801,0.07936,0.01784,-0.06246]},{"domain":"discrete_math","key":"bipartite","name":"Bipartiteness test","package":"discrete-math-ai999x","example":"Is the graph with edges A-B, B-C, C-D, D-A 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C-D?","v":[0.07668,0.11485,-0.03944,0.00665,-0.07743,0.03793,0.17875,-0.10782,0.134,-0.08332,-0.03143,0.0038,0.03288,0.0621,-0.04027,-0.05776,-0.01463,-0.00131,-0.01388,0.04778,0.07883,0.01934,-0.08005,-0.05401,0.06318,0.09793,-0.05355,0.03736,-0.07698,0.02158,-0.08723,0.01453,0.03815,0.06462,0.05229,0.00874,0.0281,0.10053,-0.02434,0.01194,-0.11886,-0.04316,0.10652,-0.01639,0.03521,-0.03448,0.06443,0.04382,0.08609,0.04547,0.03613,-0.05846,-0.06861,-0.05424,-0.0473,-0.03476,-0.13221,-0.0448,-0.02765,0.01532,0.03843,0.02432,0.00761,0.09361,-0.06351,-0.02462,0.01512,0.09585,0.05681,0.12114,-0.06579,0.10302,0.00487,-0.04017,-0.07886,-0.02679,-0.02843,0.09855,-0.07654,0.01478,0.0989,0.04284,-0.04065,-0.02362,0.00685,0.11607,-0.06861,-0.00497,-0.00971,-0.0471,-0.02692,0.01166,0.07374,-0.06259,-0.11207,-0.1042,-0.03016,-0.05432,-0.04263,0.02241,-0.07984,-0.05194,-0.0338,0.05288,0.15402,0.06073,-0.01894,-0.08467,0.00121,-0.06501,-0.06891,0.01056,-0.04303,-0.03523,-0.03323,-0.02983,0.1269,-0.051,-0.06497,0.02481,0.07869,-0.04044,-0.04241,0.03861,0.00838,0.01226,0.01589,-0.08439,0.00135,-0.05988,0.0501,0.01764,0.00698,-0.0267,-0.0835,0.04035,-0.04958,0.09447,0.10512,-0.02914,-0.00401,0.02127,-0.00824,-0.00846,-0.08024,-0.21314,-0.02961,-0.06349,-0.03577,-0.0043,0.02504,-0.04549,-0.04812,-0.04137,-0.06934,0.03607,0.08219,-0.07337,-0.01699,-0.06399,-0.15227,0.02047,0.01603,-0.00831,0.05388,0.08625,0.01113,0.11172,0.02522,0.09306,0.08418,0.01709,0.00561,0.01864,0.01591,-0.02986,0.05618,-0.00015,-0.06462,-0.03732,-0.14351,-0.02795,0.06305,0.05012,-0.0469,0.00716,0.05553,0.02291,0.09393,0.11354,-0.01328,-0.03247,0.00922,0.01405,0.03002,-0.04888,-0.02127,0.03548,0.01165,-0.06769,-0.05002,0.07595,0.08928,-0.0032,-0.02094,-0.04798,0.03735,0.03114,0.01099,0.13314,-0.01069,-0.05661,-0.07493,0.07898,0.03424,0.03484,0.06616,-0.00017,0.03186,0.13348,0.02178,-0.05552,0.04814,-0.10862,-0.02378,-0.09723,-0.02355,-0.05893,-0.07497,-0.02153,0.12564,0.06973,-0.01241,0.02041,0.08403,-0.10306,0.01514,0.03528,-0.08657,-0.05685,0.08164,-0.06587,0.03128,0.00965,-0.02746,0.00435,-0.02505,0.01843,-0.00012,0.1188,0.00049,0.04996,-0.09334,-0.03959,0.00345,0.03472]},{"domain":"discrete_math","key":"clique_number","name":"Clique number","package":"discrete-math-ai999x","example":"What is the clique number of the graph with edges A-B, B-C, C-A, C-D, B-D, A-D, D-E?","v":[0.04575,0.05704,-0.05645,-0.0572,-0.04654,-0.01854,0.13892,-0.14093,0.11969,-0.03572,-0.03985,0.02945,-0.03834,0.06767,0.01133,-0.00317,0.07653,-0.04445,-0.02967,-0.04658,0.01577,-0.01955,0.02769,0.04751,0.08034,0.08877,0.01754,-0.05388,-0.06946,0.0143,0.05185,-0.01448,-0.0279,0.01508,-0.04851,0.00427,-0.04522,0.0688,-0.06868,0.04128,-0.18474,-0.01665,0.03812,0.01457,0.05676,0.0323,0.02892,0.02748,0.00055,-0.01235,0.02057,-0.00829,0.01955,0.01628,-0.03174,-0.02275,-0.13708,-0.00375,-0.03555,0.03333,0.06594,0.01286,-0.01177,0.08638,0.08993,-0.03327,0.03878,-0.04765,0.05293,-0.00749,-0.07341,0.07137,-0.01032,-0.02876,-0.0991,-0.01744,0.01143,0.06908,-0.02849,0.10199,0.00311,-0.03065,-0.01724,0.01837,-0.02422,0.13228,-0.09658,0.04944,-0.03306,-0.04209,0.06592,0.01355,0.03017,-0.02544,-0.09797,-0.07115,-0.00318,-0.07623,0.05074,0.08122,-0.06402,0.09037,-0.0104,0.03506,0.11812,0.06969,-0.02177,-0.09981,-0.03264,-0.07094,-0.03839,0.03521,-0.11924,0.02714,-0.05165,0.03074,-0.03575,-0.05278,-0.02939,-0.02418,0.10872,0.06355,-0.13038,0.09175,-0.02565,0.07704,0.06755,-0.01382,0.06769,-0.05106,-0.03779,0.05421,0.05485,-0.04583,-0.10616,0.01456,-0.06453,-0.05092,0.10197,-0.12811,0.09476,0.09941,-0.00021,0.03168,-0.11825,-0.2261,-0.02028,-0.07739,0.01138,0.01395,0.08251,0.08074,-0.02071,-0.04326,-0.1274,0.02873,0.01437,0.05028,0.00185,0.02946,-0.09677,-0.0131,-0.00656,0.0502,-0.0038,0.08561,0.16068,0.08233,0.01794,0.07989,0.06733,0.03797,-0.1052,0.05012,-0.0384,-0.04112,0.0115,0.07676,-0.00152,-0.02094,-0.04987,-0.01621,0.13371,0.08393,-0.12572,-0.01802,0.0264,0.08778,0.12657,0.02474,0.06517,-0.00321,0.07979,-0.05084,-0.10327,0.00784,-0.01015,0.03658,0.01052,0.00409,-0.0082,0.00229,0.06217,0.05342,0.05299,-0.03644,0.05021,-0.02855,-0.04239,-0.02609,0.01043,-0.12484,-0.01798,0.08328,-0.01169,0.02,-0.03653,-0.09181,0.03968,0.06779,0.02798,-0.01776,-0.08685,-0.08998,0.06912,-0.06547,-0.03821,0.03286,-0.00488,0.0224,0.01066,0.0735,-0.03497,-0.02689,0.00367,-0.13927,-0.00555,0.06429,-0.05993,-0.00159,-0.01516,-0.06036,-0.02156,-0.03092,-0.01355,0.04131,-0.01037,0.05261,0.0448,0.11166,-0.01884,-0.10928,0.02895,0.03576,-0.06645,-0.02788]},{"domain":"discrete_math","key":"combinations","name":"Combinations C(n, k)","package":"discrete-math-ai999x","example":"How many ways are there to choose 3 books from 10?","v":[-0.05786,0.14023,-0.00548,0.02219,0.02808,-0.07567,0.10513,0.02381,-0.0194,0.00486,0.00977,-0.04889,0.01844,-0.00234,0.03031,-0.0856,-0.03677,0.03953,-0.09345,0.05614,-0.07128,0.05313,0.14251,-0.04875,-0.04711,-0.02075,-0.02802,0.03935,-0.11268,0.0549,-0.08384,-0.06459,-0.014,-0.04294,0.00447,-0.00756,-0.03216,0.01851,0.05309,0.00211,0.03283,0.12824,0.09504,0.02049,-0.10075,0.03794,-0.11932,-0.04015,-0.03479,0.00028,0.01591,0.05996,-0.03327,-0.07089,0.02629,0.01858,-0.05239,0.10406,0.08996,0.01893,-0.05302,0.04528,-0.01761,-0.09564,-0.06033,0.0251,0.06983,0.09854,-0.06928,-0.05176,0.06282,0.04722,0.01211,0.17776,-0.03618,0.03414,-0.02922,0.03892,-0.0245,-0.01043,-0.07744,-0.06736,-0.00661,-0.14008,-0.09599,-0.11377,-0.03415,-0.04609,-0.01973,-0.02145,0.12682,-0.01739,0.04174,-0.0114,0.03745,0.00103,-0.02464,0.00744,-0.01112,-0.04515,-0.05392,0.05699,0.06435,-0.10619,0.11215,0.06005,0.02264,-0.08939,0.06288,0.04716,-0.00601,-0.0215,-0.01442,0.06345,0.08377,0.00398,0.04868,-0.03788,0.02905,0.0369,-0.15673,0.03855,0.05478,0.07896,0.09934,0.05483,-0.00036,0.02129,-0.06352,0.06999,0.07275,-0.02489,-0.00263,-0.01353,0.03342,-0.0295,0.07323,-0.11399,-0.00887,0.02262,-0.11941,0.10463,-0.01013,0.04474,-0.01008,-0.01426,-0.04463,0.09105,-0.12934,-0.06263,0.0532,-0.06118,-0.0576,0.00063,0.02716,-0.00367,-0.05146,-0.0358,0.11918,0.04333,0.05505,0.02276,-0.02812,0.00756,0.03593,0.10143,0.0284,-0.12042,0.09419,-0.04049,0.02204,-0.00794,0.00802,0.01642,0.00298,-0.07059,-0.04894,0.15995,0.02119,-0.03057,-0.10613,0.00439,0.02687,-0.01704,0.01196,0.12132,-0.0554,-0.02134,-0.08556,-0.02965,0.03392,0.08011,-0.0454,-0.09334,-0.04032,-0.09711,0.06327,-0.06553,-0.08066,0.05503,0.04117,-0.06402,0.1083,0.01478,0.00358,0.01088,-0.1287,-0.0587,-0.00314,-0.08258,-0.03234,-0.08233,0.08585,-0.04376,0.01541,-0.02187,0.01708,0.06503,-0.02507,-0.01122,-0.00662,-0.0103,0.02781,-0.08705,0.05985,0.02268,0.11292,0.04469,-0.0861,0.00487,-0.06033,0.08807,-0.1079,-0.02222,0.00731,0.01485,0.11988,0.07837,0.11846,0.03686,0.03306,-0.06197,-0.02012,0.04348,-0.02052,0.1108,-0.04516,-0.01076,0.00463,0.01643,-0.09548,-0.07471,0.02488,0.04718,0.00472,-0.04574]},{"domain":"discrete_math","key":"connected_components","name":"Connected components","package":"discrete-math-ai999x","example":"How many connected components does the graph with edges A-B, C-D, D-E have?","v":[-0.1024,0.02297,0.03655,-0.09025,-0.02689,-0.0573,0.09754,-0.07247,0.07798,-0.07724,-0.00447,-0.01204,-0.03523,-0.06604,0.04478,-0.09266,0.05132,-0.01514,0.05013,-0.07394,-0.09965,0.06164,0.11334,0.04794,-0.04772,0.08268,0.0533,0.01198,-0.12035,0.03021,-0.04307,0.00963,-0.08486,-0.0899,-0.04178,-0.08383,0.00256,0.09707,0.00186,0.02202,-0.03994,0.10824,0.02261,0.00901,-0.01288,0.04431,-0.02187,0.06639,-0.02592,-0.03538,-0.09553,0.00334,0.01242,0.05104,-0.02112,-0.11302,-0.05531,0.00658,0.02135,-0.0315,-0.00842,-0.00844,-0.12494,-0.05089,0.02677,0.0185,0.00046,0.0922,0.05806,-0.0388,-0.01499,0.04474,0.10291,0.02557,-0.09372,-0.08259,-0.03163,0.0439,0.08451,-0.04471,0.02785,-0.13901,0.06278,-0.01852,-0.09927,0.06508,-0.0366,-0.0704,-0.01885,0.0213,0.12217,-0.06783,-0.00255,0.0042,-0.01714,-0.05718,-0.06561,0.10773,0.00837,0.02511,0.04039,0.11277,0.00717,0.09649,0.05572,0.06134,0.11095,-0.1861,-0.09196,0.0129,0.0189,-0.02817,-0.0972,0.01132,-0.05959,0.02194,-0.02128,0.0388,0.02935,-0.05947,-0.03754,0.04465,-0.0923,0.09328,0.01481,0.06171,0.06055,0.04961,0.04852,-0.01956,0.0608,0.07867,-0.09526,-0.00728,0.01513,-0.01987,-0.09461,-0.03416,0.05867,-0.04197,-0.10692,0.0974,-0.03828,0.07904,0.00809,-0.10787,-0.0159,0.07862,-0.00467,0.05803,-0.03632,0.04698,-0.07945,0.08182,0.03034,-0.05493,-0.05017,0.0261,0.01506,0.1516,0.0828,0.05443,-0.04656,0.01153,0.15434,0.09115,-0.01361,0.05887,-0.02335,0.03672,0.08552,0.04657,-0.10502,0.02293,-0.02129,-0.06403,-0.0355,0.09641,0.03082,0.02909,-0.07994,0.0474,0.04107,0.03593,-0.2017,0.10098,0.11848,0.01545,-0.05271,-0.01148,0.05248,0.07066,0.00057,-0.03123,-0.09498,-0.06599,-0.02028,0.03773,-0.02828,-0.0192,-0.07638,-0.04976,0.08205,-0.05153,-0.01105,-0.01837,-0.04958,-0.03735,-0.00522,-0.04552,0.10433,-0.07774,-0.03886,0.0505,-0.0392,-0.07601,0.08566,0.0276,-0.01197,0.03095,-0.04408,0.03409,-0.01505,-0.0681,0.08271,0.09281,0.00606,-0.05184,-0.07778,-0.04645,-0.07256,0.11204,0.02389,0.00467,0.02095,-0.02953,0.06273,0.01874,0.02814,0.01493,0.03387,0.0131,0.03556,0.03538,-0.00682,0.00334,-0.00026,0.00941,0.11623,-0.04302,-0.06093,-0.03499,-0.0621,0.03973,-0.03761,-0.00723]},{"domain":"discrete_math","key":"crt","name":"Chinese remainder theorem","package":"discrete-math-ai999x","example":"Solve x ≡ 2 (mod 3), x ≡ 3 (mod 5), x ≡ 2 (mod 7).","v":[-0.11389,0.11426,-0.10246,0.0324,-0.05939,-0.04082,0.08439,0.05474,0.0716,0.01456,-0.04171,0.05893,-0.03905,0.12724,0.01692,-0.03879,0.07764,0.00813,-0.08902,-0.07426,0.11434,-0.06431,-0.03983,0.05969,0.0794,0.06121,-0.06096,0.02944,0.09352,-0.02297,0.02158,-0.09773,-0.02448,0.02546,0.07789,-0.03523,0.03003,-0.00636,0.07416,0.154,0.0435,-0.01949,0.10557,-0.10408,-0.06375,0.04961,-0.0287,0.06215,0.02091,0.01565,0.04892,0.04203,0.00813,0.05395,-0.075,0.02965,-0.07236,0.03845,-0.08498,0.03799,-0.00412,-0.01233,0.00634,0.154,0.05064,0.05975,-0.00226,0.0197,0.01501,0.0602,0.05966,0.05001,0.02696,-0.09066,-0.03609,0.13315,0.15004,-0.01408,-0.05438,0.07098,0.06433,0.08987,-0.06856,-0.02478,-0.00427,0.05307,0.01678,0.12134,-0.02852,0.0022,-0.00906,0.0529,-0.06062,0.02389,-0.00614,-0.01044,-0.06156,-0.03357,-0.04926,0.01756,0.05126,0.06116,0.05545,-0.03724,0.05983,0.03691,-0.08036,-0.00886,0.01381,0.05353,0.04218,-0.05986,-0.00097,-0.05767,0.06993,0.12494,0.00271,-0.08313,0.02802,0.05501,0.05288,-0.05437,-0.01783,0.10821,-0.02624,-0.04506,0.12866,-0.04861,-0.06542,-0.08237,-0.0591,-0.00606,-0.07045,-0.12198,-0.01708,-0.04511,-0.09547,0.01325,-0.02331,0.00694,0.07818,-0.04808,-0.01057,-0.08044,-0.01705,0.02473,0.069,-0.00193,0.01967,-0.07887,-0.06401,0.07932,-0.0275,0.10226,-0.01392,0.0031,-0.16903,0.0268,0.04206,0.03194,-0.11811,-0.08369,0.05984,-0.06674,0.00483,-0.04106,0.07237,0.08441,0.05169,0.07348,0.08308,0.00575,0.01956,-0.06755,0.03034,-0.01184,0.04898,-0.05902,0.03524,-0.03127,0.04826,-0.02695,-0.01137,-0.09887,-0.02392,-0.04879,0.00148,0.0126,0.00667,-0.0138,0.03679,0.01282,0.06154,0.02583,-0.01804,-0.02496,-0.15225,-0.08314,-0.05449,0.01367,0.04807,0.02341,-0.07966,-0.062,-0.13326,0.05061,0.06884,0.07554,0.04187,0.03501,0.00836,-0.00166,-0.01569,0.02168,-0.04493,-0.0481,0.06893,-0.06622,0.06444,-0.11158,0.01435,-0.03265,0.04701,0.07405,0.01013,0.05021,0.02724,-0.14675,-0.09719,0.07238,-0.05512,-0.06953,0.05514,0.0108,-0.01009,-0.08681,-0.11554,-0.01931,-0.07567,0.00313,0.08604,0.01598,-0.04108,-0.0732,0.06554,0.01309,-0.11246,0.01435,-0.0658,-0.00509,-0.00727,0.07146,0.0709,-0.11906,0.02302,0.0209]},{"domain":"discrete_math","key":"cycle_rank","name":"Cycles in an undirected graph (cyclomatic number)","package":"discrete-math-ai999x","example":"What is the cyclomatic number of the graph with edges A-B, B-C, C-A, D-E?","v":[0.00039,0.14383,-0.04601,-0.00358,0.01449,-0.02872,0.07124,-0.01815,0.07081,0.03338,0.07514,-0.0349,0.10783,0.07203,-0.06045,-0.02941,0.04406,-0.06676,0.02299,-0.04444,-0.10126,0.03435,-0.01533,0.02244,0.08081,-0.03348,-0.02099,-0.01816,-0.08148,0.04366,-0.00858,-0.01007,-0.03861,0.00887,0.00916,-0.05732,-0.05483,-0.00797,0.09711,0.10707,0.03073,-0.03489,-0.05862,0.05812,0.07384,0.00634,-0.02392,0.16404,0.03493,-0.04432,-0.03,-0.12499,-0.00668,0.00307,-0.00978,-0.04012,-0.12392,0.05416,-0.08574,-0.01529,-0.00405,0.04259,-0.03522,0.03755,-0.00299,-0.01063,0.00844,-0.04519,0.00656,0.04617,-0.04168,0.11047,0.04182,-0.01862,0.0605,0.02433,-0.04581,0.05837,0.00832,0.07838,0.00636,-0.08005,0.08625,-0.0209,-0.04061,0.06214,0.05292,-0.0202,-0.07358,-0.00562,0.0379,0.03966,0.00816,0.0634,0.06123,0.00508,-0.04753,-0.01315,-0.01214,0.03089,0.03452,-0.06602,-0.05666,0.03269,0.04635,0.09149,0.13833,-0.10446,-0.14162,0.05444,0.02741,0.0077,-0.11198,-0.01973,-0.00026,0.03449,-0.08524,-0.08035,-0.00967,0.02975,0.01754,-0.02762,-0.10475,0.0954,0.04176,-0.03493,0.03639,-0.03641,0.04171,0.08011,-0.09083,0.00649,-0.04223,-0.03913,-0.01947,0.0242,-0.17347,0.02865,-0.02219,0.01373,0.02501,0.05435,-0.03585,0.05868,0.03413,-0.14764,-0.0894,-0.08573,0.06833,0.02879,0.07201,0.03949,0.00871,0.0216,-0.03761,-0.08183,-0.05015,-0.12978,0.02065,-0.02086,-0.17406,-0.03325,-0.03558,-0.06024,-0.01052,0.00476,-0.04685,0.14067,0.01331,0.08724,0.1055,0.0513,-0.08711,-0.04979,0.00333,-0.03447,0.00558,0.00213,0.01521,0.04602,-0.10057,-0.13211,0.18653,0.07201,-0.09052,0.00416,0.04265,-0.02121,0.01051,-0.00294,0.01736,0.03232,0.00625,-0.08476,-0.01899,-0.00832,-0.09393,0.06999,0.06019,0.01442,0.00438,0.0522,0.0549,0.00118,0.05729,-0.02583,0.04878,0.01499,-0.07494,-0.09405,0.04545,-0.05483,0.03104,0.10578,0.09737,-0.0195,0.05074,-0.01934,0.11212,0.08404,-0.06937,0.01814,-0.05698,0.06105,-0.05,0.03782,-0.00771,-0.00713,-0.17018,0.03075,-0.10041,0.0702,0.02397,0.04473,-0.00641,-0.04099,0.09846,-0.00391,-0.04209,-0.04886,0.03866,-0.08961,0.07049,0.01282,0.06284,-0.00789,0.07179,-0.00291,0.02592,0.02221,-0.01194,-0.11149,0.04434,0.13098,-0.10241,-0.07216]},{"domain":"discrete_math","key":"derangements","name":"Derangements","package":"discrete-math-ai999x","example":"How many derangements of 5 objects are there?","v":[0.06474,0.05881,0.0226,-0.06318,-0.04576,0.029,0.07592,0.02169,0.01043,0.11475,0.01742,-0.01697,-0.01864,0.01023,0.06361,0.00997,0.07524,0.04277,0.01353,0.00661,-0.02499,0.03354,-0.03878,0.01599,0.0512,0.03827,0.02005,-0.0169,0.00236,-0.00915,-0.06944,-0.09764,0.06951,-0.07759,-0.03916,0.04245,-0.04904,0.04356,0.07096,0.06588,0.06139,-0.00249,0.14879,0.04539,0.03331,0.11959,-0.06014,-0.03569,0.02399,0.08265,0.02438,-0.05204,-0.008,0.05209,0.06381,-0.08442,-0.07901,0.05323,0.01402,-0.04952,-0.01658,0.07365,-0.05674,-0.04913,-0.10947,-0.04381,-0.03788,0.03517,0.04294,0.03831,-0.01325,0.05503,0.0511,0.16801,0.03535,0.06063,-0.02466,0.03693,-0.01243,0.00184,0.00468,0.04406,-0.00392,-0.20373,-0.12842,-0.079,-0.07304,-0.0522,-0.05172,-0.04198,0.01933,-0.10974,0.01198,0.01197,-0.05677,0.16709,-0.09422,0.01302,0.04208,-0.04841,0.02303,0.04969,0.00828,-0.07232,0.07784,0.10957,0.01984,-0.11918,0.00337,0.02704,-0.06016,0.05457,0.01079,-0.02476,0.10721,-0.02715,0.00764,-0.09164,0.05567,0.02993,0.00421,0.05477,-0.0353,-0.06302,0.06979,-0.09131,-0.06633,0.02889,-0.05799,0.08356,0.01687,0.00542,0.09206,-0.10143,0.07473,0.0636,0.10779,-0.11132,0.01996,0.04664,-0.0713,0.0658,-0.08382,0.07429,0.03757,-0.08555,-0.03121,0.05369,-0.13282,-0.07255,-0.02816,-0.05179,-0.09868,-0.06342,0.0364,0.10001,-0.08158,0.03038,0.0668,0.02023,0.02411,0.04189,-0.02089,-0.00846,0.04202,-0.01594,0.04961,-0.08044,0.04247,0.0638,0.04268,-0.00636,-0.01375,0.03784,0.05855,0.03467,-0.07316,0.0986,-0.05748,-0.00931,-0.03714,-0.03061,0.07344,0.0436,0.05715,0.05021,0.02509,-0.04355,-0.02523,-0.04587,0.0289,-0.0197,-0.01364,-0.1785,-0.0519,-0.04923,-0.02351,0.01996,-0.09437,-0.00411,-0.04818,-0.08418,0.08395,0.0465,-0.03562,0.06289,0.02961,-0.09989,-0.01871,0.03087,-0.03718,-0.04517,-0.00722,-0.00134,-0.00386,-0.12659,-0.04523,-0.01845,-0.03056,0.01379,0.04926,0.04104,0.14449,-0.13031,0.07667,0.04546,0.06594,0.00028,-0.09314,-0.055,0.07369,0.063,-0.0123,-0.00425,-0.08383,0.11143,-0.08025,0.04122,-0.01052,-0.01535,-0.09174,0.04205,0.01311,0.06695,0.01038,0.03989,-0.05816,0.03247,0.02082,0.03988,-0.0088,-0.01517,-0.04071,0.00221,0.17759,-0.1026]},{"domain":"discrete_math","key":"dfs_order","name":"Depth-first search order","package":"discrete-math-ai999x","example":"Give the depth-first search order from A in the graph with edges A-B, A-C, B-D, C-D, D-E.","v":[0.06929,0.085,0.01718,-0.06122,0.10866,-0.02029,0.1006,-0.09127,0.12614,-0.1096,0.00346,0.01212,-0.02378,0.07665,0.02885,-0.00669,0.07987,-0.08865,-0.06547,-0.00114,-0.00898,0.08962,0.01272,0.03682,0.01048,0.02439,0.04884,-0.02271,-0.07679,0.02221,0.08741,0.01466,-0.00275,-0.00436,0.02605,0.05777,-0.02315,0.00524,-0.04671,0.09429,-0.14995,0.06707,-0.01653,-0.06942,-0.00026,0.01576,-0.01566,0.0831,-0.02842,-0.04124,-0.01163,-0.01933,-0.04298,-0.07518,-0.10909,-0.02802,-0.0772,0.00222,-0.06995,0.00671,0.01759,0.02048,0.00389,-0.02638,0.024,0.05375,0.13707,-0.03344,0.0137,-0.0297,0.00801,0.07573,0.06253,-0.05781,-0.05047,-0.03464,-0.00896,0.1473,-0.05761,-0.02414,0.01902,-0.00739,-0.00104,-0.05017,0.05055,0.12655,-0.08378,0.01402,0.0244,-0.01613,0.1149,-0.00604,0.03983,-0.08114,-0.10258,-0.08302,0.01952,0.03067,0.07713,0.0264,-0.02782,0.08169,0.0099,0.04813,0.06893,0.08353,0.03217,-0.09518,-0.04936,-0.05442,-0.01889,0.03279,-0.12918,-0.04989,0.00542,0.03862,-0.07188,-0.01655,-0.01305,-0.06644,0.05126,-0.03004,-0.1191,0.09203,0.03922,-0.01205,0.01064,0.03104,0.05795,-0.01731,0.02098,0.0113,0.07431,-0.03942,-0.02925,-0.04239,-0.10075,0.00974,0.06757,-0.14223,0.0471,0.12434,-0.06826,-0.01292,0.00523,-0.16738,-0.09234,-0.06461,0.00283,0.03615,0.0251,0.00653,-0.00805,0.00926,-0.09065,0.02344,-0.08471,-0.02266,0.06022,-0.11225,-0.11266,-0.09016,-0.00207,0.06921,0.01942,0.0825,-0.00299,0.06952,-0.02184,0.0508,0.02171,0.15313,-0.05869,-0.03271,0.01124,-0.01545,-0.04293,-0.00177,0.0189,0.05333,-0.04003,-0.06713,0.11299,0.01788,-0.13907,0.06164,0.02306,0.04817,0.12326,0.05625,0.04565,0.04616,0.00654,-0.01705,-0.03274,0.02008,-0.00368,0.10911,-0.05878,-0.01792,-0.07172,-0.07047,0.11562,0.03592,-0.01569,-0.04266,0.01227,-0.03296,0.0611,-0.01894,0.03946,-0.05425,0.00154,0.10287,0.02899,-0.05766,0.12154,-0.088,0.04759,0.08192,0.02252,0.02753,-0.03974,-0.06389,-0.01735,-0.0902,-0.06203,-0.0185,-0.05459,0.05968,-0.00148,0.01705,-0.08441,-0.02199,0.0525,-0.12307,-0.00416,0.11566,-0.00801,0.03617,-0.00142,-0.01552,0.04894,-0.01955,-0.0205,0.01128,0.05726,0.07381,0.0935,0.07665,-0.01427,-0.23098,0.00372,0.03867,-0.03464,-0.00745]},{"domain":"discrete_math","key":"diffie_hellman","name":"Diffie-Hellman key exchange","package":"discrete-math-ai999x","example":"Diffie-Hellman with p = 23, g = 5, a = 6, b = 15: find the shared secret.","v":[-0.01445,-0.07451,-0.1165,0.09517,0.08394,0.06343,0.03968,0.02075,0.00693,0.03355,-0.00451,-0.04211,0.06886,0.01053,-0.02412,-0.09788,0.08101,-0.05383,0.01211,0.02815,0.12251,-0.08529,0.05111,0.13871,-0.12834,0.02139,0.06455,0.10565,-0.00693,0.20644,-0.02895,-0.05663,-0.06046,-0.07528,0.01089,0.09818,-0.10547,0.06859,0.04655,0.02258,-0.06193,0.0639,-0.06206,0.02914,-0.11277,0.05575,-0.02182,-0.00723,0.05673,-0.02116,0.03286,0.0193,-0.01464,-0.00287,-0.03877,0.00657,0.03158,0.01071,0.10862,-0.02287,-0.14228,-0.14039,0.02719,-0.01966,-0.10579,-0.03767,0.00424,-0.01457,-0.03605,-0.01742,0.09678,-0.06643,0.03264,-0.09231,0.03974,-0.04958,0.03911,-0.02179,-0.1077,0.00061,-0.00916,-0.02551,-0.01372,0.04933,0.01199,-0.00074,-0.03171,0.00075,-0.00845,0.00905,-0.05584,-0.13871,-0.00836,-0.03467,-0.01422,-0.06711,-0.04019,0.00323,0.02619,-0.08245,-0.06838,0.05276,-0.00329,-0.03232,0.05686,0.00017,-0.07487,-0.05725,0.09399,0.01015,0.08166,0.08367,0.06544,0.09786,0.08272,-0.02368,-0.01663,-0.07029,-0.03381,-0.05239,0.08174,0.04454,-0.16199,-0.01549,-0.02503,-0.14614,-0.12733,-0.02102,0.00202,-0.06466,0.06798,0.04539,-0.07165,-0.06615,0.00426,0.00805,-0.04537,0.0266,0.02656,-0.1203,0.00886,-0.08255,0.1024,0.01586,0.03235,0.07688,-0.01722,0.03913,-0.04039,0.15959,0.01624,-0.00546,-0.06515,0.09239,-0.05263,-0.01643,0.02408,-0.00479,0.06537,-0.07708,-0.00081,-0.04489,0.04466,-0.02506,0.05427,-0.05035,-0.06064,0.05054,-0.09466,-0.00511,0.00164,-0.00971,0.07355,0.08775,0.0567,-0.03558,-0.07,0.01935,-0.07626,0.02341,0.0211,0.03916,0.08392,0.03569,0.04177,-0.04395,-0.03538,-0.04296,-0.04579,-0.06202,0.01181,0.12524,0.02335,0.00166,0.02165,-0.0559,-0.06606,0.0395,0.04822,0.01903,-0.00463,0.02826,0.00962,0.07329,0.01828,-0.05324,-0.02271,-0.02449,0.10755,-0.05444,-0.0069,-0.07347,-0.09866,-0.00965,0.02694,-0.10196,0.00758,0.03954,0.10151,-0.05157,0.09078,-0.01495,0.01847,-0.01795,0.00177,-0.04334,0.01817,-0.04881,0.13445,0.06065,-0.00273,0.08778,0.09056,0.00015,0.06143,-0.02538,0.19385,0.03372,-0.0274,0.03425,0.03504,0.07735,-6e-05,0.04831,0.04525,0.02199,-0.07256,0.11578,0.01063,-0.09047,0.0495,-0.02753,-0.02294,0.0588,0.00629,-0.01554]},{"domain":"discrete_math","key":"directed_cycle","name":"Cycle detection in a directed graph","package":"discrete-math-ai999x","example":"Does the directed graph with edges A->B, B->C, C->A have a cycle?","v":[0.04229,0.05538,-0.00304,-0.02854,0.03264,-0.00512,0.00223,-0.05675,-0.00966,0.00814,0.01922,0.05367,0.0043,0.09678,0.07402,-0.01598,0.05024,-0.04939,-0.06963,-0.10107,-0.15838,-0.02367,-0.05131,0.03333,0.03506,-0.05882,-0.06971,-0.00519,-0.01526,0.09187,-0.00184,-0.06265,0.05746,0.0614,0.06505,0.01574,-0.06294,0.04227,0.1142,0.06382,0.05005,0.01839,0.00721,0.02603,0.105,0.01789,0.03055,0.08743,-0.00071,-0.01155,0.02164,-0.09835,0.03002,0.04032,-0.01843,-0.05783,-0.09727,-0.00065,-0.12905,0.0396,-0.01109,0.01737,-0.01121,-0.01085,0.03693,0.00655,-0.04878,-0.05963,0.02115,0.07032,0.01757,0.08063,0.08255,-0.09143,0.08551,-0.08441,-0.06422,-0.00896,-0.05885,-0.00473,-0.00812,-0.04503,0.07214,-0.06029,-0.03422,0.15325,-0.06691,-0.11164,-0.05555,-0.01661,-0.05047,-0.03219,0.09064,-0.01033,0.08329,0.01642,0.048,0.02187,0.07665,0.10167,0.02854,-0.02829,-0.08051,0.09974,0.01229,0.08054,0.06816,0.01155,-0.11612,0.00283,-0.05386,0.08071,-0.01148,-0.10837,0.01802,0.07093,-0.10918,-0.04804,-0.01166,-0.0381,0.0092,-0.05227,-0.11791,0.02705,-0.01859,-0.06796,-0.00747,0.00197,0.02304,0.07628,-0.13347,-0.03202,-0.01201,-0.09206,-0.01156,0.04505,-0.16152,-0.08608,0.00218,-0.08036,-0.02485,0.06768,-0.04867,-0.01944,0.09396,-0.02197,-0.0467,-0.01379,0.07313,0.0622,0.05155,0.05358,0.04051,0.02039,-0.06191,-0.04012,-0.02254,-0.01053,-0.02903,-0.08349,-0.11726,0.14283,-0.03652,-0.11773,-0.05088,-0.03371,0.03657,0.07664,0.04373,0.03171,0.10595,0.05446,-0.07055,-0.04932,0.09258,-0.01863,-0.05264,0.02173,0.04164,0.01721,-0.0051,-0.03518,0.08852,0.07041,-0.09207,0.00138,0.11601,0.03538,0.03663,-0.07135,0.02617,0.00675,0.03201,-0.09121,-0.04526,0.00692,-0.08495,0.15221,0.08951,0.01737,-0.01029,0.01392,0.07541,-0.01589,0.07547,-0.01346,0.0227,-0.01023,-0.06998,-0.10365,0.02705,-0.04725,-0.06889,0.09275,0.12391,-0.08243,0.06771,-0.05006,0.03451,0.07671,0.01636,0.01102,-0.0507,0.04599,0.1236,0.08823,-0.04137,0.04349,-0.09173,0.03175,-0.12401,-0.01814,0.00031,0.02844,-0.00589,-0.02477,0.09101,0.03761,0.06761,0.04497,-0.03702,0.07905,0.06897,-0.02821,0.01397,-0.00993,0.05918,-0.02935,0.04436,0.03276,-0.04385,-0.08586,0.04736,0.09707,-0.05536,-0.1346]},{"domain":"discrete_math","key":"discrete_log","name":"Discrete logarithm","package":"discrete-math-ai999x","example":"Find the smallest x with 3^x ≡ 13 (mod 17).","v":[-0.03979,0.03683,-0.08479,0.03197,0.04054,0.06137,0.07861,-0.00148,0.00028,-0.04488,-0.04472,0.01897,-0.06096,0.0721,0.02885,0.0166,0.14436,-0.11244,-0.03442,-0.01509,-0.01779,0.00919,0.03093,-0.02195,-0.06359,0.06935,-0.08124,-0.01385,0.01527,0.06758,-0.06381,-0.13725,-0.05282,-0.0741,0.044,0.04546,-0.08098,-0.00949,0.05289,0.07713,-0.02986,-0.00045,0.03057,-0.10211,0.04223,0.10226,-0.02074,-0.0018,0.0127,-0.06363,0.09348,0.03573,0.01041,0.01285,-0.05188,0.0125,-0.10341,0.00168,-0.06255,-0.00128,-0.01795,-0.09026,-0.03141,0.17059,-0.00424,0.07731,-0.01998,0.03889,0.05289,0.1478,0.07088,-0.05396,-0.02567,-0.00212,-0.02948,0.08033,0.03211,0.01794,-0.11256,0.03695,0.05521,0.11421,-0.01076,0.0699,-0.08895,0.04082,0.00461,0.08761,0.05463,-0.01242,-0.03512,-0.10703,0.04228,0.04561,0.05689,0.00907,-0.05621,0.03963,0.08793,-0.02781,0.02539,0.03642,0.02392,-0.05994,0.03931,0.03626,-0.04645,0.0089,0.03241,-0.10489,0.00471,0.00122,0.01179,0.03708,0.06502,0.07886,-0.07934,-0.10292,0.00505,-0.04744,0.07996,-0.01306,-0.04849,-0.02922,-0.10978,-0.09085,-0.00603,-0.02361,-0.10331,0.02002,0.0097,0.04288,-0.00746,-0.01442,0.01894,0.07656,-0.05012,-0.00442,0.04252,-0.09033,0.07706,-0.07741,0.01742,-0.03749,-0.08399,-0.02127,0.04556,-0.07115,-0.06901,-0.01769,-0.06315,0.08621,-0.08963,0.12114,-0.01039,-0.04178,-0.11855,0.08838,-0.01172,0.01819,-0.04159,-0.026,0.10204,-0.02753,-0.06203,-0.00802,0.01292,0.0196,0.06275,0.12799,0.08195,0.019,0.04244,-0.04209,0.01363,-0.0421,-0.00971,0.11573,-0.10294,0.00206,-0.01632,0.00823,-0.02779,0.00022,0.05802,-0.10986,0.02627,0.00822,-0.05273,0.04207,0.00432,-0.07782,0.06213,-0.03212,-0.03798,0.01723,-0.18344,-0.05686,-0.0682,0.11903,-0.05564,0.0397,-0.0067,-0.11363,-0.07379,0.04387,0.05575,0.04207,0.07323,0.01313,0.00346,-0.01233,0.02015,-0.02151,0.08839,-0.10099,-0.03211,-0.08308,0.13238,-0.11964,0.11864,-0.03641,0.00479,0.08001,0.10188,0.03258,0.08209,-0.01392,-0.08007,-0.03098,-0.01792,-0.06656,0.07925,0.06726,-0.02513,-0.05095,0.02147,0.04174,-0.06517,0.09327,0.01192,0.02974,-0.07162,-0.05408,0.04964,0.01867,-0.16541,0.0936,-0.0299,-0.01638,0.00809,-0.02337,0.08849,-0.04202,0.06507,0.0881]},{"domain":"discrete_math","key":"divisor_functions","name":"Divisors, divisor count and divisor sum","package":"discrete-math-ai999x","example":"How many divisors does 360 have?","v":[-0.01973,-0.06729,-0.02189,0.02865,0.08386,-0.05841,0.00891,-0.01567,-0.10634,-0.04171,0.0091,0.01779,0.04854,0.00227,-0.0436,0.04928,-0.07461,0.04254,-0.01731,0.05475,-0.01601,-0.10286,-0.07061,-0.08074,0.00278,0.12486,0.00775,-0.05497,0.11479,0.01194,-0.17588,-0.05777,0.00372,-0.02356,-0.05113,-0.04721,-0.05875,-0.00876,0.0885,-0.02734,-0.05178,0.02527,0.03759,-0.08911,0.02094,-0.0008,-0.15434,0.17052,0.05767,0.0051,-0.05091,-0.08377,-0.02494,0.05277,0.043,-0.0252,-0.17532,-0.02114,0.11092,-0.04435,-0.14247,0.10913,0.01201,0.06888,0.08608,-0.03376,-0.0352,-0.07881,0.0465,-0.00077,-0.03069,-0.03495,-0.08867,0.13003,-0.01977,-0.02419,-0.08276,0.07867,-0.00386,-0.03191,-0.0262,-0.02435,-0.03271,0.01147,0.09211,0.0184,-0.00537,-0.049,-0.04329,-0.02973,0.00154,-0.04857,-0.0377,-0.12489,-0.02293,-0.02811,0.01791,-0.00631,-0.01257,-0.02904,0.02407,-0.01701,0.03326,-0.05943,-0.02308,0.09225,0.07491,-0.07554,0.07836,0.02317,0.02977,-0.02742,-0.08947,-0.01918,-0.01698,-0.02252,0.04335,-0.00019,-0.08343,0.02688,-0.01335,0.17856,-0.0213,-0.02108,0.13172,0.02137,-0.0377,-0.02371,0.07071,0.03377,0.05021,-0.02661,-0.01923,0.01097,0.0443,0.02022,0.00224,-0.07798,0.04889,0.18333,-0.00803,0.1507,0.007,-0.00873,0.01714,0.02193,-0.0719,0.04488,0.01293,-0.05266,-0.04408,-0.02133,-0.03255,0.01628,-0.01262,0.0399,-0.1187,0.02044,0.00848,0.06944,-0.03102,-0.10197,0.00903,0.0825,0.01159,-0.06195,0.01412,-0.00195,0.07169,0.03392,0.06219,0.03199,-0.07596,0.14687,0.00288,0.06959,-0.09941,-0.0094,-0.08494,0.10203,0.0333,0.10758,-0.02263,-0.01311,-0.06236,0.06516,0.07694,0.0329,-0.03947,-0.05115,0.04711,0.0113,-0.04387,-0.00527,-0.09787,-0.01222,0.04075,0.09875,-0.04142,-0.02399,-0.02314,-0.02978,0.05822,0.03562,0.11088,0.09688,-0.02824,0.00599,-0.07057,-0.01375,0.01091,-0.02259,-0.03563,-0.03536,0.06428,-0.01084,-0.06375,-0.07316,0.08728,0.06568,-0.03398,-0.12777,0.01152,0.04361,0.0819,-0.03883,0.01985,-0.0914,-0.10638,0.03082,-0.03798,0.02965,-0.07535,-0.05366,0.0137,-0.02205,0.05134,-0.03428,0.0156,0.10107,-0.04632,0.05633,0.0621,-0.03982,0.17667,-0.01467,0.01273,-0.02778,0.09323,0.05253,0.07251,-0.02676,0.00709,0.05802,-0.03979,0.0699]},{"domain":"discrete_math","key":"elgamal_encrypt","name":"ElGamal encryption","package":"discrete-math-ai999x","example":"ElGamal: encrypt m = 10 with p = 23, g = 5, x = 6, k = 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totient function","package":"discrete-math-ai999x","example":"What is Euler's totient of 36?","v":[0.01483,-0.06276,-0.01115,0.0143,0.01966,-0.00152,0.14145,0.02788,-0.0139,0.00933,0.03975,-0.0362,-0.05282,0.05774,-0.04543,0.04851,-0.04034,0.00921,-0.00552,-0.011,0.04685,-0.05145,-0.16173,-0.03545,-0.01056,0.15491,-0.05074,0.0032,0.0089,0.01707,-0.12094,-0.07679,-0.0336,-0.0971,0.01284,-0.00488,0.06194,-0.05566,0.02976,0.06157,0.01251,0.0354,-0.00824,-0.0067,0.04904,-0.03841,-0.12809,0.08841,-0.03832,0.09285,0.02168,-0.04362,-0.03057,-0.07218,-0.03431,-0.00891,-0.16531,0.00596,-0.00284,-0.00567,-0.06941,0.05223,-0.05252,0.09242,0.02094,0.0055,0.04646,-0.01021,-0.02101,0.00833,-0.09754,0.00661,-0.05351,-0.03833,0.01397,-0.0375,0.03019,0.00344,0.01906,-0.03639,0.00111,0.01204,-0.03825,0.01071,-0.03807,0.01282,0.02251,0.08996,0.00737,-0.01409,0.00809,-0.11359,-0.14059,-0.05559,-0.07378,0.01955,0.0478,-0.08856,0.04609,0.07518,0.05908,0.0669,0.10233,-0.04578,0.02537,0.01893,-0.02294,0.00263,0.11058,0.01528,-0.02475,0.0161,-0.02403,-0.03536,0.0658,0.02863,0.06783,-0.08787,0.00943,0.01857,-0.00052,0.1297,-0.05565,-0.0271,0.06731,0.00743,0.03733,-0.03389,-0.07096,0.07028,0.083,0.01491,-0.01097,0.01734,0.04466,0.09937,0.01651,-0.03939,0.09627,0.11875,-0.09333,0.07236,-0.00486,-0.09405,-0.00531,-0.04539,0.0076,0.05819,-0.08439,0.01083,-0.03284,-0.00293,-0.00014,0.00548,0.03516,0.10924,-0.07782,0.06224,0.00578,0.11622,-0.12705,-0.01506,0.03245,0.09456,0.07362,-0.02049,-0.0104,0.01013,0.06408,0.06947,0.11647,-0.07187,-0.11189,0.01161,0.09064,0.09457,-0.0344,0.06227,-0.07423,0.09305,-0.07514,0.05978,0.03169,-0.04414,0.00251,0.12728,-0.03087,0.0287,-0.05607,0.00841,0.05982,-0.03181,0.01513,0.0217,-0.12148,-0.00482,-0.06609,-0.00214,-0.12939,0.03656,0.0118,-0.05234,0.06319,0.02517,0.042,0.0056,0.00126,-0.04142,0.0786,-0.00705,0.08425,-0.04812,-0.05072,0.03721,-0.08374,-0.08415,-0.10878,-0.04442,0.12134,-0.01823,-0.05732,-0.17987,0.01398,-0.01039,0.18803,-0.01843,0.08039,-0.17099,-0.05146,-0.00859,-0.04154,0.06277,-0.13551,0.06109,0.00786,0.00723,0.05546,0.00104,-0.01987,0.01579,-0.16955,0.06293,-0.01983,-0.06109,0.0803,-0.05215,-0.05954,-0.00919,0.02445,0.00929,0.03632,-0.00331,-0.03344,0.02031,0.04291,0.04071]},{"domain":"discrete_math","key":"eulerian","name":"Eulerian circuits and paths","package":"discrete-math-ai999x","example":"Does the graph with edges A-B, B-C, C-A, C-D, D-E, E-C have an Euler circuit?","v":[0.04676,-0.01749,0.01866,-0.04552,0.15187,-0.0569,0.12374,-0.1205,0.12523,0.0186,0.02794,-0.05208,0.01166,0.1133,0.01366,-0.01278,0.03671,-0.11119,-0.01184,-0.03188,0.01272,-0.04606,0.03656,0.03675,-0.01314,0.05591,0.03089,-0.00141,-0.00067,-0.06905,0.12591,0.04524,-0.07515,-0.01552,-0.0818,-0.00715,0.0716,-0.06663,0.04916,-0.05835,0.01606,-0.05792,0.04463,0.07765,0.0497,0.01448,-0.00859,0.10419,-0.02405,-0.02207,-0.02127,-0.12275,0.03011,-0.05729,0.01628,-0.12721,-0.13423,0.11085,-0.08098,-0.0539,0.08515,-0.08299,-0.01938,-0.08557,0.01385,0.1118,0.0355,-0.0913,0.00963,-0.1218,0.01529,0.07147,0.04966,0.06603,0.08334,-0.06696,0.10583,0.01564,0.03679,-0.01763,-0.03506,-0.04893,-0.00595,0.07352,-0.02725,0.12367,0.04997,-0.00026,-0.0001,-0.11361,0.0621,-0.03172,-0.00302,0.03271,-0.07103,0.12164,0.02572,-0.04336,0.00266,0.03722,0.10694,0.04454,-0.01327,0.04748,-0.03436,-0.04409,-0.00929,-0.07649,-0.0751,-0.00274,0.0178,0.07996,-0.00987,-0.10022,0.10121,0.00945,0.01963,0.06467,-0.06668,-0.05586,0.01038,-0.00519,-0.11834,0.07191,-0.0397,-0.12449,0.01458,-0.01236,0.00119,0.04246,0.0026,-0.01448,-0.04575,-0.06318,-0.04094,0.02108,-0.08253,-0.12691,-0.01679,-0.01031,-0.05432,0.01011,0.00652,0.03928,0.03107,-0.03639,-0.033,-0.02644,-0.01215,0.06317,0.01911,0.08236,0.11708,0.05031,0.01976,-0.02141,-0.07672,-0.0554,0.05328,-0.07842,-0.04691,-0.10212,0.10883,0.02822,0.01412,-0.00239,-0.02197,0.06722,0.0232,0.04757,-0.03852,0.05646,0.04336,0.01427,0.05264,-0.00882,-0.11049,-0.00483,-0.00828,0.0468,0.02032,0.02956,0.13858,0.08367,-0.17225,0.05157,-0.0237,-0.00773,-0.02946,0.01859,0.11381,0.01245,0.0461,-0.04081,-0.03363,-0.00391,-0.04133,0.07385,-0.06623,-0.03943,-0.02011,0.00431,0.03205,0.04114,0.04608,0.06634,-0.01238,0.01002,0.0337,-0.03951,0.06366,0.00862,0.03775,0.08936,0.097,-0.08436,0.0392,0.07969,-0.09373,-0.00387,0.0473,-0.00394,0.05533,0.01628,0.00468,0.0092,-0.06406,-0.10702,-0.07616,0.02513,-0.04577,0.00264,0.03608,0.07039,0.09783,-0.07145,-0.09448,-0.04786,-0.07279,-0.01414,-0.08584,-0.02714,0.12484,-0.00152,0.02878,-0.12776,0.0786,-0.03293,0.06612,-0.03214,0.07969,-0.14149,0.01899,0.08292,-0.02327,-0.05748]},{"domain":"discrete_math","key":"extended_gcd","name":"Extended Euclidean algorithm (Bezout coefficients)","package":"discrete-math-ai999x","example":"Find the Bezout coefficients of 240 and 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numbers","package":"discrete-math-ai999x","example":"What is the 30th Fibonacci number?","v":[-0.01039,-0.04984,0.04511,-0.01531,0.04823,0.04703,0.05403,0.07659,-0.08625,0.01669,-0.02202,-0.10826,-0.08024,0.00955,-0.06597,0.02848,0.03219,0.05382,0.04797,-0.09649,-0.04973,0.04467,0.00728,0.01799,-0.03882,0.01638,-0.0724,-0.03497,-0.09529,-0.0809,-0.10186,-0.03565,0.02672,-0.06971,0.07427,-0.02241,-0.02602,0.0117,0.01182,0.03696,-0.02496,0.10651,-0.02745,-0.07634,-0.02731,0.02261,-0.17924,-0.02595,-0.04101,-0.03474,-0.05657,0.06458,-0.04622,0.00134,-0.05571,0.04405,-0.05327,-0.08088,0.12427,-0.02477,-0.02292,-0.02641,0.0252,-0.04234,-0.00063,-0.01736,0.09237,-0.01309,0.00918,-0.03869,-0.06016,-0.01404,-0.05115,0.04029,-0.12978,-0.12342,0.05616,0.05366,0.07083,-0.08477,-0.0461,-0.09159,-0.01346,0.05372,-0.05359,-0.0522,0.00813,-0.03584,0.01371,-0.00118,0.06329,-0.01105,0.04938,0.01914,-0.01445,0.06153,-0.00343,0.06782,0.02923,-0.00444,-0.03604,0.12022,0.03487,-0.05324,0.02373,-0.00879,0.07028,-0.00783,0.04434,-0.04797,-0.04347,-0.06887,-0.05035,0.03836,0.15325,-0.02075,0.09699,-0.14429,0.04719,-0.04347,-0.01491,0.04467,0.07584,0.0042,0.05479,-0.03185,-0.03019,0.02078,-0.01866,0.0301,0.04516,0.04899,0.02425,0.00252,0.10403,0.09098,0.06588,-0.02781,0.09995,-0.09213,-0.04166,0.05748,0.05151,-0.02112,-0.03618,-0.08186,-0.00329,-0.04052,-0.03837,-0.06092,-0.01683,-0.05858,-0.01074,-0.00554,0.04948,0.03363,-0.14751,-0.04398,-0.04147,0.02377,-0.00523,-0.06004,0.07041,0.00261,0.0801,-0.00127,-0.05335,-0.034,0.00957,-0.01365,-0.05491,-0.0228,0.04102,0.08659,0.07605,0.04186,-0.05992,-0.01748,-0.10015,-0.03159,0.01003,0.01254,0.07569,0.02098,-0.01119,0.09163,-0.03618,0.01751,-0.06521,0.00202,0.14818,0.07929,-0.03937,-0.00649,0.00654,0.11007,0.01128,0.00815,-0.07069,-0.07106,0.03943,0.02545,-0.0395,-0.07573,0.03924,0.06552,0.03466,0.07162,0.04834,0.02933,-0.06623,-0.14114,0.02696,0.145,-0.06172,-0.13602,0.09491,0.03866,0.09638,0.07275,0.08604,-0.00958,0.04239,0.05015,0.01453,0.06905,0.15494,0.04629,-0.0381,0.02921,-0.04354,-0.02173,-0.10559,-0.01732,-0.00468,-0.0623,0.0846,0.1233,0.10824,0.07771,-0.08576,-0.11573,-0.08736,0.03798,-0.07654,-0.08567,0.00799,0.02797,0.05101,0.16765,0.0654,-0.01842,-0.08618,0.06773,0.04015,-0.12692]},{"domain":"discrete_math","key":"gcd_lcm","name":"Greatest common divisor and least common multiple","package":"discrete-math-ai999x","example":"What is the gcd of 84 and 36?","v":[-0.12798,0.00671,0.03959,0.10016,0.01657,-0.11222,0.01924,0.00885,-0.05347,0.02201,-0.00152,0.08053,0.08825,0.00242,0.00768,-0.05025,-0.01636,0.02303,-0.0406,0.07908,-0.00024,0.0407,-0.00861,0.01889,0.11378,0.18866,-0.1309,-0.02837,-0.00631,0.12288,-0.1113,-0.05983,-0.08272,0.08585,-0.04693,-0.00154,-0.00353,0.00973,-0.06476,-0.03142,-0.04194,0.02709,0.08183,-0.16621,0.00544,0.02169,-0.03098,0.10913,0.00636,0.04207,0.05021,-0.02462,-0.00442,0.00167,-0.05596,0.06793,-0.10256,0.01185,-0.09658,0.07641,-0.06611,-0.04825,0.03926,0.03825,0.02726,0.06287,0.0467,0.05163,0.03802,0.02104,0.09799,-0.05066,-0.12191,-0.07432,-0.04031,0.01159,-0.07943,0.05724,-0.05064,-0.02334,0.07588,0.0395,-0.01891,0.09331,-0.01968,0.09297,-0.01902,0.03767,0.06222,0.08262,-0.01656,0.08791,-0.03792,-0.07387,0.03297,-0.07885,0.03479,0.00447,-0.067,-0.0486,0.04802,0.10435,-0.09461,-0.05374,0.03711,0.05376,-0.11604,-0.03887,0.00877,-0.07517,-0.05567,0.01785,-0.04123,0.04823,0.01455,0.06789,-0.00935,0.03235,0.06793,-0.06393,0.06452,0.12653,0.02478,-0.00144,-0.08378,-0.04148,0.04032,-0.04201,-0.01828,0.02858,0.00255,-0.05501,-0.10551,-0.00588,0.01702,0.0302,-0.03019,0.00197,0.04553,0.06273,-0.01468,0.09951,0.0804,0.02346,0.00815,0.08872,0.01453,-0.05403,0.14514,0.05354,-0.0703,-0.04074,-0.03545,0.03121,-0.06004,-0.10766,-0.03665,-0.05926,-0.02267,0.0588,-0.03583,0.13915,0.16527,-0.01829,0.0208,-0.0551,0.10866,-0.00899,0.03099,0.10658,0.07588,0.01385,-0.11343,0.02737,-0.00865,0.05747,-0.06855,0.03166,0.01458,-0.07934,-0.00968,0.0222,-0.02511,0.01025,-0.07814,-0.05397,-0.00856,0.07304,-0.03522,0.01442,-0.05161,0.09186,0.03497,0.0766,-0.10884,-0.03883,-0.00971,0.03236,0.02916,0.00785,0.06282,-0.00983,-0.02998,0.01156,0.03568,0.09839,-0.13776,0.01314,-0.03952,-0.05619,-0.01341,-0.06528,-0.07875,-0.05894,-0.07321,0.0503,0.04257,0.02419,0.06834,-0.05402,-0.02704,-0.09193,-0.09155,0.02824,0.04996,0.04176,0.10981,-0.04356,-0.0694,-0.08148,-0.08656,0.03261,-0.04335,-0.00646,0.07577,-0.03335,0.01874,-0.0277,-0.05623,-0.10424,0.10333,0.06465,0.00531,-0.07008,0.0669,-0.07562,-0.09315,-0.00172,-0.05108,-0.04336,0.08704,-0.02079,0.00465,-0.01256,-0.04535,0.04645]},{"domain":"discrete_math","key":"girth","name":"Girth (shortest cycle length)","package":"discrete-math-ai999x","example":"What is the girth of the graph with edges A-B, B-C, C-D, D-A, A-E, E-F, F-A?","v":[-0.10211,0.08532,0.05804,-0.03277,0.06235,0.03539,0.04264,0.02614,0.06937,0.06075,-0.00868,0.03317,0.07832,0.13865,-0.02402,-0.02826,0.06857,0.01052,-0.12324,-0.09375,-0.05108,-0.06292,-0.10655,0.05696,0.13351,0.01314,-0.06834,0.03192,-0.05189,0.12203,-0.04382,0.02206,-0.01386,0.0765,0.01876,-0.04757,-0.05533,0.04053,0.07962,0.11492,0.00822,-0.0208,-0.01058,0.05348,0.07458,0.05268,0.05603,0.07273,-0.04307,-0.01682,-0.05541,-0.06118,-0.00242,-0.02628,-0.09187,-0.06847,-0.00709,0.00989,-0.01544,-0.0168,0.02651,0.00268,0.01209,0.10452,0.02219,0.03174,-0.05616,0.02549,-0.07226,0.07052,-0.01056,0.05302,-0.05655,-0.1144,-0.00323,-0.00237,-0.10137,0.03998,-0.06227,0.11292,0.01885,-0.02129,0.09164,0.007,-0.01869,0.09929,0.02265,-0.02037,0.01435,-0.02643,-0.02544,-0.05001,0.03007,0.03975,0.12244,0.05372,0.02557,0.06445,-0.05452,0.07553,0.00286,0.0293,-0.00874,0.08057,0.01612,-0.0323,-0.05943,-0.10726,-0.04403,-0.05425,-0.03162,0.02289,0.00273,-0.01972,-0.01607,-0.01382,-0.11887,-0.01708,0.07622,-0.00162,0.05535,0.07459,-0.06461,0.0664,-0.09317,-0.0535,-0.01889,-0.02838,0.00337,-0.05659,0.00706,0.03739,0.05381,-0.04866,0.01043,0.11859,-0.12364,-0.01743,0.04466,-0.0439,-0.00848,0.01269,-0.00753,0.00097,0.0747,-0.06385,-0.03734,-0.09324,0.05507,0.02327,0.03427,-0.0126,0.00202,-0.03709,-0.04465,-0.03829,0.01543,-0.09398,0.00736,-0.07205,-0.19969,0.11159,0.01442,-0.01811,0.02105,0.00594,0.06188,0.09056,0.04167,0.08087,0.09209,0.03712,-0.02843,0.0297,-0.07483,-0.0653,-0.11298,-0.01142,0.05869,0.00356,-0.07132,-0.09839,0.16773,-0.00431,-0.12387,0.04001,0.08988,0.03568,-0.02837,-0.00605,0.02661,-0.03584,0.02394,-0.04985,-0.00126,-0.05857,-0.02409,0.06725,0.15619,-0.05961,-0.01335,-0.00278,0.01824,-0.03559,0.03462,-0.04383,0.06726,-0.0258,-0.06355,-0.17181,-0.03105,-0.05887,0.02535,0.04939,0.09811,-0.01178,0.04068,-0.0527,0.13649,0.05101,-0.03914,0.03171,-0.00498,-0.02041,0.08146,-0.05591,-0.05556,0.1134,-0.11223,-0.06151,-0.07627,0.01411,-0.03321,0.06584,0.02438,-0.04018,0.11346,0.07696,-0.03648,-0.07346,0.04898,0.06662,0.0078,-0.12041,-0.00012,-0.01823,0.03316,0.04311,-0.04645,0.02308,0.0876,-0.02697,0.01431,-0.04497,-0.13034,-0.11203]},{"domain":"discrete_math","key":"graph_degrees","name":"Vertex degrees and degree sequence","package":"discrete-math-ai999x","example":"Find the degree sequence of the graph with edges A-B, A-C, B-C, C-D.","v":[-0.08464,0.04884,0.02692,0.005,0.02011,-0.07659,0.10165,-0.05676,0.11109,-0.08998,-0.05505,0.04008,-0.00159,-0.00784,0.07347,-0.03841,0.00485,-0.03851,-0.04663,-0.03836,-0.0338,0.05144,0.06068,0.02715,-0.03639,0.06877,0.00936,0.02375,-0.1127,-0.00074,0.03883,0.01161,-0.06055,-0.01083,-0.03784,-0.11244,-0.03379,0.02628,-0.00719,-0.06314,-0.05169,0.00749,0.04338,-0.04819,0.01622,0.03353,-0.06608,0.03496,0.00863,0.00253,0.0217,0.07667,-0.07842,-0.03436,-0.04352,-0.13147,-0.07182,0.00532,-0.05616,-0.05222,0.05399,0.04764,-0.07566,-0.00811,0.0994,0.01725,0.05189,0.07783,0.01369,0.08946,0.01841,0.06613,0.01472,0.03796,-0.10578,-0.09329,-0.06028,0.08077,0.01337,-0.09689,-0.03054,-0.06807,0.00382,-0.00277,-0.00472,0.13269,-0.04737,-0.05334,0.02648,0.01677,0.15771,-0.01882,0.0318,-0.00983,-0.0354,-0.03843,0.02395,0.08325,-0.06547,0.13852,0.02978,0.15457,-0.01738,0.0355,0.0669,0.02502,-0.06412,-0.10855,-0.17757,-0.08897,-0.04531,0.02444,-0.02424,-0.07405,-0.06574,-0.03138,0.01352,-0.01311,-0.05136,-0.01874,0.07754,0.03015,-0.03652,0.02468,-0.03106,0.07953,0.05422,0.06264,0.05341,-0.04932,0.01911,0.05337,-0.00604,0.00821,-0.05612,0.0264,-0.16282,-0.04688,0.13204,-0.02094,-0.07754,0.14727,0.01796,0.02986,0.04252,-0.01918,-0.0303,0.02168,-0.00126,0.01612,-0.04432,0.07477,-0.09454,0.05459,-0.05035,-0.00712,-0.08547,0.01729,-0.03802,0.10711,0.04661,0.08873,-0.06091,0.01756,0.0742,0.10621,0.02467,0.00558,0.00336,-0.03384,-0.03322,0.04838,-0.00267,-0.05619,0.021,-0.02016,-0.07138,0.07645,-0.02132,0.03469,-0.02582,0.08907,0.01373,0.04435,-0.17937,0.06013,0.0387,0.08736,0.05761,0.02011,0.0766,0.0683,0.00214,0.0672,-0.0685,-0.07547,0.07302,0.05084,0.0198,-0.04017,-0.02213,-0.06375,0.16121,0.03392,0.00189,-0.05089,-0.03902,0.00025,-0.03286,-0.08404,0.10811,-0.13064,-0.04609,0.03235,0.00112,0.00084,0.1889,0.05895,-0.04164,-0.01556,-0.03283,0.01284,-0.03147,-0.05173,0.11298,-0.02005,0.00011,0.02126,-0.08344,-0.0934,-0.09479,0.10877,0.0288,-0.03047,0.07258,-0.04298,0.00729,0.10037,-0.0145,-0.05343,0.0174,0.05821,-0.01976,-0.0113,-0.1106,-0.05046,0.03632,-0.00237,0.04616,-0.01759,-0.07563,-0.02741,-0.06257,0.07192,-0.03203,-0.07724]},{"domain":"discrete_math","key":"graph_diameter","name":"Diameter, radius and center","package":"discrete-math-ai999x","example":"What is the diameter of the graph with edges A-B, B-C, C-D, D-E, B-F?","v":[-0.03475,-0.05827,0.09419,-0.02481,0.06702,-0.01686,0.02578,0.0307,0.12232,-0.02322,0.03173,-0.0118,0.02037,0.0367,-0.05229,-0.00955,0.07012,-0.00544,-0.04458,-0.01654,0.05828,-0.10358,-0.00705,-0.0438,0.06746,0.04189,0.02231,-0.03481,-0.06263,0.05897,0.12098,0.10189,-0.04081,-0.07226,-0.07409,-0.0902,-0.01469,0.04859,0.01101,0.01581,-0.07185,0.08085,0.00449,0.04163,-0.02824,0.10664,0.04273,-0.14055,-0.02204,-0.11987,0.05605,-0.02349,0.04873,0.11048,-0.04982,-0.12387,0.00463,0.02837,-0.04751,-0.00478,0.08258,-0.0599,-0.06755,0.05621,-0.0012,-0.00176,0.02155,0.01017,0.01105,0.06689,0.05787,0.03745,-0.01388,-0.05983,-0.06832,-0.09536,-0.09986,0.01181,-0.06709,0.02847,-0.05888,0.04267,0.03961,0.01451,-0.02208,0.07994,-0.01666,0.03958,-0.04048,-0.13758,0.09458,0.04482,0.01018,0.04989,0.02105,0.03017,-0.02545,0.12136,-0.05582,0.0633,0.03465,0.05701,0.02769,0.0571,-0.03749,0.00046,-0.08503,-0.14236,-0.08745,-0.0718,-0.01121,0.04974,0.00281,0.01961,-0.00336,-0.05528,0.0649,0.08695,0.03228,-0.06791,0.11514,0.04213,-0.05163,0.06068,-0.12987,-0.06924,-0.01861,-0.05378,-0.01646,-0.07844,-0.06836,0.03783,0.00357,-0.02302,-0.09058,0.10116,-0.07369,-0.05467,0.087,-0.05169,0.08985,0.10906,0.03483,0.06801,0.0746,0.02819,0.05063,-0.05373,0.01334,0.05995,0.02117,0.12752,-0.01824,-0.00056,0.0736,-0.06429,0.05279,-0.04345,0.05279,0.02919,-0.03136,0.00737,-0.0706,0.00333,0.11884,0.0766,0.07271,0.03337,0.0083,-0.00812,-0.0205,-0.00923,-0.00204,-0.03947,-0.09671,-0.06651,-0.01509,0.04692,0.0532,0.08132,0.03275,0.0232,0.10425,0.07614,-0.13567,0.04673,-0.018,0.07488,0.03833,-0.04522,0.00084,-0.0532,-0.01502,0.01134,-0.01331,-0.05959,0.0277,0.04429,0.14528,-0.12014,-0.06779,0.0169,0.05071,0.01827,-0.03636,-0.06616,0.08733,-0.09587,-0.01444,-0.10332,-0.03665,-0.10607,0.09882,0.05246,-0.10437,-0.05301,-0.02502,0.04065,-0.01763,0.1284,-0.01588,0.00659,0.02228,-0.04364,0.06236,-0.00807,-0.10278,0.00333,-0.07121,-0.00578,0.03927,0.0762,0.03796,0.04344,-0.06933,-0.06118,-0.02475,0.01454,-0.01654,-0.06505,0.09284,0.12167,-0.01369,-0.08088,-0.09206,-0.12382,-0.11453,0.03241,-0.08097,-0.04669,0.07288,0.01325,0.01925,0.04022,-0.06641,-0.01365]},{"domain":"discrete_math","key":"graph_triangles","name":"Number of triangles","package":"discrete-math-ai999x","example":"How many triangles does the graph with edges A-B, B-C, C-A, C-D, D-A have?","v":[0.03753,0.06558,0.02356,-0.0378,0.0213,-0.04901,0.17997,-0.11884,0.14584,-0.04665,0.07094,-0.06691,0.01815,0.10576,-0.08776,-0.05436,0.05888,-0.05506,-0.05659,0.05683,-0.01421,0.01085,0.07375,0.00499,0.04525,-0.01295,0.07428,-0.02078,-0.13659,0.02517,0.01276,0.00819,-0.08328,-0.0391,0.00195,-0.02197,0.00484,0.03302,-0.01769,0.05464,-0.08487,-0.00239,0.06413,0.03977,-0.01478,0.06529,-0.08248,0.16905,-0.00352,0.00974,0.01697,-0.05974,0.03356,-0.08929,0.03295,-0.01895,-0.13418,-0.00596,-0.08705,-0.09314,0.08706,-0.00208,-0.08712,0.06601,0.01852,0.09623,0.0247,0.06156,-0.00715,-0.07655,0.01956,0.09107,0.06164,0.00905,-0.00794,0.01973,-0.00783,0.0491,-0.04569,0.02435,0.02689,-0.10463,-0.04249,0.03037,-0.01103,0.02801,0.01321,-0.0939,-0.02001,-0.05432,0.05936,-0.06142,0.0586,-0.05094,-0.06696,-0.02122,-0.02198,0.0502,0.0006,0.0111,0.03849,0.09216,-0.04174,0.06483,0.05687,0.07898,0.03042,-0.15209,-0.05532,0.0086,0.0212,-0.0364,-0.04467,-0.06194,-0.02925,0.02697,-0.0596,0.06927,-0.05892,0.05737,-0.01997,0.05499,-0.05602,0.10222,0.04244,0.00972,-0.00238,-0.00558,0.05744,0.00676,0.03756,-0.04203,0.00709,0.03091,-0.1118,-0.00274,-0.06146,-0.06809,0.09509,-0.06568,-0.00134,0.10961,-0.00293,0.08186,-0.03208,-0.11826,-0.06473,-0.00774,-0.00452,0.05845,0.05734,0.03329,0.01995,-0.05687,-0.11297,-0.07049,-0.0738,-0.15104,0.1216,-0.06137,-0.05027,-0.04464,-0.03782,0.07771,0.09708,0.0259,0.01872,0.10151,0.00942,0.03443,0.04026,0.09529,-0.05646,-0.04135,-0.07252,-0.05353,-0.03765,-0.03757,0.05197,0.14526,-0.07202,-0.04735,0.13052,0.08954,-0.14947,0.02546,-0.03578,0.01751,0.08744,0.02138,0.01261,0.02817,0.03898,-0.08181,-0.03603,0.01314,0.07652,0.02772,-0.01336,-0.01359,-0.04632,-0.03567,0.15393,0.07158,0.00306,-0.01329,-0.03733,-0.06623,0.01692,-0.07429,0.12879,-0.09547,-0.00468,0.06445,0.06693,-0.01403,0.03423,-0.00227,0.00845,0.03904,-0.05719,-0.00117,-0.05734,-0.02763,-0.03219,-0.03282,-0.09724,-0.04295,-0.10401,0.04519,-0.02695,0.01136,-0.04528,0.02669,0.05807,-0.02545,0.01898,0.02918,-0.10654,0.02962,0.02158,-0.02701,0.11516,0.01298,0.03199,-0.03323,0.0186,0.05551,0.05884,-0.06519,0.01537,-0.14657,-0.03688,0.062,-0.05742,-0.08335]},{"domain":"discrete_math","key":"graphical_sequence","name":"Graphical degree sequence","package":"discrete-math-ai999x","example":"Is the sequence 3, 3, 2, 2, 2 graphical?","v":[-0.06254,0.0298,-0.00276,-0.04277,0.08239,-0.00667,0.12674,-0.07638,0.01649,-0.09777,-0.02292,0.08284,-0.08852,0.03193,0.05903,-0.02027,-0.00467,-0.03297,-0.10407,-0.07396,-0.09791,0.03948,0.04091,0.0123,-0.0406,0.03483,-0.01593,0.0297,0.01303,-0.01404,-0.05003,-0.01442,0.01489,-0.00737,-0.07026,-0.08273,-0.03888,-0.0252,0.00708,-0.07712,-0.12906,-0.09898,0.03022,0.05703,0.05862,-0.01879,-0.05563,0.11674,0.1196,0.12447,0.04482,-0.01271,0.02896,0.03429,-0.07421,-0.10662,-0.08669,-0.06433,-0.10996,-0.05517,-0.00454,0.0688,-0.05569,-0.06842,0.10565,0.00813,0.02764,-0.04228,0.03011,0.04324,0.063,0.0732,-0.0277,0.06995,0.05014,-0.01774,-0.01251,0.08038,0.01923,-0.11358,-0.07024,-0.00045,0.01434,0.00925,0.03322,0.17275,-0.01995,-0.01911,0.11312,0.026,0.03367,-0.00258,0.00833,-0.02116,-0.00528,0.04365,0.00941,0.05805,-0.02281,0.13639,-0.0254,0.01961,-0.02642,-0.0052,0.08781,-0.01831,0.06854,-0.05665,-0.1488,-0.06153,-0.04899,0.04435,-0.07722,-0.15284,-0.03513,0.00814,0.00821,-0.13678,-0.01367,-0.05248,0.06104,0.0629,-0.08085,-0.02935,0.00677,0.04382,0.11616,0.0856,-0.03526,0.0019,-0.02062,0.03316,-0.00106,-0.02079,-0.0474,-0.0317,-0.08944,0.08291,0.07391,-0.05849,-0.04109,0.10128,-0.13522,0.03722,-0.0221,-0.0121,-0.00498,0.02693,0.00577,-0.01787,0.0597,0.10789,-0.0682,0.04354,-0.04788,0.12386,-0.01444,0.04917,0.01667,-0.10274,-0.01614,-0.03985,-0.11476,-0.06291,-0.00841,0.02735,0.03931,-0.04743,0.00771,0.04911,0.07315,-0.00737,-0.00324,-0.03942,0.0917,-0.07481,-0.02839,0.02586,-0.04498,0.0724,-0.00485,0.08291,0.08249,-0.04272,-0.06815,0.05254,0.09015,0.0356,0.04974,-0.03246,0.10517,-0.00624,0.02431,0.03891,-0.05878,-0.02746,0.06053,0.0265,-0.03704,-0.02589,-0.03005,0.04402,0.05327,-0.0235,0.00654,0.04778,0.01485,-0.05492,-0.04991,0.06407,0.1358,-0.03912,-0.00085,0.03182,0.10766,-0.10391,0.19236,-0.07027,0.04462,0.0068,0.01109,-0.04677,0.04392,-0.01494,0.14277,-0.07728,-0.02242,0.00327,-0.05694,0.02988,-0.10634,0.00621,0.02304,-0.01859,0.06456,-0.02715,-0.06033,0.07964,-0.08076,0.04535,0.01934,0.04352,-0.00304,0.00032,-0.05271,-0.01066,0.06854,-0.01915,0.08017,0.02636,-0.13858,-0.00964,-0.02169,0.06743,-0.00257,-0.12733]},{"domain":"discrete_math","key":"hamiltonian_cycle","name":"Hamiltonian cycle of a small graph","package":"discrete-math-ai999x","example":"Does the graph with edges A-B, B-C, C-D, D-A, A-C have a Hamiltonian cycle?","v":[-0.00233,0.10044,0.01024,-0.07419,0.11866,-0.01594,0.17933,-0.02289,0.07204,-0.01317,-0.00317,0.06283,0.12093,0.09739,0.0213,-0.03127,0.10611,-0.06693,0.0112,-0.04694,-0.02119,0.05157,-0.01421,-0.01118,0.11677,-0.00479,0.01071,0.03949,-0.03357,0.06909,0.02684,0.06811,0.06303,0.07998,-0.05394,-0.08814,0.01005,0.03071,0.05174,0.08277,-0.02905,-0.05543,-0.0834,0.00109,0.01538,0.06961,-0.04908,0.07096,0.03489,0.01087,0.02985,-0.16281,0.01906,0.00627,-0.01037,-0.13809,0.00317,0.00636,-0.02435,-0.0052,-0.0114,-0.0535,-0.00336,0.0768,-0.01763,0.05265,-0.07818,0.05335,0.01796,-0.01651,0.07322,0.07003,0.0643,-0.09743,0.06623,0.05693,-0.08142,0.05314,0.03384,0.00988,0.01627,-0.05743,0.09701,-0.07452,-0.01106,0.13498,-0.02439,-0.07518,0.0502,0.0075,-0.01399,-0.03143,0.04487,-0.03812,0.00614,0.05229,0.08523,0.00256,0.065,0.09959,0.04535,0.0029,-0.08256,0.01746,-0.0491,-0.02942,-0.03443,-0.15011,-0.16892,0.06641,-0.02834,0.03788,0.00833,-0.0546,0.00562,0.00419,-0.12989,0.01219,-0.05275,-0.0448,0.02668,-0.04053,-0.08849,0.01666,-0.04093,-0.06154,-0.04743,-0.04005,0.0652,0.06864,-0.02943,-0.03786,0.0182,-0.05151,-0.02689,-0.04706,-0.1448,-0.17251,0.05232,-0.006,0.07001,0.01582,-0.06549,0.04457,0.04198,-0.05532,-0.08694,-0.12857,-0.00225,0.00469,0.02021,-0.0195,0.00387,0.02703,-0.00175,-0.02529,-0.02457,0.03739,0.03106,-0.15874,-0.12124,0.02402,0.01444,-0.10524,0.00141,-0.09834,-0.02304,-0.08178,0.02801,0.10643,-0.00036,0.01843,-0.01205,-0.07602,0.0221,0.00558,-0.00999,0.00804,0.02488,-0.0039,-0.00963,-0.01813,0.10754,0.09089,-0.2028,0.00145,-0.01165,-0.06502,-0.01099,0.00833,0.03119,0.05806,0.02536,-0.12382,0.02868,-0.03549,-0.12479,0.09865,0.02304,-0.0525,0.03096,0.04029,0.00216,0.02154,0.02642,0.04116,0.09376,0.01926,-0.11433,-0.06194,-0.02729,-0.03621,-0.05134,0.10566,0.09411,-0.01368,0.03838,0.01854,0.07652,0.0652,0.00397,0.04128,-0.00644,-0.04291,0.07616,0.0338,-0.03207,0.01498,-0.13204,-0.01404,0.02785,0.02598,0.04496,0.11139,0.04955,-0.01952,0.06509,0.01287,-0.01414,-0.09655,-0.00378,-0.00194,0.01007,-0.03581,0.0269,-0.00536,0.12443,0.0029,0.05797,0.07485,0.02242,-0.01205,0.04983,0.06249,-0.04941,-0.08968]},{"domain":"discrete_math","key":"inclusion_exclusion","name":"Counting multiples by inclusion-exclusion","package":"discrete-math-ai999x","example":"How many integers from 1 to 1000 are divisible by 3, 5 or 7?","v":[-0.02724,-0.08368,0.01692,0.06072,-0.01378,-0.12209,0.06996,-0.0115,-0.02443,-0.01833,0.00354,0.05605,0.00658,-0.05034,0.03186,-0.10251,-0.08147,-0.02648,-0.02369,0.092,-0.03723,0.04887,0.02539,0.00606,0.01172,0.16553,-0.0311,-0.02619,-0.0167,0.03468,-0.18374,-0.09587,-0.08578,-0.02953,-0.01124,-0.07787,-0.04762,-0.03128,-0.02136,0.00634,-0.04551,0.06741,0.08946,-0.04086,-0.02429,-0.008,-0.13245,0.19379,0.02163,0.04856,0.00803,-0.02409,0.02911,0.03642,-0.00038,0.10062,-0.01734,0.00788,0.04536,-0.04341,-0.11084,0.08711,-0.04757,0.06208,0.105,-0.01395,0.08386,0.04913,0.04121,-0.01656,0.02451,-0.0299,-0.0711,0.00235,-0.04132,0.11044,-0.06842,0.05509,0.08901,-0.0109,0.03115,-0.05539,-0.07554,0.00895,-0.01109,0.03798,0.05932,-0.12053,-0.07113,0.04212,0.01698,0.03033,-0.00606,-0.09364,0.03347,-0.10131,0.05871,0.04696,-0.00563,0.09027,0.06787,0.0195,0.02278,-0.00892,0.05728,0.03558,0.00993,-0.04597,0.0476,0.01653,0.00894,-0.0822,-0.04217,-0.03877,-0.05673,0.07267,-0.03968,0.03199,0.06135,0.0797,-0.07603,0.07907,-0.02898,-0.01027,0.10885,0.03436,0.02488,0.03563,0.07608,0.08767,0.05776,-0.03432,-0.05975,-0.05212,-0.01032,-0.00266,-0.03959,-0.11204,0.01968,0.10797,-0.14027,0.16523,-0.07692,0.03377,0.00853,0.04744,0.00457,-0.02045,0.10423,-1e-05,-0.01099,0.07779,-0.08417,0.00377,0.01136,-0.04044,-0.09562,-0.04765,0.04205,0.03044,0.0951,-0.01852,-0.00656,0.02926,0.06086,-0.09283,0.06897,-0.03232,0.0845,0.02935,0.14907,0.01394,-0.06916,-0.01798,0.03726,-0.015,-0.1087,-0.06102,-0.02066,-0.00843,0.00852,0.06059,0.00173,-0.02652,-0.03604,0.1077,0.08439,0.00308,-0.04058,-0.09437,-0.01923,0.05212,-0.01115,-0.02388,-0.14758,-0.03633,-0.01215,-0.01955,-0.01465,0.02792,0.02188,-0.06956,0.01018,-0.03629,0.03674,0.16279,-0.14158,0.04004,-0.10372,-0.0479,0.03585,-0.13162,0.01832,0.02268,-0.01539,-0.03345,0.04516,0.01838,0.06995,-0.01299,-0.02732,-0.00962,0.07049,-0.03371,0.05436,0.05747,-0.00687,-0.12976,-0.06218,0.06241,-0.10458,0.06705,-0.04548,0.02686,0.04395,0.04024,-0.02183,-0.0567,-0.01121,0.0182,0.06579,-0.03934,0.0911,-0.08184,0.08112,0.04,-0.10568,-0.04203,0.07629,-0.02022,-0.05761,-0.03862,0.07534,0.0412,0.01209,0.02378]},{"domain":"discrete_math","key":"independence_number","name":"Independence number","package":"discrete-math-ai999x","example":"What is the independence number of the graph with edges 1-2, 2-3, 3-4, 4-5, 5-1?","v":[0.02179,0.0975,-0.06639,-0.01807,-0.08929,0.0207,0.07371,-0.04024,0.0687,0.01311,-0.05205,-0.01257,-0.03675,0.04633,-0.06106,0.0455,0.03594,-0.02712,-0.01067,0.01507,-0.00093,0.13143,0.05092,0.01723,0.06128,0.00792,-0.0101,0.0281,-0.10625,-0.01036,0.00738,0.02505,-0.06114,-0.06314,0.00596,0.03058,-0.07047,-0.01199,-0.0773,0.08862,-0.13936,0.0009,-0.04294,0.01019,0.00138,0.0503,0.04561,0.02158,0.06083,-0.02197,0.06592,-0.00491,0.00569,0.06863,-0.10549,-0.03182,-0.06577,-0.00618,-0.08537,0.08515,0.04901,0.05972,-0.04688,-0.00759,0.02803,-0.02568,0.08344,0.04198,0.03301,-0.00342,0.002,0.04754,0.05176,-0.05573,-0.05188,0.04671,0.02686,0.06905,0.02404,0.04901,-0.03986,0.03309,-0.00245,0.00849,-0.06897,0.04278,-0.0351,0.11693,-0.03096,0.00962,0.065,0.02072,0.05668,-0.03549,0.01738,-0.08345,-0.13882,-0.10416,0.02629,-0.05759,-0.04682,0.0319,-0.02777,0.06713,0.13414,0.1162,0.0237,-0.15624,-0.05337,-0.11052,0.03786,0.05426,-0.11173,0.06405,0.01822,-0.04885,0.00943,-0.03669,-0.04146,-0.01857,0.09207,0.06437,-0.05035,0.1417,0.00073,0.05943,0.01054,0.02765,0.04899,-0.0093,-0.12727,0.02229,-0.0473,-0.04246,-0.09231,0.03929,-0.13509,0.04093,0.08346,-0.15567,0.13547,0.06994,-0.00836,0.03097,0.0249,-0.20247,-0.04413,-0.07726,0.03818,0.01112,0.08579,0.03479,-0.12164,0.03416,-0.02234,-0.05399,0.0318,-0.04835,-0.00855,0.05296,0.00784,-0.13239,-0.03181,0.02911,-0.02939,0.08722,0.01239,0.09255,-0.04126,0.09545,0.05483,0.05226,-0.03082,-0.01986,-0.05834,-0.08056,0.05772,0.08565,-0.0247,0.02153,-0.1582,-0.04273,0.12083,0.16728,-0.12742,0.03076,0.0245,-0.01895,0.10946,0.06861,0.02757,-0.06986,0.07701,-0.0404,-0.02185,0.0645,-0.02891,0.02589,0.00996,-0.01677,-0.02882,-0.00824,0.03043,0.01526,-0.00761,-0.08067,0.10055,-0.00485,-0.03721,-0.00192,0.01363,-0.07238,0.0155,0.10076,-0.01378,0.06854,-0.06834,-0.1008,0.06296,0.0453,-0.01132,-0.03999,-0.06556,-0.02451,-0.00838,0.02758,-0.02975,-0.02881,-0.05297,0.00103,-0.03598,0.06491,-0.05561,-0.02516,-0.01844,-0.05332,0.01013,0.0131,-0.14486,0.01894,0.06837,0.01622,0.08936,0.0307,-0.07732,0.06437,0.00933,0.04568,0.01118,0.05552,0.01757,-0.07712,-0.07696,-0.0279,-0.01269,0.08459]},{"domain":"discrete_math","key":"integer_partitions","name":"Integer partitions p(n)","package":"discrete-math-ai999x","example":"How many partitions of 10 are there?","v":[-0.08395,-0.03054,0.04859,-0.02627,0.01513,0.02485,0.13377,0.03644,-0.05138,0.07735,-0.07983,-0.03139,-0.05373,0.01101,-0.04326,-0.00623,0.05984,0.03235,-0.05602,0.01947,0.01317,-0.10173,0.00952,-0.0513,-0.05141,0.08461,-0.06676,0.01202,0.04051,0.02335,-0.11168,-0.14644,0.00561,-0.09574,0.08586,-0.04391,0.0108,0.00158,0.01417,0.021,0.01483,-0.00927,0.12643,0.03153,0.00731,0.06029,-0.11789,0.10277,-0.01204,0.06179,-0.06817,-0.0319,0.02108,-0.01014,0.045,-0.02674,-0.08267,-0.0335,0.1373,-0.09545,-0.10166,0.03179,0.02886,-0.02074,0.01718,-0.12454,0.00125,-0.00357,-0.04318,0.01474,-0.03297,-0.01757,-0.05872,0.0919,-0.02412,0.01538,0.0295,0.04725,0.04976,-0.089,-0.03577,-0.13846,-0.01523,-0.03387,-0.03622,-0.1063,0.11147,0.00468,-0.03054,-0.04097,0.02134,-0.01457,-0.05396,-0.01889,-0.03004,0.01044,0.04467,0.00595,-0.00539,0.0121,-0.0236,-0.0542,0.14258,-0.03448,0.00257,0.05539,0.0771,-0.12518,0.0415,-0.00685,-0.08657,-0.01299,-0.02267,0.04604,0.05782,-0.058,0.13475,-0.07436,-0.07392,-0.0363,0.00463,0.16096,0.00904,-0.03222,0.05387,-0.07526,-0.04718,0.10114,-0.01223,0.02891,0.11622,0.0401,0.07113,0.0215,-0.04919,0.0993,0.09356,-0.03887,0.04842,0.13438,-0.03392,0.00376,0.0875,-0.05295,0.01462,-0.10447,-0.03203,-0.02643,-0.17048,-0.08254,-0.009,-0.05958,0.02517,0.01415,0.12083,0.05129,-0.07715,-0.03425,0.0731,0.06722,-0.01269,-0.05047,0.02481,0.11106,0.01527,-0.02889,0.02937,0.00788,-0.02815,-0.0273,-0.01442,-0.0472,-0.03887,0.03848,0.01506,0.10286,0.01252,0.10686,-0.10186,0.06337,-0.0375,0.01937,0.05189,0.04513,0.03298,0.05206,-0.05282,-0.05075,-0.08526,-0.06786,0.03145,-0.00695,0.00837,0.02097,-0.04157,0.03447,0.06788,0.0171,-0.11033,-0.08622,0.07075,0.01366,-0.01249,0.02654,0.08205,-0.02755,0.02366,-0.12158,0.01067,0.05784,0.00412,-0.12051,0.0998,0.0451,0.06024,-0.00926,-0.03277,0.01754,0.06038,0.03087,0.12021,-0.13137,-0.01665,0.04966,-0.00225,-0.01769,0.0462,-0.06002,-0.11076,0.00224,0.02286,0.0168,-0.07225,-0.11982,8e-05,-0.00478,0.05672,0.0453,0.0238,0.05857,-0.01338,-0.01522,-0.07841,0.16743,0.05389,-0.08367,0.02272,-0.10077,-0.00871,0.02836,0.01081,0.07197,-0.02961,-0.00321,0.07363,-0.02453]},{"domain":"discrete_math","key":"integer_sqrt","name":"Integer square root and perfect squares","package":"discrete-math-ai999x","example":"What is the integer square root of 1000?","v":[-0.02949,-0.06084,0.06924,0.02921,0.04384,-0.06641,-0.00994,0.04654,-0.0756,-0.03502,0.02583,-0.05513,0.09455,-0.03806,-0.0929,0.07206,0.13083,-0.04765,0.0519,-0.01182,0.0408,-0.08144,0.03685,0.0596,-0.05296,0.11255,-0.11489,0.03632,0.00957,0.03098,-0.08212,0.00517,0.03765,-0.03999,0.00585,-0.06457,0.07278,-0.03086,0.0971,-0.00231,0.06203,-0.02193,0.02633,-0.03318,0.06805,-0.03418,-0.03779,-0.0774,-0.02103,-0.00268,-0.00011,0.05236,0.04679,-0.01403,-0.03827,-0.08608,-0.05786,0.02554,0.10574,0.00136,-0.03197,-0.06614,0.04501,0.12534,0.01765,0.05215,-0.00701,0.01029,-0.10337,0.03722,-0.04086,-0.0792,-0.09846,0.05923,-0.1171,-0.0812,0.00871,0.01327,-0.16862,0.0399,-0.00122,-0.07658,-0.0043,0.03153,-0.05203,0.02648,-0.00913,0.03696,0.03971,-0.07424,0.02597,0.07497,0.00543,0.0079,0.02373,-0.01003,0.07151,0.05278,-0.01792,0.10012,-0.04913,0.04955,-0.0013,-0.06558,-0.10417,0.01515,-0.02089,-0.10646,-0.03266,-0.01982,-0.18202,-0.10651,-0.041,0.07546,0.0975,-0.01645,0.07688,-0.03144,-0.00465,-0.04284,0.13287,0.05782,0.04935,-0.07212,0.0035,0.02724,0.02943,0.10272,0.02965,-0.02063,0.07912,0.10622,-0.05265,-0.02455,0.01171,0.0658,0.00864,-0.00345,0.07909,0.12833,-0.03699,0.07118,0.06984,0.03002,-0.08978,-0.08443,-0.03042,0.01532,0.04575,-0.07291,-0.00342,0.0794,-0.00205,0.03836,-0.06044,0.03794,-0.17966,0.01168,-0.02812,0.11609,0.04789,0.12459,-0.003,0.00627,-0.0277,0.0426,0.07243,0.04151,0.08641,-0.05067,-0.02405,-0.00211,-0.10563,0.09308,0.00937,-0.00844,-0.04139,0.04976,-0.05763,-0.02335,0.03549,0.07952,-0.07062,-0.02025,0.05414,0.05563,-0.00343,-0.01285,-0.11414,-0.03295,-0.01563,-0.07293,0.07796,-0.00047,-0.03856,0.00607,-0.07163,-0.01746,-0.05206,0.04972,0.16533,0.05368,-0.07392,-0.05124,0.01025,-0.01531,-0.05843,0.00585,0.09932,-0.00134,0.03275,-0.01367,0.04024,0.08147,-0.05261,0.08749,0.00202,-0.03666,0.13137,-0.04345,-0.01813,0.02121,-0.03247,0.05565,0.15466,-0.02574,-0.048,-0.11523,-0.08944,0.04778,0.02953,-0.03461,-0.03781,0.07856,0.02168,0.00511,-0.04298,-0.02214,0.09608,0.00932,-0.05432,-0.08558,-0.08704,0.02908,-0.02004,-0.10619,-0.03314,-0.03537,-0.02834,0.08997,0.05555,-0.10619,-0.08661,-0.01457,0.02646,0.01122]},{"domain":"discrete_math","key":"is_prime","name":"Primality test","package":"discrete-math-ai999x","example":"Is 97 prime?","v":[0.03621,-0.00185,-0.01703,-0.02042,0.01086,-0.02291,0.01045,0.01383,-0.08675,-0.13396,-0.10499,0.00179,0.08515,0.02923,-0.01933,0.01487,0.14574,0.00429,0.05237,0.08479,-0.03655,0.04098,0.03911,0.03093,-0.05321,0.13344,0.03508,-0.02341,0.12851,0.13313,-0.20327,0.01145,0.02613,-0.03565,-0.03305,-0.09212,-0.02462,-0.05579,0.00447,0.02332,-0.01836,-0.0288,-0.01268,-0.03851,-0.01586,0.00223,-0.08135,0.02785,0.03509,0.0087,-0.00045,-0.06398,-0.002,0.08258,-0.03564,-0.08488,-0.09611,-0.02937,0.03967,-0.01655,-0.19002,-0.09325,-0.00656,0.18003,-0.0506,0.05789,-0.09591,-0.04751,-0.03472,-0.01448,-0.04888,-0.04001,-0.06227,-0.03165,-0.0561,-0.05105,0.10171,0.07059,-0.05774,0.06659,-0.01036,0.03754,0.03484,-0.02709,-0.07217,0.09767,-0.0323,-0.02823,-0.02651,-0.02967,-0.02419,0.10535,-0.0377,-0.16295,0.10836,-8e-05,0.04443,-0.00923,0.07492,0.13068,-0.03279,-0.03812,0.0911,-0.04402,-0.01458,0.01709,0.01497,-0.0948,0.02585,0.05943,-0.04316,0.00125,0.00182,-0.04186,0.00465,0.02991,-0.06237,0.02603,0.04029,0.02131,0.11118,0.10834,-0.05469,0.02059,-0.04606,-0.01974,-0.05582,0.07318,0.10845,0.01093,0.06435,-0.05238,-0.04277,0.01317,-0.0123,0.01124,-0.02232,0.00915,0.05636,0.0679,0.02864,0.11087,-0.00166,-0.02102,-0.06253,0.05179,0.01208,-0.00044,0.00659,0.02985,0.04462,0.0635,-0.04442,0.0861,0.07117,0.02548,-0.01202,-0.03548,-0.08841,-0.00467,-0.0692,-0.01778,-0.01781,-0.07018,0.12687,-0.04,-0.00029,-0.0234,-0.01565,0.06341,0.03972,-0.0029,-0.09927,0.08726,0.12573,0.12735,-0.05112,-0.07875,-0.03923,0.01333,-0.02486,0.12744,0.02358,-0.0327,-0.05516,0.02984,-0.0423,-0.02094,-0.09821,0.06305,0.02009,-0.14667,0.01228,0.00109,-0.00947,-0.0085,-0.02359,-0.00383,-0.06813,-0.01435,-0.04024,-0.00585,-0.0507,0.00849,0.06376,0.07322,0.01183,0.08706,0.01891,-0.14386,-0.00791,0.04704,-0.06701,0.05262,-0.01141,-0.14511,-0.0142,0.03372,0.13247,0.08217,-0.09982,-0.03252,0.04454,-0.07742,-0.01963,0.01445,0.00665,-0.07501,0.00534,0.10013,0.0194,0.03745,0.05405,0.0119,-0.03871,-0.0595,-0.01053,-0.06133,-0.08379,-0.01994,-0.02848,-0.02053,0.01713,-0.08263,0.07643,0.01619,-0.02815,0.03143,-0.05894,0.09429,0.01458,-0.02407,0.1081,0.11022,-0.00106,0.01614]},{"domain":"discrete_math","key":"is_tree","name":"Tree test","package":"discrete-math-ai999x","example":"Is the graph with edges 1-2, 1-3, 3-4, 3-5 a tree?","v":[-0.03116,-0.01896,0.10213,-0.08938,-0.02415,-0.01709,0.05302,0.00258,0.02628,-0.06986,-0.00163,-0.02221,-0.08349,-0.10236,0.00834,-0.03363,0.108,-0.11332,0.04573,-0.10159,-0.03627,-0.00629,0.04511,-0.06726,-0.06377,0.07189,0.05507,0.02898,0.00716,0.00324,0.05992,-0.00082,-0.01239,0.01762,-0.10026,-0.06432,0.06575,0.05239,0.01206,0.02775,-0.10069,0.05849,-0.04542,0.08818,-0.03257,-0.02063,0.02072,-0.02651,-0.08014,-0.01908,-0.02363,-0.03899,-0.05212,-0.0263,-0.02174,-0.04469,-0.06744,-0.01621,-0.06525,-0.02862,-0.01913,-0.04633,-0.14098,-0.05915,-0.05289,0.12962,-0.00075,0.00927,0.0034,-0.00131,-0.03365,-0.01616,0.06043,0.03515,0.08055,-0.19779,-0.05441,0.03066,-0.05123,-0.00569,-0.06383,-0.11194,0.08009,0.06436,0.03535,0.12084,-0.03602,-0.08053,-0.04686,-0.01088,0.05081,0.03197,-0.01713,-0.00737,0.03679,0.01879,0.06745,0.15294,-0.02183,0.03013,0.011,0.03723,0.00608,0.02778,-0.079,-0.03674,0.05259,-0.04851,-0.13423,-0.06527,0.02784,-0.02454,-0.12795,0.02777,-0.03452,0.04798,-0.03244,-0.01672,0.00084,-0.03736,0.05819,0.16101,-0.02377,0.04822,0.07272,2e-05,0.04171,0.01978,0.02398,-0.03206,-0.06797,0.1101,0.0447,0.04386,-0.08124,0.03968,-0.12808,-0.12146,0.04381,-0.05236,-0.0579,0.14248,0.03169,-0.04404,-0.04512,-0.04332,0.0064,0.0948,0.01163,-0.0504,-0.0026,0.03514,0.05849,-0.0167,-0.03677,0.05357,-0.04096,-0.0101,-0.0148,-0.04681,-0.0605,0.17197,-0.06862,0.1425,0.01043,-0.00576,0.02775,-0.02292,-0.04441,0.04487,0.04646,-0.00059,-0.00494,0.01925,-0.01485,-0.03418,-0.06829,0.04254,0.02906,0.12085,-0.02689,0.0117,0.06541,0.09707,-0.1341,0.02298,0.07829,0.07197,-0.02097,0.13276,0.04402,0.04672,-0.02469,0.01858,-0.12728,-0.01393,0.00916,0.05756,0.06541,0.01483,-0.07935,0.06135,-0.02605,0.01731,0.0022,0.01367,0.00761,-0.02096,0.01779,-0.09509,0.08728,-0.05109,-0.06509,0.09713,0.08324,-0.19465,0.03476,0.02679,-0.00153,0.03717,0.03035,-0.0074,0.00054,-0.05182,0.05373,0.03433,-0.06737,0.04736,-0.03458,-0.0893,-0.00766,0.01423,0.05275,0.04136,0.0965,-0.01244,-0.03301,0.06433,-0.09655,0.01242,-0.00437,0.02909,0.077,-0.03807,-0.05635,-0.06913,0.03661,0.17088,0.09328,0.01543,0.02034,0.01116,0.02002,0.06268,-0.07071,-0.09353]},{"domain":"discrete_math","key":"jacobi_symbol","name":"Jacobi symbol","package":"discrete-math-ai999x","example":"Compute the Jacobi symbol (1001/9907).","v":[0.06359,0.00783,-0.05304,-0.08622,0.07165,-0.01447,0.10897,-0.01713,0.01047,0.01276,0.03321,-0.08259,0.13958,0.01552,-0.05735,-0.01134,-0.04002,-0.02543,-0.07096,0.02733,0.1058,-0.03106,-0.03014,-0.02407,-0.0252,0.11019,-0.04706,-0.05094,0.06043,0.05664,-0.0036,-0.00715,-0.02686,0.05018,0.02725,-0.04892,0.04671,-0.10616,0.08884,-0.01983,0.0958,0.00715,0.02831,-0.08583,0.04621,-0.06246,-0.07209,0.04963,-0.0058,-0.03749,0.0049,-0.09522,0.00621,0.15211,0.02903,-0.02609,-0.10186,-0.01267,-0.02334,-0.012,-0.1022,-0.14509,0.04082,0.00604,0.05844,0.01663,0.10354,0.02811,-0.07561,0.04624,0.0888,-0.04906,-0.0398,-0.0074,0.02566,-0.02688,0.07603,-0.02626,0.00513,-0.05863,0.05664,0.02597,-0.00622,0.07178,0.01831,-0.02315,0.06294,-0.08321,-0.06703,0.01857,-0.02164,0.02013,-0.01479,0.02754,0.00186,0.11035,0.07852,-0.08154,0.1852,0.02554,-0.00693,0.02599,0.07822,-0.06107,0.04822,0.02523,-0.13702,0.01311,0.03066,-0.01431,-0.09499,0.08524,0.08507,-0.0893,0.09878,0.00759,0.04361,0.00113,-0.06361,-0.14188,-0.00502,-0.01291,-0.04472,-0.07752,-0.04189,0.0129,-0.08168,-0.01325,-0.0153,0.09541,0.13201,-0.02171,0.03379,-0.07311,0.01583,0.00758,-0.06144,-0.02417,0.05711,-0.01747,0.0954,-0.01828,0.08839,-0.06476,-0.03341,0.05736,0.00937,0.01334,-0.03975,0.0705,0.05245,-0.0675,0.05052,-0.00564,0.04812,-0.03101,0.02952,0.01021,0.01708,-0.02335,0.01183,0.04173,0.10375,-0.02111,0.08318,-0.00711,0.07243,-0.05196,0.10454,-0.00051,-0.05985,-0.00645,-0.03365,-0.06979,0.08159,0.00042,-0.02282,0.11012,-0.0309,-0.12071,-0.01945,0.16675,-0.03313,-0.03196,-0.01444,-0.00311,-0.05121,-0.01483,-0.15292,-0.00636,0.02413,0.03105,0.08116,0.05419,-0.05796,-0.04352,-0.02365,0.11061,-0.12696,0.03073,0.08049,-0.0301,-0.07815,0.01207,0.0368,0.00722,-0.01963,0.06876,0.01295,0.04656,-0.04692,-0.09176,-0.06775,-0.00986,0.09993,-0.01663,0.03408,0.05217,-0.07062,-0.0577,0.09859,-0.11828,0.02436,0.03737,0.055,0.04453,0.06094,-0.10387,-0.00058,-0.05389,-0.1429,0.04429,-0.08439,0.03691,0.03111,-0.00735,-0.05407,0.00819,0.05546,0.0147,-0.05382,0.06074,-0.04345,-0.04631,-0.00478,-0.17085,-0.02137,-0.03375,0.05635,0.02021,0.06477,0.13384,-0.04461,0.05637,-0.07127,-0.01132]},{"domain":"discrete_math","key":"lattice_paths","name":"Lattice paths in a grid","package":"discrete-math-ai999x","example":"How many lattice paths go from (0, 0) to (5, 3) moving only right and up?","v":[-0.10915,0.02538,0.14579,0.001,0.04413,-0.06457,0.10222,0.01402,0.05841,-0.00023,-0.02009,-0.0887,-0.05406,0.1278,0.02998,-0.00754,0.07177,0.00468,0.0269,0.00751,-0.03604,-0.09586,0.0131,-0.00651,-0.01609,0.10484,-0.14607,-0.02916,-0.05729,0.07907,0.06527,-0.07049,-0.11702,-0.00579,0.01146,-0.01016,-0.01496,0.15889,0.0448,0.01253,0.05443,0.0139,0.20898,-0.07386,-0.03934,0.14382,-0.11323,0.01342,-0.04256,0.01872,-0.01998,0.07156,0.01622,0.0565,0.03364,-0.00126,-0.01152,0.04153,0.13106,-0.07736,-0.04454,0.03552,0.0594,-0.16858,-0.09113,-0.03973,0.06568,0.00789,-0.06873,0.03917,-0.07645,0.1019,-0.02095,0.1363,0.05598,-0.028,-0.01399,0.12125,-0.00351,0.04217,-0.10338,-0.08944,-0.03898,-0.02859,-0.04575,-0.00761,-0.04981,0.03609,-0.01056,0.01207,0.08247,-0.01462,0.05468,0.10534,-0.01594,0.06177,-0.03177,0.09712,-0.03184,0.04695,0.04442,0.05142,0.00625,-0.0116,0.0004,0.09397,-0.0544,-0.08328,-0.11318,0.01892,-0.06537,-0.02467,-0.09174,0.05678,0.08621,0.02161,0.08737,-0.06792,-0.03851,0.01737,0.04657,0.04896,0.06176,-0.00715,-0.00815,-0.08623,0.0752,0.02624,-0.01699,-0.00803,0.08102,-0.01211,-0.00467,-0.03197,-0.01382,0.08548,0.04179,-0.1457,0.07149,0.03947,-0.08475,-0.00751,0.02536,-0.00964,0.03337,-0.10189,-0.10225,0.05011,-0.02615,-0.11984,-0.08506,-0.06474,0.0003,0.02352,-0.00193,0.04183,-0.14019,-0.07645,0.06757,-0.01693,0.0674,-0.02151,0.03332,0.05322,0.01579,-0.04277,-0.01032,-0.02604,0.07395,-0.01999,-0.07728,-0.07468,-0.00649,0.02624,0.00252,0.02222,0.02764,0.05238,-0.00824,0.02531,-0.00668,0.03299,0.07727,0.07457,-0.03709,0.08926,-0.03368,0.03947,-0.07061,-0.0597,0.00105,0.00698,-0.01861,-0.04317,-0.08015,0.00512,-0.04086,-0.04882,-0.12721,-0.0289,0.06991,-0.03413,0.07446,0.08399,0.05177,0.08328,0.05151,0.02575,-0.03917,-0.04191,-0.04918,-0.04657,-0.01502,0.00127,0.02627,-0.063,0.05996,-0.02248,-0.08461,0.0651,0.05101,-0.00286,0.02554,0.05417,0.03954,0.04978,0.0121,0.0792,-0.13426,-0.08794,-0.08222,0.04112,0.04213,0.01065,-0.02907,0.03009,-0.01006,0.05335,0.04018,-0.09244,-0.02529,-0.04039,-0.09488,-0.03013,-0.05075,-0.0261,0.02147,0.00723,-0.00028,0.0432,0.05345,-0.0323,-0.02145,0.01285,0.01715,-0.15048]},{"domain":"discrete_math","key":"legendre_symbol","name":"Legendre symbol","package":"discrete-math-ai999x","example":"Find the Legendre symbol 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Diophantine equation ax + by = c","package":"discrete-math-ai999x","example":"Find all integer solutions of 12x + 18y = 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test","package":"discrete-math-ai999x","example":"Is p & ~p a contradiction?","v":[0.05074,0.02731,-0.09172,-0.02888,-0.1087,0.00495,0.16454,-0.02916,0.02854,0.05195,0.08547,0.00094,-0.06381,0.04704,0.05952,-0.03082,0.00472,-0.05552,-0.05444,-0.11442,-0.06852,0.00816,-0.00326,-0.00396,0.01948,-0.05215,0.02189,-0.0471,0.08334,0.00442,-0.06326,-0.01847,0.01037,-0.01123,0.01674,0.00731,-0.02294,-0.02317,0.06836,0.03844,0.04468,-0.02362,-0.02414,0.07819,0.09264,-0.02064,0.07332,0.03347,-0.01848,0.00953,0.08465,0.00609,0.06351,0.00585,-0.00951,-0.04775,-0.07176,0.06793,-0.04311,-0.01763,-0.0785,0.0965,-0.00474,-0.04517,0.03139,0.03077,-0.00874,-0.07972,0.00712,-0.05196,0.04029,0.03329,0.06328,-0.00294,0.08238,-0.00261,0.06099,-0.11738,-0.00722,-0.0046,-0.0046,0.11288,-0.04466,-0.15325,-0.0217,0.15923,-0.03442,-0.19756,-0.08211,-0.05461,0.06606,0.12099,-0.0331,0.0417,-0.0035,0.03775,0.02187,0.04426,0.02936,0.10592,0.00936,0.03062,-0.00564,0.12614,0.00379,0.00965,0.06291,0.03183,-0.15314,-0.07081,-0.00155,0.01419,-0.05626,-0.03877,0.06071,0.12468,-0.05141,0.04068,-0.06293,-0.06191,0.02276,-0.14117,-0.05091,0.03683,0.04935,0.0809,0.11105,0.07484,0.01153,-0.02422,-0.0877,-0.09997,-0.07193,-0.09587,0.09079,-0.00525,0.05783,-0.06283,-0.00674,0.00439,0.04116,0.04581,-0.06352,-0.09014,-0.05584,0.06207,0.02644,-0.04745,-0.10009,-0.00134,0.1457,-0.02838,0.00346,0.03456,-0.03436,-0.03804,0.09742,0.00761,-0.00084,-0.06099,0.02538,-0.05203,-0.01057,-0.07189,-0.05732,0.026,0.0798,0.00456,0.12789,0.04506,-0.02665,0.03931,-0.0956,0.03299,0.12499,-0.0422,-0.00482,0.01271,0.02674,-0.04886,0.07383,0.03898,-0.01797,-0.06585,0.02713,-0.01394,-0.00583,0.04007,0.05304,0.01836,0.04293,-0.1045,-0.00228,-0.16463,-0.0546,0.01808,-0.02926,0.06845,-0.1126,0.04959,-0.02453,0.15679,-0.00797,-0.1702,0.01678,0.04129,-0.07063,0.1168,-0.01998,0.00912,0.05164,-0.01171,0.08547,0.01259,0.0205,-0.02541,0.07286,0.01658,-0.00763,-0.03493,0.02862,-0.03864,0.08524,0.00801,0.05732,0.06648,-0.02405,-0.04261,0.10069,0.06928,-0.01417,0.0134,0.01389,-0.09203,0.02501,0.00875,-0.1329,-0.0408,-0.0044,0.04108,-0.09419,-0.06339,0.07047,-0.01155,-0.05626,-0.01912,0.01935,-0.0458,-0.00785,0.01802,0.03449,-0.10214,0.01936,0.01847,0.07472,-0.02107]},{"domain":"discrete_math","key":"logic_equivalence","name":"Logical equivalence of two formulas","package":"discrete-math-ai999x","example":"Are (p -> q) and (~p | q) logically equivalent?","v":[0.07152,-0.02821,-0.00858,0.07522,-0.08966,0.00904,0.09937,-0.00289,0.02158,0.04603,0.0138,0.00332,-0.13931,0.04564,0.02046,-0.13679,0.00059,-0.11374,0.09859,-0.11603,0.03888,0.08002,0.12995,0.09727,0.00625,-0.01724,-0.05319,-0.00241,-0.02611,0.1048,-0.08115,-0.0136,-0.02043,0.05401,0.05396,0.06893,-0.0602,-0.02146,0.07949,0.05765,0.01776,0.02458,-0.00744,0.07049,-0.04882,-0.06085,0.0008,0.13796,0.02962,0.05966,-0.03362,0.16336,-0.04898,0.02291,0.04092,0.00584,-0.00125,0.06769,-0.00676,0.001,-0.11661,-0.05387,-0.03668,-0.05281,-0.03662,0.00857,0.09681,-0.06401,0.11922,-0.01719,-0.01501,0.04047,0.08807,-0.08595,0.02588,-0.00748,0.02006,-0.10567,0.05244,-0.03161,0.02088,0.02093,0.01059,-0.0512,-0.07091,0.04528,0.00791,-0.16183,-0.0745,0.03627,0.0687,-0.05302,-0.02376,0.00795,-0.04782,-0.09399,0.02643,0.05091,0.06713,0.01399,0.01602,0.03285,-0.05244,0.04943,0.01266,-0.04063,0.00993,-0.07636,-0.0881,-0.10415,0.04637,-0.05121,-0.0303,-0.01071,0.0129,0.06652,-0.01353,0.06694,-0.02915,-0.06753,-0.08306,-0.10972,-0.0251,0.01248,0.07891,0.11334,-0.02619,0.04752,0.02403,0.00469,-0.00935,0.03396,-0.06969,-0.0958,0.05358,-0.04352,-0.06184,0.03798,-0.05368,-0.08671,0.10557,-0.0869,-0.05653,-0.06882,0.05348,0.06599,0.00399,0.02113,-0.08985,0.03077,0.05397,0.03374,-0.06278,-0.04579,0.07116,-0.06901,0.08232,-0.0095,0.05585,-0.09206,0.047,-0.0283,0.07083,-0.04698,-0.00417,0.00386,-0.08644,0.02853,0.07783,0.07172,-0.04319,0.07245,-0.05322,-0.00362,0.1006,-0.0125,-0.00698,0.08382,-0.04701,-0.1175,-0.02046,0.08861,-0.03423,-0.00427,0.01231,-0.0152,-0.05315,-0.04687,-0.06377,0.03631,0.0621,0.1219,-0.07883,0.0589,-0.03275,-0.00701,0.00167,0.0201,-0.12378,-0.0399,-0.02013,0.05407,0.02697,-0.05594,0.04936,0.06511,-0.08978,-0.02366,0.1007,0.03088,-0.05287,-0.08358,-0.00791,0.02321,-0.02232,-0.05177,0.05351,0.02767,-0.03571,-0.00868,0.11563,-0.07464,0.09028,-0.11416,-0.00232,0.02264,-0.00272,-0.04006,0.11591,0.04207,0.05581,0.18519,0.02218,-0.04861,0.06265,0.06186,0.03528,-0.03046,0.07191,0.00668,-0.1047,-0.02614,0.05458,0.06102,-0.0055,-0.06401,-0.04656,-0.07619,-0.01183,0.03828,-0.01694,0.06341,0.00287,-0.05667,0.00412,0.16018]},{"domain":"discrete_math","key":"logic_evaluate","name":"Evaluate a propositional formula","package":"discrete-math-ai999x","example":"Evaluate (p -> q) & ~r when p = true, q = false, r = 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of a propositional formula","package":"discrete-math-ai999x","example":"Is (p | q) & ~p & ~q 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tautology?","v":[0.07753,-0.04207,-0.05291,-0.00124,-0.08825,0.0542,0.13321,-0.03038,0.03428,-0.01172,0.10154,0.00893,-0.04393,0.00649,0.10375,-0.00244,0.06313,-0.10355,0.08197,-0.13089,0.00045,-0.01084,-0.0189,0.04123,0.01437,-0.06299,-0.0118,0.03462,0.10895,0.03591,-0.11713,-0.0539,0.03424,0.02157,-0.00501,0.03698,-0.02294,-0.04113,0.09281,0.11472,0.00821,-0.0569,-0.02287,0.05673,0.00568,-0.07918,0.03403,0.06658,0.04696,0.02889,-0.01565,0.02383,-0.04998,-0.02781,0.02194,-0.04678,-0.01573,0.01984,0.01267,-0.00247,-0.14187,0.07608,-0.02423,-0.05154,-0.07401,-0.02437,-0.02902,-0.07929,0.07587,-0.04116,-0.07465,0.04274,0.06095,-0.03972,0.06723,-0.02835,0.06461,-0.05399,-0.10457,0.04101,0.03484,0.06732,0.01567,-0.12055,-0.05664,0.15052,-0.04275,-0.14156,-0.08049,-0.05035,0.05949,0.02563,-0.03175,-0.06734,-0.07574,-0.0002,-0.05669,0.06847,0.06922,0.0886,-0.05112,0.00194,-0.03899,0.11305,0.02959,0.03596,0.10593,-0.01495,-0.09746,-0.07232,0.05193,0.02143,-0.11038,0.03224,0.07969,0.09946,-0.09926,-0.01595,0.01128,-0.07767,-0.00393,-0.12636,-0.04795,0.00515,0.04059,0.1131,0.06421,0.06094,0.0191,-0.06224,-0.06331,-0.01534,-0.02613,-0.10958,0.10411,-0.02599,0.00755,-0.02381,0.01913,0.00839,0.18334,-0.04431,-0.1236,-0.06246,-0.02883,0.00785,0.01915,-0.02596,-0.0737,-0.01191,0.05101,-0.03,-0.05643,-0.01451,-0.01226,0.0101,0.07215,-0.00339,0.00582,-0.07491,-0.05168,-0.04116,0.0033,-0.01543,0.02344,0.02959,-0.01217,0.07058,0.12952,0.07977,0.01486,0.01363,-0.04616,0.08073,0.12278,0.02334,-0.02346,-0.00019,-0.0599,-0.01192,0.02815,0.01338,-0.01055,-0.04889,0.00815,-0.06302,0.00818,-0.04814,-0.03174,0.02621,0.01193,-0.05502,-0.09548,-0.08202,-0.05743,0.06091,0.01471,0.11891,-0.07699,0.05659,-0.0924,0.07964,-0.07312,-0.13557,0.09033,0.0333,-0.02135,0.0604,0.09134,-0.02127,-0.01509,0.07187,0.02694,0.03147,0.04263,-0.09064,0.0258,0.01327,0.04546,0.05221,-0.01413,-0.01249,0.14838,-0.09278,-0.01901,-0.0268,0.0292,-0.02389,0.06084,-0.00591,0.11094,0.02547,-0.02869,-0.03154,-0.00666,0.09327,-0.00876,-0.07229,0.07019,0.0907,-0.1548,-0.01479,0.08534,0.0597,-0.00402,0.00257,0.08592,-0.04042,0.04384,0.06254,0.03354,-0.02578,0.03248,-0.04928,0.01189,0.10491]},{"domain":"discrete_math","key":"lucas","name":"Lucas 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there?","v":[-0.038,0.03858,0.08172,0.02699,0.04442,-0.12221,0.11566,0.00966,-0.08214,-0.00671,-0.08305,-0.00239,-0.03729,0.0482,-0.06486,-0.04377,0.0598,0.02759,-0.08248,0.0026,-0.0271,-0.05828,-0.00888,-0.0111,-0.0374,0.06024,-0.06787,-0.00842,0.02949,-0.00404,-0.05243,-0.01968,-0.00965,-0.0885,0.00224,-0.04781,-0.03662,-0.07222,0.05804,-0.04695,0.02038,-0.0067,0.05439,0.05286,-0.05825,0.06306,-0.1773,0.11771,-0.00273,0.01754,-0.08548,-0.02473,0.05618,-0.05973,0.09205,0.01675,-0.02356,0.02431,0.14166,-0.11452,-0.06833,-0.05565,-0.02463,0.03161,0.04598,-0.0828,0.03059,-0.00777,-0.03581,0.06747,0.01156,-0.00925,-0.08554,0.13388,0.07005,-0.03099,0.05104,0.13018,0.11207,-0.0399,-0.03885,-0.13279,-0.03857,0.0452,-0.06786,-0.10628,0.11051,-0.04484,0.02776,-0.03681,0.00173,-0.07355,0.07642,-0.01798,0.00416,0.01243,0.05878,0.05783,-0.03917,0.03308,0.03617,-0.04534,0.1007,-0.044,-0.02666,0.0374,0.10227,-0.10011,0.05989,-0.17622,-0.02975,-0.06584,0.01217,0.03746,0.09631,-0.02278,0.09835,-0.04197,-0.07476,-0.02434,-0.05404,0.19065,-0.01404,-0.05081,0.01593,-0.05936,-0.00493,0.06674,0.00469,0.05542,0.05015,0.04086,-0.04563,0.03099,0.01723,0.02166,-0.00903,-0.05368,-0.08114,0.01915,-0.03725,-0.05054,-0.00167,-0.03767,0.02964,-0.06987,0.05487,0.01944,-0.06015,-0.0397,0.02832,-0.04667,-0.06252,-0.0667,0.16695,0.01523,-0.10647,-0.0859,0.01025,0.02259,-0.00494,-0.12147,0.03721,0.06195,0.02911,-0.02891,0.01636,0.07227,-0.01666,-0.04192,-0.06886,0.02224,-0.02849,-0.0132,-0.00654,0.056,0.02887,0.02219,-0.12995,0.04329,0.00812,0.10064,0.04853,0.01878,0.02692,-0.00531,-0.0856,-0.04188,-0.07313,-0.07407,0.04357,-0.00587,0.0179,0.06683,-0.02466,0.0204,0.02612,0.04232,-0.09097,-0.03971,-0.02936,0.06535,0.01384,-0.05221,0.00844,0.06052,-0.00254,-0.09635,0.04426,0.03893,-0.0047,-0.12551,0.0528,0.09437,0.10629,-0.06574,-0.11204,0.02584,0.10263,0.05964,0.08953,-0.12339,0.07262,0.03818,0.02773,0.00417,0.02865,-0.03937,-0.10167,0.03308,0.00591,0.07592,-9e-05,-0.04121,0.01143,0.04548,0.08404,-0.01112,0.02792,0.1107,-0.08615,-0.09016,-0.03088,0.06826,0.0261,-0.1056,0.06149,-0.0351,0.07085,0.02668,-0.04427,0.07123,0.02279,0.04672,0.03395,0.08919]},{"domain":"discrete_math","key":"partitions_k","name":"Partitions 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there?","v":[-0.06856,-0.01029,0.03426,-0.05632,0.02582,0.00729,0.11355,0.0049,-0.03773,0.07779,-0.07411,-0.03672,-0.07043,-0.02726,0.00107,-0.03048,0.05667,0.04341,-0.08006,0.03434,0.00869,-0.06491,0.05839,-0.08789,-0.01708,0.05306,-0.01561,0.05096,0.06333,-0.00572,-0.10484,-0.18823,0.00727,-0.10079,0.10595,-0.08032,0.0007,0.03977,0.01289,0.02571,-0.01092,-0.01356,0.11706,0.06687,-0.03009,0.08463,-0.12438,0.1002,0.05829,0.0625,-0.05584,-0.06262,0.03144,0.01732,0.05404,-0.04339,-0.03815,-0.05847,0.16115,-0.09156,-0.06111,0.01852,-0.00432,-0.03269,-0.00233,-0.09745,0.0043,0.03681,-0.03211,0.05944,0.00773,0.00254,-0.05662,0.10834,0.01442,0.04812,0.02187,0.03824,0.08983,-0.10317,-0.0282,-0.12047,-0.03177,-0.02613,-0.05868,-0.12401,0.11332,0.00592,-0.07954,-0.04458,-0.00737,-0.01497,-0.03277,0.0064,-0.0283,-0.01309,0.00874,-0.0189,-0.01747,-0.01129,-0.01897,-0.05163,0.11902,-0.01973,-0.02487,0.06648,0.04531,-0.13598,0.02599,-0.02245,-0.00469,-0.03294,0.04409,0.03539,0.02555,-0.04062,0.12844,-0.06908,-0.06726,-0.054,-0.02179,0.16127,0.00952,-0.0332,0.08464,-0.07508,-0.00216,0.07941,0.01558,0.00954,0.09348,0.00266,0.05482,0.02887,-0.0712,0.0405,0.09643,-0.028,0.04172,0.11845,-0.02676,-0.04331,0.04029,-0.01071,-0.00331,-0.09188,-0.02135,0.00489,-0.16669,-0.10607,-0.01534,-0.00925,0.01055,-0.02994,0.13137,0.03959,-0.0801,-0.06578,0.08577,-0.02643,-0.00132,-0.04611,-0.02959,0.09179,-0.03866,-0.01568,0.05214,-0.01534,-0.04007,0.05464,-0.01695,-0.04397,-0.02283,0.04582,0.02846,0.07178,-0.00372,0.106,-0.07892,0.04979,-0.0567,-0.0155,0.04475,0.04491,0.04041,0.00744,-0.06926,-0.07437,-0.07585,-0.03954,0.05134,0.04352,0.0024,-0.04357,-0.01846,0.05202,0.09026,0.03568,-0.07492,-0.09142,0.03121,0.01633,0.00273,0.05735,0.05257,-0.01957,0.0242,-0.14849,0.01392,0.05566,0.02282,-0.1111,0.08325,0.04325,0.10449,0.03268,-0.11954,0.01384,0.0288,0.03917,0.06203,-0.11481,0.01895,0.03769,-0.06912,0.0495,0.02953,-0.06857,-0.10501,0.01975,0.00216,0.06077,-0.0692,-0.14746,-0.03859,-0.00126,0.05821,0.03293,0.01038,0.07706,-0.01295,-0.03331,-0.04296,0.17113,0.05847,-0.00269,0.00729,-0.08226,0.0503,0.04214,-0.02355,0.11407,-0.02405,-0.01148,0.07174,-0.02459]},{"domain":"discrete_math","key":"pell_equation","name":"Pell's 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100?","v":[-0.12514,-0.0381,-0.01839,-0.03382,-0.09087,-0.07857,0.12595,-0.03419,-0.08943,-0.01816,-0.05323,0.09808,-0.03375,0.02957,-0.0366,-0.03387,-0.03578,-0.02322,0.05749,0.05541,-0.04241,0.03271,0.0646,-0.0401,-0.03928,0.12102,-0.04229,0.02787,0.07169,0.10271,-0.1513,-0.04311,-0.03746,-0.06045,-0.0287,-0.06823,0.02789,-0.04192,-0.04623,0.03652,-0.0776,0.06803,0.04232,0.08693,0.00435,-0.05806,-0.11519,0.11149,0.02932,0.07153,-0.03306,0.01524,0.01768,0.01432,-0.06514,-0.03754,0.0396,-0.03695,0.07898,-0.13027,-0.10248,-0.0461,-0.11205,0.18994,-0.04088,-0.09279,-0.03065,-0.01639,-0.00092,0.03949,-0.09684,-0.05849,-0.02467,-0.03504,-0.03334,0.01757,0.08531,0.08299,0.02406,-0.04941,-0.0224,-0.07253,-0.04963,-0.00348,0.00679,0.05099,0.03024,0.06241,-0.05595,-0.03387,0.09008,0.01586,-0.06567,-0.00523,0.01257,-0.0616,0.10627,-0.04251,0.0445,0.12009,0.0078,-0.02869,0.05618,-0.01746,0.03282,0.05213,-0.03175,-0.02286,-0.04389,0.06705,-0.14272,-0.06387,0.07872,-0.00243,-0.01314,0.01499,-0.03921,0.02072,-0.00408,0.08707,0.07395,0.1312,0.02151,0.07001,-0.07616,0.06561,0.02204,0.0668,0.13011,0.0339,0.09581,0.05746,0.00779,0.05669,-0.09487,0.06104,0.04221,-0.02689,0.02769,0.09993,-0.11339,0.11966,0.06571,-0.00018,-0.03343,0.02676,0.06431,0.00767,0.02314,0.06176,0.03948,0.06152,0.05361,-0.05506,0.03973,0.01899,0.01932,-0.05648,-0.06611,0.05276,-0.03311,0.01117,-0.05626,0.00813,-0.02745,-0.11623,0.0102,-0.17698,-0.09139,0.0352,-0.01839,-0.06875,-0.05869,-0.06982,0.08707,0.05445,-0.02657,-0.02574,0.04525,0.16228,0.00279,0.01076,0.09227,-0.02073,0.00867,0.07911,-0.07072,-0.00299,0.0089,-0.05019,0.01514,-0.02322,0.04487,0.02645,-0.03627,-0.02847,0.07943,-0.06314,-0.05607,-0.00393,0.0465,-0.09643,-0.07126,0.08276,0.00504,0.01264,-0.0721,0.024,-0.02852,-0.0853,0.04163,-0.0323,0.03396,0.02076,-0.0135,-0.04279,0.01832,0.15257,0.07282,0.03161,0.01363,0.01323,-0.03126,-0.12636,0.00337,-0.01191,-0.08416,-0.07979,0.01923,-0.01247,-0.03577,0.11383,-0.01772,-0.01463,0.04571,-0.0441,0.01085,0.0143,-0.08832,-0.11336,0.02548,0.04032,-0.06873,0.0802,0.00655,0.02513,-0.06482,-0.01437,-0.01436,-0.01235,-0.11043,0.0129,0.01758,0.10139,-0.04361,0.01274]},{"domain":"discrete_math","key":"prime_factorization","name":"Prime factorization","package":"discrete-math-ai999x","example":"Find the prime factorization of 360.","v":[-0.01052,0.00543,-0.00425,0.06685,0.04991,-0.0251,-0.04818,-0.00982,-0.08168,-0.12863,-0.07459,0.04428,0.06422,0.02357,0.05778,0.05772,0.05058,0.05088,0.03374,0.16125,-0.00675,0.05564,0.06288,0.01755,0.02442,0.10647,0.05834,-0.02272,0.03113,0.1765,-0.13909,-0.05095,-0.03191,-0.05377,-0.06897,-0.04267,-0.05864,0.0055,-0.03819,-0.01993,-0.03935,0.04171,0.05075,-0.09922,-0.0661,0.05501,-0.05092,0.04756,0.00998,-0.04049,-0.02722,-0.03384,-0.04558,0.04891,0.00468,-0.08452,-0.10656,-0.00549,0.0469,0.01607,-0.09628,-0.05098,-0.0183,0.12061,0.00179,0.01016,-0.07084,-0.06212,-0.00139,0.0155,0.00546,-0.00303,-0.11612,-0.00243,-0.08676,-0.01551,0.04891,0.07386,-0.00349,-0.03164,-0.00377,-0.02588,-0.03068,-0.0289,0.00652,0.03003,-0.05346,-0.01107,-0.00244,-0.04093,0.00402,0.08379,-0.02514,-0.19301,0.06663,-0.07977,0.00118,-0.02087,0.05633,0.04866,-0.03335,-0.00091,0.02436,-0.0625,-0.02596,0.04234,-0.0498,-0.10234,0.03728,0.0092,-0.01772,0.10213,0.07288,0.00934,-0.02324,0.02448,-0.05192,0.04636,0.04221,0.01966,0.10671,0.1392,-0.02,0.07201,-0.09173,0.01359,-0.1213,0.05525,0.12841,0.04506,0.04342,-0.00811,-0.0415,-0.029,-0.03433,0.05583,-0.06917,-0.05874,0.09869,0.06758,0.10686,0.06187,0.04426,0.08312,-0.02404,0.09256,0.02249,0.0063,0.06766,0.06898,-0.01192,0.00449,-0.07562,-0.01751,0.08364,0.00189,-0.06972,-0.01015,-0.10658,0.08624,-0.0166,-0.04007,0.09761,-0.06209,0.11767,0.01296,0.00866,0.02078,0.00049,0.08398,0.03191,0.06248,-0.1286,0.07999,0.06345,0.13564,-0.04913,-0.04713,-0.03074,0.03479,-0.02409,0.1193,-0.01785,-0.00821,-0.10657,0.01981,-0.04665,0.04119,-0.10315,0.00733,0.04204,-0.1074,0.02046,-0.00365,-0.01728,-0.04328,-0.00334,-0.04554,-0.05279,0.00215,-0.01689,-0.08674,0.05994,0.14272,0.09018,0.14472,-0.05658,0.05879,-0.01555,-0.11974,0.03004,0.02657,-0.06582,-0.01279,-0.02673,-0.00874,-0.03775,0.01292,0.048,0.09989,-0.14632,-0.06982,0.00531,-0.11594,-0.08303,-0.0024,-0.02188,-0.0194,-0.05651,-0.02528,-0.05077,0.08218,0.00906,-0.00748,-0.02727,-0.05426,0.06644,-0.0868,-0.05783,-0.06038,0.01117,0.06338,0.04277,-0.08336,0.00054,-0.02101,-0.03396,0.00676,-0.04492,0.00354,0.06912,-0.00857,0.12176,0.0878,-0.00208,0.05838]},{"domain":"discrete_math","key":"primitive_root","name":"Smallest primitive root modulo a prime","package":"discrete-math-ai999x","example":"Find the smallest primitive root modulo 23.","v":[-0.0041,0.01248,-0.01333,0.04339,-0.09406,-0.02635,0.05237,0.0119,-0.05963,-0.07286,-0.08742,-0.01715,0.00412,0.13262,0.01365,0.02822,0.21093,-0.03712,-0.0276,0.05152,0.08606,-0.02052,-0.01366,0.06207,-0.00036,0.11986,0.01283,0.02803,0.10711,0.22974,-0.0858,-0.04481,-0.02388,-0.04566,-0.03628,0.00927,-0.04256,-0.01573,0.05793,-0.01202,0.0548,-0.02875,0.02804,-0.05226,-0.05952,0.05407,-0.00991,0.04441,-0.00929,0.01091,0.00521,-0.01579,0.04068,0.0539,-0.09659,-0.11166,-0.11465,-0.04475,0.00872,-0.05229,-0.07856,-0.06726,-0.10135,0.14008,-0.04774,0.06902,-0.08622,-0.03909,-0.10133,0.04673,0.02592,-0.03649,-0.03526,-0.06815,-0.01633,0.07598,0.11474,0.04897,-0.12251,0.06384,0.04903,0.09517,0.03704,-0.01205,-0.0927,0.04442,-0.07975,0.07259,0.0279,-0.02899,-0.07499,0.01639,0.011,-0.0934,0.07173,0.04149,-8e-05,0.02199,0.11404,0.02724,-0.02389,0.02285,0.06266,0.00503,0.02994,-0.03603,-0.0027,0.0055,0.03553,0.09011,-0.07514,-0.01495,0.06143,0.04082,0.03289,0.08262,-0.12421,-0.17066,0.02267,-0.02163,0.15995,0.07141,-0.04857,0.01516,-0.13431,-0.07364,0.00025,-0.01973,0.01458,-0.04825,0.00417,-0.00415,0.00803,0.01601,0.07569,0.01664,-0.05001,0.02051,0.03926,-0.06723,0.11969,0.00835,-0.02762,0.00151,0.00202,-0.0105,-0.019,-0.02362,-0.0063,0.07009,-0.02638,0.04638,-0.11486,0.03174,0.04544,-0.00888,-0.02632,0.0193,-0.00955,-0.03535,-0.13906,-0.01558,0.03642,-0.0496,-0.04856,-0.02928,-0.06663,0.086,-0.03769,0.09389,0.0716,-0.01198,0.04558,0.03671,0.08448,-0.03429,0.01697,0.03886,-0.09578,0.0999,-0.06508,-0.06586,0.00587,-0.05834,0.06795,-0.0174,-0.03182,-0.04824,-0.04767,0.02278,-0.06379,-0.10893,0.07182,-0.03415,0.03013,0.02976,-0.11533,-0.05544,-0.07748,0.04735,-0.03891,-0.00835,-0.04516,-0.00166,-0.01228,0.03342,0.12104,-0.03805,0.05606,-0.0853,0.04092,0.08892,0.00606,0.00877,0.05246,-0.18734,-0.0138,-0.03653,0.16288,-0.02657,-0.01167,-0.05718,0.0492,-0.02248,0.05419,0.0269,-0.07375,-0.07549,-0.02212,0.029,0.00736,0.01782,0.02734,0.04899,0.02345,0.00513,0.00434,-0.0066,-0.10981,-0.00881,0.0279,0.04142,-0.02571,-0.00416,0.02571,0.05697,-0.08542,0.01215,-0.05337,-0.02131,-0.01212,0.00073,0.0445,-0.01739,0.09448,0.07842]},{"domain":"discrete_math","key":"prufer_decode","name":"Tree from a Prüfer code","package":"discrete-math-ai999x","example":"Decode the Prüfer sequence [4, 4, 4, 5].","v":[0.0829,-0.00738,0.07328,-0.10438,-0.00189,0.06215,0.10331,0.03976,0.00706,-0.01553,-0.02522,-0.10064,-0.10416,0.03072,0.0309,0.06947,0.07339,-0.10242,-0.01505,-0.01464,0.01172,0.00794,0.00859,-0.02292,0.05225,0.05961,0.03248,-0.02422,0.07937,-0.00694,0.03587,-0.04664,-0.00555,-0.04146,-0.0937,-0.01007,0.04357,0.01285,-0.03334,-0.02349,-0.12319,-0.00599,0.05455,-0.02354,0.02726,0.01817,-0.05104,0.09376,-0.05917,-0.04023,-0.04015,0.03593,-0.07803,-0.05269,-0.02398,-0.04036,-0.13119,-0.00982,-0.00464,-0.079,-0.05116,0.04061,-0.14132,-0.08061,0.00793,0.03496,-0.02165,-0.03133,0.02917,0.03319,-0.07185,0.06036,0.01623,0.06129,-0.0236,-0.11177,-0.01017,0.10289,-0.04464,-0.00295,-0.07929,0.00266,0.06883,-0.00843,0.00334,0.0794,-0.00543,0.02244,-0.04861,-0.03562,0.08112,-0.03071,0.01404,-0.06356,-0.00771,0.04996,0.02528,0.07803,0.10245,0.04352,-0.04413,0.00565,0.12158,0.02947,-0.03308,-0.04365,-0.02402,-0.08176,-0.07805,-0.11142,-0.01367,0.00812,-0.1054,0.0525,0.00805,0.02443,-0.00179,-0.16835,0.01209,-0.11636,-4e-05,0.0489,-0.0524,0.05744,0.07009,0.05435,-0.0043,0.06706,0.02714,-0.13072,0.06351,0.07685,0.15285,-0.04843,-0.08372,0.05549,-0.03233,-0.00493,0.1033,-0.0696,0.03112,0.14686,0.01582,-0.03932,-0.01901,-0.0802,-0.08488,0.00201,-0.0676,-0.04731,-0.01053,-0.05357,0.03694,-0.03913,-0.02039,0.114,-0.0097,0.00322,0.04476,-0.09744,-0.10653,0.05497,0.05763,0.10657,-0.00894,0.05746,0.06227,0.0598,-0.11736,0.05539,0.07393,0.0167,-0.04583,0.06378,0.00441,0.04014,-0.07829,0.06693,0.00419,0.02296,-0.14201,0.03697,0.07615,-0.02113,0.00507,0.01217,0.0464,0.01518,0.01978,0.10104,0.08943,-0.01314,-0.03049,0.00716,0.03318,-0.08216,0.05453,0.09215,-0.0484,-0.00917,-0.04318,0.01331,0.06165,-0.01585,0.00926,0.01194,-0.00084,-0.07028,0.06147,0.01805,-0.01107,-0.04643,0.05762,0.1473,0.13664,-0.12706,0.05126,-0.04848,0.0587,0.04152,0.07061,-0.05836,-0.00817,-0.08983,-0.06705,-0.06625,-0.00761,0.02387,-0.09985,-0.09313,0.0404,0.00973,-0.07285,-0.0562,0.05047,-0.05881,0.01631,0.14093,-0.07297,0.01662,0.03882,-0.01421,-0.03336,-0.00502,0.0136,0.00714,0.02066,0.10336,0.10842,0.11903,0.03878,0.03036,-0.04665,0.10321,0.06688,-0.11153]},{"domain":"discrete_math","key":"prufer_encode","name":"Prüfer code of a labelled tree","package":"discrete-math-ai999x","example":"Find the Prüfer code of the tree with edges 1-4, 2-4, 3-4, 4-5, 5-6.","v":[0.06966,-0.02863,0.12656,-0.11952,-0.02811,0.0241,0.07017,0.04982,-0.00197,-0.04892,-0.01927,-0.07761,-0.11379,0.01534,0.00208,0.05698,0.05936,-0.09823,0.04224,-0.05312,0.0049,0.01582,0.01055,-0.06846,0.04531,0.08209,0.03914,0.00424,0.05824,0.01519,0.06633,-0.03936,-0.01472,-0.0293,-0.13603,-0.05033,0.03199,0.00721,-0.03396,-0.00686,-0.135,0.03071,0.02624,0.01067,-0.00087,0.02162,-0.04355,0.0503,-0.07923,-0.04496,-0.00405,0.02851,-0.07798,-0.05447,-0.03451,-0.00991,-0.11753,0.01132,-0.00488,-0.06218,-0.03939,0.04582,-0.15355,-0.08565,-0.025,0.06174,0.00945,-0.05824,0.04123,0.06283,-0.10625,0.02,-0.03009,0.07267,0.02223,-0.16099,-0.02144,0.09574,-0.07935,-0.00603,-0.10358,-0.00251,0.06643,0.00883,0.02788,0.08346,-0.03875,0.00142,-0.06282,-0.05537,0.09504,-0.0308,-0.00969,-0.05789,0.01613,0.06119,0.01641,0.10593,0.0357,0.02781,-0.05057,0.05545,0.09778,0.01366,-0.05641,-0.03755,-0.00187,-0.08411,-0.07437,-0.11124,0.00597,0.00505,-0.11337,0.04862,-0.00551,0.02961,0.00716,-0.13412,0.02677,-0.08092,0.02066,0.10072,-0.00092,0.04851,0.07169,0.02487,0.01443,0.03327,0.04131,-0.10008,0.00429,0.10496,0.13772,-0.01392,-0.07612,0.06732,-0.04986,-0.02723,0.08314,-0.06975,0.01142,0.15957,0.02549,-0.03484,-0.03294,-0.0823,-0.07964,0.07366,-0.0472,-0.07187,-0.02938,-0.05276,0.03069,-0.05846,-0.0304,0.1241,-0.03141,0.01117,0.019,-0.08155,-0.12505,0.10102,-0.00018,0.16687,-0.01959,0.03187,0.05339,0.03421,-0.0945,0.02065,0.06786,-0.01535,-0.03906,0.05801,-0.00879,-0.00397,-0.08652,0.07733,-0.03068,0.06783,-0.10848,0.02789,0.06649,0.01709,-0.01678,0.00899,0.05724,0.04755,0.04009,0.14642,0.03085,-0.00848,-0.03096,0.03998,-0.03394,-0.06705,0.05899,0.10046,0.01007,-0.01411,-0.06965,0.04267,0.02988,0.0058,0.02362,0.05201,0.03313,-0.05011,0.04228,-0.01398,-0.01193,-0.02778,0.04785,0.1457,0.08118,-0.16488,0.04676,-0.0325,0.04983,0.04617,0.05975,-0.04141,0.03596,-0.09416,-0.04319,-0.01968,-0.02503,0.04311,-0.081,-0.08916,0.0226,-0.00145,-0.04749,-0.01696,0.05711,-0.01885,0.01956,0.08859,-0.07769,-0.00142,0.03746,-0.00673,-0.0233,-0.02075,0.01673,-0.01331,0.01868,0.13899,0.09552,0.09208,0.05549,0.03124,0.00763,0.07855,0.0173,-0.11731]},{"domain":"discrete_math","key":"rsa_decrypt","name":"RSA decryption","package":"discrete-math-ai999x","example":"RSA: decrypt c = 2790 with d = 2753 and n = 3233.","v":[-0.07244,0.01834,-0.04351,0.12244,0.00897,-0.03172,-0.00857,-0.01089,-0.05263,0.04729,0.04139,0.06406,0.03444,-0.01071,-0.12125,-0.00981,0.01533,-0.02921,-0.15585,-0.022,-0.07744,-0.00519,-0.01396,0.05543,-0.14754,0.11615,-0.01843,0.01183,-0.00933,-0.06097,-0.03673,-0.03151,0.05727,-0.13032,0.04797,0.12597,0.03023,-0.04911,0.06334,-0.02704,0.05054,0.02154,0.00139,-0.1207,-0.10704,0.00591,0.04281,-0.0414,-0.0775,-0.03065,0.08801,-0.06535,-0.03113,-0.10463,0.02542,0.00927,0.00933,0.15201,0.01876,-0.0408,0.01786,0.01001,-0.00159,0.03221,-0.05964,0.02571,-0.01759,0.03447,-0.09682,0.05311,0.04494,-0.08447,0.07861,-0.01364,0.00941,-0.05351,0.00198,0.07366,-0.06885,0.04422,0.04049,-0.00519,0.08727,0.00021,0.06491,0.04269,-0.00688,0.03095,0.01936,-0.10314,0.03008,-0.04919,-0.02964,-0.01745,0.0885,0.01435,0.00011,-0.09583,0.04025,0.01304,-0.04722,0.07199,0.01612,-0.02945,-0.00997,0.03571,0.04646,0.05491,-0.04201,0.07949,0.0457,0.0819,0.03776,0.02166,0.12331,0.10636,0.04168,-0.0826,-0.06459,0.01328,-0.01032,-0.0623,-0.0827,-0.01155,0.04237,0.0824,-0.05407,0.01943,-0.13378,0.00146,0.05397,0.11055,-0.0359,-0.08346,0.04299,-0.06362,-0.09302,0.07217,-0.07231,-0.04033,-0.01192,-0.04734,0.15255,-0.10817,0.02535,0.12861,0.09042,0.09289,-0.05834,-0.06671,-0.03768,-0.05934,0.11548,0.00958,-0.07675,-0.05492,-0.01601,-0.04748,0.0698,0.04583,-0.01281,0.1343,-0.03786,-0.09846,0.05037,0.00806,0.00121,-0.02209,0.0142,-0.02822,-0.06353,-0.04576,0.05309,0.02568,0.00708,0.04929,-0.0541,-0.06947,0.08037,-0.06213,-0.00821,0.0558,0.04478,-0.04101,0.02499,-0.05139,0.02889,0.07621,0.00741,0.06178,0.07014,-0.05338,0.11864,-0.00494,-0.04256,-0.05732,0.00816,0.09054,-0.06003,-0.03426,0.00328,0.07352,0.01618,-0.06572,-0.12074,-0.03847,-0.00253,0.04369,-0.0039,-0.11918,0.0333,-0.05874,0.02542,-0.02873,0.16299,-0.06133,0.07622,0.15754,-0.02858,-0.04307,-0.01817,-0.01127,0.04599,0.03246,-0.02449,0.02493,0.04622,-0.04744,-0.02475,0.07236,-0.10354,0.02176,0.03926,0.02827,-0.06586,-0.0183,-0.01569,0.00068,-0.01881,0.05511,0.07343,0.06176,-0.09556,-0.05764,0.01942,0.00797,-0.07473,0.08286,0.03363,-0.02502,0.06627,0.1471,-0.03618,0.07703,0.02095,-0.11183]},{"domain":"discrete_math","key":"rsa_decrypt_pq","name":"RSA decryption from p, q and e (CRT)","package":"discrete-math-ai999x","example":"RSA: decrypt c = 2790 with p = 61, q = 53 and e = 17.","v":[-0.05303,0.01994,-0.05576,0.08484,-0.02966,-0.01575,-0.01707,-0.00976,-0.061,-0.01146,-0.04364,0.07913,0.00716,0.02453,-0.09134,-0.0592,0.03429,-0.01364,-0.05434,-0.02314,-0.00283,0.01575,0.00886,0.10123,-0.15871,0.10828,-0.0035,0.01717,0.00585,-0.0024,-0.05857,0.01752,0.05615,-0.14626,0.00635,0.12189,0.0563,-0.0683,0.05017,-0.03189,0.00594,-0.02122,-0.06421,-0.06466,-0.14392,0.02714,0.02242,-0.00915,-0.09185,-0.01366,0.01928,-0.04021,-0.02126,-0.10131,-0.01468,0.00052,0.03518,0.1827,0.04951,-0.08137,-0.03866,-0.05508,-0.0103,0.07122,-0.10089,0.00555,0.01144,-0.04541,-0.10686,0.05865,0.0186,-0.07884,0.07517,-0.05989,-0.00398,-0.05089,0.13688,0.1121,-0.04078,0.03963,0.03426,-0.02834,0.15357,0.0032,0.02889,0.0533,0.0026,0.08925,-0.06305,-0.09353,0.01733,-0.04863,-0.04914,-0.01581,0.03693,-0.01176,0.00635,-0.10514,0.09222,0.02048,-0.04714,0.0538,0.03425,0.02158,-0.03041,0.05602,-0.00869,-0.00372,-0.00961,0.05334,0.0482,0.07682,0.03059,0.05283,0.11842,0.1215,0.01959,-0.07755,-0.02555,-0.04106,0.00734,-0.01232,-0.11721,0.00833,0.02184,0.07799,-0.06439,0.00934,-0.06274,-0.00266,0.07326,0.06728,-0.07247,-0.05828,0.0452,-0.10316,-0.09589,0.10215,-0.08492,-0.0823,0.02259,-0.07183,0.1187,-0.11517,0.07186,0.12667,0.12543,0.09129,-0.00133,0.01337,-0.04088,-0.0224,0.08772,-0.00423,0.02591,-0.00194,-0.00099,-0.05156,0.01391,0.04314,-0.08514,0.05049,-0.0148,-0.07321,0.074,0.01813,-0.06476,0.04799,-0.04375,0.0311,-0.04014,-0.03681,0.00164,0.04004,0.07513,0.08379,-0.02292,-0.11081,0.02173,-0.0444,-0.04722,0.06157,0.07671,-0.0784,0.02881,-0.03343,-0.01669,0.00488,0.01621,0.06544,0.07679,-0.05655,0.06955,0.04932,0.0018,-0.06946,-0.0102,0.07279,-0.02619,-0.10273,-0.00877,0.03424,0.00222,-9e-05,-0.13926,-0.03976,0.01672,0.0146,0.05194,-0.11446,0.00623,-0.02701,0.01833,0.0389,0.13462,-0.08288,-0.01875,0.11788,0.01409,-0.00284,-0.06142,-0.01878,0.0858,-0.00513,-0.05263,-0.01956,-0.01048,-0.08544,0.02592,0.11089,-0.02304,0.06941,0.06528,0.02084,-0.03553,-0.06232,0.06129,-0.05058,-0.07639,-0.01193,0.07489,0.0139,-0.06566,-0.03183,0.01199,0.03319,-0.11567,0.0838,0.04537,0.00596,0.02567,0.14622,0.0266,0.10404,0.02201,-0.04507]},{"domain":"discrete_math","key":"rsa_encrypt","name":"RSA encryption","package":"discrete-math-ai999x","example":"RSA: encrypt m = 65 with e = 17 and n = 3233.","v":[-0.03805,0.03409,-0.08599,0.02042,0.01734,-0.08182,0.06711,0.00465,0.00372,0.05312,0.09312,0.02378,0.10822,0.02851,-0.04676,0.04439,0.09612,-0.01912,-0.05526,0.00179,-0.00574,0.00202,-0.10061,0.044,-0.13979,0.11781,-0.0106,-0.04421,-0.07052,0.02615,0.00914,-0.0719,-0.03423,-0.13477,-0.00049,0.06708,0.11431,0.02949,0.0783,0.01553,0.07515,0.03021,-0.02181,-0.0911,-0.03334,0.13246,-0.00109,-0.08919,-0.08384,-0.07938,0.05954,-0.0688,-0.08513,-0.04346,-0.0041,0.05883,-0.055,0.11977,-0.00971,-0.05449,-0.05602,-0.07218,0.03396,0.04955,-0.00347,0.07491,0.02911,0.03599,-0.08776,0.08628,0.01048,-0.00625,0.04719,0.05952,0.05445,0.02674,0.10419,-0.00865,-0.09449,0.02463,0.0035,-0.02733,-0.01076,0.00069,0.05055,0.02153,-0.01398,0.03222,0.03235,-0.14873,-0.01905,-0.03104,-0.08238,0.00323,0.04657,0.07565,-0.0568,-0.08905,0.07131,0.01406,-0.06493,0.09313,0.04997,-0.04142,0.02445,0.02363,0.02162,-0.03606,0.017,0.00453,0.03595,0.10233,0.0294,0.00269,0.14118,0.05769,0.02431,-0.08554,-0.04351,0.02993,0.03415,-0.03804,-0.09686,-0.05448,0.02574,-0.01123,-0.02543,-0.04495,-0.12993,0.00487,0.04637,0.09073,-0.09105,0.00857,0.07598,-0.03744,-0.04387,0.01161,-0.05523,0.01335,-0.0323,-0.0113,0.11501,-0.02037,0.03324,0.02199,0.02378,0.14916,-0.202,-0.03391,-0.04632,0.00493,0.03344,-0.03956,-0.07395,0.05299,-0.1009,0.06909,0.14496,0.02819,-0.08703,0.13878,-0.00801,-0.01301,0.08625,0.02194,-0.09994,0.03326,0.06176,-0.01117,-0.08647,-0.12416,0.02864,0.10373,-0.00621,-0.01859,-0.06132,-0.00529,-0.04979,-0.01968,0.00826,0.03342,0.07728,-0.03835,0.01984,0.00741,0.01771,0.02509,-0.03576,0.0622,-0.00187,-0.03808,0.04611,0.01128,-0.08842,-0.0744,-0.07238,0.05643,-0.1162,-0.00033,-0.01691,0.01628,0.08193,0.07465,-0.10257,-0.03974,-0.00729,0.02359,0.0517,-0.08734,-0.00575,-0.02044,-0.00043,-0.00898,0.01282,-0.09192,0.03002,0.02078,0.01866,-0.10202,-0.04809,-0.01774,0.06584,0.08255,0.0631,-0.01672,0.06916,-0.09551,-0.06403,-0.00596,-0.08438,-0.00048,0.06095,0.1485,-0.06274,-0.012,0.01808,-0.05653,-0.04304,0.01138,0.00821,-0.00538,-0.10769,-0.06397,0.04422,0.01075,-0.02927,0.09497,0.03508,0.01541,0.11104,0.10175,-0.01839,0.05695,-0.04534,-0.09141]},{"domain":"discrete_math","key":"rsa_keygen","name":"RSA key from p, q and e","package":"discrete-math-ai999x","example":"Find the RSA private key d for p = 61, q = 53, e = 17.","v":[0.04853,-0.04957,-0.10502,-0.04915,-0.01111,-0.05399,0.0019,-0.01866,-0.03601,-0.08987,-0.09434,0.03413,-0.00389,0.09066,-0.02538,0.00765,0.02905,0.02204,0.02533,-0.01514,0.07669,0.05053,-0.02666,0.09151,-0.18336,0.12652,-0.04624,0.02465,0.01034,0.08492,-0.04283,0.00817,-0.02215,-0.1134,0.00797,0.05458,0.05408,-0.01263,0.0699,0.06835,0.02008,0.06407,-0.0961,-0.0353,-0.07347,0.11536,-0.04326,0.01399,-0.10301,-0.10653,0.00692,0.09564,-0.05634,-0.03187,-0.06096,-0.01063,-0.02445,0.14753,0.08204,-0.08692,-0.10492,-0.12758,-0.01704,0.0739,0.00265,-0.03091,0.01242,-0.05156,-0.02751,0.01772,-0.05234,-0.00254,0.04945,-0.10398,0.02045,-0.05566,0.15657,0.01554,-0.01872,-0.05808,-0.02844,-0.03588,0.01133,0.04901,0.02924,0.04277,0.00098,0.02947,-0.09151,-0.07455,-0.00659,-0.09198,-0.05671,-0.10501,0.02862,0.02657,0.00306,-0.06403,0.1091,0.05229,-0.06939,0.05222,0.11379,0.06505,-0.06488,0.01549,0.00919,-0.04021,0.10388,-0.04618,0.05145,0.02742,-0.01215,0.00472,0.13053,0.01978,0.0193,-0.06364,0.02671,-0.07923,0.00352,0.0233,-0.13899,0.03397,0.01804,-0.03511,-0.06669,0.01457,-0.05506,0.01,0.04783,0.02888,-0.08282,-0.04363,0.09085,0.02621,-0.07803,0.10314,-0.04866,-0.05198,0.03199,-0.00147,0.0574,-0.10988,0.07725,0.09403,0.05355,0.10395,-0.07109,0.11464,-0.05011,0.02604,-0.04475,0.03994,0.11177,0.04344,-0.09083,0.08115,0.04201,0.0589,-0.0637,-0.02543,0.05374,-0.02614,0.05757,0.05699,-0.15094,0.08562,-0.06408,0.04203,-0.02905,-0.03752,-0.00626,0.03435,0.14794,0.04915,0.01272,0.00188,-0.0854,-0.01415,-0.03889,0.05713,0.0754,-0.04161,0.03878,0.03454,-0.11153,0.00493,-0.02135,0.10313,0.0642,-0.03449,0.08025,0.06914,-0.03341,-0.08506,0.00418,0.0131,-0.02815,-0.0344,-0.0288,-0.03974,0.0985,0.0112,-0.02956,-0.02217,-0.00461,-0.00891,0.12416,-0.1056,0.02562,-0.03602,0.01305,0.03525,-0.00691,-0.12372,-0.09313,0.00867,0.09011,-0.07253,-0.04047,-0.06358,0.09148,0.01088,0.02422,0.02484,0.03065,-0.09722,0.06909,0.07475,-0.02798,0.0241,-6e-05,-0.01458,-0.0793,-0.03331,0.10275,-0.02855,-0.0525,0.05729,0.00326,-0.02728,-0.00028,-0.0098,0.03119,-0.01748,-0.08211,0.09965,0.04331,-0.01796,0.03988,0.03974,0.00588,0.04918,0.03665,0.01318]},{"domain":"discrete_math","key":"sequences_with_repetition","name":"Sequences with repetition (n^k)","package":"discrete-math-ai999x","example":"How many sequences of length 4 can be formed from 10 digits with repetition allowed?","v":[-0.04828,0.01903,-0.03604,-0.03072,-0.00762,-0.07179,0.13492,0.04812,-0.01441,0.01103,0.01526,-0.04143,-0.02127,-0.03028,0.06484,0.00226,-0.0182,-0.05502,-0.02879,0.10086,-0.05792,0.07107,-0.01933,0.04495,-0.00061,-0.03218,-0.03445,-0.00815,-0.04483,0.11674,0.07198,-0.11008,-0.04184,-0.09638,0.04836,-0.0389,-0.07893,0.03351,0.0215,0.08765,0.01299,0.0728,-0.0214,0.02817,-0.08231,0.11096,-0.14625,0.0874,0.00328,-0.04387,0.00501,0.12317,-0.01873,0.01498,0.07477,0.03821,-0.0908,0.02398,0.03467,-0.03325,-0.0901,0.10233,-0.05176,-0.10543,-0.02609,0.04499,0.04231,0.00694,0.04443,0.02343,0.08698,0.07792,-0.08097,0.15588,-0.00376,0.08111,-0.11064,0.03815,-0.05694,0.00056,-0.08293,-0.02335,-0.02537,-0.15215,-0.05083,-0.07301,-0.07386,-0.0764,0.02442,-0.04714,0.05777,-0.02918,0.05757,0.04106,0.04994,-0.01101,-0.03656,0.15223,0.08427,0.04568,-0.03056,0.06241,-0.04698,-0.01117,0.05281,0.0385,-0.03334,-0.07238,-0.01179,-0.01246,0.00181,-0.05547,-0.03975,0.02472,0.08398,0.02208,-0.12079,-0.07147,0.07768,-0.00469,-0.07014,0.0635,0.07857,-0.0634,0.05406,0.07028,0.02027,0.03904,-0.0077,0.01432,0.01754,0.007,0.02882,-0.03546,0.03482,0.02102,0.03014,-0.11404,-0.00726,0.03437,-0.15486,0.10594,-0.10067,0.0556,-0.00994,-0.03814,-0.10326,0.07078,-0.07461,-0.06616,-0.02655,0.09596,-0.105,-0.08692,-0.04613,-0.00882,-0.12243,0.04717,0.02163,-0.00015,0.03441,0.07538,0.06159,0.01573,0.02046,0.08044,0.03403,-0.0228,0.05541,0.0123,0.06056,0.01564,-0.02267,0.09679,-0.01038,-0.04807,-0.0482,0.06438,-0.04929,0.0453,-0.1147,0.06719,-0.05388,-0.00209,0.06029,0.05455,-0.07555,-0.00259,-0.10669,-0.04117,-0.06884,0.06633,-0.01584,-0.05091,0.00809,-0.02216,0.00926,-0.06581,-0.06067,0.00577,0.00713,-0.03559,0.12985,-0.00653,-0.0348,0.15786,-0.13078,-0.03905,-0.05488,0.01301,-0.00663,-0.07491,0.06032,-0.00552,0.00503,-0.02612,0.02646,-0.05816,-0.00112,0.00519,-0.00963,0.01107,-0.09098,-0.10245,0.07435,0.03956,0.07671,0.02275,-0.08839,-0.04731,-0.07756,0.0627,-0.05401,-0.00499,0.03169,0.09296,0.03442,0.12442,0.11889,0.02394,-0.00817,0.04088,-0.01412,0.01493,-0.0459,0.15553,-0.03396,0.0786,-0.01539,0.04273,0.0256,-0.03498,-0.02115,0.05183,0.07099,-0.05941]},{"domain":"discrete_math","key":"spanning_tree_count","name":"Number of spanning trees (Kirchhoff)","package":"discrete-math-ai999x","example":"How many spanning trees does the graph with edges A-B, B-C, C-D, D-A, A-C have?","v":[0.02917,-0.02682,0.05682,0.04039,-0.05358,0.15252,0.136,-0.00739,0.08959,-0.01172,0.04134,0.05796,-0.08716,0.01945,0.04529,-0.00414,-0.03414,-0.06716,0.01296,-0.0091,0.01417,0.05586,0.04818,-0.09697,0.05134,0.03193,0.04216,0.02988,-0.06361,0.02509,-0.00082,-0.03044,-0.00553,0.04238,-0.14964,0.00186,-0.0543,0.07723,-0.02868,0.01329,-0.1667,0.05642,0.03041,0.08648,-0.01164,-0.02916,-0.00606,0.03576,0.03263,0.05901,-0.03351,-0.07029,-0.03346,0.0127,0.12928,-0.02269,-0.07312,-0.01885,-0.04554,0.05428,-0.03666,0.03459,-0.05891,-0.13413,-0.10625,0.0565,-0.10331,0.01534,0.05439,-0.02501,0.01013,0.0081,0.02604,0.06711,-0.01896,-0.06936,-0.10369,0.00998,-0.13106,0.01845,0.08119,-0.08041,-0.00808,0.0323,0.06539,0.02183,-0.00642,0.02432,-0.06525,0.01449,-0.09539,-0.03808,0.03286,-0.03638,-0.01266,-0.03649,-0.0226,0.06144,-0.09288,-0.08592,0.02885,-0.03605,-0.00086,0.0335,-0.04942,0.08584,0.0895,-0.10208,-0.05177,-0.06665,0.02978,-0.0442,-0.13519,0.00134,-0.0035,0.02684,0.00434,-0.07718,-0.05137,0.06616,0.07826,0.1278,0.01357,0.0513,0.01178,0.03877,0.06958,-0.01852,-0.04361,-0.02482,-0.12993,0.06428,0.0785,0.02285,-0.09089,0.03715,-0.10578,-0.13709,0.06428,-0.03051,0.02884,0.04098,-0.06385,0.0322,-0.06923,-0.07285,-0.00795,-0.01194,-0.06124,-0.04049,0.07879,-0.0311,0.07056,-0.01822,-0.04007,-0.0081,0.02171,-0.10401,0.10321,-0.08637,-0.0781,0.08013,-0.01775,0.11431,-0.0584,-0.01069,0.00689,0.06084,-0.10646,0.14857,0.11502,0.04192,-0.01089,0.0454,-0.07556,-0.04046,-0.05833,0.0575,0.00212,0.18844,-0.04259,-0.08018,0.07297,-0.01585,-0.01561,-0.01744,0.09545,-0.01626,0.01261,0.0715,0.01484,0.01954,-0.01845,-0.07259,-0.04353,-0.02688,0.05825,0.06034,0.00979,0.01626,0.01008,0.08237,0.00549,0.0972,0.03805,-0.00443,0.04365,-0.04938,-0.08279,-0.04626,0.04765,-0.01202,-0.01353,0.06278,0.18499,-0.03921,-0.06263,-0.02699,0.06574,0.18807,0.04131,-0.00745,0.0304,-0.09197,-0.00644,0.01496,-0.0703,0.00465,-0.05233,-0.09507,0.0238,0.02857,-0.05428,-0.0678,0.03731,0.06785,0.0277,0.03491,-0.09679,0.00351,-0.00596,-0.01628,0.00836,-0.00988,-0.00684,0.01838,0.06739,0.04426,0.03684,0.05429,0.02602,-0.01832,0.0005,0.01395,-0.10988,-0.05791]},{"domain":"discrete_math","key":"sqrt_mod","name":"Square roots modulo a prime","package":"discrete-math-ai999x","example":"Solve x^2 ≡ 10 (mod 13).","v":[-0.06683,-0.01128,-0.08964,0.0188,-0.04753,-0.05329,0.03663,0.03948,-0.05081,-0.1121,-0.01322,-0.00529,-0.00653,0.08813,-0.03029,0.02816,0.18971,-0.0839,0.00126,-0.00494,0.10638,-0.08771,0.05396,0.05872,-0.05895,0.10644,-0.02436,0.03746,0.09928,0.13842,-0.06406,-0.04191,-0.02363,0.01057,-0.00644,-0.04557,0.02748,-0.04966,0.16881,0.0378,0.041,0.01135,0.11011,-0.04334,-0.04014,-0.00217,-0.04331,0.00277,-0.0153,-0.01745,0.05723,0.0833,0.0588,0.0488,-0.08276,-0.0742,-0.1136,0.03905,0.0087,-0.0165,-0.09303,-0.0854,0.00302,0.2234,-0.01786,0.0482,-0.08681,-0.05443,-0.12081,0.05906,0.01662,-0.05663,-0.01427,-0.05382,-0.04805,0.08774,0.13069,0.01551,-0.0974,0.06736,0.02481,0.02999,-0.03102,-0.00361,-0.04089,0.04113,-0.04637,0.08574,-0.0024,-0.05922,-0.04616,0.02623,-0.02387,-0.04875,0.02091,-0.05198,0.06872,0.00148,0.0319,0.12205,-0.00676,0.06141,0.03758,-0.00306,-0.001,0.04934,-0.05685,-0.04068,-0.01576,0.10156,-0.08878,-0.08233,0.01409,-0.01831,0.03766,0.06658,-0.03146,-0.15198,-0.01126,0.03182,0.16591,0.0295,-0.03105,-0.02146,-0.0932,-0.04599,0.07435,0.01075,-0.00117,-0.0485,0.04445,0.07892,-0.03183,-0.04586,-0.01233,0.03399,-0.07222,-0.05045,0.1044,0.01613,0.13576,-0.00971,0.03029,-0.06085,-0.08613,0.00893,-0.01575,0.03414,0.02326,0.00675,-0.00335,0.10962,-0.04502,0.03715,0.01981,0.05624,-0.163,0.09076,-0.05143,0.06335,-0.06962,0.02406,0.0079,-0.02792,-0.05927,-0.03188,0.0035,0.10249,0.03259,0.04927,0.08438,0.0466,0.01144,0.03986,0.02267,-0.04325,-0.0106,0.05248,-0.10347,0.0466,-0.00078,0.06112,-0.06125,-0.05882,0.0546,-0.01119,-0.02966,0.00518,-0.05566,0.00673,0.00556,-0.08348,0.06113,-0.00062,-0.01191,-0.00403,-0.1555,-0.11038,-0.05015,0.0632,0.10213,0.03787,-0.09019,-0.00086,-0.04993,0.02808,0.02607,-0.02806,0.08373,-0.00885,0.06236,0.03615,7e-05,0.01393,-0.00913,-0.05991,-0.02416,-0.07352,0.13066,-0.08635,0.02817,0.01212,0.00335,0.03997,0.10096,0.04235,-0.05593,-0.169,-0.08103,0.06544,-0.01489,-0.04776,0.02495,0.04318,0.03873,-0.04112,-0.04855,-0.03443,-0.02054,0.01328,0.02191,0.0443,-0.00336,-0.03356,0.05495,-0.01479,-0.10381,-0.03977,-0.06249,-4e-05,-0.01176,0.00525,0.0149,-0.03607,0.07184,0.04914]},{"domain":"discrete_math","key":"stars_and_bars","name":"Integer solutions of x1 + ... + xk = n (stars and bars)","package":"discrete-math-ai999x","example":"How many non-negative integer solutions does x1 + x2 + x3 = 10 have?","v":[-0.10761,-0.03893,-0.04787,0.04509,-0.02182,0.02377,0.13704,-0.04071,-0.0122,-0.03708,0.08218,0.00747,-0.03184,-0.00686,0.05695,-0.07322,0.00253,0.04172,-0.02036,-0.02403,0.00549,-0.07897,0.03682,0.02612,0.04491,0.09739,-0.04432,0.06454,-0.00539,-0.117,-0.07079,-0.19256,-0.07458,-0.02631,0.00614,0.00292,-0.06663,0.00508,0.07736,0.11615,-0.05819,0.03897,0.06753,0.00328,-0.0108,-0.00198,-0.08654,0.1201,0.05013,0.09722,0.03655,0.0772,0.00711,0.02598,0.08346,0.0059,-0.02654,0.02416,0.06244,0.02467,-0.1166,0.0855,-0.01265,0.02099,0.08625,-0.00157,0.0212,-0.03285,0.0751,-0.02877,0.00826,-0.00013,0.02228,0.12533,-0.01847,0.037,-0.08369,-0.01998,0.01683,0.00131,0.00233,-0.1024,-0.11515,-0.09486,-0.09416,-0.05159,0.01208,0.10695,-0.06189,0.07059,0.05131,0.02255,-0.04876,0.00948,0.00503,-0.01952,-0.07162,6e-05,-0.07517,-0.01843,-0.01663,-0.006,-0.00689,-0.01999,0.01667,0.04457,0.00956,-0.08779,0.03884,0.01744,-0.05283,-0.06582,-0.01797,0.01839,0.14289,-0.01516,0.17793,0.0047,0.01451,0.03248,-0.02289,0.15833,0.09251,0.00879,0.0964,0.00397,0.0719,0.13163,0.0038,-0.08323,0.01885,0.02714,0.04029,-0.05695,-0.03644,0.03295,0.0265,-0.10417,0.06364,0.10394,-0.15124,-0.00231,-0.07044,0.02118,-0.08327,-0.09286,-0.01593,0.02227,0.01124,-0.16226,-0.06664,0.05561,0.0106,-0.06442,0.00723,-0.01437,-0.13903,-0.00202,0.04764,0.07902,-0.04017,-0.0255,0.01855,0.07846,0.01301,-0.07739,0.12767,-0.0231,0.00095,0.09999,0.05621,-0.02582,-0.05616,-0.02255,-0.01009,0.08045,-0.02729,0.002,-0.07796,-0.01832,0.02057,-0.04231,-0.00226,0.00211,-0.02325,0.06,0.02194,-0.00168,-0.01212,-0.13016,-0.06868,0.00595,-0.00132,-0.00307,-0.00185,-0.04488,0.03946,-0.09553,-0.07993,-0.00086,0.08082,0.0503,-0.06422,-0.02596,0.07558,0.05265,-0.03586,0.01632,-0.10409,0.01735,0.01808,-0.06669,0.05383,0.09736,-0.00822,0.11329,0.02083,0.0025,-0.02832,-0.01042,0.04049,-0.02003,-0.01241,-0.01772,0.00163,0.00825,-0.03406,-0.06507,-0.11872,0.05433,-0.02764,-0.05839,-0.13638,-0.13843,0.03213,0.01281,0.00964,0.10672,0.01901,0.12964,0.00482,-0.01701,0.03346,0.1349,0.05994,0.04026,0.00733,-0.02208,0.02059,0.10287,-0.07865,0.04373,-0.03029,-0.02352,0.06976,-0.04606]},{"domain":"discrete_math","key":"stirling1","name":"Stirling numbers of the first kind","package":"discrete-math-ai999x","example":"Compute the Stirling number of the first kind c(5, 2).","v":[0.08376,-0.01208,-0.04216,-0.02685,-0.04778,0.06976,-0.02761,-0.01225,0.03388,0.0756,0.02615,-0.02479,0.00485,0.11318,0.06249,-0.0151,-0.0398,0.07524,-0.06081,-0.11692,-0.04618,-0.02451,-0.04506,-0.06524,0.07189,-0.10657,-0.00444,-0.01101,-0.05111,-0.00258,-0.06468,-0.08206,-0.00382,-0.08825,0.01814,-0.09116,-0.12098,0.0494,0.16517,-0.00201,0.05106,0.06211,0.07108,0.0731,0.04898,0.07731,-0.11384,0.13993,0.05867,-0.06183,-0.11734,-0.00024,0.07898,0.12954,0.10846,-0.10562,-0.07191,0.0887,0.05757,-0.0042,-0.06328,0.05343,0.0009,-0.00788,0.01489,-0.06631,-0.08378,-0.02436,0.01417,0.05303,-0.0218,0.12937,-0.02785,0.09774,0.05575,0.11483,-0.09476,-0.00072,0.09432,0.02163,-0.01926,-0.04025,0.07559,-0.09603,-0.03583,-0.03436,0.09109,-0.05895,-0.1394,-0.02393,-0.0061,-0.08301,0.06177,0.09801,0.06577,0.03838,-0.1104,-0.01888,0.03222,-0.02348,0.03942,-0.0176,0.04096,0.03723,0.09768,0.06678,0.04921,-0.10399,0.01219,-0.01052,0.00801,-0.00773,0.06804,0.01178,0.07106,-0.03064,0.01121,-0.10155,-0.03409,-0.01826,-0.03959,-0.0207,-0.03442,-0.00159,0.04334,-0.0945,0.02284,0.00929,-0.00484,0.02605,0.02644,0.01145,0.02448,-0.08952,0.01822,0.06122,-0.01171,-0.08118,0.04965,0.05477,0.04301,-0.01494,-0.05532,0.02112,0.02285,-0.1199,-0.09154,0.01339,-0.02502,-0.03963,0.03074,-0.05831,-0.0337,-0.03433,0.00554,-0.03088,-0.04461,-0.09868,0.08188,-0.02306,-0.03513,0.07042,-0.01433,-0.00297,-0.03588,0.00894,0.00314,0.05689,0.06318,0.12953,0.1016,0.0129,0.01651,0.08331,-0.03717,0.04731,-0.04014,0.07313,-0.02263,0.00744,-0.07914,-0.09596,0.13347,-0.03465,0.08205,0.02528,0.04848,-0.09053,-0.07426,0.03471,0.06357,-0.01194,0.05841,-0.08884,-0.00884,-0.02254,0.01926,0.10797,0.00567,-0.04654,-0.00706,0.04274,0.03485,-0.03592,0.03222,0.04526,0.01778,-0.12806,-0.05636,-0.05864,0.02693,-0.03379,0.08044,0.08137,0.03947,-0.01274,-0.11863,-0.05241,0.05396,0.02403,0.04205,-0.0458,0.08509,-0.00059,-0.03967,0.08763,0.01156,-0.03518,-0.13825,-0.04374,-0.02076,-0.06711,-0.04538,-0.01928,-0.01447,0.05178,0.06121,0.05476,-0.00641,-0.01761,0.04788,0.02444,-0.0671,0.05968,-0.04902,0.02833,0.03364,-0.09786,0.04293,0.03777,0.05032,0.13828,-0.09239,0.08587,-0.02768,-0.13068]},{"domain":"discrete_math","key":"stirling2","name":"Stirling numbers of the second kind","package":"discrete-math-ai999x","example":"Compute the Stirling number of the second kind S(7, 3).","v":[-0.03399,-0.01709,0.00827,-0.13508,-0.1067,0.02572,0.11185,-0.00518,0.03274,0.05333,0.00442,0.01723,-0.03122,-0.01754,0.11733,-0.02301,-0.00594,0.03376,-0.02566,-0.04018,-0.0413,0.00491,0.06001,-0.0974,0.01521,-0.05949,-0.01354,0.01182,0.02143,-0.09082,-0.07337,-0.14352,0.0311,-0.04388,0.00828,-0.0376,-0.09326,0.04126,0.00188,0.08562,0.02032,0.06871,0.12192,0.0544,0.02305,0.0858,-0.02994,0.09717,0.06266,0.01103,-0.06361,0.02072,-0.01687,0.04731,0.08354,0.00178,0.02499,0.04717,0.06119,0.05598,-0.04449,0.11778,0.02615,-0.02847,0.02439,-0.04123,0.00653,0.00447,0.14058,0.02327,0.01039,0.0266,-0.03965,0.1388,-0.06721,0.13474,-0.10764,-0.04713,0.04717,-0.00594,0.00733,-0.04451,-0.01665,-0.09308,-0.11544,-0.10391,0.0613,0.0172,-0.10745,0.00031,-0.07577,0.03752,0.01965,-0.00066,0.04801,-0.01626,-0.10731,-0.06519,-0.01721,-0.02596,0.00042,0.0241,0.142,0.04824,0.00851,0.06141,0.14847,-0.09253,-0.00863,-0.03563,-0.00191,-0.04701,0.02576,-0.00204,0.01396,0.0211,0.08193,-0.00514,-0.00322,-0.00122,-0.04261,0.09506,0.04484,0.01527,0.08594,0.00233,0.01675,0.06591,0.02414,-0.00967,0.04648,-0.0192,0.02356,-0.10395,-0.05539,-0.0053,0.05875,-0.04173,-0.04444,0.13389,-0.0039,-0.00228,-0.01616,-0.0032,0.0315,-0.13381,-0.01153,0.0273,-0.10101,-0.02871,0.05232,0.00027,-0.03404,-0.06834,0.03977,-0.04251,-0.02229,-0.03946,0.04531,-0.01335,0.05295,0.06421,-0.00924,0.00649,-0.08613,0.00833,0.11139,-0.00102,0.03621,0.04876,0.06726,0.02288,-0.07951,0.03767,-0.00769,0.03873,-0.03182,0.16961,-0.12842,-0.06253,-0.06866,-0.04382,0.0326,-0.03923,0.04769,-0.02558,0.07515,-0.02207,0.02875,0.00997,0.02616,0.04961,0.06402,-0.11992,-0.10733,-0.02618,0.02547,0.0678,-0.07865,0.02707,-0.03005,0.09573,-0.03656,-0.07321,0.10906,0.01252,-0.00641,-0.10237,-0.04602,0.02247,0.01054,-0.05831,0.05657,0.11222,0.0587,0.06141,-0.15325,-0.00734,0.08692,0.06144,0.03782,-0.06012,0.09271,-0.02262,-0.09973,0.0617,-0.00354,-0.10889,-0.06415,-0.01082,-0.00841,0.0249,-0.09594,-0.17867,-0.02232,0.0305,0.01374,-0.03813,-0.02541,0.04392,-0.01556,-0.06955,-0.05503,0.11532,0.05146,0.05163,0.00089,-0.0384,0.13898,-0.01391,-0.08817,0.06482,-0.07701,0.0091,0.0655,-0.01628]},{"domain":"discrete_math","key":"strongly_connected","name":"Strongly connected components","package":"discrete-math-ai999x","example":"Find the strongly connected components of the directed graph with edges A->B, B->C, C->A, C->D.","v":[-0.02265,-0.02778,0.02016,-0.05453,-0.03458,-0.00676,-0.03254,-0.08705,0.05374,-0.08974,-0.00143,0.0104,-0.11612,0.0283,0.09849,-0.01101,-0.03788,0.00827,-0.00169,-0.08292,-0.13403,0.04287,0.06816,0.03655,0.06839,-0.00345,-3e-05,0.02335,-0.11964,0.08807,-0.01492,-0.10352,-0.05897,-0.03298,-0.03156,0.03965,-0.12068,0.02315,0.02083,0.06224,-0.01656,0.14977,0.1106,0.00589,0.07302,0.02607,0.02291,0.12732,-0.01415,0.00361,-0.05415,-0.04102,-0.00967,0.0613,-0.00202,0.04534,-0.13426,0.04663,-0.03555,0.04913,-0.02333,0.0586,-0.01441,-0.10121,0.04351,-0.06955,0.0052,-0.02631,0.09605,0.02134,-0.06316,0.05079,0.03732,0.03518,-0.07242,-0.0644,-0.09725,0.09754,-0.03755,-0.03174,-0.00643,-0.06052,-0.01513,-0.00354,-0.05973,0.07532,-0.14648,-0.1204,-0.03324,-0.00143,0.04795,-0.10164,0.05979,-0.01779,0.03348,-0.0978,-0.0372,0.0038,0.09398,0.0427,0.03999,0.1046,-0.02467,0.13039,0.04979,-0.00812,0.09602,-0.00289,-0.01845,-0.0007,-0.03952,0.06126,-0.03044,-0.04314,-0.03828,0.09948,-0.03592,-0.01336,-0.0053,-0.04529,-0.04282,0.00046,-0.05103,0.03467,-0.06474,0.02731,0.08294,-0.00866,0.05393,0.07298,-0.12018,0.04452,-0.04507,-0.10763,0.01261,0.0424,-0.08537,-0.08258,0.0255,-0.0991,-0.02154,0.07977,-0.02082,0.02242,0.03002,-0.13583,-0.07719,0.06251,-0.01562,0.07496,0.04575,-0.00761,0.05822,0.04082,-0.01351,-0.0437,-0.02748,0.00469,-0.01021,0.1318,0.03712,0.15123,-0.06011,-0.03849,-0.02868,0.06354,-0.00471,0.10405,-0.07398,0.06526,0.11345,0.10044,-0.08019,0.00916,0.05041,-0.02103,-0.0691,0.1752,-0.0541,0.0545,-0.01341,0.02366,0.05168,-0.04043,-0.06774,0.0976,0.15382,0.07992,0.04664,0.02267,0.06565,0.01278,0.02,-0.06253,-0.08789,-0.03025,-0.07526,0.11422,-0.01601,0.03911,-0.02266,0.01794,0.09567,-0.01562,0.03995,0.04049,-0.07261,-0.05504,-0.04379,-0.05034,0.0095,-0.04421,-0.03941,0.08849,0.07446,-0.05013,0.05099,0.00359,0.01491,0.03953,-0.00327,-0.02327,-0.03462,-0.0529,0.05671,0.12066,-0.00234,-0.00473,-0.09407,-0.03315,-0.0996,-0.01756,-0.02937,-0.01561,-0.0308,-0.03851,0.12069,0.01053,0.02113,0.07359,-0.07454,0.09938,-0.01518,0.05272,0.02562,0.04003,-0.00719,-0.02429,0.04488,0.02582,-0.05263,-0.05161,0.04827,0.07191,0.01386,-0.08761]},{"domain":"discrete_math","key":"topological_sort","name":"Topological sort","package":"discrete-math-ai999x","example":"Find a topological sort of the directed graph with edges A->C, B->C, C->D, 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25?","v":[-0.03985,0.01685,-0.03974,-0.0618,-0.04291,0.03475,-0.00052,0.07168,0.04566,0.01617,0.02556,0.00834,-0.02356,-0.06803,-0.02678,-0.05172,0.03361,-0.1191,-0.0065,-0.03698,0.04096,-0.06457,0.1185,-0.05312,-0.02294,0.07674,-0.03736,-0.06632,-0.04226,-0.02747,0.0105,-0.05075,-0.04237,0.10595,0.01327,-0.05843,-0.01878,0.07784,-0.04478,0.06683,0.02669,0.09105,0.0835,0.02687,-0.10138,0.06067,-0.04471,0.09356,-0.06066,0.09034,0.16301,0.03915,0.06079,0.06344,-0.05857,0.07047,-0.08512,0.05269,-0.07247,0.08507,-0.01587,0.06603,-0.05044,0.04272,0.02858,-0.08102,-0.01411,-0.01193,-0.04533,0.01857,-0.08793,-0.04335,-0.05272,-0.07486,0.03511,-0.02816,-0.16263,0.04889,0.03637,-0.00917,0.0181,-0.0522,0.095,0.00956,0.09985,-0.008,0.10931,-0.04194,-0.02837,0.05664,0.04533,-0.02814,0.00723,0.03625,0.00801,-0.07353,0.0349,0.00136,-0.02758,-0.05123,-0.01369,-0.08838,0.01228,-0.07237,-0.00133,0.09153,-0.05652,-0.06287,-0.00039,-0.01116,-0.05211,0.05846,-0.02834,0.03163,0.1124,-0.0169,0.03207,-0.10578,0.02053,0.02907,-0.07145,-0.15841,-0.01675,-0.03206,-0.04835,0.05358,0.12147,0.04425,0.05862,-0.01424,-0.03591,-0.00699,0.01427,-0.02462,-0.01138,-0.0186,-0.01775,-0.008,0.06071,-0.02334,-0.08305,0.01782,0.03398,0.02413,0.01657,0.0327,-0.01745,-0.0455,0.01137,0.01494,0.04641,0.09592,0.15927,0.11076,0.0814,-0.03895,0.03621,0.06532,0.02054,0.07478,0.01381,-0.01042,-0.04097,-0.06172,0.0507,-0.06166,0.05143,-0.18832,0.0502,-0.0087,-0.01475,-0.04849,-0.11279,-0.03275,0.04693,-0.0527,-0.09032,0.03652,0.03384,-0.02197,0.1191,0.10703,0.11748,-0.09849,-0.07143,-0.04914,-0.03842,0.03872,-0.06086,-0.0777,0.08634,0.08042,-0.04231,0.01535,-0.00166,-0.09494,0.05713,0.03408,0.02221,0.02253,0.04519,0.08798,-0.01691,0.01509,-0.04337,-0.06186,0.04291,0.04143,-0.101,0.02978,0.02448,0.04961,0.17136,0.0149,-0.12213,-0.00672,0.06654,-0.00068,-0.02768,0.12602,-0.01175,0.01824,-0.0425,-0.00862,0.04375,0.0018,0.06531,0.10454,0.01455,0.12844,-0.16996,0.02579,0.03762,0.02473,-0.07546,-0.04792,-0.06779,-0.12848,-0.05546,0.02034,0.06114,-0.05397,0.07157,-0.09411,-0.01666,-0.02442,-0.05125,-0.02988,-0.0415,0.00519,-0.13836,-0.00503,0.04253,0.01194,-0.02239,-0.01989]},{"domain":"geometry","key":"circle_measures","name":"Circle: area, circumference and diameter","package":"geometry-ai999x","example":"Find the area of a circle with radius 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1?","v":[-0.09517,-0.143,0.10824,0.06141,0.01801,0.04038,0.04408,-0.0105,0.10642,-0.00579,0.03538,-0.03178,0.10964,-0.01739,0.00744,-0.04172,-0.01711,-0.05182,0.08014,-0.0174,-0.04894,-0.04403,0.12681,-0.03706,0.06,-0.01953,-0.02548,0.03592,-0.02595,-0.06434,-0.03782,0.06438,-0.07956,-0.00078,0.01184,-0.09586,0.01728,0.06298,-0.0299,0.04484,-0.0429,0.08702,0.03589,0.06218,0.00364,-0.02539,0.01673,0.12451,-0.03915,-0.01541,-0.00505,-0.07467,0.01522,0.00455,-0.03827,-0.06171,5e-05,0.11883,-0.03916,-0.03007,0.07489,-0.07789,-0.12495,-0.11014,0.00419,0.07836,-0.00064,0.02306,-0.02781,-0.00372,-0.01967,-0.0305,-0.06827,-0.07362,-0.05728,-0.00142,-0.10747,-0.02708,-0.02917,-0.02685,-0.01793,-0.00444,0.07029,0.10168,0.01655,-0.03208,0.07633,0.09911,0.10079,0.03882,-0.0036,-0.01511,0.04316,-0.08737,-0.03574,-0.08368,0.05958,0.01953,-0.06883,-0.03484,0.03776,-0.04127,0.04195,0.00083,-0.07824,-0.03449,-0.1316,0.02883,-0.09607,-0.02224,0.09717,0.02638,0.04691,0.00582,0.0404,-0.02096,0.03844,0.07813,0.00854,-0.01981,-0.04368,0.0103,-0.00896,-0.13468,0.02159,-0.01681,-0.02947,0.02438,-0.0021,0.04813,-0.00749,-0.07171,0.13113,0.04605,-0.07471,0.00169,0.09096,0.01218,-0.05467,-0.02122,-0.08389,0.15603,0.0421,-0.0214,0.06184,0.09073,0.1259,-0.00439,-0.08323,0.07032,0.09735,0.04029,0.07058,-0.00025,0.03647,-0.04377,0.00187,-0.05298,0.05038,0.07771,0.11167,0.03287,0.03293,-0.06609,0.01743,-0.01899,-0.04467,-0.13925,0.01155,-0.03547,-0.07761,0.07821,0.00978,-0.06562,-0.03434,-0.1354,-0.03962,0.02519,0.08338,-0.06022,0.00793,0.07374,0.08222,-0.02812,0.04696,0.05839,-0.00128,-0.05586,0.0614,-0.05061,-0.04926,0.12859,0.03218,0.07141,-0.02584,0.01352,-0.04595,-0.08257,0.04894,-0.02915,0.02411,-0.00578,0.04098,-0.10911,-0.03635,-0.02592,-0.00115,-0.04203,0.0381,-0.04535,0.06834,-0.00271,0.01165,0.02561,-0.03691,-0.03637,-0.02061,0.09491,-0.0055,0.08918,-0.09934,-0.07805,0.05644,-0.02431,0.06413,-0.02345,0.01446,-0.05243,0.14593,0.03699,0.00644,0.09793,-0.08768,-0.06484,-0.12007,0.01984,0.00574,-0.16454,-0.08183,-0.15554,0.06569,0.06715,-0.02063,-0.00416,-0.14219,0.02864,-0.06356,0.03691,-0.02661,0.01364,0.02239,0.05054,-0.01237,0.01737,-0.12076,0.08703]},{"domain":"geometry","key":"hausdorff_distance","name":"Hausdorff distance between two point sets","package":"geometry-ai999x","example":"Find the Hausdorff distance between the set (0, 0), (1, 0) and the set (0, 0), (3, 4).","v":[-0.06303,-0.11799,0.07099,-0.03738,0.02135,-0.06735,-0.02798,0.01803,0.03369,-0.00966,-0.09604,0.08475,-0.05864,0.12099,0.017,-0.02602,0.00874,-0.00784,-0.00552,0.00358,-0.00452,-0.01764,0.11228,-0.13745,0.09895,0.00025,-0.08788,0.07243,-0.06203,-0.04964,0.06259,0.12168,-0.05059,0.00196,0.00899,0.03119,-0.00629,0.11409,-0.03651,0.03659,0.01597,0.11828,0.07039,-0.02087,-0.12153,-0.01569,0.01921,0.06596,-0.06996,-0.00977,0.08989,0.06335,-0.0411,0.00816,-0.03991,0.00167,0.02365,0.11706,0.00159,-0.03847,0.02188,-0.10765,0.00925,-0.09037,-0.05753,-0.02201,0.00026,0.16159,0.00862,0.04699,0.03525,-0.04517,-0.10247,-0.12251,0.01105,0.06481,-0.04627,-0.11141,0.01831,-0.01049,-0.00555,0.01504,-0.0256,-0.03048,0.00588,0.01754,-0.06698,0.02936,-0.00854,0.00653,-0.10261,-0.05384,0.10434,0.02015,0.03572,-0.04934,0.08705,-0.0242,-0.11853,0.03927,0.07625,-0.06181,-0.02129,-0.00148,-0.15015,-0.06144,-0.11199,-0.04927,-0.07936,-0.09611,-0.00311,-0.05929,0.06393,0.14765,0.05741,-0.03608,0.03034,0.1362,-0.04514,0.04464,0.09127,0.00053,-0.02413,0.04675,-0.07913,-0.03679,-0.09849,0.08211,0.12243,-0.05671,-0.0201,0.03225,0.0046,-0.09224,-0.01698,0.02923,0.01485,0.01253,-0.04282,-0.05642,-0.02518,0.03049,0.01436,-0.03078,0.15059,0.02305,0.04124,0.04717,0.01233,0.02054,0.0223,-0.01394,0.02823,0.02104,0.04996,-0.08545,0.09629,-0.03507,0.01999,0.06096,0.05463,-0.07123,-0.04388,-0.03308,0.08043,-0.03117,-0.06408,-0.15992,0.06652,-0.04412,-0.0537,0.00362,0.03675,-0.08922,-0.05327,-0.09694,-0.04054,0.05296,0.06793,0.11095,0.09067,-0.00537,0.03162,0.09479,-0.05613,0.02844,0.03017,0.02344,0.09672,-0.05017,-0.00982,-0.05242,0.0178,0.10388,0.03513,0.02509,-0.01797,0.01582,0.03151,-0.07899,0.03581,0.05086,0.07845,-0.08246,0.02737,0.01459,-0.0188,-0.08769,0.00833,0.00316,-0.04428,-0.05209,0.04119,0.0214,-0.05772,0.01296,-0.01872,0.10885,0.03086,0.08265,0.10306,-0.01561,0.02998,0.03833,0.00024,0.07363,-0.01006,0.05388,0.07191,0.04068,0.00545,0.01311,-0.05071,0.01821,-0.03747,0.06961,0.00451,-0.01432,0.01063,-0.06148,0.09741,0.02554,-0.04915,0.06508,-0.12967,-0.10608,-0.07585,0.07582,-0.01417,-0.05744,0.1404,-0.0009,-0.01765,-0.07101,-0.05752,0.02662]},{"domain":"geometry","key":"helix_measures","name":"Helix: curvature, torsion and length per turn","package":"geometry-ai999x","example":"Find the curvature and torsion of a helix with radius 1 and pitch 6.283185307179586.","v":[-0.03782,-0.06914,-0.10159,0.07214,-0.05775,0.09779,-0.02515,0.06294,0.17405,0.11401,-0.05332,-0.05077,-0.01337,0.07772,-0.01788,0.04332,-0.07947,0.08297,0.03372,-0.09867,-0.02651,0.00723,-0.06969,-0.05636,0.03404,-0.0373,-0.0035,-0.00428,0.07558,0.01239,-0.09104,0.00881,0.06166,-0.04025,-0.00051,-0.07853,0.07385,0.00524,0.01707,0.17904,-0.00075,0.00903,0.06451,0.00204,0.06411,-0.04233,0.08525,0.00136,0.0269,-0.07307,0.05351,-0.05378,-0.01823,-0.02743,-0.1462,0.0348,0.03578,0.0237,-0.03786,-0.0437,0.05481,0.02404,0.03175,0.05755,-0.05888,0.05599,0.01504,0.0133,-0.03446,-0.10478,0.03989,0.05492,-0.05496,-0.02174,0.0156,0.02493,-0.04743,0.04023,0.09588,-0.04703,-0.07308,0.08167,-0.03204,-0.14745,0.07402,-0.01251,-0.05823,0.035,0.02114,-0.04668,-0.02816,-0.09505,0.02016,0.05275,0.0432,0.00718,-0.00156,-0.07649,0.05397,0.16324,0.04507,-0.10585,0.06886,0.10169,0.00144,-0.02293,-0.03758,0.00046,0.01604,0.06368,-0.02574,-0.00948,0.08443,-0.04849,0.00234,0.05148,0.03383,-0.02952,0.037,-0.05314,-0.03524,0.0557,-0.01306,0.10085,-0.0522,0.02362,0.03135,0.00342,-0.06231,0.00318,-0.03242,-0.07938,0.0008,-0.03117,0.16344,0.05548,0.02961,0.04845,-0.04257,0.10868,0.09937,-0.02294,0.07395,-0.12831,0.10581,-0.00305,0.0945,-0.03108,-0.02271,0.05876,-0.01438,-0.03932,0.03715,0.03307,0.03388,0.01856,-0.04541,-0.01343,0.0398,-0.06613,-0.01676,-0.06349,-0.02031,0.03487,-0.09545,-0.12431,-0.02382,-0.04556,-0.06764,0.01654,0.10496,0.03586,-0.02245,-0.0073,-0.03291,-0.01147,-0.01804,0.07421,0.05101,0.07969,-0.08759,-0.12653,0.01385,0.0022,0.10153,0.01593,0.02463,-0.01286,-0.01055,-0.0745,0.08625,0.03016,-0.03958,-0.09704,0.12206,-0.06869,-0.03883,0.00197,0.00335,-0.06651,0.11312,-0.07278,-0.11075,0.0013,0.01727,-0.08679,0.0843,-0.03081,-0.0277,-0.1026,-0.07969,0.02551,0.08097,0.10346,0.00979,-0.04775,-0.07746,-0.03426,0.03861,0.07651,-0.10938,-0.01595,0.02352,0.05072,0.07244,-0.12152,-0.01057,0.09494,-0.01974,-0.03159,-0.0189,-0.00348,-0.05104,-0.07842,-0.12215,0.02575,-0.046,-0.05501,0.01905,-0.09264,0.0417,0.07362,0.08038,0.02859,-0.01486,-0.00016,-0.0555,0.02443,-0.15141,-0.05595,-0.01733,0.08626,0.04675,0.03667,-0.02766,0.0439]},{"domain":"geometry","key":"initial_bearing","name":"Initial bearing (forward azimuth) along a great circle","package":"geometry-ai999x","example":"Find the initial bearing from (0, 0) to (0, 90).","v":[0.02135,0.05547,0.06938,0.00328,0.05383,0.06882,-0.00286,-0.03878,-0.00854,-0.02879,-0.06223,0.08079,0.03366,0.03706,0.14324,0.0243,-0.0277,-0.09228,-0.04126,0.05698,0.00895,0.05197,0.02021,0.09366,-0.01204,-0.04093,-0.09241,0.00029,-0.01307,0.02532,0.00795,-0.023,0.02085,0.08441,0.02815,0.03575,-0.04396,0.05026,-0.07289,-0.02605,0.03472,-0.0189,-0.02267,-0.09098,0.05356,0.10112,-0.01498,0.13334,0.05848,0.01639,-0.01057,-0.11494,0.11266,-0.00086,0.01489,0.07449,0.05122,-0.00904,0.00538,0.08397,-0.02676,0.04036,0.00841,-0.12119,0.02871,0.06783,-0.04894,-0.08304,-0.11883,0.0014,-0.13305,-0.04799,0.02511,-0.05492,-0.07696,-0.02614,-0.09827,0.07551,-0.03132,0.00799,0.1517,0.03956,0.1557,-0.01852,-0.01526,-0.03697,-0.08752,0.05564,0.11546,0.08148,0.00525,-0.05762,0.0071,-0.13211,-0.05359,-0.05964,0.03547,-0.01975,-0.04629,-0.06692,0.02051,-0.03322,0.01161,-0.0747,0.03759,-0.03695,-0.12277,0.03769,-0.06827,0.0237,0.0556,0.09507,0.02726,-0.09822,0.0014,0.02586,-0.02993,-0.11271,-0.04194,0.0077,-0.10349,-0.07046,-0.02312,-0.07262,-0.04528,0.10252,0.02556,0.01992,0.13246,0.05183,-0.01394,-0.02594,0.01618,-0.04553,-0.0251,-0.08456,-0.00393,0.03439,0.02612,-0.13532,-0.1032,0.13928,-0.06321,-0.09286,0.12318,-0.04933,0.10565,0.00953,0.01097,-0.00708,0.00605,-0.02961,0.08298,0.01552,0.03528,-0.0308,-0.10981,0.04613,0.0828,0.00508,0.09509,0.02638,0.05631,-0.0688,-0.06596,-0.01848,0.01203,-0.09363,-0.04217,0.02325,-0.00958,0.04057,-0.05882,-0.06585,-0.03073,-0.01874,-0.02939,-0.00145,-0.01898,-0.13748,-0.01221,-0.02101,0.0646,-0.06702,-0.0372,-0.04651,0.00518,0.01475,0.02842,-0.0355,0.00611,0.07584,0.03746,-0.05678,-0.02668,0.03668,-0.06148,-0.04103,-0.07145,0.0361,-0.05376,-0.00601,0.02821,-0.00393,0.00964,0.0337,0.0682,0.05513,0.01776,0.01349,0.0213,-0.03899,-0.04365,0.16894,0.04872,-0.12513,0.13328,-0.01377,0.02111,0.1388,-0.05769,-0.01016,-0.04526,5e-05,0.01905,0.04318,0.01581,0.05561,0.0576,0.06344,0.00477,0.0461,-0.05447,0.02763,-0.10451,-0.04316,0.03076,-0.0291,0.01029,0.02634,0.02771,0.03865,-0.02636,0.04161,-0.11619,0.01723,0.06044,0.05652,-0.077,0.04635,-0.10005,-0.04063,0.14051,-0.00544,0.0289,0.15092]},{"domain":"geometry","key":"line_intersection","name":"Intersection point of two lines","package":"geometry-ai999x","example":"Find the intersection of the lines 2x + y = 5 and x - y = 1.","v":[-0.05427,0.03973,-0.00675,-0.03162,-0.06546,0.04317,-0.00976,0.00157,0.04123,0.04514,-0.03036,0.06568,0.00473,-0.04187,0.0051,-0.09217,0.00139,-0.07405,-0.00518,0.01373,0.05237,0.02602,0.11856,0.05011,0.07077,0.06218,-0.07382,-0.00971,-0.06645,0.01232,-0.04842,-0.0561,-0.04253,0.21143,0.02619,0.05915,-0.05315,0.07132,-0.05214,0.01397,-0.02079,0.03788,0.05921,-0.11197,-0.11985,-0.04266,-0.02845,0.04058,-0.00226,0.16113,0.14735,0.10163,0.00508,0.08995,-0.0202,0.1238,-0.0892,0.11988,-0.10516,0.12545,-0.06637,0.06571,-0.05566,-0.05577,0.01839,-0.04631,0.00813,-0.02201,0.10001,-0.1218,-0.01243,-0.03979,0.04613,-0.08141,0.06101,-0.02545,-0.01708,-0.03623,0.07303,-0.01938,0.00506,-0.07417,0.05307,0.03697,0.04202,0.01403,0.03031,0.03591,-0.05457,0.18647,0.01645,-0.08899,-0.01789,-0.02002,0.02936,-0.125,0.07212,-0.02555,-0.05963,-0.09186,-0.00685,-0.05209,0.02974,0.01088,-0.02982,0.09133,0.06027,0.01466,-0.05716,-0.01149,0.02644,0.01363,-0.07052,-0.00613,0.12427,-0.03417,-0.04753,-0.04684,-0.01139,0.05799,-0.07009,-0.02081,0.03979,-0.02671,0.02655,0.07439,0.06708,0.03345,0.05765,-0.03495,-0.02613,0.00628,-0.02715,-0.03239,-0.01624,-0.11812,-0.01068,-0.00689,0.02888,-0.03777,-0.03902,-0.03754,-0.01381,0.05959,-0.03734,0.03032,-0.11891,-0.057,0.07255,-0.01901,-0.03392,0.01705,0.07588,0.1032,0.06167,-0.07164,0.02012,0.0173,-0.01591,-0.00655,0.00767,0.00706,0.07715,-0.02945,0.05087,-0.08908,0.02492,-0.13786,-0.08033,0.01717,0.07842,-0.04492,-0.09184,-0.0562,0.06914,0.0159,-0.01126,-0.0782,0.01177,-0.07807,0.06698,0.03142,0.08584,-0.05527,-0.10405,-0.01672,-0.08819,0.00469,-0.03726,-0.06003,-0.01,0.1095,-0.07742,0.03837,0.03043,-0.10863,0.04838,-0.00046,-0.01726,-0.00973,0.08031,0.09208,-0.03983,0.03393,0.0097,-0.02464,0.02178,0.06743,-0.13463,0.09461,-0.00068,0.07052,0.02441,-0.04042,-0.06726,0.04497,0.12554,0.0047,-0.07786,0.14476,0.00964,-0.03721,-0.05195,-0.0046,0.00636,0.01725,0.01995,0.04663,0.01849,0.14443,-0.15761,-0.05271,0.01311,-0.11775,0.03663,-0.01258,-0.03988,-0.06398,-0.03759,-0.0287,0.0636,0.01904,0.10573,-0.05996,0.04919,-0.02927,0.03165,-0.02456,0.02298,-0.0035,-0.07317,0.00336,0.01124,-0.01766,0.04663,-0.03579]},{"domain":"geometry","key":"line_plane_intersection","name":"Intersection of a line and a plane","package":"geometry-ai999x","example":"Where does the line through (1, 0, 0) with direction (1, 2, 3) meet the plane x + y + z = 7?","v":[-0.07097,0.03693,-0.00987,-0.08642,-0.10873,0.00494,-0.07735,0.03791,0.06293,0.04436,-0.06773,0.01288,-0.01127,-0.0341,0.01609,-0.02487,-0.0101,0.02451,-0.05844,0.01312,0.0648,-0.04438,0.03641,-0.00629,0.04404,-0.02093,-0.11009,0.06214,-0.03555,0.0748,-0.03816,-0.10884,0.06615,0.14641,0.07114,0.08308,-0.00869,0.05982,0.04156,-0.01893,0.02091,0.04358,0.06218,-0.0595,-0.12639,-0.07649,0.06332,0.03775,-0.03099,0.03176,0.12771,-0.0047,-0.02834,-0.0024,-0.08477,0.11494,-0.05288,0.07335,-0.14148,0.03541,0.00724,0.04627,-0.01062,-0.03466,0.03146,-0.06123,-0.05496,-0.05461,0.00257,0.03329,0.00861,-0.08542,0.10026,0.02184,0.02553,-0.08644,-0.01885,-0.05249,0.09344,-0.05117,0.00935,-0.0113,0.01076,-0.02281,-0.03405,0.08832,-0.02699,-0.04151,-0.13255,0.06753,-0.004,-0.17201,-0.03214,-0.03296,0.03948,-0.08764,0.07696,-0.05675,0.08805,-0.0183,-0.02151,-0.10272,-0.00258,-0.05964,-0.03282,0.11144,0.06847,0.11613,0.0675,-0.02398,0.02623,0.10877,0.08385,-0.01173,0.10139,-0.0172,-0.08159,-0.04541,-0.00952,0.09337,0.01121,0.04171,-0.0256,0.02432,0.04189,0.071,0.06574,-0.00161,0.10995,-0.05476,-0.0617,0.01141,0.07668,-0.08037,0.04389,-0.03373,0.02282,-0.04352,-0.01331,-0.00956,-0.03367,-0.04861,0.0224,-0.06881,0.07922,-0.00438,-0.06018,-0.03549,0.04058,0.02626,0.01192,-0.01376,0.11177,0.15105,0.01666,0.01515,-0.0007,0.02913,0.00145,-0.10224,0.00567,0.0036,0.06216,0.00126,-0.0656,-0.01874,0.06058,-0.07411,-0.02744,-0.03358,0.07819,-0.12017,-0.10958,0.01901,0.10439,0.01188,0.02587,-0.02825,0.03415,-0.02227,0.1234,-0.0705,0.07396,-0.03497,-0.07447,-0.08044,-0.06572,0.05833,0.00944,-0.10402,0.09931,-0.00426,-0.08342,-0.03153,0.02419,-0.11198,-0.01468,0.07949,0.00918,0.02738,-0.03127,0.00279,-0.05774,0.00203,0.08441,-0.0199,0.09827,0.06157,-0.10879,0.01658,-0.0393,0.14589,0.02709,-0.02113,0.00598,0.00544,0.07443,0.09494,-0.01646,0.14721,0.05415,-0.02936,0.01049,-0.06236,-0.01926,0.01,-0.03073,0.03041,0.01544,0.10751,-0.07216,-0.03437,-0.07339,-0.10663,0.05624,-0.0304,0.01005,-0.05887,0.02176,0.02326,0.03783,0.02688,0.13595,0.00574,0.05992,-0.00833,0.04354,0.00979,0.07917,0.00649,-0.06273,-0.06339,0.00531,-0.15005,-0.01549,-0.08843]},{"domain":"geometry","key":"min_area_rectangle","name":"Minimum-area enclosing rectangle","package":"geometry-ai999x","example":"Find the minimum area bounding rectangle of the points (0, 0), (2, 2), (4, 0), (2, -2).","v":[-0.06892,-0.12962,0.10708,-0.03735,-0.05674,-0.05474,0.02164,0.01512,0.01971,-0.01198,-0.00605,0.02743,-0.00151,-0.06381,-0.01965,-0.0422,0.16433,-0.03604,-0.00033,0.11963,-0.02122,-0.03852,0.0377,-0.00403,0.0561,0.15587,0.02918,0.03827,0.00685,0.02879,0.02054,0.05705,0.0342,-0.1052,-0.04932,-0.04765,0.06164,0.01486,-0.04193,0.03807,0.04668,0.11581,-0.02162,-0.04348,0.04847,0.10372,0.03446,0.02738,-0.031,0.09188,0.08679,-0.0589,0.05242,0.03249,-0.06865,0.01071,0.01862,0.03278,0.09015,0.02604,0.00706,-0.00351,-0.0574,0.11049,-0.00169,0.0817,-0.15594,0.18138,0.01311,0.02746,-0.08402,0.04052,-0.06563,-0.08506,-0.08034,0.04824,0.09232,0.00791,-0.01581,0.0615,0.04364,0.00755,0.02328,-0.08116,-0.05073,0.09768,0.02128,0.08206,0.05369,0.0251,-0.01291,0.02065,-0.00282,-0.00477,-0.05547,-0.03516,0.10088,0.07207,0.04916,0.08423,-0.07744,0.13295,-0.05952,-0.09924,-0.06117,-0.05572,-0.1397,-0.03249,-0.15796,0.00085,-0.09272,-0.0768,0.03867,0.0428,-0.03757,0.02966,-0.0841,0.09113,0.00076,0.12224,0.01516,0.03372,0.06958,0.04316,-0.0881,0.02152,-0.04343,-0.02088,0.08134,-0.05226,-0.01509,-0.04682,0.09284,-0.00154,-0.03396,-0.05979,0.01746,0.06112,-0.00211,0.05321,0.02095,-0.09651,-0.02504,0.07135,-0.02792,-0.1261,-0.06098,-0.03959,0.00577,-0.09731,-0.02388,-0.03153,-0.04706,-0.06238,0.02933,-0.02738,0.01778,-0.00117,0.01839,0.07081,-0.0192,0.03515,-0.01493,0.10438,0.07304,-0.0259,0.05657,0.05443,0.01287,-0.02169,-0.14504,-0.00125,0.07448,0.05446,-0.042,-0.08911,0.04532,0.03135,0.00512,-0.01695,0.01002,-0.00877,-0.01966,0.00992,0.00698,-0.01216,-0.03257,-0.02427,0.02871,-0.03423,-0.11229,-0.09274,0.10751,-0.03425,-0.01464,0.01341,0.01564,-0.01568,0.03492,-0.1051,0.00176,-0.04608,0.00823,-0.07708,-0.00509,0.07085,-0.00818,-0.00412,-0.09792,0.03611,0.00052,-0.09339,0.22791,0.04954,0.00563,0.03469,-0.03345,-0.06885,0.00188,-0.06571,-0.09798,0.08579,-0.12731,-0.06538,0.0495,0.05631,-0.11834,-0.00191,-0.00668,-0.04446,0.04388,0.03262,-0.06799,-0.00238,-0.06835,-0.01116,-0.00341,-0.02624,-0.08153,-0.0215,0.05987,-0.00954,-0.00048,-0.01202,0.01782,-0.0105,0.0432,0.02153,-0.10108,0.00453,0.06369,-0.02924,-0.02856,-0.01585,0.12682,-0.04063]},{"domain":"geometry","key":"min_enclosing_circle","name":"Smallest enclosing circle of points","package":"geometry-ai999x","example":"Find the smallest enclosing circle of the points (0, 0), (4, 0), (2, 1).","v":[-0.08073,-0.00855,0.01576,-0.00446,-0.08099,-0.0037,-0.01229,0.09335,0.07797,-0.06746,-0.03204,-0.05595,0.00219,-0.0574,-0.02693,-0.02679,0.13432,-0.03859,-0.00148,0.04464,0.01984,-0.06841,-0.01838,-0.1304,-0.00215,0.10271,-0.01416,-0.02651,-0.03878,0.05116,0.0828,-0.03218,0.0176,-0.06217,-0.03253,-0.14417,0.02105,0.02247,-0.01844,0.07852,0.0422,0.15017,-0.02197,0.0241,-0.01061,0.19824,0.00935,0.0793,-0.01682,0.00825,0.15114,-0.09172,0.01007,0.09687,-0.09881,0.0019,0.02056,-0.02674,-0.01139,0.03534,0.02141,-0.02949,-0.05248,0.16707,-0.01865,0.00972,-0.12738,0.09879,0.00169,0.09482,-0.0943,-0.00811,-0.08614,-0.13185,-0.08097,0.09269,-0.07882,0.0341,0.02013,0.06498,0.03311,0.07736,0.07063,-0.06617,0.01062,0.04661,0.01536,0.02359,0.03789,-0.00342,0.01402,0.06942,0.04866,-0.02494,-0.02004,-0.02247,0.00673,0.10896,-0.00084,0.05917,-0.06933,0.00871,0.04025,-0.12465,-0.03752,0.00149,-0.10913,-0.08653,-0.09422,0.01735,-0.01686,0.00449,0.08097,0.06712,0.01097,-0.00567,0.01074,0.02385,0.01054,0.0982,0.05011,-0.10569,-0.00372,0.02171,-0.11759,-0.01735,0.04553,-0.03161,0.08492,-0.06759,-0.03039,-0.10542,0.03481,0.02519,-0.01751,-0.02552,-0.08821,0.01769,0.00457,0.03296,0.0176,0.03947,-0.00985,0.05048,0.08176,0.01937,0.04489,-0.03455,-0.07072,-0.01896,0.02789,0.02273,0.05237,0.0161,0.09139,-0.03814,0.05993,0.06264,0.03589,0.11351,-0.00956,0.03809,-0.07005,0.00163,0.08672,-0.02665,0.08632,-0.08288,0.05749,-0.00249,-0.08051,-0.00645,-0.0483,-0.03231,-0.06684,-0.07397,-0.03948,0.08234,0.0718,0.03989,-0.00217,0.05475,0.09983,-0.01575,-0.00541,-0.10243,-0.02285,0.04842,-0.005,0.03153,-0.01242,-0.09979,0.03688,-0.04594,0.00479,0.0247,0.0144,0.00446,0.06728,-0.10439,-0.09245,0.02118,0.0013,-0.06956,-0.07268,-0.04161,0.09609,-0.0106,-0.05468,-0.01534,0.0024,-0.06153,0.25062,0.02477,-0.0925,-0.04398,-0.05968,-0.02591,0.02279,0.06253,-0.10872,0.07868,-0.04165,-0.00621,0.00967,0.07087,-0.03916,0.04248,0.00192,0.03272,0.03192,0.09196,-0.02423,0.03629,-0.13339,-0.07272,-0.07578,-0.07894,-0.02921,-0.02861,0.04806,0.00851,-0.03496,-0.06889,-0.01712,-0.01562,-0.08165,0.00997,-0.14927,-0.00745,-0.00233,-0.00379,0.02993,-0.02008,0.00824,-0.02612]},{"domain":"geometry","key":"nearest_neighbor","name":"Nearest neighbour of a query point","package":"geometry-ai999x","example":"Which of the points (0, 0), (5, 5), (2, 3) is nearest to the point (3, 3)?","v":[-0.13335,-0.03153,0.08494,-0.1338,-0.04818,-0.10594,-0.04903,0.05822,0.01821,-0.10087,-0.17656,0.00552,-0.00762,-0.00422,-0.05023,0.00104,0.0853,-0.05097,-0.02857,-0.02632,0.01694,-0.06497,-0.00419,-0.10999,-0.01193,0.07819,-0.10571,-0.01257,-0.04759,-0.01917,0.06354,0.08082,-0.00791,-0.01486,0.0134,-0.0357,0.06784,0.01661,-0.02127,0.02851,0.03001,0.12392,-0.02538,0.02624,-0.15857,0.10645,-0.02901,0.04115,-0.03292,-0.00529,0.06591,0.01362,-0.03954,-0.00939,-0.08386,-0.0207,0.07507,0.04844,0.04888,-0.02571,-0.02341,-0.12868,-0.11265,-0.03,-0.07559,0.0183,-0.02645,0.1397,-0.03173,0.20405,-0.08152,-0.05751,-0.0204,-0.12238,-0.07896,0.01224,0.05671,-0.03948,0.10481,-0.02648,-0.06224,-0.03126,0.07791,0.00688,-0.01717,0.024,0.02237,-0.03575,0.09059,0.00017,0.011,-0.00507,0.04412,0.05191,0.02414,-0.00299,0.07828,0.12633,-0.04508,0.00383,-0.05822,-0.00126,-0.00051,-0.05011,-0.11989,-0.00717,-0.07437,-0.05881,-0.04024,-0.07945,-0.01643,-0.08281,-0.02946,0.08334,0.10049,0.00768,0.08358,0.09886,-0.00361,0.025,0.07768,-0.01558,0.02495,0.00578,-0.00657,-0.00893,0.00766,0.07211,0.12166,-0.03776,0.06164,-0.03186,0.02847,0.00064,0.07512,0.04289,-0.0175,0.08504,-0.05707,-0.01438,-0.06717,0.0545,0.00522,-0.08306,0.06762,-0.00728,0.03066,0.02417,0.01671,-0.05455,0.03049,0.01641,0.02386,0.0865,0.10286,-0.04015,0.03285,0.00429,-0.02989,0.09131,-0.07233,-0.02381,-0.06138,0.05965,0.13591,-0.03159,0.02376,-0.15063,0.02733,-0.04947,-0.12781,-0.09169,-0.06713,-0.05762,0.05042,0.00413,0.02489,-0.02113,0.04198,0.10096,0.0355,0.04633,0.03184,0.02841,-0.01099,0.01855,0.04247,0.00362,-0.01472,0.03793,0.03811,-0.05745,0.04791,0.1175,-0.0199,0.0619,-0.01766,0.01572,0.01522,-0.08624,-0.04811,0.07073,0.05672,-0.02094,0.02627,-0.00704,0.03059,-0.03857,0.02522,0.06441,0.00462,-0.07629,0.11523,-0.00812,-0.12921,-0.06048,0.01889,0.0562,0.00687,0.07068,0.0629,0.05306,0.02998,0.06309,0.03068,0.11377,0.03881,-0.06689,0.01309,0.06181,-0.04252,0.06573,-0.01433,0.0042,-0.04637,-0.04493,0.0546,0.02682,-0.01056,0.01655,0.03693,-0.06592,-0.05671,-0.03555,-0.16451,-0.13094,-0.0083,0.09293,-0.02343,0.04829,0.04417,0.02024,-0.09743,-0.0803,-0.01661,-0.07015]},{"domain":"geometry","key":"parabola_arc_length","name":"Arc length of a parabola","package":"geometry-ai999x","example":"Find the arc length of y = x^2 from x = 0 to x = 1.","v":[-0.11257,-0.0717,0.00163,-0.04897,0.06398,-0.04172,0.01602,0.02573,0.06953,0.01511,0.11513,-0.04169,-0.01325,0.01191,0.01821,0.0489,0.06156,-0.05868,-0.02394,-0.03885,-0.07546,-0.01208,0.09929,0.01103,0.02143,-0.02593,0.0541,0.01533,0.03757,0.02113,-0.02504,0.00369,-0.05913,0.11324,0.0467,-0.05993,0.01212,-0.03671,0.06259,0.01794,0.00117,-0.00275,0.00228,-0.02585,0.04027,-0.06515,0.01506,0.00569,-0.00532,-0.0516,0.02401,0.08938,-0.02997,-0.05246,-0.12777,0.03657,0.10452,0.08223,0.05559,-0.009,0.0481,-0.03793,0.00736,0.06174,-0.13557,0.06945,0.01199,-0.02582,-0.07115,-0.07768,-0.01177,0.00914,0.00201,-0.04532,0.02203,0.02667,0.03504,-0.00516,0.06359,0.04334,0.02514,-0.05164,0.04184,0.01881,0.12513,0.07051,-0.01453,-0.02798,0.13957,0.01996,0.01226,-0.13304,0.01678,0.07147,-0.05025,-0.08895,0.07107,-0.06036,-0.01473,0.04698,-0.094,0.06146,-0.0421,-0.01106,0.04839,-0.13105,-0.14639,-0.05677,0.05031,0.02833,0.01133,0.04431,0.03328,-0.08959,0.03697,-0.11857,0.03611,-0.00693,-0.04334,0.09212,-0.09821,0.03948,0.00705,-0.08288,-0.0156,0.02458,0.01117,0.01707,0.02925,0.03221,0.08142,0.06621,0.09535,-0.05738,-0.07384,0.10647,0.05888,0.09815,0.03812,0.0877,0.02573,-0.07904,0.1489,-0.03833,-0.02633,-0.03118,0.0828,-0.03884,0.05761,-0.01681,0.03686,0.00969,0.00816,-0.00758,0.01507,-0.03809,0.00724,-0.11148,0.11112,0.01784,-0.07372,0.03473,-0.04604,0.09446,0.01614,0.03361,0.11249,-0.05468,-0.07106,0.00186,0.02034,0.05027,0.06536,-0.01848,-0.12896,-0.14231,-0.11,-0.01111,-0.02124,0.09555,0.07624,-0.09948,-0.05958,-0.06667,-0.10256,0.13147,-0.00292,-0.09415,-0.01886,-0.08033,0.08909,-0.05469,-0.01933,0.00962,0.01585,-0.131,-0.06327,-0.15206,0.07058,-0.02934,0.1302,0.04766,-0.00232,0.0368,0.08796,0.0009,-0.01871,-0.0648,-0.06539,0.02684,-0.07784,0.01396,0.06307,-0.00832,0.0564,0.08398,-0.03183,-0.00683,-0.08909,0.10802,0.06068,-0.01042,-0.11944,0.0183,0.11384,-0.11061,0.01112,0.09865,-0.08349,-0.09056,-0.03688,-0.04977,0.03582,-0.06882,0.04085,0.02127,0.02765,0.04434,0.00292,-0.07018,-0.06791,0.02988,-0.01904,-0.0314,0.06133,-0.01645,-0.05844,0.06314,0.05903,-1e-05,0.02763,0.04009,-0.01757,-0.03474,0.01588,0.00076]},{"domain":"geometry","key":"pick_lattice_points","name":"Pick's theorem: lattice points of a polygon","package":"geometry-ai999x","example":"How many lattice points are inside the polygon with vertices (0, 0), (4, 0), (4, 3), (0, 3)?","v":[-0.02223,-0.15913,0.18009,0.00392,0.02023,0.01952,0.01644,0.03567,-0.00458,-0.00365,0.02408,-0.0476,-0.13035,-0.0049,-0.06159,0.03662,0.05804,-0.03531,-0.04763,0.10586,0.03479,-0.07404,0.06441,0.06249,-0.0542,0.17537,-0.0135,0.06714,0.01391,0.03644,-0.03622,-0.00129,-0.09328,-0.09264,-0.0695,-0.01207,-0.05373,-0.05955,-0.07836,-0.05351,0.03525,0.09744,0.0303,-0.01614,-0.00697,0.02806,-0.0933,0.11097,-0.09192,0.0407,0.07017,-0.03074,0.10471,-0.01519,0.03394,0.03736,-0.13764,0.00176,0.07451,-0.00097,0.03489,0.04706,-0.09429,-0.01309,-0.01007,-0.07048,-0.06268,0.10254,0.02045,-0.00374,-0.08192,0.041,-0.01733,-0.01057,0.01339,0.019,0.047,0.05518,-0.13467,-0.03392,-0.03997,-0.06838,0.01265,0.00491,-0.01985,0.0189,0.00534,0.00537,-0.00748,-0.03261,0.0231,-0.01539,-0.05408,0.05817,-0.04757,0.05064,0.11946,0.12504,0.03588,-0.00946,-0.00344,0.12294,0.0243,-0.05471,0.01657,0.01134,0.03411,-0.06523,-0.12374,0.01439,-0.09842,-0.11824,-0.0846,0.05246,0.02588,0.09263,0.08565,-0.02036,0.0325,0.05603,-0.00111,0.04973,0.02056,-0.06218,-0.02357,-0.01879,-0.09162,0.0551,-0.04308,-0.04276,0.0137,0.05163,0.12417,-0.00417,0.02536,0.04327,0.05166,0.00034,0.07345,-0.06114,-0.02338,-0.10354,-0.01441,0.0346,0.02162,-0.10139,-0.11891,0.01062,0.0495,-0.04372,0.01219,-0.04152,0.09822,-0.01144,-0.01412,0.07588,-0.09153,-0.01119,0.01785,-0.01394,0.02623,-0.01001,0.01556,0.10228,0.13608,-0.00111,0.04348,0.04311,-0.02395,-0.10553,-0.0488,-0.01165,0.0418,-0.00697,0.07209,0.00225,-0.03198,0.06254,-0.13521,-0.02809,0.02385,0.03333,-0.0544,-0.0095,0.02442,0.03954,-0.0696,-0.0286,0.03792,-0.02944,-0.10766,0.01623,0.06367,0.12122,0.04636,-0.03822,0.03,-0.02647,0.03234,-0.01981,-0.01144,-0.06919,0.05234,-0.04485,0.13456,0.05716,-0.05749,0.01681,-0.06183,0.10428,0.08098,-0.07203,0.23198,0.05045,-0.01616,0.00877,0.06487,-0.04934,-0.08487,-0.07531,-0.02886,0.0239,-0.09052,-0.01244,0.08638,-0.02374,-0.01196,-0.0128,-0.07317,-0.05666,-0.0244,-0.03833,-0.14113,-0.05899,0.04652,-0.00863,-0.02737,0.03858,0.01871,0.03048,0.05318,0.00397,0.00095,0.09432,0.0303,-0.0818,0.02569,-0.06414,0.01488,-0.0507,0.0229,-0.11562,-0.02407,0.03627,0.09349,-0.01319]},{"domain":"geometry","key":"plane_through_points","name":"Plane through three points","package":"geometry-ai999x","example":"Find the equation of the plane through (1, 0, 0), (0, 1, 0) and (0, 0, 1).","v":[-0.09617,-0.03206,-0.02018,-0.09315,0.0206,0.03387,-0.13371,-0.02187,-0.00168,0.04817,0.02106,-0.00838,-0.03319,-0.05217,-0.05692,-0.07425,0.0448,0.02182,-0.01537,0.03455,0.0108,-0.12245,0.02537,0.03077,0.0628,-0.06008,-0.10046,0.12851,0.02444,0.04224,0.02355,-0.00734,0.01509,0.06236,0.002,0.00498,0.08098,0.05527,-0.01184,0.02942,-0.02572,-0.03698,-0.06303,-0.05407,-0.15651,-0.08322,0.03798,0.00208,-0.12326,0.07667,0.11717,-0.06287,-0.05351,0.06126,-0.06974,-0.0104,-0.00945,0.0443,-0.04654,-0.06112,0.07902,-0.02262,-0.0932,-0.00462,0.05152,-0.03239,-0.07768,-0.01647,-0.03077,0.0454,-0.0047,-0.01297,0.1309,0.10099,-0.06795,-0.04431,0.10513,-0.07335,0.19805,0.03486,0.00453,-0.06736,-0.02888,0.03577,-0.04008,0.08849,0.01259,-0.0607,-0.06247,-0.0214,0.09224,-0.13703,-0.12846,-0.05261,0.00388,0.00722,0.00704,-0.02526,0.07223,-0.12228,-0.11192,-0.05011,0.0287,-0.10439,-0.02452,0.12119,0.06302,-0.01165,0.04858,-0.06093,0.05447,0.06415,0.06932,0.0313,0.05355,-0.07353,-0.00485,-0.04806,-0.07372,0.09788,-0.09241,0.11681,0.02602,-0.03077,-0.02794,0.05369,0.14415,0.056,0.08124,-0.14482,-0.06574,-0.00851,0.03339,-0.05967,0.01144,-0.08803,-0.02566,0.039,0.02013,0.04454,-0.08041,-0.00213,-0.03383,0.03305,0.01757,0.0027,-0.01235,-0.02246,0.05181,0.02651,0.05252,0.00221,0.03083,0.15074,-0.00094,0.02138,-0.01379,-0.01624,0.05021,-0.01193,0.06343,0.09681,0.06225,0.05922,0.13299,0.00176,0.05203,0.03519,-0.05441,-0.07814,0.03764,-0.12797,-0.03214,0.00436,0.03128,-0.02495,-0.04561,-0.03755,-0.02447,0.03732,0.08035,-0.08936,-0.03533,0.01342,0.00422,-0.03125,0.00234,-0.03097,-0.02513,-0.11367,0.09315,-0.06515,-0.01106,-0.0054,0.03061,-0.0707,0.02769,0.07511,0.00162,0.06238,-0.06339,-0.03803,-0.03154,-0.04887,0.08595,-0.08309,0.13047,0.08664,-0.0185,0.01276,0.01995,0.13084,0.03454,-0.09706,0.03165,0.07376,0.08341,0.14639,-0.03629,0.11453,-0.0515,0.03545,-0.03374,-0.05673,0.03175,0.02414,-0.05862,-0.02533,-0.02493,-0.00851,0.01871,-0.04532,-0.03863,0.02125,-0.0302,0.07392,-0.00839,0.00776,0.00242,0.01353,-0.02833,0.03114,0.04767,0.00972,0.07855,0.05159,0.01645,0.04245,0.04007,0.06871,0.03736,0.01142,-0.01178,-0.0427,-0.05956,-0.09707]},{"domain":"geometry","key":"platonic_solid","name":"Platonic solids: counts, Euler characteristic, volume, surface, radii","package":"geometry-ai999x","example":"Find the volume and surface area of a regular icosahedron with edge 2.","v":[0.01981,-0.11971,0.03609,-0.09478,0.13737,-0.02416,0.05575,0.0622,0.09191,0.03931,0.10464,-0.044,-0.01498,0.03946,-0.09397,0.09923,0.08211,-0.06673,-0.06737,0.02055,0.09477,-0.04378,-0.02714,0.08059,0.04269,-0.00241,0.08106,-0.01539,-0.02586,-0.06845,0.00548,0.00533,0.05831,-0.118,0.00279,-0.14024,0.10109,-0.03994,0.01014,0.04707,-0.04561,0.02592,-0.03649,0.00207,-0.0131,-0.03491,-0.01844,-0.02657,-0.09349,-0.07113,0.08463,-0.04045,0.07541,-0.0569,-0.07478,-0.01076,-0.10209,0.06795,-0.07686,-0.00838,0.12435,0.06431,-0.04687,0.07588,0.06706,0.01619,0.07936,-0.06382,0.00353,0.08871,0.0319,0.04172,-0.14943,0.05184,-0.02434,0.01509,0.02371,0.00176,-0.02286,-0.04377,-0.01534,0.02744,-0.03427,0.02164,0.053,0.18352,-0.01131,0.04597,0.01716,-0.09194,0.0772,-0.09761,-0.04115,0.02166,-0.10495,0.054,-0.07445,0.00925,0.10502,0.02412,0.01028,0.0816,0.06822,-0.01231,-0.0871,0.06389,0.03262,-0.058,0.07231,0.00276,-0.00553,-0.05888,-0.00546,0.08653,-0.04673,-0.04306,0.05122,0.01551,-0.0605,-0.01691,0.10991,0.03907,-0.03257,-0.03103,0.03773,0.00318,-0.02363,0.00774,-0.05937,-0.04905,-0.03603,-0.01154,0.04321,-0.0145,-0.01939,0.09073,-0.05178,0.00546,-0.07013,-0.03571,0.08193,0.00742,0.0529,-0.03453,-0.04287,-0.04746,-0.04745,0.00944,-0.02992,0.01935,0.01202,0.08797,0.07231,-0.09453,-0.09194,0.10026,-0.0677,-0.03177,0.05188,-0.0227,-0.05428,-0.02733,-0.00082,0.07711,-0.00777,0.13709,0.00819,0.13058,0.07262,0.01003,0.00163,0.04304,-0.09617,0.08275,-0.03498,0.03983,-0.05683,-0.02427,0.03917,-0.02867,0.06803,-0.02857,0.11899,0.04666,0.01933,0.03844,-0.00222,-0.04026,0.05197,0.02616,0.0497,-0.03977,0.00227,0.02364,0.06935,0.0176,0.06005,0.04194,-0.05056,-0.05387,-0.03146,-0.09857,0.10905,0.07795,-0.03876,-0.06879,-0.01065,-0.11787,-0.02966,-0.03229,-0.07162,-0.09689,0.10491,-0.04335,-0.07411,-0.00514,-0.09116,-0.07013,0.07128,-0.06471,-0.02441,0.03427,0.01811,-0.1094,0.07458,-0.08954,-0.04649,0.03827,-0.10094,0.05494,0.04392,0.04922,-0.08648,-0.00753,-0.01222,-0.04442,-0.02621,-0.10154,-0.10799,-0.0248,0.06498,0.00638,0.09174,0.03748,0.07963,-0.06519,0.00904,0.02373,-0.01243,0.08718,0.0865,-0.16432,-0.0415,0.01446,-0.08352,-0.03292]},{"domain":"geometry","key":"point_in_polygon","name":"Point in polygon test","package":"geometry-ai999x","example":"Is the point (2, 3) inside the polygon with vertices (0, 0), (5, 0), (5, 5), (0, 5)?","v":[-0.01174,-0.01763,0.08056,-0.08788,0.03246,-0.02751,0.01139,-0.01013,-0.0363,-0.05306,-0.03547,0.03081,-0.10156,-0.03894,-0.02957,0.02273,-0.00264,-0.07497,-0.01368,0.03104,-0.05364,-0.05048,-0.05786,-0.03024,-0.02101,0.03692,0.01454,0.05897,0.11873,0.05672,0.13363,0.05515,-0.01562,-0.05992,-0.09277,-0.06976,-0.11772,-0.11497,-0.09511,-0.00552,-0.06142,0.02673,-0.0657,0.07408,-0.0156,0.06146,-0.08866,0.08668,0.05455,0.05744,0.13258,-0.09206,0.09302,0.03309,-0.02938,0.08177,-0.07336,-0.00102,-0.06287,0.01547,-0.06663,-0.03769,-0.04439,-0.01859,-0.05184,-0.02034,-0.01753,-0.04195,0.06593,0.03323,-0.03703,0.03027,0.0289,-0.09847,0.10608,-0.08008,0.06587,0.0341,0.02077,0.00149,-0.07047,0.00985,0.11392,0.00964,0.04312,0.09382,0.04204,-0.10387,0.06124,-0.05953,0.06219,0.10551,-0.06087,0.03284,0.0693,0.10332,0.11731,0.09787,-0.02846,-0.03382,-0.00756,-0.00391,0.03024,-0.06787,-0.03626,0.03538,0.08382,-0.01794,-0.07622,0.00862,-0.03461,-0.03064,-0.00173,-0.05571,0.05742,0.03526,0.06164,-0.00243,-0.02105,-0.01283,0.01191,-0.03783,-0.13411,-0.06879,0.07346,0.07445,-0.00145,0.03161,0.03978,0.01397,0.01055,-0.05178,0.1116,0.00138,0.01183,-0.04463,-0.02331,0.09476,-0.00062,-0.05372,0.0432,-0.07039,-0.0052,-0.08341,0.08894,0.00272,-0.14222,-0.06614,-0.0313,0.03169,0.04187,0.04198,0.10924,0.01252,-0.00534,-0.02907,0.02147,-0.02876,-0.02235,-0.0492,0.00795,-0.11836,-0.10206,-0.02966,0.08598,-0.01528,0.07504,-0.13883,0.10891,-0.0953,-0.08689,0.00072,-0.12857,-0.01331,0.03477,0.02904,0.03674,-0.1052,-0.05418,0.00925,0.12184,0.05914,-0.03777,-0.04177,-0.00215,-0.04454,-0.01111,-0.03127,0.05936,0.04046,-0.02336,-0.04267,0.02008,0.0279,0.01908,-0.04586,-0.04247,0.09397,0.05659,0.09508,-0.15413,0.06457,0.05489,0.03922,0.05351,0.0053,0.02486,0.092,-0.07471,0.09857,-0.00336,0.07943,0.1805,-7e-05,-0.02861,-0.02622,0.07531,0.0787,-0.03912,-0.05506,-0.00785,0.0971,-0.05934,-0.02418,-0.05171,0.03324,0.00077,-0.041,0.01028,0.08047,-0.06162,-0.04815,-0.03306,0.02674,-0.04122,-0.12492,-0.03502,0.0422,-0.02285,0.0772,-0.02961,-0.03408,0.08119,0.06272,0.03093,-0.11749,0.044,0.02581,0.03195,0.01249,0.02128,-0.12687,0.00056,0.10084,0.03961,-0.06957]},{"domain":"geometry","key":"point_plane_distance","name":"Distance from a point to a plane","package":"geometry-ai999x","example":"Find the distance from the point (1, 2, 3) to the plane 2x - y + 2z = 3.","v":[-0.02633,-0.01041,-0.0068,-0.03253,-0.02358,-0.00857,-0.12592,0.00742,0.01877,0.1113,-0.07291,-0.06376,0.02405,0.00612,-0.07191,-0.00197,0.07444,0.04344,-0.01707,0.04235,0.03304,-0.1488,0.03876,-0.04195,0.07687,-0.08317,-0.1152,0.03794,0.06476,0.07079,0.07143,0.00947,0.00643,0.0642,0.01826,0.08134,0.06844,0.02706,-0.02547,0.0527,-0.04467,-0.04671,0.07092,0.02796,-0.1211,-0.08413,0.0147,-0.02789,-0.03595,0.02948,0.16794,0.03971,0.0336,0.08482,0.009,0.04343,-0.03507,0.05526,-0.02612,-0.06615,0.03087,-0.08205,-0.05719,-0.05703,0.0112,-0.08912,-0.07092,0.00426,-0.03706,0.039,0.06388,-0.0149,0.00696,-0.03787,0.00122,-0.01055,0.08594,-0.14138,0.14033,0.02912,-0.01773,-0.02499,0.05068,-0.01388,0.00229,0.09554,-0.01534,-0.07677,-0.05748,0.0573,0.02981,-0.09045,-0.09849,0.01474,0.03295,-0.01965,0.03631,-0.01633,0.03089,-0.04364,-0.05266,-0.07801,0.02995,-0.03507,-0.1,0.10148,-0.01123,-0.02005,0.0417,-0.0461,0.12125,0.05964,0.0778,0.06399,0.14591,-0.11626,-0.05093,-0.00851,-0.11147,0.06368,0.06616,0.05639,-0.00865,0.0055,0.03921,0.09651,0.042,0.04372,0.16471,-0.09005,-0.05774,0.01142,0.12261,-0.11607,0.00574,-0.00906,0.05189,-0.06325,-0.00247,0.04316,0.00949,-0.04348,0.0534,-0.02609,0.07174,-0.00163,-0.03082,-0.07246,0.05601,-0.01592,0.01246,0.0363,0.03487,0.09792,0.03535,-0.03873,0.05943,-0.01415,0.07046,-0.08336,0.0122,0.06588,-0.03614,0.04503,-0.02647,-0.0745,0.0445,-0.0434,0.00967,-0.03041,0.0175,-0.06672,-0.06552,0.07024,0.04313,-0.01619,-0.05162,-0.03506,0.09149,0.13882,0.1601,-0.04335,0.05274,-0.03105,0.01255,-0.06082,-0.02023,-0.04217,0.02246,-0.1418,0.08609,-0.13567,-0.0322,-0.03052,-0.01897,-0.03306,-0.00141,0.10997,0.04498,-0.0685,0.00981,0.02725,0.03234,-0.02605,0.01258,-0.06566,0.0784,-0.08791,-0.02428,-0.02558,-0.15866,0.05666,0.09995,-0.094,-0.0013,0.03208,0.00159,0.13875,-0.00657,0.11808,0.08365,-0.00081,0.0296,0.01186,-0.06694,0.00152,-0.03452,0.03079,0.00433,0.06754,0.02326,-0.07548,0.00889,-0.00478,-0.10455,0.05405,-0.04619,0.00694,-0.00292,-0.05568,0.04064,0.06146,0.03384,-0.04519,-0.03374,-0.00173,-0.04159,0.04805,-0.00523,0.03115,0.06975,0.01791,-0.01892,-0.13227,-0.04412,-0.09615]},{"domain":"geometry","key":"point_segment_distance","name":"Distance from a point to a segment","package":"geometry-ai999x","example":"Find the distance from the point (3, 4) to the segment from (0, 0) to (6, 0).","v":[-0.09571,-0.00757,0.069,-0.11872,-0.00456,-0.11919,0.00106,0.0004,-0.01484,-0.03637,-0.15069,-0.03117,0.05996,0.00746,-0.05825,-0.03871,0.05814,-0.08287,-0.07265,0.0302,-0.03542,-0.06809,0.03977,-0.05873,0.10634,0.03029,-0.10044,0.0923,-0.00023,0.10994,0.08775,0.0792,-0.07519,0.0446,-0.01229,-0.0443,0.01551,-0.05605,-0.1031,0.01195,0.01683,0.06196,0.08466,0.03855,-0.07186,0.10669,-0.04891,0.06888,-0.01751,0.02793,0.11959,0.00691,-0.03986,-0.05129,-0.04159,0.00796,0.03338,0.07759,0.04872,-0.0533,-0.01072,-0.14218,-0.05801,-0.01402,-0.11271,0.00237,-0.02132,0.11332,-0.05306,0.10738,-0.03464,-0.00489,-0.02596,-0.19063,-0.0242,0.01069,0.07565,-0.01845,0.06339,0.00896,0.0257,-0.00756,0.0308,0.04804,0.0455,-0.01322,0.05967,-0.00829,0.11503,0.07635,-0.0433,-0.05965,0.03315,0.03517,0.05776,-0.01996,0.08801,0.09153,-0.04634,0.0338,-0.0147,0.00237,0.0532,-0.02211,-0.13291,-0.07736,-0.09494,-0.06795,-0.02544,-0.0493,0.02809,0.01212,0.09263,0.00815,0.02604,-0.07437,-0.0242,0.04451,-0.03506,0.0235,0.09455,0.02835,0.04106,-0.04382,-0.05341,0.01756,-0.03658,0.05775,0.16725,-0.03207,0.10857,-0.00925,0.03995,0.03843,0.02487,0.00189,0.02638,0.10188,-0.10476,0.05396,-0.02235,-0.00885,0.12909,-0.06723,0.05927,0.04323,0.03724,0.00781,-0.04949,-0.01187,-0.01047,-0.06934,0.04954,0.03236,0.14491,-0.07904,0.04704,-0.08244,0.04464,-0.01215,-0.06337,0.02354,-0.01602,0.05037,0.04666,-0.01148,0.03224,-0.12466,0.00815,-0.03453,-0.13672,-0.04534,-0.02064,0.02635,-0.06254,-0.08799,0.00527,-0.06688,0.00278,0.13932,0.04725,0.03846,0.02829,0.00598,-0.04642,-0.00047,-0.00065,-0.01024,0.05145,-0.00085,-0.12309,-0.13348,0.02252,0.05389,0.01954,-0.04338,-0.00383,0.04045,0.10601,-0.06741,-0.00801,0.07105,0.07369,-0.04942,0.03386,-0.03053,0.01165,-0.08248,-0.00719,-0.01646,-0.09729,-0.01348,0.09494,-0.00808,-0.04805,0.04045,-0.05558,0.10502,0.00085,0.13404,0.08525,-0.01856,0.01329,0.05087,0.02301,0.04265,-0.00108,0.04637,0.02722,0.01725,-0.00373,-0.03256,0.00057,0.01323,-0.09969,-0.01646,0.02111,-0.0613,-0.06347,-0.07335,0.00148,0.02732,0.01405,-0.07185,-0.08214,-0.1049,-0.03791,0.08943,-0.04724,-0.04306,0.11022,0.01185,0.00822,-0.13817,-0.00323,-0.04691]},{"domain":"geometry","key":"polygon_area","name":"Polygon from vertices: area, perimeter, orientation","package":"geometry-ai999x","example":"Find the area of the polygon with vertices (0, 0), (4, 0), (4, 3), (0, 3).","v":[0.01229,-0.07857,0.13319,-0.01812,0.0706,-0.01965,-0.02227,0.06508,0.01031,-0.00123,0.01846,0.0057,-0.07736,0.02697,-0.08462,0.03556,0.03628,-0.06192,-0.05144,0.07217,-0.02992,-0.08011,-0.02066,-0.04343,-0.04876,0.09832,0.10358,0.05676,0.02934,0.06486,0.04734,0.0258,0.01997,-0.08104,-0.13168,-0.08166,-0.04796,-0.07308,-0.08376,-0.04421,-0.00656,0.1201,-0.0921,0.07035,0.014,0.10132,-0.04648,0.0949,0.02527,0.05731,0.11821,-0.10032,0.14035,0.02444,-0.01172,0.02835,-0.13739,-0.01801,0.02932,-0.02242,0.05406,0.01857,-0.09743,0.01667,-0.06523,-0.09935,-0.03071,0.06052,0.03797,0.06801,-0.05656,0.07652,-0.05903,-0.12948,0.0535,0.00203,0.04629,0.07837,-0.06479,0.03846,-0.0766,0.03627,0.11241,-0.04468,0.08961,0.08644,-0.01189,-0.0594,0.07004,-0.07203,0.04966,-0.05738,-0.06214,0.05569,-0.0387,0.08479,0.13773,0.13157,0.00242,-0.02931,-0.02233,0.09479,0.00897,-0.08731,0.04572,-0.02173,0.03206,-0.09284,-0.06799,0.02307,-0.04832,-0.055,-0.03904,-0.02366,0.0068,0.0672,0.08524,-0.04193,0.00878,0.05042,-0.017,-0.01398,-0.03051,-0.08371,0.02812,0.02657,-0.03105,-0.02739,0.00514,-0.0058,0.00154,-0.01,0.08684,0.00593,0.06262,-0.00667,-0.01555,0.10075,0.03945,-0.0696,0.01695,-0.12491,-0.0823,0.01382,0.08173,-0.04341,-0.18745,-0.0013,-0.01274,0.00704,-0.02947,0.02216,0.04363,-0.02839,-0.01257,0.09279,-0.09244,-0.00922,0.04972,-0.07101,-0.02395,-0.08558,-0.08056,0.07101,0.07515,0.05925,-0.00599,0.0016,0.01305,-0.09105,-0.02774,-0.02751,0.00378,0.0364,0.00754,-0.03325,-0.03372,-0.03363,-0.02615,0.0497,0.05154,0.00943,-0.04062,-0.04047,0.01599,0.02981,-0.05569,-0.02579,0.03667,0.00504,-0.03029,-0.03203,0.00331,0.00669,0.02223,-0.02214,0.04747,0.08972,0.06148,-0.00495,-0.09641,-0.04354,0.11744,0.08689,-0.01733,0.08024,0.08438,-0.03943,-0.06667,0.06509,0.00707,-0.07527,0.24304,0.00265,-0.03214,-0.05086,0.04362,-0.08982,-0.046,-0.09461,-0.05438,0.09101,-0.08544,-0.04307,-0.03194,0.05323,-0.07553,0.01558,0.00956,0.05242,0.01865,-0.00783,-0.07126,0.0122,-0.05167,-0.05144,0.02005,0.02848,-0.01154,-0.01697,0.03123,0.0766,0.01449,0.08218,-0.01185,-0.12583,0.09719,0.03622,-0.01307,-0.06656,0.0441,-0.12245,-0.04646,0.02958,0.07401,-0.02216]},{"domain":"geometry","key":"polygon_centroid","name":"Centroid of a polygon","package":"geometry-ai999x","example":"Find the centroid of the polygon with vertices (0, 0), (4, 0), (4, 2), (0, 2).","v":[0.01486,0.02671,0.15196,-0.07851,0.05621,-0.02629,0.01294,0.02601,-0.04924,-0.01278,0.01688,0.02546,-0.11813,-0.01724,-0.02961,0.03439,-0.00654,-0.05335,-0.05296,0.03024,0.00789,-0.0357,-0.03142,-0.07944,-0.08201,0.07284,0.04206,0.0334,0.03219,0.02336,0.07601,0.03794,-0.00491,-0.09678,-0.07925,-0.08926,-0.07997,-0.11518,-0.10829,-0.00352,-0.0769,0.11607,-0.07443,0.07121,-0.04059,0.07984,-0.05211,0.09653,0.05556,0.05249,0.06998,-0.09719,0.07244,-0.00087,0.03887,0.05732,-0.08487,-0.02613,-0.04937,0.01585,-0.01119,-0.02547,-0.03127,-0.01088,-0.05157,-0.09355,-0.02997,0.00855,0.09921,0.0962,-0.03666,0.05393,-0.00257,-0.11468,0.08152,0.02473,-0.02867,0.10227,-0.02192,0.01219,-0.03316,0.03392,0.08621,-0.02721,0.07727,0.06392,0.03565,-0.07531,0.06412,-0.08783,0.0751,0.05732,-0.02359,0.05234,0.02715,0.09988,0.10514,0.14358,-0.03347,-0.02139,-0.04987,2e-05,0.01629,-0.071,0.04082,0.00948,0.10507,-0.06091,-0.04885,0.01255,-0.08257,-0.01228,0.0331,-0.10909,0.00786,0.06101,0.15142,-0.03154,-0.06538,0.06394,-0.0311,-0.0762,-0.02424,-0.10033,0.05186,0.09544,0.04902,-0.06281,0.01959,-0.03645,0.04599,-0.05108,0.05751,0.01832,-0.0247,-0.01303,-0.01873,0.11468,0.00529,-0.09351,0.07106,-0.09849,0.05457,-0.02713,0.04672,0.0312,-0.14803,-0.0029,-0.04597,0.05099,0.01946,0.03685,0.11428,0.01853,0.05295,-0.00971,-0.01595,-0.04319,-0.02284,0.00466,0.0081,-0.1102,-0.04504,-0.00035,0.06509,0.04451,0.01837,-0.09625,0.06345,-0.0658,-0.08912,-0.05758,-0.07004,-0.07207,-0.01943,0.00248,-0.02495,-0.02787,-0.08375,0.05935,0.08978,0.09724,-0.03852,-0.05976,0.02012,-0.00425,-0.01712,-0.00286,0.06801,0.05067,-0.05723,-0.01867,0.01081,0.04698,-0.01074,-0.0892,0.03264,0.08073,-0.00118,-0.00017,-0.16618,-0.00326,0.07633,0.07233,-0.01477,0.00786,0.08558,-0.01273,-0.0841,0.07521,-0.01756,0.03101,0.20322,-0.06615,0.0281,-0.05846,0.03937,0.0754,-0.03911,-0.02211,-0.07035,0.08421,-0.07899,0.00386,-0.05242,0.05077,-0.05775,0.03692,-0.01072,0.07553,0.03265,-0.04001,-0.09396,0.04304,0.00325,-0.0978,-0.01938,0.03266,-0.022,0.05656,-0.02492,0.02009,0.02964,0.0376,0.04691,-0.15513,0.10543,0.06239,-0.02985,-0.01883,-0.01181,-0.10523,-0.02517,0.06905,-0.03977,-0.06739]},{"domain":"geometry","key":"polygon_interior_angles","name":"Interior angles of a polygon from its vertices","package":"geometry-ai999x","example":"Find the interior angles of the polygon with vertices (0, 0), (2, 0), (2, 2), (1, 1), (0, 2).","v":[-0.02582,-0.02004,0.13209,-0.0137,0.01452,0.0492,0.0096,-0.01808,0.01596,-0.08885,0.05246,0.0066,-0.11508,0.0458,-0.03674,0.06483,-0.05244,-0.05527,0.03404,0.03217,-0.03015,-0.00904,-0.04192,-0.01166,0.01681,0.07368,0.07089,0.08471,0.01894,0.06744,0.01128,0.02814,-0.08358,-0.08366,-0.0816,-0.11531,-0.10801,-0.13254,-0.03378,-0.07839,-0.08238,0.00076,-0.0386,0.02459,0.04141,0.02931,-0.081,0.11855,0.02543,0.04912,0.06768,-0.0293,0.0576,0.05172,0.01268,0.03782,-0.18376,-0.01065,-0.07453,-0.03478,-0.00331,0.06799,-0.11336,-0.04338,-0.00034,0.00643,0.03903,-0.04073,-0.01249,0.02357,-0.0526,0.07755,-0.04066,0.01714,0.04807,-0.01447,0.04145,0.14222,-0.02251,-0.0325,-0.1595,0.00851,0.09666,0.01892,0.08756,0.05985,0.00995,-0.05471,0.06086,0.00909,0.10047,-0.01298,-0.04358,-0.03076,0.04504,0.07127,0.10452,0.06487,-0.06243,-0.02035,0.01323,0.08109,0.04795,-0.09945,0.05847,0.01412,0.10656,-0.00961,-0.05417,-0.0481,-0.06788,-0.05554,-0.01528,-0.06158,0.02322,0.03996,0.1362,-0.07471,-0.03201,-0.01766,-0.01907,0.0238,-0.02265,-0.13396,0.09803,0.05316,-0.03952,-0.02646,-0.0433,0.01273,0.00887,-0.03919,0.02343,0.03933,0.04516,0.04539,-0.00774,0.12667,0.10739,-0.05206,0.00474,-0.04103,-0.05259,-0.00851,0.1253,-0.02564,-0.13672,0.06066,-0.04474,0.00932,0.03239,0.04457,0.01937,-0.03641,0.04721,0.09472,-0.14441,-0.01177,0.03177,-0.01076,-0.02268,-0.13567,-0.081,0.07375,0.09193,0.04431,-0.00722,-0.09095,0.02496,-0.07052,-0.04757,0.02302,0.01264,0.01847,-0.02442,0.01014,-0.0245,-0.05948,-0.17027,-0.01882,0.04826,0.06485,-0.10669,-0.04368,0.03692,0.01111,-0.07013,-0.08257,0.10699,0.05861,-0.0452,0.02925,0.01986,0.00412,0.0329,-0.04285,-0.01549,0.08333,0.02624,0.01093,-0.15424,-0.00641,0.15308,0.09771,-0.00988,0.02784,0.04158,0.00983,-0.0022,0.10309,0.02771,-0.01473,0.15995,-0.01374,-0.07255,-0.00614,0.07299,-0.0353,-0.07279,-0.09629,-0.014,-0.00767,-0.02185,-0.01073,-0.00036,-0.03946,0.01412,0.02051,-0.03277,0.02778,-0.03319,-0.03452,-0.10407,-0.02756,0.01201,-0.08828,0.07318,0.07045,-0.00338,0.06167,-0.02138,0.0304,0.09758,0.04605,0.00165,-0.07343,0.02193,-0.02853,-0.00732,-0.05686,0.01258,-0.129,0.00429,0.03334,0.05445,0.01573]},{"domain":"geometry","key":"polygon_is_convex","name":"Is a polygon convex?","package":"geometry-ai999x","example":"Is the polygon with vertices (0, 0), (4, 0), (4, 4), (2, 1), (0, 4) convex?","v":[0.00711,-0.02443,0.12378,-0.09196,0.00909,-0.04263,0.01027,-0.02427,-0.03752,-0.07019,-0.02544,0.06966,-0.07792,-0.04898,-0.02654,-0.02449,0.01296,-0.07124,-0.00639,0.01532,-0.07189,-0.02004,-0.02335,-0.082,-0.00256,0.05985,0.03546,0.05089,0.08753,0.02824,0.07962,0.08334,0.01991,-0.07449,-0.1206,-0.11378,-0.10586,-0.1103,-0.07271,-0.04624,-0.03918,0.04009,-0.03058,0.0165,0.00887,0.07374,-0.02775,0.12767,0.02374,0.05951,0.0733,-0.12411,0.12088,-0.02516,-0.00054,0.04273,-0.10768,0.01144,-0.04756,-0.00978,-0.01215,-0.02924,-0.05611,0.00365,-0.09662,0.02195,-0.0148,-0.00673,0.03154,0.02063,0.01238,0.05703,-0.06954,-0.10538,0.1815,-0.01604,0.00636,0.09337,0.01932,-0.03004,-0.07999,0.00291,0.1439,-0.0591,0.10713,0.09213,0.01293,-0.09893,0.11505,-0.07113,0.11271,0.06849,-0.02101,0.04302,0.07151,0.05579,0.1421,0.09949,-0.01732,0.00954,-0.02073,0.01038,-0.01167,-0.03745,-0.02044,-0.00225,0.11918,-0.03903,-0.097,-0.01326,-0.03902,0.0033,-0.00196,-0.06112,0.0239,0.0717,0.05361,-0.0307,0.00428,-0.01516,-0.02147,-0.04005,-0.11918,-0.074,0.09517,0.04981,0.02286,0.01173,0.04276,0.03547,0.04307,-0.08167,0.02926,0.00427,0.0188,-0.11877,-0.03881,0.10662,0.01194,-0.02883,0.06085,-0.02341,-0.04629,-0.08261,0.06022,0.02067,-0.13457,0.00624,-0.025,0.02107,0.03804,0.05664,0.03053,0.01395,0.0116,-0.00653,-0.00161,-0.01138,-0.07208,-0.06918,0.04681,-0.1179,-0.09395,-0.03155,0.09001,-0.0082,0.02556,-0.10595,0.10998,-0.0988,-0.05176,0.00707,-0.13421,-0.03844,0.00363,-0.00158,0.01034,-0.12565,0.01241,-0.04398,0.05832,0.08902,-0.04314,-0.05114,-0.00036,-0.00357,0.00297,-0.01881,0.09638,0.089,-0.01559,-0.07944,0.00164,0.00733,0.00536,-0.06257,-0.00917,0.07567,0.05502,0.06661,-0.14193,0.06803,0.07223,0.00917,0.01997,0.02378,0.08964,0.06483,-0.09533,0.0761,0.05701,0.01677,0.18165,-0.0123,0.01437,-0.05354,0.05939,0.03539,-0.0213,-0.06707,-0.0847,0.08476,-0.01657,-0.02663,0.04641,0.06347,-0.05978,-0.06506,-0.03622,0.01856,-0.05264,-0.01386,-0.01424,0.04305,-0.00076,-0.05714,-0.04619,-0.00641,-0.03564,0.06024,0.02418,0.01794,0.08026,0.05772,0.00197,-0.09098,0.06928,0.04041,0.00857,0.00083,0.00949,-0.09851,-0.00529,0.1067,0.05137,-0.04952]},{"domain":"geometry","key":"polyline_length","name":"Length of a polyline (path through points)","package":"geometry-ai999x","example":"Find the length of the path through (0, 0), (3, 4) and (3, 10).","v":[-0.15005,-0.07947,0.12812,-0.07817,0.06378,-0.10755,0.07347,0.00278,0.0525,-0.08709,-0.00951,-0.0233,0.06469,0.01474,-0.02677,-0.05154,0.00998,0.00396,-0.03682,-0.0493,-0.0603,-0.04429,0.02587,-0.00263,0.05458,0.06788,-0.05331,0.02503,0.02529,0.07016,0.04617,0.01015,-0.09939,0.03395,0.09575,-0.09971,0.0097,0.04983,-0.0232,0.05437,0.01401,0.06886,0.02832,0.02013,-0.07077,0.13823,-0.0598,0.09576,-0.04411,-0.05147,-0.0296,-0.00224,-0.01294,-0.00061,-0.07055,-0.0429,-0.03066,0.08954,0.07373,-0.0725,0.0586,0.03494,-0.05223,-0.10176,-0.12476,0.01723,0.02383,0.02936,-0.04233,-0.00969,-0.0979,0.11777,-0.00666,-0.086,0.03544,0.00785,0.1157,0.05429,0.04651,-0.01815,-0.06197,-0.07542,0.08508,-0.02179,0.15464,0.02835,-0.05647,0.07133,0.14413,0.04768,0.021,-0.10958,-0.06415,0.04246,-0.0015,-0.03957,0.03791,0.12477,-0.03773,0.00975,-0.0092,0.08379,-0.0183,-0.05524,-0.06836,0.00148,-0.13416,-0.08691,-0.11039,0.05155,-0.01753,0.00238,0.02081,0.02893,0.04382,-0.03241,-0.00498,-0.0006,0.05684,0.05876,-0.03966,0.10875,-0.02568,-0.04093,0.01367,0.03766,0.04539,0.07319,0.00115,-0.01358,0.04755,0.00136,0.08255,0.01301,0.0199,-0.02366,0.01483,0.02026,-0.03943,0.03883,-0.11283,0.00266,0.03996,-0.03541,0.06059,-0.01629,-0.07678,0.07296,-0.02948,-0.04809,-0.07364,0.02825,0.00852,-0.00461,0.02933,-0.01296,-0.08597,-0.0711,0.06608,-0.04417,0.00371,-0.06595,-0.01545,0.13047,0.12914,0.04154,0.0511,-0.07273,-0.02438,-0.10059,-0.11371,-0.05983,-0.01148,0.08006,-0.05938,-0.12161,-0.01214,-0.02474,0.03355,0.17449,-5e-05,-0.0382,0.10174,0.00238,-0.14323,0.15057,0.02358,-0.06119,0.04098,0.03023,-0.07066,0.0108,0.01449,0.07169,-0.01032,-0.04001,-0.04498,-0.07228,0.06084,-0.02564,0.03871,-0.02668,0.08626,0.02316,-0.00711,0.06318,0.0896,-0.06473,-0.0296,0.03955,0.02671,-0.0072,0.12431,0.01013,-0.02852,-0.00703,0.04226,0.01806,-0.13635,0.06992,-0.03964,0.02918,0.0417,0.01471,0.08029,-0.03099,-0.03747,0.03958,-0.07522,0.0207,-0.08292,-0.03188,0.00075,-0.07296,-0.06707,-0.00082,0.02497,-0.00161,-0.06793,-0.0825,-0.01279,-0.01081,0.06228,-0.05093,-0.02518,-0.01085,0.00347,0.07248,0.02344,0.00028,0.1446,-0.11825,-0.08392,-0.06167,0.01657,-0.05909]},{"domain":"geometry","key":"pyramid_measures","name":"Right rectangular (or square) pyramid: volume and surface area","package":"geometry-ai999x","example":"Find the volume of a square pyramid with base side 6 and height 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of two line segments","package":"geometry-ai999x","example":"Do the segments from (0, 0) to (4, 4) and from (0, 4) to (4, 0) intersect?","v":[-0.05668,-0.08492,0.07038,-0.05191,-0.08075,0.01156,0.01764,0.05775,0.02246,-0.02709,-0.03472,0.12508,0.0256,-0.07313,0.02421,-0.09043,-0.02013,-0.1329,-0.04511,0.06445,0.0075,0.06646,0.12025,0.01049,0.04949,0.06063,-0.07585,0.0507,-0.09646,0.03698,0.01462,0.02249,-0.04551,0.1246,0.01812,0.03311,-0.0849,-0.02605,-0.09674,-0.00225,0.02727,0.14435,0.10193,-0.01011,-0.10819,-0.02015,-0.06561,0.14345,-0.03758,0.0925,0.09325,0.02065,0.06571,0.04194,-0.03165,0.11349,-0.04668,0.12017,-0.03392,0.0835,-0.03032,-0.00462,-0.05605,-0.10651,-0.02985,0.03632,0.03309,0.08263,0.05018,-0.05512,0.005,-0.00743,0.01299,-0.20948,0.05776,-0.01964,-0.0649,-0.03357,0.0936,-0.01661,0.01671,-0.07973,0.04106,-0.00438,0.05817,0.00565,0.05183,-0.0217,0.04386,0.1179,-0.03575,-0.01185,-0.03676,0.03927,0.04384,-0.10919,0.16914,0.05267,-0.10657,0.0322,0.03015,-0.00696,-0.04082,9e-05,-0.05622,0.03913,-0.04115,0.00254,-0.07368,0.00915,0.00702,0.00177,0.01193,-0.0477,0.01952,0.03739,-0.04198,-0.02556,0.01594,0.04687,-0.0608,-0.03886,-0.03448,0.02062,0.01122,0.07011,-2e-05,0.00353,0.09448,0.0562,0.0392,-0.03979,-0.04446,-0.03484,0.00131,-0.13757,-0.03392,0.04164,-0.02059,-0.00588,-0.04877,-0.0235,0.04326,-0.00683,-0.02886,0.0917,-0.08173,0.00796,0.00824,0.01973,0.03436,0.05268,0.07582,0.06845,0.04685,-0.12417,0.03635,-0.05823,0.03974,-0.02567,0.04644,-0.01094,0.05046,-0.05782,0.07309,-0.01647,0.08467,-0.1241,0.02907,-0.06248,0.00815,-0.00308,-0.09154,-0.06717,0.08456,-0.01349,-0.03307,-0.03796,0.01854,-0.05005,0.03188,0.07149,0.0462,-0.02202,-0.11049,0.01737,0.00973,0.02388,0.02123,-0.01609,-0.07012,0.08972,-0.03354,0.03707,0.01217,-0.12248,-0.03746,-0.00592,0.05807,-0.00256,0.01342,0.0482,-0.00332,-0.03777,-0.02042,0.13463,-0.08773,-0.00459,-0.11084,0.05553,0.0368,-0.00075,-0.0237,0.00701,-0.11987,0.06283,0.05273,0.0706,-0.09176,0.11172,0.10535,-0.0264,-0.04007,-0.03398,0.05135,0.05818,-0.00249,0.01314,0.03911,0.0822,-0.21008,-0.02967,0.0105,-0.06941,0.0265,0.00241,0.01001,-0.14813,-0.0496,-0.02235,0.04666,0.03993,0.12654,-0.05198,-0.00344,-0.09656,-0.02383,0.02181,0.0624,-0.02936,0.01689,-0.05873,0.03398,-0.07441,0.01926,-0.0747]},{"domain":"geometry","key":"skew_lines_distance","name":"Distance between two lines in space (skew or parallel)","package":"geometry-ai999x","example":"Find the distance between the lines through (0, 0, 0) with direction (1, 0, 0) and through (0, 1, 1) with direction (0, 1, 0).","v":[-0.04153,-0.08378,0.06498,-0.04422,-0.05731,-0.08525,0.01981,0.00383,0.10472,0.04236,-0.09436,0.01585,0.02773,0.09478,-0.02293,-0.01404,-0.01363,0.08903,-0.03226,0.01066,0.05298,-0.01412,0.05274,-0.04632,0.157,-0.00363,-0.14876,0.05652,-0.08871,0.02999,-0.05225,0.017,0.01636,0.08185,0.01971,0.05388,-0.00063,0.06626,-0.0206,0.02358,0.00761,0.00988,0.17053,-0.00615,-0.18803,-0.03735,0.03615,0.04906,-0.02789,-0.02513,0.11385,0.01959,-0.06621,0.04908,-0.05669,0.04338,-0.00286,0.13117,-0.07427,-0.02722,0.01673,-0.03173,-0.01346,-0.08188,-0.02276,0.09557,-0.03813,-0.00423,-0.06455,-0.01685,0.0494,-0.00279,-3e-05,-0.0311,0.06263,-0.03601,-0.0019,-0.1157,-0.00815,-0.01212,0.04324,0.00561,0.04438,0.04692,0.00558,0.0196,-0.02309,-0.02312,-0.01652,0.02701,-0.1668,-0.02562,-0.02769,0.01583,0.04212,-0.04598,0.09646,0.00578,-0.02106,0.03137,0.00605,-0.01618,-0.03628,0.06962,-0.09663,-0.05694,-0.07841,-0.00137,-0.00548,-0.0222,0.06952,0.07359,0.08755,0.05535,0.04868,-0.13065,-0.09304,0.02333,-0.0447,0.06408,0.06241,0.09449,0.00019,-0.01116,-0.0803,-0.00594,0.03847,0.08702,0.07329,-0.04534,0.01457,-0.05224,0.01863,0.02248,0.04724,0.02418,0.01923,0.02698,-0.02429,0.06032,0.00367,-0.01199,0.02603,-0.0676,0.13867,0.10453,-0.10387,-0.0117,-0.04875,-0.01662,-0.02719,-0.02102,0.0451,0.07829,0.02189,-0.05401,0.02539,-0.13948,0.06034,-0.03974,0.03461,0.00927,0.08488,0.00334,0.00223,0.0138,0.0518,-0.08346,-0.00157,-0.13821,-0.05815,-0.03381,-0.10682,0.07599,-0.01062,-0.03234,0.02151,0.01938,-0.01229,-0.02783,0.08704,-0.11514,0.09355,0.05106,-0.01912,0.05596,0.01168,-0.00769,0.04283,-0.06316,-0.03666,-0.05764,-0.04396,-0.00579,0.07414,-0.12443,0.01345,0.04888,0.056,-0.11769,-0.00061,0.02927,0.00138,-0.12653,0.04347,0.02422,0.10286,-0.08951,-0.02495,0.03064,-0.06229,0.08093,0.07552,-0.00717,0.00625,-0.05421,-0.0274,0.12788,-0.01002,0.12804,0.07954,-0.11726,0.12462,-0.03144,0.02694,0.02522,-0.06092,-0.05802,0.03762,0.04077,-0.05898,-0.06808,-0.03245,-0.10131,-0.02099,0.05383,-0.05708,-0.07303,-0.04051,-0.09971,0.0319,0.03479,0.13496,0.03477,0.00547,-0.04215,-0.05581,-0.00544,0.02281,-0.05696,0.13254,-0.0675,-0.01098,-0.15576,-0.03074,-0.00287]},{"domain":"geometry","key":"solid_angle_cone","name":"Solid angle of a cone","package":"geometry-ai999x","example":"What is the solid angle of a cone with half-angle 60 degrees?","v":[0.01509,0.00632,0.00029,-0.02485,0.06899,0.09912,-0.00374,-0.07089,0.11342,-0.02985,0.08567,-0.0215,-0.10415,-0.01531,-0.00354,0.07601,-0.02772,-0.05132,0.01964,-0.03151,0.01945,0.05632,0.03265,-0.0113,0.04265,-0.03464,-0.0757,0.20026,0.07045,0.04321,-0.07286,-0.0057,0.01389,0.00362,-0.05946,-0.04087,-0.0583,-0.01689,-0.01486,0.00257,-0.04046,-0.0052,-0.00264,0.00843,0.08466,-0.06847,0.05203,0.03473,-0.05371,-0.03509,0.06952,0.00342,0.05259,0.01899,0.07304,0.04515,-0.01992,0.02137,-0.08453,-0.06415,0.07593,0.15369,-0.0542,0.06033,0.06878,0.03471,0.0567,-0.12093,-0.12241,-0.02791,0.01496,0.02624,-0.11978,0.16494,0.08497,0.03433,-0.13914,-0.0215,-0.00781,-0.11873,-0.06969,-0.05523,0.05758,0.03974,0.10824,-0.01146,-0.02291,-0.01252,0.05006,0.04036,0.04328,-0.03634,0.05942,-0.11827,-0.00287,-0.00689,0.02303,0.09278,0.06159,0.07555,-0.00704,0.03742,0.13279,0.08044,-0.02511,0.03535,0.09002,0.10082,0.05171,0.02659,0.01836,0.07155,0.02951,0.02003,0.04444,0.04872,0.14125,-0.10376,-0.06563,-0.04571,-0.01122,0.02904,0.01273,-0.06044,-0.02225,-0.07933,-0.04934,-0.02895,0.07234,-0.03877,0.02201,-0.09026,-0.00244,-0.06021,0.01699,0.07249,0.03782,0.01546,-0.11242,-0.03016,-0.08127,-0.00318,0.01485,0.0256,-0.00257,-0.04063,0.05186,0.03082,-0.13971,0.08541,0.03362,0.09187,-0.03074,-0.03339,-0.00708,0.07547,-0.08121,0.03026,-0.00231,-0.04976,0.06056,-0.03035,-0.08627,0.03586,-0.04584,0.03259,-0.03466,0.01542,0.06296,-0.0179,0.07396,0.06532,0.05605,-0.06239,0.01094,0.02316,-0.101,0.00777,0.01761,-0.07734,-0.06138,0.04398,0.00282,-0.02455,0.09111,0.05133,-0.04982,-0.00626,0.06623,-0.00643,-0.14225,0.00748,0.02974,-0.12554,-0.00884,0.07215,-0.03027,-0.07788,-0.03545,-0.02558,-0.04979,-0.04435,0.02052,0.04576,0.11326,0.03897,0.02488,-0.10343,0.02149,-0.08689,0.0055,0.01655,0.06331,0.01294,-0.04906,-0.01372,-0.07796,-0.10349,0.03938,-0.07925,-0.11614,-0.09457,0.06443,-0.07754,0.05039,-0.0844,-0.00738,-0.05052,0.10476,-0.03821,-0.01575,-0.01781,-0.04287,-0.00575,-0.01568,0.05627,0.04977,-0.20645,-0.05515,-0.01562,0.00456,0.03916,0.10059,0.11328,0.02608,0.08169,-0.04176,0.05224,-0.02231,-0.04477,-0.03368,-0.03353,0.0612,-0.04822,-0.03471,0.01791]},{"domain":"geometry","key":"solid_angle_triangle","name":"Solid angle subtended by a triangle","package":"geometry-ai999x","example":"What solid angle does the triangle with vertices (1, 0, 0), (0, 1, 0), (0, 0, 1) subtend at the origin?","v":[0.04932,-0.03107,0.03876,-0.05255,-0.02109,0.09953,-0.06905,-0.06987,0.14418,-0.08734,0.09363,-0.06975,-0.14722,-0.00821,-0.07772,0.1105,0.01406,-0.08122,-0.04671,-0.01226,0.05476,0.00405,0.02178,-0.00675,0.02077,-0.03527,0.01553,0.19291,0.05466,0.03898,-0.037,-0.03484,-0.05342,-0.06608,-0.06898,-0.02213,-0.03617,-0.02568,-0.05746,-0.05926,-0.02473,0.00839,-0.02297,0.05289,-0.04977,-0.09837,-0.01294,0.08006,-0.11068,0.0893,0.10472,-0.00682,0.04696,-0.02973,0.01948,0.0387,-0.12822,0.00185,-0.05205,-0.01532,0.08635,0.15244,-0.07238,-0.01054,0.04148,0.04805,-0.01671,-0.08597,-0.10546,-0.0234,-0.01913,0.02247,0.01894,0.11837,0.04078,0.02572,-0.03517,0.03464,0.00754,-0.06303,-0.00205,-0.00771,0.04668,0.01545,0.01176,0.01781,-0.05958,-0.03468,0.00889,-0.03333,0.02141,-0.10851,-0.02065,-0.07651,0.01883,0.02638,0.02574,0.14591,0.08675,0.04165,-0.01423,0.01469,0.05554,-3e-05,0.03923,0.03291,0.08389,0.08328,0.0587,0.05309,-0.00654,0.03728,0.07877,0.03576,0.01504,0.0421,0.02507,-0.10029,-0.02049,0.01951,-0.03188,-0.00707,-0.05175,-0.06345,0.03463,-0.02863,-0.04415,-0.04059,0.08115,-0.04922,0.01507,-0.0537,0.04223,-0.00235,0.00217,0.00352,0.00624,-0.03733,-0.01497,-0.12764,-0.02763,0.00014,-0.04856,0.03306,-0.04974,-0.07242,-0.04909,0.02211,-0.03597,0.09314,0.03941,0.04746,-0.00508,-0.03176,-0.08374,0.04657,-0.10168,-0.00918,0.06595,-0.05285,0.08194,-0.03411,-0.06035,0.08091,0.07122,0.04823,-0.00053,0.03011,0.10633,-0.06123,0.12554,0.04409,0.02734,-0.0503,0.00311,0.0631,-0.10149,0.0206,-0.02516,0.00308,-0.00859,0.04894,-0.02822,-0.05323,0.04623,0.06523,-0.08282,-0.02229,0.08323,-0.04735,-0.13426,-0.05089,0.10239,0.02425,0.04789,0.01305,0.06935,-0.01546,-0.01004,-0.0353,-0.16187,-0.05741,0.07518,-0.02569,0.105,0.09898,-0.01438,-0.09734,0.01365,-0.0359,0.0875,0.09218,0.07263,-0.01936,-0.01843,-0.0375,-0.08443,-0.0582,-0.0223,-0.04789,-0.05058,-0.01626,0.00478,-0.03822,-0.02907,-0.03418,-0.06702,-0.02915,0.07728,0.02303,0.04845,-0.09337,-0.14458,-0.03049,0.04332,0.06769,0.07307,-0.08416,-0.08161,0.04648,0.03009,0.06108,0.14915,0.11385,0.03464,0.06275,0.00505,0.13142,0.00686,0.03948,0.00314,-0.11672,0.08272,-0.08486,-0.08449,-0.09429]},{"domain":"geometry","key":"sphere_four_points","name":"Sphere through four points (circumsphere of a tetrahedron)","package":"geometry-ai999x","example":"Find the sphere through (1, 0, 0), (0, 1, 0), (0, 0, 1) and (0, 0, 0).","v":[-0.04637,-0.05052,-0.028,-0.00709,0.06073,0.1245,-0.07487,0.05273,0.1306,-0.01319,-0.00206,-0.03467,0.01543,-0.09202,-0.06701,-0.01066,0.05601,-0.00405,0.09027,-0.018,0.10192,-0.13605,-0.00615,-0.04646,-0.03342,-0.02971,0.00866,-0.00937,-0.0037,0.04273,0.07422,-0.04683,-0.03811,-0.02068,-0.02186,-0.13126,0.04558,0.02655,-0.00895,0.02977,-0.05436,0.15144,-0.07908,0.0709,-0.16036,0.0335,-0.02761,0.06392,-0.08305,-0.00268,0.1508,-0.07495,0.02652,0.00568,-0.0657,-0.01159,-0.0196,0.08818,-0.07371,0.01712,0.11625,0.00033,-0.05897,-0.05333,0.05261,-0.02302,-0.02209,-0.04892,-0.03862,0.07274,0.0188,-0.00124,-0.11535,0.00276,-0.09475,0.08771,-0.14644,0.04984,0.10427,-0.02421,-0.00723,-0.02784,-0.01303,0.03339,0.0687,0.04461,-0.05978,-0.04046,0.02125,-0.14068,0.13761,0.07365,-0.03763,-0.02529,0.01694,0.04081,-0.05547,0.08805,0.01719,-0.08772,-0.02245,-0.097,0.05417,-0.1069,-0.10818,0.07613,-0.07914,-0.01317,0.01166,-0.00024,0.03297,0.07508,0.0917,0.0628,0.07232,-0.07179,0.10655,0.00826,-0.07348,0.04571,-0.01957,-0.06212,-0.06832,-0.00994,0.04141,-0.01962,0.11135,-0.05522,0.06601,-0.02177,-0.00817,-0.06719,-0.00951,0.01259,-0.04705,-0.02253,-0.04635,0.00114,0.01295,-0.0161,-0.00943,-0.01429,0.02902,0.03863,-0.01148,0.03195,0.03809,0.02552,-0.00731,0.01752,0.03706,0.06231,0.06392,0.04163,0.01861,0.00346,-0.05458,-0.01544,0.05194,0.03811,0.04198,-0.06679,-0.02379,0.02458,0.04229,0.04791,0.11577,-0.03717,0.06939,-0.01819,0.01813,-0.05333,-0.07426,-0.08225,-0.06718,-0.02638,-0.08669,0.03952,0.07533,0.09129,0.11866,0.02106,0.13012,0.0032,0.07494,-0.03403,0.03593,-0.00681,0.02073,-0.03433,0.02862,-0.00033,-0.02662,0.06376,0.01319,-0.00964,0.10017,-0.00909,0.00812,-0.01007,-0.15285,-0.0262,-0.00706,0.00234,-0.05479,0.0156,0.01812,-0.01705,-0.05921,0.01215,-0.07224,0.02919,0.09628,-0.11336,-0.06565,-0.03223,-0.07019,0.07177,0.07987,0.11836,0.00284,0.06469,0.06657,-0.03615,0.04802,-0.03372,-0.09392,0.05715,-0.03428,0.05224,0.03451,0.02342,-0.10914,-0.01594,-0.06373,0.04429,-0.06831,-0.14088,-0.07571,0.04462,0.0475,-0.01566,0.12088,0.02743,0.00595,0.04201,-0.08386,0.06614,-0.07746,0.0816,-0.01604,-0.06607,0.06176,-0.03392,-0.16172,-0.04261]},{"domain":"geometry","key":"sphere_measures","name":"Sphere: volume and surface area","package":"geometry-ai999x","example":"Find the volume of a sphere with radius 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cap: volume, curved area, base radius","package":"geometry-ai999x","example":"Find the volume of a spherical cap of height 2 cut from a sphere of radius 5.","v":[0.02417,-0.0352,-0.04122,-0.01806,0.08681,0.03325,-0.00736,-0.05998,0.0852,0.08752,0.01735,-0.02755,0.05992,0.0576,-0.06752,0.05888,0.0355,0.01245,0.069,-0.08487,0.0434,-0.05293,0.06893,-0.01744,-0.037,-0.06354,0.00679,0.02983,0.01974,-0.12239,-0.12591,0.04711,0.02429,-0.05099,-0.0218,-0.02935,0.02955,-0.10161,-0.06544,0.01773,-0.02101,0.02838,-0.04865,0.01438,-0.02149,-0.08838,0.06609,0.03406,-0.12105,-0.08385,0.06508,-0.10162,0.04983,-0.00579,0.05351,0.07012,0.01296,0.03279,-0.1188,0.02581,0.12084,-0.08114,-0.04532,0.03324,-0.05159,-0.02084,0.06136,0.00361,0.00626,0.05728,0.08367,0.06231,-0.14188,0.03592,-0.09235,0.01707,-0.19128,-0.04307,0.01802,-0.09906,-0.05647,0.03114,0.00559,-0.09277,0.03484,-0.00049,0.05256,0.10215,0.05971,0.0635,0.0578,-0.01746,0.03153,0.02503,0.05587,-0.0229,-0.00298,-0.04373,0.13352,-0.01814,-0.03941,-0.03766,0.08886,0.02377,-0.16579,-0.02761,-0.04232,0.05969,0.07224,0.02446,0.05298,-0.00596,0.09797,0.12739,-0.00807,-0.02653,0.07432,0.03967,-0.06525,-0.09068,-0.04089,-0.02253,0.01207,-0.03331,-0.07532,0.06262,-0.00334,0.01362,-0.02269,-0.01806,-0.0036,-0.04088,0.04848,-0.00486,-0.0103,-0.04071,0.09302,0.02818,-0.09619,0.16675,-0.03085,0.01881,0.09085,-0.02865,0.06338,-0.04702,0.11322,0.07176,-0.07128,0.02814,-0.02099,0.04464,0.06417,0.01512,0.00928,-0.02789,-0.05407,-0.05113,-0.00268,0.01332,0.06774,0.07532,0.12118,-0.01429,-0.01839,0.0957,-0.07916,0.03674,0.04166,-0.06232,0.00831,0.12102,0.00651,-0.16792,-0.08281,0.017,-0.08433,0.05255,0.10507,0.05024,-0.05293,0.01893,0.09025,0.09394,0.04642,-0.00541,-0.01814,-0.03949,-0.02331,-0.04423,0.02488,-0.01537,0.07946,0.01056,0.03675,0.02419,0.00324,-0.0079,0.0403,-0.03694,0.04072,-0.04288,-0.00654,-0.0474,0.00661,-0.06104,-0.08569,0.03392,0.07193,-0.11094,-0.05737,-0.05955,0.13136,0.02021,-0.11702,0.01597,-0.06213,-0.05918,0.1092,0.03861,-0.02331,0.05961,0.02542,-0.09535,0.00339,-0.01069,-0.03646,0.05044,0.03246,-0.02705,-0.01492,0.05414,-0.09823,-0.09903,0.01499,0.0528,-0.02086,-0.12105,-0.1004,-0.08618,0.01635,-0.04239,0.04831,0.08041,0.04674,-0.05928,-0.10227,0.06988,-0.03955,0.04472,-0.03721,-0.0578,0.01184,0.02239,-0.05387,0.06851]},{"domain":"geometry","key":"spherical_triangle_area","name":"Area 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3).","v":[0.05522,-0.01887,0.10527,-0.03514,0.01778,0.02586,-0.06365,-0.01162,0.02608,0.02699,0.05458,-0.05046,-0.03016,0.05809,-0.08296,0.0184,0.07517,-0.05082,-0.01454,0.07001,-0.04831,-0.06521,0.02933,-0.01745,-0.02332,-0.03404,0.157,0.10291,0.01523,0.0615,-0.01132,0.02832,-0.06343,-0.04362,-0.11748,-0.05588,-0.01944,-0.01982,-0.14383,-0.04488,-0.01186,0.10891,-0.01625,0.13329,-0.03613,0.04338,-0.09442,0.06105,-0.04861,0.11535,0.16361,-0.04667,0.12355,-0.00393,0.04507,0.05975,-0.11731,-0.0182,0.00327,-0.05106,0.06612,-0.01167,-0.10457,0.01622,-0.05092,-0.0788,-0.02822,0.10027,0.01788,0.03951,-0.05435,0.08081,-0.02264,-0.14934,-0.03826,-0.01387,0.04091,0.02117,-0.01656,0.07696,0.04549,0.01104,0.07989,-0.03744,0.01409,0.0408,-0.02772,-0.11924,0.01666,-0.01588,0.0635,-0.12137,-0.05068,0.00441,-0.0286,0.04286,0.03754,0.14786,-0.01193,-0.04157,-0.05212,0.08678,0.02206,-0.0549,0.10883,-0.00054,-0.05398,-0.0513,-0.05163,0.02887,0.03436,-0.02208,-0.00487,-0.03297,-0.03282,0.05169,0.01216,0.03738,-0.04188,0.08005,-0.05776,-0.00392,0.0274,-0.09141,0.01424,0.02177,-0.03155,-0.0549,0.08533,-0.05386,0.06278,-0.05912,0.07622,-0.00182,-0.05857,-0.02948,-0.02231,0.02661,0.04726,-0.11774,-0.0205,-0.1075,-0.03516,0.03628,-0.01039,-0.04665,-0.11257,0.04087,-0.02027,0.03146,0.04406,0.01371,0.02139,-0.02601,-0.04173,0.05959,-0.08299,-0.06833,0.13561,-0.07223,0.06331,-0.00465,-0.05012,0.08793,0.10377,0.0585,0.00043,0.02682,-0.00463,-0.06007,0.00176,-0.01543,0.04696,-0.03152,-0.03102,-0.06284,-0.09034,-0.07094,0.00189,0.14913,0.11464,0.07369,-0.07087,-0.01976,-0.04373,0.0488,-0.06154,-0.03275,0.04059,-0.01477,-0.05134,-0.03362,0.01331,0.05236,-0.04302,0.02543,0.11871,0.10843,0.08043,0.03346,-0.08441,-0.06185,0.08444,0.0351,-0.0316,0.07594,0.01908,-0.08447,0.01433,0.05394,-0.00553,-0.00841,0.05003,-0.00258,-0.02437,-0.08162,0.01615,-0.04136,-0.0578,0.0061,-0.06455,0.02058,-0.14642,0.02136,-0.08768,0.03749,-0.08251,0.04338,0.08189,0.10233,0.04227,-0.03449,-0.06444,0.04482,-0.05343,-0.03402,0.07647,-0.00993,-0.06443,-0.01006,0.09098,0.11522,0.03433,0.0012,-0.01653,-0.12645,0.07848,0.13305,-0.05346,-0.07887,0.05068,-0.00784,-0.03135,0.02049,0.01167,-0.1045]},{"domain":"geometry","key":"triangle_incircle","name":"Incircle of a triangle: incentre and inradius","package":"geometry-ai999x","example":"Find the incenter and inradius of the triangle with vertices (0, 0), (4, 0) and (0, 3).","v":[0.06185,0.05924,-0.00117,-0.08529,0.01035,0.10891,-0.0594,0.09348,0.08302,0.00818,0.06779,-0.01079,-0.06579,-0.04269,-0.09498,0.00968,0.03613,-0.00625,0.00844,0.09164,0.02818,-0.10839,-0.03573,0.01117,0.00657,-0.04692,0.04596,-0.02785,0.08754,0.01478,-0.01331,0.00926,-0.05943,-0.05161,-0.0116,-0.02976,-0.04889,0.02728,-0.07602,-0.00194,0.05001,0.00122,-0.0816,0.04091,-0.0615,0.12528,-0.01875,-0.05119,-0.04057,0.05634,0.20039,0.00447,0.03083,0.0471,-0.11842,0.05358,-0.03769,-0.00266,-0.05057,-0.00177,0.05414,0.10255,-0.0568,0.10011,0.0205,0.01751,0.01798,-0.0005,0.05454,0.0015,-0.12538,0.03776,-0.01265,-0.04827,-0.13529,-0.06335,0.02822,-0.00768,-0.0679,-0.01222,0.0709,0.05222,0.0891,-0.00738,-0.01295,-0.01903,0.01751,-0.10899,-0.10776,-0.05036,0.11682,0.06044,-0.10478,0.02873,0.07618,0.07844,-0.09761,0.06776,-0.02284,-0.04742,-0.00029,0.00916,0.01904,-0.06681,-0.03837,0.06975,-0.04682,-0.08818,-0.01378,-0.06664,-0.0204,-0.01355,-0.09105,0.01552,0.0303,-0.08958,0.0567,0.02278,-0.02241,0.02733,0.02322,-0.05584,0.00916,-0.05602,0.01085,0.0837,0.05913,-0.06339,-0.00076,-0.07154,-0.08665,-0.03522,0.02627,0.00369,-0.06476,0.03631,-0.11174,0.05668,0.02048,-0.07623,0.06666,0.02039,-0.02603,0.00499,0.04123,-0.0627,-0.05084,-0.03258,0.04543,0.06736,0.02996,0.10149,0.01883,0.04102,0.00805,-0.03864,-0.00398,-0.07101,0.1604,0.01034,0.01476,-0.05077,-0.12514,0.05905,0.14081,0.04193,0.10349,0.01518,0.0621,-0.01225,-0.02662,-0.02013,-0.06475,-0.08036,-0.06446,-0.05434,0.0464,0.07467,0.03623,0.02268,0.08587,0.04794,0.03583,-0.01161,-0.02784,-0.00754,-0.01062,0.02131,0.06114,-0.05069,0.0378,-0.04458,0.05634,0.05006,0.05194,-0.0089,-0.00563,0.10422,0.01978,0.01443,-0.12817,0.05057,0.0084,0.01526,-0.14199,-0.11466,0.01474,0.05004,-0.06554,0.04228,0.01433,0.04898,0.17656,0.01135,-0.12312,-0.0107,-0.08229,-0.03346,0.03522,-0.01997,-0.02014,-0.01849,-0.16981,0.06234,-0.0977,-0.03103,-0.05525,0.03001,-0.03326,0.06765,0.03443,-0.09066,-0.05702,-0.00855,-0.06255,-0.06462,-0.02627,0.0801,-0.02803,0.14817,0.14189,0.02725,0.00352,-0.04848,0.09457,-0.07895,-0.07486,0.07115,-0.03318,-0.026,0.01267,0.04274,0.02627,0.09646,-0.05108,0.03752]},{"domain":"geometry","key":"triangle_orthocenter","name":"Orthocentre of a triangle","package":"geometry-ai999x","example":"Find the orthocenter of the triangle with vertices (0, 0), (4, 0) and (1, 3).","v":[0.05928,0.07842,0.01306,-0.07743,0.01731,0.10632,-0.08725,0.01665,0.01074,0.07065,0.01541,0.0233,-0.0885,0.10056,-0.05436,-0.01946,0.09724,-0.02546,0.01613,-0.00716,-0.1016,-0.01175,-0.04853,-0.04507,0.03298,0.02221,-0.04023,0.08404,-0.00433,-0.00887,0.0132,0.0163,0.01491,0.05178,-0.12169,0.00671,-0.03408,0.006,-0.08345,-0.07878,-0.03262,0.1314,-0.05576,0.06297,-0.1235,0.02044,-0.14157,-0.07568,-0.07816,0.16109,0.16883,-0.02849,0.05271,0.0236,0.00984,0.02108,-0.12688,-0.03668,-0.00245,-0.12693,0.0452,-0.01146,0.0029,-0.04421,-0.03692,-0.03817,0.00558,-0.07022,0.0503,0.00933,-0.06295,0.01199,0.04272,-0.08349,-0.00993,-0.02355,0.01919,0.07199,0.05349,0.00183,0.01085,0.0587,-0.03398,0.07095,0.02552,0.00126,0.01167,-0.06595,-0.02851,0.05701,0.13494,-0.00171,-0.06924,0.04554,0.01776,0.08261,0.04813,0.13894,-0.10116,-0.0367,0.0071,-0.01055,0.05047,-0.05286,-0.03527,-0.00421,-0.08683,0.05497,-0.05628,-0.03583,-0.04582,0.0877,0.00487,-0.01554,0.03175,0.02689,0.05684,-0.00718,0.00718,-0.04497,0.03669,-0.03445,-0.02914,-0.05013,-0.00683,4e-05,0.0223,-0.12083,0.05325,-0.0028,-0.04271,-0.09214,-0.04381,-0.01423,-0.06103,-0.05328,-0.09149,0.00759,0.07655,-0.12201,0.05146,-0.06176,-0.00117,0.04249,-0.00497,-0.01706,-0.09513,0.02682,0.12485,0.07566,0.00359,-0.05678,0.0044,0.13572,-0.0426,-0.03355,-0.05755,-0.07782,0.03916,-0.02693,0.0691,-0.05652,0.05209,0.02478,0.01989,-0.00191,-0.01995,-0.03267,0.0595,-0.05088,0.05049,-0.05134,-0.05319,-0.00853,-0.02841,0.02488,-0.07107,0.08373,0.05388,0.0364,0.12898,0.12909,0.01014,-0.01075,-0.04357,-0.08671,0.00277,0.00999,-0.00858,0.01443,0.00311,-0.09718,0.07025,0.06679,0.05131,0.02124,0.03603,0.08609,-0.00795,-0.02592,-0.12474,-0.04255,0.00129,0.11027,-0.08159,0.03022,0.1282,-0.00706,-0.05258,0.02447,-0.04235,0.04156,0.09365,-0.00439,-0.07858,-0.03181,-0.04559,0.06539,-0.05605,0.06355,0.04511,-0.06701,-0.0754,0.12215,-0.10048,0.04746,-0.04501,0.08998,0.00662,0.08272,-0.11751,-0.04438,-0.01416,-0.02775,-0.0233,-0.03581,-0.00339,0.04005,-0.07183,0.05023,0.04551,0.0686,0.03328,-0.04898,-0.01417,-0.17155,0.08975,0.13208,0.01693,0.01594,0.07359,0.05984,0.12486,0.00313,0.0582,-0.08841]},{"domain":"linear_algebra","key":"adjugate","name":"Adjugate (classical adjoint) of a matrix","package":"linear-algebra-ai999x","example":"Find the adjugate of [[1, 2], [3, 4]].","v":[0.0961,0.07316,0.00757,0.15835,0.03321,0.0352,-0.07902,0.00264,0.0799,0.12251,-0.0282,-0.01711,0.0912,-0.02713,-0.02346,0.00324,-0.00581,0.00414,0.08566,0.05931,-0.03192,0.05901,0.01196,-0.02085,0.01476,0.03138,-0.00952,-0.07177,-0.02493,0.02863,0.02397,-0.02028,-0.0223,-0.00427,0.03691,-0.06827,-0.03159,-0.10329,0.03457,0.03426,0.02843,-0.10321,-0.02644,-0.05582,0.03139,-0.01021,-0.05395,-0.02206,0.02533,0.02281,0.1119,-0.05707,0.00844,0.06582,-0.00449,-0.0647,-0.0513,-0.04023,-0.00502,0.03213,0.01405,0.01718,0.02977,-0.01331,-0.13449,-0.0885,0.05133,0.08817,0.03934,0.11853,0.02704,0.01822,0.07505,-0.00764,-0.00948,-0.07759,0.0164,-0.03325,0.01809,0.05674,0.04257,-0.01142,-0.03744,-0.02283,0.08905,0.01157,0.04578,-0.11773,-0.05696,-0.00982,0.01045,-0.03978,0.06986,0.08226,-0.06459,-0.07241,-0.00265,-0.05517,0.06786,-0.01332,0.08074,-0.0209,0.05505,-0.09359,0.07713,-0.00784,0.04871,0.00658,-0.0742,-0.00183,0.05613,0.13606,0.00603,-0.00598,0.05332,-0.08909,-0.00825,-0.07462,-0.07693,-0.06609,-0.05341,-0.03185,-0.03348,-0.03724,0.02462,0.06026,0.00963,-0.01901,0.04149,0.03878,-0.08051,-0.10011,-0.09053,-0.13212,0.05662,0.05035,0.02021,0.03167,0.07705,-0.09381,0.14725,-0.18036,0.07567,0.00496,0.01671,0.05149,-0.10766,-0.00053,0.05167,-0.10118,0.00575,-0.03592,-0.10132,-0.02297,0.04742,0.11596,-0.0289,0.04626,0.06105,0.10884,-0.0069,-0.05551,0.03728,0.00287,-0.07776,0.05294,-0.00504,0.01557,-0.055,-0.0021,0.05784,0.13224,0.00219,0.08759,-0.08522,-0.02804,-0.02385,0.04677,0.03745,-0.01431,0.03806,-0.01895,0.05171,0.01067,0.0776,-0.04322,0.06718,-0.00548,0.02747,0.01167,0.20351,0.02773,-0.08426,-0.09471,-0.11348,0.01437,-0.01646,0.05701,-0.01919,0.05733,-0.00673,-0.01738,0.03793,0.05516,0.01049,-0.13586,0.16124,0.06298,0.06763,0.07675,0.00223,-0.04082,-0.08455,-0.07297,0.04689,-0.02265,-0.06283,-0.13514,0.14106,-0.02166,0.08949,0.01671,0.08255,-0.02253,-0.04701,0.05273,-0.05138,-0.1229,0.04282,-0.06129,0.02656,0.02035,-0.04012,-0.05009,0.06316,0.00339,-0.05581,-0.04072,-0.06054,0.04121,-0.06105,-0.00802,0.02723,0.00217,-0.08812,0.02348,0.00374,-0.11577,-0.01207,-0.02899,-0.02986,0.1311,-0.01602,-0.06371,0.01479,0.08235]},{"domain":"linear_algebra","key":"angle_between_vectors","name":"Angle between two vectors","package":"linear-algebra-ai999x","example":"Find the angle between the vectors (1, 0) and (1, 1).","v":[-0.03526,-0.14029,0.04675,0.07128,-0.07358,-0.01233,0.04615,-0.05232,0.02054,-0.04094,0.06517,0.11398,0.04325,0.03452,0.09222,0.01925,-0.16981,-0.08414,-0.10139,0.04042,-0.05191,0.10429,0.05998,0.03198,0.03677,0.01457,-0.00469,0.13099,-0.12553,0.01823,-0.08361,0.09209,-0.16299,0.0482,-0.09195,-0.07678,0.00065,0.01457,0.00474,-0.00931,0.0275,0.0579,0.17568,-0.0743,0.01786,-0.11164,0.01409,0.10123,-0.03725,-0.05158,0.01266,0.04006,-0.09694,-0.03342,-0.02797,-0.00381,-0.02596,0.04174,-0.13893,-0.04375,0.00327,0.05117,-0.05053,-0.02433,0.14943,0.11465,0.03765,-0.02429,-0.15082,-0.03665,0.00262,0.03605,0.08898,0.07785,0.0437,0.00996,0.02558,-0.00856,0.05255,-0.08779,-0.02479,-0.03983,0.05714,0.06398,0.00107,0.05386,0.0659,0.01467,0.03042,0.12016,-0.08125,-0.09725,0.03279,-0.10616,0.02625,-0.03247,0.07168,-0.02153,-0.00221,0.01864,0.00684,0.00027,0.03579,-0.03505,0.02436,-0.05381,0.07822,0.07749,-0.06362,-0.07814,0.00192,-0.01764,0.0262,-0.09098,-0.08653,0.06049,0.0174,-0.04959,-0.00989,0.02063,0.02991,0.03936,0.01469,-0.07391,-0.0671,-0.04083,0.04075,0.03964,0.04784,0.01117,0.03929,-0.07824,-0.03733,0.01603,0.02293,-0.09832,0.00461,0.05088,0.06575,-0.00724,-0.05542,0.04953,-0.07574,0.06493,0.10393,0.03701,-0.00089,0.06107,-0.01068,0.03711,0.06327,0.05049,0.037,0.01496,-0.0185,-0.03219,-0.08578,-0.07075,0.09242,0.04211,0.04303,-0.02265,0.03943,-0.04821,0.00635,-0.01128,-0.03845,-0.03077,-0.03415,-0.11318,0.04246,0.07922,0.08194,-0.00594,0.08053,0.05276,-0.01526,0.01058,0.03768,-0.18988,0.00459,0.01403,0.02511,-0.04683,0.06649,0.03864,-0.03197,-0.07289,0.07678,-0.03825,-0.03066,0.06893,-0.00702,0.03448,-0.04162,-0.03415,-0.00982,0.03366,-0.0073,0.01664,-0.08469,-0.07101,0.06054,-0.07127,-0.04215,0.07792,0.00408,-0.02419,0.03644,0.05126,0.09789,-0.01787,0.00166,0.08496,-0.04714,-0.06178,0.02508,-0.00276,-0.00813,-0.07146,-0.00298,-0.10783,0.01302,-0.01389,0.00217,0.00332,0.12032,-0.04149,0.08176,0.0638,-0.13649,0.0587,-0.01699,-0.03842,-0.07529,0.0492,-0.01771,-0.02438,-0.00844,-0.06084,0.13354,0.00377,0.0877,0.04524,-0.02955,-0.03195,-0.05298,0.02565,0.02447,-0.0975,-0.00428,-0.02982,-0.04378,-0.18003,-0.02899,0.04562]},{"domain":"linear_algebra","key":"bisection_root","name":"Root of a polynomial by bisection","package":"linear-algebra-ai999x","example":"Find the root of f(x) = x^2 - 2 between 1 and 2 by the bisection 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decomposition","package":"linear-algebra-ai999x","example":"Compute the Cholesky factor of the matrix [4 12 -16; 12 37 -43; -16 -43 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2).","v":[-0.04097,0.08822,0.02268,0.05322,-0.04455,-0.07895,0.04577,-0.06859,0.01314,0.08124,0.03458,-0.03276,-0.04789,0.01662,-0.00886,-0.09403,-0.16065,-0.02098,0.08567,0.05188,-0.02956,0.02863,0.12883,-0.00483,0.03278,-0.00238,0.01924,0.05416,0.02312,0.05367,-0.0116,-0.10285,0.00491,0.10645,0.02692,-0.03629,-0.03052,0.05187,0.0087,-0.05409,-0.01097,0.05765,0.05557,-0.06585,-0.01527,0.02049,0.09294,-0.02441,-0.01665,0.07451,0.09262,-0.01125,0.10404,0.08049,-0.07452,-0.00201,0.02336,-0.06928,-0.05509,-0.06106,0.04532,-0.08396,0.04351,-0.01955,-0.08683,0.06759,-0.01512,-0.03449,-0.07702,0.04942,0.17317,-0.03153,-0.09902,0.07654,0.06773,0.0753,-0.06085,-0.04729,-0.04305,0.00239,0.03331,-0.00746,-0.06408,0.0401,0.01804,0.03893,-0.01018,-0.12655,-0.04459,0.03562,-0.02337,-0.03644,0.10618,0.04217,-0.08853,-0.05433,0.04055,-0.01906,0.08807,0.05771,0.15127,0.02586,0.02601,0.02304,0.04537,-0.14127,0.0552,0.009,0.0319,0.04547,-0.07484,0.05563,0.00684,-0.0741,0.06529,0.01949,0.07829,-0.02505,-0.08483,-0.07004,0.07085,-0.02781,0.05418,-0.02327,-0.06579,-0.04395,-0.07051,-0.00362,0.13761,0.06097,0.04623,-0.09605,0.02361,-0.12039,-0.03428,0.04966,-0.00938,0.0139,-0.02253,-0.05017,-0.10982,-0.13411,0.04693,-0.01436,0.04244,0.06693,0.01448,-0.07719,-0.02247,-0.01463,0.0113,-0.06251,0.06684,0.04754,0.03163,0.06469,0.05874,-0.02999,-0.00544,-0.00516,-0.02672,0.03226,0.05559,-0.01304,-0.17542,-0.01817,0.12061,-9e-05,-0.03689,0.1114,0.02587,0.08526,0.07346,-0.06193,0.07204,-0.00166,0.05376,-0.0433,0.04204,-0.09735,0.06984,0.03507,-0.05062,-0.07932,0.03425,-0.03602,-0.01512,0.03702,0.01199,0.03732,0.05914,0.06312,0.02105,-0.11124,0.04168,0.05433,-0.02109,0.02544,0.06876,0.04486,0.09478,0.05685,0.05375,0.09687,0.0005,-0.09371,0.05875,-0.00733,-0.06951,0.07569,-0.0308,-0.0899,-0.03302,-0.0508,0.09343,-0.00365,0.09942,-0.06525,0.10802,-0.02862,0.1104,-0.12095,0.01792,0.09649,0.03317,-0.01761,-0.05762,-0.07499,0.00843,-0.07769,-0.09182,-0.03735,-0.03716,-0.03321,0.02123,0.01617,-0.09388,-0.00575,-0.06143,-0.01163,0.04837,0.04879,-0.12265,-0.01124,-0.01867,-0.01211,-0.0672,-0.06938,-0.05299,-0.09253,-0.01199,-0.00229,0.01565,-0.04418,0.11822,0.04955]},{"domain":"linear_algebra","key":"cross_product","name":"Cross 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sparse column (CSC) form of a matrix","package":"linear-algebra-ai999x","example":"Convert [[1, 0, 2], [0, 0, 3], [4, 5, 0]] to CSC 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sparse row (CSR) form of a matrix","package":"linear-algebra-ai999x","example":"Convert [[1, 0, 2], [0, 0, 3], [4, 5, 0]] to CSR 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8]].","v":[0.00175,0.01708,0.09562,0.02473,0.03904,0.00757,-0.04853,0.01211,0.07842,-0.04927,0.0007,-0.0548,0.02121,0.00681,-0.06902,0.12415,-0.01229,0.01219,0.00412,0.09769,-0.07451,0.01455,0.05686,0.04679,-0.11516,0.01512,0.00222,0.07399,-0.13577,-0.02185,-0.09713,-0.01596,0.03704,-0.04822,-0.08947,-0.11156,-0.00967,-0.0508,0.11716,-0.04776,0.14106,0.01959,0.06348,-0.03355,-0.01712,-0.03643,-0.08655,0.00486,-0.05759,-0.04393,-0.02091,-0.04264,0.13773,-0.07594,-0.0076,-0.02317,-0.07476,0.06762,-0.05831,0.07057,0.01847,-0.05982,0.02153,-0.06755,-0.10694,-0.04629,0.00315,0.02396,0.02819,0.0856,0.02825,-0.02505,0.07094,0.00832,-0.03966,0.00722,-0.01279,0.04438,-0.08386,-0.01485,-0.04191,-0.00934,0.06236,0.00307,0.04227,-0.04919,-0.01341,-0.04288,0.02838,0.00285,-0.07848,0.02105,0.05073,-0.04956,0.03933,0.03914,0.11838,0.06462,0.05196,0.01557,-0.04171,0.06757,-0.04025,-0.1787,-0.07731,0.11047,-0.02923,-0.05674,0.05003,0.06088,-0.05709,0.03387,-0.06917,0.01734,-0.01764,-0.06086,0.0475,-0.01758,0.04369,-0.02456,-0.0421,-0.0939,-0.05604,-0.08244,0.09074,-0.06844,0.05602,0.02568,-0.02856,0.07448,0.00671,0.07141,-0.10415,0.05295,-0.00301,0.0276,0.12129,-0.00661,0.08765,0.02512,-0.02445,-0.12238,-0.02488,0.09527,-0.15104,0.04021,-0.06491,0.12816,0.02703,-0.08567,-0.01147,-0.06536,-0.08104,-0.03882,0.07476,0.09254,-0.01904,0.04692,0.02772,0.08379,0.06418,0.007,0.02021,-0.06062,0.06208,0.01013,0.05852,-0.05907,0.00674,-0.08988,0.10655,-0.05773,-0.04342,0.00113,-0.0597,-0.05348,-0.08246,0.06291,0.0638,0.00647,0.03332,0.12256,0.07668,0.04558,0.04273,0.12297,-0.05269,0.01403,-0.08499,0.00065,0.11696,0.01873,-0.11754,0.04128,-0.07651,-0.08114,-0.05158,-0.03907,-0.06607,0.05547,-0.03166,-0.10892,0.0175,-0.04536,-0.0419,-0.03155,0.07035,0.03207,0.03805,0.07725,-0.07931,-0.00808,-0.06899,0.04107,0.03769,-0.05937,-0.04289,-0.06801,0.12646,-0.02993,0.02784,0.13088,-0.00355,-0.02138,0.0232,0.04594,0.0235,-0.12929,0.0796,0.05079,0.12415,-0.00208,-0.07757,-0.04239,0.10334,-0.01606,-0.04303,-0.0075,0.02687,0.0448,-0.03137,-0.00053,-0.01653,-0.06395,-0.06211,-0.07832,0.08626,-0.04993,0.03083,-0.04004,0.034,-0.03003,-0.05112,0.02611,0.04453,0.08178]},{"domain":"linear_algebra","key":"determinant_2x2","name":"Determinant 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2]].","v":[0.08332,0.03639,0.01129,-0.03196,0.04409,0.11374,-0.0985,-0.01037,0.09213,0.04943,-0.03286,-0.03457,-0.01661,0.03218,-0.04526,0.08384,-0.0585,0.0359,-0.02684,0.04335,-0.03682,0.10292,0.00578,0.01635,-0.10446,0.00855,0.01967,0.06263,-0.09011,-0.01582,-0.08359,0.02907,-0.0233,0.01103,-0.0637,-0.09745,-0.01277,-0.04824,0.00203,-0.0408,0.06565,-0.05456,-0.008,-0.03966,-0.04324,-0.04097,-0.02085,0.0356,-0.02081,-0.01188,0.03569,-0.06793,0.05367,-0.01436,0.06862,-0.00226,-0.12747,0.01934,-0.10414,0.07315,0.04713,-0.0615,-0.01941,-0.1227,-0.06785,-0.00145,-0.09701,0.06321,0.08884,0.01702,0.0562,0.07719,0.08798,-0.00876,0.04042,0.04078,0.05157,-0.00699,0.01454,-0.05911,-0.0267,0.04116,0.07801,-0.02029,0.0565,0.05062,-0.01056,-0.08571,-0.0437,0.03613,-0.13704,-0.02899,0.00683,-0.01536,-0.01181,0.05551,0.03301,0.03038,0.02025,-0.05076,-0.05646,0.12159,0.01712,-0.09938,0.0558,0.11162,-0.00745,-0.01311,0.06097,0.06829,0.08295,-0.01569,-0.06307,-0.01464,-0.00404,-0.10167,0.01021,0.00959,-0.02675,0.03615,-0.072,-0.04045,-0.03146,-0.07154,0.07034,-0.0401,0.14412,0.11235,-0.08189,0.0127,-0.06918,-0.10426,-0.03398,0.01726,0.03394,-0.01187,-0.00855,0.06718,0.02999,0.04231,-0.02351,-0.15493,-0.09315,0.00065,-0.03341,0.01479,-0.11688,0.12526,0.07449,-0.10043,-0.07724,-0.09675,-0.07741,-0.03652,0.06777,0.11654,0.00613,-0.00593,0.0465,-0.01929,0.00219,-0.00179,0.05869,-0.00743,0.15812,-0.01228,-0.01208,0.03191,-0.05494,0.04579,0.11516,0.00265,0.0269,-0.04739,-0.05656,-0.07869,-0.04059,-0.04068,0.10307,0.06232,0.0421,0.00017,0.11227,0.04391,0.0662,0.08535,0.00699,-0.08997,-0.01805,0.08701,0.02952,0.00542,-0.10465,0.11527,0.05162,-0.02482,0.01554,0.06385,-0.08918,0.02675,-0.13668,-0.12999,0.05975,0.03419,-0.06481,0.00647,0.06615,0.02726,0.06312,0.03069,0.04165,0.06943,-0.01806,-0.075,0.03532,-0.06295,-0.07154,-0.10559,0.04896,0.001,0.00701,0.11399,-0.02732,-0.04921,-0.06408,0.09946,0.04962,-0.12646,0.06683,-0.02057,0.05819,-0.04616,-0.0523,-0.03728,0.08376,-0.00236,-0.11398,-0.01725,-0.06546,0.00906,-0.05395,-0.0018,0.03765,-0.09477,-0.04472,-0.02141,0.07135,-0.01288,0.058,-0.07034,0.13525,0.02538,-0.05975,0.02776,-0.0061,0.06279]},{"domain":"linear_algebra","key":"distance_between_points","name":"Distance 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6).","v":[-0.01268,-0.13998,-0.08447,-0.00517,-0.05417,-0.06011,0.02555,0.07712,-0.06857,0.00548,0.08536,0.03101,0.05058,-0.00043,-0.09658,0.09348,-0.1425,-0.05063,-0.02337,0.05504,0.04527,0.07356,0.05311,0.03595,0.00405,0.05797,-0.06115,0.03254,-0.14401,0.10919,0.01305,0.0471,-0.0199,0.05513,-0.03493,-0.07394,0.03457,0.06537,0.01045,0.05787,0.00678,0.10588,0.02648,-0.05304,-0.02625,-0.0548,0.06956,-0.01015,-0.01216,-0.08481,-0.01871,-0.04045,-0.13835,-0.02279,0.01617,-0.07094,-0.08899,-0.02316,-0.08355,-0.00271,-0.02858,-0.05201,0.00619,0.06114,-0.00699,0.12101,-0.10042,-0.01368,-0.0298,0.02838,0.04338,-0.02628,-0.02536,0.07771,-0.02865,0.03938,0.04213,-0.09805,-0.12627,0.01947,0.01122,0.04796,0.06643,-0.05441,0.04038,0.02095,0.0376,-0.06605,-0.01184,-0.02639,-0.00259,-0.00138,0.05777,0.01295,-0.00975,0.00659,0.02208,-0.03995,0.16121,-0.03903,-0.00345,-0.06349,0.00087,-0.08612,-0.04671,-0.04178,0.06172,-0.00451,0.07913,-0.10487,-0.01729,-0.02987,0.01878,-0.01168,-0.06467,0.05238,-0.00345,0.02211,-0.01025,-0.02887,0.04768,-0.0008,0.05167,0.02458,-0.0467,-0.11888,0.00458,0.03996,-0.00553,0.02235,0.05734,0.03329,-0.0403,0.00192,0.10838,-0.02906,-0.00365,0.07301,-0.05063,0.06856,-0.0021,-0.003,0.03943,0.03618,0.04124,0.0537,-0.08095,-0.01389,0.0177,0.06746,0.03116,0.08886,-0.02662,0.0367,-0.1108,-0.0859,-0.03705,-0.09646,-0.01611,0.02652,-0.03359,0.0479,0.11782,-0.04193,0.02382,0.02351,-0.03987,0.06932,-0.00674,-0.12198,-0.06141,0.10503,0.01975,-0.01766,-0.03514,0.0403,0.04684,0.02243,0.0945,-0.09633,0.08096,0.09714,0.06659,0.08966,0.02348,-0.13797,-0.03441,0.00459,-0.02672,0.11949,-0.09237,0.03473,0.0227,0.07502,-0.06219,-0.13619,0.02505,0.04954,0.01663,0.00151,-0.11701,0.00439,0.02937,-0.03184,-0.01574,0.00135,-0.0762,0.00526,0.11661,0.15042,0.1154,0.00829,0.07735,0.06006,-0.04964,0.05397,-0.02759,0.00799,0.00798,0.01594,0.06466,-0.02491,-0.07121,0.06195,0.06435,0.02691,0.13626,-0.04446,-0.00196,0.00893,-0.1332,0.04802,-0.04933,-0.117,0.03606,-0.01514,-0.01702,0.09656,-0.08864,-0.0151,0.06293,-0.05506,0.01253,-0.04778,0.01371,-0.11837,0.02264,0.02106,0.03677,-0.02263,0.16262,-0.05143,-0.09896,-0.09844,-0.13158,0.06194]},{"domain":"linear_algebra","key":"eigenvalues_2x2","name":"Eigenvalues 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2]].","v":[-0.0994,-0.09729,-0.07675,0.01584,-0.08145,-0.02542,0.03419,0.0112,0.05346,-0.02705,0.04476,0.05375,0.04411,-0.01195,0.0358,0.0212,-0.07066,-0.02449,0.0582,-0.03414,-0.10024,0.14207,0.03123,0.09269,-0.09285,-0.08036,-0.03175,0.0222,-0.02597,0.06941,-0.01977,0.0411,0.05768,-0.01379,0.0767,-0.1474,0.07442,-0.03109,0.05036,-0.01481,0.0207,-0.09683,0.00929,0.02183,-0.01019,-0.02194,-0.06305,0.00312,-0.01072,0.13543,-0.01479,0.0371,0.00906,0.09618,-0.03632,0.01827,-0.03632,0.01527,-0.01823,0.07777,0.0359,-0.08223,0.09124,0.16177,-0.04299,-0.00968,-0.06035,-0.00679,0.17093,-0.03448,0.01166,0.06232,0.07178,-0.02278,-0.01821,-0.02138,0.053,0.01487,0.01807,0.00957,0.05539,-0.00527,0.00862,-0.00281,0.03269,-0.02398,0.00923,0.02791,-0.03056,0.15987,-0.15689,-0.15437,-0.06717,0.03312,0.0138,-0.01164,0.01267,-0.03406,0.06944,0.06107,0.00439,0.13527,-0.01426,-0.12695,0.05772,0.05717,0.03578,-0.05858,0.01888,-0.00933,0.01424,-0.0589,-0.11155,0.01329,-0.01409,-0.04955,0.02083,0.05584,0.10115,-0.00247,0.05591,-0.05247,0.08658,0.01102,0.0032,0.07409,0.03596,0.05974,0.00373,-0.04014,-0.04518,0.00925,0.09196,-0.00514,0.0272,-0.09213,-0.01489,0.04628,0.05148,-0.02041,0.09584,-0.00045,-0.05607,0.04752,-0.07871,0.11283,0.00208,-0.01266,0.04541,0.0081,0.01469,0.06309,0.04203,-0.01368,0.10017,-0.04793,0.03055,0.08126,-0.0583,0.10261,-0.05618,-0.08622,-0.10793,0.00787,-0.08679,0.05515,-0.10843,0.04962,-0.05885,0.06667,0.05933,0.03704,0.01785,0.03689,-0.05389,-0.05226,0.0432,-0.10432,0.02305,-0.11129,0.01818,0.06136,0.05057,0.03873,-0.07545,0.03842,0.00842,0.03007,-0.00581,0.01716,0.12319,0.01159,0.00673,0.01864,-0.05684,-0.05826,-0.04423,-0.00139,0.11021,-0.0763,0.13538,-0.00194,0.00744,0.06419,-0.05587,-0.10646,0.04416,-0.04597,-0.03428,0.00482,-0.07351,0.06306,-0.04954,0.014,0.04121,-0.01066,-0.04631,-0.05842,0.09948,-0.02171,-0.07079,0.01053,-0.14085,0.06237,0.01462,-0.00174,-0.04815,-0.14711,0.06369,-0.04338,0.03823,0.04932,0.00186,-0.11336,0.02269,-0.04673,-0.0168,-0.01313,-0.11568,-0.05757,0.03539,-0.08648,-0.00789,0.02406,-0.00838,-0.03628,0.07926,-0.14376,-0.04765,-0.03104,-0.09897,0.01493,-0.1303,0.03767,-0.0414,0.01718]},{"domain":"linear_algebra","key":"gauss_legendre_integral","name":"Gauss-Legendre 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12).","v":[0.02476,0.09627,0.04383,0.07004,-0.02139,-0.04447,-0.01893,-0.05986,-0.02259,0.07508,-0.0308,-0.08041,-0.04226,0.03744,-0.00764,-0.06227,-0.08801,0.05671,0.04276,0.08843,0.01927,-0.05896,0.05083,0.11066,0.01788,0.0053,0.08523,0.07662,-0.01622,0.0236,0.00678,-0.05731,-0.09385,0.0206,-0.01852,0.00937,-0.03797,0.09209,-0.0485,-0.05077,0.00637,0.08112,0.02516,0.02778,-0.04104,0.03077,0.08622,-0.00059,0.00132,0.069,0.07374,-0.05084,0.22248,0.00418,-0.04083,0.02137,0.0347,-0.0011,-0.01124,-0.03889,0.10836,-0.13118,-0.02443,-0.04575,0.02865,-0.02133,0.04179,-0.10558,0.02511,-0.03782,0.0811,-0.06625,-0.00306,0.0636,-0.0122,0.06521,-0.04145,0.00091,-0.11115,0.0477,0.01341,0.02858,-0.08711,0.1216,0.035,-0.0035,-0.01839,-0.11501,0.03265,-0.13141,-0.0251,-0.08462,0.00971,-0.06441,0.02445,-0.0638,0.00848,-0.00264,0.0323,0.03405,0.12087,-0.03879,-0.01968,0.01607,0.03908,-0.045,0.06794,-0.07485,0.01541,0.03183,-0.01809,0.06726,0.03585,-0.02958,0.0266,-0.01419,0.04761,0.01551,-0.07727,-0.0439,-0.0232,-0.04332,-0.05734,-0.01107,-0.03996,-0.09131,0.00222,0.09293,0.1357,-0.03156,0.10218,-0.05428,-0.14463,-0.03178,-0.04233,-0.0227,0.06179,0.02061,0.00438,-0.03535,-0.14778,-0.10003,0.04625,0.12227,0.03922,0.01572,0.01286,-0.02398,-0.04845,-0.01453,-0.04918,-0.06819,0.10711,0.05086,-0.02175,0.08232,-0.02906,-0.01259,-0.01216,-0.06128,-0.12945,-0.09291,0.00483,-0.05671,-0.10371,-0.05811,0.09099,0.00856,-0.06887,0.11378,0.0104,-0.0331,0.14879,-0.05169,0.06766,0.04378,-0.07884,-0.06343,-0.01295,-0.01042,0.11078,0.05682,-0.03745,-0.0664,-0.00838,-0.01782,-0.04722,0.04433,0.04418,-0.00297,-0.03728,0.07903,-0.01227,-0.1314,0.05826,0.0394,0.08148,0.08231,0.04867,0.02857,0.07196,0.05026,0.04572,0.01469,0.06871,-0.06922,-0.08672,-0.01791,-0.0395,-0.00474,-0.02183,-0.02129,-0.06036,-0.04841,0.07771,-0.03668,0.0575,-0.01138,0.06003,-0.04228,0.16562,-0.04989,-0.03372,0.02959,0.03222,-0.02486,0.01493,-0.07872,0.04366,0.03331,0.01651,-0.06281,-0.13291,-0.00959,0.02817,0.02655,-0.09488,-0.02854,0.05874,-0.10077,0.08728,0.10708,-0.11902,0.00635,0.0668,0.02844,-0.01426,-0.03269,0.07873,-0.04951,0.10224,3e-05,-0.09241,-0.02518,0.097,-0.01199]},{"domain":"linear_algebra","key":"general_eigenvalues","name":"Eigenvalues 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2]].","v":[-0.0783,-0.05762,0.00362,0.0608,-0.05874,-0.08526,-0.04155,-0.02708,0.02611,-0.1014,0.08379,0.11172,0.05763,-0.01619,0.07779,0.06752,-0.02396,0.02617,0.07359,0.02066,-0.01343,-0.02085,-0.01259,0.01399,-0.00949,0.00063,-0.03116,0.02094,-0.00869,0.01149,0.00508,-0.03645,0.01983,-0.12378,0.00647,-0.11474,0.03355,-0.04309,0.09564,-0.08608,0.05689,-0.11206,0.02864,0.04358,-0.02149,0.01902,-0.02029,-0.10535,-0.01725,-0.01891,-0.00468,-0.07197,0.11236,0.10758,-0.12391,-0.08906,0.03399,-0.01013,0.0845,0.00924,0.1219,-0.12801,0.1116,0.11852,0.01543,-0.10296,-0.01752,-0.0667,0.02201,0.05482,0.11896,0.07574,0.02499,0.02816,-0.03818,0.02034,-0.00457,0.07752,0.03315,0.05379,0.04969,-0.02539,-0.03582,-0.0097,0.04377,-0.05318,0.07461,0.04476,0.00467,-0.08118,-0.10275,0.00473,-0.04566,0.02627,0.02138,-0.02244,0.01603,0.02107,0.07959,0.032,0.02739,-0.03755,-0.08314,-0.14134,0.00547,0.07595,-0.08936,-0.1163,0.00071,-0.04571,-0.09999,0.05722,-0.09786,0.10282,0.00875,-0.0918,-0.03566,0.0206,0.10621,-0.1507,0.08199,-0.06662,-0.05326,-0.07384,-0.01763,0.03858,0.06325,0.04564,0.0617,0.03142,-0.06494,0.08864,-0.06212,0.03341,-0.05667,-0.04015,0.02963,-0.03632,0.12966,-0.05354,0.04347,0.03144,0.00962,0.15272,-0.03467,0.04484,0.06977,-0.07609,-0.00444,0.03102,0.02186,0.10267,0.05856,-0.0291,0.01132,0.02958,-0.05847,0.06617,-0.0341,0.10485,-0.01303,-0.03827,-0.06372,-0.0408,-0.09995,0.0928,0.05687,0.02919,0.05537,0.0349,0.06326,-0.05765,-0.10471,0.03009,-0.08195,-0.03943,0.01601,-0.00978,-0.04921,-0.06273,0.01688,0.15971,0.02307,0.00521,0.03083,-0.01277,-0.02383,0.02057,0.02199,-0.00337,0.04761,0.01262,0.02578,-0.05174,0.02101,-0.02383,-0.03285,0.03225,0.12518,-0.00506,0.14211,0.02915,0.06095,0.12048,-0.09551,-0.07232,0.02382,-0.01037,-0.04098,0.01742,-0.05746,0.03983,-0.05093,0.05076,-0.00565,-0.00544,-0.106,-0.05726,0.12855,-0.04835,-0.03049,-0.00334,-0.09416,0.04875,0.04693,0.00983,-0.09664,-0.12714,0.0361,-0.06864,0.08594,-0.00571,-0.0557,-0.03379,-0.05296,-0.01625,-0.01731,-0.08284,-0.03591,-0.02969,0.01124,-0.01007,-0.01098,0.0618,-0.07552,-0.01678,-0.00145,-0.1082,-0.0264,0.04553,0.00383,-0.0386,-0.03495,0.0804,0.02043,0.07385]},{"domain":"linear_algebra","key":"gram_schmidt","name":"Gram-Schmidt 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0).","v":[0.03021,0.03736,-0.05944,0.00293,-0.10623,-0.05122,-0.03284,0.08851,0.05391,0.06254,0.03187,-0.05123,-0.04069,0.02125,0.01493,-0.01215,-0.05177,-0.03432,0.09977,0.06714,-0.06281,0.0335,-0.03761,-0.0396,0.03263,-0.02364,0.01279,0.06931,-0.11457,0.02181,-0.02954,-0.03428,0.02403,0.03213,-0.09048,-0.05019,0.02008,0.03399,-0.08195,0.04313,0.06844,-0.00182,-0.02144,-0.05999,-0.07736,-0.03209,0.01118,-0.00984,-0.08191,0.05325,-0.00308,-0.04874,-0.0146,0.0247,-0.05573,-0.02967,0.096,0.00945,-0.00476,0.07612,0.06517,0.01704,-0.00474,-0.03002,0.05621,0.07013,0.07034,-0.05213,0.05516,0.04436,0.04975,-0.00932,0.09049,0.12357,-0.00641,0.13334,0.10636,0.00559,0.01657,0.02746,0.01168,0.0733,-0.01438,-0.02582,-0.0695,0.00377,-0.02992,0.08262,-0.08662,-0.10691,-0.04444,0.04384,-0.03278,-0.05104,-0.00543,-0.02769,-0.03525,-0.03141,0.10319,-0.04917,0.00607,-0.04784,0.06649,-0.02208,0.04233,-0.05966,0.1048,-0.05359,0.03889,-0.1795,-0.03869,0.02935,-0.02536,0.04014,-0.12723,0.06182,-0.1354,-0.04758,0.00936,-0.09032,-0.01558,0.10276,-0.04957,-0.01469,-0.01789,-0.08092,0.10749,0.07183,0.07173,-0.00386,0.01717,-0.08591,-0.10888,-0.04089,0.05157,-0.11288,-0.05552,0.04201,0.05191,-0.00127,-0.00797,-0.01151,-0.0648,0.13107,0.12224,-0.02725,-0.06519,-0.131,0.08754,0.00111,0.01028,0.08262,-0.04684,0.13128,-0.10376,-0.04868,0.02239,-0.06776,0.08855,0.01742,-0.01872,0.037,0.16407,-0.05388,-0.05523,0.0309,-0.07271,0.06247,-0.04073,-0.00016,0.04484,0.02204,0.05045,-0.00445,0.00192,0.04441,0.03303,0.06307,-0.07694,-0.10605,-0.01638,-0.06384,0.03543,0.0043,0.08143,0.02733,0.05729,-0.07518,-0.00884,-0.07007,0.0465,0.00689,0.05552,-0.05485,0.07577,0.02438,0.05001,0.03571,0.03932,0.02801,-0.11001,-0.07636,-0.05788,-0.00599,-0.05289,-0.05756,0.11956,-0.00529,-0.07027,0.0109,0.01904,-0.0002,0.06024,0.09565,0.01512,-0.01404,-0.14198,-0.04387,0.05245,-0.01289,0.04002,0.0475,0.04279,0.15328,0.03465,0.0604,-0.02398,-0.14043,-0.03755,0.05767,-0.05605,0.08592,-0.07352,-0.12689,-0.07064,0.01625,0.02731,-0.00089,-0.11599,-0.04856,0.10995,-0.0039,-0.06445,0.03815,0.07221,0.05422,-0.02229,-0.00594,0.03843,0.08622,0.05401,0.00161,-0.04856,-0.08948,0.05963,0.05181]},{"domain":"linear_algebra","key":"interpolating_polynomial","name":"Coefficients 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12).","v":[0.00549,0.04974,0.02343,0.05265,-0.05914,-0.04421,-0.0317,-0.05,0.02631,0.04135,0.01327,-0.11322,-0.00777,-0.02668,-0.04723,-0.12467,-0.11039,0.08321,0.01679,0.03662,0.03138,-0.03037,0.06611,0.04407,0.07171,0.00994,0.04919,0.02288,-0.0226,0.00455,-0.00054,-0.08386,-0.04115,0.10365,0.01963,-0.04681,0.04926,0.05054,-0.03256,-0.0357,0.02663,0.04958,0.02774,-0.08266,0.03589,-0.06194,0.03205,-0.02711,-0.07919,0.13576,0.08166,-0.07744,0.10574,0.10626,-0.04217,0.06471,0.10298,-0.08383,0.00334,-0.04103,0.0613,-0.12683,0.06146,0.00606,0.02776,-0.04465,0.0339,-0.01571,0.00376,0.02193,0.04184,-0.03153,0.0405,0.02099,-0.08506,0.06036,-0.0734,-0.03612,-0.03265,0.00239,-0.00917,-0.03216,-0.05654,0.08111,-0.00858,-0.02172,0.00031,-0.17311,-0.07198,-0.09298,-0.03669,-0.05684,0.06164,-0.02605,-0.03579,-0.06916,0.04992,-0.08596,0.13105,0.05497,0.08972,-0.00395,-0.09382,-0.08612,0.04402,-0.02059,-0.02386,0.01503,-0.03345,0.03185,-0.06824,0.06008,0.05937,-0.082,0.02387,-0.02989,0.09398,0.00613,-0.03179,-0.07301,-0.04339,-0.06124,0.03554,-0.08538,-0.0221,0.05797,-0.03139,0.02958,0.12042,0.04749,0.07477,0.00703,-0.01647,-0.00335,-0.10065,0.00874,0.02724,0.00303,0.0732,0.00849,-0.10933,-0.09105,0.09343,0.05667,-0.02388,0.11355,0.04301,-0.03669,0.01823,-0.02349,-0.00583,-0.10261,0.14185,0.07315,0.04169,0.0146,-0.01061,-0.01253,-0.00516,0.01573,-0.0605,0.04417,-0.00976,-0.01233,-0.07882,-0.05377,0.10061,-0.07298,-0.07903,0.15045,0.06066,-0.07353,0.0885,-0.12778,0.09988,0.0043,-0.02364,0.03079,-0.03604,-0.12544,0.03105,0.11986,-0.03571,-0.01791,-0.06245,-0.0109,0.00895,0.07647,0.0328,0.03308,-0.00235,0.04094,0.05228,-0.07495,0.00977,-0.0291,0.0347,0.07419,0.04773,-0.02516,0.20012,0.0598,0.03554,0.04665,0.0219,-0.09299,-0.05413,0.05031,-0.0478,0.05486,-0.09443,-0.09454,-0.10145,-0.01656,0.09429,0.02217,0.05863,-0.02871,0.0153,-0.01455,0.1194,-0.04158,-0.10229,0.08087,0.03157,0.07394,-0.03718,-0.06303,0.02997,-0.04516,0.01793,0.01345,-0.14031,-0.05421,-0.00929,-0.01004,-0.07619,0.07286,0.04115,-0.07043,-0.02363,0.10308,-0.11781,-0.00203,0.0266,0.01816,-0.04698,-0.07961,-0.03915,0.03535,0.01421,0.04962,-0.00657,0.0335,0.0797,-0.02559]},{"domain":"linear_algebra","key":"kronecker_product","name":"Kronecker 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4]].","v":[0.05401,0.09624,0.01316,0.04945,-0.06074,-0.10415,-0.07415,-0.06638,0.05224,0.07329,0.01805,-0.14622,0.02232,0.04476,0.04043,0.08573,0.00879,0.02591,0.0005,0.08066,0.00371,0.00061,-0.03233,-0.02223,-0.01661,-0.01683,0.07956,-0.00736,0.02368,0.02653,-0.07322,-0.02132,-0.01799,-0.03796,-0.02958,0.07972,-0.05519,-0.0593,-0.06809,0.09487,0.09468,-0.0741,0.0405,-0.09298,-0.01852,0.03194,0.00323,0.08664,-0.02865,-0.04714,-0.0146,-0.13807,0.01069,0.01508,0.03253,0.02147,0.01673,-0.08508,-0.02052,-0.01189,0.1027,-0.08096,-0.00257,-0.04194,0.02286,-0.04771,-0.01216,-0.01744,-0.01956,-0.01301,0.04108,0.02756,0.08208,0.03394,-0.04337,0.08467,0.00527,0.0082,-0.01811,-0.01618,-0.03291,-0.01467,-0.02986,0.04523,0.02959,-0.1491,0.03791,-0.11469,-0.0103,-0.0799,-0.0066,0.07655,-0.05989,-0.04667,0.02489,0.04736,0.00286,0.02454,0.14329,-0.01401,0.0267,0.03043,0.02732,-0.04311,-0.05112,0.03293,0.04911,-0.12685,0.03545,-0.00386,0.02763,0.04993,0.06333,-0.02566,-0.0438,-0.01546,-0.03524,0.05957,-0.06121,-0.14059,-0.08722,-0.10481,-0.09928,0.04365,0.05391,-0.05026,-0.03902,0.15981,0.14196,0.10002,0.16321,0.03698,-0.00139,0.00344,-0.08289,-0.01563,0.0891,-0.01953,0.13459,-0.04093,0.06681,-0.10921,0.20428,0.09789,-0.00077,0.07541,0.07898,-0.09683,0.02038,0.02935,-0.01834,-0.05481,0.09789,-0.05131,0.04804,-0.02046,-0.01428,-0.04118,0.08404,0.04618,0.00745,0.00587,0.03041,-0.00791,0.03864,-0.00429,0.07919,-0.05107,-0.05877,0.00569,0.01053,0.10235,0.04725,0.00828,0.01548,0.15624,0.01881,-0.02032,0.06051,-0.04055,-0.03383,0.04444,0.06332,-0.01095,0.06364,-0.04389,0.04453,-0.00644,-0.05693,0.0029,0.11352,0.01691,-0.0428,-0.06395,0.00409,-0.07321,0.02918,0.10724,0.09757,0.05152,-0.01958,-0.08743,-0.03919,-0.04793,0.00853,-0.06249,0.00071,0.02296,-0.00488,-0.05534,0.03125,0.04327,-0.07563,0.04152,0.07153,-0.00209,-0.03216,0.0246,-0.02611,-0.16938,0.00158,-0.07489,-0.08042,0.05348,-0.10017,0.00402,-0.03204,-0.11413,0.0312,-0.08869,0.00635,-0.01446,-0.16235,-0.08731,0.01078,0.01674,-0.09191,-0.0951,-0.04994,-0.05062,0.02697,0.084,0.00033,-0.00128,-0.03515,-0.03627,0.063,-0.04901,0.0558,-0.04755,-0.04362,-0.00775,-0.02034,0.01777,0.10193,-0.01897]},{"domain":"linear_algebra","key":"matrix_addition","name":"Sum of two matrices","package":"linear-algebra-ai999x","example":"Add the matrices [[1, 2], [3, 4]] and [[5, 6], [7, 8]].","v":[-0.05901,-0.05839,0.06742,0.06645,-0.01691,-0.06585,-0.02613,0.01471,0.02814,0.05357,0.01037,0.02879,0.02124,0.04734,-0.07908,-0.19396,-0.06986,0.04137,0.12046,0.03356,0.01259,-0.04825,0.04566,0.08427,-0.04688,-0.01858,-0.01891,0.08188,-0.09719,0.09764,0.00679,0.04243,-0.04909,-0.01953,0.02956,-0.0979,0.04366,-0.01824,0.01186,-0.02053,0.00381,0.06606,-0.00903,-0.11313,-0.08598,-0.05328,-0.1097,0.03672,-0.06877,0.08274,-0.08108,0.02204,0.11547,0.03222,-0.02487,0.09548,0.06239,-0.02886,0.04267,0.07952,-0.01114,0.04175,0.0794,-0.10714,-0.172,0.07539,0.07204,0.03886,0.06013,-0.03541,-0.02367,0.027,0.03874,-0.0584,-0.07078,-0.0458,0.0512,0.04803,-0.03657,0.04348,-0.02723,-0.07239,0.0669,0.01212,0.02728,-0.00795,0.03917,0.08735,-0.0094,0.05717,-0.11401,0.00456,-0.00535,0.04707,-0.02742,-0.14086,0.09151,0.02941,-0.09795,-0.00374,-0.037,0.02276,-0.0812,-0.03018,-0.02191,0.00727,0.01325,0.0143,-0.0846,0.02301,-0.0236,-0.02105,-0.0088,0.05676,0.04171,-0.04391,0.0357,-0.03024,0.01113,0.02826,-0.15292,0.0127,0.04256,-0.00884,0.07491,0.02249,-0.05368,0.03578,0.05816,0.04718,0.11319,-0.05103,-0.21557,0.05196,-0.01625,-0.13822,0.01115,0.07001,-0.0508,-0.02313,-0.05231,-0.04031,-0.04206,0.04581,0.00875,0.11064,-0.0055,0.10323,0.01748,0.02705,-0.14714,0.04284,-0.04185,-0.07735,0.07048,-0.06836,0.00718,-0.05644,-0.01479,-0.0009,0.00329,-0.1031,-0.00864,0.03373,0.10765,0.04518,-0.12165,0.03593,-0.06054,-0.04104,-0.00688,-0.01344,0.03411,-0.03475,-0.00877,-0.01514,0.05197,-0.14404,-0.01293,0.02202,-0.01714,0.03547,0.0943,0.06088,-0.04809,0.06568,0.03638,-0.03382,-0.02306,0.01102,-0.03992,0.17354,-0.07496,0.14144,-0.06822,-0.0458,-0.01535,-0.01546,0.05907,-0.05033,-0.00631,0.04668,-0.0046,0.07938,-0.03857,-0.02166,-0.02101,0.08934,0.03753,0.03771,-0.02256,-0.02307,-0.09661,0.0283,-0.02198,0.04658,0.00192,-0.0674,-0.03211,0.0467,0.0682,0.00061,-0.00171,0.03457,0.00047,0.07429,-0.04706,-0.02185,0.13343,0.09558,0.07292,0.0163,0.04253,-0.00697,0.06874,0.00249,0.07153,-0.00118,-0.08164,-0.06206,0.02598,-0.14385,-0.08753,0.03352,-0.05519,-0.07746,0.00111,-0.02303,0.043,-0.04582,-0.02289,0.08061,-0.06042,0.04904,-0.06836,0.05426]},{"domain":"linear_algebra","key":"matrix_exponential","name":"Matrix exponential","package":"linear-algebra-ai999x","example":"Find the matrix exponential of [[0, 1], [0, 0]].","v":[-0.03719,-0.03301,-0.03073,0.1214,-0.02418,-0.05205,-0.06739,0.02026,-0.02658,0.04876,0.04313,-0.05245,-0.02158,0.03819,0.07211,-0.04917,-0.02906,-0.04398,0.14707,0.03313,-0.00299,0.0015,0.0032,0.02066,-0.07396,-0.01767,-0.00782,0.11759,-0.08677,0.18973,0.01029,0.05687,0.01329,-0.01604,-0.0382,-0.07506,-0.04149,-0.02825,0.00604,0.04578,0.03728,0.01408,0.0379,0.00272,0.06905,-0.04317,-0.03834,-0.0686,-0.07232,0.03976,0.044,-0.0269,0.08908,0.04686,-0.03018,0.06713,0.08966,-0.02488,-0.04479,-0.05395,0.07371,-0.12492,0.06404,-1e-05,-0.15799,-0.0246,0.02739,0.03954,0.00187,0.08035,0.0863,-0.02733,0.03955,-0.00867,-0.03263,-0.01767,-0.05479,-0.09121,-0.06435,0.00515,-0.02064,-0.06756,-0.07803,-0.07479,0.00228,-0.13027,0.00091,-0.00605,0.0672,-0.05172,-0.08811,-0.02288,0.01563,-0.01953,-0.06206,-0.0951,0.05348,0.02826,0.13945,0.03991,-0.01651,0.03063,-0.00679,-0.0363,0.00575,0.0294,-0.00351,-0.11062,0.05404,0.03859,-0.0322,0.06728,0.00887,0.08804,0.0592,-0.01759,-0.13969,0.01186,0.07713,-0.05608,0.02599,-0.06625,-0.05965,-0.07534,0.0304,-0.01272,-0.08269,-0.01079,-0.01071,0.04514,0.02746,0.07477,-0.03437,0.01788,0.01905,0.07334,0.02825,-0.03225,0.13192,-0.01897,0.00786,-0.08076,-0.05517,0.07636,-0.13328,0.09759,0.0218,0.0453,-0.09517,0.05845,-0.00283,0.03412,-0.00347,-0.04465,-0.01463,0.02317,-0.12268,0.11431,0.13804,0.10607,-0.03662,-0.03183,-0.02529,0.02271,-0.0064,0.03135,-0.02309,-0.04176,-0.05988,-0.00493,-0.02212,0.00305,-0.00596,0.16,0.00442,-0.07067,-0.06009,0.01011,-0.03698,0.09986,0.01376,0.07165,-0.03738,-0.03538,0.08389,0.06134,0.0188,0.04096,-0.03351,-0.02111,0.09161,-0.04868,-0.05731,-0.12738,-0.02707,-0.01541,-0.00428,-0.09915,0.07506,0.01537,0.07361,-0.06035,-0.02215,0.06482,-0.04601,-0.02887,0.07886,0.01721,0.10083,0.08498,-0.10083,0.01253,-0.08862,-0.02962,0.05471,-0.07154,-0.00484,-0.07194,0.03691,0.0413,0.12219,-0.10075,0.00041,0.09827,0.1472,-0.06121,-0.06002,-0.12381,0.08366,-0.1174,0.10525,-0.03141,-0.01483,0.14131,0.03428,0.02074,0.02803,-0.07481,-0.0046,-0.04613,0.0411,0.03159,-0.0691,-0.02084,-0.05495,-0.08468,0.00437,-0.07233,0.00163,0.04487,0.03159,0.0613,-0.01467,-0.01356,0.07005,-0.01276]},{"domain":"linear_algebra","key":"matrix_inverse","name":"Inverse 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6]].","v":[0.04755,0.05065,0.01439,0.07947,0.05125,-0.06524,-0.11214,0.0202,0.01697,-0.04188,-0.00885,-0.06818,-0.01551,-0.00242,0.04181,0.04273,-0.07194,-0.02313,0.1059,0.07642,-0.1038,-0.00765,0.02517,0.01693,-0.09739,-0.08714,0.052,0.0119,0.08959,0.09239,-0.0523,0.04577,-0.04029,-0.0175,-0.08441,-0.09618,-0.06527,-0.10497,0.01035,-0.00934,0.07928,-0.0612,-0.03378,-0.00983,0.07191,0.06359,-0.06053,0.05111,-0.09154,0.00066,0.10167,-0.11615,0.02748,0.06207,-0.04197,0.02155,0.05919,-0.03942,-0.01124,0.06012,0.06962,0.0143,-0.03243,-0.06015,-0.12136,-0.07369,-0.01835,0.01033,0.06432,0.06297,0.04606,-0.05779,0.07309,-0.07406,-0.06753,-0.01445,-0.01981,0.01566,-0.012,0.06654,-0.0098,0.0065,-0.04728,0.01703,0.08478,-0.04032,-0.0084,-0.11868,0.03448,-0.06595,0.00753,-0.06097,0.08495,0.00083,0.02195,-0.01989,0.07703,-0.0215,0.08508,0.0648,0.0462,0.02075,-0.042,-0.07968,-0.13682,-0.05217,0.03986,-0.04225,-0.023,0.04497,-0.04074,0.05998,-0.08099,0.01902,0.04146,-0.07967,0.00491,-0.01704,-0.05884,-0.04912,-0.06915,-0.08096,0.03756,-0.0997,0.10392,0.08369,-0.0295,0.13063,0.04844,0.08145,0.04028,0.11318,-0.08952,-0.08561,0.05122,-0.04259,0.03067,0.04241,0.03258,-0.04298,0.05696,-0.06891,0.04967,0.03011,-0.06144,0.0413,-0.00908,0.05433,-0.01412,-0.06232,-0.0361,0.00551,4e-05,0.03881,0.11361,0.12454,-0.09405,0.02916,0.1582,0.15242,-0.00112,-0.02055,-0.02697,-0.05782,-0.01258,-0.00468,0.00935,-0.04876,-0.05625,0.00812,0.01679,0.0833,0.10815,0.08736,0.00619,-0.09811,0.03215,0.02001,-0.00135,-0.03169,0.0371,0.0379,0.06873,0.03999,0.06406,0.02424,0.0609,0.05374,0.01012,-0.01821,0.11411,-0.02231,0.01118,-0.13187,-0.08275,0.00363,0.05191,0.02805,0.04408,0.11397,0.01098,-0.03291,-0.02539,-0.10851,-0.01638,-0.09453,0.07885,0.02611,0.02417,0.02365,0.02805,-0.02779,-0.11799,-0.04213,0.07114,-0.02087,-0.02691,0.03206,0.13756,-0.11242,0.09227,0.02401,-0.02979,0.01849,0.07261,0.02682,-0.06751,-0.14191,0.09563,-0.02549,0.11357,-0.01533,-0.08325,-0.00991,0.05223,0.02427,-0.1036,-0.02591,-0.0881,-0.02611,-0.00235,0.02841,-0.0221,-0.03886,0.067,-0.02627,-5e-05,-0.03949,0.04768,-0.10572,-0.03029,0.12119,-0.08887,0.01098,-0.01016,0.09757]},{"domain":"linear_algebra","key":"matrix_multiplication","name":"Product of two matrices","package":"linear-algebra-ai999x","example":"Multiply the matrices [[1, 2], [3, 4]] and [[5, 6], [7, 8]].","v":[-0.04978,-0.08414,0.05253,-0.01589,-0.04439,-0.02515,-0.04166,0.00524,0.022,0.12252,0.00323,0.01764,0.0135,0.0801,0.02041,-0.05216,-0.08547,-0.05655,0.08611,0.07997,-0.031,0.01528,0.05223,0.0682,-0.06942,0.01258,0.0161,0.06254,-0.10036,0.12352,0.02687,0.01943,-0.04545,0.05543,-0.08356,-0.03636,0.05705,0.06001,-0.11215,0.01484,-0.00952,0.04145,0.07379,-0.08101,-0.09172,-0.0513,-0.07378,0.01521,-0.05932,0.06107,0.00731,-0.05237,0.08574,-0.01837,0.01113,0.11044,0.01719,-0.04814,0.02167,0.08529,0.01539,-0.08291,0.05762,-0.1813,-0.1224,0.12644,0.03666,0.06383,0.02164,0.01323,0.00301,-0.0225,0.01419,-0.03037,-0.02,-0.03347,0.00496,0.02214,-0.03247,0.01726,-0.1009,-0.02136,0.04345,-0.04484,0.04112,-0.0423,0.05733,-0.06646,-0.06425,0.06545,-0.0814,-0.02694,0.0311,0.02926,0.06518,-0.08991,0.14713,-0.00863,0.04492,0.11603,0.02914,-0.00692,-0.01673,-0.10867,-0.10339,0.0358,-0.08306,-0.00483,-0.03866,-0.05254,-0.03656,0.01397,0.02017,-0.0247,-0.02513,0.07827,0.01819,0.02867,-0.02549,-0.02,-0.06826,-0.02514,0.06145,-0.02987,-0.01554,0.04541,-0.11133,0.07934,0.0299,0.15359,0.09467,-0.01136,-0.07375,-0.00321,-0.01346,-0.12727,0.02979,0.05248,-0.03975,-0.0511,-0.07986,-0.02823,0.03111,0.03047,-0.12651,0.08969,-0.00397,0.04761,-0.04497,0.0464,-0.04033,-0.00669,-0.03056,-0.06835,0.09696,-0.0299,0.02407,0.01807,-0.00084,-0.04364,-0.01913,0.00519,0.14679,-0.03868,0.01288,-0.04841,-0.12096,-0.02085,-0.07792,-0.00378,-0.01165,0.027,0.035,-0.06786,0.08673,0.02611,0.05668,-0.09262,0.06615,-0.01128,-0.01235,0.11188,0.01699,0.09571,-0.01222,-0.00932,0.03769,0.05704,-0.10546,0.03605,-0.00322,0.18444,-0.0557,0.01538,-0.14194,-0.05696,-0.00483,-0.00073,0.00487,0.01675,-0.00537,-0.02145,-0.04226,0.09044,0.01682,0.01071,-0.06869,0.10923,0.01813,0.05188,-0.03053,-0.05329,-0.2017,0.05386,0.05211,0.01481,0.01939,-0.04712,0.05692,0.04416,0.15889,-0.02348,-0.10374,0.04966,-0.00322,0.12108,0.05178,-0.02871,0.1311,-0.00339,-0.00939,0.0492,-0.02627,0.03728,0.03642,-0.05134,0.07849,-0.01925,-0.05663,-0.04488,-0.02499,-0.00342,-0.06748,-0.06772,-0.05036,-0.07778,0.04005,0.04599,0.02785,0.06089,0.06427,0.02624,-0.07221,0.03656,-0.0545,-0.04449]},{"domain":"linear_algebra","key":"matrix_norms","name":"Norms 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1]].","v":[-0.05299,-0.08106,-0.05462,0.01215,0.07174,-0.04045,-0.0768,0.03645,0.01048,-0.00661,0.0365,-0.14327,0.01486,-0.02781,0.03647,-0.01751,0.02668,-0.06684,0.10297,0.0905,-0.02706,0.02262,0.09458,0.00988,-0.14142,0.00929,-0.00927,0.05453,-0.09139,0.17618,-0.04095,-0.01902,0.01206,0.01173,0.00137,-0.13232,-0.02344,-0.02554,0.06038,0.01687,0.0289,-0.01554,-0.04986,-0.04592,-0.01436,0.02094,-0.07831,-0.05365,-0.01521,-0.03904,0.05687,0.04311,0.05671,0.01145,-0.04682,-0.00188,0.0583,-0.05233,0.07187,-0.02441,0.08187,-0.08468,0.02126,-0.02071,-0.1293,0.02062,0.04471,0.04748,-0.05874,0.13543,0.05766,-0.06624,-0.05191,0.01632,-0.09549,0.02617,-0.05124,-0.0083,-0.13028,0.03484,-0.07333,-0.08002,-0.05033,-0.05034,-0.02454,-0.0931,0.04677,-0.08642,0.07183,-0.1208,-0.02206,0.02681,0.04778,0.01791,-0.0251,-0.12409,0.13303,0.09475,0.08706,0.06979,-0.0307,0.05872,-0.0158,-0.03541,-0.09975,0.06067,0.00336,-0.10091,0.0359,0.02179,-0.0511,0.02917,0.01593,0.04086,0.01505,-0.04575,-0.05884,-0.09032,-0.01973,-0.08385,-0.0237,-0.03308,0.04748,-0.11425,0.03717,0.02557,-0.02153,0.01048,0.02902,0.02145,0.06173,0.07881,-0.08566,0.02659,-0.00937,0.06044,0.05355,-0.00455,0.09383,0.00587,-0.01652,0.04292,0.01906,0.07166,-0.14459,0.03145,-0.07652,0.07692,-0.07319,-0.00868,-0.06874,0.13817,-0.07037,-0.0075,0.01246,0.01883,-0.15694,0.05464,0.04521,0.13503,-0.00313,0.02366,-0.0017,0.04178,-0.0375,0.08931,-0.01934,-0.00915,0.01514,-0.00742,0.01944,-0.01963,-0.01652,0.12532,-0.00513,-0.02834,-0.07797,0.04335,-0.04422,0.01619,0.01829,0.16342,-0.02628,0.07134,0.09096,-0.04167,-0.06573,-0.01971,-0.10774,0.02001,0.08885,-0.02026,-0.0434,-0.0646,-0.05839,0.02528,-0.01337,-0.07735,0.03667,0.0486,0.04737,-0.01113,0.01892,0.02386,-0.05841,-0.01973,-0.00878,-0.0405,0.14481,0.05744,-0.07381,-0.06309,-0.03823,0.00352,0.11955,0.07124,-0.0801,-0.03021,0.08494,-0.00633,0.13475,-0.06116,-0.05788,0.09751,0.13508,0.04805,-0.01564,-0.13665,0.08324,-0.01051,0.03556,0.04946,-0.03256,0.02981,0.01501,0.06239,0.07958,-0.00585,0.0241,0.02996,-0.0747,-0.047,-0.06183,0.01096,-0.07358,-0.02631,-0.01039,-0.0342,0.03654,0.06973,-0.02649,0.0267,-0.03055,0.05421,0.0284,0.02926]},{"domain":"linear_algebra","key":"matrix_rank","name":"Rank 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1]].","v":[-0.04586,0.04011,-0.09223,0.07636,-0.11695,-0.10125,-0.03809,-0.02598,0.08735,0.05611,-0.03363,-0.115,0.00864,0.04403,0.06173,-0.02377,-0.03926,-0.0282,0.06605,0.05438,-0.05833,0.00791,-0.00684,0.01579,-0.04314,-0.02251,0.02064,-0.04324,-0.05612,0.03506,-0.0737,0.01089,-0.02843,-0.11861,-0.0758,-0.02598,0.01578,0.05297,-0.02051,-0.02831,0.03109,-0.08652,0.07485,-0.05151,-0.1038,0.02394,-0.04692,-0.02607,-0.09017,0.08557,0.04643,0.03533,0.03079,0.13416,-0.05851,0.0426,0.08599,-0.03366,-0.00751,0.05219,-0.01744,0.08861,-0.01097,-0.02013,-0.03624,-0.00082,0.06163,0.06659,0.0339,0.07085,-0.01275,0.10217,0.01375,0.13211,0.01828,0.07529,-0.02431,0.0058,-0.0281,-0.0892,-0.07776,-0.0822,-0.01407,-0.1105,0.07144,-0.01554,0.04323,-0.00099,-0.08177,-0.00032,-0.04807,0.07998,-0.11068,-0.07597,0.05346,0.00498,0.04513,-0.01174,0.02298,0.15641,-0.03376,-0.03181,-0.07489,-0.04673,0.07055,0.17306,0.08177,-0.02234,-0.04958,-0.07601,-0.1203,0.07895,-0.09336,0.09049,-0.05555,-0.00147,-0.08349,-0.10603,-0.09112,0.01392,-0.02757,-0.0065,-0.08158,-0.02135,0.05373,-0.01083,0.05309,0.10372,-0.01313,0.08602,0.01689,0.03401,-0.07608,0.04988,-0.05154,-0.08058,0.0774,0.05273,0.04628,-0.02372,-0.12436,-0.00657,-0.04718,0.11814,-0.08469,0.01486,0.0181,-0.00426,0.05671,-0.08937,-0.04474,-0.03011,0.00397,-0.00449,0.02403,-0.06597,0.05003,0.08769,-0.01881,0.03016,0.04016,-0.01047,0.00306,-0.0677,0.00083,0.02436,-0.09516,-0.10183,0.08227,0.01506,-0.00703,-0.04639,-0.05903,-0.00178,-0.01663,-0.03487,0.09986,-0.04611,0.04261,0.03538,-0.00487,0.06122,0.12928,0.09677,0.05152,0.08469,-0.05006,0.013,0.06324,-0.07371,0.02104,0.04164,-0.09633,-0.04048,-0.08344,0.01167,-0.00267,0.02569,0.03422,-0.01774,-0.02915,-0.10942,0.04394,-0.01127,-0.00541,-0.1205,-0.0081,0.02972,-0.06374,0.01661,0.01535,0.01221,-0.10217,0.08355,0.09052,-0.10079,-0.00455,0.0001,0.01189,-0.0589,0.07895,0.01569,0.05369,0.11917,0.07337,0.0566,-0.0233,-0.1736,-0.04879,-0.06302,0.03722,0.04938,-0.07023,0.05609,0.0803,0.07138,-0.01327,-0.03194,-0.10921,0.02347,-0.00466,0.04669,0.01315,-0.09081,-0.0272,0.04851,0.0502,0.01987,0.06722,0.07846,-0.04981,0.11177,-0.04656,0.04088,0.06135,0.03212]},{"domain":"linear_algebra","key":"matrix_square_root","name":"Square 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5]].","v":[-0.02001,-0.03189,0.07392,0.06706,0.02618,-0.0559,-0.05242,0.08397,0.01349,-0.10616,0.02954,-0.00772,0.0309,-0.00899,0.02253,0.15694,-0.00431,-0.04446,0.018,-0.01303,-0.03137,-0.03396,0.06739,0.05612,-0.1108,-0.0561,-0.06614,0.09034,0.0939,0.10102,-0.02169,0.04583,0.05987,-0.01831,-0.03845,-0.10303,0.09881,-0.09967,0.08525,0.01245,0.07049,0.00378,0.01097,-0.021,0.01628,-0.03094,-0.01954,-0.0702,-0.00284,0.06508,0.05284,0.02412,0.09486,0.04004,-0.0772,-0.07793,0.01759,0.00317,0.07528,-0.01154,0.01857,-0.11962,0.03374,0.07534,-0.07787,-0.00776,-0.10164,-0.01377,-0.01297,0.0171,0.0902,-0.13207,-0.03508,0.05625,0.0159,0.00946,-0.01628,-0.0201,-0.0395,-0.01416,-0.12534,-0.10276,-0.02814,-0.04867,0.05601,-0.0641,-0.05933,0.01086,0.04908,-0.01771,-0.01163,0.061,-0.01006,0.02918,-0.04916,-0.04197,0.06621,0.09137,0.09055,0.01663,0.0504,0.03355,-0.05365,-0.02364,-0.09005,-0.05077,0.02116,-0.06041,0.05188,0.00163,-0.14138,-0.01075,0.04434,0.07705,0.06726,-0.01508,-0.08894,-0.05442,-0.07581,-0.12855,0.07013,-0.01658,0.00344,0.00846,-0.04108,0.01591,-0.00502,0.04263,0.09995,0.04466,-0.01063,0.09848,-0.01249,-0.03461,-0.0051,0.0647,-0.02165,-0.0185,0.10343,0.00435,0.07488,-0.01423,0.05619,0.06462,-0.06141,0.00472,-0.02946,0.06032,-0.04243,0.03996,0.02616,0.05066,-0.01977,-0.03348,-0.00222,0.03707,-0.03891,0.05418,0.01993,0.1077,-0.02279,0.03579,-0.00642,0.04454,-0.19517,0.03824,0.03239,0.00558,0.01852,0.01605,-0.05882,0.0848,0.02802,0.14659,-0.05963,-0.06669,0.00612,-0.01696,0.00101,0.032,0.05561,0.1238,-0.02466,0.04025,0.13312,0.0133,0.01731,-0.0784,-0.06055,-0.03511,0.03227,0.00699,0.03347,-0.01796,-0.01639,-0.08187,-0.05537,0.07821,0.06829,0.07919,0.10392,0.0071,-0.02049,0.10762,-0.05959,-0.08512,-0.00042,-0.06188,0.03639,-0.00744,-0.05005,0.02226,-0.09642,-0.03762,0.09093,0.04335,-0.15308,-0.04516,0.0736,-0.07652,0.00905,-0.10834,-0.07036,0.02129,0.23423,-0.0177,-0.16081,-0.17531,0.02525,0.00014,-0.00518,-0.01269,-0.01558,0.08678,-0.04455,0.0408,-0.04035,0.00964,-0.02181,0.07607,-0.031,-0.0034,-0.05483,0.00194,-0.00413,-0.05496,-0.01937,-0.05793,-0.01492,0.03867,0.02241,0.01774,-0.11442,-0.00662,-0.02192,0.10077]},{"domain":"linear_algebra","key":"matrix_subtraction","name":"Difference 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8]].","v":[0.0408,-0.04595,0.07092,0.09109,0.02575,-0.03964,-0.11085,0.0097,0.01418,0.11447,0.01406,-0.01569,-0.05058,0.0519,-0.02326,-0.18391,-0.07435,-0.02095,0.06124,-0.02126,0.00394,0.04348,0.07632,0.06358,-0.06057,0.00319,-0.04216,0.01996,-0.14138,0.08176,0.02536,0.10708,-0.16122,-0.02615,-0.0326,-0.00197,-0.00392,-0.04639,-0.02709,-0.05217,0.00823,0.03239,0.04109,-0.09312,-0.08721,-0.04815,-0.05572,0.04589,-0.07919,0.03102,0.03533,0.12854,0.04566,-0.0892,0.01982,0.03107,0.07155,-0.05574,0.103,0.03353,-0.00658,-0.06648,0.14781,-0.15685,-0.03128,0.09273,0.08368,0.09431,-0.03589,0.02167,-0.05787,0.05129,0.08887,-0.01213,-0.14103,-0.07395,0.01709,-0.01003,-0.0353,0.01719,-0.05619,-0.04958,0.03533,0.02565,-0.00848,0.00949,0.06188,-0.03846,-0.02748,0.06722,-0.0619,-0.05634,0.05321,0.09498,0.04507,-0.10072,0.06662,-0.04223,-0.03465,-0.01012,-0.07543,0.02623,0.00652,-0.05027,-0.0154,0.06548,-0.00064,0.00544,-0.05123,-0.06007,0.02948,0.01441,-0.04298,0.0417,0.02167,0.00986,-0.01617,0.04663,0.00411,-0.01596,-0.09993,-0.05815,0.00233,0.08895,0.05854,0.04947,-0.06514,0.11306,0.01048,0.01581,0.05583,-0.07105,-0.08919,-0.05239,0.01658,-0.09868,0.03163,0.00269,0.03446,-0.06679,-0.11574,-0.01845,0.03465,0.05728,-0.02654,0.13121,0.0128,0.07329,-0.00984,0.06297,0.00657,-0.09357,-0.04308,-0.04658,0.07139,-0.07981,0.07045,-0.047,-0.00381,0.06879,0.04894,-0.00899,0.01752,-0.0465,0.0542,0.02016,-0.11391,-0.04298,-0.07436,-0.00707,-0.01998,-0.02966,0.11499,0.01987,0.04344,-0.00065,-0.0091,-0.09052,-0.04973,-0.04721,0.0034,0.12327,0.06296,0.06213,0.05895,0.03366,0.02727,-0.04428,0.01047,-0.00755,0.07081,0.19198,-0.02106,0.14623,-0.03634,0.00508,0.03996,0.0575,0.05728,0.05928,-0.05173,0.03547,0.01273,-0.0953,0.00605,-0.02779,-0.06546,0.0512,0.0455,-0.00104,-0.09168,-0.05523,-0.08008,0.06208,-0.02783,-0.0256,0.0294,0.03918,0.05649,-0.04436,0.16817,0.00939,-0.03699,-0.02897,0.00957,0.02678,0.01914,-0.03632,0.10884,0.02044,0.09711,0.00811,0.01004,0.08206,0.08492,-0.07323,0.05768,0.02016,-0.05044,0.00549,0.00606,-0.12939,-0.10355,0.00051,-0.04721,-0.07282,-0.04944,-0.06242,-0.00666,0.03529,-0.03107,0.06463,-0.10167,0.07235,-0.02485,0.04581]},{"domain":"linear_algebra","key":"matrix_trace","name":"Trace 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divided differences","package":"linear-algebra-ai999x","example":"Find the Newton divided differences for the points (1, 1), (2, 4), (4, 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of equally spaced data (finite differences)","package":"linear-algebra-ai999x","example":"Estimate the derivative of the samples y = (0, 1, 4, 9, 16) with spacing h = 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Poisson equation by finite differences","package":"linear-algebra-ai999x","example":"Solve the 1-D Poisson equation -u'' = f with zero boundary values, L = 1 and f = (1, 1, 1) at the interior 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0].","v":[0.06409,0.00798,-0.00422,0.06562,0.04613,-0.05492,-0.06547,0.03871,0.03983,-0.02984,-0.01882,-0.03471,0.01519,0.05908,0.00438,0.19117,-0.03745,-0.04691,-0.00054,0.0313,-0.00695,-0.02373,-0.00088,-0.02923,-0.0895,-0.06387,0.05386,0.07581,0.10081,0.05563,0.00896,0.02469,0.02215,-0.04958,-0.08368,-0.03358,0.02251,-0.10364,0.00657,0.07089,0.05224,0.0016,0.05713,-0.05852,-0.0399,-0.01559,0.0169,0.03253,0.05744,-0.04472,0.01072,-0.08594,-0.00989,0.05192,0.02429,-0.07389,-0.06303,-0.03024,0.00367,-0.01248,0.05205,-0.10803,0.04537,-0.04486,-0.05149,-0.00712,-0.11806,-0.06006,-0.03989,-0.05331,0.09923,-0.06656,0.05475,0.06977,0.04239,0.05561,0.06216,-0.02995,0.0745,-0.00206,-0.08975,-0.03972,-0.05124,-0.01006,0.09265,-0.11598,0.04312,-0.07573,0.03663,-0.07,0.01988,0.04183,-0.06043,0.03609,-0.06445,0.03285,0.02758,0.06122,0.15157,-0.00679,0.06271,-0.04818,-0.01254,-0.07478,-0.11109,-0.04592,0.03864,-0.10818,0.04164,-0.00544,-0.02537,0.0976,0.11305,-0.02797,-0.01444,-0.02479,-0.11007,0.05422,-0.05007,-0.15674,0.03593,-0.04128,-0.04299,0.02724,0.02103,-0.03301,-0.11271,0.07736,0.09214,0.10902,0.06714,0.05314,0.06227,-0.04637,-0.02154,0.03662,0.07913,-0.06061,0.0705,0.02969,0.15423,-0.14822,0.09903,0.08838,0.04464,0.08694,0.00987,-0.03723,-0.04918,0.09288,0.04082,-0.06254,0.0258,-0.05928,0.03973,0.02595,-0.03511,-0.00974,0.06766,0.03375,-0.01094,0.00428,0.07936,-0.00318,-0.04426,0.03302,0.03727,-0.04188,0.01217,0.00858,-0.06,0.14145,0.08917,0.12743,-0.01764,0.05878,0.00363,-0.01841,0.0336,-0.05742,0.01014,0.09102,0.01008,0.03802,0.10574,-0.07425,0.04148,-0.05459,-0.0996,0.0247,0.10647,-0.00964,0.03115,-0.10335,-0.00738,-0.08534,0.07833,0.14648,0.05337,0.05827,0.00913,-0.05356,0.03186,0.03562,-0.03593,-0.06052,0.00616,-0.03745,0.02082,-0.01229,0.05207,0.03584,-0.04364,0.00543,0.08656,-0.00462,-0.16335,0.00931,-0.01965,-0.13559,-0.00803,-0.15169,-0.03106,0.07487,0.03295,-0.01511,-0.07,-0.1397,0.04994,-0.06921,-0.01576,0.02212,-0.02816,0.00573,-0.08956,0.06243,-0.05599,-0.03028,-0.10938,0.03099,0.01216,0.0633,0.00314,0.00574,-0.02917,-0.10496,0.02717,-0.06192,0.00082,-0.05202,0.05327,0.02424,-0.04573,-0.02976,-0.00372,0.03371]},{"domain":"linear_algebra","key":"polynomial_evaluation","name":"Evaluate 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definiteness test (Sylvester's criterion)","package":"linear-algebra-ai999x","example":"Is the matrix [[2, -1], [-1, 2]] positive definite?","v":[-0.01806,-0.04141,0.01898,0.09073,-0.01024,0.00985,0.02336,0.0369,0.0777,-0.07662,-0.07251,0.02055,-0.02833,-0.01648,0.01814,0.11123,-0.02142,0.01498,0.02835,-0.05225,-0.08483,0.08963,-0.00556,0.06007,-0.14019,-0.10402,0.03776,0.09881,0.10998,0.15683,-0.03855,0.04402,0.03287,0.01395,0.01645,-0.11945,-0.05134,-0.11555,0.10621,0.03293,0.03987,-0.03816,-0.04635,0.00497,0.03484,-0.054,-0.06592,-0.00655,0.06986,0.14645,0.10661,-0.08842,0.08325,0.13821,-0.06445,-0.00831,-0.0255,-0.00159,0.01463,0.01397,-0.04571,-0.0483,0.02193,0.12977,-0.04367,-0.05066,-0.07834,-0.02456,0.10162,-0.02741,0.0978,-0.07125,0.08118,0.00635,0.07209,-0.00413,0.01072,-0.02956,0.08318,-0.08049,-0.09825,-0.04017,0.02082,-0.04585,0.0673,0.03093,-0.05976,-0.06214,-0.08003,0.04522,-0.04191,-0.01395,-0.08706,0.06878,-0.02433,-0.05632,0.05289,0.0783,0.06062,0.0513,0.03522,0.01842,-0.0574,-0.06123,0.0401,0.00626,0.06351,-0.03246,-0.0164,-0.01515,-0.03762,0.05229,0.04022,-0.00796,-0.01744,-0.03187,-0.17684,-0.02948,-0.05246,-0.05303,0.01483,-0.04356,-0.00602,0.01805,-0.00887,0.0416,-0.04576,0.04269,0.11754,0.03493,-0.07102,0.02885,0.00205,-0.04045,0.03216,0.00954,0.01073,0.0057,0.05198,-0.02673,0.08029,-0.04311,-0.0316,0.04162,-0.05249,0.04763,0.02759,0.03019,-0.01036,0.0287,0.05093,0.06382,0.0183,-0.0424,0.01556,-0.04341,0.08366,0.04771,0.02643,0.10361,-0.00722,-0.0341,-0.08233,0.05542,-0.14073,0.01514,-0.00869,-0.03598,-0.0117,0.07277,-0.05051,0.00778,0.01385,0.06556,-0.01027,-0.01661,0.01165,-0.05027,0.08584,-0.02673,0.06487,0.05682,-0.02464,0.01676,0.07921,-0.02957,0.0193,-0.07525,-0.01734,-0.01136,0.11157,-0.01459,-0.07505,0.00876,-0.04453,-0.08215,-0.03572,0.13771,0.12093,0.02754,0.02384,-0.00148,0.00991,0.05713,-0.09789,-0.09249,0.01858,-0.0644,-0.07968,-0.06941,-0.03154,0.01567,-0.08852,-0.03441,0.14424,-0.04169,-0.14495,-0.05389,0.10556,-0.07183,-0.02415,-0.13076,-0.08098,-0.04455,0.17531,0.01537,-0.1248,-0.15984,0.03572,-0.0015,0.00204,-0.01029,-0.00266,0.05085,-0.03971,0.04444,-0.05122,0.0508,-0.1344,0.0983,-0.04929,0.02885,0.01461,-0.01376,0.01976,0.0133,0.03959,-0.072,0.01564,0.01487,-0.02497,0.06127,-0.00422,0.02848,0.04093,0.08858]},{"domain":"linear_algebra","key":"power_iteration","name":"Dominant eigenvalue by power iteration","package":"linear-algebra-ai999x","example":"Find the dominant eigenvalue of [4 1; 2 3] by the power 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projection matrix onto a column space","package":"linear-algebra-ai999x","example":"What is the projection matrix onto the column space of [1; 2]?","v":[-0.09954,0.01476,-0.11523,-0.04537,-0.04095,-0.00292,0.05207,-0.00967,0.02163,0.10705,0.08564,-0.04068,-0.01009,0.00379,-0.0103,0.01345,-0.02279,-0.01297,0.09391,0.03335,-0.02612,0.03519,0.03077,-0.07056,-0.05029,-0.02425,-0.09653,0.09995,0.01353,0.10777,0.02382,-0.05863,0.10797,0.02581,-0.09544,0.03015,0.02934,0.01436,-0.13305,0.19255,0.01965,-0.11621,0.00942,-0.05339,-0.07907,-0.06055,0.01571,-0.01781,-0.03039,0.12919,0.05327,-0.04918,0.01502,0.05929,-0.06393,0.06776,0.13895,-0.05657,-0.00945,0.02678,0.05284,0.04434,0.04295,0.03259,-0.03537,0.01538,0.03852,-0.03708,0.10158,0.0538,-0.0325,-0.07801,-0.03759,0.10573,-0.09571,0.06621,0.10619,-0.06376,-0.02163,-0.00568,0.01545,-0.06055,0.06746,0.00452,0.04566,-0.0984,0.0174,-0.04084,-0.03081,0.01899,-0.03852,0.09449,-0.06896,-0.03733,0.01943,-0.0146,0.10842,0.01399,0.09276,0.12308,-0.03572,-0.0606,0.03297,-0.14062,0.00421,-0.03458,0.08343,0.03972,0.02979,-0.05182,0.0033,0.11303,0.01531,-0.01545,-0.06007,-0.02871,-0.0572,-0.10418,-0.06507,-0.08128,0.03827,0.09981,0.02226,-0.02636,0.01056,-0.04291,-0.07553,0.04202,0.01367,0.03416,-0.01336,-0.09493,0.0059,-0.06074,0.03186,-0.02481,0.05172,0.0018,-0.05478,-0.00672,-0.0646,-0.07981,0.06008,-0.03452,0.05008,0.03844,0.02416,-0.08597,-0.04086,0.01571,0.03844,-0.04672,0.09595,-0.03342,0.01203,-0.02802,0.02702,-0.01042,-0.01105,0.01551,-0.02245,0.06511,0.09986,-0.01472,-0.15371,-0.03933,0.01512,-0.01338,-0.04745,-0.05476,-0.04506,0.08071,-0.07115,0.03225,0.04254,0.07259,0.08094,0.02685,-0.13377,-0.08107,0.03053,0.01652,0.092,0.00753,0.08793,-0.01855,0.07731,-0.01123,0.00882,-0.08176,0.09362,0.04119,0.00691,-0.0811,-0.04336,-0.00853,0.05578,0.03037,0.00137,-0.00637,-0.01585,-0.06103,-0.11657,0.015,-0.01791,-0.19361,0.03371,-0.00976,-0.00286,0.0174,-0.00334,-0.04642,0.01064,0.10748,0.12607,0.06459,-0.02109,0.09111,0.10872,0.02154,0.12408,-0.06056,0.00533,0.11198,0.00717,0.01255,-0.06222,-0.11148,0.08176,-0.07645,0.00226,0.07369,-0.03502,-0.01695,-0.03279,0.07385,-0.00594,-0.02159,-0.12359,0.00666,-0.05505,-0.01971,-0.06937,0.04191,0.05094,-0.07919,0.04916,0.01819,-0.05207,0.01034,-0.12426,0.08709,-0.01596,0.00799,0.05159,0.03101]},{"domain":"linear_algebra","key":"pseudoinverse","name":"Moore-Penrose pseudoinverse (full rank)","package":"linear-algebra-ai999x","example":"Find the pseudoinverse of [[1, 0], [0, 1], [1, 1]].","v":[0.05015,0.05199,-0.08583,0.09238,-0.08359,-0.0904,-0.01895,-0.02663,0.02133,0.03594,-0.0168,-0.02446,-0.01703,-0.02763,0.00161,0.01884,0.00271,-0.02386,0.13629,0.08608,-0.00281,-0.05995,-0.02747,0.02847,-0.0299,-0.06634,-0.03956,0.00316,0.09971,0.1436,-0.00446,-0.01019,-0.00865,-0.03947,-0.08605,-0.04496,-0.05024,-0.05967,-0.01489,0.08889,0.03381,-0.09227,-0.024,-0.10556,-0.03604,0.02468,-0.02272,0.02453,0.00679,0.07579,0.12343,-0.09072,0.06073,0.14841,-0.09192,0.0244,0.1189,-0.04822,0.08634,0.0036,0.03487,0.05235,-0.0753,0.06252,-0.09321,-0.0295,0.05226,-0.0081,0.02582,0.0272,0.03694,-0.04078,-0.00544,-0.00268,0.04418,0.0646,0.04539,0.01981,-0.03699,0.04347,-0.01704,-0.01776,-0.03434,-0.00228,0.1186,-0.04841,-0.00451,-0.0792,-0.00288,-0.04311,0.03998,0.05634,-0.00238,0.0202,-0.05332,-0.06363,0.06358,0.05515,0.05311,0.1428,0.0191,-0.07773,-0.01763,-0.0111,-0.04382,-0.06,0.05832,-0.01107,-0.05687,-0.02772,-0.03997,0.13338,-0.01118,0.08157,-0.03435,-0.05273,-0.13619,-0.10366,-0.11372,-0.03584,-0.00256,-0.01986,-0.0451,-0.05239,0.09026,0.06865,-0.06622,0.0973,0.08021,0.02825,-0.03767,0.04666,-0.0531,-0.04699,0.00781,-0.01475,0.02513,-0.01382,-0.03989,0.00506,0.02496,-0.02465,0.05535,0.04612,0.04877,0.00049,0.06097,-0.1109,-0.00103,-0.08655,-0.0909,0.0215,0.04926,0.00949,0.04231,0.04371,-0.01582,0.05274,0.0947,0.03235,-0.05819,-0.01713,-0.0161,0.0014,-0.07858,-0.02989,-0.01655,0.00774,-0.06577,-0.06261,-0.0721,0.08256,0.05396,0.02354,0.02948,0.00092,0.12394,-0.08476,0.0098,0.0386,0.03479,-0.05151,0.07498,0.02441,0.11741,-0.0684,-0.03913,-0.02932,0.02244,-0.06856,0.07938,0.04624,-0.09421,-0.1624,-0.05883,0.051,0.07174,0.01571,0.13968,0.06444,-0.03008,-0.07268,-0.06067,-0.04423,-0.04494,-0.17672,0.11501,0.01107,0.02974,-0.03931,-0.05295,-0.01627,-0.0261,-0.0225,0.11871,-0.06685,-0.06638,-0.00837,0.0859,-0.12213,0.15665,-0.02467,0.05408,0.05538,0.01471,0.01675,-0.10107,-0.15758,0.04006,-0.05801,0.01964,0.01157,-0.01278,0.06173,0.00885,0.10535,-0.05323,0.03172,-0.10532,0.04331,-0.00054,0.10271,-0.05205,0.00208,0.09,0.02111,-0.00059,0.0255,-0.00485,-0.00559,-0.10334,0.0972,0.03028,-0.01822,0.04438,0.0325]},{"domain":"linear_algebra","key":"qr_decomposition","name":"QR decomposition (Householder)","package":"linear-algebra-ai999x","example":"Find the QR decomposition of [[3, 1], [4, 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9]].","v":[0.04673,0.08957,-0.04226,0.02782,-0.04544,-0.04759,-0.00021,-0.1165,0.05628,0.01057,-0.05078,-0.05598,-0.03033,0.06846,0.00616,-0.04767,0.00611,-0.01075,0.04251,-0.00253,-0.12076,-0.00778,-0.03305,0.01123,0.00313,0.03991,0.01042,-0.14123,-0.00844,-0.00801,-0.09998,-0.03417,-0.08637,-0.05878,-0.07105,0.03349,0.06976,0.02833,-0.03858,-0.06762,0.0633,-0.04457,0.10134,-0.11696,-0.08254,0.01077,-0.02136,0.04344,-0.22052,0.0244,0.06966,0.07237,-0.00251,-0.05182,-0.05624,-0.01918,-0.0369,-0.02081,-0.04169,-0.06281,0.04171,0.10209,0.06828,-0.08272,0.08283,0.01601,0.074,-0.07896,0.06463,0.11876,-0.02375,0.11434,0.0365,0.08307,-0.05334,0.02496,0.06484,0.08574,-0.01174,0.00332,-0.05138,0.01971,-0.00704,-0.00877,0.11509,0.05493,-0.01745,-0.01993,-0.03524,-0.03362,-0.0527,0.06665,-0.06392,-0.01207,0.08952,0.05895,0.03498,0.00463,-0.06733,0.02282,-0.06854,-0.04723,0.04954,0.03897,0.00645,0.11832,0.11245,0.01232,-0.05264,-0.12181,-0.02402,0.0837,-0.13831,0.01412,-0.04092,0.12754,-0.00246,-0.0947,-0.04652,-0.0543,-0.08983,-0.10102,-0.13245,-0.02718,-0.03645,0.1035,0.11581,0.14367,0.03944,0.06822,0.01275,-0.06334,-0.079,0.02537,-0.02092,-0.0642,0.05624,-0.01488,0.03863,0.04003,-0.04216,-0.02534,-0.01598,0.03828,-0.08833,0.07404,0.11316,0.02948,0.06148,-0.02742,-0.0506,-0.07203,0.07212,-0.0418,0.05027,-0.03274,0.06422,0.04287,0.02684,-0.02001,-0.04435,-0.00973,0.04592,-0.00272,0.03681,-0.03997,-0.07835,-0.05411,-0.03114,0.08682,0.05444,0.03971,-0.00609,0.02706,0.03199,0.05429,-0.02944,-0.03539,0.01599,0.04618,-0.01863,-0.0158,0.02409,-0.02774,0.11188,0.04512,-0.02626,0.00281,0.13187,-0.02338,0.02205,0.00363,-0.08658,-0.03506,0.03609,0.03902,0.05304,0.0009,0.01446,-0.00395,-0.10255,-0.10219,0.05332,-0.07811,-0.02496,-0.11352,4e-05,0.03853,-0.0623,-0.04642,0.02555,0.03504,-0.0908,0.11849,0.06044,-0.08744,-0.01509,-0.02106,0.08524,-0.10666,0.10675,0.0299,0.00037,0.07273,-0.01143,-0.00885,0.02911,-0.06629,-0.01415,0.01758,0.08574,-0.04693,-0.09083,0.07039,-0.03066,-0.01878,-0.07096,0.02152,-0.05733,-0.00559,0.03351,-0.05623,-0.00462,-0.07783,0.0283,0.14912,0.10474,-0.01029,0.01441,0.08835,-0.09582,0.03805,-0.0736,0.05321,0.05033,0.00787]},{"domain":"linear_algebra","key":"scalar_matrix_multiplication","name":"Scalar 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5).","v":[-0.03305,0.08862,-0.0051,0.01946,0.03015,-0.05967,-0.07231,0.01225,0.03958,0.0572,-0.01121,-0.11895,-0.03707,0.07945,0.05876,-0.02482,-0.05906,0.02887,0.05321,0.06217,-0.05611,-0.09591,0.0847,0.05827,-0.0,-0.04614,0.0934,0.04338,0.00074,0.02124,-0.0788,-0.036,-0.0033,0.12963,-0.01848,-0.0423,0.01818,-0.02579,-0.03348,-0.01224,-0.0329,-0.02289,0.08514,0.00034,-0.06125,0.041,-0.0318,0.01512,-0.13733,0.05316,0.10791,-0.00279,0.10531,0.0412,0.01383,0.05809,0.0226,-0.03307,-0.06993,0.07196,0.04614,0.01087,0.03807,-0.0967,-0.03329,-0.01631,0.09168,-0.03331,-0.00267,0.028,-0.00102,-0.0117,0.00094,0.05283,0.02125,0.02807,0.02126,-0.08601,-0.0054,0.08053,-0.1153,-0.09087,-0.1018,-0.05225,0.02259,-0.04008,-0.04246,-0.05701,0.02445,-0.13182,-0.02808,-0.12808,0.04197,-0.14286,0.01887,-0.02832,0.01726,-0.05715,0.0762,0.0324,-0.01124,-0.02363,0.01774,-0.09311,0.03549,-0.02137,0.03235,-0.11003,0.08122,0.01534,-0.01888,0.05589,-0.01606,-0.00047,0.01542,-0.06694,0.08422,0.01528,-0.07171,-0.0043,-0.05833,-0.03977,-0.01104,-0.02065,0.06903,0.0215,0.07111,0.16056,0.10764,0.01011,0.07093,0.03888,-0.07906,-0.02612,-0.06521,-0.03097,0.0757,-0.02526,0.04022,0.0119,-0.13914,-0.10503,0.06088,0.0738,-0.07768,0.04059,0.03742,0.0446,-0.0802,-0.13754,-0.05978,-0.00229,0.10249,0.07228,-0.01215,0.14889,-0.08249,0.01795,0.07878,0.063,0.01496,-0.09663,0.0003,-0.04712,0.01495,-0.08533,-0.01071,-0.0956,-0.04894,0.08254,0.07147,-0.03048,0.0546,-0.0193,0.03347,-0.00084,-0.06949,-0.1083,0.03437,0.07099,0.10103,0.08733,0.02075,0.03527,-0.05097,0.05698,0.04922,0.11989,-0.0386,-0.00906,0.04061,0.05881,-0.03332,-0.10294,0.00355,-0.02466,0.1066,-0.08259,-0.01578,0.05988,0.10448,0.00209,0.02955,0.07063,0.06645,-0.05279,0.04304,0.11282,-0.04883,0.05222,-0.03011,-0.01845,-0.15771,-0.02113,0.07147,-0.06157,0.10827,0.01213,0.03096,-0.04833,0.10936,-0.03383,-0.06112,0.1091,-0.03825,-0.00075,-0.03936,-0.1179,0.0695,0.06666,0.0114,-0.09554,-0.08749,-0.00875,-0.00054,0.03366,-0.08147,0.00405,-0.0498,-0.06867,0.03919,0.05626,-0.05259,-0.0661,0.08478,-0.01225,0.08364,-0.05635,-0.01977,-0.04726,-0.0413,0.05778,0.02059,-0.04197,0.033,0.014]},{"domain":"linear_algebra","key":"sparse_matvec","name":"Sparse 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1].","v":[0.04613,0.04057,-0.08849,-0.02246,-0.14188,0.02312,-0.09042,0.02828,0.11912,-0.06158,0.02984,-0.04307,0.04957,0.02561,-0.01719,0.01984,-0.16812,0.01021,-0.0759,-0.01409,-0.00494,0.08185,-0.02497,0.09066,0.00872,0.01808,-0.02422,0.035,-0.13956,0.02172,0.00775,-0.11505,-0.02655,0.08717,-0.03145,-0.00817,0.03554,0.10894,-0.0134,0.00128,-0.07636,0.0252,-0.03229,-0.03218,-0.0701,-0.02272,-0.01165,-0.03068,-0.11497,-0.08694,-0.00796,-0.09504,0.06269,-0.06529,-0.03091,0.11844,0.09343,-0.05256,-0.07942,0.03693,0.06428,-0.05662,-0.06637,-0.06345,-0.0654,0.039,-0.09057,0.03646,-0.05659,0.03211,0.01224,0.04882,0.06762,0.04706,-0.11102,0.14704,0.01664,-0.09077,0.01499,-0.01308,0.00822,0.02409,-0.00716,-0.09681,0.01946,0.0035,-0.06782,-0.05546,-0.01915,-0.05669,-0.04737,0.01263,0.00731,-0.00183,0.04569,-0.08348,0.02264,0.05451,0.13351,0.08199,0.0107,-0.05086,0.0269,0.02697,0.07655,-0.14252,0.02124,0.06932,0.0011,0.03955,0.04094,0.02756,0.01428,-0.05905,-0.06397,0.13593,-0.02335,-0.00284,-0.0299,0.07103,-0.11229,-0.02028,0.08144,0.01376,-0.02788,-0.05137,-0.10316,0.05418,0.0468,-0.00087,0.02393,-0.02339,-0.03963,0.00126,0.13007,0.01492,-0.08119,0.00104,0.01655,-0.02351,-0.03081,-0.12679,0.01061,0.07073,0.00352,0.08083,0.03462,-0.09183,-0.05551,0.04953,-0.03661,-0.01382,0.06751,-0.02703,-0.01278,-0.06766,0.05321,0.02814,0.02814,-0.05955,-0.11442,0.03567,0.14946,-0.004,0.08517,-0.03018,-0.00123,0.00692,-0.12487,0.08126,0.04508,-0.05427,0.07082,-0.04352,0.03602,0.04687,-0.05943,0.02403,0.13855,0.09403,-0.00032,0.05742,-0.01502,0.01774,-0.00741,0.01128,0.06062,0.01367,-0.10784,0.06364,0.06693,-0.05209,0.01295,-0.03104,0.04485,-0.02673,0.04651,0.01411,-0.04568,0.0311,-0.02818,-0.01742,0.04962,0.05238,-0.08171,0.00465,-0.06685,0.08498,0.04119,0.0651,0.05156,-0.01971,-0.04901,0.02296,-0.00159,-0.04686,0.04052,-0.11248,0.0443,0.08199,0.14322,0.00678,-0.12101,0.16375,0.06226,0.0902,0.05065,-0.04806,0.02924,0.00776,-0.13025,0.01926,-0.07363,-0.01228,0.04843,-0.06413,0.01144,0.09951,-0.08931,0.0002,0.04854,0.06104,-0.0874,-0.02768,-0.06858,-0.01886,0.03514,0.07087,0.01629,0.04022,0.00083,0.04221,-0.09953,0.04616,-0.04415,-0.0237]},{"domain":"linear_algebra","key":"symmetric_eigenvalues","name":"Eigenvalues of a symmetric matrix (Jacobi method)","package":"linear-algebra-ai999x","example":"Find the eigenvalues of [[2, 1, 0], [1, 2, 1], [0, 1, 2]].","v":[-0.02144,-0.08154,0.00869,0.02874,-0.02266,0.0329,0.01563,-0.00967,0.08357,-0.0952,0.09097,0.04978,0.02649,-0.11644,0.04534,0.02972,-0.09149,0.04532,0.07531,-0.01199,-0.07035,0.10045,-0.07554,0.0207,-0.0432,-0.04687,0.05108,0.05679,-0.02056,0.04414,0.03777,-0.06684,0.00317,-0.03732,0.08229,-0.12232,0.04709,-0.07915,0.08902,-0.06356,0.10243,-0.05915,-0.01321,0.02058,-0.01178,-0.02446,-0.05237,-0.03004,-0.01504,0.12067,0.01741,-0.1108,-0.02718,0.10076,-0.10301,-0.00644,0.03353,-0.05887,0.01127,-0.03023,0.04967,-0.03528,0.05105,0.09238,0.0331,-0.07008,0.03673,-0.01258,0.12377,0.05218,0.08993,0.03887,0.07198,-0.00857,-0.01812,-0.02536,-0.05414,0.04966,0.14679,-0.09283,0.03192,-0.04789,-0.03752,0.01781,0.04846,-0.05902,0.04761,-0.03685,-0.05536,0.05862,-0.07087,-0.05936,-0.10453,0.06693,0.00044,0.01997,-0.01965,-0.07077,0.09144,0.04843,-0.01007,0.05378,-0.09745,-0.12982,0.10054,0.03755,-0.03417,-0.07372,-0.03243,-0.03658,-0.00383,0.05753,-0.07136,0.03594,0.00662,-0.03355,-0.0084,0.0506,0.04633,-0.09362,0.00262,-0.05587,0.03194,-0.11519,-0.03149,0.09836,0.01176,0.0236,0.05557,0.07526,0.03063,0.01885,0.02355,0.02771,-0.01884,-0.08968,-0.05981,0.04564,0.10412,0.00975,0.0214,-0.00017,-0.02856,0.15022,-0.04974,0.1162,0.02995,-0.03564,0.03982,0.02398,0.0114,0.00198,0.09733,-0.04708,0.07021,-0.02663,0.06952,0.07914,-0.03841,0.11608,-0.02076,-0.04845,-0.03617,0.05322,-0.03817,0.03232,-0.01764,-0.02826,-0.04635,0.15673,0.12681,-0.04864,0.03097,-0.05604,-0.11849,-0.06269,0.03732,0.00056,-0.04465,-0.12425,-0.00631,0.07946,-0.00709,0.03161,-0.01939,0.04163,0.0363,-0.0157,0.03979,0.07949,0.09688,0.04556,-0.01748,0.00037,-0.08283,-0.01957,-0.01131,0.15627,0.06305,-0.01052,0.10176,-0.0413,0.0381,0.1071,-0.11253,-0.07879,0.02517,-0.01178,-0.082,-0.01161,-0.02695,-0.05226,-0.11514,-0.00954,0.06258,0.00458,-0.04646,-0.02637,0.08098,-0.08435,-0.01339,-0.02831,-0.09575,0.01743,0.03138,0.07714,-0.07092,-0.17465,0.01328,-0.12903,0.03856,0.04907,-0.03143,-0.06294,-0.03877,-0.02902,-0.04794,-0.0023,-0.09485,-0.07873,0.01654,-0.0018,0.03388,-0.01879,-0.03563,0.01886,0.00969,-0.10776,-0.0386,0.00062,-0.03162,0.08314,-0.11805,0.05745,-0.01829,0.02455]},{"domain":"linear_algebra","key":"symmetric_eigenvectors","name":"Eigenvalues 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2]].","v":[-0.00939,-0.05804,-0.01107,0.0813,0.00013,-0.00717,0.02669,-0.01294,0.04975,-0.04147,0.04925,0.06591,0.03289,-0.03133,0.04973,0.02381,-0.05643,-0.02812,0.04263,-0.04468,-0.10474,0.06783,-0.05627,-0.01832,-0.04122,-0.05051,0.04454,0.06285,-0.03572,0.01363,0.07711,-0.01235,0.03532,-0.08668,0.01258,-0.09951,0.07418,-0.05016,0.02445,-0.01658,0.12595,-0.04319,0.01862,0.05083,-0.08547,0.00173,-0.07452,0.00177,0.00444,0.04223,-0.01861,-0.05117,-0.0528,-0.01208,-0.02728,-0.05364,0.0583,-0.06209,0.01198,-0.01381,0.08655,-0.0639,0.04395,0.13447,0.06351,0.05807,0.02582,-0.05691,0.09391,0.05409,0.1023,-0.01653,0.08488,0.04193,0.04033,-0.01646,0.0462,-0.00221,0.11196,-0.08149,0.01949,0.00764,0.0024,-0.02283,0.0187,-0.08188,0.05468,0.01192,-0.05073,0.00983,-0.0301,-0.07769,-0.04431,0.04795,0.00724,0.03798,-0.04825,-0.03764,0.07039,0.00575,0.01966,0.03356,0.0018,-0.12337,0.05501,-0.06544,0.04538,-0.11779,0.01622,-0.13423,0.0083,0.05013,-0.0459,0.04611,-0.01258,0.03138,-0.10151,0.02094,0.04081,-0.17655,0.01717,-0.00291,-0.02825,-0.04071,-0.07729,0.03935,-0.06253,0.04868,0.01929,0.00539,0.01965,-0.01104,0.01666,0.01073,0.08117,-0.13319,-0.1197,0.043,0.04703,-0.01936,0.0656,-0.00934,-0.02518,0.17049,0.11401,0.15047,0.05234,-0.0724,0.0419,0.09369,0.01479,0.02122,0.08174,-0.0201,0.06287,-0.05882,0.03394,0.01656,0.03744,0.08501,-0.03253,-0.09679,0.0093,0.03264,-0.04169,0.04784,-0.08664,0.00341,-0.05344,0.12511,0.05566,0.03764,0.13519,-0.00015,-0.06165,0.00952,0.04361,-0.03277,-0.10073,-0.17292,0.02996,0.06884,-0.01459,0.07092,-0.024,0.00934,0.04185,-0.06884,0.03395,0.03229,0.11309,0.07809,0.00026,0.018,-0.01493,-0.0115,0.03848,0.18569,0.09715,0.00341,-0.03699,-0.02551,0.02715,0.02638,-0.10263,-0.08493,0.05061,-0.06138,-0.04372,-0.02814,0.01673,-0.01088,-0.09163,-0.01033,0.0739,-0.01527,-0.08864,-0.01219,0.10261,-0.0744,-0.01835,-0.07958,-0.02745,0.06318,0.01851,0.03693,-0.07528,-0.15833,0.01118,-0.11902,-0.04391,0.07264,-0.04891,-0.06723,-0.14049,0.0227,0.03713,-0.06557,-0.13956,-0.01916,0.08768,-0.03937,0.04765,0.00788,-0.00857,0.00502,0.03805,-0.07999,-0.01205,0.02346,-0.02057,0.02552,-0.14939,-0.02733,-0.03016,0.04794]},{"domain":"linear_algebra","key":"trapezoid_rule","name":"Trapezoidal rule for tabulated data","package":"linear-algebra-ai999x","example":"Use the trapezoidal rule to integrate the data (0, 1), (1, 3), (2, 2), (4, 0).","v":[0.00948,-0.02363,0.10924,-0.04189,-0.03828,0.08434,0.00242,-0.00138,-0.03136,-0.12624,0.05488,0.00652,0.0543,0.02944,-0.0274,0.08436,0.05049,-0.02493,-0.03052,0.03802,-0.09158,-0.07073,-0.04693,-0.07126,-0.08234,0.08134,0.09383,-0.03874,-0.00191,-0.07018,-0.01845,0.03676,-0.11298,-0.00828,0.12488,0.05121,-0.03677,0.08473,0.01342,0.01277,0.01214,0.0358,-0.08939,0.05623,-0.02889,-0.07878,-0.03255,0.05564,0.03127,0.03895,-0.07022,-0.05085,-0.01843,-0.05161,0.07536,-0.09363,0.09045,-0.07939,0.01328,-0.02102,0.05054,-0.10279,-0.05081,0.03401,-0.10998,0.02163,-0.0454,0.0655,0.02448,0.04405,-0.00405,0.04568,0.03893,-0.06095,0.05717,0.1078,0.04,0.05341,0.01214,-0.04609,0.04179,-0.07912,0.00575,0.01651,0.05771,0.02226,-0.10079,-0.01999,0.0484,-0.00673,-0.0614,0.10751,-0.07284,0.07238,-0.05359,-0.03646,0.02514,-0.02558,-0.03134,0.12188,-0.0691,-0.04286,0.01554,0.03562,0.14834,-0.07094,-0.03479,-0.01044,0.094,-0.01893,0.00683,-0.06433,-0.00346,0.03321,0.04989,0.07044,-0.09462,0.02156,-0.00271,0.09581,-0.1196,0.02203,0.02292,-0.02206,0.0344,0.05265,-0.03595,0.01017,-0.05322,-0.02521,-0.05786,-0.09943,0.03194,-0.00289,-0.08879,-0.01851,0.0334,0.11827,0.04169,0.08764,-0.02776,-0.09229,-0.04626,0.02567,-0.0058,0.01305,-0.01699,0.0686,0.16212,-0.04809,-0.00117,0.04698,0.02573,-0.03338,-0.00852,0.06986,0.08856,-0.07434,0.01903,-0.0342,-0.09385,0.0118,-0.02322,0.08907,0.1172,-0.03506,-0.05777,-0.04543,-0.05928,0.10739,-0.01056,-0.1486,0.06994,-0.07005,0.0027,0.10931,0.07553,0.06838,-0.08597,0.01637,0.04376,0.01634,0.05004,-0.07046,-0.06206,0.011,0.03602,0.01015,0.01994,-0.02935,-0.06547,0.07737,0.05408,0.16948,0.01878,-0.03401,-0.06357,0.03992,-0.07221,-0.01201,0.04347,-0.06694,-0.03484,0.00449,-0.01073,0.05482,-0.0421,0.00358,0.03508,-0.05034,-0.00136,0.01406,-0.01748,-0.11162,0.01594,0.00961,0.0372,-0.10726,-0.03073,0.04946,0.15073,0.08687,-0.08995,0.00726,-0.0246,0.0046,-0.0066,0.05761,-0.10521,-0.04927,0.04425,-0.10734,-0.1039,-0.05284,0.1347,0.00074,0.00461,0.0128,-0.11915,-0.00983,-0.12011,0.04442,0.13204,0.09139,0.03746,-0.13976,-0.01258,-0.05018,0.05307,-0.0413,0.01086,0.00569,0.0354,0.0429,-0.04002,-0.05052]},{"domain":"linear_algebra","key":"tridiagonal_solve","name":"Tridiagonal system (Thomas algorithm)","package":"linear-algebra-ai999x","example":"Solve the tridiagonal system with sub-diagonal (1, 1), diagonal (4, 4, 4), super-diagonal (1, 1) and right-hand side (5, 6, 5).","v":[-0.04195,0.02968,0.13134,-0.00118,0.0259,-0.07121,-0.02591,0.02366,0.05454,0.04057,0.03555,-0.04928,-0.0625,0.03896,-0.0346,-0.04082,-0.10357,0.12909,-0.0302,-0.01386,-0.08282,-0.03753,0.07115,0.00284,0.0372,-0.01649,-0.00751,0.01743,-0.02599,-0.03575,-0.02463,-0.07766,-0.06447,-0.0108,0.10846,0.09274,-0.0552,0.04862,0.03029,-0.04314,-0.01999,0.07763,0.04673,-0.06177,-0.06112,0.06867,0.0188,0.04906,-0.05627,-0.03627,-0.0128,0.02552,0.07057,-0.09848,-0.00392,0.02338,0.07312,0.0163,0.09803,-0.0178,0.15034,-0.06945,0.08167,-0.0103,0.11422,-0.07484,0.17375,-0.04814,-0.04954,-0.01534,-0.01325,0.04332,-0.05398,0.12219,-0.0871,-0.02717,-0.0896,0.00208,-0.05526,0.07094,-0.11012,-0.05442,-0.02203,0.13351,-0.03393,-0.08255,-0.02049,-0.10166,-0.00773,-0.05625,0.01088,-0.01962,0.09314,0.02229,0.01978,-0.02825,-0.01795,0.02447,0.03781,-0.05375,0.09347,-0.02458,-0.0333,-0.02858,0.08711,0.01958,0.08785,0.04571,0.07009,-0.06644,-0.03577,0.0049,-0.01057,0.04294,0.03006,-0.01732,0.02675,0.00941,0.02282,-0.09171,-0.04463,0.03284,-0.04134,0.06279,0.0338,0.05228,-0.01473,0.0732,0.12432,-0.02986,0.0062,-0.05656,-0.06231,-0.0814,0.012,0.0421,0.00044,-0.05787,0.10734,-0.09342,-0.04978,-0.07297,0.08065,0.04587,0.02039,0.13491,-0.01315,0.09141,-0.04459,-0.03919,0.00657,0.00107,-0.00524,0.10709,-0.02374,-0.0361,0.0015,-0.13529,-0.03091,0.05465,-0.01944,-0.07647,-0.04113,0.01452,-0.02737,-0.00121,0.01833,-0.01477,-0.05047,0.16736,0.0129,-0.02333,0.12045,-0.0613,0.01348,0.12897,-0.08006,0.0048,-0.05145,-0.00478,0.03816,0.10159,0.0394,0.05718,-0.12264,-0.04696,0.13415,0.08157,-0.02024,0.03064,0.03688,0.11736,0.0448,0.0227,0.11291,-0.05371,0.03645,0.06545,0.0115,-0.03356,0.09059,0.01311,0.04711,0.06402,0.00664,-0.10153,-0.00437,0.10819,-0.12324,-0.03565,-0.03409,-0.11239,-0.032,-0.04504,0.09404,-0.06218,0.00756,0.02756,0.03436,-0.01156,0.10346,0.00903,-0.13106,-0.00346,0.03277,0.01536,-0.0231,-0.03584,0.01127,0.01284,0.01444,-0.09301,-0.15262,-0.09126,-0.02995,-0.07645,0.03414,0.06409,-0.07183,0.03105,-0.03648,0.02879,-0.07386,0.01694,-0.08851,0.03609,0.0105,-0.11621,-0.01073,-0.0435,0.00693,0.03427,-0.01962,0.00271,0.03812,-0.05557]},{"domain":"linear_algebra","key":"triple_scalar_product","name":"Scalar 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1).","v":[0.13659,-0.0729,-0.06011,0.00377,-0.05198,0.10743,-0.11388,-0.00737,0.09077,0.01688,0.04539,0.0937,0.01119,0.03574,-0.05564,-0.00074,-0.07627,0.06439,-0.06586,0.04632,0.05886,0.09466,-0.0202,0.10269,0.09335,-0.0077,0.05091,0.04921,-0.13583,0.11017,-0.03886,-0.06888,-0.04967,0.02387,0.01824,-0.04417,-0.04196,0.01938,-0.01342,0.00978,-0.03286,0.018,0.0734,-0.01889,-0.0751,-0.09034,0.06647,-0.02351,-0.04919,-0.08606,0.02617,-0.07688,-0.02679,-0.04174,0.038,-0.03297,-0.10918,-0.02414,-0.10394,0.02634,0.04652,0.00206,-0.0186,0.03104,0.03706,-0.01135,-0.00326,-0.05236,-0.01763,-0.01798,0.07678,0.08173,0.05118,0.02018,-0.03239,0.12103,-0.00534,-0.10268,0.10328,0.02243,-0.00042,-0.01289,-0.00644,-0.08414,-0.03369,0.16115,-0.00857,-0.03272,-0.04164,-0.06057,-0.08413,-0.02067,-0.04613,0.04947,-0.07759,0.00914,-0.07894,0.02615,0.10921,-0.02936,-0.03631,-0.06822,0.02661,-0.00991,0.07885,-0.00218,-0.0426,-0.03294,0.11602,0.02919,0.05164,-0.07815,-0.02438,0.00623,-0.09503,-0.01826,-0.09739,0.02998,-0.04677,0.08138,0.08471,-0.01442,-0.08943,0.02414,0.03401,-0.04624,0.12241,0.01113,-0.00528,-0.01941,0.01173,-0.09275,0.01238,-0.04018,-0.03104,-0.07068,0.04154,-0.02403,0.08458,-0.02197,0.02711,-0.16815,-0.0923,0.01145,-0.01138,-0.06308,-0.1096,-0.03101,0.05999,-0.01145,0.05829,0.0734,0.02629,0.00338,-0.13209,0.0742,-0.04192,-0.19055,0.093,-0.07649,0.07818,-0.00972,0.0637,0.02429,0.01931,0.07063,0.01346,0.10242,0.02167,-0.00713,0.072,0.10712,-0.04604,0.00179,-0.04601,0.05071,0.02716,-0.07049,0.13085,0.00228,0.14534,-0.04646,0.05559,0.01828,0.04908,0.01534,0.03725,-0.00272,-0.02349,0.03628,0.01149,-0.05309,-0.02288,0.03031,0.04694,-0.06284,0.07983,0.04955,-0.08193,0.00505,-0.16174,-0.06956,0.05298,0.0713,-0.0242,0.09356,0.02198,-0.0718,0.00594,0.011,-0.00272,0.06019,0.03194,-0.02189,-0.00263,-0.04279,-0.08013,-0.07471,0.07785,0.05816,-0.01066,0.05818,-0.00137,-0.00848,0.03038,0.02283,-0.03222,-0.0485,0.03958,0.02056,-0.01361,-0.06998,-0.06702,0.00599,0.06244,0.06695,-0.04588,0.00804,-0.03655,-0.0245,0.0735,0.02897,0.09326,0.00195,0.05144,-0.01301,-0.01705,0.10253,0.06501,0.03725,0.14828,-0.12163,-0.02459,-0.09334,-0.10141,-0.02777]},{"domain":"linear_algebra","key":"unit_vector","name":"Unit 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4).","v":[-0.05938,-0.092,-0.0158,-0.04662,0.022,-0.07884,-0.07328,0.04993,-0.00496,-0.01276,0.08584,0.01563,0.04586,-0.03186,0.13014,-0.00513,-0.07914,0.03557,-0.11205,0.05851,-0.07645,-0.07451,-0.08333,0.00531,0.02597,-0.02322,-0.09653,0.05639,0.00195,0.01561,-0.00086,0.07997,0.03294,0.10238,-0.1183,-0.10197,0.07864,0.02867,0.0501,0.05273,0.13825,-0.02439,0.11616,-0.09327,0.0338,-0.00696,0.01657,-0.02279,-0.09679,-0.0263,-0.01978,-0.06775,-0.13893,-0.0884,-0.02506,-0.11527,0.01339,-0.01672,-0.08052,-0.0191,0.02757,0.00817,-0.01857,-0.01271,0.09782,0.06301,-0.00789,-0.00192,-0.09593,0.07264,0.0223,0.05391,0.12991,0.14656,0.03395,0.00519,0.03962,-0.05654,0.01113,-0.02098,0.0097,0.08402,-0.03917,-0.06056,-0.04564,0.12418,-0.03319,-0.02395,-0.00393,-0.09434,0.00793,-0.05868,0.01374,-0.08559,0.05529,0.10303,0.00218,-0.01525,0.14122,0.00486,0.03671,-0.04132,0.02592,-0.01947,0.00849,-0.10584,0.06664,-0.02376,0.07698,-0.08959,-0.05071,0.05468,-0.01684,-0.0524,-0.10086,0.03905,-0.00396,-0.01646,0.01082,0.01534,0.01832,0.02713,-0.0224,-0.07422,-0.03532,-0.03691,0.12052,0.10603,0.01507,-0.10775,0.00116,-0.06402,-0.02643,-0.08723,0.05571,-0.06224,-0.01486,0.02016,-0.02341,0.09926,0.07317,0.07305,-0.01918,-0.00713,0.13708,0.03367,0.00795,-0.01523,-0.00899,0.05584,0.03242,0.07923,0.09871,0.12464,-0.10474,0.02538,-0.08924,-0.09068,0.00498,-0.01371,0.03614,0.04534,0.0808,-0.04874,0.06882,0.00845,0.06176,0.07468,0.01789,-0.13641,0.00827,-0.00754,0.01294,0.0202,-0.03906,-0.02417,0.03419,0.02845,0.02018,-0.08333,0.05291,-0.09611,0.02234,-0.022,-0.01185,0.00972,0.0725,-0.0241,-0.00876,-0.06343,0.06907,-0.07323,0.01781,-0.06654,0.00266,-0.05841,-0.07748,0.00628,-0.00568,0.11004,-0.09766,-0.05703,-0.03656,-0.0875,0.07102,0.02608,0.16079,0.06931,0.03672,0.049,0.03833,0.12888,0.02452,-0.00099,0.04892,-0.05968,0.09407,0.05134,0.07576,0.0011,-0.08032,-0.01367,-0.01361,0.0395,0.12163,-0.01596,0.00922,-0.06442,-0.00621,-0.02228,-0.09215,-0.00742,-0.04051,0.02643,-0.01462,0.11039,-0.04819,-0.05153,-0.00828,0.01488,0.02842,0.02294,0.00101,0.00141,0.10709,-0.07336,0.07437,0.01772,0.01236,-0.05521,0.07562,-0.02818,-0.04508,-0.12062,0.06827,-0.03884]},{"domain":"linear_algebra","key":"vector_addition","name":"Sum 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6).","v":[-0.03502,-0.09434,0.0004,0.02928,-0.05127,-0.07338,0.02399,0.03525,-0.03526,-0.01211,0.10203,0.04865,0.03858,0.03164,-0.05268,-0.14827,-0.11279,0.03843,0.07234,-0.00507,0.02549,0.00801,-0.00773,0.06036,0.06971,-0.00838,-0.02512,0.04098,-0.11405,0.08019,0.0091,0.09124,-0.09889,0.0075,0.05214,-0.15314,0.06631,0.03172,0.02579,0.0555,0.01519,0.05873,0.06298,-0.15441,-0.08387,-0.03028,-0.02691,0.03896,-0.08191,-0.03145,-0.11351,0.06335,-0.05571,0.0104,-0.00487,-0.02556,-0.02104,-0.05753,-0.03637,-0.00661,-0.0317,0.06129,0.01042,0.00077,-0.0237,0.10033,0.06569,-0.03127,-0.00198,-0.04605,0.01438,0.09984,-0.00637,0.05774,-0.05188,0.0542,0.08845,-0.00437,0.03197,0.08701,0.00838,-0.03356,0.07015,-0.01832,-0.01118,0.09934,0.04747,0.1225,0.02871,-0.01953,-0.12288,0.02623,-0.02858,0.02292,-0.04517,-0.09075,-0.01569,-0.00449,0.01323,-0.08525,-0.07159,0.02642,-0.03099,0.01903,0.05479,-0.04084,0.02354,-0.04165,-0.03263,-0.03471,0.01232,-0.08092,-0.00551,0.09847,-0.02222,-0.00957,-0.03529,-0.02167,-0.01669,0.03836,-0.04986,0.07587,-0.02109,0.00977,0.07128,-0.00715,0.13488,0.06983,0.05223,-0.01733,0.14704,-0.0939,-0.18078,0.00377,-0.0073,-0.16707,-0.00665,0.04341,-0.02136,-0.0128,0.01791,0.01085,-0.05423,0.03055,0.12333,0.03212,-0.07505,0.0556,0.04753,0.0108,-0.08877,0.14047,-0.01576,-0.00586,-0.09117,-0.02658,-0.07935,-0.1147,-0.05554,-0.04109,-0.01074,-0.05887,0.03286,0.05645,0.09424,0.0555,-0.03877,0.0772,-0.01602,-0.11775,-0.0146,0.0746,0.06344,-0.04534,-0.0878,0.01642,0.03512,-0.13931,0.11345,0.01062,0.00897,-0.03531,0.12487,0.0332,-0.05884,0.04845,0.09882,-0.09736,0.01314,0.03275,-0.05564,0.07159,-0.04447,0.14465,-0.01411,-0.10202,-0.05039,0.00093,0.00765,-0.03537,-0.06899,0.01412,0.02237,0.00953,-0.11525,0.02443,0.02671,0.04281,0.04261,0.07881,0.04238,0.04139,0.09379,0.03738,-0.0466,0.03172,0.02969,-0.00331,-0.0745,0.01322,0.00749,0.05495,0.0271,0.03426,0.01175,-0.00839,-0.01141,0.01109,-0.01492,0.10728,-0.01784,-0.00866,0.02729,-0.0794,0.02984,0.04321,0.03541,0.04662,-0.07004,-0.05634,0.13453,-0.11967,-0.05487,0.01994,0.06166,-0.06049,-0.01977,0.01185,0.05968,-0.09866,0.05577,-0.00578,-0.06237,-0.10493,-0.10964,0.04689]},{"domain":"linear_algebra","key":"vector_norm","name":"Length 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i.","v":[-0.03233,-0.05142,-0.12233,0.04785,0.01463,-0.02225,0.04916,-0.03308,0.05159,-0.01264,0.00034,0.13184,-0.02335,0.03352,0.05864,0.02745,-0.07103,0.08887,0.00881,0.02183,0.10598,-0.08101,-0.04978,0.03351,0.02749,0.00445,-0.01837,0.1254,0.17179,0.05506,-0.00166,0.04481,-0.04145,-0.01153,-0.05804,-0.01348,-0.02666,-0.06217,0.05815,0.05708,-0.02202,-0.13076,0.05505,-0.01498,0.00139,-0.12545,-0.00568,-0.09131,0.0615,-0.12242,-0.02664,-0.02666,-0.02133,0.01401,-0.05702,-0.02588,-0.0716,-1e-05,-0.04279,-0.0506,-0.02188,-0.00373,-0.0143,0.06553,0.10007,-0.11124,-0.05768,-0.00953,-0.1212,0.00691,0.00141,0.0815,0.03718,0.04601,0.06528,-0.02462,0.08222,-0.03419,0.07891,-0.00673,0.0715,0.06188,0.02486,0.03673,0.0725,0.08209,0.01454,-0.01482,-0.02039,-0.05575,-0.01585,-0.05955,-0.14811,0.04177,-0.0103,0.01083,-0.01892,-0.08611,0.03564,0.02348,0.01649,-0.10366,0.0813,-0.03529,0.06075,0.04648,-0.03944,0.00214,-0.10073,-0.04087,0.04434,0.10101,-0.01257,-0.02829,0.04176,-0.03793,-0.02089,-0.0581,0.0515,0.0619,0.09426,-0.06929,0.02028,0.00768,0.08501,0.08047,0.02628,0.05031,0.03804,-0.099,-0.08889,-0.00395,0.11293,-0.09848,0.00828,0.03711,0.09704,0.01453,-0.03746,0.01607,0.08128,0.00111,-0.06681,0.06779,0.05206,-0.10423,0.02032,-0.01545,-0.05822,0.00049,0.05395,0.1117,-0.00725,0.01536,-0.0225,0.06051,-0.01231,0.10196,0.06079,0.00644,-0.06321,0.02088,-0.07513,0.04764,-0.09751,0.06673,0.02107,0.06231,0.05958,-0.04118,0.05829,-0.0975,0.0319,0.05266,-0.02924,-0.09025,0.06632,-0.00612,-0.03599,0.09042,0.06319,-0.12319,0.0035,-0.11889,0.03604,-0.04215,-0.03834,0.03543,0.08301,-0.12216,0.06996,-0.05398,0.05357,-0.10026,-0.05851,-0.05417,-0.04077,0.06474,0.011,0.14093,-0.00838,0.0369,-0.03158,0.03121,0.02606,0.07133,0.0769,0.01674,0.03493,-0.04684,-0.00279,0.04898,0.06942,0.07077,0.01289,-0.01755,-0.0224,-0.01128,0.1086,-0.07073,-0.05293,-0.05133,-0.02576,-0.10426,-0.13654,-0.07477,0.07705,-0.0851,0.04988,0.04822,0.07742,-0.12371,0.03797,0.01528,-0.06486,0.01063,-0.05173,0.01473,0.04786,0.00659,-0.01924,0.02124,0.01735,0.10673,-0.05632,0.00854,-0.04111,-0.0015,-0.11152,-0.06858,0.03615,-0.04433,0.06942,-0.14079,0.01929,0.13176]},{"domain":"math_foundations","key":"complex_nth_roots","name":"The 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8i.","v":[-0.01279,-0.05881,-0.02063,0.03617,0.06255,-0.03876,-0.00616,0.03837,0.01101,-0.0208,0.06676,0.03764,-0.01693,0.00388,0.03396,0.05442,0.02627,0.02572,0.03043,0.04601,0.11949,-0.12344,0.04311,0.05691,0.03137,0.00761,-0.03591,0.10459,0.12927,0.0362,-0.03324,0.01317,-0.02074,-0.10371,-0.07567,0.01111,0.00641,-0.03362,0.12367,-0.02178,0.02703,-0.02553,0.03904,-0.03415,-0.05906,-0.09062,-0.04832,-0.12293,0.01716,-0.08991,-0.03488,0.05461,0.01305,0.00346,-0.07543,-0.04154,-0.13364,0.06158,-0.01242,-0.02549,-0.00643,-0.02453,-0.03165,0.01356,0.07243,-0.02947,0.00346,-0.02016,-0.18004,0.05604,0.01569,0.00571,-0.06519,0.10733,-0.03729,0.00118,-0.04454,0.00201,0.05035,0.00678,-0.01799,-0.00096,-0.00434,-0.03662,0.03138,-0.01597,-0.00616,0.02048,0.01628,-0.12147,-0.02534,-0.02427,-0.10747,0.01835,0.07956,0.02107,-0.00727,0.00219,0.05008,0.04313,0.03652,0.00987,0.10135,-0.04545,-0.02129,0.05462,0.00799,-0.01419,-0.0526,-0.04366,-0.09843,-0.02107,-0.05416,0.01904,0.01361,-0.00257,0.02933,-0.1311,0.05095,0.03488,0.11832,-0.02986,0.07058,-0.02732,0.0647,0.0227,0.09581,0.07795,-0.01136,-0.07456,-0.04341,0.08076,0.07899,-0.04306,-0.00019,0.0638,0.03954,-0.00333,0.04612,-0.053,0.00289,0.0514,-0.08517,0.1004,-0.03181,-0.13184,-0.00148,0.02261,-0.06603,-0.08867,0.12851,0.16896,-0.05559,0.00908,-0.0351,0.02919,-0.16507,0.11222,0.0137,0.12045,-0.03985,0.00573,-0.0397,0.02505,-0.11605,0.0624,0.02335,0.10165,0.15377,-0.09679,0.08256,-0.0392,-0.02346,0.024,-0.02826,-0.10115,-0.00299,0.02008,-0.15305,0.10369,0.00582,-0.02645,-0.09823,-0.13099,0.07415,0.01998,-0.03421,0.03648,-0.02911,-0.10657,0.06458,-0.01109,0.04125,-0.08744,-0.10297,-0.02263,-0.09357,0.01058,-0.03759,0.13748,0.05942,0.0444,-0.02641,0.02035,0.01921,0.11274,0.04439,0.0002,0.05366,-0.01619,0.03442,0.04099,0.02311,0.08669,0.05914,0.02007,-0.02059,-0.01385,0.1206,-0.00929,-0.03149,0.02113,0.03127,-0.02547,0.00348,-0.04829,0.02187,-0.10488,-0.05129,0.09562,0.0355,-0.06714,-0.02385,0.0148,-0.03233,0.01302,-0.08283,-0.02611,0.1459,0.04671,-0.02057,0.03279,-0.00056,0.09379,-0.07512,-0.07026,-0.02047,0.00954,-0.0585,-0.00847,0.04632,-0.08295,-0.03788,-0.09455,0.03912,0.09757]},{"domain":"math_foundations","key":"complex_product_modulus","name":"Product and modulus of complex numbers","package":"math-foundations-ai999x","example":"Multiply (1 + 2i)(3 + 4i).","v":[0.09865,-0.05253,-0.10006,0.10208,-0.07237,0.00696,0.00855,-0.00638,0.03939,0.03976,0.00832,0.20086,0.03144,-0.01862,-0.01847,0.01278,-0.13708,0.03865,0.06957,0.13699,0.1202,0.03262,0.07313,0.1882,-0.03278,0.09579,0.00626,0.07138,-0.04823,0.03101,0.02441,-0.0031,-0.04141,-0.00402,-0.03139,0.0591,-0.08067,0.04465,-0.00895,0.079,-0.03417,0.01552,0.03534,-0.03809,-0.11464,-0.07517,-0.08935,-0.04352,0.09313,-0.03579,-0.14927,-0.0077,-0.01796,0.04614,0.01049,0.1137,-0.18487,0.02402,-0.05467,-0.00916,-0.07034,-0.04948,-0.06961,-0.06288,-0.1282,-0.05482,-0.02764,0.01867,0.10065,-0.03226,0.0605,0.04033,-0.0561,-0.0202,-0.00665,0.00857,-0.01498,-0.03497,0.02342,0.01562,0.08148,-0.02529,0.04929,-0.07969,0.10562,-0.01515,0.0256,0.01859,-0.08127,0.07508,-0.08464,-0.02625,-0.0709,0.13119,0.0425,-0.04196,0.03746,-0.07811,0.0766,0.01047,0.06326,-0.04112,0.00606,-0.03964,0.02508,0.06003,-0.06998,0.00928,-0.14108,0.01156,0.0773,0.04232,0.01077,0.00663,-0.01355,-0.00359,-0.07251,0.01689,0.10223,0.07006,0.04623,-0.07497,0.06652,0.07989,0.04144,0.03889,-0.13614,0.03579,-0.0233,0.03035,-0.09817,-0.00669,0.04108,-0.13302,0.02077,-0.0085,0.00215,0.03718,-0.1443,-0.03297,0.00042,-0.00762,-0.08033,0.07558,0.00192,-0.01729,0.0373,-0.04154,-0.03004,0.02824,0.0864,0.09711,-0.02973,0.04231,0.02566,-0.08281,-0.02588,0.01182,0.02218,0.00928,-0.02067,-0.00634,0.03544,-0.03566,-0.00236,0.01546,-0.00703,0.11709,-0.04799,-0.01053,0.06761,0.03681,-0.04133,-0.00063,0.028,-0.05444,0.06061,-0.03038,0.05337,0.05355,-0.00363,-0.09544,-0.07992,-0.08773,-0.02404,-0.08055,-0.0308,-0.01924,-0.01226,-0.02442,0.01105,0.03487,-0.00761,-0.02835,-0.06066,-0.09473,-0.01031,0.03623,0.00315,0.04012,0.07983,0.00146,0.01389,0.08135,-0.03077,0.20751,-0.02131,0.03673,0.03955,0.0688,0.04666,0.03311,0.02202,0.05671,0.04957,0.02358,0.04442,-0.0042,0.08721,0.05031,0.02441,-0.03975,-0.06296,-0.00501,-0.07904,-0.01973,0.08151,-0.0155,0.09335,0.04826,-0.03191,-0.10173,-0.0305,0.03223,0.01963,-0.03039,-0.04588,0.00933,0.04998,-0.0288,0.07095,0.02594,-0.01977,0.03584,-0.11959,-0.08446,-0.03424,0.13501,-0.05061,-0.02299,0.07085,-0.1056,-0.05402,-0.02882,0.00281,0.0476]},{"domain":"math_foundations","key":"compose_linear_functions","name":"Composition of two linear functions","package":"math-foundations-ai999x","example":"If f(x) = 2x + 1 and g(x) = 3x - 4, find f(g(x)).","v":[-0.03418,0.05214,0.01168,0.03976,-0.07115,0.05883,0.03166,-0.0336,-0.01182,-0.01552,0.00953,0.00901,0.03161,-0.05547,0.03489,-0.04655,0.01683,0.04651,0.12032,0.09425,-0.04939,0.0032,0.05453,0.01519,0.02993,-0.02673,-0.06805,-0.1123,-0.10303,0.06237,-0.14466,-0.08382,0.05584,0.04109,0.01748,0.05707,-0.11911,0.038,0.04309,0.13919,-0.13114,0.00101,-0.10913,-0.01354,-0.01278,0.03517,-0.01634,0.09486,0.05319,0.00212,-0.02452,0.11924,-0.08174,0.06296,0.05429,0.08965,-0.0936,-0.10485,0.01167,0.10014,-0.04071,-0.03416,0.02944,-0.13537,-0.08166,0.0581,-0.02494,0.04248,0.0703,-0.05992,-0.0006,-0.00591,0.01268,-0.09293,0.0999,-0.00045,-0.01464,-0.05698,0.01464,-0.02281,0.1224,0.01577,0.02484,-0.01762,-0.03854,-0.09582,-0.09334,0.03645,-0.03633,0.0935,-0.02162,-0.00852,0.06851,0.0339,-0.0495,-0.15769,-0.00408,0.0112,-0.00693,-0.05667,-0.04681,0.00807,-0.00461,0.06938,0.01838,0.03238,0.19098,0.02935,0.01116,0.04929,-0.01661,0.07053,0.01647,0.07518,0.06913,0.02981,-0.12235,-0.11487,0.0348,-0.01917,-0.04139,0.03421,-0.01758,0.01548,-0.00604,-0.03496,-0.00586,-0.07608,-0.04892,0.01243,-0.06218,-0.00189,-0.04631,-0.05252,-0.02509,0.02061,-0.01421,0.06457,0.01593,-0.13524,-0.00956,-0.12604,-0.06761,0.04683,0.05245,-0.00317,-0.13274,-0.08337,-0.00208,0.11722,-0.06753,-0.09393,-0.03659,-0.05901,0.02211,0.00308,0.12223,0.01333,0.02738,0.01395,0.01982,-0.00074,-0.02349,0.0586,-0.00795,0.10419,-0.02813,0.00858,-0.07671,0.04907,0.11563,0.05926,0.00747,0.11675,0.00832,0.01455,-0.01591,-0.02418,-0.04906,-0.06798,-0.04438,-0.03703,0.00958,-0.04793,0.03472,-0.08615,0.03523,0.00356,-0.05872,-0.06107,0.05983,0.16123,-0.04778,-0.04625,0.03639,-0.02714,0.00687,0.11262,-0.03094,0.10231,0.01853,0.03606,-0.01146,-0.0312,-0.02597,-0.04148,0.04003,0.04192,0.01637,0.04327,0.00253,0.09221,-0.00043,0.0186,-0.07036,-0.08509,-0.01272,-0.00224,0.05522,0.14488,0.05359,-0.00464,-0.00979,0.04229,-0.0747,0.00106,0.05455,0.09419,-0.05555,-0.05075,-0.08697,0.02504,-0.03114,-0.14763,-0.01194,-0.02835,0.14202,0.03692,-0.03965,0.04278,0.0633,-0.07933,0.00149,0.06175,0.06878,0.05916,0.02083,0.06896,-0.00452,-0.07218,-0.08583,-0.0259,0.00452,0.04107,-0.01885,0.0977]},{"domain":"math_foundations","key":"composite_function_value","name":"Value of a composite function","package":"math-foundations-ai999x","example":"If f(x) = x^2 + 1 and g(x) = 2x - 3, find f(g(2)).","v":[-0.01547,-0.03719,0.00306,-0.05711,-0.00558,0.02645,0.05385,0.00606,-0.01112,-0.08105,0.02855,-0.0183,-0.04456,-0.04529,0.06328,0.02227,0.01338,-0.0222,0.07176,0.08373,-0.10015,-0.06267,0.06674,0.00556,0.01406,-0.03211,-0.08473,-0.028,-0.06789,0.00151,-0.0876,-0.1188,0.02621,-0.01722,-0.01449,0.02152,-0.09705,-0.04386,0.07484,0.05831,-0.04153,0.00016,-0.19903,0.08143,0.04207,-0.00539,-0.017,0.11006,0.00726,-0.04669,-0.0369,0.06893,-0.03797,-0.00454,-0.05843,0.00665,-0.02808,-0.10166,-0.01185,0.06303,-0.04828,-0.04068,0.01454,-0.10197,-0.0914,0.02355,0.01816,-0.0459,0.00771,-0.00468,-0.05132,-0.10238,-0.00518,-0.03182,0.03339,-0.06095,-0.0007,-0.02889,-0.02202,0.03947,0.16441,0.09723,0.05337,0.0642,-0.02351,-0.06856,-0.04737,-0.01876,0.02393,0.06014,0.01464,0.01634,-0.02236,0.05849,-0.0693,-0.02746,-0.02956,0.03622,0.01422,-0.08415,-0.03956,0.02556,0.02473,0.00018,0.03335,-0.03249,0.14224,-0.02376,0.08371,-0.05486,-0.04038,0.0572,0.03882,0.02564,0.07571,-0.00711,0.00841,-0.16926,0.0474,-0.06285,-0.00231,0.0757,-0.06051,-0.01954,0.00087,-0.06032,-0.03066,-0.07301,-0.02402,-0.00652,-0.0219,0.05216,0.01275,-0.00415,-0.03573,0.06951,0.00642,0.09843,0.10349,-0.09217,0.07565,-0.13037,-0.02552,0.02381,-0.02502,-0.0726,-0.03603,-0.10478,-0.00203,0.08797,-0.01601,-0.03889,0.00636,-0.0294,0.0058,0.03168,0.11567,0.02133,-0.02306,-0.04474,0.0368,-0.09084,-0.01581,0.03021,-0.07292,0.10311,0.03513,0.03263,0.06149,0.00954,0.04243,0.02766,0.0012,0.16065,-0.01739,0.01236,-0.01813,0.06491,-0.07588,-0.05819,0.06699,0.0203,0.00161,-0.10929,0.01545,-0.14583,-0.03408,0.0065,-0.08618,-0.00851,0.11141,0.0632,-0.04878,-0.03158,0.01061,-0.029,-0.00408,0.05487,-0.10528,0.1476,-0.04337,-0.01601,-0.03774,-0.04945,-0.06296,-0.08599,-0.03697,0.04207,0.05299,0.07616,0.00206,0.1141,0.08889,0.01313,-0.08607,-0.06634,0.03664,-0.04025,0.1528,0.06463,0.17832,0.05612,-0.08841,-0.03063,-0.02898,-0.03818,0.18885,0.04891,-0.01105,-0.008,0.02898,0.09658,-0.02503,-0.04749,0.03665,-0.01697,0.11887,0.10058,0.00542,0.05259,0.02669,-0.12759,-0.0009,0.04857,0.10715,0.00095,-0.02726,0.08668,0.06358,-0.00994,-0.04368,-0.072,0.03259,0.01977,-0.03224,0.10042]},{"domain":"math_foundations","key":"compound_interest","name":"Compound interest","package":"math-foundations-ai999x","example":"Find the amount after 2 years if 1000 is invested at rate 0.05 compounded 1 times a 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How much remains after 15 years?","v":[0.00499,0.09064,-0.08964,-0.0048,0.14567,-0.01852,-0.06155,-0.00547,0.07292,0.04425,-0.01609,0.1019,-0.04246,-0.02864,-0.05956,-0.06903,0.00172,-0.00208,0.08901,0.06818,-0.09632,0.00062,-0.03385,0.06598,-0.04923,-0.04514,-0.01879,0.0588,0.08611,-0.00881,-0.1419,0.12805,0.04261,-0.06349,-0.08369,-0.0234,-0.03256,-0.04491,-0.01914,-0.07102,0.06863,-0.01294,0.08451,-0.03299,-0.05409,0.01479,-0.00342,0.00915,-0.08143,-0.06134,-0.04671,0.02391,-0.0097,-0.13785,0.09106,0.04802,-0.00793,-0.01252,-0.07759,-0.06328,0.04431,-0.02649,0.09612,0.05304,0.02537,0.06476,0.03704,0.03437,0.05834,-0.00558,0.00962,-0.15774,-0.04595,0.10068,0.02119,-0.12867,0.01626,0.05661,-0.08401,0.0129,0.04225,-0.04119,0.06446,0.06588,0.06551,-0.01379,0.01838,-0.03345,0.09913,0.00978,0.01339,-0.09183,0.05042,-0.03903,-0.02083,0.13515,0.03506,0.03794,-0.01171,-0.05328,0.0387,-0.10113,0.02394,0.03605,-0.11902,-0.04285,-0.01136,-0.09231,0.04397,-0.11378,0.00815,-0.0123,-0.07541,-0.0071,0.05312,0.06172,0.09409,0.00597,-0.03391,0.02626,-0.0385,0.0652,0.03371,0.0218,-0.08406,0.01468,0.00019,0.01949,-0.00148,0.04233,0.03589,-0.02505,0.02421,-0.04025,-0.04967,-0.05164,0.15052,0.00608,-0.04387,0.0707,-0.04571,-0.01973,-0.02424,0.02246,-0.12524,0.04383,0.08958,0.18857,-0.02569,-0.00728,0.01249,-0.02317,-0.09753,-0.01101,-0.0317,-0.02865,-0.03127,-0.00075,0.02491,-0.07639,-0.05517,0.0936,-0.047,-0.04655,-0.05346,-0.04127,0.11195,-0.01467,-0.03524,-0.04463,-0.03647,-0.07036,0.00982,-0.00013,-0.0269,-0.03747,-0.1132,-0.1127,-0.02239,0.05981,0.10675,0.0071,0.01264,-0.01847,0.03869,-0.00096,0.05907,-0.0577,0.02623,-0.02776,-0.02425,-0.04474,0.02161,-0.03943,0.03452,0.07546,-0.03228,-0.01259,-5e-05,0.09537,-0.0094,0.04315,-0.07834,-0.06803,0.16681,-0.02661,0.08915,-0.01287,0.0625,-0.04804,0.0611,-0.01542,0.09619,0.04747,0.12966,-0.03077,0.04231,0.02276,-0.09405,0.04056,0.05576,-0.08109,0.03992,-0.15863,0.09232,0.03494,0.14664,-0.08644,-0.00934,0.06429,0.05252,0.08139,0.05345,0.05646,0.01501,0.05726,0.0067,-0.12389,0.01066,-0.06752,-0.06261,-0.03461,-0.09673,0.12736,0.01778,-0.04179,0.01061,0.01906,0.03938,-0.0179,0.01421,-0.06836,0.03636,-0.03098,0.01726,0.07154]},{"domain":"math_foundations","key":"heron_area","name":"Area of a triangle from its three sides (Heron)","package":"math-foundations-ai999x","example":"Find the area of a triangle with sides 13, 14 and 15.","v":[0.03828,-0.04848,0.07266,-0.06224,0.15521,0.0173,0.02569,-0.0567,-0.02316,0.07038,0.12668,-0.0187,0.01851,0.06296,-0.05882,0.02944,0.06971,0.01422,0.02796,0.11849,-0.08667,-0.08105,0.07066,0.08055,-0.00848,-0.04509,0.10358,0.05997,0.05476,0.0374,-0.12464,0.0674,-0.02963,0.02482,-0.05778,0.03511,-0.00827,-0.02729,-0.08089,-0.04354,0.0565,-0.05188,-0.04359,0.02681,-0.02197,0.06019,-0.04176,-0.07967,-0.06648,0.04696,0.0761,-0.03501,0.09508,-0.01279,0.03856,0.09805,-0.04622,0.00058,0.03349,-0.07573,0.11035,-0.03911,-0.06361,0.19656,-0.02603,0.00036,0.09983,0.08166,0.00381,-0.01012,0.03095,0.09883,-0.12981,0.02265,-0.1706,-0.05662,0.05587,-0.06717,-0.10393,0.00746,-0.00277,-0.0052,0.04348,0.0522,0.04927,0.05404,0.02988,-0.13688,0.01125,-0.01794,0.00465,-0.14413,-0.05183,-0.02799,-0.00531,-0.00264,-0.03463,0.0524,0.05309,-0.04266,-0.03633,0.18677,0.0302,-0.00622,0.04112,-0.00199,-0.01787,-0.01211,0.00102,0.01086,0.02446,-0.07129,-0.11253,0.04934,-0.00307,0.03566,-0.04684,0.08848,-0.11187,0.02954,-0.04854,0.10272,0.02052,0.02174,-0.08362,0.05116,0.0538,-0.01156,0.02713,-0.00508,-0.0061,-0.04028,0.02113,-0.04437,-0.08691,0.01366,0.02845,0.01673,-0.01252,-0.00518,-0.02435,-0.07289,0.02505,0.05135,-0.04032,-0.08754,-0.06983,0.03905,-0.0839,0.03482,0.01533,-0.01235,-0.03982,0.00411,-0.07728,0.06571,-0.02564,-0.09224,0.12127,-0.12752,0.04223,0.04797,-0.07165,0.0751,-0.01319,0.07686,-0.00902,0.16015,0.0332,0.00385,-0.05155,0.03347,0.0641,0.10035,-0.05819,-0.11027,-0.03787,-0.00742,0.037,0.15763,0.14336,-0.002,-0.04625,0.02776,-0.06321,0.06401,-0.03888,-0.05776,0.00538,-0.08343,-0.05809,-0.00761,0.0601,-0.07655,-0.02527,0.02012,0.07928,0.0755,-0.03687,0.12763,0.05853,-0.00784,0.03971,0.03519,-0.04355,0.0102,-0.01034,-0.07136,-0.03612,0.06415,-0.03877,-0.07809,0.04922,-0.01666,-0.00546,-0.03642,0.01595,-0.03979,-0.00286,-0.01071,-0.04079,-0.07798,-0.12815,-0.09933,-0.0016,-0.0056,-0.01761,-0.02856,0.11991,0.0361,0.06745,-0.02593,-0.00702,0.00751,-0.06733,-0.02052,0.02733,-0.01669,-0.04325,-0.03518,0.04727,0.00834,-0.00881,-0.02324,-0.01129,-0.11292,0.0118,-0.00043,-0.04397,-0.10195,0.10959,0.03564,-0.00738,0.03276,0.00885,0.00187]},{"domain":"math_foundations","key":"hyperbola_parameters","name":"Foci, eccentricity and asymptotes of a hyperbola","package":"math-foundations-ai999x","example":"Find the foci and asymptotes of the hyperbola x^2/16 - 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6.","v":[0.05817,-0.0026,-0.05782,0.04014,0.03054,0.00058,-0.10259,0.03185,-0.01553,-0.0434,-0.05953,0.01202,-0.02124,-0.0966,0.04498,0.02834,-0.01987,0.00563,0.07088,0.02354,-0.05493,-0.0662,-0.01251,0.03428,0.00223,-0.14229,0.05566,-0.13264,0.12234,-0.01856,-0.12082,-0.03313,0.00664,-0.01127,-0.04145,-0.00681,-0.08455,-0.04228,-0.0139,0.08035,0.00237,-0.05903,0.00219,-0.0648,0.12679,0.05831,-0.07166,0.02013,0.04822,0.0258,0.045,-0.00071,-0.20376,-0.00283,0.01896,0.02197,0.04522,-0.02439,0.0339,0.09503,-0.03576,0.04831,-0.01295,-0.0684,-0.066,-0.02076,-0.06325,-0.02996,0.09003,-0.01371,0.00704,-0.01922,0.06524,-0.1233,0.07304,-0.05615,0.01751,-0.05339,0.07169,-0.00813,0.07587,0.04817,0.01001,-0.07468,0.01653,-0.10464,-0.09626,-0.03411,-0.02598,0.03805,0.12506,-0.06337,0.10736,0.02557,0.00263,-0.04878,0.01052,-0.02557,0.03427,0.02279,0.038,-0.00099,-0.0291,0.02194,-0.10006,-0.01095,0.17324,0.04668,-0.02437,0.09192,0.00207,0.10106,-0.0874,0.05374,0.12331,-0.04938,-0.08918,-0.03488,-0.04579,0.03002,-0.02281,0.00454,-0.00615,-0.07004,0.06869,0.09445,-0.03627,0.03982,0.00454,0.04473,-0.05293,0.07447,0.06461,-0.1532,0.03772,-0.0467,0.00493,-0.01557,-0.01333,-0.10596,0.11735,-0.05048,-0.01173,-0.02899,-0.02393,-0.02597,-0.05765,-0.02762,0.03351,-0.01999,-0.06964,-0.0443,-0.00601,0.0138,0.10685,0.0202,0.02824,-0.02142,0.19589,0.08819,0.04704,-0.04089,-0.11452,0.04341,0.04804,-0.00198,0.01055,0.02388,-0.0856,0.0721,0.04084,0.07844,0.14315,0.08469,0.01233,-0.0368,-0.00085,-0.04055,-0.02841,-0.0859,-0.07158,-0.04302,0.10094,0.03546,0.00951,0.01416,0.04916,0.06118,0.02098,-0.03217,0.1089,0.07974,-0.01088,-0.1335,0.00857,-0.01791,0.03715,0.03305,-0.00425,0.10553,0.00455,0.0632,-0.0139,-0.13156,0.04411,-0.05557,0.09281,0.05079,-0.02342,0.09193,0.00841,0.07908,-0.00818,-0.01612,-0.07143,-0.05525,-0.00306,0.04772,0.08017,0.08159,0.00607,0.06323,0.03567,0.09101,0.01339,-0.02841,-0.03083,0.05337,-0.05085,-0.06597,0.04551,-0.04788,-0.06588,-0.06096,-0.02314,0.04067,0.04343,0.00234,-0.07827,0.06011,-0.06084,-0.0124,0.06586,-0.03866,0.14232,-0.0431,0.02089,0.05797,0.01341,-0.13863,-0.04243,0.04927,-0.05171,0.04932,-0.00018,0.07264]},{"domain":"math_foundations","key":"law_of_cosines_sas","name":"Law of cosines (two sides and the included angle)","package":"math-foundations-ai999x","example":"In triangle ABC, b = 5, c = 7 and A = 49 degrees. 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Find the angles.","v":[-0.04198,0.08161,0.05106,-0.07101,0.05386,0.07449,0.05112,-0.08525,-0.00687,0.07931,0.12948,-0.01961,0.01106,0.07541,0.03121,0.01567,-0.0141,-0.00305,-0.00094,-0.0055,-0.08791,-0.05521,0.01768,0.00497,-0.01405,-0.10869,0.12601,0.1721,0.00164,-0.02806,-0.10608,0.06892,-0.08916,0.02146,-0.03814,-0.02348,0.0068,-0.04731,-0.07415,-0.05444,-0.0047,-0.14079,0.02297,0.05306,0.02311,-0.07947,-0.1145,-0.00891,-0.02863,0.0393,0.10114,-0.06736,0.03143,-0.0214,-0.02212,0.03979,0.00606,-0.00286,-0.02678,-0.04574,0.07965,-0.03926,-0.05861,0.04534,0.04573,0.0088,0.05557,0.02399,-0.13715,-0.0789,0.00065,0.06079,-0.03839,-0.0113,-0.08686,-0.11214,0.10221,-0.02402,-0.05248,0.00851,0.02313,-0.04029,0.11709,0.04131,0.05264,0.01399,0.07643,-0.12585,0.04983,0.01464,0.11931,-0.09743,0.02432,-0.03876,0.10082,-0.04064,-0.01373,0.0087,-0.02091,0.0119,-0.03952,0.08481,0.02538,-0.06805,0.1507,-0.00076,-0.00385,0.04765,0.04477,-0.01085,0.05488,-0.01901,0.03323,-0.07816,0.00796,0.00712,-0.03885,0.06655,-0.15908,-0.00128,-0.10362,0.08198,0.00707,-0.06668,0.03438,0.1482,0.0644,0.04405,0.09433,-0.0371,0.0572,-0.05361,-0.04593,-0.01796,-0.08239,-0.03046,-0.04014,0.06591,0.00753,-0.09206,-0.08098,-0.00132,0.03767,-0.03458,0.00274,-0.05378,0.02946,0.12993,-0.14852,-0.01961,0.02545,-0.00145,-0.00784,-0.03381,-0.03954,0.0565,-0.04115,-0.06863,0.15867,-0.05511,0.0038,0.04357,-0.07842,0.0899,-0.04189,-0.0002,-0.02706,-0.06979,-0.01033,0.0276,-0.00725,0.05631,0.04768,0.04926,-0.07909,-0.03934,-0.05231,-0.08202,-0.0013,0.03474,0.05301,0.0587,-0.0317,0.04388,-0.05536,-0.00732,-0.04653,-0.02517,0.03977,0.03748,-0.03639,0.02843,0.0899,-0.09247,-0.06632,0.08963,0.0318,0.1327,0.00149,0.07414,0.00696,0.01865,-0.01397,0.07491,-0.1141,0.00227,-0.01547,-0.00965,0.12169,0.01803,-0.07141,-0.05522,-0.13604,0.0283,0.05883,-0.04328,0.02245,0.01815,-0.05222,0.00348,-0.03906,-0.09538,-0.12033,-0.00445,-0.0496,0.05788,0.07512,-0.00188,0.1082,0.10647,0.01187,0.02781,0.02338,0.08657,-0.03861,-0.06135,0.1455,0.034,-0.05356,0.00407,-0.00025,-0.01208,0.0108,-0.01817,0.0298,-0.02521,-0.01003,0.04241,-0.02075,-0.08454,0.06653,0.06932,0.04846,-0.02726,-0.0717,-0.0496]},{"domain":"math_foundations","key":"law_of_sines_aas","name":"Law of sines (two angles and a side)","package":"math-foundations-ai999x","example":"In triangle ABC, A = 40 degrees, B = 60 degrees and a = 10. Solve the triangle.","v":[-0.1046,0.03616,0.02553,-0.0459,0.06994,0.0687,0.09217,-0.08161,0.01369,0.05508,0.10497,0.04216,0.01746,0.07324,0.09862,-0.01113,-0.04194,0.01683,0.01091,-0.00413,-0.08469,-0.07749,0.03323,0.00731,-0.04512,-0.12784,0.13501,0.16991,0.03207,-0.02803,-0.0985,0.07724,-0.11374,0.00798,-0.03419,-0.01222,0.00819,-0.08089,-0.05882,-0.04618,-0.00265,-0.08728,0.01189,0.04456,0.02737,-0.05073,-0.12916,0.02016,0.0037,0.08143,0.04995,-0.05088,0.01325,-0.00338,-0.04007,0.02839,0.04368,0.0508,0.01586,-0.01,0.0481,0.02044,-0.05497,0.02043,0.06843,0.05084,0.09799,0.00614,-0.14566,-0.09729,0.00242,0.00784,-0.04397,-0.05199,-0.065,-0.12248,0.0872,-0.06116,-0.05548,0.00602,-0.00619,-0.04699,0.09349,0.02631,0.05316,-0.00323,0.09421,-0.06992,0.06128,0.03537,0.10805,-0.07986,0.02419,-0.03843,0.10009,-0.03995,0.01885,0.00312,-0.06005,0.01837,-0.01028,0.0863,0.04221,-0.06852,0.13243,-0.02439,0.01162,0.04227,0.00423,-0.0424,0.01306,0.01139,0.03153,-0.08004,0.00994,-0.03416,-0.01154,0.06503,-0.18357,-0.02815,-0.07871,0.10397,0.00443,-0.06159,0.02226,0.12374,0.04396,0.03996,0.10021,-0.04124,0.03273,-0.0355,-0.04772,-0.02342,-0.0806,-0.03489,-0.01174,0.07553,-0.04215,-0.07886,-0.13373,-0.0064,0.01674,0.00406,0.02909,-0.04683,0.04978,0.15098,-0.15188,-0.02569,-0.00714,-0.01114,-0.00228,-0.03969,-0.00425,0.02984,-0.02838,-0.04381,0.14615,-0.05838,-0.02048,0.00202,-0.10965,0.07736,-0.04016,-0.04942,-0.05856,-0.0765,0.01464,0.01617,-0.00185,0.05111,0.08699,0.04534,-0.0383,-0.03749,-0.02838,-0.11877,0.00601,0.00032,0.03336,0.08664,-0.00731,0.04721,-0.034,0.02853,-0.03271,-0.01468,0.02956,-0.04011,-0.05654,0.09216,0.06917,-0.06289,-0.05501,0.07134,0.00739,0.14262,0.02356,0.0761,0.01823,-0.00162,-0.06523,0.05937,-0.06622,0.02859,-0.0339,0.02222,0.08097,0.02513,-0.08513,-0.05401,-0.14743,0.08373,0.06928,-0.02096,0.01297,0.04755,-0.02662,-0.01896,0.0182,-0.11858,-0.0556,-0.03002,-0.01541,0.05853,0.01396,-0.00987,0.13431,0.13062,-0.00201,0.04288,-0.02025,0.06764,-0.00913,-0.07175,0.13388,-0.00096,-0.03495,0.0135,-0.01246,-0.01889,-0.0051,0.00625,0.01814,-0.03621,0.02237,0.00552,0.0068,-0.10434,0.03211,0.09003,0.04576,-0.06319,-0.07234,-0.04655]},{"domain":"math_foundations","key":"law_of_sines_ssa","name":"Law of sines, the ambiguous case (two sides and a non-included angle)","package":"math-foundations-ai999x","example":"In triangle ABC, a = 8, b = 10 and A = 40 degrees. Solve the triangle.","v":[-0.06174,0.03433,0.04798,-0.03718,0.02856,0.04604,0.17596,-0.11365,0.06744,-0.00145,0.11952,-0.03308,-0.02601,0.09877,0.08064,-0.02731,-0.03632,-0.0002,-0.01033,0.07572,-0.05752,-0.09686,0.09364,0.00565,-0.02197,-0.10455,0.17438,0.13717,0.01463,-0.01342,-0.15659,0.01716,-0.15869,-0.00516,0.00028,-0.01884,-0.06368,-0.01301,-0.0046,0.00578,0.03968,-0.04455,0.05903,0.04537,0.00832,0.01867,-0.13508,0.10966,0.0484,0.12727,0.02513,-0.021,0.06778,0.00591,0.01096,0.0876,-0.04533,0.05956,-0.00844,-0.04852,-0.0009,0.09329,-0.11731,0.02886,0.08619,0.09621,0.09889,0.02699,-0.04861,-0.12606,-0.0011,0.05618,-0.01272,0.0407,-0.00477,-0.09129,0.04695,-0.04052,-0.01996,-0.02342,-0.03969,-0.10609,0.02245,0.01536,0.03289,-0.05338,0.05546,-0.10988,0.03411,0.05727,0.0784,-0.08296,0.01031,-0.07707,0.04019,0.00884,-0.00694,0.03585,-0.03957,0.01055,0.0371,0.14731,0.01502,-0.03338,0.11042,0.0042,0.01468,0.02523,-0.00478,-0.04438,0.02243,-0.08511,0.04815,-0.09921,0.00115,-0.06663,-0.01753,0.03427,-0.13088,0.02125,-0.06278,0.08354,-0.03587,-0.01718,0.0957,0.06749,0.07317,0.04065,0.08224,-0.01432,0.0112,-0.06543,-0.038,-0.0395,-0.10712,0.01202,0.04543,-0.01492,0.02116,-0.0148,-0.1515,0.04162,0.03079,0.02427,0.04546,-0.0786,-0.03233,0.06625,-0.11709,-0.03071,0.04511,0.03041,-0.02021,-0.02329,-0.03714,0.06725,-0.07117,-0.08245,0.16982,-0.06485,0.03762,-0.0505,-0.16286,0.07593,-0.0525,-0.07108,-0.00942,-0.07024,0.05584,0.02547,-0.01286,0.08455,0.00668,0.02954,0.00244,-0.01197,-0.01084,-0.03423,-0.01572,0.03357,0.03306,0.02786,0.00849,0.03326,-0.04297,0.05223,-0.01686,-0.00165,0.07463,-0.04886,-0.05991,0.0816,0.04189,-0.10632,-0.02781,0.03433,0.00313,0.0133,-0.09707,0.07747,0.00329,0.01087,0.00794,0.06232,-0.06511,0.05875,-0.04262,-0.00719,0.01242,0.09479,-0.0415,-0.04841,-0.07685,0.02513,0.05352,-0.00054,-0.00719,0.02852,-0.0139,-0.05672,-0.0036,-0.09033,-0.02007,-0.06337,-0.05071,0.02948,-0.01984,-0.07186,0.0485,0.09169,-0.0642,0.02377,-0.06094,-0.02487,0.02667,-0.01537,0.05237,0.03433,-0.12633,0.03405,-0.0313,0.00119,0.10529,0.06489,0.06415,-0.03089,-0.02701,0.01065,-0.01988,-0.12787,-0.01248,0.01486,0.1043,-0.02539,0.028,-0.06722]},{"domain":"math_foundations","key":"line_intercepts","name":"Intercepts 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2?","v":[-0.03088,-0.06697,0.03571,-0.06139,0.03092,-0.10474,0.00361,-0.05514,-0.03616,0.11559,0.02131,-0.00127,0.07833,0.03829,-0.02676,-0.11863,0.09697,-0.00443,0.01603,0.02165,-0.02823,-0.08991,-0.04881,-0.07049,-0.00548,0.04927,0.03739,-0.11098,0.02612,0.09005,0.0488,0.15656,0.06128,-0.00736,-0.05303,-0.03236,0.13003,0.00242,-0.03437,0.0006,-0.02493,-0.12666,0.07149,-0.04196,0.04205,0.04463,-0.01378,-0.13954,-0.1075,0.03557,-0.07512,0.03345,-0.03675,0.09721,0.0156,0.05416,0.07867,0.02335,0.04334,-0.00298,-0.09368,-0.02175,0.04577,0.04446,0.04237,0.09122,0.02846,-0.03784,-0.10809,0.01899,0.0226,0.1365,-0.06488,-0.00553,-0.05231,-0.06835,0.1438,0.01828,-0.00646,0.04864,0.02579,-0.03903,0.03748,-0.01184,-0.06294,0.05163,-0.0529,0.07128,0.01516,0.10119,0.03477,0.04476,-0.11901,0.07657,0.03526,0.01319,0.04824,0.01205,0.01182,0.06204,-0.12076,0.10628,0.0032,0.0062,-0.01715,0.11084,-0.06795,-0.01721,-0.09787,-0.00734,-0.08796,-0.10652,-0.05302,0.08274,-0.01959,0.03965,-0.01429,0.07181,-0.08851,-0.00372,-0.04979,0.06685,-0.01818,0.03781,0.06863,0.15951,0.03143,0.01694,0.00512,0.03213,0.00978,-0.00486,0.04286,-0.03848,-0.03465,-0.03672,0.08783,0.00949,0.02151,0.09963,0.07334,0.04243,0.03183,-0.03056,0.04917,-0.09763,-0.01817,-0.02744,0.0108,-0.05298,-0.12342,0.0264,-0.08581,0.04581,0.08183,-0.11116,0.05161,0.01233,0.01777,-0.03138,-0.02624,-0.02981,-0.04315,0.03904,-0.00143,-0.03282,-0.01479,-0.03291,-0.01091,-0.00057,-0.06485,0.01381,-0.00144,0.03641,-0.19186,-0.02799,0.04785,-0.04218,0.10457,0.06655,0.00848,0.05401,0.13026,0.02956,0.0038,-0.00989,0.06582,-0.14051,-0.04907,-0.07931,-0.04192,-0.00503,-0.03433,0.01932,-0.06905,-0.03002,-0.03531,0.05568,0.04805,0.02006,0.05652,0.01346,0.02294,0.05119,-0.10635,-0.01292,0.0418,-0.03831,-0.04992,-0.07197,-0.06538,-0.07514,0.09941,0.03238,-0.01915,0.06609,0.09479,0.041,-0.04334,-0.0725,0.04658,0.00559,-0.10321,0.0154,0.11189,0.00459,-0.054,0.03819,-0.01951,-0.05581,0.04681,0.02601,0.01216,0.10249,-0.03139,-0.09113,0.04314,0.0792,-0.036,-0.08002,0.03569,-0.03582,-0.10487,-0.14423,-0.11023,-0.02318,0.00123,0.04462,-0.02908,0.06088,0.10655,-0.04034,0.0135,-0.00158,0.04476,-0.05466]},{"domain":"math_foundations","key":"perpendicular_lines_slope_product","name":"Slope 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What is the slope of a line perpendicular to 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Find the dimensions that minimize the surface area.","v":[-0.00525,-0.03602,-0.04202,0.07602,0.00814,-0.01552,0.01707,0.02935,0.077,0.09221,-0.02557,-0.03888,0.07214,-0.03637,-0.06594,0.07195,0.09349,0.04898,0.03769,-0.02741,-0.00266,0.00123,-0.01963,-0.02598,0.1364,0.04251,-0.04285,0.04685,-0.0314,0.05136,-0.00307,-0.00299,0.02674,0.0116,-0.03074,-0.07115,0.04704,-0.05175,0.06057,0.06259,0.05579,0.02009,-0.07031,-0.04342,0.02989,0.02274,0.0251,-0.08599,0.01037,-0.06199,0.13712,-0.11769,-0.06963,0.04904,-0.10614,0.02514,0.11473,-0.0154,-0.10975,0.05105,0.05121,0.05108,-0.03941,0.16373,-0.0399,0.00772,-5e-05,0.02416,-0.02228,0.13012,-0.00445,0.03432,-0.16272,0.07503,-0.05788,-0.02988,-0.1009,-0.00659,-0.0273,-0.0237,0.09371,0.06186,-0.03884,-0.04911,-0.03283,0.12787,-0.01304,0.05286,0.05285,0.11124,-0.00591,0.04345,0.00224,-0.04559,0.00419,0.04413,-0.06717,0.01383,0.04361,0.18125,-0.1048,-0.02379,0.03267,-0.02986,-0.09337,0.01906,-0.02328,0.00041,-0.00496,0.00084,-0.04071,0.01535,0.0995,-0.02617,-0.08145,-0.04596,-0.02045,-0.02447,-0.05434,-0.00179,0.10051,0.07737,0.0855,-0.0012,-0.16508,-0.00946,-0.034,-0.01613,0.00053,-0.06513,-0.04993,-0.05659,0.00544,0.03611,0.0089,-0.00737,-0.04798,0.0596,0.03578,0.10234,0.0218,-0.03726,-0.00884,0.01713,0.03738,0.00067,0.03813,-0.03245,0.05491,-0.08452,-0.0474,0.00568,0.03447,-0.00991,0.02407,0.0033,-0.05042,0.02612,0.01049,0.0517,-0.02906,0.14198,0.04688,0.00816,-0.04496,0.07723,0.00385,0.07827,0.03756,-0.0477,-0.02087,0.05746,0.03399,-0.02954,-0.03135,-0.07138,-0.00066,0.02422,0.03516,-0.0427,-0.07715,-0.09709,0.02536,0.06834,-0.02203,-0.06443,-0.0629,-0.06423,-0.07452,0.0478,-0.12695,-0.06222,0.07318,-0.04771,0.0677,-0.05154,0.04604,0.00061,-0.01453,-0.08527,0.0694,-0.02448,-0.07506,-0.10161,0.01948,-0.02679,0.01173,-0.01267,-0.02748,-0.12422,-0.04534,-0.11888,0.14567,-0.04313,-0.06382,-0.0162,0.06365,-0.10281,0.10962,0.00843,-0.1056,0.0242,-0.04035,-0.10087,-0.01978,0.05222,-0.06298,0.07191,-0.09017,-0.07946,0.00811,0.11093,-0.05586,0.02593,-0.06017,0.04947,0.02939,-0.03782,-0.00549,-0.11951,0.00335,0.06661,0.09197,0.01902,0.03489,-0.09497,-0.06805,0.01188,-0.17253,-0.02569,0.06365,0.09037,0.12238,-0.04994,0.06208,0.05417]},{"domain":"optimization","key":"critical_path_method","name":"Critical path method (project duration and slack)","package":"optimization-ai999x","example":"Activities A, B, C, D have durations [3, 4, 2, 5]; precedences: A-B, A-C, B-D, C-D. Find the critical path and the project duration.","v":[-0.07656,0.10374,-0.08078,0.08462,0.01201,0.05495,0.05045,-0.06301,0.16971,-0.02787,0.05327,0.10441,0.06972,-0.05415,0.06935,-0.04699,-0.00166,0.09328,0.12601,0.02838,-0.05718,-0.04023,0.02519,0.06077,0.01669,0.0701,-0.07973,0.04653,0.08605,0.07258,-0.0168,-0.04626,-0.0864,0.07816,-0.00232,0.05686,-0.05869,0.00376,0.01884,-0.02121,-0.01698,-0.06359,-0.15431,-0.01707,0.04901,-0.0323,-0.08288,0.00397,-0.05765,0.05334,-0.03346,0.00061,-0.08597,0.02967,-0.02983,0.00301,-0.0915,-0.01367,0.00533,-0.01477,0.04228,0.10915,-0.09468,-0.02406,0.0476,0.00481,0.07265,-0.01272,-0.00571,-0.01427,-0.02294,0.03801,-0.06108,-0.12586,-0.10187,-0.06135,0.07079,0.07187,-0.03452,0.05852,-0.01928,-0.04081,0.04991,-0.03518,0.0628,0.11383,-0.12573,0.04856,0.05183,-0.10351,-0.02594,0.03429,-0.11757,-0.08647,-0.06433,-0.14229,0.07352,0.01246,-0.05324,0.02117,-0.0596,0.12172,-0.11652,0.09786,0.00333,0.0044,-0.20765,-0.0087,0.00892,0.03295,-0.01654,-0.00357,0.03946,-0.06903,0.07197,-0.00429,-0.0483,0.01391,0.02744,-0.0217,0.03839,0.04015,0.0457,-0.01362,0.03499,-0.00617,0.05703,-0.02359,0.04808,-0.01742,0.06088,-0.03499,-0.00444,-0.06083,-0.06274,0.05431,-0.00394,0.06059,-0.0269,-0.02494,-0.11747,-0.01923,0.05586,-0.03964,-0.06463,0.07634,0.00101,0.02534,0.0159,0.03685,-0.00727,-0.07759,-0.05383,0.03562,-0.07505,0.03964,0.06289,-0.02661,-0.06485,0.01924,0.08012,0.10012,0.03076,0.06748,-0.04223,0.13129,0.05761,0.08187,-0.06462,0.09473,0.08783,-0.01095,-0.066,0.00361,-0.01457,-0.00945,-0.07686,-0.02434,0.05509,-0.00473,-0.04402,-0.12137,0.10524,-0.03666,-0.06516,0.14663,0.03074,0.06609,0.09442,-0.04785,0.0418,-0.04738,-0.01534,0.05667,-0.00765,-0.0474,0.04391,0.04948,0.16704,0.01667,0.03634,0.13583,-0.00721,-0.0554,0.01921,0.00058,0.01642,-0.02611,-0.03599,-0.02047,-0.02061,-0.05052,-0.05804,0.03575,-0.01841,0.05207,0.02361,-0.09292,0.06592,0.06465,-0.01793,-0.06762,0.0091,-0.13456,-0.04792,-0.09654,-0.03331,0.06162,-0.03113,-0.08421,0.01637,-0.01073,-0.05962,-0.03359,-0.01591,-0.04476,0.00836,0.1029,0.01664,0.04741,-0.0005,0.03123,-0.00103,0.08307,-0.08804,-0.0286,0.0085,-0.09652,0.0893,0.06316,-0.02944,0.01221,0.06278,-0.03626,0.01776,-0.03824]},{"domain":"optimization","key":"critical_point_two_variables","name":"Critical point of a two-variable quadratic and its classification","package":"optimization-ai999x","example":"Find and classify the critical point of f(x, y) = 3x^2 + 2xy + y^2 - 4x + 6y + 1.","v":[-0.05739,0.00673,-0.12739,0.0403,-0.04121,0.08414,-0.06058,-0.05187,0.06251,-0.06726,-0.08697,0.02392,-0.00239,-0.11396,0.03657,0.02712,0.0353,-0.00544,0.1407,-0.03952,-0.12169,-0.06149,0.08082,-0.03903,-0.05384,-0.02168,0.05841,0.03724,0.03536,0.05096,0.00143,-0.01133,-0.0198,0.04677,0.0293,-0.07548,-0.06968,-0.06495,0.09313,-0.11631,0.03224,-0.06111,-0.07366,-0.02152,-0.00815,-0.06181,-0.03227,-0.02343,0.06449,0.05827,0.17893,0.04775,-0.04663,0.02205,0.00369,0.00487,-0.08927,0.06867,-0.02755,0.03135,-0.02642,0.00285,0.04753,0.04354,-0.07498,-0.0104,-0.10757,-0.01371,0.00312,0.02886,0.01437,-0.02882,0.01857,0.06657,0.03536,-0.10426,0.02165,-0.04212,0.07033,0.0577,0.09476,0.02738,-0.08186,0.02262,0.01698,0.0376,-0.10314,-0.0585,-0.10818,0.00441,-0.00154,-0.05646,-0.03483,0.12722,-0.04645,-0.07821,-0.01404,0.01429,-0.13065,-0.00792,-0.08721,0.01098,-0.01311,-0.04074,-0.01912,0.1507,0.00578,-0.03445,-0.17068,-0.04401,0.02424,0.06364,0.0257,0.01683,0.06418,-0.10705,0.01315,-0.00414,-0.07873,0.097,0.03516,0.09404,0.05207,-0.06557,-0.02221,0.03064,0.00611,-0.03099,0.14216,-0.00462,0.01349,0.01736,-0.0212,-0.00173,-0.05895,0.09507,-0.08466,0.06349,0.05367,0.06539,0.06843,-0.1147,0.01581,-0.01591,-0.03258,-0.01688,0.03619,0.00926,0.07042,0.00355,0.03157,0.0374,-0.03066,-0.01079,0.03374,0.03552,0.03525,0.0633,-0.16585,0.09007,0.08458,-0.05112,-0.11753,0.01045,0.06467,0.05464,0.02039,0.08791,0.0152,-0.02222,-0.03518,0.02276,-0.04027,-0.05744,-0.03559,-0.06192,-0.01755,-0.02283,0.06042,-0.0334,0.02502,0.03321,-0.0327,-0.01967,-0.05835,-0.04149,-0.02024,0.09814,-0.0284,0.00817,0.05156,-0.02688,-0.08929,0.07696,0.02249,-0.09075,-0.04317,-0.05127,0.08599,-0.10255,0.03639,0.12464,0.00563,0.05395,-0.03765,-0.04516,-0.00172,0.09292,-0.0921,-0.07304,-0.00263,0.11564,0.10212,-0.03477,-0.01964,0.14013,-0.01256,0.04912,-0.04006,0.05716,-0.09425,-0.01667,-0.11158,0.0387,0.06549,0.08133,-0.03828,7e-05,-0.12607,0.01202,0.06033,-0.00199,0.0299,-0.05913,0.05491,0.05847,0.04093,0.0507,0.08709,0.11303,0.04988,-0.03529,0.06744,-0.02566,-0.03556,0.03956,-0.00342,0.02013,0.04604,-0.10734,-0.11613,0.07266,0.0475,0.05782,-0.02359,-0.04615]},{"domain":"optimization","key":"edd_max_lateness","name":"Earliest due date rule (minimum maximum lateness)","package":"optimization-ai999x","example":"Jobs have processing times [2, 4, 1, 3] and due dates [5, 6, 3, 9]. Find the sequence that minimizes the maximum 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order quantity (EOQ)","package":"optimization-ai999x","example":"Find the EOQ for an annual demand of 1200 units, an ordering cost of 50 per order and a holding cost of 3 per unit per year.","v":[-0.03629,0.0842,-0.08664,-0.12079,0.06879,-0.06975,0.11606,-0.02026,0.05784,0.02265,0.03599,-0.07739,-0.01694,-0.0104,-0.00292,0.09708,0.06586,0.02108,-0.02236,-0.00214,-0.03489,0.00803,-0.07485,-0.02283,-0.07587,0.03296,0.04282,-0.10949,-0.06786,0.04548,-0.02258,0.0644,0.11333,0.01506,-0.13247,-0.03647,0.02591,-0.02322,0.16991,0.02018,0.04234,0.09616,-0.16167,0.06918,0.07054,0.09864,-0.0213,0.07101,0.03005,-0.02138,0.00265,-0.04977,-0.05369,-0.06677,0.06012,-0.07845,-0.13415,0.0441,-0.01196,-0.01041,-0.03791,-0.05701,-0.05432,0.04427,0.04232,0.05294,0.00134,-0.06023,0.06339,0.00535,0.03587,0.01815,-0.05537,0.00635,-0.01916,0.01893,0.13873,0.00713,0.10685,0.02501,0.09569,0.03499,0.1037,-0.07513,0.06341,-0.00666,-0.03972,-0.04289,-0.05251,0.06366,-0.02578,-0.07107,0.07523,0.03512,-0.00965,-0.06082,-0.0272,-0.01598,-0.08906,-0.00459,-0.06064,0.01201,-0.0013,0.04443,-0.09042,-0.01327,0.01868,-0.04608,0.15781,-0.00647,-0.02689,-0.02662,0.08009,0.02617,0.05985,-0.05839,-0.12151,0.04871,0.01533,0.05645,0.08725,0.02917,0.00564,-0.02969,-0.06138,-0.14667,-0.09554,0.04618,-0.06775,0.03094,0.02461,0.02129,0.04749,0.04652,0.07952,-0.0468,-0.00717,0.04069,0.04142,0.0435,-0.07334,-0.04642,0.03783,0.05716,0.01881,0.09856,-0.07161,-0.02423,-0.05455,0.00085,0.05222,-0.03009,-0.04235,-0.02714,0.00476,0.00263,0.03723,0.17147,0.08267,-0.01795,-0.04182,-0.05074,-0.02111,0.07342,0.04524,0.03908,-0.01301,0.00198,-0.00475,0.03534,-0.00798,-0.05161,-0.07578,0.00349,-0.01686,0.01408,0.00142,0.10582,0.05601,0.06719,-0.02254,0.03785,0.00666,0.01412,0.05312,-0.08969,-0.04013,-0.03497,-0.06434,-0.01487,-0.03536,-0.06345,0.06197,0.01416,-0.03012,-0.04802,-0.03329,0.07338,0.06293,-0.13037,0.03068,-0.04178,0.049,-0.03643,-0.12085,-0.0207,0.04852,-0.07034,0.05883,0.00531,-0.1292,0.00589,0.06496,-0.05195,0.07197,0.00791,-0.11382,-0.10147,0.02609,-0.11976,-0.12117,0.10132,-0.04641,-0.03138,0.10522,-0.08807,-0.04364,0.05101,-0.07975,0.06156,0.04344,-0.00792,-0.02696,0.01876,-0.04636,0.05378,0.04377,-0.06899,0.03378,-0.02187,-0.09324,0.05365,0.03118,-0.04273,-0.0352,0.04045,0.11754,-0.02914,-0.04006,0.08135,0.06923,-0.01607,0.04453,-0.1662,-0.10085,-0.02178]},{"domain":"optimization","key":"eoq_planned_shortages","name":"EOQ with planned backorders","package":"optimization-ai999x","example":"Find the EOQ with backorders for an annual demand of 1200 units, an ordering cost of 50, a holding cost of 3 and a shortage cost of 6 per unit per year.","v":[-0.00586,0.04901,-0.04353,-0.00642,0.05126,0.00266,0.07245,-0.00824,0.06172,0.14112,-0.07887,-0.01904,-0.01497,0.0726,0.00964,-0.00453,0.02403,0.02025,-0.02647,0.02845,0.01249,-0.08446,-0.07127,0.00154,-0.1059,0.01899,0.07224,0.05718,0.00118,0.00855,0.03102,0.0934,0.0453,0.03218,-0.13574,-0.02641,-0.02551,-0.05744,0.05671,-0.03266,0.0673,0.07065,-0.03271,0.06052,0.05148,0.06726,-0.02909,0.085,-0.00856,0.01273,0.00038,-0.02764,-0.00988,-0.10602,0.0335,0.03293,-0.07409,0.00806,-0.0052,-0.03486,-0.05613,-0.01971,-0.04646,0.04676,0.04161,0.00436,0.09122,-0.05754,-0.03305,0.01171,0.05528,-0.04552,-0.11416,-0.0399,-0.02401,-0.02509,0.14113,-0.01114,0.09177,0.06779,0.0578,0.12035,-0.04277,-0.11214,0.10766,-0.01777,-0.02136,-0.0313,0.07344,0.03211,0.06706,-0.01563,0.09784,0.04051,0.00111,-0.04562,0.02796,-0.05283,-0.15692,-0.01711,-0.02503,0.0223,0.02437,0.05367,-0.08102,-0.08342,-0.13224,0.01985,-0.02102,-0.01725,-0.04538,0.0173,0.01153,0.00513,0.14882,-0.08992,-0.16138,0.00796,-0.00131,0.04268,0.0966,0.09127,0.11092,-0.02936,-0.05036,-0.11372,-0.03445,0.07408,-0.0098,0.03657,0.03233,0.04877,0.03737,-0.03836,0.12117,-0.04582,-0.05299,0.01641,0.06522,0.06249,-0.07943,-0.08983,0.04256,0.00545,-0.01004,0.12525,-0.02743,0.03615,-0.05905,-0.03778,0.04598,-0.0206,-0.06812,-0.01594,-0.01052,0.01264,0.00042,0.14976,0.00381,-0.05614,0.00503,-0.03005,-0.04242,0.05532,-0.02182,0.03537,0.03981,0.05236,0.0026,-0.01221,-0.09211,-0.04375,-0.05819,-0.06239,-0.00664,-0.02872,0.02212,-0.05321,0.12903,0.10662,-0.03121,-0.04555,0.00392,0.04246,0.03099,-0.03999,-0.00198,0.06399,0.00193,-0.06871,-0.04766,-0.11829,0.01084,-0.08766,-0.03933,-0.01767,0.01669,0.10384,0.09085,-0.04794,0.09124,-0.03147,0.16284,-0.02879,-0.06171,-0.00875,0.01621,-0.02234,0.04439,-0.02781,-0.1118,0.00398,0.09142,-0.00526,0.08255,0.10445,-0.08565,0.03903,0.033,-0.06406,-0.01886,-0.00522,-0.02134,-0.04189,-0.02353,-0.05274,-0.108,0.01521,0.01316,0.03844,-0.05736,0.00266,-0.04644,0.08821,0.00917,0.04568,-0.11846,0.02319,0.01172,0.01124,-0.03871,0.16817,-0.02789,-0.0286,-0.10275,-0.0659,0.10804,0.02148,-0.07285,-0.02935,0.00835,0.00548,0.10597,-0.17563,-0.11545,0.01238]},{"domain":"optimization","key":"eoq_quantity_discount","name":"Order quantity with quantity discounts (all-units)","package":"optimization-ai999x","example":"Quantity discounts: annual demand 5000, ordering cost 49, holding rate 20%, price breaks at [0, 1000, 2000] with prices [5, 4.8, 4.75]. Find the best order 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production quantity (EPQ)","package":"optimization-ai999x","example":"Find the EPQ for an annual demand of 1000 units, a production rate of 2000 units per year, a setup cost of 100 and a holding cost of 4 per unit per 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quadratic program (Lagrange multipliers / KKT)","package":"optimization-ai999x","example":"Minimise the equality-constrained quadratic with Hessian Q = [[2, 0], [0, 2]], linear term c = [0, 0], constraint matrix A = [[1, 1]] and right-hand side b = 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B blocking probability (M/M/c/c loss system)","package":"optimization-ai999x","example":"A trunk group of 5 lines is offered traffic of 3 erlangs. 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Which facilities should open?","v":[-0.01488,0.02439,0.02436,-0.02932,-0.0563,-0.02879,0.0448,-0.04245,0.14357,-0.10215,-0.04967,-0.02989,0.01962,0.00248,-0.04752,-0.07299,0.00356,0.0517,0.0792,0.0165,0.00834,0.05927,0.07165,0.03099,0.00478,0.04685,0.04467,-0.00212,0.01218,0.0148,0.01562,0.08829,0.02506,-0.03762,-0.09526,-0.02055,0.05505,0.03224,-0.02693,0.06897,0.02417,0.05622,-0.10823,-0.02673,-0.0115,0.04118,-0.02219,0.08403,0.03526,0.00368,0.06637,0.03102,-0.00448,-0.0275,0.05959,-0.00381,0.0397,-0.03614,0.06207,0.0896,0.04575,-0.0389,-0.10351,-0.00583,0.01711,0.08876,-0.05196,-0.05834,-0.05728,-0.02743,0.01853,0.00571,-0.05785,0.08601,-0.00252,-0.01904,-0.10781,-0.00457,0.00615,-0.05225,0.12755,0.03352,0.18031,-0.01959,-0.0146,-0.03273,-0.04257,-0.0278,-0.02038,0.0828,-0.01546,0.01069,0.03305,-0.18172,-0.06301,-0.06917,-0.11266,0.11788,-0.14935,-0.01423,-0.07747,-0.03842,-0.04285,-0.03342,-0.08794,-0.09962,0.08707,-0.0976,-0.00597,0.02753,0.01431,0.03537,0.0939,0.08798,0.08956,-0.04439,-0.03854,-0.00848,0.06119,0.05232,0.06171,-0.00812,0.05552,0.08646,-0.02461,-0.07639,-0.10197,0.01425,0.08246,0.01719,-0.069,-0.04148,0.00609,0.05379,-0.00426,-0.01855,0.00653,-0.07621,0.03807,-0.14107,0.02374,-0.08668,-0.16236,-0.06165,-0.02343,0.09122,-0.09813,-0.00141,-0.0332,0.005,-0.06355,-0.06507,-0.01037,0.03283,0.04396,-0.09453,0.01786,-0.00423,0.01962,0.07047,-0.11046,-0.06443,0.14756,0.11343,0.05902,0.03068,0.01261,-0.08721,0.00996,0.0029,0.02545,0.00631,0.07295,0.06221,0.01401,0.0448,-0.03278,0.04569,-0.00485,0.05668,-0.05075,0.03296,-0.08625,0.02335,-0.02579,-0.06045,-0.07922,-0.04276,-0.08638,0.04474,-0.10627,-0.06319,0.05066,-0.0477,0.0017,0.07093,-0.01204,-0.01868,0.03007,-0.08634,-0.05267,0.09688,-0.02441,-0.08438,-0.04427,-0.05971,0.05974,0.01519,0.01304,-0.08489,-0.09501,0.04164,0.01946,0.02199,-0.01308,0.04357,-0.03203,0.0108,0.08672,-0.02001,-0.05596,0.04236,0.0979,-0.0065,-0.04265,0.02355,-0.07232,0.0359,-0.06318,-0.00022,0.15639,-0.03192,-0.07464,-0.08698,-0.07983,0.09234,0.10077,-0.05826,0.07467,0.1108,-0.06048,-0.04772,-0.01884,0.0049,0.04633,0.06066,0.11406,-0.01781,-0.03944,0.06204,0.11821,0.13841,-0.06182,-0.01923,-0.01481,-0.02112]},{"domain":"optimization","key":"fence_max_area","name":"Largest rectangle for a given length of fencing","package":"optimization-ai999x","example":"A farmer has 200 m of fencing to enclose a rectangular field. What is the maximum area?","v":[-0.1245,-0.09769,0.03499,0.05318,0.00787,-0.0489,0.04673,-0.04706,0.00384,0.13431,0.0099,0.09873,0.06284,-0.06857,-0.03673,0.01,0.09229,0.07627,0.05167,0.07606,-0.0348,-0.09436,0.01093,0.00122,0.01872,0.07326,-0.04555,-0.05235,0.07072,0.02824,0.04341,0.1037,0.06103,0.03094,-0.06095,0.0119,0.09157,0.01566,-0.01002,0.06272,0.07263,-0.11465,0.05214,-0.06644,0.04446,0.04132,-0.01395,-0.14634,0.06282,0.11065,0.0231,0.08494,-0.01383,0.05095,-0.04236,-0.02474,0.06622,0.05342,0.13073,0.0105,-0.05882,0.04912,-0.04145,0.0963,0.01799,0.06509,-0.04011,-0.05252,-0.04599,-0.04488,-0.02529,0.10439,-0.14028,0.04428,-0.0638,-0.1449,0.15701,-0.02171,-0.08916,0.07806,0.07547,-0.05491,-0.00708,-0.03243,-0.05941,0.12367,-0.01115,0.08253,0.0385,0.02361,0.06085,0.0675,-0.08333,0.03104,0.02396,-0.00468,0.01551,-0.00514,-0.06526,0.03304,-0.05301,0.15039,-0.09115,-0.00022,0.00703,0.05742,-0.05981,-0.02364,-0.11524,-0.04462,-0.13711,-0.04043,0.01937,0.08402,0.08196,-0.0276,0.02501,0.08879,0.00644,0.04546,0.05524,0.12802,0.03139,0.04081,-0.07024,0.1096,0.03831,0.06631,0.02454,-0.07775,-0.07936,0.02834,-0.01871,-0.13526,0.01283,-0.01555,0.04646,-0.00752,0.07937,0.01233,0.09723,-0.03323,0.02228,-0.01261,-0.02262,-0.09507,-0.02588,-0.06405,0.05244,-0.0991,-0.11797,0.04128,-0.01445,-0.04033,-0.03163,-0.07607,-0.02291,-0.01066,-0.0827,0.01466,-0.01376,0.02049,-0.10705,0.02001,-0.0404,0.01486,0.13348,0.07195,0.04825,0.00853,-0.11455,-0.0354,0.01323,0.11714,-0.0327,-0.05994,0.04577,-0.06334,0.02854,-0.04513,0.07624,-0.01453,0.01011,0.0065,-0.07414,0.01798,0.03966,-0.0241,-0.03525,-0.12169,-0.0092,-0.0538,0.0389,-0.05154,-0.02251,0.02492,0.00973,-0.00142,-0.03424,0.03265,0.12596,0.07657,-0.06485,0.09931,-0.06297,-0.02221,-0.01364,0.01345,-0.0809,-0.02192,-0.04526,-0.05465,0.0517,0.04695,-0.02064,0.15643,0.04753,0.03186,0.03789,-0.0626,-0.0718,0.05768,-0.10084,-0.04858,0.04807,-0.01876,-0.07504,-0.00042,0.00712,-0.05565,-0.00791,-0.00322,0.01203,0.01774,-0.06028,0.00413,0.00513,0.01904,-0.0583,-0.01372,-0.02779,0.01433,-0.09144,-0.04453,-0.04894,-0.07607,0.05306,0.03554,-0.04145,0.03647,0.05249,0.02172,0.01382,0.01407,0.08792,-0.01299]},{"domain":"optimization","key":"graph_coloring","name":"Chromatic number (minimum graph colouring)","package":"optimization-ai999x","example":"Find the chromatic number of the graph with edges A-B, B-C, C-A, 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linear program (branch and bound)","package":"optimization-ai999x","example":"Maximize 5x + 4y subject to 6x + 4y <= 24, x + 2y <= 6, x, y >= 0 and 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rule (two-machine flow shop)","package":"optimization-ai999x","example":"Use Johnson's rule: machine 1 times [5, 2, 6, 7] and machine 2 times [3, 4, 8, 2]. 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knapsack problem","package":"optimization-ai999x","example":"Solve the knapsack problem with values [60, 100, 120], weights [10, 20, 30] and capacity 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knapsack problem","package":"optimization-ai999x","example":"Solve the unbounded knapsack problem with values [10, 40, 50, 70], weights [1, 3, 4, 5] and capacity 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flow (transshipment)","package":"optimization-ai999x","example":"Find the minimum cost flow with capacity [[0, 10, 5], [0, 0, 10], [0, 0, 0]], cost [[0, 1, 4], [0, 0, 2], [0, 0, 0]] and supply [8, 0, 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spanning tree (Kruskal's algorithm)","package":"optimization-ai999x","example":"Find the minimum spanning tree of the graph with edges A-B 4, A-C 1, B-C 2, B-D 5, C-D 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vertex cover (and maximum independent set)","package":"optimization-ai999x","example":"Find the minimum vertex cover of the graph with edges A-B, A-C, A-D, B-C, 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Nash equilibrium of a 2 x 2 game","package":"optimization-ai999x","example":"Find the mixed-strategy Nash equilibrium of the game with row payoffs [[3, -1], [-2, 1]] and column payoffs [[-1, 2], [1, -1]].","v":[-0.08433,-0.07353,0.00843,-0.05653,0.04915,-0.02655,0.10197,-0.01889,0.06642,-0.02141,0.021,0.00508,-0.0614,0.08192,-0.00565,-0.13889,-0.08184,0.01521,-0.05156,-0.06773,-0.01819,0.051,0.06009,-0.03164,0.01777,0.00844,-0.06313,0.04847,-0.03596,-0.07481,0.06243,0.06048,-0.00739,-0.02827,0.04038,0.0903,-0.03578,0.06088,0.04226,-0.00441,0.03864,-0.08769,-0.06717,0.09481,-0.03919,0.01499,0.0276,0.05701,-0.01225,0.02791,0.00366,0.06846,-0.0049,-0.04006,-0.03407,0.10244,0.03983,-0.01561,0.03515,0.03182,-0.07848,-0.02409,0.08408,-0.07352,-0.00931,-0.08405,0.03109,-0.0495,0.08544,-0.10195,-0.03178,-0.09476,0.01456,0.10483,-0.01254,-0.00876,0.04688,0.05338,0.0401,0.02695,0.05091,-0.0687,-0.03012,0.05053,-0.09523,-0.15639,0.05489,0.04811,-0.08056,0.01933,0.00861,-0.02403,-0.08966,0.00083,0.15925,0.02425,-0.08299,0.01993,-0.05838,0.09567,-0.04032,0.01284,0.06311,-0.00891,0.01541,-0.09546,-0.06169,0.00729,-0.01585,-0.13864,0.06385,-0.02459,0.00666,-0.03145,0.04881,-0.07422,0.10229,0.04107,-0.15304,-0.01544,-0.08183,-0.01509,0.01248,-0.07568,0.01786,0.06022,0.03621,0.03219,0.02897,0.06395,-0.00638,-0.08845,-0.12241,-0.01435,-0.03251,0.01515,-0.02214,0.13272,-0.03805,-0.04773,0.07964,-0.04882,0.00292,-0.03155,0.11332,0.07803,0.07215,-0.02734,-0.0095,0.05974,0.00995,0.02925,0.05042,0.06184,0.09957,0.05221,0.10224,-0.04135,0.00824,0.01063,-0.0728,0.01471,0.08672,0.00418,0.03354,-0.08118,-0.10527,-0.04389,-0.07946,-0.0426,-0.01808,0.07486,-0.01562,-0.08684,0.01515,0.07228,0.0297,-0.19365,-0.05093,-0.0199,-0.03467,0.04529,-0.04749,0.08906,-0.03213,0.0536,0.0363,-0.01871,0.03097,-0.01299,0.00823,0.17853,-0.02816,0.09099,-0.06869,0.00787,-0.02031,-0.01386,-0.08577,-0.00104,0.05451,0.03498,0.00879,0.0419,0.0363,-0.05484,-0.04897,0.15213,-0.00397,0.04675,-0.05485,-0.0034,-0.09368,0.09704,-0.06056,0.03893,-0.01433,0.01587,0.0526,0.06726,0.0722,0.08247,-0.11852,-0.01221,0.04219,0.06434,-0.06707,-0.04976,0.09012,0.16955,-0.06718,0.04746,0.01914,0.02686,-0.01996,-0.04958,0.03361,-0.01109,-0.07948,0.02177,0.07503,-0.03392,0.00312,0.02085,0.00517,-0.16513,0.02497,-0.10543,-0.06593,0.02522,-0.07858,0.04644,-0.06056,0.00567,0.02102,0.02074]},{"domain":"optimization","key":"mm1_queue","name":"M/M/1 queue","package":"optimization-ai999x","example":"In an M/M/1 queue customers arrive at 8 per hour and are served at 10 per hour. Find L, Lq, W and Wq.","v":[-0.07836,-0.057,-0.02331,0.02268,-0.05617,-0.17572,-0.06791,-0.01071,0.02249,0.05289,0.0557,0.02726,0.039,0.01687,-0.00591,0.00811,-0.05698,-0.01574,0.01852,-0.04388,0.04308,0.08945,-0.05389,-0.0021,-0.05367,-0.00669,0.00093,0.04928,0.07502,-0.02196,0.04368,0.0055,0.00437,0.09621,0.03313,-0.06169,0.02554,0.02422,0.04066,0.1002,0.01916,0.08158,-0.03245,0.07538,0.04863,0.10473,-0.03947,0.01713,-0.0225,-0.04645,-0.04882,0.0244,0.01569,-0.05597,0.05102,0.05196,0.11421,-0.01166,-0.13515,0.01861,-0.02696,-0.06904,0.06802,0.04824,0.11069,0.02707,0.00475,0.07789,-0.08796,0.09887,-0.06834,0.02397,-0.10514,-0.04409,0.14764,-0.02363,-0.01695,0.02923,-0.01206,-0.05326,-0.00176,-0.01036,0.02244,-0.04474,-0.01549,-0.10342,0.043,0.00147,-0.0472,-0.0051,0.01003,0.00549,-0.05249,-0.11689,-0.01055,0.04976,-0.08173,-0.04913,-0.0275,-0.01497,0.00231,0.01358,0.03333,-0.02359,0.16401,0.04097,0.13881,-0.03824,0.07353,-0.09534,0.02657,-0.14323,0.00613,0.00354,0.03585,0.01645,-0.00748,-0.02583,0.08332,-0.04666,0.16695,0.00463,0.00326,0.01432,0.09079,-0.00473,0.03399,-0.0067,-0.06905,0.01503,-0.01722,-0.11585,0.00917,-0.0131,0.07916,-0.03268,-0.04562,0.01235,-0.02167,-0.03178,-0.00144,0.05457,-0.09868,-0.03251,-0.00837,0.09507,-0.10381,0.08229,0.03566,-0.08325,-0.0452,-0.0049,0.02378,-0.03179,0.00541,0.00369,-0.06082,-0.00195,-0.04553,0.07106,0.10316,-0.11197,0.09329,0.00172,0.09165,0.04733,-0.1716,-0.01968,-0.04708,0.11452,0.09269,-0.00591,-0.03332,0.04431,0.01364,-0.01857,0.07194,0.01131,-0.0899,0.15998,-0.02836,0.05864,0.04591,0.07335,0.04141,0.06009,0.0087,-0.00267,-0.02882,0.05934,-0.08888,0.06043,0.00671,-0.05775,-0.02662,0.03415,0.00702,0.01032,-0.02055,-0.02547,0.036,-0.02713,0.10106,-0.02928,0.06172,-0.06024,0.03749,0.03191,-0.03907,-0.00487,-0.02854,0.11748,-0.01236,-0.1229,-0.1355,-0.10705,0.03341,0.05613,-0.03398,0.00106,-0.00157,-0.00151,0.00346,0.12161,0.03056,-0.10687,0.05317,-0.00778,0.02104,-0.11326,-0.10892,-0.05325,0.03877,0.10486,-0.01148,-0.01582,0.01478,0.01946,-0.05958,0.07128,0.0291,-0.04793,-0.04352,-0.1293,0.03947,-0.06864,0.15672,-0.04657,-0.05313,-0.04474,0.02908,0.01605,-0.08608,-0.08001,-0.05248,-0.11185]},{"domain":"optimization","key":"mmc_queue","name":"M/M/c queue (Erlang C)","package":"optimization-ai999x","example":"Customers arrive at 24 per hour at a bank with 3 tellers; each teller serves 10 per hour. Find the probability of waiting and Lq for this M/M/c queue.","v":[-0.0978,-0.0364,0.00769,-0.02057,-0.04255,0.01285,-0.04812,0.0218,0.04736,-0.01766,0.04476,0.08441,0.02374,0.04496,-0.1055,-0.05895,0.01282,0.07257,0.08737,0.05749,0.03988,0.05363,-0.03111,0.00924,0.01759,-0.00623,0.05027,0.08321,0.00241,0.03167,-0.04088,-0.08241,-0.0945,0.0738,0.071,-0.01775,-0.09835,-0.05057,-0.03732,0.04289,0.06894,0.05091,-0.02729,0.08869,0.04345,0.06256,0.04539,-0.04758,0.00937,-0.01564,-0.00376,0.00041,0.02346,0.02414,-0.01553,0.14781,0.11344,0.08154,-0.05594,0.01838,0.04157,-0.11569,0.03222,0.08321,0.04321,0.11739,-0.04145,-0.00656,-0.07843,0.02274,-0.03917,0.04579,-0.06074,-0.01987,0.02695,-0.07891,-0.10794,0.05575,-0.04899,-0.05167,0.09681,-0.03946,0.03556,-0.00285,-0.03611,-0.14134,0.17242,0.00314,-0.08191,-0.0361,-0.00211,0.06412,-0.06443,-0.12107,-0.07447,-0.06739,-0.1177,0.01856,-0.10595,-0.03471,-0.01282,0.04136,0.01189,0.04049,0.17179,0.02493,-0.0169,-0.07546,0.03968,-0.08109,0.02789,-0.09825,0.06016,-0.03154,0.04968,0.00415,-0.06328,-0.01805,0.01871,0.04718,0.11204,0.02386,-0.01629,-0.08112,0.13376,0.0073,-0.00745,-0.03176,-0.04734,0.05421,0.02296,-0.09283,-0.1148,0.0119,0.00343,-0.01219,-0.04215,0.03407,-0.05469,-0.03114,0.00825,-0.01996,-0.08491,-0.01736,-0.01999,0.00738,-0.09389,0.03307,-0.09113,-0.06631,0.01772,0.03865,-0.00791,0.01075,0.02254,0.03971,-0.09079,-0.02488,-0.05333,0.05511,0.01807,0.04059,0.05948,0.02866,-0.01252,0.09213,-0.0697,0.03633,-0.08177,0.07563,0.08898,0.06752,-0.12695,0.08196,0.06348,0.01239,0.02686,0.09853,-0.02096,0.14565,-0.0048,-0.01285,-0.0073,0.03032,0.12423,0.13894,-0.0182,-0.00711,-0.02324,0.03353,-0.06141,0.07952,0.00692,-0.09816,-0.05752,-0.08838,-0.01651,-0.02424,0.02597,-0.11292,0.09801,0.10888,0.08113,-0.00396,0.03539,-0.0476,0.00969,-0.01562,-0.04466,-0.06243,-0.0902,0.06735,-0.00429,-0.08836,-0.05734,-0.00541,-0.02828,0.03896,-0.06778,0.07754,-0.06972,-0.05785,0.0139,0.02872,0.09779,-0.11883,0.05434,0.01054,0.0118,-0.00832,-0.02349,0.08129,0.04799,0.00012,-0.01897,-0.04369,0.00849,0.05775,0.05709,0.00799,-0.00893,-0.03643,-0.04587,-0.1131,0.08082,-0.08233,0.07232,-0.11056,-0.00299,0.04387,0.05685,0.06301,0.01276,-0.06613,-0.11317,-0.08112]},{"domain":"optimization","key":"mmc_staffing","name":"Minimum number of servers for a service target (Erlang C)","package":"optimization-ai999x","example":"Calls arrive at 24 per hour and each agent serves 10 per hour. How many agents are needed so that the probability of waiting is at most 0.2?","v":[-0.03438,0.0138,0.00359,0.00375,-0.06723,0.033,0.03275,-0.0156,0.04567,-0.0464,0.01077,0.10675,0.04743,0.0339,-0.12064,-0.04087,0.06978,0.09453,0.06403,0.06113,-0.01654,0.02758,-0.0578,-0.00513,0.05661,0.0827,0.04658,0.06274,0.0266,0.07359,-0.07307,-0.08456,-0.12964,0.04142,0.03984,-0.08378,-0.08141,-0.0802,-0.05294,0.02128,0.06479,0.02254,-0.03493,0.03488,0.07587,0.08248,0.0405,-0.05004,0.08779,0.02821,0.03129,-0.0192,0.00191,0.00676,-0.02767,0.08901,0.02643,0.05013,-0.02388,0.07015,0.00827,-0.0054,-0.06021,0.12077,0.07624,0.13254,-0.11839,-0.03317,-0.09735,0.03938,-0.03662,0.0516,-0.07192,-0.00456,-0.00753,-0.08886,-0.09043,0.1378,-0.06334,0.06913,0.12777,0.02479,0.01383,0.02212,-0.06338,-0.04219,0.1519,0.01642,-0.0512,0.00824,0.01659,0.06544,-0.00965,-0.17588,-0.02475,-0.07691,-0.07603,0.07493,-0.11745,0.03697,-0.01169,0.048,-0.01364,-0.00222,0.07047,-0.02126,-0.09704,-0.04113,0.06256,-0.08133,0.0081,-0.0613,0.04807,-0.05316,-0.00949,-0.00689,-0.08375,0.00153,-0.01629,0.08983,0.12419,0.06753,0.06275,-0.10052,0.07125,-0.00545,-0.01911,-0.0474,0.07213,0.03367,0.01986,-0.08852,-0.09478,-0.00219,0.01962,-0.06514,-0.00201,-0.00878,-0.01188,0.03989,-0.0207,-0.01833,-0.03817,-0.01547,-0.06902,-0.06996,-0.04783,-0.04438,-0.08699,-0.07976,0.04511,0.01545,-0.0028,0.06411,-0.03334,0.05798,0.00363,-0.00935,-0.04422,0.04384,-0.00352,0.16201,0.00765,0.09521,-0.08461,0.04785,0.03696,0.04508,-0.03656,0.05923,0.03147,0.06284,-0.1554,0.05286,0.06982,-0.04126,0.00562,0.08582,-0.0213,0.0968,0.03669,-0.04203,0.01037,0.01728,0.08443,0.07876,-0.0394,0.03665,-0.01856,0.0366,-0.11753,0.02446,-0.05943,-0.08338,-0.05425,-0.10575,0.02309,-0.04892,0.02921,-0.04838,0.06546,0.12431,0.03234,-0.07712,0.02391,-0.0361,0.01377,-0.02802,-0.10444,-0.10046,-0.07482,0.06016,0.05508,-0.05338,-0.00798,0.00329,-0.00873,-0.03481,-0.00288,0.09213,-0.10918,-0.03308,-0.0304,-0.05277,0.10557,-0.09697,0.02314,0.03937,0.02223,0.04585,-6e-05,0.08015,0.01138,-0.03673,-0.04303,-0.02526,-0.00589,0.09223,0.02344,-0.01808,-0.00611,-0.0408,-0.1023,-0.0939,0.09472,-0.04032,0.07602,-0.09633,-0.03576,0.03176,0.01935,0.07926,0.08332,-0.07678,-0.04655,-0.08725]},{"domain":"optimization","key":"mmck_finite_queue","name":"M/M/c/K queue (finite capacity)","package":"optimization-ai999x","example":"An M/M/1/3 queue has arrival rate 2 per hour and service rate 2 per hour. Find the blocking probability and L.","v":[-0.12498,-0.04599,-0.00056,-0.13512,-0.0263,-0.03049,-0.06643,-0.06887,0.04745,0.01408,0.07622,0.09606,0.01009,0.02219,-0.05183,0.02177,-0.07056,0.06459,0.07195,-0.05802,0.0784,0.11121,-0.02798,-0.01547,-0.02196,-0.05575,0.13118,0.04736,0.0794,-0.04613,-0.01822,-0.13876,-0.07868,0.09135,0.04139,0.00767,-0.0662,-0.05716,-0.0586,0.03286,0.06904,-0.02374,0.04554,0.08041,0.03587,0.09219,-0.01803,-0.02566,0.01814,0.00822,0.03639,-0.00112,0.0374,0.01778,0.06787,0.11252,0.05897,0.02529,-0.0362,0.0552,-0.00507,-0.10434,0.01257,0.03393,0.07992,0.08728,-0.03569,0.01154,-0.06933,0.06497,0.0069,0.02653,-0.05577,0.02593,0.02339,-0.03794,-0.12848,0.03872,0.01005,0.00082,0.04063,-0.0472,0.02093,-0.02257,0.01643,-0.11282,0.12098,0.01751,-0.08186,-0.05124,0.05048,0.07594,-0.04097,-0.12001,-0.02096,-0.05627,-0.10102,-0.10424,-0.04021,-0.07624,0.02534,0.02101,0.01675,-0.01413,0.08919,0.01504,0.01065,-0.01071,-0.00272,-0.08767,0.01118,-0.06885,0.15529,0.01367,0.00643,0.04041,0.02805,0.01987,0.06091,0.02196,0.14635,0.03236,0.07998,-0.02836,0.14056,0.05917,-0.00234,-0.00808,0.00135,-0.0029,-0.02835,-0.08871,-0.01684,-0.03851,0.00246,-0.07381,-0.03553,-0.03751,-0.10852,0.02221,-0.06796,0.01231,-0.06379,-0.07865,-0.03884,0.00344,-0.05556,0.03203,-0.07812,-0.15148,-0.01899,-0.00238,0.01836,-0.10447,0.02477,0.01784,-0.0828,0.02153,-0.10058,-0.00143,0.08331,0.04549,0.02041,0.01738,-0.0168,0.08164,-0.01501,-0.04375,-0.05083,0.13512,0.06534,-0.02058,-0.1441,-0.0089,0.02261,0.02113,-0.04352,0.04147,-0.00671,0.17713,0.04527,0.01149,0.02672,0.0857,0.03851,0.04625,0.0023,-0.0203,0.00149,0.03741,-0.02756,0.13046,0.00526,-0.05859,-0.15787,-0.0582,-0.0059,0.04954,0.03802,-0.05886,0.12832,0.04904,0.08944,-0.02729,0.11984,-0.03454,-0.08116,0.0367,-0.10072,-0.026,-0.05779,0.06346,0.02594,0.00457,-0.06139,0.04888,-0.00825,0.09235,-0.07433,0.04207,-0.01149,0.02569,-0.027,0.0314,0.00929,0.01883,-0.02144,-0.00101,0.01672,0.04503,-0.07268,0.00695,-0.0158,-0.03402,-0.00375,-0.04108,0.04697,0.07827,-0.01532,0.05254,0.01058,-0.04341,-0.07059,-0.09844,0.11573,0.00933,0.12164,-0.03408,-0.03268,0.05363,0.02146,0.09084,0.00833,-0.03188,-0.09915,-0.15198]},{"domain":"optimization","key":"moore_hodgson_tardy_jobs","name":"Moore-Hodgson algorithm (minimum number of tardy jobs)","package":"optimization-ai999x","example":"Jobs have processing times [4, 3, 2, 5, 6] and due dates [5, 6, 8, 12, 15]. Find the minimum number of tardy jobs.","v":[0.08312,0.08787,-0.1129,0.03805,-0.10098,0.11653,-0.00985,-0.00181,0.0731,0.02569,0.00515,0.04227,0.05443,0.03697,-0.05407,-0.02669,0.02735,-0.00168,0.08248,0.05066,0.04663,-0.00993,-0.03376,0.01492,-0.0141,0.04062,-0.12933,0.0282,0.04865,-0.04003,-0.01495,-0.02671,-0.09942,0.08708,-0.06545,-0.02004,-0.0527,-0.07292,-0.00148,0.06772,-0.00799,0.03726,-0.04854,-0.078,0.06789,-0.06072,-0.04356,-0.07062,-0.03142,-0.00833,0.00043,0.04852,-0.09167,0.03629,-0.01099,0.05902,-0.07427,-0.0234,-0.05797,-0.03434,-0.00636,-0.03768,0.08113,0.10105,0.0556,-0.00485,0.01578,0.01298,-0.0217,0.12975,0.00301,-0.00599,-0.07411,-0.021,-0.07353,-0.14735,0.1745,0.01271,-0.04461,0.01298,0.01382,0.02931,-0.01013,-0.06018,-0.02883,0.1038,0.00871,-0.0099,0.06322,-0.10848,-0.06931,0.07038,-0.0724,0.04317,-0.12124,-0.06268,0.00175,-0.06506,-0.09883,0.02348,-0.05484,0.08912,-0.0592,0.0855,0.02099,0.05408,-0.14224,-0.03203,0.0206,-0.07284,-0.01114,-0.02285,0.06558,-0.09055,0.06438,0.01757,-0.097,0.01191,0.04384,0.08496,0.08064,-0.04696,0.01373,-0.03186,0.06532,-0.07186,0.03612,-0.01319,-0.08246,0.02078,0.02968,0.01686,0.00676,-0.01362,0.02283,0.11497,-0.06838,0.00664,0.06826,0.00306,-0.03543,-0.10075,-0.00665,0.02465,0.01336,0.10671,0.00643,0.02806,-0.09857,-0.03572,0.0298,-0.07492,-0.13129,0.10285,-0.06111,-0.03855,0.09822,0.03319,-0.13544,-0.01238,0.06938,0.07342,-0.02347,0.06918,-0.00844,0.06414,0.07968,0.01833,0.04241,0.054,0.01585,-0.07017,0.03286,-0.07926,0.04414,0.06091,-0.04484,0.07217,-0.01568,0.03923,0.05419,-0.09313,0.10599,0.07362,0.03816,0.04847,0.06313,-0.0537,0.0423,0.00492,-0.00337,-0.0907,-0.06409,0.03714,-0.05428,-0.01086,0.08566,0.14899,0.07546,-0.03964,0.01362,0.13321,0.0284,-0.01278,-0.0132,-0.00616,-0.01623,0.01728,-0.02447,0.01323,-0.00506,0.03625,0.05603,-0.02224,-0.02236,-0.03238,0.02898,-0.02291,-0.02496,-0.03459,0.02619,-0.03537,0.04267,-0.11342,0.01647,-0.0718,0.03503,-0.02611,-0.08144,-0.06474,-0.03448,-0.03149,-0.00595,0.02328,0.00069,0.02231,-0.07613,0.14357,0.07829,0.06444,-0.07736,0.10848,0.01269,0.09738,-0.04573,-0.03971,-0.01764,-0.21576,-0.0957,0.11718,0.07498,0.01276,0.00637,-0.08621,-0.03332,-0.03105]},{"domain":"optimization","key":"newsvendor_discrete","name":"Newsvendor order quantity (discrete demand)","package":"optimization-ai999x","example":"Newsvendor: a cake sells for 10 and costs 4; demand values [10, 20, 30, 40] have probabilities [0.1, 0.3, 0.4, 0.2]. How many should be ordered?","v":[-0.03101,0.03404,0.0392,-0.04297,0.15338,0.02209,0.01323,-0.01126,-0.02664,-0.04541,-0.07949,0.04086,0.00124,0.04475,0.05437,-0.01164,-0.05645,0.05796,-0.05249,-0.02902,-0.07981,-0.04047,-0.00251,-0.05722,-0.06756,0.08249,0.00758,-0.03591,0.06384,-0.01952,-0.05017,0.15582,-0.04599,-0.00245,-0.12424,-0.00951,0.086,-0.07811,-0.04804,-0.09479,0.07288,-0.00531,0.05939,0.09907,-0.06406,-0.03204,0.08737,-0.0073,0.04669,-0.02691,-0.04879,-0.13192,-0.03187,-0.10832,0.05088,0.0104,-0.04158,-0.06561,0.00971,-0.07055,-0.06486,-0.04125,-0.0562,-0.06172,-0.07425,-0.01013,-0.0153,0.03167,0.02003,0.00294,0.07779,-0.00523,-0.0112,0.10312,-0.04,0.05565,0.09693,-0.06084,0.0595,0.04548,0.01,0.10347,0.08111,-0.02922,-0.04661,-0.03396,0.00044,0.08416,0.06947,-0.01622,0.06216,0.04275,0.07294,-0.02122,0.05733,-0.07554,-0.01609,-0.04393,-0.0517,-0.02993,0.03054,0.08054,0.0323,-0.05408,-0.0154,-0.00287,-0.14332,-0.02706,0.0647,0.03028,-0.04134,0.00105,-0.03583,0.06811,0.10723,-0.04283,0.037,-0.14128,0.03425,0.04211,0.07295,0.07977,0.06923,-0.01326,-0.02425,-0.04377,0.00997,0.08534,-0.06612,0.04126,-0.00534,-0.1078,0.03622,0.04998,-0.07207,-0.00493,-0.02912,0.0006,-0.05785,-0.00368,0.00609,-0.01021,0.0954,0.03865,-0.0483,0.11996,-0.08061,0.06304,-0.05263,0.01327,-0.02954,-0.18644,-0.0197,0.03536,0.03389,0.03878,-0.0331,-0.017,0.00705,-0.11884,-0.05547,-0.03032,-0.03924,-0.12001,0.05672,-0.02301,-0.04974,0.04628,-0.06222,0.04975,-0.00979,0.0467,0.03542,-0.06383,0.09863,0.00171,0.00986,-0.0348,0.11535,0.12272,-0.08999,0.00089,0.07036,0.07288,0.0671,0.00018,-0.01365,-0.0349,0.00549,0.09726,-0.0121,-0.02314,0.04305,-0.05205,0.07641,-0.03717,0.02539,-0.02399,0.00868,-0.08469,0.02723,0.01927,0.12157,0.10889,-0.09122,-0.06742,0.06431,0.04558,0.08351,0.0162,-0.03974,0.01565,0.04539,-0.1602,0.01228,0.03912,0.03922,0.074,0.03797,-0.04601,-0.0577,0.05795,-0.01775,0.00196,0.05316,-0.06499,-0.17869,0.13148,-0.02957,0.01959,0.09301,0.03974,0.04662,-0.03708,0.00366,-0.00766,-0.04892,-0.12293,-0.01939,0.00767,0.00869,0.04601,-0.00337,0.06328,-0.07589,-0.10634,0.10032,-0.04606,0.01085,-0.11122,0.01242,0.06141,0.08302,-0.10388,-0.03827,-0.09358]},{"domain":"optimization","key":"newsvendor_normal","name":"Newsvendor order quantity (normal demand)","package":"optimization-ai999x","example":"Newsvendor problem: a paper sells for 2 and costs 0.5, leftovers are sold for salvage of 0.2, and demand is normal with mean 100 and standard deviation 20. Find the optimal order quantity.","v":[0.01231,0.0543,-0.00265,-0.04743,0.06299,0.03806,-0.06938,0.06859,0.03257,0.03024,-0.06107,0.02487,0.01767,0.04954,0.03297,-0.00245,-0.03925,0.08887,-0.02493,0.01842,-0.05686,-0.06026,-0.05895,-0.0387,-0.0686,0.0239,0.02573,-0.01923,0.01877,-0.04063,-0.01306,0.15302,0.04032,0.04889,-0.10071,-0.05603,0.08709,-0.05066,0.00487,-0.12648,0.08924,0.02532,0.00584,0.0633,0.0422,-0.02336,0.08915,0.03508,-0.00069,0.01621,-0.01868,-0.1219,-0.01617,-0.1119,0.1132,0.00407,-0.10634,0.02373,-0.01073,-0.11258,-0.07853,-0.00447,-0.06604,-0.05109,0.01771,-0.038,-0.0041,-0.02028,0.02921,0.0339,0.00655,0.01387,-0.00878,0.07775,-0.01092,-0.01476,0.03252,-0.06729,0.03491,0.06798,0.04226,0.16962,-0.02404,-0.00205,0.03853,0.00543,-0.04319,0.04871,0.0229,-0.04207,0.05758,0.07574,0.1023,0.01656,0.07546,-0.04821,0.00044,-0.06161,-0.1729,-0.07482,-0.01077,0.03901,0.04755,0.04658,-0.03153,-0.0218,-0.0581,-0.0471,0.07336,-0.01805,-0.07712,0.04691,-0.03908,-0.02053,0.06023,-0.01489,0.04937,-0.10568,-0.00343,0.02619,0.10068,0.05106,0.1086,-0.03225,-0.11749,-0.05663,-0.01524,0.09801,-0.08877,0.06183,-0.01384,-0.07182,-0.01035,0.01996,0.02681,-0.02153,-0.01665,0.02201,-0.09247,0.02041,0.00574,-0.00344,0.08269,0.06265,-0.02317,0.11298,-0.05668,0.04226,-0.1005,-0.00896,0.08848,-0.15939,0.01199,0.12657,0.01333,-0.03932,0.00172,0.00754,-0.0154,-0.12015,0.00052,0.0374,0.00052,-0.08855,0.02812,0.02877,-0.05283,0.06258,-0.01649,-0.03519,-0.03101,0.03265,0.01347,-0.04321,0.10618,-0.05327,0.00458,-0.00263,0.08333,0.08247,-0.0903,-0.01408,-0.0047,-0.02034,0.14063,-0.0085,-0.06498,0.0217,0.00236,0.02874,0.05592,-0.10586,0.09414,-0.13012,0.10653,-0.05686,0.02553,-0.0477,-0.00042,-0.06018,0.07032,0.04076,0.12036,0.04582,0.01431,-0.06531,0.07483,0.02379,0.01034,-0.01676,-0.07062,0.0772,0.0495,-0.18404,0.06151,0.07275,-0.01679,0.04711,0.0807,-0.04415,-0.10837,-0.04577,-0.03212,-0.01985,0.08913,-0.10456,-0.13499,0.03184,-0.03859,-0.01809,0.01464,0.02979,0.02465,-0.00166,0.01269,0.00729,-0.02753,-0.1109,0.03876,0.00513,0.01667,0.09308,-0.04332,0.04618,-0.08392,-0.06054,0.1096,-0.02826,0.01381,-0.07121,0.04774,0.10423,0.06918,-0.13515,-0.06204,-0.07537]},{"domain":"optimization","key":"newsvendor_uniform","name":"Newsvendor order quantity (uniform demand)","package":"optimization-ai999x","example":"Newsvendor: an item sells for 10 and costs 4, with uniform demand between 100 and 300. Find the optimal order quantity.","v":[0.02067,0.07102,0.03149,0.00878,0.0825,0.03961,0.0188,-0.03783,0.03444,0.01943,-0.10194,0.03076,0.06803,0.01604,0.05869,-0.01459,-0.03468,0.0705,-0.0341,-0.01173,-0.03608,-0.07809,-0.02659,-0.05049,-0.00838,0.06509,0.02823,-0.05402,0.02548,-0.00545,-0.02557,0.21712,-0.00639,-0.00346,-0.16388,0.00929,0.05784,-0.08303,-0.0095,-0.07976,0.07443,0.00708,0.00564,0.03868,0.00325,-0.04363,0.05273,0.04073,0.02747,0.04298,-0.02966,-0.08814,-0.11358,-0.13538,0.08729,0.03759,-0.02123,-0.01116,-0.00857,-0.04194,-0.07983,0.00146,-0.03245,-0.00496,-0.00242,-0.02859,-0.04395,0.0055,-0.03668,-0.03082,0.06287,0.06004,0.03201,0.05993,-0.08677,0.09485,0.07781,-0.01247,0.07139,0.06311,0.06977,0.1015,0.05026,-0.06037,-0.03692,-0.01709,0.00622,0.05797,0.03147,-0.01411,0.0653,0.08451,0.10065,-0.00381,0.05432,-0.02409,-0.01,-0.07503,-0.0714,-0.00947,-0.01574,0.06337,0.03829,0.02785,-0.04202,-0.00474,-0.06429,-0.04704,0.01207,-0.00901,-0.00691,0.02272,-0.05978,0.01209,0.0956,-0.02057,0.00502,-0.10746,-0.04489,0.01924,0.04413,0.01381,0.07619,0.02085,-0.05049,-0.00237,0.00754,0.11726,-0.09625,0.0281,0.04492,-0.11012,0.04627,0.02127,-0.10685,-0.09411,-0.01743,0.0401,0.00467,0.03357,0.01802,-0.05771,0.11534,0.0613,-0.02982,0.13165,-0.03999,-0.01342,-0.04335,0.06493,0.0465,-0.19941,0.03371,0.02341,0.06003,-0.07079,-0.01444,-0.02054,0.01765,-0.06628,-0.03483,-0.01756,0.01664,-0.07289,0.02773,0.00039,0.03831,0.00593,-0.01146,0.01152,0.01422,0.00624,0.03692,-0.11274,0.05492,0.00578,0.02854,-0.04576,0.12272,0.09121,-0.12757,-0.03164,0.03325,0.00994,0.11077,-0.05294,-0.03549,-0.02653,0.01178,0.08086,-0.06981,-0.08607,0.08846,-0.13758,0.06148,-0.05451,-0.00406,-0.00823,0.0421,-0.05917,-0.00118,0.04482,0.02734,-0.03313,-0.03324,-0.04566,0.07421,0.01561,-0.00463,-0.0103,-0.0838,0.01121,0.0214,-0.07062,0.07994,0.12051,0.02529,0.05631,0.068,-0.03193,-0.15616,-0.00846,-0.0114,-0.04493,0.05398,-0.08932,-0.23896,0.06618,-0.02174,0.02156,0.09491,-0.00512,-0.01563,-0.03736,0.01903,0.04299,-0.11315,-0.13895,-0.02534,0.01228,-0.06053,0.04698,0.02058,0.03304,-0.03943,-0.05679,0.18976,-0.02099,-0.03568,-0.05019,0.03765,0.0988,0.06187,-0.12382,0.00181,-0.05614]},{"domain":"optimization","key":"open_box_max_volume","name":"Open box of maximum volume from a rectangular sheet","package":"optimization-ai999x","example":"An open box is made from a 12 by 12 sheet by cutting equal squares from the corners. Find the maximum volume.","v":[-0.04576,-0.0548,0.05544,0.06349,-0.06006,-0.06265,-0.04032,-0.09441,0.02352,0.13894,-0.03054,0.09408,0.00613,-0.02083,0.03377,0.04081,0.00222,0.06282,0.03929,-0.12182,-0.01652,0.07923,0.05905,0.02891,0.0047,0.03785,-0.0386,0.11257,0.0047,0.00013,0.09877,0.07481,0.03462,0.04033,-0.08034,-0.05087,0.05886,-0.12563,-0.02458,0.03628,-0.01188,-0.06623,0.02107,0.00418,-0.01029,-0.1516,0.07733,-0.11638,-0.00015,0.00744,0.10004,0.02427,-0.03912,0.03366,0.03744,-0.02923,0.06485,0.06041,0.05629,0.01583,0.03473,0.04156,0.03808,0.04629,0.02499,-0.04579,0.04313,-0.06719,0.00228,0.02412,0.02893,-0.01225,-0.07742,0.09584,-0.086,-0.02087,0.07961,-0.08604,-0.03666,0.02416,0.06559,0.01225,-0.09215,-0.0234,-0.06448,0.15834,0.03085,0.13028,0.04471,0.03295,0.06769,0.00448,0.01624,0.08157,-0.02298,-0.01526,0.0281,-0.01639,0.04387,0.02164,-0.09249,0.125,-0.00104,-0.06432,-0.06392,0.06386,-0.20475,0.02109,-0.09648,-0.063,-0.06553,0.01299,0.07316,0.09251,0.05668,-0.02631,0.03369,0.08839,0.03835,-0.07492,0.08078,0.12248,0.08194,0.12041,-0.12181,0.08571,0.05602,0.03807,-0.09303,-0.01546,0.00415,0.06454,0.02797,-0.08722,-0.03499,-0.03499,-0.02798,0.03374,0.08231,0.07596,0.01158,-0.0378,0.03148,-0.02104,-0.08238,-0.08184,-0.0681,0.00083,0.0761,-0.05493,-0.08435,0.00551,-0.00958,-0.04756,-0.10755,0.00505,-0.07383,0.00869,-0.06891,0.04872,0.03284,-0.00701,-0.0303,-0.02228,-0.02217,0.06655,0.11176,-0.01697,0.04486,-0.08043,-0.06466,0.06218,-0.03636,0.06734,0.00746,-0.04471,0.04451,-0.15661,0.01148,-0.10561,0.0094,0.0662,0.01272,-0.01635,0.00079,-0.02571,-0.00405,-0.05003,-0.00985,-0.04995,-0.03316,-0.06476,0.05923,-0.07002,0.02576,-0.029,0.09305,0.02504,-0.01793,-0.01402,0.09206,0.00407,-0.08629,-0.00635,-0.05578,-0.00174,-0.06536,0.00416,-0.04873,-0.13192,-0.14538,-0.06026,0.05236,-0.02086,-0.02573,0.17547,-0.03494,0.07616,0.0088,-0.07353,-0.01768,0.03451,-0.03415,-0.10538,0.03037,0.01296,-0.07068,0.09637,0.0211,-0.01902,0.02052,0.03579,-0.08974,0.02058,0.05796,-0.00815,-0.01892,0.00074,-0.04746,-0.04718,0.07058,0.07884,0.03533,0.00907,-0.02784,-0.05565,0.08478,0.06516,-0.02934,0.03621,0.09313,-0.01633,-0.00818,0.05625,0.01522,-0.07598]},{"domain":"optimization","key":"order_up_to_level","name":"Periodic-review order-up-to level","package":"optimization-ai999x","example":"In a periodic review system, demand averages 20 units per day with a standard deviation of 4, the review period is 7 days, the lead time is 2 days and the service level is 95%. Find the order-up-to level.","v":[-0.02083,0.00952,-0.0194,-0.0436,-0.00308,0.00041,-0.02566,-0.01188,-0.01165,0.12975,-0.0346,0.01573,0.0235,0.08282,0.07076,0.03863,-0.03045,0.05527,-0.04736,-0.07017,-0.05684,-0.09651,-0.10461,0.00462,-0.0081,-0.07992,0.00743,-0.09109,0.00035,0.05731,-0.0293,0.03558,0.08225,0.04904,-0.00547,-0.02095,0.01884,-0.02902,0.01181,0.05474,0.0278,0.08553,-0.01772,0.10386,0.03831,0.00983,0.0142,0.16631,-0.02054,-0.14272,-0.04674,0.07031,0.0078,-0.08505,0.17895,-0.03385,-0.121,0.08446,0.01085,0.01211,-0.09397,0.01274,0.01447,-0.00297,0.10871,0.00048,-0.03923,-0.11632,0.0669,-0.00124,0.00997,0.00703,-0.10918,-0.044,0.11444,0.0304,-0.01733,0.02512,0.05808,0.02135,0.0371,0.07614,0.06365,-0.07393,0.15374,0.01758,-0.0439,-0.04276,-0.02489,0.00554,0.01097,0.05333,-0.04054,0.05302,0.11964,-0.0118,0.01971,-0.00552,-0.06935,-0.05332,-0.0317,0.03589,-0.0439,0.04317,0.01115,-0.02274,0.02851,-0.00766,0.06234,0.00071,0.00838,-0.06417,-0.08197,0.0423,0.12029,0.03084,-0.09097,-0.06334,-0.06459,-0.031,0.05329,-0.04266,0.02178,-0.00254,-0.04451,-0.06251,0.00704,0.01434,0.03597,0.07276,-0.03443,0.0441,0.01419,-0.02967,0.14831,0.03863,-0.00248,-0.00766,-0.00195,-0.0324,0.015,0.00456,-0.03343,-0.01359,-0.00047,0.00492,-0.11624,0.04187,-0.03279,0.00105,0.03408,-0.11951,0.1089,0.05148,-0.0049,-0.05665,0.01857,0.09907,0.01924,-0.1668,0.06799,-0.09347,0.02262,0.0195,0.02222,0.01568,-0.02067,0.04909,0.06806,0.03066,0.01009,0.0567,-0.12621,-0.03087,0.05528,-0.04151,-0.00328,-0.00511,0.1539,0.08185,-0.067,-0.01248,0.05479,0.04998,0.15198,-0.04045,0.05208,0.04998,0.03474,-0.11596,0.00904,0.04188,0.07204,-0.1176,0.03002,-0.07654,-0.02885,-0.00017,0.12924,0.02573,0.07478,0.01811,0.07314,-0.12782,-0.00733,0.00084,0.04207,-0.0683,-0.03598,-0.02553,-0.06705,0.02149,-0.03559,-0.1464,0.04903,0.01604,-0.05042,-0.05684,0.05408,-0.10804,-0.07439,0.00019,0.01207,0.00738,0.04255,-0.05477,-0.00764,0.0,-0.08112,0.05384,-0.04885,-0.11231,-0.0879,0.00942,-0.06483,-0.01032,0.09688,-0.08343,0.02033,0.04814,-0.03937,0.08118,-0.0118,-0.09604,-0.03743,0.00956,0.13236,-0.07918,0.05019,0.01868,0.04791,0.00591,0.01593,-0.13821,-0.12091,-0.01828]},{"domain":"optimization","key":"parallel_machine_makespan","name":"Minimum makespan on identical parallel machines","package":"optimization-ai999x","example":"Jobs with processing times [7, 5, 4, 3, 3, 2] are scheduled on 2 identical machines. Find the minimum makespan.","v":[0.01164,0.02863,-0.10106,0.0191,-0.1226,0.063,0.06763,-0.04748,0.05808,0.03239,-0.01551,0.02175,0.07971,-0.01387,-0.01102,-0.03008,0.04592,0.08106,0.14996,0.08953,0.06411,0.05506,0.00827,-0.01248,0.05191,0.06357,-0.15968,0.0891,0.02974,0.01592,0.0043,-0.08054,-0.15818,0.03668,-0.04141,-0.04746,-0.11739,-0.03975,0.01725,-0.00679,-0.06105,0.05814,-0.03795,-0.09634,0.13197,-0.11329,0.0512,-0.00776,0.02606,0.01972,-0.02281,0.01567,-0.17565,0.03436,-0.05229,0.08325,0.05732,0.0159,0.02259,0.0282,0.0216,0.01637,0.04818,0.06751,-0.00336,0.01541,-0.02626,-0.05927,0.04965,0.09996,0.00455,0.03056,-0.06669,-0.04133,-0.04994,-0.06461,0.01683,0.04992,-0.00397,0.03235,0.11087,-0.0176,0.01089,-0.03818,-0.06986,0.02735,0.0546,0.0233,0.04767,-0.06984,-0.05554,0.0747,-0.06508,0.06089,-0.00946,-0.09541,0.01434,0.01461,-0.15823,0.02916,-0.04433,0.07834,-0.08324,0.02373,-0.02337,-0.02552,-0.10632,-0.12291,-0.08856,-0.05528,-0.05924,-0.03042,0.03409,-0.01357,0.06668,-0.00547,-0.02828,0.03536,-0.00769,0.08848,0.03092,-0.00106,0.00725,-0.01516,0.0107,0.03818,0.01721,0.0569,0.06003,0.06956,0.04409,0.04108,-0.07463,0.01488,0.00846,0.02884,-0.06949,0.04493,0.04382,0.07239,-0.01162,-0.11716,-0.02559,0.00122,-0.01028,0.04173,0.0367,-0.0378,-0.08999,0.00193,0.00193,-0.01976,-0.11353,0.09125,-0.021,-0.03567,0.07524,-0.00894,-0.06656,0.06638,0.02695,0.07291,0.00535,0.02691,-0.09675,0.02479,0.09529,0.02498,-0.07316,0.08167,0.08598,-0.06297,-0.0087,-0.0255,0.01597,0.05105,0.03029,0.1338,-0.06164,-0.0272,-0.02724,-0.13077,0.03559,0.04519,0.03162,0.10529,0.01022,-0.08538,0.00658,0.00717,-0.07609,-0.02041,0.03972,0.03364,-0.04172,-0.04671,0.0086,0.05756,0.05757,-0.04341,0.06092,0.14894,-0.12882,-0.00256,0.05583,0.01187,-0.03414,-0.11525,-0.14078,0.05318,-0.06814,-0.06899,-0.05919,0.00488,-0.0084,0.13487,0.01829,-0.02888,-0.01848,0.05499,-0.06549,-0.05243,0.00656,-0.13756,-0.04007,-0.0792,-0.02733,-0.0635,-0.03965,-0.03736,0.05357,0.07035,-0.02625,-0.03272,-0.00302,0.05484,-0.05298,0.06202,-0.05384,0.00834,-0.04634,0.0274,0.03023,0.12885,0.08893,-0.02595,0.0161,-0.14393,-0.09485,0.08418,0.0736,0.06724,0.02778,-0.05965,0.02485,0.06928]},{"domain":"optimization","key":"pert_project","name":"PERT project duration and completion probability","package":"optimization-ai999x","example":"PERT: activities A, B, C have times [[2, 4, 6], [3, 5, 13], [1, 2, 3]]; precedences: A-B, A-C. Find the expected project duration.","v":[-0.09719,0.02912,-0.06104,0.01701,0.05357,0.06856,0.07734,-0.07996,0.1204,-0.00272,0.15793,0.14573,0.07115,0.00579,0.04518,-0.07402,-0.00175,0.07845,0.10857,0.056,-0.02408,-0.04107,0.06639,1e-05,0.04306,0.02196,-0.12918,0.05067,0.13088,0.09862,-0.00521,0.05062,-0.08191,0.09218,-0.05585,0.01044,-0.04994,-0.02613,0.00176,0.02769,0.03077,-0.0396,-0.09117,0.02427,0.0409,-0.06238,-0.02094,-0.00203,-0.00711,0.00569,-0.03515,-0.05865,-0.06999,0.0398,-0.01506,0.03278,-0.01968,0.01916,0.01123,-0.10918,0.05715,0.07121,-0.09871,-0.00789,-0.0054,-0.05878,0.08442,-0.01457,0.02107,-0.02034,-0.01637,0.00447,-0.12994,-0.11042,-0.04082,-0.03972,0.04484,0.01177,-0.02106,0.03664,-0.06104,-0.01084,0.03651,-0.00161,0.02628,0.04925,-0.05989,0.03785,0.04183,-0.13749,-0.05023,0.04536,-0.16824,-0.03952,-0.00178,-0.11357,0.06127,0.00193,-0.07714,0.03853,-0.00938,0.07714,-0.10026,0.04679,0.02215,-0.04508,-0.23483,0.03092,0.07972,0.00641,0.02923,0.02638,0.04055,-0.03012,0.0549,-0.05215,-0.04106,-0.03792,0.03272,0.01414,0.05983,0.10213,-0.01175,-0.0434,0.05715,-0.04655,0.02757,0.02488,-0.01544,0.00379,0.0442,-0.0036,0.03066,-0.047,-0.07099,0.06716,-0.02202,0.04835,-0.04842,-0.00057,-0.0691,0.00358,0.04532,0.00013,-0.09586,0.07088,0.02567,-0.01829,0.00092,0.07687,0.04692,-0.04517,0.00748,0.05057,-0.06221,0.07575,0.08246,-0.07379,-0.13669,-0.03152,0.04086,0.07208,0.03629,0.01598,-0.02741,0.08313,0.03186,0.10605,-0.07539,0.0379,0.02182,0.01524,-0.07931,0.05549,-0.0004,0.02326,-0.05435,0.02892,0.04434,-0.0242,-0.05047,-0.19121,0.06849,-0.04926,0.00535,0.14234,0.0401,0.04712,0.03717,-0.08606,-0.00394,-0.05211,-0.04006,0.00162,0.02054,-0.08404,0.07188,-0.01592,0.15905,0.07471,0.04469,0.13023,0.02543,0.05286,-0.00272,-0.05292,0.02837,-0.04581,-0.06914,-0.01869,-0.01472,-0.00323,-0.05569,-0.04653,0.03376,0.03921,0.01883,-0.00893,0.07221,0.02263,-0.02034,-0.04511,-0.02445,-0.1518,-0.07125,-0.12119,-0.04663,0.03288,-0.01701,-0.10305,0.03983,-0.01405,-0.01915,0.09974,-0.00669,-0.03976,8e-05,0.09344,-0.02082,0.07693,0.01945,0.09035,-0.01925,0.10852,-0.06413,-0.05547,-0.02231,-0.09755,0.08357,0.06474,0.00606,-0.04082,0.03735,-0.04578,-0.01006,-0.04871]},{"domain":"optimization","key":"polynomial_extrema_interval","name":"Absolute extrema of a polynomial on a closed interval","package":"optimization-ai999x","example":"Find the absolute minimum and maximum of the polynomial with coefficients [1, -3, 0, 2] on the interval [-1, 3].","v":[-0.02197,-0.03999,-0.09014,0.10964,-0.02359,0.07054,0.0129,0.01175,0.0027,-0.0519,-0.08451,0.08275,0.01771,-0.01753,0.03508,-0.02733,0.16816,-0.12877,0.01413,-0.04772,0.02582,-0.00843,0.04866,-0.06849,0.12203,0.09533,0.07579,0.07419,0.04955,0.09007,0.03552,0.03355,-0.01794,0.08324,-0.08552,-0.09136,0.02406,-0.01549,0.08159,-0.04813,-0.102,-0.01678,-0.04594,0.00831,0.06348,0.0138,0.02667,-0.02661,0.13753,-0.00557,0.15085,0.03575,-0.00438,0.03545,-0.08087,-0.08777,0.00225,-0.06418,0.09057,0.00478,-0.03993,-0.0101,-0.05904,-0.0074,0.02771,-0.05057,-0.03235,0.01569,0.01867,0.01373,-0.02881,0.06132,0.06533,-0.02525,0.07581,0.04604,-0.04113,-0.00125,0.10159,0.07545,0.11678,0.02443,-0.04183,-0.0028,0.06051,0.12256,-0.02471,-0.04729,-0.0166,-0.02709,-0.02561,0.05193,-0.06556,-0.0718,0.00532,-0.12597,0.11317,-0.00186,-0.04291,0.15161,-0.07265,-0.01863,-0.08809,-0.02021,-0.02943,-0.00604,-0.13129,-0.07797,-0.04752,0.04652,0.00621,0.07653,-0.00581,0.00111,0.0278,-0.02345,-0.05084,-0.06903,-0.02291,0.12,0.13829,0.04522,0.0281,-0.08802,-0.05959,0.03935,0.0581,-0.02825,0.0502,-0.03001,-0.11113,-0.05385,0.01084,-0.05829,-0.07302,-0.0066,-0.04472,-0.04821,0.10094,0.05531,-0.03979,-0.11748,0.1177,0.03924,-0.04741,-0.0239,0.03813,-0.05954,0.08852,-0.03257,-0.05454,-0.03803,-0.06678,-0.10187,-0.01257,0.04889,-0.01005,-0.02315,-0.04497,0.06093,-0.04303,0.03738,-0.05496,0.08782,-0.00155,0.04339,0.05133,-0.07734,0.0012,0.02661,-0.04062,-0.03337,0.01579,-0.00481,-0.03531,0.01722,-0.02074,-0.01359,0.01053,-0.00874,0.02975,-0.08998,-0.10746,0.0524,-0.0245,-0.02404,-0.04933,0.02796,0.10179,0.08458,-0.1174,-0.02425,0.07994,0.10002,-0.03907,-0.01228,-0.02555,-0.05846,0.08742,-0.08157,0.04541,0.07823,0.02894,0.04698,0.00532,0.02288,-0.03486,-0.04389,-0.1383,-0.08643,-0.01027,-0.03232,0.13836,-0.00445,-0.05575,0.14126,-0.10013,0.02197,-0.01143,0.0147,0.00218,0.07433,-0.08241,-0.1159,-0.05148,0.08945,0.04513,0.04423,-0.09478,-0.08047,0.06229,-0.0118,-0.05622,-0.0092,0.07206,0.11307,-0.00157,-0.02371,0.01792,-0.07225,0.00911,0.05138,-0.0102,0.05169,-0.00117,0.03739,-0.03845,-0.00863,-0.12298,0.01343,0.01683,0.05393,0.08396,0.02878,0.02922,0.00062]},{"domain":"optimization","key":"profit_max_linear_demand","name":"Profit-maximising output with linear demand","package":"optimization-ai999x","example":"The demand is p = 100 - 2q and the cost is C = 300 + 20q. Find the profit-maximizing quantity.","v":[-0.00887,0.0813,-0.02181,-0.15774,-0.03163,0.04381,0.01366,-0.07619,-0.01733,0.0049,-0.04747,0.06189,-0.0096,-0.02562,0.03089,0.02893,-0.00427,-0.021,0.06874,-0.05831,-0.03203,0.0273,0.0461,-0.04107,-0.08926,0.1064,0.07421,-0.07856,-0.00308,0.02492,-0.03459,0.08345,-0.05041,0.04032,-0.12888,0.01795,0.08774,-0.01585,0.01704,-0.07471,-0.02841,-0.05104,0.01105,0.03898,-0.05729,-0.05268,0.03762,-0.0267,0.05712,0.04851,0.08699,-0.06681,-0.07097,0.02742,-0.01653,0.15601,-0.04851,-0.04512,0.04734,0.05004,-0.02719,-0.00261,-0.02676,0.05244,-0.05286,-0.04523,-0.02001,-0.04083,0.02195,-0.01084,-0.02161,0.04188,0.04362,0.03941,0.03483,-0.0384,0.0456,-0.07285,0.09229,-0.02204,0.08822,0.02072,0.06657,-0.02025,-0.02313,-0.03335,-0.0699,-0.05879,-0.07493,0.06922,0.12042,0.06367,0.10219,0.02451,0.04544,-0.11719,0.11208,-0.07951,-0.00416,-0.02839,-0.02407,0.025,-0.04426,-0.11538,-0.05544,0.09076,-0.05426,-0.0458,-0.04581,0.03916,-0.05543,0.07312,0.02637,0.03785,0.00925,-0.00025,0.03337,-0.14333,-0.03089,0.14639,0.11694,0.04612,0.00476,-0.06321,-0.05107,0.04086,-0.02245,0.13,-0.00797,0.02972,-0.12188,0.04232,0.06683,-0.03135,-0.05258,-0.02296,0.03809,-0.07276,-0.04679,-0.0302,-0.16287,0.01458,0.08302,-0.04749,-0.0321,0.09204,-0.04278,-0.03018,-0.00848,0.12318,0.01039,-0.02987,0.02314,0.007,0.03418,0.01058,0.09292,0.09522,-0.00707,-0.02127,-0.06478,0.09041,-0.06246,-0.02976,-0.10889,0.04594,0.06745,-0.08808,-0.14064,0.08342,0.02529,-0.03236,-0.01405,-0.00359,0.01137,-0.01433,-0.06256,-0.02304,-0.05674,0.05276,-0.03893,0.03829,-0.02921,-0.02131,0.00915,0.00599,0.01796,0.01758,-0.02333,0.00904,0.00824,0.13922,-0.01933,-0.00162,-0.08131,-0.0141,0.02166,0.04565,-0.05209,-0.08866,0.06504,0.06303,0.0412,0.13816,-0.01977,-0.06515,0.11482,0.08418,0.00257,0.00753,-0.10102,-0.02185,-0.04033,-0.07247,-0.02338,0.12957,-0.04091,0.12765,0.09424,0.05932,0.01751,-0.03249,-0.07101,-0.08954,0.09999,-0.06822,-0.14691,0.13152,-0.0499,-0.06183,0.06658,-0.08375,-0.03126,-0.05572,0.02701,0.01102,0.00197,0.02416,0.01643,-0.01996,-0.12276,0.08032,0.0126,0.01875,-0.01595,0.0059,0.10994,0.07527,-0.06389,-0.0503,0.01102,0.07025,0.08655,-0.00171,0.02514,-0.05723]},{"domain":"optimization","key":"pure_nash_equilibria","name":"Pure-strategy Nash equilibria of a bimatrix game","package":"optimization-ai999x","example":"Find the pure-strategy Nash equilibria of the bimatrix game with row payoffs [[3, 0], [5, 1]] and column payoffs [[3, 5], [0, 1]].","v":[-0.07042,-0.12543,0.01436,0.03483,0.0182,-0.0048,0.14034,-0.07449,0.0488,-0.01309,0.0136,-0.01989,-0.03228,-0.02605,-0.08009,-0.07257,-0.01303,0.04877,0.00054,-0.01471,-0.05114,-0.06472,-0.00632,-0.05307,0.05273,-0.00616,0.04809,0.08496,-0.0353,-0.0389,-0.00917,-0.07972,0.03311,-0.09508,0.05769,-0.04375,-0.03185,0.10822,0.10055,-0.07655,0.04535,-0.00704,0.00531,0.05847,0.01469,0.04029,-0.02915,0.06514,0.0101,0.04686,0.0401,0.01827,0.00184,-0.04982,0.02415,0.01704,-0.10918,0.00493,0.10387,-0.00105,-0.05865,0.0361,0.07246,0.03432,0.06362,-0.01616,-0.0194,-0.14035,-0.00155,-0.07588,-0.0261,0.00398,0.07589,0.16122,0.03354,-0.03873,-0.00879,0.0727,0.02655,0.05359,-0.01664,-0.16468,-0.11372,0.01146,-0.03717,-0.11901,-0.00134,-0.07608,-0.05485,-0.08022,0.04355,0.00473,-0.08558,0.0291,0.02668,0.01859,-0.08937,0.03475,-0.04242,0.13568,-0.01802,-0.05298,0.02801,0.00281,-0.02824,-0.06242,-0.00252,-0.0434,-0.13876,-0.10317,0.03345,-0.0015,0.04561,0.01901,0.01996,-0.01488,0.05074,0.09033,-0.19228,0.06549,-0.04392,0.05673,0.05785,-0.07348,0.01672,0.07963,0.09961,0.09797,0.06091,0.03025,0.06983,0.04487,-0.14826,-0.00169,-0.1038,-0.04765,-0.00536,0.04891,-0.00205,0.062,0.06536,0.00564,-0.02885,0.01115,0.11219,0.01079,0.00302,0.00711,0.00954,-0.00529,0.06493,0.15989,0.0055,0.05407,0.04286,0.05181,0.01263,0.00463,-0.001,-0.01254,-0.01955,-0.04565,0.05999,0.04993,-0.0097,-0.07712,-0.07892,0.00011,0.04302,-0.08851,-0.0314,-0.01361,-0.04664,-0.09206,0.02594,0.01744,0.00794,-0.15668,0.01716,0.00256,-0.02793,0.02139,-0.06228,0.06166,0.00827,0.08658,0.03351,-0.0089,0.00089,-0.02987,-0.03592,0.15539,-0.00136,0.03141,-0.10379,0.02695,0.00787,-0.03106,-0.09077,0.00941,0.07394,-0.01444,0.08411,0.01601,-0.02289,0.02611,-0.03616,0.09993,-0.01752,-0.00842,0.00308,-0.05741,-0.11705,0.07684,-0.00773,0.02707,-0.03776,0.03131,0.03867,0.00679,0.05409,-0.01581,-0.08613,-0.00147,0.09047,0.07489,-0.12184,-0.12221,-0.02556,0.19545,-0.01847,0.06747,-0.00756,0.03498,-0.08533,0.0448,-0.11001,0.04114,0.0403,-0.05894,0.00206,0.02514,0.0553,-0.02135,0.0589,-0.108,0.05493,-0.14674,-0.02163,0.10127,0.0189,0.00174,-0.02558,0.00301,0.03186,0.03195]},{"domain":"optimization","key":"quadratic_optimum","name":"Optimum of a quadratic function","package":"optimization-ai999x","example":"Find the minimum of f(x) = 2x^2 - 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Find the sequence minimizing the total weighted completion 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x 2 zero-sum game (saddle point or mixed-strategy formula)","package":"optimization-ai999x","example":"Solve the zero-sum game with payoff matrix [[3, -1], [-2, 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zero-sum game (value and optimal mixed strategies)","package":"optimization-ai999x","example":"Solve the zero-sum game with payoff matrix [[3, -1, 2], [-2, 4, 1], [0, 1, 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test for equal variances","package":"statistics-ai999x","example":"Bartlett's test for [21, 24, 19, 26, 23], [22, 23, 22, 24, 23] and [18, 28, 20, 30, 24].","v":[-0.03469,0.01794,0.02671,0.00234,-0.12901,0.00449,-0.00788,0.00311,-0.01736,-0.05946,-0.12168,0.05467,-0.03553,-0.01935,0.00771,-0.11827,0.0155,0.00888,0.05384,-0.03342,-0.05471,-0.04543,-0.10198,-0.01935,-0.04043,-0.03608,0.03917,-0.045,0.04285,-0.01011,-0.09786,-0.02812,0.04651,0.00181,0.09491,-0.02943,-0.02154,0.06392,-0.0352,-0.00432,0.02816,-0.02182,-0.06067,0.07177,0.03985,-0.11471,0.03539,-0.01363,0.04221,0.05073,0.03549,-0.04557,0.03193,-0.04734,-0.03813,-0.11768,0.12794,-0.05201,-0.00452,0.01181,0.03028,0.04273,0.06938,-0.03514,-0.02408,0.02118,0.06177,0.02515,0.00188,0.11594,-0.09404,0.06304,0.0783,0.00775,-0.01236,-0.01217,-0.01718,-0.03488,0.09089,-0.07113,0.0145,0.02588,0.05764,0.04566,-0.10731,0.07361,0.0587,-0.0744,-0.06145,0.09225,-0.14614,0.0553,0.0232,-0.0674,0.03126,-0.11161,-0.10541,-0.06337,-0.04067,-0.11568,0.03461,0.08468,0.06872,-0.00989,0.09628,-0.02616,-0.0209,-0.09562,0.01737,-0.04006,0.02734,0.04089,0.07348,0.07253,-0.1081,-0.08105,0.15861,0.00104,0.04944,0.01434,-0.05879,0.05373,-0.02017,-0.04293,0.01912,0.01163,-0.05732,-0.0031,0.04977,0.1051,0.0743,0.04721,-0.07056,0.02608,-0.05871,-0.09186,-0.04278,0.12534,0.10616,0.06924,-0.01402,-0.02321,0.04004,0.04627,0.1238,-0.07168,-0.05272,0.0869,0.00963,0.04656,0.01637,0.00067,-0.12492,0.04285,0.03033,0.04532,0.14892,-0.06523,-0.00715,-0.02005,-0.02025,-0.06628,0.03705,-0.0695,0.00468,0.00445,-0.08609,0.13178,0.05464,0.08347,-0.01235,-0.01065,0.01906,0.05403,-0.10992,-0.09221,-0.004,0.02466,-0.11313,-0.14534,-0.03566,-0.02554,-0.04265,-0.00239,0.0657,-0.04522,0.08277,-0.05867,-0.01802,0.11593,-0.01187,0.029,-0.02955,0.03202,0.01353,-0.03313,-0.05431,-0.00039,0.01057,-0.00726,0.02261,-0.00417,-0.09751,-0.04638,-0.05586,0.04868,0.07028,-0.05654,0.0675,0.10582,0.02597,-0.03955,-0.10607,-0.05159,-0.04008,-0.03644,-0.07461,-0.05895,0.03007,-0.02149,-0.01611,-0.05915,0.00036,-0.06807,0.04641,-0.03227,0.0195,-0.14852,0.01203,0.05902,0.059,0.10989,0.10907,-0.07999,-0.02621,-0.02795,0.06177,-0.01613,0.02605,0.00571,0.05988,-0.08885,0.1135,0.05806,0.00514,0.04919,0.01581,0.04872,0.13316,-0.06249,0.013,0.06483,-0.03357,0.06892,-0.05053,0.10017]},{"domain":"statistics","key":"binomial_at_least","name":"Binomial probability: at least k successes","package":"statistics-ai999x","example":"Find the binomial probability of at least k = 3 successes in n = 10 trials with p = 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probability: at most k successes","package":"statistics-ai999x","example":"Find the binomial probability of at most k = 3 successes in n = 10 trials with p = 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interval for the difference of two means","package":"statistics-ai999x","example":"Find the 95% confidence interval for the difference in means of [12, 15, 11, 18, 14] and [10, 9, 13, 11, 8] using 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16].","v":[0.01749,0.03426,0.00423,0.00389,-0.09895,0.02046,0.00493,-0.10324,-0.03657,-0.12945,-0.03745,-0.03208,-0.03871,0.02215,0.03972,-0.04918,0.04772,-0.03869,-0.08271,-0.08744,0.03983,-0.02212,-0.10851,-0.06276,0.02947,0.09711,-0.03329,-0.10992,-0.0925,0.02708,-0.01462,0.00099,0.02035,0.03717,0.12201,-0.00869,-0.06028,0.08553,-0.04809,-0.06841,0.0162,0.05592,-0.09725,0.10153,0.12649,-0.08017,0.02628,0.083,0.08972,0.03873,0.05373,-0.00454,0.00119,-0.00744,-0.02141,0.0261,0.22146,0.00959,0.01305,-0.01272,0.07414,0.09882,0.02563,0.08092,0.01878,0.05763,0.02203,-0.00768,-0.01669,0.00302,-0.06636,0.06049,0.05355,0.09493,0.04175,0.05935,-0.1059,0.0351,-0.01996,-0.12284,-0.01435,-0.01564,-0.01352,0.02002,0.03854,0.09474,-0.06502,0.10335,-0.06428,0.06304,-0.01255,0.09298,-0.04969,0.01628,-0.00162,-0.08039,-0.033,0.02364,-0.0276,0.02628,0.00935,0.13187,-0.0302,-0.01314,0.0721,-0.04226,-0.09677,-0.03304,0.0943,-0.01719,0.07153,0.07055,-0.02213,0.06751,-0.04333,-0.04238,0.12479,-0.09019,0.04296,0.02413,0.04921,0.07753,-0.02248,-0.02658,0.00709,0.10011,-0.07559,0.00811,0.00762,0.00469,0.05322,0.12588,-0.06909,-0.04323,-0.03599,-0.03096,-0.02399,-0.02158,0.14136,0.08667,-0.04609,0.02905,0.0104,0.00206,-0.02681,-0.12218,-0.07636,0.06245,0.06702,-0.05445,0.03475,0.02689,-0.00288,-0.02693,0.06956,0.10325,0.15272,0.01691,-0.04131,0.07009,-0.05974,-0.03638,-0.0175,-0.04589,-0.00132,-0.05124,-0.00085,0.06109,0.06953,-0.0366,-0.08717,0.02582,-0.01387,0.0126,-0.07305,-0.04233,-0.06173,-0.00083,0.00881,-0.09166,0.07051,-0.00799,0.00829,-0.00679,0.03723,0.00725,-0.0526,-0.04684,0.13287,0.02146,-0.08457,-0.14163,-0.01824,0.00413,0.10434,-0.09499,-0.10109,-0.02464,0.02794,0.0391,0.14399,0.00135,-0.18786,-0.08601,-0.04985,-0.0006,0.03659,-0.09366,-0.04817,0.0008,-0.03262,-0.01716,-0.03355,-0.0299,0.02921,0.04,-0.02132,-0.0262,-0.00863,-0.05951,-0.13738,0.04068,0.02442,-0.10256,0.00667,-0.02927,0.02551,-0.11237,0.03182,0.07524,0.04894,-0.08349,-0.00766,-0.02242,-0.04095,-0.03918,0.01964,0.05263,-0.00371,0.00607,-0.05595,-0.02934,0.06235,0.08825,0.00647,0.02758,0.02313,0.09857,0.09661,-0.06471,0.00301,0.02085,-0.01608,-0.00423,-0.04814,0.00184]},{"domain":"statistics","key":"coefficient_of_variation","name":"Coefficient 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18].","v":[0.07362,0.06265,-0.00531,0.13829,-0.05058,-0.00358,-0.14221,0.02625,-0.03101,-0.13004,-0.03164,-0.00393,-0.02111,-0.0398,0.05051,0.0527,-0.02415,0.0545,-0.1597,-0.06881,0.00234,0.04528,-0.03044,-0.00111,0.05568,0.05782,0.0163,-0.21873,-0.08049,-0.02195,0.05373,0.02128,0.00447,0.01463,0.06034,-0.10311,0.02083,0.05722,0.02135,-0.07212,-0.01586,0.11736,-0.0423,0.14058,0.02098,-0.01917,-0.0186,0.02504,0.03486,0.01821,0.03943,-0.01074,0.06894,-0.00689,0.06056,0.03046,0.17213,0.0168,-0.08008,-0.03777,0.04688,0.00224,0.02783,0.03042,0.04781,0.0323,-0.02578,0.02615,0.04319,0.05424,0.01533,0.00973,-0.01075,-0.09258,-0.03602,0.09436,-0.07712,0.04899,0.03746,-0.00271,-0.03315,0.01273,-0.00023,0.03936,0.09179,0.16889,-0.0694,0.01369,0.01355,0.00877,0.08299,0.02102,0.03817,-0.03297,0.01889,-0.07613,-0.07045,0.05432,-0.05513,0.04245,-0.07305,0.02013,0.02289,-0.03039,0.01584,-0.06971,0.00709,0.02618,0.13152,0.01574,0.07527,0.0022,-0.001,-0.09177,-0.10792,0.06855,0.03486,0.0135,0.05701,-0.08135,0.03982,0.07265,0.00384,0.01537,-0.09877,0.09798,0.0165,-0.002,0.01824,0.05929,0.02659,-0.00705,-0.03163,-0.04224,-0.0107,-0.06291,-0.00824,-0.08173,-0.04848,0.04099,-0.04539,0.023,0.05856,0.07218,0.00964,0.00983,-0.10755,0.05177,0.08397,-0.03556,-0.06208,-0.07637,0.04148,-0.09906,-0.00853,-0.04138,0.12799,-0.02098,-0.03018,0.06486,0.0826,0.02879,0.02207,-0.08435,-0.04992,-0.03142,0.00498,-0.02221,0.05284,-0.03972,0.09787,-0.04515,-0.04212,-0.01623,-0.01621,-0.17799,-0.0521,0.03046,0.01053,-0.0319,0.03791,0.10653,-0.00464,-0.00596,-0.03252,-0.00435,-0.16193,0.03654,0.03151,0.03123,-0.04374,-0.04965,0.06044,-0.14296,0.0268,-0.0074,0.08459,0.00721,-0.08556,-0.00167,0.14225,0.06819,-0.09736,-0.03015,0.02535,0.02131,-0.07231,-0.05197,-0.03622,-0.00401,-0.07848,-0.03909,-0.047,-0.10532,0.00992,-0.09687,0.11803,0.00225,0.05165,0.03564,-0.10547,-0.03243,0.03907,-0.03152,-0.02783,-0.00237,0.08945,0.08209,0.06144,0.03638,0.03915,0.01076,-0.03053,-0.02358,-0.00954,0.01275,0.04179,0.05687,0.10937,-0.06034,0.10597,0.03235,-0.03132,0.0735,0.02691,-0.09069,0.0452,-0.0008,0.02319,-0.14084,0.01462,0.0228,-0.12153,-0.04777,-0.08995,-0.04273]},{"domain":"statistics","key":"cohens_d","name":"Cohen's 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5].","v":[0.01207,-0.02536,-0.04013,0.09588,0.03879,0.041,-0.07419,0.00113,0.08091,-0.14962,-0.02742,0.01405,0.07592,-0.05441,0.00058,0.0601,-0.08904,-0.00862,-0.07561,-0.02437,-0.05949,0.05839,0.04262,-0.05116,-0.032,0.04801,0.01719,-0.1757,-0.07848,-0.02131,0.08795,-0.10295,-0.07662,0.05245,0.04432,0.00676,-0.07251,-0.00615,-0.12081,-0.10436,0.06934,0.06154,-0.13133,-0.03065,-0.03103,0.0248,-0.05968,0.1201,-0.00953,0.06515,0.04146,0.05774,-0.0391,0.01499,-0.02646,0.02575,0.12514,-0.00035,-0.0654,0.00253,0.01186,-0.02664,0.02363,-0.01979,-0.01965,-0.03295,-0.03807,0.01548,0.00021,-0.00618,0.12295,-0.08355,0.03496,-0.00199,-0.10713,0.08784,-0.06553,-0.0569,0.13983,-0.04657,0.07245,-0.03229,-0.0195,0.0547,0.10652,0.07275,-0.10296,0.02389,0.0408,0.08079,0.06275,-0.07721,0.05966,-0.03914,0.0052,0.00152,-0.04123,4e-05,-0.04048,-0.01135,-0.03036,-0.00617,0.02682,-0.05055,-0.03756,-0.06685,-0.02388,0.03482,0.11434,-0.03851,0.00707,-0.00756,-0.0863,-0.02836,-0.00118,0.05595,0.05527,0.01971,0.00605,-0.12403,-0.05105,0.05515,0.00477,0.0426,0.03284,0.09538,-0.04897,0.03414,0.08094,0.09451,0.08088,0.05327,-0.03557,-0.00573,0.0217,-0.02102,-0.05706,0.05284,-0.00171,0.06722,-0.06845,0.0439,0.05786,0.00248,0.06202,0.05988,-0.12407,0.038,0.05433,0.00505,0.07484,-0.02954,-0.03299,0.01557,0.04441,-0.05983,0.09253,0.01288,0.06095,0.20122,0.08933,0.00695,0.02425,-0.06221,-0.05209,-0.03862,-0.02203,0.00932,-0.10257,0.03722,0.02298,-0.02194,-0.0184,-0.03751,-0.04733,-0.06755,-0.01484,0.03575,-0.00497,-0.06654,0.05051,0.06561,-0.00831,0.01263,-0.10373,-0.00667,-0.08611,-0.06637,-0.0773,0.06828,0.09908,0.11878,0.00246,-0.0336,-0.0841,-0.02652,0.07244,0.0626,-0.01906,0.04611,0.07544,0.02717,-0.00583,-0.00825,0.09394,0.04947,-0.10042,0.01443,0.04123,0.02104,-0.06011,-0.21693,-0.04413,-0.10119,0.00658,0.0085,0.03932,0.00924,-0.00316,0.05512,0.02187,-0.0225,-0.00996,-0.01535,-0.02645,0.11251,0.15179,0.04504,-0.00441,0.03297,-0.07303,0.02532,-0.08543,-0.05438,-0.05765,-0.08214,0.01243,0.05267,-0.01258,0.00281,0.01834,-0.03103,0.07981,-0.02225,0.03378,-0.11541,0.07996,0.10405,0.00514,-0.10413,-0.03229,-0.0103,-0.10726,0.0419,-0.09003,0.03412]},{"domain":"statistics","key":"cronbach_alpha","name":"Cronbach's alpha (internal consistency)","package":"statistics-ai999x","example":"Find Cronbach's alpha for [[4, 5, 4], [3, 3, 4], [5, 5, 5], [2, 3, 2], [4, 4, 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0.2].","v":[-0.05886,-0.06843,0.03227,-0.06961,0.13957,0.0515,0.05653,-0.01825,-0.09903,-0.14223,0.12018,0.04636,-0.07401,0.07312,0.07905,-0.08066,-0.02314,-0.03313,-0.0533,-0.01745,-0.0345,-0.00355,-0.034,-0.05009,-0.0378,0.06141,-0.06636,-0.08503,0.04395,-0.03769,-0.06152,0.09079,0.00731,-0.0009,0.0331,-0.04238,0.00309,-0.04628,-0.02304,-0.00254,-0.0341,-0.02897,0.04222,0.12117,0.06106,0.02959,-0.0111,-0.05587,0.03803,-0.03616,-0.07656,-0.08171,0.02241,-0.03913,0.0531,-0.07719,0.05087,-0.10312,0.00289,-0.0368,-0.00432,-0.01358,-0.03557,-0.05276,-0.07623,-0.01607,-0.02189,0.03854,0.0757,0.01013,-0.05088,0.03699,-0.08985,0.08489,0.04374,0.04477,-0.0091,-0.0592,-0.07497,0.00894,-0.04101,0.08153,0.04943,0.01571,-0.03054,0.01805,0.0408,0.16301,-0.01865,-0.04507,-0.04894,-0.07236,-0.09619,0.00424,-0.01516,-0.06206,-0.10688,-0.07612,-0.04736,0.00239,0.0365,0.07528,0.00409,-0.0531,0.08,0.00165,-0.03896,-0.01366,0.1327,0.02003,0.06355,0.00961,-0.046,0.06955,0.06058,-0.06638,0.10147,-0.10216,0.12965,-0.03277,0.09902,0.08877,-0.03131,-0.04241,0.05536,-0.09997,0.0534,0.03476,-0.02283,0.03938,0.02562,-0.02403,0.09763,-0.01578,-0.0059,0.05359,-0.00446,0.01255,-0.0087,-0.00033,0.06791,0.04457,0.00684,0.0584,-0.09572,0.04497,-0.11771,0.05684,0.0083,0.01183,-0.08142,0.01168,-0.02137,0.01649,0.01612,0.14665,0.06437,-0.00681,-0.02591,-0.04175,-0.12636,0.01918,0.00127,-0.00175,0.08389,-0.06027,-0.15507,0.06383,-0.09309,0.00215,-0.01885,0.04105,0.01936,0.0569,-0.01101,-0.00136,-0.03998,-0.01964,-0.03042,0.07461,0.03119,0.0389,0.12732,0.04304,0.04292,0.04145,0.0695,0.00541,0.08959,0.00528,-0.04571,-0.05318,-0.01367,0.00313,0.11195,-0.0803,0.07851,-0.05054,-0.04976,-0.04457,-0.01319,0.02765,0.03633,0.19087,-0.06736,-0.08457,0.0219,0.00424,0.02002,0.11833,-0.01073,0.12823,-0.01657,-0.14707,-0.02117,-0.06299,0.02314,-0.00411,-0.00241,-0.02699,-0.10404,0.13496,-0.01819,0.04451,0.05382,-0.08543,0.02713,0.10368,0.07354,0.00263,0.03424,-0.03849,0.05776,0.08867,0.00882,-0.06879,0.11369,0.04011,-0.08638,-0.00784,0.04853,-0.02775,-0.01749,0.06843,0.00693,-0.09684,-0.01895,0.01403,0.04473,-0.07978,-0.00868,-0.01855,-0.07603,-0.08157,-0.13774,-0.02185]},{"domain":"statistics","key":"durbin_watson","name":"Durbin-Watson statistic","package":"statistics-ai999x","example":"Compute the Durbin-Watson statistic for residuals [0.5, -0.2, 0.3, -0.4, 0.1, 0.6, -0.5].","v":[0.09775,-0.02004,-0.00157,0.13306,0.05361,-0.00898,-0.03235,-0.0363,0.06724,-0.08237,-0.01124,-0.02253,-0.07732,0.06687,-0.15378,0.02936,0.05285,-0.03933,0.00643,-0.05555,-0.0239,-0.07475,-0.04257,0.11504,-0.11779,0.0331,-0.07638,-0.011,0.02081,0.04098,0.0046,-0.00111,0.09887,-0.02822,0.1386,-0.02343,0.01342,-0.03703,0.02671,-0.01398,0.03727,-0.06052,-0.02984,-0.0138,-0.12234,0.0029,-0.01081,0.0527,-0.04728,0.04472,-0.02037,0.13805,0.11343,0.07043,0.09383,-0.09055,-0.01657,-0.04369,-0.01934,0.01762,0.02622,0.01299,-0.00199,-0.03723,0.08569,-0.01632,0.05537,-0.06426,-0.01452,-0.04253,-0.05937,0.04418,-0.09636,0.01248,0.0068,-0.02979,0.0791,0.02003,-0.04088,-0.02548,-0.0957,0.06076,-0.04911,0.03483,0.0437,0.02164,-0.02197,0.07039,0.05982,-0.09627,-0.05729,0.05213,0.06631,-0.02811,0.05288,-0.07078,0.04837,0.03526,-0.08204,0.0042,0.05291,-0.01034,-0.02867,-0.01541,-0.07438,-0.01189,0.02334,0.05103,0.08841,0.05623,-0.04485,-0.03863,-0.05823,-0.07024,-0.02517,0.11877,-0.07641,-0.04743,0.02179,0.09154,0.05194,0.05962,-0.12051,-0.03216,-0.01258,-0.08417,0.01407,0.01509,-0.01046,-0.06891,0.01193,0.00242,-0.06695,-0.04509,0.06416,0.01593,0.02508,-0.01385,0.03046,0.01069,-0.04467,0.03742,-0.04172,0.06945,0.08001,0.03556,-0.00946,0.04129,0.1252,-0.13007,0.03726,-0.0077,-0.04407,-0.06032,-0.07973,0.08733,-0.04068,0.0315,0.05395,0.01692,0.07532,-0.09171,-0.01499,-0.11575,0.07055,0.05978,-0.16034,0.17249,0.03574,-0.0359,-0.00046,0.0656,0.05514,0.05726,-0.03357,-0.05943,0.03819,-0.04575,0.0014,-0.00392,-0.05314,-0.05634,0.00926,-0.03029,0.06614,0.05867,-0.14145,0.03441,-0.07847,0.03401,-0.05587,0.01858,0.02788,0.09604,0.04033,-0.04087,-0.06215,0.00711,0.09727,-0.07787,0.00787,0.02155,0.04223,-0.14249,-0.0126,0.09326,-0.03382,-0.03413,0.08745,0.02911,0.07981,0.05159,-0.00821,0.06914,-0.02866,-0.113,0.0574,-0.1068,-0.01356,-0.01579,0.03127,0.05474,0.02787,0.06818,0.08981,-0.01689,0.05009,-0.04847,-0.05011,0.09869,0.01116,-0.14793,0.01329,-0.01559,0.05656,-0.0116,-0.07698,0.13677,0.10902,-0.02308,0.0359,-0.06873,0.04981,-0.00894,0.00595,-0.00671,0.09394,0.0104,-0.00364,0.00466,0.0318,-0.20788,-0.07565,-0.03033,-0.03726,-0.03682]},{"domain":"statistics","key":"exponential_probability_above","name":"Exponential probability above a value","package":"statistics-ai999x","example":"For an exponential distribution with rate = 0.5, find P(X > 3).","v":[-0.07487,-0.16234,0.00215,0.14164,-0.05198,-0.0053,0.01344,-0.03656,-0.02275,0.10253,-0.02022,0.14781,-0.07007,0.01528,0.07521,-0.08669,0.03785,-0.04993,0.05428,0.04183,-0.1003,0.0238,0.02037,-0.05582,-0.00335,0.00527,-0.10359,0.05846,0.01844,0.01469,-0.03684,0.06302,-0.0288,0.03587,0.00083,0.02249,-0.08652,-0.02521,-0.10341,0.07884,0.00902,0.02015,0.07353,0.14375,0.04239,0.0998,-0.0379,-0.02955,0.05785,0.05259,0.02243,-0.05302,0.0646,0.03363,0.07,0.04427,0.12335,-0.04665,-0.13543,-0.02961,0.00377,-0.06702,0.02559,-0.04597,0.00671,-0.05068,-0.00371,0.05513,0.0801,0.00324,0.04772,-0.0172,-0.05761,-0.09081,0.01804,-0.04849,0.01304,-0.04109,0.03878,-0.04412,0.01807,-0.02185,0.01659,-0.08782,-0.10858,-0.07164,0.08353,0.09525,-0.02989,0.02772,-0.01896,0.03854,-0.03773,-0.08386,-0.00926,-0.10566,-0.07331,0.04959,0.0868,0.02528,0.05009,-0.01322,0.05063,0.05048,0.11176,0.02696,-0.05315,-0.02579,0.09669,-0.00476,0.01769,0.02469,-0.02664,0.0458,0.08522,0.05121,-0.06139,0.00847,0.10913,-0.00432,0.05603,0.1111,-0.05604,0.00251,0.03243,0.0176,-0.06325,-0.12591,-0.02498,0.01466,0.00648,-0.09773,0.06729,-0.03289,0.02186,0.05105,0.06809,-0.04599,-0.01915,-0.08734,0.03448,0.0125,-0.07604,0.03508,-0.12232,0.09464,-0.02043,-0.00508,0.03453,0.03838,-0.04152,-0.02951,0.0352,0.01362,0.0126,-0.01061,-0.10502,0.01012,0.0448,-0.07523,-0.02187,-0.01696,0.05778,-0.08533,-0.03788,-0.00215,-0.07993,-0.01196,-0.032,0.01133,-0.01082,0.16529,-0.0459,0.08635,0.05981,0.08182,0.04741,-0.06535,0.00476,0.15342,-0.08041,0.01122,-0.00246,-0.07547,0.07891,0.0174,0.03334,-0.0567,0.01674,-0.11011,-0.05054,-0.10386,-0.03632,-0.14824,0.04143,0.02106,0.00459,-0.11391,0.0777,-0.09072,0.07865,0.01799,0.08207,0.10232,0.03785,-0.03532,0.0286,-0.06425,-0.00778,0.05482,-0.05909,0.10795,-0.02249,-0.16449,0.0181,-0.06178,0.01672,0.0909,-0.03057,0.085,-0.0075,-0.02833,0.02428,0.05898,0.03889,-0.10652,0.02282,-0.04906,0.07144,-0.10744,-0.03356,0.00225,0.0588,0.05971,0.02414,0.00061,0.0104,0.00823,-0.05871,-0.02525,0.01956,0.04886,0.02822,0.01114,0.0149,-0.06733,0.0241,-0.10056,0.09302,-0.01862,-0.02571,0.0085,0.10477,-0.06265,-0.01452,-0.11445]},{"domain":"statistics","key":"exponential_probability_below","name":"Exponential probability below a value","package":"statistics-ai999x","example":"For an exponential distribution with rate = 0.5, find P(X < 3).","v":[-0.08866,-0.17962,-0.01382,0.10058,0.00591,0.00453,0.02876,-0.03611,-0.04874,0.11067,-0.03355,0.08273,-0.03719,-0.01375,0.04694,-0.10564,0.02249,-0.04671,0.01693,0.0322,-0.13975,0.01958,0.01539,-0.05262,-0.00964,0.00359,-0.09243,0.04814,0.02604,-0.00352,-0.04531,0.09359,-0.02812,0.02061,0.03,0.01139,-0.04216,-0.04047,-0.11546,0.08521,0.01795,-0.00594,0.04527,0.11928,0.05807,0.09656,-0.06643,-0.0149,0.05013,0.03148,0.01584,-0.06305,0.0471,-0.03891,0.0558,0.03016,0.14618,-0.07451,-0.13081,-0.03228,0.01422,-0.1036,0.02573,0.0172,0.00511,0.01875,-0.03748,0.06515,0.03019,0.04677,0.0201,-0.02804,-0.05346,-0.09835,0.00285,-0.05223,0.03349,-0.04112,0.02906,-0.06159,0.02219,0.03108,0.07787,-0.0688,-0.09577,-0.08884,0.08958,0.11137,-0.01075,0.04828,-0.01681,-0.00033,-0.04638,-0.10663,-0.02501,-0.06952,-0.09571,0.01756,0.08275,0.00658,0.04053,0.02862,0.09048,0.01966,0.10936,0.03416,-0.04084,-0.05523,0.11158,-0.03462,0.06109,-0.01084,-0.00757,0.0457,0.06134,0.03915,-0.06052,0.01981,0.1147,0.00319,0.05167,0.09434,-0.04682,0.01162,0.03453,0.00269,-0.05139,-0.10359,-0.04784,-0.00406,0.05334,-0.08034,0.11689,0.00087,0.03696,0.05576,0.03114,0.01191,-0.00415,-0.06742,0.05157,0.00982,-0.09442,0.03002,-0.16739,0.10159,-0.01002,-0.00018,0.0176,0.02478,-0.03043,-0.02472,0.01925,0.00975,0.05448,-0.00245,-0.05562,0.0155,0.04912,-0.04463,-0.04984,-0.02144,0.04902,-0.05959,-0.03299,-0.01615,-0.08632,-0.01079,-0.08034,0.00936,-0.03805,0.18316,-0.00281,0.11548,0.03923,0.04961,0.07809,-0.06679,-0.00809,0.10607,-0.099,0.01359,0.02162,-0.0477,0.1083,0.03845,0.02012,-0.05932,0.01592,-0.08194,-0.03236,-0.1259,-0.03107,-0.12207,0.04018,0.02492,0.057,-0.09556,0.06601,-0.05005,0.05201,0.01385,0.06378,0.06601,-0.00855,-0.08225,0.03605,-0.0574,0.00692,0.0568,-0.0568,0.1088,-0.01043,-0.16485,0.02764,-0.05809,0.02064,0.11659,-0.00012,0.06637,-0.02617,-0.01041,0.01783,0.06156,0.05076,-0.11218,0.06911,-0.02037,0.0853,-0.08942,-0.03131,1e-05,0.06789,0.09487,0.00128,-0.06565,0.00243,0.01554,-0.11062,-0.00987,0.01598,0.00456,0.01517,-0.00607,0.03578,-0.04797,0.06028,-0.11105,0.07449,-0.01202,-0.01004,-0.02131,0.07057,-0.06943,-0.0593,-0.12295]},{"domain":"statistics","key":"exponential_reliability","name":"Exponential reliability (constant failure rate)","package":"statistics-ai999x","example":"Find the reliability at t = 1000 hours for a constant failure rate = 0.0002 per 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value of F","package":"statistics-ai999x","example":"Find the F critical value with df1 = 3, df2 = 20 and alpha = 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for equality of two variances","package":"statistics-ai999x","example":"F-test for equality of variances of [21, 24, 19, 26, 23, 25] and [22, 23, 22, 24, 23], 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3].","v":[-0.09916,0.01819,-0.0421,-0.03852,0.02488,-0.11285,0.02718,0.02781,0.00861,-0.04475,-0.05092,0.00618,-0.00914,0.03462,0.01398,0.05208,-0.00632,-0.02054,-0.0497,-0.00212,-0.05776,-0.01931,-0.04461,-0.06477,0.01353,-0.04449,0.02207,-0.0733,-0.0666,-0.0145,0.05712,0.0021,0.0213,0.09544,0.02032,-0.13813,0.00057,-0.05113,0.03153,-0.01727,-0.07237,-0.06417,0.05957,0.0754,-0.04068,0.0455,-0.10001,0.08222,0.0367,-0.03333,-0.02465,0.00201,-0.06892,-0.07584,-0.11769,-0.01692,-0.02045,-0.08411,-0.03576,-0.04471,-0.02107,-0.04817,0.05111,0.13492,0.01224,-0.00706,-0.05852,0.13166,0.002,0.14508,0.06614,0.08542,-0.06268,0.01958,0.02448,0.09323,0.05164,0.00051,0.03626,-0.07609,-0.03996,0.03527,-0.00815,0.03778,0.02471,0.0335,0.00126,-0.06559,0.02563,-0.00052,0.05245,0.00196,-0.12259,0.00959,-0.00676,0.02271,-0.04641,-0.04691,-0.04438,0.05507,-0.00433,0.09405,-0.04262,-0.12912,0.12079,0.06359,-0.05302,-0.03229,0.00914,-0.07397,0.01916,-0.02456,0.00383,0.04288,0.03436,-0.04968,0.05169,0.01853,-0.04901,0.06333,0.06048,-0.04737,0.0589,-0.01408,0.00224,0.09389,0.09917,-0.03784,-0.00727,-0.04414,0.09844,0.07992,-0.06117,0.11062,-0.03329,0.03772,-0.06823,0.00122,0.05097,0.18185,-0.06009,0.09755,0.05584,-0.01681,-0.08448,0.14474,-0.05169,-0.03297,-0.00935,-0.03433,-0.00049,0.02431,0.00219,0.00699,-0.0185,0.07164,-0.05834,0.08288,-0.08546,-0.02501,-0.02708,0.00089,-0.03069,-0.03207,0.05386,-0.049,0.02551,0.05976,0.08051,-0.03835,0.03011,-0.05387,0.09906,-0.02188,-0.12665,-0.04096,-0.00629,-0.02236,-0.05942,0.00492,-0.01524,0.15983,0.0858,0.05218,-0.09792,-0.05601,-0.04411,0.10731,-0.00423,0.00954,0.02254,-0.00055,-0.05342,-0.02966,-0.0905,-0.01303,0.06807,-0.015,-0.0609,0.02822,0.00433,0.03283,0.08205,0.12118,-0.1221,-0.04532,-0.07789,0.12894,0.03219,0.01603,-0.00495,-0.02638,-0.08522,-0.13319,-0.05773,0.05348,0.07,0.1121,-0.00161,-0.18873,-0.03986,0.0791,0.0079,0.01113,-0.03389,0.09653,0.06157,-0.07873,-0.08532,-0.1274,0.02796,0.11017,0.02294,0.02864,0.02704,0.0532,-0.03817,0.02147,-0.12706,-0.00984,-0.07769,-0.02522,0.09278,-0.01786,0.05815,-0.09477,0.01929,-0.04905,-0.02693,-0.11174,0.02129,-0.00547,0.03237,0.06162,-0.06387,-0.04718]},{"domain":"statistics","key":"multiple_linear_regression","name":"Multiple linear regression","package":"statistics-ai999x","example":"Fit a multiple regression of y = [10, 12, 15, 19, 22, 25] on X = [[1, 2], [2, 1], [3, 4], [4, 3], [5, 6], [6, 5]].","v":[0.08995,0.02978,-0.04548,0.01546,-0.03356,0.00482,-0.05709,-0.05574,0.14526,-0.09583,-0.01389,-0.08396,0.07895,0.02316,-0.08245,0.03748,0.10031,-0.05804,0.04853,0.00249,-0.067,0.01025,0.01687,0.07072,-0.06999,0.00468,-0.02988,-0.15872,-0.01464,-0.00399,0.02293,-0.09414,0.0894,-0.02652,0.04181,-0.03454,0.08713,0.00999,-0.12836,0.07518,-0.00533,0.03678,-0.05133,0.04266,-0.11392,-0.01601,0.04597,0.09332,-0.05446,-0.00049,0.00934,0.16104,-0.00594,0.02463,-0.03953,-0.04643,0.16412,-0.06819,-0.0027,0.07428,0.05345,0.09433,-0.00175,0.00188,0.05476,-0.05024,0.05837,-0.00959,0.06505,0.01708,0.04314,-0.01309,-0.11916,-0.06038,0.0173,0.06622,0.09022,-0.03795,0.01252,0.06688,0.00561,-0.00655,-0.03159,0.01148,0.06124,-0.02151,0.00932,-0.00077,-0.06563,-0.02223,-0.02894,-0.01089,0.03956,-0.08277,-0.03524,-0.0551,-0.04905,0.03279,-0.10381,-0.04255,0.09904,-0.02902,0.02324,-0.01158,-0.08165,-0.02428,0.11164,0.07667,0.16902,-0.02238,-0.05512,0.07626,-0.06794,0.01412,-0.06025,0.06915,-0.01749,-0.05744,0.00906,-0.06274,-0.04446,0.05926,-0.09011,-0.07449,-0.00594,-0.01782,-0.00435,0.05076,0.01499,0.0186,-0.11991,-0.06894,-0.05929,-0.03971,0.06819,-0.00767,-0.04594,-0.00621,0.01472,0.04785,-0.06797,-0.06669,0.08398,0.07282,0.03712,0.04122,-0.02312,0.08613,0.17486,-0.14988,-0.05166,0.04511,0.02186,-0.01579,-0.04533,-0.03517,0.02337,-0.03162,0.00366,0.18692,0.04475,0.02148,0.06648,-0.00477,-0.0196,0.08364,-0.08958,0.00895,-0.07951,0.08451,-0.03213,0.06382,-0.02781,0.07043,-0.02757,-0.00807,-0.00195,-0.0689,-0.11163,-0.0136,0.00019,-0.00801,-0.0363,-0.03869,0.06133,-0.02223,-0.04963,-0.00613,-0.05036,0.02947,0.06184,0.05992,0.02542,-0.02604,-0.01049,0.01298,0.00498,0.08315,0.01682,0.0224,0.07065,0.08068,-0.02795,-0.01745,0.00025,-0.05344,-0.0663,0.16304,0.02461,0.05356,0.00838,-0.07552,0.01082,0.03201,-0.08663,-0.02556,0.05517,-0.07676,0.08932,0.12767,0.02614,0.05312,-0.02656,0.09022,-0.08083,0.09798,0.08544,-0.04624,-0.04673,0.05205,-0.06258,-0.03,-0.02343,-0.06391,-0.01268,-0.03644,0.02988,-0.00788,-0.07956,-0.00413,-0.02869,-0.06535,0.06929,-0.03007,-0.0796,-0.06133,0.15746,0.01553,-0.09489,0.03899,-0.09103,-0.09319,-0.06047,0.01539,-0.04714,0.01852]},{"domain":"statistics","key":"negative_binomial_probability","name":"Negative 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0.4.","v":[-0.01021,-0.15789,-0.03994,-0.02482,0.11313,-0.00689,0.15361,0.0114,0.02362,0.00229,-0.0255,0.01304,-0.01476,0.06257,-0.04078,0.06645,0.09401,0.00298,0.03848,0.02176,-0.08734,-0.05699,0.04541,0.01533,0.00047,0.04316,-0.0838,-0.08184,0.07655,-0.07307,-0.06053,0.04094,-0.01926,-0.05721,-0.05796,0.03021,-0.08552,0.01983,0.00152,0.02119,0.05838,-0.08108,0.09045,0.02244,-0.03632,0.00767,0.01445,-0.08753,0.01105,-0.02039,0.02118,0.01076,0.02322,0.03345,-0.0936,0.01737,-0.14311,0.05991,0.09514,-0.04892,-0.00231,-0.03325,0.04609,-0.13307,-0.03791,0.03145,0.05979,-0.04279,-0.08442,-0.08881,-0.07181,-0.03821,0.04497,0.14463,-0.01869,-0.00297,0.00153,-0.03715,0.04945,-0.03352,-0.07388,0.01582,0.10451,-0.0176,-0.10966,-0.02512,0.08623,-0.0015,-0.048,-0.08953,0.00437,0.04045,-0.04517,0.02697,0.07458,0.0439,0.03051,0.16072,0.09858,-0.06861,0.02693,-0.04856,0.06663,0.01184,0.01379,-0.00295,-0.08617,0.02267,0.0571,-0.02258,-0.05378,9e-05,-0.08145,0.06586,0.04713,0.04961,0.06446,-0.07533,-0.06675,0.00681,-0.09215,0.02173,0.03326,-0.04091,0.00562,-0.04956,0.07068,-0.02772,-0.02951,-0.07338,0.0326,-0.03113,0.00525,0.05323,0.00359,0.10109,0.08913,-0.067,-0.0769,-0.06662,-0.0733,0.04925,-0.02898,-0.03465,-0.07908,-0.07327,0.09193,-0.03404,-0.02172,-0.02896,-0.04595,0.01113,0.0417,0.09211,-0.01852,0.18251,-0.1233,-0.0718,0.07038,-0.07716,-0.11724,-0.05388,0.0386,-0.1301,0.02973,-0.02615,-0.09783,0.02756,-0.0093,0.01111,-0.04425,0.01302,-0.05092,-0.0174,0.08062,-0.05123,0.05536,0.08299,-0.04949,0.01741,-0.08032,0.03815,0.10559,0.06291,0.04297,0.09033,-0.07826,0.00616,-0.09783,-0.07381,0.05103,0.00464,0.01581,-0.02422,-0.01635,-0.05668,-0.04403,-0.05671,0.02926,-0.00232,0.01623,0.06419,0.00404,0.02346,-0.01384,-0.04938,0.03797,0.03689,0.04326,0.01342,0.05013,-0.06523,0.02413,-0.0595,-0.01629,-0.05297,0.0259,0.07002,0.12116,0.02447,0.11933,0.02499,-0.05488,-0.04727,0.01739,0.00501,0.07075,0.06926,-0.01539,0.04865,0.03279,-0.03716,-0.06689,0.04627,-0.16777,-0.06596,0.04035,0.19046,0.03746,0.01954,-0.07492,-0.09395,-0.03747,0.02988,-0.06052,0.09745,0.08396,0.04557,0.06435,0.13352,0.02069,-0.04919,0.00429,-0.03436,0.04996,-0.04019]},{"domain":"statistics","key":"normal_probability_above","name":"Normal probability above a value","package":"statistics-ai999x","example":"For a normal distribution with mean = 100 and standard deviation = 15, find P(X > 130).","v":[0.01145,-0.1192,0.04278,0.01828,-0.02307,-0.01642,-0.07537,0.07006,-0.0377,0.04752,0.01325,0.11874,-0.0769,0.12721,0.05043,-0.02284,0.05858,-0.02006,0.02476,0.02433,-0.04181,-0.00401,-0.05486,0.01815,-0.04284,-0.03221,-0.08434,0.07071,0.05686,-0.06264,0.02703,0.04321,0.0518,0.00661,-0.05648,-0.03883,-0.04725,-0.08427,0.01305,0.05606,-0.00191,0.01162,0.07075,0.11677,0.0619,0.03836,0.01281,0.00077,0.05157,0.02506,-0.00068,-0.11908,0.11541,0.0245,-0.0092,-0.01294,0.01563,0.02456,-0.0325,-0.04881,-0.0451,-0.07312,0.01317,-0.09681,0.0882,-0.11427,0.09278,0.00713,0.15174,0.0387,-0.04536,-0.02061,-0.09366,0.03676,0.05641,-0.03924,-0.02744,-0.08645,0.08317,0.09753,-0.07275,0.05551,-0.06729,-0.01224,-0.02481,0.05344,0.02499,0.06214,0.00218,-0.04297,0.05563,0.00823,-0.03864,0.05792,0.06396,-0.08846,0.0478,0.02428,-0.01704,-0.01198,0.0402,-0.0606,0.02818,0.01473,0.04977,-0.06192,-0.03265,0.0283,0.12231,-0.0617,-0.12951,0.17988,-0.03912,-0.03081,0.06141,-0.0558,0.08962,-0.00045,-0.02458,-0.01018,0.04345,0.06894,0.04502,-0.03889,-0.11721,-0.07765,-0.0024,-0.0746,0.05772,0.03026,-0.01879,-0.05958,0.01162,-0.101,0.07296,0.08972,0.1014,-0.08656,-0.07841,-0.03033,0.0648,0.0717,-0.06708,0.03194,-0.03264,0.0224,-0.01027,-0.02429,-0.01598,-0.03935,-0.01497,0.05427,0.04176,0.14416,-0.08394,-0.03294,0.00554,-0.05446,0.03438,-0.10932,0.02372,0.06726,0.05031,-0.04711,-0.0217,0.02156,-0.09711,0.04793,0.01567,-0.0893,-0.0571,0.06359,0.00189,-0.00993,0.04204,-0.00158,0.02039,-0.08528,-0.03753,0.10712,0.08552,0.01072,-0.05796,-0.07075,0.00849,-0.00482,0.01228,0.05255,0.00645,-0.19302,0.06599,-0.0567,-0.0261,-0.12872,0.0287,-0.07582,-0.01594,-0.02286,0.01152,0.09259,0.0601,0.01099,0.05711,0.15803,0.13619,-0.03076,0.01363,0.03632,-0.04123,0.00424,-0.00877,0.09719,-0.02648,-0.17069,-0.00421,0.01934,-0.02026,0.13488,0.00756,0.04262,0.02609,0.01479,-0.05887,-0.11979,-0.0021,-0.04708,0.00637,-0.0701,0.03077,-0.08077,-0.0829,0.02426,0.05833,-0.00658,0.03986,0.02002,0.06113,0.08131,-0.01498,0.04116,-0.05318,0.13449,-0.0349,0.07381,-0.03109,-0.07406,-0.04142,0.04493,0.06718,-0.10173,-0.04032,0.07319,0.00646,0.00208,-0.03272,-0.04062]},{"domain":"statistics","key":"normal_probability_below","name":"Normal probability below a value","package":"statistics-ai999x","example":"For a normal distribution with mean = 100 and standard deviation = 15, find P(X < 120).","v":[-0.01159,-0.13069,0.0175,-0.05375,0.04228,-0.03245,-0.05483,0.06399,-0.06479,0.04885,-0.00459,0.03047,-0.01772,0.08685,0.01556,-0.04642,0.02769,-0.01841,-0.03953,0.01907,-0.1034,0.01301,-0.08125,0.01053,-0.04599,-0.05293,-0.06561,0.05691,0.07821,-0.08891,0.01454,0.07161,0.06166,-0.01159,-0.00893,-0.06234,-0.00599,-0.14686,-0.02436,0.05475,0.01993,-0.0327,-0.00404,0.08769,0.09096,0.01977,-0.05322,0.04445,0.03966,-0.01561,0.00223,-0.14433,0.0559,-0.08892,-0.03511,-0.01965,0.04362,-0.01246,-0.04461,-0.04393,-0.04353,-0.08571,-0.00083,-0.01518,0.09009,-0.01942,0.04042,0.01718,0.12794,0.07692,-0.08616,-0.03699,-0.0665,0.00773,0.03244,-0.05209,-0.01403,-0.08759,0.06513,0.08163,-0.06619,0.14306,0.04279,0.02361,-0.00266,0.01856,0.019,0.07677,0.02756,-0.01434,0.08088,-0.04132,-0.04983,0.04002,0.0845,-0.04565,0.02656,-0.02259,-0.0347,-0.04872,0.02378,0.00287,0.08575,-0.04545,0.03915,-0.07479,-0.00482,0.01821,0.15748,-0.11416,-0.06669,0.11557,-0.01858,-0.05406,0.033,-0.05476,0.11409,0.03206,-0.01244,-0.00381,0.00891,0.03601,0.0826,-0.02301,-0.12867,-0.07343,0.01861,-0.02813,0.0364,-0.01576,0.03887,-0.03927,0.08748,-0.04775,0.09136,0.07824,0.05345,-0.0085,-0.06943,-0.01653,0.09232,0.07861,-0.09864,0.01519,-0.08344,0.02263,0.01885,-0.00338,-0.0494,-0.06167,0.03567,0.05573,0.02765,0.14725,-0.02224,-0.04862,0.10707,-0.05878,0.03356,-0.05896,-0.0078,0.08821,0.03866,-0.01662,-0.03246,-0.00033,-0.07873,0.04537,-0.06577,-0.0884,-0.07072,0.10423,0.05581,0.01205,-0.00176,-0.03777,0.05401,-0.11347,-0.05468,0.02596,0.07983,0.02862,-0.03737,-0.03929,0.05282,0.01162,-0.00169,0.06307,0.00526,-0.15404,0.09586,-0.05059,-0.00571,-0.05654,0.023,-0.08784,0.05849,0.01415,0.00013,0.18175,0.0232,0.00405,-0.00355,0.08577,0.11376,-0.06554,-0.02254,0.03899,-0.02658,-0.02186,0.02645,0.11489,0.00788,-0.1673,0.01886,0.04884,0.01137,0.18068,0.05104,0.02166,0.00267,0.03252,-0.11068,-0.13096,-0.00868,-0.02381,0.07936,-0.05024,0.04348,-0.0394,-0.07178,0.03361,0.06593,-0.01309,0.00766,-0.07958,0.05762,0.10241,-0.08037,0.07373,-0.06242,0.07092,-0.0456,0.04822,-0.00614,-0.02646,0.01212,0.03019,0.03059,-0.11428,-0.04941,0.02845,-0.05696,0.00838,-0.09374,-0.01882]},{"domain":"statistics","key":"normal_probability_between","name":"Normal probability between two values","package":"statistics-ai999x","example":"For a normal distribution with mean = 100 and standard deviation = 15, find P(85 < X < 115).","v":[-0.06113,-0.16679,0.0768,-0.00132,-0.01534,-0.02878,-0.00465,0.03447,-0.05252,0.10443,0.05166,0.09156,-0.02817,0.09456,0.05026,-0.10704,0.03223,-0.03554,-0.00131,0.04601,0.02174,-0.02466,-0.02004,0.01271,0.03808,-0.03484,-0.01093,0.07349,0.01176,-0.03997,0.04107,0.08672,-0.03862,-0.03629,-0.06046,-0.01452,-0.00534,-0.13762,0.00465,0.06062,-0.02433,0.05214,0.0255,0.06676,0.08488,-0.04332,-0.04408,0.1002,0.04042,0.05943,-0.00542,-0.10345,0.04103,-0.02295,-0.04349,0.04581,0.11217,0.04146,-0.02648,-0.02263,-0.09127,-0.109,-0.00057,-0.07697,0.05902,-0.02373,0.10856,0.06968,0.08721,0.02282,-0.05095,-0.01457,-0.03086,-0.0751,0.01938,-0.00458,-0.13806,-0.048,0.05585,0.0429,-0.02682,0.02073,-0.03356,-0.00993,-0.01527,-0.03172,0.10238,0.05462,0.00915,-0.03749,0.05736,0.02168,-0.04413,0.04127,0.07932,-0.10559,0.10915,-0.05344,-0.05039,0.04573,0.00327,-0.00666,0.02724,-0.01718,0.03297,-0.13466,-0.06747,-7e-05,0.16342,-0.04768,-0.07488,0.0719,0.07083,-0.05838,-0.00945,-0.07633,0.12053,0.06933,-0.07383,0.06968,-0.06469,0.05406,0.03675,0.03627,-0.09698,-0.02942,-0.01574,0.00832,0.04369,0.00435,0.10462,-0.03573,0.05752,-0.04546,-0.01644,0.02714,0.10338,0.04158,-0.07494,0.01717,-0.02915,0.08575,-0.00494,0.0182,-0.09478,0.05743,0.04766,-0.00828,-0.0509,0.01447,0.03859,0.03566,0.03439,0.01662,-0.01315,-0.09524,0.10175,-0.1284,0.04946,0.00791,0.06502,0.07941,0.03449,-0.04714,0.02056,-0.03937,-0.0708,-0.02716,-0.04555,-0.09918,-0.05403,0.0856,0.06934,-0.04906,-0.0406,-0.01866,0.06136,-0.12396,-0.09409,-0.00034,0.02365,-0.01989,-0.05574,-0.01748,0.0517,0.06153,-0.04129,0.07406,0.06029,-0.17929,0.00585,-0.00356,0.00615,-0.01764,0.00928,-0.08874,0.01605,0.00396,0.07483,0.14478,0.09208,-0.00848,-0.02327,0.06596,0.10412,-0.06741,-0.07092,0.06426,-0.04843,-0.03672,-0.03466,0.04391,-0.07302,-0.05414,0.04229,0.14758,-0.00049,0.18569,0.03719,0.04389,0.02585,0.03516,-0.06007,-0.12943,-0.04739,-0.00308,-0.04859,-0.06248,0.04797,-0.03508,-0.06214,0.01625,-0.0209,0.02323,0.07917,-0.01063,0.0269,0.05402,-0.08031,0.08156,-0.02423,0.01735,-0.02349,0.0815,-0.04906,-0.05955,-0.03892,0.01092,0.05315,-0.11288,-0.0672,-0.00131,-0.05102,0.00356,-0.11917,-0.01214]},{"domain":"statistics","key":"one_way_anova","name":"One-way ANOVA","package":"statistics-ai999x","example":"Perform a one-way ANOVA on groups [23, 25, 21, 22], [30, 28, 31, 29] and [26, 27, 24, 25].","v":[0.02965,0.10099,-0.03182,-0.02698,-0.10893,-0.01877,-0.03713,-0.04797,-0.00348,-0.11402,-0.08889,-0.02693,-0.02533,-0.04231,-0.06076,-0.08164,0.02513,-0.0087,0.07324,0.01771,-0.07432,-0.00518,-0.06035,-0.07512,-0.02923,-0.00742,0.02703,-0.05145,-0.00095,0.02107,-0.08723,-0.08411,-0.00667,-0.01128,0.07946,-0.02478,-0.04978,0.05666,0.00188,0.08012,0.03098,0.01513,-0.10887,0.04195,0.03644,-0.06325,0.01196,0.11493,0.07261,-0.01803,0.02745,0.01212,0.05488,0.01187,0.00846,-0.12318,0.15607,-0.06944,0.00928,0.00646,0.05401,0.095,-0.00175,-0.01424,0.02551,0.00093,0.09435,-0.04831,-0.01888,0.01583,-0.04816,0.09013,0.05401,0.04695,-0.03062,0.07343,-0.00882,0.00073,0.1176,-0.02957,0.00871,-0.00749,0.04999,0.05102,-0.13129,0.02655,0.02826,-0.00779,-0.04108,0.0859,-0.16683,0.05947,0.03127,-0.14361,0.03394,-0.13319,-0.07336,-0.00229,-0.0099,-0.13749,0.01962,0.07173,0.08049,0.01008,0.06959,-0.01701,0.00282,-0.06481,0.03232,0.01681,0.04773,0.01823,0.09394,0.11845,-0.11366,-0.0935,0.07695,-0.04431,0.0357,0.0009,-0.04269,0.13094,-0.03842,0.00095,0.11058,-0.01919,-0.06704,0.0194,0.06961,0.12373,0.04221,0.0505,-0.10844,0.02211,-0.02509,-0.03959,-0.08973,0.0932,0.09335,0.07809,-0.04598,-0.02248,0.08019,0.06847,0.1395,-0.05561,-0.02866,0.02155,0.08848,0.00517,-0.02178,0.01968,-0.10894,0.09537,-0.0659,0.02102,0.08554,-0.02208,0.05562,0.01742,0.02682,-0.08399,0.02145,-0.02935,-0.05605,0.00055,-0.10134,0.10931,0.05338,0.07567,-0.06359,0.03619,0.00025,0.03487,-0.11808,-0.07345,0.01241,0.05672,-0.10679,-0.10154,-0.08868,-0.05216,-0.07649,0.00684,0.00422,0.01017,0.07183,-0.09615,-0.00666,0.09116,-0.07636,0.0337,-0.05412,-0.00394,0.0243,0.02449,-0.012,-0.03019,0.01814,-0.02363,-0.01468,-0.05296,-0.08602,-0.06339,-0.08179,0.0102,-0.00213,-0.10129,0.00218,0.00043,0.03487,-0.00505,0.00365,-0.032,-0.08633,-0.03567,-0.09536,-0.0944,0.02475,-0.00074,0.04254,-0.00886,-0.00654,0.04752,0.01438,-0.01994,0.07174,-0.09097,0.0236,0.01395,-0.01161,0.08817,0.04913,-0.09149,-0.04049,0.03954,0.06289,-0.05278,0.09959,0.00284,0.08985,-0.02771,0.13005,0.05206,0.03517,0.05984,-0.02803,0.07978,0.08064,-0.03022,0.013,-0.04703,-0.04473,0.06509,-0.0794,0.01008]},{"domain":"statistics","key":"p_chart","name":"p chart limits (fraction defective)","package":"statistics-ai999x","example":"Find the p chart limits for defectives [4, 6, 3, 5, 7, 2, 5] with sample size n = 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t-test","package":"statistics-ai999x","example":"Perform a paired t-test on before [200, 190, 210, 220, 205] and after [195, 185, 200, 214, 200], 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confidence?","v":[-0.00827,0.11026,0.06373,-0.07128,0.01666,-0.04608,0.07211,-0.0417,0.01384,0.01446,0.00687,-0.09562,0.09471,0.035,-0.12127,0.02318,0.1119,0.10907,-0.00632,-0.04879,0.04618,-0.03961,-0.0096,-0.12738,-0.01985,0.07591,0.06531,-0.11305,-0.04567,0.10778,-0.01432,-0.02755,-0.00225,-0.02124,0.04676,-0.00052,0.02475,0.0171,0.03825,0.0804,0.07851,0.00284,-0.08015,-0.00021,0.12044,0.09361,0.0056,0.01141,0.06368,-0.0717,0.01487,-0.06669,-0.00405,0.08129,-0.04909,0.05704,-0.06116,0.01406,0.00937,-0.0158,-0.08768,0.01014,-0.04609,0.02434,0.00097,0.06928,-0.0362,-0.02334,-0.01275,0.01624,0.01843,0.07603,-0.06508,0.05333,-0.0483,0.07116,-0.01356,0.01205,-0.00478,0.01913,-0.02796,0.01787,-0.05598,0.02268,0.03508,0.06045,0.02127,0.05876,0.01901,-0.04184,0.06577,-0.0099,0.06149,-0.04762,-0.03853,-0.01499,-0.10552,-0.00776,0.03717,0.0353,-0.08511,0.03718,0.08899,-0.09541,-0.04504,0.03884,0.00987,-0.0602,0.20379,0.02174,-0.0314,-0.03133,-0.08602,-0.00424,0.00747,-0.03884,0.0148,0.02428,0.00637,-0.00421,0.07606,0.0688,0.0343,0.01683,0.0597,0.06653,-0.08096,-0.10732,0.10395,-0.01349,0.08352,0.04869,-0.00213,-0.02062,0.05403,-0.05423,0.08293,0.02225,0.00732,0.01938,0.03226,0.02133,0.03051,0.01942,0.02008,-0.03988,-0.06999,-0.05291,-0.11183,-0.04095,0.10941,0.02801,0.02641,0.07205,0.10319,0.0243,0.07188,0.11494,0.07001,-0.02082,-0.00142,0.09293,-0.08132,0.06876,-0.10736,0.005,0.04785,0.0156,0.03221,-0.02411,-0.13029,-0.06087,-0.06138,-0.02334,0.04138,-0.00469,-0.04627,0.04497,0.01032,-0.05074,0.08194,-0.11014,0.06538,-0.0362,-0.01766,0.01601,-0.01947,0.16371,0.0327,-0.08732,-0.00257,-0.07685,-0.06363,-0.05323,-0.0458,-0.01099,-0.04405,0.01509,-0.02072,0.10708,0.08312,0.00295,-0.03284,-0.0101,0.01437,-0.05384,0.12211,-0.04805,0.00884,-0.08003,-0.06936,-0.04812,0.04667,-0.08304,0.00747,0.13004,-0.08612,0.03744,0.04834,-0.0223,-0.05245,0.00113,0.00964,-0.16718,-0.00928,-0.14694,0.051,-0.10534,-0.00748,0.03776,0.08985,-0.0143,-0.01495,-0.10408,-0.10623,-0.09007,-0.04873,-0.01666,-0.06585,-0.06262,-0.11827,-0.03264,-0.09502,0.02131,0.10876,0.0132,0.13207,-0.03774,-0.06992,-0.04459,-0.01009,0.00493,0.0598,-0.11749,-0.08344,0.09279]},{"domain":"statistics","key":"sample_size_proportion","name":"Sample size to estimate a proportion","package":"statistics-ai999x","example":"What sample size is needed to estimate a proportion within margin of error = 0.03 at 95% confidence?","v":[0.0062,0.15391,0.0397,-0.12452,0.00893,-0.06163,0.14411,-0.01827,0.02655,-0.02499,-0.01837,-0.02009,0.1181,0.00417,-0.11687,0.04716,0.08895,0.09685,0.00146,-0.05893,-0.01884,-0.06965,-0.00089,-0.16163,-0.02,0.05778,-0.00844,-0.09447,-0.04513,0.12895,-0.02589,-0.01504,-0.02152,0.01855,0.01123,0.01756,0.00368,0.01755,-0.01587,0.111,0.07692,0.01859,-0.00039,-0.02037,0.07228,0.04457,0.00687,0.02901,0.02894,-0.03623,0.04123,-0.05522,-0.06055,0.06223,-0.06172,0.05418,-0.01477,-0.05792,0.04201,-0.07312,-0.06103,0.00202,-0.06109,-0.00424,-0.09916,0.06511,-0.03129,-0.00504,0.00967,0.01765,0.02666,0.00671,-0.04023,0.02339,-0.06778,0.08764,0.05482,0.06174,0.00514,0.01178,-0.03982,-0.05085,-0.05952,-0.00337,0.06046,0.01456,0.02246,0.03931,0.04066,-0.03155,0.10057,0.04427,0.0352,-0.0086,-0.04477,0.02055,-0.07766,0.03724,0.11295,0.09846,-0.10251,-0.00292,0.08435,-0.06317,-0.0965,0.00416,-0.00313,-0.00634,0.16354,0.07737,-0.04424,-0.10168,-0.09455,0.02718,-0.02817,-0.00994,0.02764,0.02275,0.049,0.01733,0.09608,0.08033,0.0128,-0.00167,0.06619,0.09988,-0.05934,-0.09385,0.08547,-0.02462,0.07796,-0.00172,-0.02858,-0.06549,-0.02561,-0.03397,0.07023,0.07379,-0.03467,-0.01151,0.00085,0.02067,0.05532,-0.03587,0.01005,-0.01274,-0.03095,-0.03993,-0.10984,0.01015,0.12955,-0.05102,0.06959,0.03734,0.1222,0.02329,0.05917,0.07128,0.08306,0.00013,-0.02213,0.0466,-0.09407,0.05042,-0.04784,-0.05494,0.06004,0.01189,-0.01153,0.0164,-0.09125,-0.04751,-0.09782,-0.05307,0.06356,0.02006,-0.04341,0.00057,0.04939,-0.07201,0.07143,-0.1268,0.11817,-0.03451,0.01231,-0.03915,-0.00368,0.14182,0.00309,-0.04523,-0.01549,-0.07279,-0.03459,-0.00628,-0.10629,-0.0191,-0.04153,-0.01305,0.01892,0.06399,0.11669,-0.00658,-0.04467,0.018,-0.00575,-0.04084,0.10558,-0.05078,0.03533,-0.03066,-0.05819,-0.12084,0.03511,-0.04776,0.019,0.15929,-0.0188,0.06532,0.02252,-0.01985,-0.02522,0.03443,0.02193,-0.09392,-0.03637,-0.11156,0.03363,-0.09203,0.02578,-0.01595,0.09463,0.02177,0.02031,-0.05912,-0.12182,-0.08641,-0.07637,-0.04888,-0.0429,-0.09131,-0.06828,-0.08585,-0.07475,0.03106,0.12253,-0.00967,0.1488,0.00217,-0.08925,-0.01887,-0.02927,-0.0162,0.09302,-0.06652,0.01691,0.0898]},{"domain":"statistics","key":"sample_size_two_means","name":"Sample size per group to compare two means (z-test power)","package":"statistics-ai999x","example":"What sample size per group is needed for two groups with effect size d = 0.5, alpha = 0.05 and power = 0.8, two-sided?","v":[-0.02693,-0.01601,0.04678,-0.08152,-0.02548,0.01898,-0.05822,-0.01248,0.00738,0.0463,-0.00226,0.0201,0.0434,-0.05228,-0.09319,-0.0578,0.08531,0.10148,0.0679,0.00456,-0.01206,0.03901,0.05976,-0.02622,-0.06416,0.0396,0.05107,0.0147,-0.02804,0.05364,-0.15237,-0.05408,-0.09723,-0.03194,-0.01712,0.04636,-0.0548,0.08701,0.0711,0.04054,0.09067,0.01206,-0.04106,-0.0711,0.01129,0.0526,0.0017,-0.02382,0.08509,-0.09263,0.07594,0.03262,0.06991,0.09398,-0.03796,-0.0213,-0.02702,0.0446,-0.06595,0.0438,-0.06291,0.00778,0.01262,-0.05594,0.02393,0.09412,-0.01608,0.02626,0.03763,-0.00971,-0.02459,0.07256,0.01201,0.04508,-0.0561,0.0141,-0.06763,-0.00993,0.10813,0.09175,-0.03493,0.026,-0.01304,0.04518,-0.11078,0.0752,0.06153,-0.0132,-0.00359,0.00223,-0.05846,-0.00595,0.09923,-0.05257,0.07072,-0.06754,-0.09964,0.07505,-0.01076,-0.11497,-0.00846,0.06855,0.11055,-0.08302,0.00448,0.04722,-0.0097,-0.01917,0.09305,-0.00704,-0.05662,0.06733,-0.04011,-0.00885,-0.10084,-0.12213,0.05371,0.02037,-0.02174,-0.09865,-0.02871,0.08445,0.02382,0.03954,0.00091,0.02822,-0.10093,-0.02198,0.0739,0.01408,0.0098,0.08477,-0.0523,0.02828,0.04381,-0.06487,0.03001,-0.02619,-0.03358,-0.07434,0.01528,0.07188,-0.00988,0.11052,0.14123,0.03591,-0.05292,-0.10783,-0.01955,0.02809,0.06119,0.11217,-0.05949,0.15406,-0.03178,-0.01375,0.11466,0.05344,0.05108,0.04142,0.04431,0.02051,-0.03992,0.06628,-0.16041,0.01656,-0.00814,0.09084,-0.00714,-0.01781,-0.01648,-0.07223,-0.10277,-0.02583,-0.00206,-0.16263,-0.01308,0.13129,-0.12153,-0.10758,-0.00105,-0.03942,-0.02146,-0.03831,-0.02423,0.04271,-0.02464,0.09477,-0.04701,-0.04636,-0.03958,0.03255,-0.05078,-0.07401,-0.04108,0.00305,-0.02276,-0.12278,-0.03986,0.08286,-0.03743,-0.04829,-0.02325,-0.11838,0.04248,0.06517,0.04181,-0.02466,-0.03054,-0.1366,-0.10257,-0.0062,0.05175,-0.02739,-0.01233,0.07137,-0.13118,-0.03239,0.06996,0.01782,0.08609,-0.07755,-0.03437,-0.14882,0.04,-0.06099,0.10324,-0.06413,0.04474,0.03858,-0.02615,0.04778,0.00863,-0.12496,-0.11098,-0.00723,0.03325,-0.01798,0.09829,-0.00273,-0.01724,0.02664,0.00112,0.04005,0.08769,0.08027,0.00646,0.0204,0.02558,-0.00826,-0.06019,0.02316,0.10459,-0.01454,0.00526,0.04063]},{"domain":"statistics","key":"sample_standard_deviation","name":"Sample 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9].","v":[-0.02079,-0.00461,-0.02467,0.03379,0.01381,0.01147,-0.06673,0.02659,-0.06518,-0.16695,0.01705,-0.02074,-0.04885,-0.01736,0.04352,0.02621,0.0069,0.04911,-0.13059,0.00453,-0.02617,-0.00205,-0.0659,-0.02613,0.00694,0.13124,0.06037,-0.09191,-0.04562,-0.00998,-0.0329,0.01884,-0.01288,0.02424,0.06694,-0.11295,-0.06204,0.07139,-0.0078,-0.1215,-0.03118,0.04661,-0.07691,0.08926,0.04185,0.04642,-0.10268,0.03656,0.09641,0.04614,0.03014,-0.03344,0.05371,0.0582,-0.04253,-0.02084,0.11258,-0.07608,-0.03616,-0.03136,-0.05263,0.07711,-0.06218,0.11725,0.08477,0.08273,-0.02913,0.04736,0.0142,0.10131,-0.06363,0.07114,-0.05731,0.02559,0.02051,0.03378,-0.01462,0.03888,0.0517,-0.02573,-0.01145,0.03662,-0.01427,0.06632,0.03791,0.1656,-0.0722,-0.00118,-0.01635,0.06297,0.06737,-0.03387,-0.01566,-0.02536,-0.05303,-0.03225,-0.05907,0.03987,-0.06857,0.02672,-0.04552,0.1623,-0.02287,-0.12971,0.09551,-0.01361,-0.08061,-0.05137,0.0965,-0.08664,0.09685,-0.00273,-0.09203,-0.02186,-0.04838,-0.07104,0.09166,-0.01554,0.03659,0.02038,0.06889,0.14872,0.02222,-0.01401,7e-05,0.02622,0.04375,0.04277,0.09631,-0.00483,0.0,0.04739,-0.04904,0.00442,0.0571,0.04229,-0.0072,-0.01371,0.04756,0.13352,-0.06857,0.11761,-0.03317,0.04567,-0.05552,-0.0227,-0.09501,0.0421,0.12357,-0.11521,-0.04545,0.05128,-0.08625,-0.02089,-0.05009,0.1207,0.06502,0.0325,-0.04196,0.06622,-0.06473,0.11885,-0.01966,0.02757,-0.02908,-0.08417,-0.00405,-0.00819,-0.02035,-0.05867,0.00767,-0.09187,-0.02156,-0.00149,-0.09624,-0.16825,-0.07214,-0.03174,-0.15025,0.01218,0.03773,0.11383,0.0309,0.05536,-0.01412,0.06774,0.00756,0.03762,0.06281,0.02903,-0.13883,-0.03178,-0.03937,-0.01672,0.01784,-0.04529,0.06631,-0.01232,-0.12366,0.08891,0.0136,0.00822,-0.09333,-0.00667,0.02202,0.072,-0.00164,-0.00907,-0.05312,-0.00129,0.03757,0.05019,-0.0549,-0.10544,-0.0518,-0.10563,0.08124,-0.05125,0.04942,-0.04185,-0.02722,0.03683,0.03644,-0.08833,0.05178,0.01045,0.08537,0.00085,0.02234,0.00306,0.01433,0.00413,-0.03095,0.05904,0.02303,0.04789,-0.01295,0.11161,-0.00594,-0.04893,0.03681,-0.04995,-0.02461,0.03148,0.04146,-0.0806,-0.05166,0.03679,0.02648,-0.14499,0.03453,0.02611,-0.02589,-0.03687,-0.06826,-0.04299]},{"domain":"statistics","key":"sample_variance","name":"Sample variance","package":"statistics-ai999x","example":"Find the sample variance of [2, 4, 4, 4, 5, 5, 7, 9].","v":[-0.04252,0.0069,-0.00042,0.00345,0.02358,-0.00859,-0.01302,0.00018,-0.04271,-0.20006,0.04704,-0.06319,-0.05731,-0.05109,0.05751,-0.01329,-0.0002,0.01211,-0.1539,0.02339,-0.00313,-0.01111,-0.05774,-0.044,0.02358,0.14949,0.03898,-0.11403,-0.03844,0.01578,-0.03877,-0.02514,-0.04344,0.03828,0.10326,-0.09291,-0.08049,0.05574,0.00136,-0.07162,0.00297,0.07561,-0.10361,0.05508,0.06619,0.02251,-0.07306,0.03213,0.07929,0.07255,0.04927,-0.01303,0.0512,0.05926,-0.07311,0.02018,0.12879,-0.07872,-0.04472,-0.04079,0.01583,0.0968,-0.10325,0.12598,0.03612,0.10097,-0.0267,0.00879,-0.01349,0.04545,-0.05324,0.07919,0.00771,0.01101,-0.00894,0.06032,-0.04081,0.06482,0.05518,-0.064,0.04321,0.02188,-0.04837,0.05071,0.00818,0.11609,-0.08009,0.03234,-0.05145,0.0932,0.03834,0.00291,-0.01522,-0.06149,-0.03585,-0.03308,-0.0134,0.03713,-0.01304,0.04411,-0.03569,0.18248,-0.06223,-0.14581,0.06426,-0.03366,-0.1056,-0.04891,0.10022,-0.06601,0.11248,-0.02226,-0.12483,0.01244,-0.06154,-0.06324,0.0794,-0.06289,0.06373,0.05146,0.06185,0.12353,-0.0074,-0.0262,0.06685,0.08945,0.00712,0.04014,0.07811,0.05661,0.00618,0.06304,-0.02775,0.00859,-0.00128,0.02356,-0.01108,-0.03392,0.03688,0.1727,-0.08515,0.09882,0.01583,0.05759,-0.04749,-0.08225,-0.08214,0.03721,0.1263,-0.07319,-0.03267,0.0432,-0.04699,-0.03956,-0.02961,0.14974,0.0363,0.04529,-0.03116,0.07145,-0.06495,0.06938,-0.01249,-0.01943,-0.00501,-0.08802,0.02474,0.00303,-0.0047,-0.04725,-0.02813,-0.11397,-0.05764,-0.02288,-0.08451,-0.11726,-0.05851,0.02285,-0.11418,-0.04055,0.01541,0.05588,0.03726,0.02773,-0.00695,0.03844,-0.00479,0.02126,0.06868,0.05839,-0.15838,-0.02316,-0.03886,-0.01215,0.02805,-0.03745,0.02669,-0.04765,-0.09236,0.04868,0.03662,-0.0379,-0.12028,-0.02561,0.02241,0.05958,0.03411,-0.05456,-0.06782,0.00796,0.00715,0.01349,-0.08004,-0.06643,0.00143,-0.11697,0.11213,-0.07148,0.02515,-0.03035,-0.04144,0.03899,0.05132,-0.03351,0.0395,-0.01153,0.06582,0.03738,0.02684,0.04336,0.03645,0.01197,-0.04204,0.04574,-0.03003,0.04814,-0.03327,0.10528,0.01702,-0.06503,0.04592,-0.07656,0.02071,0.0281,0.0877,-0.06155,-0.02736,0.08124,0.04989,-0.07724,0.0128,-0.02561,-0.03185,-0.02301,-0.03228,-0.03118]},{"domain":"statistics","key":"series_system_reliability","name":"Reliability of a series system","package":"statistics-ai999x","example":"Find the reliability of a series system with component reliabilities [0.95, 0.9, 0.98].","v":[-0.01065,-0.10177,0.01741,-0.02458,-0.04914,-0.04387,0.04823,0.07627,-0.03126,0.02528,-0.00228,0.04316,-0.10991,-0.09809,-0.0272,-0.01983,-0.06355,-0.09963,0.01621,-0.05511,-0.04222,0.08502,-0.00274,0.11691,-0.01738,0.09536,0.04492,0.03759,0.01229,-0.01425,-0.02519,0.00261,-0.07193,-0.02469,0.00463,-0.04709,0.0554,-0.0021,-0.04267,0.08327,0.08022,0.13997,-0.02694,-0.06916,0.00427,-0.01344,0.10659,-0.00367,0.00475,-0.02539,-0.09248,-0.02182,0.07332,-0.02132,-0.06546,0.04265,0.01566,-0.02372,-0.04898,0.08292,-0.04142,-0.02062,0.08204,-0.06279,0.03722,0.04488,-0.0052,0.02466,0.01086,0.06749,0.07267,-0.00219,0.09932,-0.05988,-0.04186,0.0177,-0.03236,0.03943,0.01109,-0.02787,0.09893,0.06948,0.03033,0.00201,0.05138,-0.06834,-0.08982,-0.03584,0.00279,-0.01485,-0.02624,0.04944,-0.05974,0.03848,0.03437,-0.03862,0.00437,0.0896,0.01195,0.02458,-0.019,0.00137,-0.04171,0.04155,-0.01297,-0.00687,-0.05421,-0.03565,-0.07127,0.05933,0.09178,-0.02083,-0.03354,0.02979,0.03561,0.01185,-0.10757,-0.15387,0.07572,-0.03746,-0.07071,-0.01319,0.02838,-0.05898,0.0381,0.06488,0.09325,-0.06762,0.06831,-0.02041,-0.04206,0.01417,-0.10358,-0.04491,-0.01023,0.00138,-0.03028,0.05146,-0.01445,0.08127,-0.15911,-0.02184,-0.11567,0.13745,-0.03172,-0.08567,0.0825,0.00659,0.07029,0.01654,-0.0972,0.00047,0.00517,-0.02136,0.09157,-0.00538,-0.03861,-0.0549,-0.07367,0.00373,0.11095,-0.02015,-0.05324,-0.16395,0.20427,0.01636,-0.06441,0.13001,0.05906,0.02667,0.00157,0.02854,-0.08365,0.00762,-0.07209,-0.03003,0.00262,0.03117,0.02574,0.06524,0.0214,-0.00999,-0.05,0.08825,0.01652,0.05995,0.01506,0.0182,-0.0471,0.09197,-0.19549,-0.02741,0.02345,0.03603,-0.02953,-0.01855,-0.00682,0.00071,0.04453,0.02308,-0.01697,-0.06296,0.08542,-0.00067,-0.11069,-0.04367,0.07163,0.04777,-0.03641,-0.00923,0.12321,-0.06373,-0.02676,-0.03849,-0.01107,-0.00722,0.05139,-0.06361,-0.09748,0.03218,0.06585,0.02011,-0.02663,-0.00145,0.02468,0.14525,0.13766,0.02839,0.05258,-0.12816,-0.05441,-0.02157,-0.06403,0.11092,-0.11048,-0.00931,-0.00947,0.07353,-0.04483,-0.10736,0.04246,0.07809,-0.02504,-0.03527,-0.03711,0.18561,0.03837,0.11636,-0.06098,0.0353,-0.00263,-0.022,0.04282,-0.01491,-0.06714,0.05627]},{"domain":"statistics","key":"sign_test","name":"Sign test","package":"statistics-ai999x","example":"Perform a sign test on before [125, 115, 130, 140, 141, 115, 140, 125] and after [110, 122, 125, 120, 140, 124, 123, 137], 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linear regression (least squares line)","package":"statistics-ai999x","example":"Find the least squares regression line for x = [1, 2, 3, 4, 5] and y = [2.2, 4.1, 6.1, 7.9, 10.2].","v":[-0.00135,-0.02756,-0.02874,0.07947,-0.02693,0.00374,-0.05338,-0.06292,0.10532,-0.15672,0.01582,-0.02911,0.07176,-0.03879,-0.05682,0.10688,0.03548,-0.08342,-0.00763,-0.07308,-0.01347,0.00236,0.05975,0.00063,-0.06563,0.05485,0.0078,-0.1536,-0.09642,-0.00259,-0.02642,-0.1158,0.02771,0.02962,0.02513,0.01462,-0.00101,0.02904,-0.11012,0.04019,-0.00848,0.0561,-0.06375,0.02386,-0.09497,0.03815,0.02481,0.12319,0.00997,0.02444,-0.00303,0.16076,-0.02505,0.02281,0.0713,-0.01591,0.12333,0.00147,-0.00367,0.10678,0.00029,0.00237,0.01417,0.00331,0.00631,-0.03677,-0.05256,0.02345,0.01757,-0.02182,0.07759,-0.09351,-0.01856,-0.12278,-0.00063,0.0774,0.07277,-0.05308,0.06914,-0.01948,-0.00201,-0.02452,-0.00124,-0.00123,0.08452,0.00168,-0.11235,0.09545,0.02459,0.03547,0.0248,-0.11558,0.08841,-0.05245,-0.02711,-0.06206,-0.0195,-0.00174,-0.07738,0.05888,-0.02769,-0.03524,-0.0021,-0.01023,-0.11017,-0.02339,0.07638,0.06026,0.17459,0.0318,-0.11758,0.01799,-0.09838,-0.05145,-0.00538,0.05688,0.03286,0.02156,0.05647,-0.10946,0.01924,0.02742,0.0004,0.012,-0.04923,0.00877,0.00078,0.05588,0.0835,0.01778,0.02763,0.06084,-0.00581,0.01802,0.03015,-0.00738,-0.00333,-0.02864,-0.00403,0.05087,-0.08998,-0.01841,0.05915,0.08212,0.04756,-0.01504,-0.0753,0.06117,0.11051,-0.05207,-0.0427,-0.00337,-0.03386,-0.01674,0.00972,-0.02059,0.04947,0.04682,0.05328,0.16445,0.09617,0.02912,-0.02174,-0.06081,-0.02342,0.0211,-0.11164,-0.02119,-0.08425,0.12315,0.00589,0.03787,-0.01732,-0.00436,-0.00411,-0.1025,0.00206,-0.05065,-0.02271,-0.04007,0.00365,0.03438,-0.01177,-0.06423,0.00713,0.01606,-0.1066,0.01447,-0.05854,0.03321,0.02004,0.07206,0.02444,-0.00487,0.01642,-0.06479,0.05537,0.06798,0.06322,-0.01898,0.11285,0.07513,-0.02553,0.00675,0.06317,0.03775,-0.09377,0.02997,0.0347,0.07307,-0.11147,-0.11432,0.01561,-0.05289,-0.0659,0.04154,0.04685,-0.0047,-0.02936,0.14349,0.01923,0.03228,0.04426,0.02292,-0.0185,0.05747,0.14712,0.08307,-0.07272,0.00766,-0.07509,-0.08141,-0.10577,-0.12958,-0.02493,-0.08879,0.00133,0.09636,-0.02597,-0.01177,-0.00664,-0.0477,0.07619,-0.05839,-0.06436,-0.09972,0.1518,0.07202,-0.10951,-0.03904,-0.06962,-0.06183,-0.08657,-0.04444,-0.10912,0.01617]},{"domain":"statistics","key":"skewness_kurtosis","name":"Skewness 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20].","v":[0.1282,-0.0395,0.04953,0.01018,0.09967,0.03308,-0.0791,0.00668,0.00902,-0.04904,-0.15063,0.00923,-0.06035,0.01316,0.01565,-0.00493,-0.01654,0.07771,-0.04828,-0.01201,-0.02637,-0.0182,-0.09718,-0.02509,0.01902,0.01095,0.06944,-0.13343,-0.01033,-0.0685,-0.00969,-0.02416,0.06801,-0.01789,0.04327,-0.06847,-0.03199,-0.00246,-0.04362,-0.07928,-0.1351,0.01806,-0.10605,0.18792,0.00587,0.07793,-0.08022,0.00775,0.09117,-0.02064,-0.03508,0.02021,0.07761,-0.04972,-0.04767,-0.0653,0.08548,-0.13796,-0.07499,-0.0471,0.02371,-0.01966,0.00872,-0.04309,-0.03833,-0.04557,0.03411,0.01558,0.00221,0.08284,0.02701,-0.03316,-0.10081,-0.06542,0.04781,0.07584,0.1333,0.04165,0.13513,-0.02864,-0.01353,0.05842,-0.07302,0.06286,0.02569,0.12956,-0.01866,-0.03266,0.09944,-0.01461,-0.0186,0.0292,0.0154,-0.00056,-0.05347,-0.00275,-0.10457,-0.04588,0.00666,-0.02833,0.01582,0.09768,0.01445,0.01862,0.04621,-0.12997,-0.06604,-0.02838,0.04391,-0.03503,0.12745,0.02917,0.07806,0.06731,0.0084,0.02074,0.02345,0.01269,0.04508,0.05113,0.05125,0.11825,-0.05253,-0.05381,-0.01333,-0.05307,0.10403,-0.05926,0.03432,0.04494,0.04035,-0.05017,-0.0905,-0.09354,-0.01116,0.04191,-0.09792,0.0243,0.02255,0.08437,0.08821,-0.05504,-0.02266,0.03351,-0.01209,0.08705,-0.09491,0.07987,0.13514,-0.07616,-0.00318,0.03545,-0.12109,-0.03505,-0.0474,0.12299,0.01118,-0.00542,0.06606,0.00457,0.03087,-0.10845,-0.00586,0.07967,-0.07304,0.0526,0.00435,0.04577,0.04649,0.07819,0.02327,-0.01093,0.06341,0.08106,-0.09168,-0.0906,-0.06724,-0.07957,-0.03018,-0.03337,0.06417,-0.02875,0.10926,-0.00145,0.01301,-0.05027,0.01526,0.04438,0.01336,0.06527,0.04663,-0.02468,-0.0504,-0.06595,-0.01279,0.04305,0.02682,0.08639,0.00906,-0.01389,0.00658,0.00357,-0.03096,0.00856,-0.0108,0.05079,0.08291,-0.02908,0.11663,0.11034,0.02612,0.03135,-0.01224,-0.06095,0.04927,-0.11102,-0.03688,-0.00459,0.115,-0.09143,-0.01129,0.04268,0.06148,-0.04605,-0.0725,0.03956,-0.0781,-0.0602,-2e-05,0.01288,-0.02278,0.06273,0.08562,-0.03453,0.00096,0.02667,-0.05896,0.08211,-0.04786,0.01926,-0.00103,-0.0309,0.09418,0.0757,-0.0609,-0.05883,0.00523,-0.01382,0.05598,-0.17571,-0.04632,-0.00032,0.04832,0.05619,-0.11006,-0.04505]},{"domain":"statistics","key":"spearman_correlation","name":"Spearman rank correlation","package":"statistics-ai999x","example":"Find the Spearman rank correlation of x = [10, 20, 30, 40, 50] and y = [12, 25, 22, 41, 48].","v":[0.02826,-0.12387,-0.03712,0.08976,-0.06896,0.00646,-0.03915,-0.0534,0.12955,-0.10637,-0.03089,0.00728,0.0397,-0.02355,0.05964,0.05759,-0.03953,-0.06139,-0.06187,-0.09078,0.02865,-0.05996,-0.0279,-0.0576,-0.04661,0.08253,0.00052,-0.09662,-0.06639,-0.0645,-0.07139,-0.07249,0.00365,-0.02329,-0.0263,0.0583,-0.01231,0.09231,0.01842,-0.03574,-0.01333,0.06172,-0.03358,0.01919,-0.05359,-0.02986,0.08805,0.05454,0.0311,0.027,-0.04159,0.17355,-0.04585,0.05637,0.03567,-0.08645,0.08799,0.00516,0.03692,0.04524,0.02501,0.00867,0.07327,0.00672,-0.06549,-0.08142,-0.10185,0.09099,0.05171,-0.00421,0.01283,-0.05156,0.03556,-0.00694,-0.00753,0.07271,0.03673,-0.0404,0.02461,-0.03006,-0.00781,0.00625,0.00599,-0.01285,0.08009,0.03514,-0.04262,0.1127,-0.02602,0.04482,-0.02597,-0.08739,-0.01055,-0.04139,-0.05987,-0.01183,-0.01787,0.06596,-0.06482,0.08489,0.00871,-0.10536,-0.01302,0.04503,-0.0446,0.0031,-0.02442,0.12722,0.08906,0.01441,-0.1779,-0.01079,-0.14795,0.01104,-0.04553,0.02947,0.12834,0.01381,0.04041,-0.09708,0.10469,0.07628,-0.00328,0.085,-0.07989,-0.0048,-0.00792,0.01559,0.04534,0.02892,0.08183,0.10466,-0.02648,0.01928,-0.03307,0.0171,0.03792,-0.02345,-0.00509,0.08259,-0.12922,0.0164,-0.01578,0.06497,0.04662,-0.07729,-0.02634,0.07237,0.09124,-0.02086,-0.00382,-0.04535,0.03461,-0.01982,-0.0355,-0.01751,0.10401,-0.00907,-0.02474,0.08275,0.0035,-0.04859,-0.05689,-0.0691,0.00155,0.00293,-0.08464,0.03036,0.04905,0.17426,-0.01493,-0.02934,-0.04597,-0.1094,0.0138,-0.06802,0.07402,0.01124,0.04153,-0.02612,0.0546,0.03421,0.01835,-0.0588,0.05864,0.07838,-0.06946,-0.01381,0.00975,0.09476,-0.03342,0.02864,0.01458,0.03686,-0.03948,-0.0329,0.00199,-0.00963,0.06488,-0.1411,0.08212,0.04043,0.01837,0.06903,0.03088,0.01148,-0.13742,-0.02639,0.01914,0.0667,-0.04953,-0.08772,-0.09411,0.00666,-0.07255,-0.00121,-0.04122,-0.02472,-0.09123,0.12921,0.09137,-0.03074,0.07203,-0.00053,0.02163,0.00518,0.15018,0.03186,-0.05882,-0.04382,-0.08238,0.01197,-0.05153,-0.08573,-0.04516,-0.07002,-0.04884,0.12083,0.02338,0.05628,0.01948,0.00347,0.02918,-0.0585,-0.08601,-0.03742,0.05232,0.17061,-0.05107,0.10387,-0.07192,0.05039,-0.09892,-0.03977,-0.08387,-0.05061]},{"domain":"statistics","key":"standard_error_of_mean","name":"Standard error of the mean","package":"statistics-ai999x","example":"Find the standard error of the mean of [12, 15, 11, 18, 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9.7]].","v":[0.04282,-0.0189,0.03231,-0.01069,-0.13494,0.00554,-0.01936,-0.09249,0.04032,0.01146,0.06896,0.01921,-0.02351,0.09145,0.0586,-0.00223,-0.05056,-0.03252,0.02723,-0.08253,-0.02182,-0.0299,-0.08417,-0.07264,0.0685,0.05205,0.01414,-0.13757,-0.06272,-0.0476,-0.00972,-0.0163,-0.06875,-0.03132,0.02457,0.03439,0.00867,0.10513,-0.03027,0.12704,-0.03139,0.07694,-0.01248,0.09125,0.04206,-0.10967,0.0303,0.11215,0.01919,-0.0334,0.09046,0.02782,0.06314,-0.00469,0.09991,0.03542,0.09194,0.02492,0.02331,0.06438,-0.00407,0.03677,-0.0066,-0.07931,0.16048,0.01444,-0.02822,-0.01193,0.01414,0.07,-0.02159,0.09275,0.02034,0.07917,-0.09307,0.10716,-0.07399,0.09971,0.08346,-0.02983,-0.01174,-0.06508,-0.04322,-0.00333,0.03129,0.01814,0.02405,-0.02836,-0.09623,0.02211,-0.06888,0.2244,0.02709,0.03503,0.00317,-0.06502,-0.04524,-0.03091,-0.00356,0.02073,-0.05624,0.02372,0.02057,0.0074,0.11585,0.01782,-0.0678,-0.10758,0.08139,0.00085,-0.00341,0.0037,0.0231,-0.0217,-0.09831,0.07798,0.07982,0.03496,-0.08438,-0.0411,-0.18372,-0.14258,0.00588,0.07147,-0.034,-0.04695,0.07625,-0.00865,0.00842,0.10944,0.04483,-0.0859,-0.03634,0.0061,-0.01757,-0.01534,0.14017,0.03835,0.06973,0.00605,-0.14187,-0.00349,0.08969,0.00162,-0.10838,0.02871,-0.09825,0.068,0.0128,0.0306,0.01578,-0.12555,0.11799,0.0005,-0.03202,-0.08375,0.08136,0.02112,-0.05678,0.02481,-0.01068,0.06452,0.11145,-0.07892,-0.10861,0.00998,-8e-05,-0.10271,0.08007,0.05682,0.03753,-0.03213,0.04582,-0.03235,-0.09868,-0.0998,0.04749,-0.02411,-0.08918,0.08234,-0.10585,0.07917,0.02615,0.03977,0.06246,-0.01993,-0.03673,0.06874,0.01118,-0.06214,-0.02482,-0.03633,0.02941,-0.10568,-0.07372,-0.02185,0.04354,-0.02778,0.01221,-0.0,-0.02254,0.02806,-0.14671,-0.15007,-0.0128,-0.02525,-0.08741,0.03575,-0.05324,-0.04261,-0.11185,0.01889,-0.04922,0.09221,-0.00014,0.03771,-0.05144,0.05623,-0.00854,-0.00812,0.02839,-0.07124,-0.02104,0.01303,0.02413,0.00586,0.02985,-0.02884,-0.02287,-0.04762,0.05256,0.02195,-0.06772,0.04974,0.05788,-0.00795,0.00504,-0.02698,0.00981,0.0772,-0.0257,-0.03148,0.00538,-0.04914,0.01457,-0.04014,0.06077,-0.00771,0.02819,-0.00422,0.00372,0.04566,-0.03188,0.05883,-0.02554,0.00091]},{"domain":"statistics","key":"xbar_s_chart","name":"X-bar 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9.7]].","v":[0.04233,0.0088,0.0202,-0.01971,-0.13398,0.02509,-0.02482,-0.08084,0.02164,0.01548,0.05356,0.02433,-0.04343,0.08958,0.04485,0.00531,-0.05628,-0.02199,0.05279,-0.08532,-0.02832,-0.02929,-0.08753,-0.07731,0.05297,0.03201,0.01672,-0.12428,-0.07999,-0.01838,-0.01814,-0.01078,-0.0528,-0.00805,0.03606,0.02536,-0.00878,0.0859,-0.04646,0.11285,-0.04074,0.07748,-0.02063,0.10404,0.05659,-0.12611,0.03098,0.12619,0.02253,-0.02206,0.08671,-0.00686,0.06841,-0.01386,0.12952,0.04685,0.05989,0.03316,0.01699,0.09987,-0.00074,0.04308,0.00025,-0.07906,0.14941,0.01618,-0.03606,-0.03731,0.0364,0.05596,-0.03622,0.07823,0.02043,0.0897,-0.08534,0.09034,-0.06335,0.08766,0.07691,-0.03211,-0.03096,-0.06329,-0.02833,0.027,0.03092,0.00944,0.00823,-0.01982,-0.09543,0.02082,-0.06112,0.19459,0.01989,0.05884,0.02205,-0.09132,-0.07804,-0.03071,0.00505,-0.01732,-0.05498,0.04497,0.03565,0.00962,0.12353,0.03954,-0.04313,-0.12811,0.0739,-0.00141,0.01335,0.02145,0.02659,-0.01021,-0.08258,0.08116,0.08287,0.03589,-0.0855,-0.06052,-0.17828,-0.12043,0.02453,0.0783,-0.04225,-0.03936,0.0763,-0.01041,0.01949,0.1023,0.05339,-0.07174,-0.03075,-0.00874,0.01938,-0.01623,0.11428,0.0402,0.07948,-0.016,-0.10158,0.00261,0.09621,-0.00477,-0.07887,0.02661,-0.11582,0.08413,-0.01419,0.03438,0.0202,-0.12492,0.11113,0.02396,-0.03569,-0.10446,0.08101,0.02636,-0.07811,0.01755,-0.01467,0.07084,0.11296,-0.06359,-0.11933,0.00771,-0.01202,-0.07223,0.0649,0.04041,0.05922,-0.00529,0.03119,-0.02441,-0.10149,-0.11381,0.0379,-0.02494,-0.09791,0.08827,-0.10233,0.09043,0.02251,0.05709,0.06821,-0.01889,-0.01548,0.05751,-0.00299,-0.06779,-0.02068,-0.02102,0.01884,-0.11067,-0.07498,-0.03249,0.06541,-0.02877,0.01995,0.01388,-0.03105,0.0538,-0.15796,-0.16322,-0.01447,-0.01752,-0.08423,0.01276,-0.0495,-0.04429,-0.11117,0.04068,-0.03845,0.05802,0.00073,0.04734,-0.07906,0.06113,-0.00919,-0.00116,0.00507,-0.09144,-0.03065,0.01041,0.01865,0.00851,0.03016,-0.03778,-0.01535,-0.0313,0.04891,0.01845,-0.06584,0.02178,0.07175,-0.02507,0.03423,-0.0396,0.04212,0.0962,-0.03246,-0.02189,-0.00685,-0.02367,0.01831,-0.06193,0.05944,-0.03285,0.03689,-0.02981,0.01783,0.04444,-0.03059,0.04537,-0.02254,0.01026]},{"domain":"statistics","key":"z_critical_value","name":"Critical 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12].","v":[0.0633,0.00139,0.01364,-0.06875,-0.00573,0.07319,0.04685,0.05463,-0.02993,-0.05841,-0.00897,0.01536,-0.11904,0.10829,0.10797,-0.09121,0.06752,-0.00064,0.05128,-0.05814,-0.02175,0.0733,-0.10551,0.0099,-0.00421,-0.08592,-0.03733,0.10308,0.03526,0.02355,0.09852,-0.04251,0.09883,-0.01243,0.01297,-0.06627,0.03797,0.03508,-0.0434,0.01856,-0.07367,-0.02413,-0.02814,-0.02784,-0.04128,-0.1098,0.07027,0.03536,-0.15847,-0.05324,0.0593,0.15123,-0.00666,-0.00182,-0.00767,-0.06515,0.1196,-0.07066,0.02154,0.0049,-0.03769,0.04523,-0.0732,0.06145,0.02734,-0.04107,0.09915,0.01039,0.0862,-0.10736,-0.04465,0.02864,-0.08184,-0.14127,0.03435,0.02497,0.03647,-0.02009,-0.02834,-0.04779,0.02157,0.01894,-0.00486,0.022,0.08607,-0.03099,-0.02159,-0.03486,0.01766,-0.0618,-0.07059,0.0096,0.03319,-0.00145,-0.06394,0.04283,-0.07228,-0.11172,-0.01801,-0.07911,0.01543,-0.02226,-0.01455,0.02336,-0.02003,-0.02012,-0.03973,0.05665,0.20721,-0.00285,0.10563,0.09432,-0.0243,-0.00728,0.09238,-0.00907,-0.02928,-0.06435,0.00188,0.01322,-0.04002,-0.04632,0.06563,-0.02588,-0.0241,0.03695,-0.01904,-0.00582,0.03122,-0.05442,-0.07573,-0.04224,0.06757,-0.08836,-0.01403,0.09188,-0.06591,-0.03487,0.08023,-0.01301,0.06292,-0.0687,0.03045,-0.11858,0.18642,0.01679,-0.05789,0.01716,-0.03408,0.01904,-0.0342,-0.03997,-0.00518,-0.06144,-0.0471,-0.02406,0.00746,0.11385,0.00199,0.13522,-0.05493,0.10599,0.008,-0.02828,0.09489,-0.01151,0.03578,0.17319,-0.04631,0.01293,0.10818,0.03675,5e-05,0.0152,-0.00516,0.02247,-0.05991,0.02559,0.00777,0.18432,0.01229,-0.00752,-0.04782,-0.03087,0.10005,-0.07149,0.00192,-0.02942,-0.03768,0.03911,0.01405,-0.06928,-0.04874,-0.06334,0.02685,-0.01518,0.0568,0.06691,0.05539,0.03743,0.0345,-0.02251,-0.00261,0.06149,0.0573,-0.06577,-0.02185,0.00093,-0.01609,0.05626,0.06638,0.03841,-0.00853,-0.01869,0.02842,-0.00175,-0.05918,0.0417,0.06841,0.09404,-0.0602,-0.06606,0.00383,-0.04399,-0.0038,0.14288,0.06792,0.01589,-0.01348,-0.0914,-0.0255,-0.10266,0.01207,0.06121,-0.01809,-0.03229,0.07767,-0.07462,-0.0048,-0.05893,-0.05498,-0.0051,-0.13819,0.01181,0.08234,-0.07274,0.02995,0.01709,-0.14416,0.15526,0.01616,-0.07808,-0.03188,-0.05491,0.00764,0.04083]},{"domain":"time_series","key":"ar_least_squares","name":"AR(p) 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12].","v":[-0.02538,0.05041,-0.02429,-0.07369,-0.03013,0.02174,0.04666,-0.01249,0.00862,-0.10085,-0.03451,-0.03305,-0.07547,0.10088,0.07556,-0.1064,0.07153,0.01121,0.02188,-0.02647,-0.04577,0.01232,-0.13416,-0.0884,-0.04189,-0.02211,-0.05158,0.10494,0.05431,0.09858,0.0382,-0.07729,0.12441,0.05376,0.12582,-0.0682,0.01056,0.01383,-0.08829,-0.00335,0.03352,-0.01484,-0.10001,-0.06524,-0.03309,-0.05429,0.10365,0.06496,-0.1433,-0.05135,0.03019,0.08083,0.02914,0.01111,-0.04057,-0.08343,0.06491,-0.03304,0.05347,0.04823,0.04833,0.11949,-0.09296,0.07991,-0.04878,0.00439,0.09503,-0.05858,0.05649,-0.0512,-0.13313,0.09329,-0.00321,-0.0797,0.07136,0.0269,0.11264,-0.01228,-0.06033,-0.05256,-0.0039,0.03263,-0.11513,0.0559,0.07189,-0.02261,0.00957,0.01653,-0.00804,-0.03686,-0.09398,0.10335,0.00581,0.00283,-0.02629,-0.01889,-0.05017,-0.04388,-0.01229,-0.04482,0.00654,-0.0032,0.01819,-0.04219,0.00458,-0.02137,-0.0984,0.04278,0.06353,0.01663,0.06341,0.09684,0.00498,0.03578,0.01966,0.02265,0.01413,-0.07714,-0.03025,0.02188,-0.00964,0.06725,0.07255,0.14568,-0.04873,0.05186,-0.04645,-0.03279,0.07947,-0.0046,-0.06177,-0.03828,-0.04735,-0.04121,0.03682,0.09512,-0.06715,-0.02909,0.05765,0.09205,0.01184,0.02429,0.04146,-0.04134,0.2114,-0.01806,-0.01951,0.06545,0.0631,-0.03665,-0.03471,-0.02886,-0.06516,-0.06037,0.02273,0.001,-0.07545,0.13102,0.08893,0.16578,-0.06588,0.07314,0.02,-0.10491,0.0804,0.02809,0.0134,0.17674,-0.07022,-0.00273,0.07438,0.05866,0.03465,-0.10726,0.00513,0.03699,-0.02203,0.07522,-0.05081,0.07616,-0.06458,-0.03633,-0.05889,-0.05899,0.13141,-0.07943,-0.06755,-0.08325,-0.03866,0.0956,-0.05973,-0.03452,0.03003,0.03159,0.0622,-0.0761,0.01953,-0.02679,0.13012,-0.03945,0.00763,-0.01742,-0.01824,-0.04397,0.03362,-0.01325,0.07306,-0.00732,-0.01511,0.04886,0.04891,-0.01177,0.00093,-0.03272,0.02959,-0.05215,-0.07245,-0.0172,-0.00942,0.05992,-0.06554,-0.04941,0.01755,-0.0016,0.01862,0.06463,0.04156,-0.03321,-0.04749,-0.04429,0.00034,-0.10628,-0.00117,-0.03187,-0.04072,-0.01316,0.04539,-0.02563,0.02175,-0.06518,-0.01703,-0.08597,-0.03275,0.03422,0.05857,-0.06313,-0.00611,0.02786,-0.04956,0.08323,0.00277,-0.13987,0.04464,-0.09045,0.04851,-0.00801]},{"domain":"time_series","key":"ar_yule_walker","name":"AR(p) estimation by Yule-Walker","package":"time-series-ai999x","example":"Estimate an AR(2) model by Yule-Walker for the series [4, 6, 5, 8, 7, 9, 8, 10, 9, 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108].","v":[0.0617,0.0506,0.00452,-0.02399,0.05917,0.07191,0.0197,0.04098,-0.05808,-0.01734,0.03289,0.02937,-0.04943,0.08963,0.07671,-0.123,0.12194,0.00938,-0.02211,-0.00191,-0.04709,0.07742,-0.05806,0.04202,-0.02552,-0.07692,-0.02566,0.06228,-0.00371,0.03822,0.09033,-0.07047,0.05585,-0.00508,0.01131,-0.0289,-0.00288,0.0356,-0.01777,0.02834,-0.06677,-0.03687,-0.00969,-0.05687,-0.09161,-0.10547,0.09167,0.04726,-0.06305,0.02287,0.03638,0.15331,-0.00579,-0.00511,0.06089,-0.12953,0.20825,-0.11152,0.0266,-0.0277,-0.05467,0.08057,-0.05245,0.04995,0.09125,0.01155,0.08279,0.0265,0.03614,-0.09085,-0.00129,0.00398,-0.09203,-0.13312,-0.0343,0.06464,-0.01711,0.01194,-0.03903,-0.03646,0.03504,-0.012,0.01196,-0.01585,0.12563,-0.07588,0.01201,-0.06767,0.00328,-0.03064,-0.06575,0.01119,0.04868,0.00406,-0.00754,0.00285,-0.0206,-0.09254,-0.03552,-0.09811,-0.01514,-0.0155,0.00998,-0.01069,-0.01182,-0.05374,-0.03728,0.04884,0.1932,0.03635,0.07861,0.04516,0.01692,-0.04642,0.05179,-0.05672,-0.09408,-0.04785,0.04969,0.06137,0.00137,-0.07441,0.02259,-0.04773,-0.00945,0.01331,-0.05835,0.00956,0.00232,-0.1529,-0.0576,-0.03028,0.04818,-0.11347,-0.03773,0.02651,-0.10633,-0.08736,0.05664,-0.0219,0.00145,-0.06977,0.03858,-0.10881,0.20955,0.02751,-0.02872,-0.03021,-0.05966,0.06299,-0.00924,-0.05013,0.02896,-0.05267,-0.07219,-0.02871,0.06428,0.07513,0.02715,0.05535,0.03113,0.06823,-0.03872,-0.01419,0.11929,-0.02956,0.06792,0.16274,0.00879,-0.01311,0.02995,0.02399,0.01837,0.06277,0.00291,0.05506,-0.06807,0.03222,0.00259,0.12822,0.0562,-0.00249,-0.04256,-0.03417,0.13312,-0.05638,0.07477,-0.01932,-0.06897,-0.04119,0.06631,-0.00466,-0.07812,-0.0243,0.05311,-0.00624,0.01804,0.04222,0.01467,0.04616,0.03944,-0.02346,-0.02757,0.00115,0.00157,-0.03402,-0.0097,0.02964,-0.06146,0.06431,0.06418,0.01788,0.00929,-0.02302,0.09864,0.05467,0.0321,0.0426,0.04927,0.05905,-0.02322,-0.0742,0.0194,-0.03208,0.03334,0.10116,0.00257,0.07047,-0.04806,-0.12266,0.02658,-0.08608,0.07709,0.09417,0.01845,-0.07494,0.07373,-0.05525,-0.05071,-0.06489,-0.05086,-0.02369,-0.12014,-0.00191,0.03359,-0.07471,0.05318,0.04129,-0.1506,0.13973,-0.02066,-0.09268,0.00406,-0.02736,0.01146,0.03]},{"domain":"time_series","key":"arma11_theoretical_acf","name":"Theoretical 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Dickey-Fuller statistic","package":"time-series-ai999x","example":"Compute the augmented Dickey-Fuller statistic with 2 lags and a constant for [10.2, 10.8, 10.5, 11.3, 11.0, 11.9, 11.6, 12.4, 12.0, 12.9, 12.5, 13.4].","v":[0.06769,0.10748,0.0425,0.09523,-0.05963,-0.00374,-0.0402,-0.01428,-0.05468,0.00059,-0.02411,-0.00363,-0.07558,0.14058,0.01886,-0.04875,0.05612,-0.03859,-0.0917,-0.00964,0.03291,0.05026,-0.13424,-0.03795,0.00629,-0.04332,-0.02947,0.00546,-0.03761,0.01674,0.03315,-0.07693,0.05332,-0.00902,0.22039,-0.01117,0.00824,0.01448,-0.00942,-0.01392,0.01163,-0.0529,-0.01314,-0.1049,-0.06486,0.00632,0.05591,0.03557,-0.0666,0.06661,-0.00543,0.13412,0.10508,0.01001,0.06856,-0.21866,0.06059,-0.05409,0.00348,0.02101,-0.02519,0.04128,0.02012,0.08304,-0.01467,-0.06389,0.14016,0.02152,0.07691,0.01067,-0.07381,0.13867,-0.00961,-0.07082,0.00496,0.00943,0.1079,0.01148,-0.03739,-0.02217,0.03272,0.0645,-0.0446,0.07901,0.10262,-0.05565,-0.01291,-0.03146,-0.00963,-0.02855,-0.11695,0.12763,0.08742,4e-05,0.02139,-0.05635,-0.08309,-0.07554,0.07286,-0.07931,0.00787,-0.02469,0.02448,-0.04207,-0.0236,0.07081,-0.12457,-0.00251,0.10783,0.00607,-0.02124,0.02887,0.14053,0.05753,-0.00496,-0.00321,-0.07308,-0.03078,-0.05749,0.0451,-0.02915,0.002,-0.03116,0.05901,0.00973,0.04448,0.0339,-0.06747,0.08508,-0.07872,-0.09438,-0.08826,-0.05691,-0.08468,0.00056,0.04146,-0.05946,-0.11908,0.0528,0.04033,-0.02633,-0.00515,0.00574,-0.00865,0.19617,0.00539,-0.04516,-0.00928,0.05288,-0.00469,0.01645,-0.13816,-0.04262,-0.10924,-0.0425,-0.05236,0.00244,0.11159,0.0562,0.03509,0.02331,0.0701,-0.02405,-0.1159,0.03913,0.06457,0.00524,0.13399,0.01925,0.03882,-0.01464,0.03011,0.02256,0.03388,-0.00753,0.08226,0.01022,0.07319,0.01637,0.10553,-0.0338,-0.01102,-0.01079,0.00401,0.15306,-0.13912,-0.02266,-0.07084,-0.00832,0.04021,0.04068,0.03811,-0.03667,0.06105,0.07334,0.00872,-0.07581,-0.05976,0.0517,-0.01872,0.01868,-0.03824,-0.00809,-0.03811,0.02363,-0.02445,0.07301,0.0253,0.00467,0.01237,0.00935,-0.01359,-0.05603,-0.04257,0.06767,-0.00971,-0.00517,-0.03103,-0.07099,-0.05849,-0.02412,0.00105,0.01665,-0.03442,0.13676,-0.00535,-0.02016,0.00105,-0.1094,-0.03254,0.00769,-0.09111,0.06905,-0.06296,-0.02026,-0.08476,0.06374,0.05633,0.01879,-0.04276,0.00202,-0.01937,0.00642,-0.0512,0.05511,-0.01907,0.06419,-0.01888,-0.02845,0.05863,-0.00398,-0.122,0.0726,-0.02178,0.01788,-0.07711]},{"domain":"time_series","key":"bartlett_standard_error","name":"Bartlett standard error of a sample autocorrelation","package":"time-series-ai999x","example":"Find the Bartlett standard error of the lag 3 autocorrelation of [4, 6, 5, 8, 7, 9, 8, 10, 9, 12].","v":[0.02058,0.00345,0.04299,0.08914,-0.05974,0.02321,-0.01141,-0.00427,0.00297,0.00047,0.07691,0.05395,-0.02596,0.01922,0.08428,-0.04853,0.05693,0.03756,-0.08717,0.01601,0.04701,0.08848,-0.04135,-0.07086,0.05983,0.02605,0.05414,0.00447,-0.04898,0.02393,0.01348,-0.08143,0.05416,0.03573,0.14946,-0.07827,-0.05382,-0.0022,-0.08474,0.01574,0.08608,-0.06956,-0.05922,-0.02067,-0.03935,0.03682,0.09852,-0.01707,-0.07027,-0.03279,-0.01647,0.02573,0.06157,0.05358,0.09874,-0.15135,0.11244,0.01123,0.0831,0.08164,-0.00179,0.04178,-0.0102,0.05358,-0.06703,0.01482,0.11741,-0.00511,0.04701,-0.01862,-0.03024,0.01204,0.05167,-0.05259,0.03451,0.04088,0.08516,-0.0417,-0.0468,-0.07307,0.07688,-0.00919,-0.15333,-0.01551,0.10791,-0.01839,-0.03877,0.00921,-0.02233,-0.03542,-0.04419,0.12122,0.07429,0.02109,-0.00868,-0.06027,0.01745,-0.06217,-0.08398,0.0174,-0.0463,-0.08806,0.02493,0.02207,-0.02467,0.03847,-0.18437,0.01595,0.00016,0.01294,-0.075,0.03098,0.10396,-0.01512,-0.01966,0.08846,0.02943,0.00616,-0.05796,-0.02491,-0.05726,0.00136,0.06516,0.16075,-0.15276,0.02287,0.0159,-0.05385,0.07876,0.00932,0.03123,-0.0206,-0.08893,-0.0192,-0.01501,-0.00026,0.0061,0.02311,0.03431,0.09238,-0.13411,0.03688,-0.02342,0.0677,0.14875,-0.09406,0.00284,0.04262,-0.00188,0.00182,0.05726,-0.06474,-0.00635,-0.12235,0.0211,-0.04218,0.03836,0.10145,-0.06143,0.04237,0.02252,0.13326,-0.02964,-0.16472,-0.00096,0.00809,-0.03646,0.10717,0.03997,-0.00214,-0.015,-0.03787,0.00163,-0.03762,-0.01623,-0.0282,-0.02718,0.0765,-0.08347,0.01983,-0.07006,0.02792,-0.09373,-0.02499,0.15754,-0.1005,-0.11898,-0.05668,0.01797,0.13497,-0.00409,0.00694,0.01448,-0.0366,-0.03189,-0.06483,-0.04434,-0.06285,0.0667,-0.03695,0.01169,0.04618,-0.0577,-0.00149,0.04823,0.01512,0.04789,-0.00065,-0.01593,0.0128,-0.02506,-0.14134,-0.0519,0.0681,0.0748,0.06483,-0.12199,-0.02466,-0.07446,0.01471,-0.04587,-0.08119,0.0282,-0.1006,0.11823,0.03027,0.08474,-0.03581,-0.09139,-0.03629,0.03587,-0.10559,-0.00901,-0.08368,-0.03374,0.0073,-0.06032,0.07397,0.02684,-0.00802,0.05674,-0.07734,-0.01108,0.02486,0.04171,0.00886,0.06144,0.00604,0.0396,0.05947,-0.01345,-0.01164,0.11577,-0.0472,-0.04932,-0.02718]},{"domain":"time_series","key":"box_pierce_test","name":"Box-Pierce test","package":"time-series-ai999x","example":"Perform the Box-Pierce test with 3 lags on [4, 6, 5, 8, 7, 9, 8, 10, 9, 12, 11, 13].","v":[-0.0137,0.0074,0.00949,-0.0247,-0.03448,0.00474,0.0722,-0.0454,0.03292,-0.05075,-0.05155,-0.00178,-0.04548,0.07154,-0.00316,-0.05352,0.12589,0.04236,0.0275,0.01413,-0.06097,0.04547,-0.13474,-0.00786,-0.04083,-0.04335,-0.02,0.09801,0.05384,0.05687,-0.02309,-0.00051,0.10809,0.06231,0.09262,-0.10821,0.05431,-0.00757,-0.04604,-0.01339,-0.00141,-0.1615,-0.02348,-0.05144,-0.01705,-0.06337,0.05766,-0.02316,-0.05704,0.02739,0.01113,0.07526,0.05673,0.00233,0.01644,-0.20505,0.08422,-0.04618,0.05607,0.0088,0.0273,0.02605,-0.05383,0.02399,-0.02114,-0.04407,0.06566,-0.04133,0.03102,0.035,-0.10655,0.12262,-0.01374,-0.07746,0.03285,0.01109,0.15638,-0.03156,-0.04173,-0.00087,0.05232,-0.01557,-0.07609,0.01243,0.06005,-0.0426,0.02522,-0.00487,0.01412,0.00463,-0.10717,0.08059,0.00413,0.02421,-0.0042,-0.03642,-0.01985,-0.00818,0.01218,-0.11353,0.00865,-0.07201,0.07268,-0.0311,-0.00132,0.07814,-0.1546,0.04096,-0.04243,0.03214,-0.04315,0.09906,0.05267,0.04762,-0.01251,0.01006,0.05935,-0.0237,-0.06731,0.02041,0.00451,0.0724,0.00149,0.12661,-0.08824,-0.00034,-0.02894,-0.02086,0.06814,-0.0118,-0.02664,-9e-05,-0.04295,-0.01491,0.05058,0.01843,-0.08046,-0.002,0.03612,0.17722,-0.01997,0.00855,0.08591,0.00386,0.20518,-0.01666,0.02142,0.05885,0.02983,-0.034,-0.00191,-0.0352,-0.10312,-0.03881,0.02918,-0.01034,-0.01192,0.07026,0.04707,0.08893,0.00417,0.03344,-0.02049,-0.14936,0.11135,-0.01034,-0.04604,0.17074,-0.02293,0.0057,0.03286,0.01864,0.05998,-0.00575,0.00208,0.09247,-0.04868,0.04284,-0.01821,0.15865,-0.08255,0.01652,0.02165,-0.02447,0.11913,-0.0745,-0.03646,-0.17141,-0.06261,0.08048,-0.00484,-0.0293,-0.04096,0.08484,-0.00783,-0.07173,-0.0694,-0.08665,0.07062,-0.0645,0.03401,0.01051,-0.05915,-0.0106,-0.02658,0.01142,0.06115,-0.00121,0.01968,0.03321,0.04903,-0.0528,-0.03542,0.03337,0.00962,-0.03113,-0.08453,-0.0062,-0.06877,0.01802,-0.07323,0.0071,-0.01959,-0.03104,0.08131,0.02587,0.02311,-0.11222,-0.11249,-0.00153,0.12335,-0.1042,0.10051,-0.07657,-0.0242,-0.04191,-0.00907,0.03379,0.04844,-0.09041,0.03502,-0.12456,0.01508,0.00857,0.0133,-0.03027,0.08048,-0.01311,-0.00332,0.08353,-0.03632,-0.11058,0.09744,-0.03085,-0.0323,-0.02341]},{"domain":"time_series","key":"centred_moving_average","name":"Centred moving average","package":"time-series-ai999x","example":"Find the 4-period centred moving average of [12, 15, 14, 18, 20, 19, 23, 25].","v":[0.04898,0.05569,0.11797,-0.00258,0.04249,-0.06568,-0.03202,0.05284,-0.011,0.03562,-0.04496,-0.05107,-0.01133,-0.04525,0.02441,-0.01509,0.04612,-0.00137,-0.11316,0.00131,0.04593,0.08863,-0.10134,-0.00555,-0.05948,0.10378,0.05744,-0.0676,-0.09552,-0.04726,0.04218,-0.00279,0.02785,0.06015,0.05473,-0.08211,-0.00628,-0.04031,0.0516,0.00431,-0.13429,0.07333,-0.05558,0.04269,-0.06477,0.06445,0.00664,0.02226,0.08575,0.00588,-0.10056,0.07392,0.03934,-0.02605,0.10994,-0.12422,0.11711,-0.06497,0.02081,-0.06387,0.01513,0.00141,-0.04665,0.03444,0.05212,-0.07057,0.00151,0.01247,0.1086,0.08773,-0.09421,0.10879,-0.07565,-0.10157,-0.10445,0.11434,-0.02725,0.14272,0.05976,-0.03381,0.03534,0.02629,0.00125,0.02205,0.08892,-0.02253,0.04022,-0.06634,-0.04737,0.01333,0.03371,0.12202,0.02926,0.00803,-0.00347,0.02334,0.05485,0.05629,0.01377,-0.00579,-0.05474,-0.03126,0.03076,0.0335,0.04965,-0.02961,-0.111,-0.0881,0.10605,-0.00025,-0.00099,-0.05212,0.0461,-0.07829,-0.06555,0.01198,-0.03137,0.00487,-0.04395,0.14965,0.03053,-0.12209,-0.02104,0.05995,-0.0773,0.03518,0.06157,-0.12305,0.08753,-0.03504,0.08965,-0.03292,-0.0612,-0.02188,-0.02777,0.0029,-0.03618,0.02854,-0.02455,0.07414,-0.04709,-0.07899,0.09103,-0.03959,0.05256,0.04276,-0.05627,0.02961,-0.02328,0.03586,0.02218,0.03271,0.04093,-0.17384,0.0374,-0.028,0.04982,0.01421,0.03622,0.1079,0.08977,0.05485,0.01917,-0.05492,-0.052,-0.02931,-0.03565,-0.10452,0.14618,-0.04641,-0.03984,-0.03144,0.09045,-0.04775,0.01237,-0.09561,-0.08723,0.00867,-0.02387,0.13028,0.05183,0.02471,0.05794,0.03992,-0.01246,0.03925,-0.05326,0.08114,-0.03517,-0.04013,0.04287,0.01084,-0.05282,-0.00873,-0.05992,0.06138,0.03915,-0.02382,-0.07423,-0.00194,-0.01341,-0.10368,-0.13992,0.03409,-0.01549,0.02338,0.09989,0.05403,-0.12795,-0.07046,0.03202,0.00659,-0.1091,0.01244,0.0445,-0.03619,0.03384,0.02989,0.03856,0.01858,-0.017,0.035,0.06283,-0.01145,-0.00494,-0.05843,-0.02888,0.05519,0.04278,0.05835,0.08039,0.07775,-0.00562,0.03236,0.10289,-0.05085,0.00696,-0.01545,0.03657,-0.04077,0.01456,-0.03816,-0.10768,-0.02517,0.0528,-0.06734,0.04402,0.0247,-0.09362,0.01005,-0.06374,-0.03462,-0.0257,-0.00042,-0.10218,-0.18262]},{"domain":"time_series","key":"change_point_mean_shift","name":"Single change point in the mean (least squares)","package":"time-series-ai999x","example":"Find the change point in the mean of [5, 6, 5, 7, 6, 12, 13, 12, 14].","v":[-0.03678,0.07292,0.05175,0.035,-0.0246,-0.03166,-0.01799,-0.04309,-0.03342,-0.07576,0.03037,-0.06188,-0.05057,-0.15113,-0.05292,-0.05545,0.03974,-0.0229,-0.00524,0.05107,-0.08309,-0.02273,0.00372,0.02907,-0.0572,0.139,-0.05055,0.01821,0.00079,-0.03169,-0.045,-0.05644,0.02765,0.01549,0.12358,-0.06781,-0.0039,-0.02113,0.02946,0.05595,-0.00502,0.08679,-0.04282,0.05259,0.09315,0.07192,0.02203,0.04103,0.01024,-0.03598,-0.12554,0.05488,0.09019,0.00972,0.03481,-0.10276,-0.03321,0.01674,0.0316,0.02931,0.00818,0.14771,-0.10582,0.0273,0.02188,0.01918,-0.04415,0.04204,0.05607,0.04664,-0.10233,0.10117,0.01291,0.02085,-0.06636,0.10309,0.05473,0.11869,-0.02834,0.05665,0.05926,0.05692,0.03525,0.04425,0.0477,-0.08412,-0.08894,0.06208,0.02509,0.03167,-0.10461,-0.00865,-0.00615,-0.0251,-0.0099,-0.10767,0.01315,0.12302,0.043,0.0244,-0.03884,0.02007,0.00482,-0.00997,-0.03788,-0.01038,-0.04013,-0.03285,-0.00977,0.13564,-0.01769,0.00925,0.15503,-0.04607,-0.13241,0.03304,0.02398,0.02985,0.08442,0.01216,0.06974,0.07731,0.05715,0.08444,-0.04578,0.00172,-0.08948,-0.14088,0.18002,-0.0306,0.05974,-0.03009,-0.03339,0.00441,0.10699,-0.06381,-0.00037,0.07079,-0.04577,0.08371,-0.12441,-0.06897,0.10891,0.04383,0.04755,-0.01776,0.0279,-0.03502,0.04304,-0.10306,-0.0726,-0.05172,0.05395,-0.09607,-0.01989,-0.01351,-0.00778,0.04372,-0.00284,0.04959,-0.03355,0.04393,0.03825,-0.00376,-0.02666,-0.01349,-0.11021,-0.07335,0.00461,0.02819,-0.01633,0.05854,0.14,0.018,-0.00172,-0.01836,0.01242,0.01724,-0.12569,0.02649,-0.10871,0.0292,-0.0918,-0.05815,-0.07684,0.00882,-0.08233,-0.03731,-0.01033,0.00441,-0.13518,-0.02259,0.02853,0.05505,0.11118,0.04441,-0.03348,-0.08761,0.0426,-0.1222,-0.03449,-0.01054,-0.0806,-0.04777,0.01469,-0.0371,0.04616,-0.04933,-0.10747,0.03359,0.00805,0.06628,0.0194,-0.01476,0.00621,0.01817,-0.03513,-0.0854,-0.0124,0.08445,-0.0129,0.0152,0.02004,0.06968,0.08882,-0.09442,0.02019,0.04249,0.00313,0.01336,-0.02398,-0.11321,-0.04619,-0.08749,0.10264,0.11236,0.01221,0.00029,0.0015,-0.00249,0.05381,-0.0718,-0.02914,0.0307,0.09589,-0.07561,-0.03325,0.09592,-0.0136,-0.00476,0.06975,-0.08671,-0.10817,-0.06776,0.00327,-0.0109]},{"domain":"time_series","key":"compound_average_growth_rate","name":"Compound average growth rate of a series","package":"time-series-ai999x","example":"Find the compound average growth rate of [100, 110, 125, 133, 150].","v":[-0.0577,0.01148,0.04433,0.07242,-0.00286,-0.09347,-0.04994,0.04452,-0.06837,0.0506,-0.01464,0.10498,0.0049,-0.00819,0.04888,0.00287,0.03047,-0.02917,-0.16128,0.05787,0.0425,-0.01274,-0.08241,0.07634,0.07835,0.01717,0.00479,-0.09267,-0.07138,0.01296,-0.07683,-0.05395,0.05067,0.03459,0.0561,-0.04778,-0.06588,-0.04849,0.0001,0.00972,-0.11457,0.14399,-0.03391,0.04033,-0.00395,0.01997,0.0152,-0.00537,0.0742,0.02128,-0.04836,0.09133,0.08947,0.02623,0.07793,-0.01322,0.04164,-0.02866,-0.03073,-0.07935,-0.02219,-0.01429,-0.04931,0.01252,0.03799,-0.01508,-0.04195,0.00121,0.13987,0.00104,0.0287,0.05063,-0.0579,-0.19792,-0.05431,0.06877,-0.05632,0.13185,0.02718,0.01519,0.05037,-0.02237,0.01508,-0.00246,0.06134,0.0338,-0.05956,-0.02736,-0.05001,0.01122,0.01853,0.09562,0.02943,-0.02487,0.01616,-0.0151,-0.00528,0.09337,0.0878,-0.00071,-0.00949,-0.03683,-0.01386,-0.01533,0.08309,-0.04946,0.02251,-0.05745,0.16,0.09255,-0.01258,-0.0842,-0.00713,-0.00417,-0.02706,0.06466,-0.09854,-0.05117,0.0206,-0.02111,0.04269,0.00652,0.01102,0.03396,-0.07943,0.08678,0.06694,-0.0878,-0.02034,0.00732,-0.06229,-0.03581,-0.002,-0.05059,0.00525,-0.07062,0.09577,0.00302,0.0198,0.01664,-0.0373,-0.00506,-0.05076,0.04784,0.02495,-0.03132,-0.06907,-0.04743,0.0544,0.17886,-0.04718,-0.11994,0.15169,-0.22445,0.01358,0.04536,-0.01148,0.00532,0.08382,-0.01978,0.03261,0.03916,0.06819,-0.06393,-0.03853,0.02655,0.08832,0.06185,0.07968,-0.08093,-0.01814,-0.13358,-0.06381,0.01242,0.03335,0.02199,-0.04774,0.02251,0.00629,0.03292,-0.03502,-0.06895,0.01265,-0.05463,0.05897,0.00884,0.03593,0.0707,-0.02582,-0.01483,-0.03739,0.03761,0.02535,-0.05842,-0.05535,0.05622,-0.01683,-0.07809,0.01733,-0.06505,0.00533,-0.0303,-0.06674,0.01073,-0.01519,0.06436,0.05299,0.02434,-0.05978,0.02217,0.05434,0.0487,-0.17687,-0.04266,0.03437,-0.10443,0.1388,-0.04461,0.00147,0.02895,-0.0345,-0.04401,0.06707,0.04121,0.05461,-0.05487,-0.14395,0.18888,0.00241,0.06142,0.00696,0.00926,-0.0055,0.03446,0.08479,0.01976,0.13838,0.03048,0.07046,-0.12216,0.03298,0.01378,-0.05935,-0.00559,0.02341,-0.08038,0.02286,0.02778,-0.01601,-0.06442,0.06826,-0.02885,-0.0103,-0.08444,-0.04141,-0.09247]},{"domain":"time_series","key":"cross_correlation_at_lag","name":"Sample cross-correlation at lag k","package":"time-series-ai999x","example":"Compute the cross-correlation at lag 1 between x = [1, 3, 2, 5, 4, 6] and y = [2, 1, 4, 3, 6, 5].","v":[-0.03218,-0.01649,0.04944,0.05519,-0.01462,-0.06149,-0.03429,0.01774,0.08404,-0.01083,-0.00808,0.05745,0.07285,-0.00438,0.03674,0.0193,-0.11034,-0.02371,-0.13833,-0.02085,-0.00486,0.15516,0.04779,-0.11574,0.06398,0.01686,-0.05609,-0.0305,-0.09021,-0.03686,0.02154,-0.0804,-0.0763,0.02623,0.08521,-0.01581,-0.01684,-0.02647,-0.06019,0.03938,0.08904,0.0169,-0.09163,-0.03471,-0.0748,0.02042,0.03925,0.08505,-0.06954,0.03224,-0.0985,0.13427,0.03855,0.02476,0.02757,-0.11743,0.0888,0.05184,-0.01332,0.07301,0.01024,-0.05882,-0.02924,-0.02887,-0.14167,0.00907,0.00028,0.04093,0.04664,-0.02829,0.04258,-0.00982,0.03274,-0.11412,-0.04937,0.05708,0.02474,-0.00798,0.06543,-0.07377,0.15938,0.00375,-0.02906,0.03338,0.13053,0.00411,-0.09644,0.04467,0.05817,-0.00342,-0.02401,-0.00224,0.09465,0.05887,0.01658,-0.0247,0.03342,0.01652,-0.0112,-0.01786,-0.00663,-0.1059,-0.0461,0.04061,-0.07149,0.00679,-0.14926,0.04774,0.06244,0.00012,-0.08309,-0.07517,0.09395,-0.00279,-0.01618,0.08286,0.01705,0.03186,-0.04204,-0.11368,-0.02581,-0.00793,0.04746,0.09757,-0.01927,0.05295,-0.01201,-0.05698,0.0912,0.06578,0.11049,-0.04879,-0.02269,0.01027,0.01668,0.0347,-0.04461,0.04975,-0.04172,0.04429,-0.18023,0.02086,-0.01928,0.00219,0.13625,-0.04043,-0.04325,0.07386,0.00022,0.00247,0.03441,-0.01733,-0.01262,-0.03957,0.02878,-0.07724,0.06192,0.09058,-0.01758,0.04726,0.06486,0.11843,0.07705,-0.17157,-0.0187,-0.00777,-0.07926,0.056,-0.0236,0.06241,-0.00876,-0.01967,-0.04678,0.04415,0.0055,-0.05849,-0.00258,0.02935,0.03996,-0.03483,-0.03331,0.04372,-0.06256,-0.01696,0.00592,-0.06187,-0.0511,-0.06911,-0.0621,0.14634,0.08699,0.09951,0.00474,0.02612,-0.01776,-0.09636,0.0039,-0.12498,0.02004,-0.07755,0.03677,0.05941,-0.00661,-0.01902,-0.03113,0.01445,0.00633,-0.00084,0.00685,-0.00319,-0.08284,-0.15881,-0.05958,0.0087,0.03704,0.05373,0.01502,0.03762,-0.04312,0.04425,-0.04635,-0.06023,0.01466,0.00264,0.09753,0.07205,0.18384,0.06701,-0.00681,-0.03983,-0.15546,-0.0617,-0.02385,-0.08868,-0.02305,-0.07259,0.01786,0.07669,0.00544,-0.02529,0.08128,-0.02995,0.03266,-0.06298,-0.031,-0.05114,0.10455,0.03116,0.06313,0.06055,0.02458,0.00699,-0.01122,-0.02925,-0.07373,-0.06548]},{"domain":"time_series","key":"cross_correlation_best_lag","name":"Lag of the strongest cross-correlation","package":"time-series-ai999x","example":"At which lag up to 3 is the cross-correlation strongest between x = [1, 3, 2, 5, 4, 6, 5, 8] and y = [3, 2, 5, 4, 6, 5, 8, 7]?","v":[-0.05505,-0.01345,0.03272,0.0689,-0.00762,-0.06199,-0.02369,-0.00878,0.11133,0.01846,-0.00984,0.04752,0.03553,0.05487,0.06427,0.02174,-0.10144,-0.04896,-0.12635,-0.01417,-0.00754,0.10568,0.00848,-0.11297,0.11493,0.00626,-0.06255,0.0003,-0.0868,0.0029,0.02843,-0.11221,-0.01282,-0.04178,0.13257,-0.05351,-0.04324,-0.0321,-0.06073,0.07395,0.09851,0.00198,0.00185,-0.07986,-0.06618,0.07531,0.04592,0.06859,-0.03052,0.0012,-0.11551,0.13415,0.027,-0.01448,3e-05,-0.16416,0.0517,-0.00012,0.04684,0.09458,0.00691,-0.02628,-0.02161,0.00662,-0.04894,-0.00677,0.02075,0.02944,0.12599,0.02812,0.0521,0.0267,-0.06419,-0.17716,-0.05113,0.04866,0.02702,0.0144,0.07908,-0.05767,0.08942,0.03293,-0.05146,0.00387,0.08636,0.03999,-0.10073,0.05084,0.05425,-0.04787,-0.06601,0.07049,0.1319,0.04709,0.01943,-0.10284,-0.00524,-0.03562,-0.01902,0.00644,-0.01039,-0.05984,-0.07048,0.08993,-0.03573,0.06,-0.17338,0.04677,0.03458,-0.02074,-0.04907,-0.02371,0.14501,0.06695,-0.0024,0.08193,-0.00933,0.02927,-0.01709,-0.08753,0.0142,-0.01793,0.07456,0.06931,-0.06689,-0.04204,0.03337,-0.07481,0.12063,0.03407,0.01176,-0.08576,-0.03457,-0.06992,-0.01773,0.0001,-0.00063,-0.00401,0.04256,0.02735,-0.07521,0.04691,-0.0331,0.02989,0.11929,-0.10059,-0.03372,0.05434,0.06228,-0.00695,0.02023,-0.0355,-0.00861,-0.05099,0.00545,-0.07731,0.00661,0.10625,-0.02694,0.06979,0.0523,0.16533,0.01928,-0.13142,-0.05118,0.06198,0.00383,0.10816,-0.01015,0.11547,-0.0365,-0.01869,-0.06037,0.02551,0.04898,-0.0053,0.02919,0.00543,0.02498,-0.03024,-0.04571,0.006,-0.05609,-0.02035,0.07049,-0.12262,-0.00908,-0.01907,-0.00507,0.09997,0.04554,0.06783,0.05936,0.01894,-0.0099,-0.04993,0.00206,-0.07481,0.01323,-0.05674,0.07068,0.10194,0.05873,-0.02387,-0.01349,0.01496,0.02339,0.02848,-0.03993,-0.02547,-0.04683,-0.09627,-0.05306,-0.00688,0.00765,0.07129,0.00974,0.02206,-0.01586,0.00908,-0.10091,-0.0547,-0.01888,-0.00264,0.08482,0.09733,0.13838,0.02104,-0.05072,-0.09819,-0.14503,-0.10476,-0.03528,-0.09824,-0.00846,-0.0459,0.07211,0.05528,-0.04131,-0.00653,0.05408,0.01643,0.02501,-0.0305,-0.10457,-0.05752,0.05861,-0.04591,0.00972,0.08077,0.03348,0.00247,0.05115,-0.05146,-0.01118,-0.03968]},{"domain":"time_series","key":"cusum_change_point","name":"CUSUM estimate of a change point","package":"time-series-ai999x","example":"Estimate the change point with CUSUM for [5, 6, 5, 7, 6, 12, 13, 12, 14].","v":[0.01076,0.10206,0.03109,0.06814,-0.05458,0.02372,-0.08507,-0.0175,-0.05106,-0.07376,-0.02478,0.01618,-0.10257,-0.04613,0.0192,-0.08307,0.04037,0.00748,0.07763,-0.03956,-0.03595,-0.01992,-0.10598,-0.06445,-0.01214,0.07168,-0.03324,0.04965,-0.01068,-0.11126,-0.06684,-0.04995,0.01278,0.01176,0.16716,-0.07442,-0.03272,-0.03183,0.02498,-0.03635,-0.01685,0.04458,-0.01135,0.05598,0.08387,0.06646,0.02609,0.06163,-0.00718,-0.10778,-0.10146,0.08146,0.1069,-0.02715,0.0557,-0.1191,-0.08294,-0.02302,0.06814,-0.0436,-0.00627,0.09786,-0.04078,-0.02419,-0.02812,-0.09604,0.03593,0.06608,0.05852,0.12524,-0.10921,0.14314,0.01023,0.02958,-0.05215,0.0337,0.13675,0.06318,0.06263,0.02701,-0.0226,0.02672,0.01231,0.00638,0.12045,-0.02607,-0.05583,-0.00813,0.00713,-0.02513,-0.03804,0.07807,0.06058,0.05149,0.01522,-0.1875,-0.01853,-0.00405,0.03571,0.0219,-0.04518,-0.02421,-0.04285,-0.01059,0.00508,0.10109,-0.14675,-0.00835,-0.0817,0.07936,0.00888,0.05058,0.1527,0.11572,-0.03724,0.03332,0.09102,-0.02108,0.04361,0.0201,0.016,0.09968,0.056,0.12965,-0.04744,-0.01483,0.01889,-0.18601,0.18004,0.01656,0.00644,-0.08003,-0.14152,-0.04706,0.08655,-0.05634,0.033,0.03783,-0.00563,0.06533,-0.08117,0.01151,0.05617,0.0798,0.03144,-0.02901,-0.01856,0.02462,0.02534,-0.07072,-0.02596,-0.14025,-0.03822,-0.12538,-0.04207,0.04041,-0.05958,0.08892,-0.0481,0.00924,-0.03773,0.02253,0.03492,-0.05928,0.03764,0.02322,-0.09428,-0.03468,0.03215,0.05131,0.02684,0.0063,0.13063,-0.01053,-0.02341,-0.02234,-0.00228,0.02169,-0.04947,0.09799,-0.0836,-0.03551,-0.01891,0.01905,-0.01629,-0.02403,-0.0252,-0.00647,0.01648,0.06576,-0.0073,0.01551,0.00252,0.07241,0.05579,0.07554,-0.03452,-0.09312,0.06952,-0.08685,-0.05246,0.06,0.04342,-0.03376,-0.00559,0.04069,0.07426,-6e-05,-0.0204,0.06489,0.00134,0.01993,0.00151,-0.02058,-0.0311,-0.03571,-0.11587,0.00808,-0.10424,0.03319,-0.03431,0.02295,0.10231,0.01113,0.05007,-0.01217,-0.00068,0.02467,-0.07469,0.00493,-0.00834,-0.09154,-0.02787,-0.09362,0.07193,0.00406,-0.0003,0.02792,0.02811,0.00856,0.04613,-0.10353,-0.02699,0.04197,-0.00678,-0.09281,-0.10224,0.04081,0.05627,-0.00922,0.05324,0.01304,0.02296,-0.02067,-0.03523,-0.02994]},{"domain":"time_series","key":"dickey_fuller_test","name":"Dickey-Fuller unit-root statistic","package":"time-series-ai999x","example":"Compute the Dickey-Fuller statistic with a constant for [10.2, 10.8, 10.5, 11.3, 11.0, 11.9, 11.6, 12.4, 12.0, 12.9].","v":[0.05431,0.04058,0.0574,0.06461,-0.03354,0.0438,-0.02969,0.01398,-0.07783,-0.05722,-0.03099,0.00253,-0.06868,0.10356,0.08097,0.01608,0.05146,-0.02359,-0.06025,-0.03193,-0.00569,0.02331,-0.10206,-0.03523,0.01136,-0.01592,-0.04112,0.04266,0.04795,-0.03794,0.04737,-0.06227,0.08858,-0.02275,0.1714,-0.02028,0.01261,0.09971,-0.03701,-0.03288,0.00796,-0.0585,-0.02947,-0.04348,-0.04527,-0.01022,0.05576,-0.00715,-0.02629,0.03901,0.00485,0.07274,0.13315,0.05108,0.04044,-0.21874,0.06829,0.00389,0.03,0.0406,-0.00284,0.04669,0.00476,0.10789,-0.03822,-0.05272,0.0563,0.05858,0.02657,-0.00513,-0.05561,0.10783,-0.00049,-0.02734,0.05637,0.01158,0.07902,-0.00096,-0.06265,-0.00556,0.06037,0.10566,-0.04594,0.10224,0.09318,-0.02034,-0.02806,0.0224,-0.01223,-0.03987,-0.10395,0.11379,0.08142,-0.05897,0.0181,-0.01811,-0.12281,-0.06508,0.05562,-0.07207,0.05057,-0.03209,-0.03162,-0.01382,-0.01362,0.05223,-0.085,0.00521,0.09006,-0.00708,-0.08286,0.05048,0.12009,0.09488,-0.05041,0.0413,-0.07506,-0.0885,-0.06902,0.02967,-0.00036,0.01967,0.00797,0.02536,-0.07058,0.01117,0.01223,-0.05591,0.03279,-0.08152,-0.16925,-0.07396,-0.07537,-0.06445,0.01019,0.05664,-0.09905,-0.10634,0.07846,0.05581,-0.03638,0.02986,-0.00325,0.06036,0.1177,-0.01817,-0.08545,-0.04024,0.11327,-0.02223,0.03908,-0.12618,-0.04868,-0.07272,-0.04656,-0.05086,0.0089,0.07937,-0.00522,0.09229,0.01605,0.1307,-0.00392,-0.11465,-0.01645,0.05307,-0.00517,0.144,0.01599,0.00546,-0.00587,0.05997,0.02245,0.02827,-0.01949,0.0071,0.03676,0.13628,0.01933,0.06664,-0.05481,-0.01604,-0.00637,0.02283,0.18162,-0.13631,-0.04065,-0.0731,-0.00609,0.11349,-0.0471,-0.04176,-0.01397,0.01834,0.08689,-0.0045,-0.14091,-0.03562,0.03165,-0.01741,-0.00125,-0.01908,-0.07963,-0.04706,0.05238,-0.06366,0.03393,0.02512,-0.00318,-0.04339,0.03418,0.04497,-0.00846,-0.01832,0.07405,0.01432,-0.01676,-0.03244,-0.05328,-0.0097,-0.06882,0.00532,-0.02858,-0.01431,0.16665,0.05779,-0.01145,-0.0343,-0.11141,-0.02232,0.02996,-0.09144,0.08999,-0.0515,-0.07516,-0.02565,0.0446,0.02792,0.00716,-0.02621,-0.0163,0.0323,-5e-05,-0.04097,0.03889,-0.00105,0.06284,0.02325,-0.06179,0.04594,0.04349,-0.10421,0.01445,0.02047,0.01089,-0.12844]},{"domain":"time_series","key":"differencing","name":"Regular and seasonal differencing","package":"time-series-ai999x","example":"Find the second differences of [3, 5, 9, 15, 23, 33].","v":[0.03061,0.10522,0.03861,0.05414,0.04665,-0.08472,-0.0759,0.01256,-0.05306,0.04596,-0.10291,0.02658,-0.02467,0.12385,-0.02852,-0.08882,0.03273,0.04492,-0.11934,0.03703,-0.02642,0.0758,-0.05708,0.03137,0.01873,-0.01085,-0.00556,-0.02457,-0.15076,0.0234,0.03199,-0.01625,-0.00613,-0.01656,0.1452,-0.04354,-0.0418,-0.10836,0.00335,-0.03866,-0.04068,0.00994,-0.0166,-0.06086,-0.11335,0.01569,0.07599,0.04133,-2e-05,0.03209,-0.06627,0.17134,0.00408,-0.12904,0.10035,-0.14788,0.1072,-0.05092,0.00288,-0.00433,0.01846,-0.00335,0.00099,0.02861,0.03343,-0.02307,0.06681,-0.0231,0.04269,0.07889,-0.03449,0.03716,-0.05534,-0.13833,-0.05231,0.02722,0.03346,0.07429,0.08829,-0.08081,0.00124,0.01783,-0.02767,0.03704,0.15632,-0.03843,-0.01949,-0.14393,-0.02065,-0.02513,-0.04987,0.04596,0.11693,0.0047,0.04586,-0.11459,0.01726,-0.04523,0.06434,-0.07186,-0.04014,-0.05236,0.04181,-0.04759,-0.00172,0.00344,-0.10034,0.02352,0.1032,-0.01944,0.04038,-0.03528,0.09091,0.04587,0.02954,-0.01498,-0.14196,0.00044,0.03051,0.06664,-0.01936,-0.06825,-0.00524,0.04338,-0.07037,-0.01453,0.03535,-0.05977,0.02764,-0.04544,-0.01309,-0.04786,-0.01445,-0.07005,0.02657,0.0296,-0.04133,-0.02925,-0.04587,0.06575,-0.08997,-0.03466,0.01701,-0.02932,0.18971,0.06007,-0.00789,-0.04342,-0.02303,0.10615,0.04118,-0.08081,-0.03398,-0.10349,0.00018,-0.04062,0.01681,0.02288,0.06029,0.03341,0.108,0.04961,-0.02916,-0.10643,0.08974,0.03121,0.05017,0.15393,0.03929,-0.015,-0.04143,0.0067,0.02453,0.04318,0.00758,0.03607,-0.06512,0.01919,0.00564,0.09051,0.03011,0.01819,-0.00296,-0.01463,0.16939,-0.10952,0.02121,-0.00416,-0.00625,0.0181,0.13794,0.06887,-0.00871,0.03667,0.033,-0.02797,0.03775,-0.04703,0.03142,0.03286,-0.04181,-0.01381,0.05649,-0.11661,-0.08425,0.05991,0.01181,0.11122,-0.00071,0.03516,0.02587,-0.08794,-0.06648,-0.03453,0.09246,-0.01325,0.03667,0.00734,-0.00425,-0.06441,-0.04574,-0.02008,0.07778,-0.0596,0.12023,0.01903,-0.04699,0.02673,-0.03241,-0.03789,0.03858,-0.0236,0.07678,0.03759,0.04851,-0.10147,0.10264,0.07302,-0.00407,-0.0707,-0.0212,-0.00624,0.04018,-0.0363,-0.07486,-0.02105,0.03723,-0.04274,-0.02183,0.02169,0.03598,-0.09967,0.06721,0.02854,-0.01731,-0.1264]},{"domain":"time_series","key":"drift_forecast","name":"Random-walk-with-drift (drift method) forecast","package":"time-series-ai999x","example":"Forecast 3 periods ahead with the drift method for [100, 104, 103, 109, 112].","v":[-0.00893,0.09489,0.11408,0.05636,0.02301,0.00246,0.02065,-0.0014,-0.0426,0.06729,0.04451,0.04554,-0.02463,0.08593,0.11076,-0.13578,0.06262,-0.05597,-0.10491,-0.00584,0.00472,0.08498,-0.10188,-0.01344,0.01096,-0.01146,-0.1077,-0.10358,-0.00622,-0.04849,0.06667,-0.05011,-0.00298,-0.05867,0.0086,0.04601,-0.03624,-0.02321,0.02095,0.03457,-0.09564,0.06494,-0.01087,-0.06816,-0.0501,-0.00582,0.11978,-0.04648,0.02422,0.01385,-0.00842,0.08951,0.04337,0.02431,0.09865,-0.14098,0.05055,0.01487,-0.03887,-0.12528,-0.06015,0.08708,-0.12215,0.07286,0.01571,-0.00659,0.1033,0.08135,0.06666,-0.06114,-0.01421,0.08698,-0.02361,-0.10555,0.02943,0.08643,0.00059,0.1594,-0.10349,-0.06041,0.07881,0.04659,-0.00208,-0.05943,0.10832,-0.06349,-0.03806,0.06243,-0.06163,-0.05636,-0.10136,0.05853,0.04689,0.059,-0.01215,-0.0228,-0.03052,-0.02944,-0.11728,-0.08437,0.01247,-0.02218,0.00401,0.01464,-0.00265,0.01425,-0.02923,0.01703,0.15812,0.09662,0.05342,0.01201,0.00772,0.03324,0.04017,0.01311,-0.0775,-0.03355,-0.02344,-0.01602,0.06894,-0.04935,-0.05164,0.04855,-0.03877,-0.02587,0.02111,-0.06055,0.01196,-0.11188,-0.05179,-0.08665,0.04797,-0.09582,-0.08515,-0.00273,0.10796,0.03787,0.01919,-0.04594,-0.09452,0.04923,-0.03519,0.03076,0.08693,-0.05679,-0.06567,0.03091,-0.07101,0.06883,0.05528,-0.14357,0.12391,-0.07632,-0.06151,0.01515,0.06494,0.0156,0.1052,0.03458,0.01443,0.09427,0.01487,-0.02262,-0.01691,-0.01326,0.05981,-0.01546,-0.03026,-0.08904,0.03268,-0.03667,-0.01863,0.03345,0.06606,0.02173,-0.01548,0.02515,0.03242,0.12643,0.02337,-0.01622,0.02459,0.01621,0.24467,-0.02914,0.04129,0.05479,0.06981,-0.01647,-0.05957,-0.04394,-0.03511,-0.02065,0.04075,0.06111,0.01805,-0.01186,-0.07532,-0.08354,0.02011,0.021,0.0144,-0.01661,0.02622,0.01539,0.09228,0.03964,-0.04981,0.03312,0.10375,0.04448,-0.01372,0.01984,0.01059,-0.05517,0.03542,0.05952,0.05775,0.04492,-0.02042,-0.02894,0.03895,-0.01047,0.04047,-0.03272,-0.06313,0.05725,-0.03374,-0.0335,-0.0265,-0.13337,-0.01459,0.05378,0.02311,-0.07289,-0.04309,-0.01582,-0.01082,-0.064,0.01986,-0.02838,-0.13778,0.01277,0.04024,-0.14398,-0.00513,0.05849,-0.06043,0.08309,0.04649,-0.06891,0.02195,-0.01486,0.05924,-0.06605]},{"domain":"time_series","key":"exponential_interpolation","name":"Exponential (log-linear) interpolation","package":"time-series-ai999x","example":"Exponentially interpolate the value at t = 2.5 from times [1, 2, 3, 4] and values [100, 120, 150, 170].","v":[-0.06337,-0.02473,0.01098,0.0066,-0.08359,0.05635,0.00086,0.0782,0.033,0.04648,0.01809,0.04644,-0.01468,0.05087,0.09959,0.06967,0.07573,-0.03254,0.12304,-0.01634,0.05357,-0.07831,-0.00957,-0.06974,-0.04366,0.0482,0.0618,-0.02843,0.00219,0.05006,0.00492,-0.00521,0.03607,-0.03646,0.07476,-0.01059,0.01313,0.07764,-0.05387,0.00663,-0.07053,0.00601,-0.07562,-0.06686,-0.15096,0.04833,0.05203,-0.1366,-0.0552,0.03913,-0.08638,-0.07127,-0.05607,0.01046,-0.08997,-0.01502,0.16688,-0.02563,-0.09198,0.05956,0.00531,0.04278,-0.12791,0.0423,0.00347,0.03051,0.02479,0.01532,0.14566,0.10761,0.09869,-0.06878,0.01801,-0.14594,0.03098,-0.07909,0.00791,-0.0556,-0.05775,-0.04877,0.00409,-0.02871,-0.01936,0.11556,-0.03978,-0.02156,0.00823,-0.02381,0.03978,-0.04746,0.03812,-0.05665,-0.01564,-0.13114,-0.08843,-0.08081,0.04038,0.01002,0.05227,0.03484,0.03207,0.03637,-0.03617,-0.06944,0.01743,-0.09192,-0.04985,0.03142,0.12947,-0.0614,-0.00948,0.00329,-0.05182,0.05708,0.12572,0.05022,-0.08349,0.1009,0.05919,0.0322,-0.00172,0.0113,0.01059,-0.02075,-0.03511,0.01632,0.05491,-0.04086,-0.11616,-0.02166,-0.01305,-0.06245,0.01104,-0.04748,0.00961,0.0235,0.01146,0.02206,0.15587,0.04929,0.03625,0.00554,0.0474,0.08865,-0.14639,0.04291,-0.04931,-0.01531,0.0084,0.09869,-0.07599,-0.09543,0.08956,-0.09558,0.01643,0.03616,0.02282,-0.00465,0.07076,-0.05002,-0.11385,0.03736,0.08075,0.11164,0.05297,0.03827,-0.01574,-0.02041,-0.10613,0.0038,-0.11887,-0.06313,-0.02048,0.01848,0.01516,0.01534,0.02553,0.01352,-0.06574,0.02318,-0.12704,-0.04366,0.09838,-0.02753,0.05318,0.04232,0.02789,0.02619,-0.02269,0.07302,-0.01471,0.03929,0.0205,-9e-05,-0.00926,0.00392,-0.05868,-0.01088,-0.00794,0.03712,-0.0394,0.0163,-0.08922,0.02652,-0.05586,0.06966,0.09925,0.06655,0.12057,0.1281,0.03832,-0.01951,0.02126,-0.02346,0.03532,0.00997,0.12751,-0.05091,-0.06873,0.10461,0.0852,-0.04322,0.00726,-0.03559,-0.06198,-0.01918,0.06666,0.00522,-0.06428,-0.10811,-0.01257,0.02284,0.05849,-0.03581,0.132,0.04516,0.09997,-0.01545,-0.05589,-0.0932,-0.11064,-0.04188,-0.00024,0.07112,0.0508,-0.11635,-0.07145,-0.05451,-0.02417,-0.00451,0.03619,-0.01438,0.05369,0.00389,0.01469,-0.05705]},{"domain":"time_series","key":"exponential_moving_average","name":"Exponential moving average","package":"time-series-ai999x","example":"Find the 3-period exponential moving average of [10, 12, 14, 13, 15].","v":[0.03532,-0.00859,0.04368,0.02748,0.03675,0.02639,-0.02537,0.0556,-0.05389,0.05176,-0.08921,-0.04182,-0.02583,-0.00654,0.07635,0.02154,0.0136,-0.02855,-0.07452,0.02455,0.03311,0.05849,-0.1179,0.00745,0.02246,0.11334,0.01469,-0.045,-0.10698,0.0149,0.0535,-0.01562,0.02952,0.09327,0.09529,-0.04487,-0.03663,-0.01042,0.01394,0.01012,-0.1202,0.06383,-0.08381,-0.01236,-0.09179,0.08513,-0.01067,-0.08124,-0.02812,0.05316,-0.09856,0.08493,0.04071,-0.00112,0.12675,-0.10321,0.16845,-0.05618,-0.04568,-0.04437,-0.01485,0.00251,-0.05353,0.02713,-0.03846,-0.05722,-0.05117,-0.01104,0.12712,0.03793,-0.06066,0.10852,-0.06575,-0.1867,-0.07026,0.10442,0.05115,0.13898,0.05265,-0.01978,0.04821,-0.01138,-0.03696,0.00932,0.05927,-0.04492,-0.01111,0.0606,0.02209,0.01338,-0.01922,0.12335,0.02303,-0.05403,0.00094,-0.06708,-0.02241,-0.02665,0.03506,-0.05504,-0.0129,0.0023,0.04013,0.028,0.01331,-0.01403,-0.09471,-0.09321,0.12383,0.02157,0.0677,-0.0369,-0.09625,0.01577,0.0246,0.01764,-0.09669,-0.02746,0.00446,0.08549,0.04206,-0.05393,-0.03433,0.03435,-0.10258,0.08354,0.0584,-0.13815,0.06624,-0.03917,0.00523,0.00237,-0.04092,0.01054,-0.03335,-0.03142,-0.05299,0.01534,-0.00273,0.13692,-0.03728,-0.03021,-0.0456,0.02494,0.02016,0.0152,-0.02283,0.04257,0.02082,0.09366,0.01771,0.02591,0.02218,-0.20956,-0.02115,-0.02889,0.01642,-0.00046,0.12626,0.10094,0.05346,0.03276,0.02407,0.00834,0.02458,-0.00758,-0.08701,0.0158,0.02538,-0.07584,-0.02283,-0.00163,0.04782,0.01515,0.06006,-0.04994,-0.02781,-0.0115,-0.02218,0.16271,0.00758,-0.10281,0.05277,0.0237,0.05831,0.06827,-0.04047,0.06975,0.02722,-0.05623,-0.02089,-0.02,-0.02965,-0.06538,-0.02316,0.10266,-0.00688,-0.11397,0.03622,-0.00789,-0.01305,-0.12405,-0.07529,0.0203,0.03061,0.05131,0.12633,0.12598,-0.07188,-0.03578,0.04692,0.02954,-0.16112,-0.01109,0.01707,-0.02656,0.07157,-0.01498,0.03126,0.07401,-0.0619,0.02396,0.04639,0.05782,0.04858,-0.05879,-0.052,0.03239,0.03493,-0.00246,0.04833,0.0297,0.01675,-0.01866,0.06477,-0.06011,0.06354,-0.0408,0.01219,-0.12907,0.00273,0.02641,-0.04275,-0.02363,0.01682,-0.11235,0.02279,-0.01968,-0.05742,0.01939,0.03346,-0.07403,0.01068,-0.01,-0.03085,-0.20343]},{"domain":"time_series","key":"exponential_smoothing_update","name":"Exponential smoothing forecast update","package":"time-series-ai999x","example":"With exponential smoothing, the previous forecast was 100, the actual value was 110 and alpha = 0.2. What is the new forecast?","v":[0.12933,0.04054,0.05648,0.02522,0.07282,0.00932,0.01596,0.05393,-0.07727,0.0383,0.04904,0.01258,0.02016,-0.04522,-0.00443,0.0026,0.07654,-0.04477,0.11284,0.05648,-0.02595,0.12762,0.02867,0.10795,-0.07781,-0.05275,-0.07427,-0.07446,-0.00149,-0.01507,0.04216,-0.03794,0.07331,-0.04302,-0.04356,-0.00827,-0.00582,-0.00166,-0.04938,0.05662,-0.07206,0.02056,-0.06632,-0.00432,-0.05529,-0.07775,0.02008,-0.0356,-0.04045,0.00666,0.02817,0.00992,-0.02556,0.08815,0.11903,-0.04622,0.07051,-0.06234,-0.12548,-0.02365,-0.04484,-0.03101,-0.0894,0.01913,0.04554,0.00818,0.00276,0.03776,-0.05719,-0.08934,0.13117,-0.06221,-0.08488,-0.08542,-0.06875,0.0311,0.10037,0.10652,-0.10519,0.05282,0.03398,0.00506,0.03323,0.01128,0.079,-0.03636,-0.04034,0.00849,0.11045,-0.00447,0.02906,-0.05359,0.02982,0.02269,-0.04656,-0.00368,-0.08344,-0.03662,-0.03246,-0.12595,-0.02643,0.12575,0.03378,0.03334,-0.09087,-0.01662,0.07617,-0.05827,0.1777,0.03277,0.11593,-0.03212,-0.12852,-0.1278,0.09659,0.02079,-0.02222,-0.0069,0.09637,0.01007,0.02004,-0.05217,0.0117,-0.10781,-0.04133,0.05484,-0.04983,-0.05635,-0.0426,-0.08392,0.00845,-0.01344,-0.04704,-0.02195,-0.04801,-0.01351,-0.04386,0.01807,0.02167,-0.08824,0.0641,-0.02088,-0.02034,-0.07299,-0.0028,-0.00556,0.06508,0.11274,-0.12638,0.09045,-0.00756,-0.06586,0.03942,-0.03228,-0.05018,-0.05038,0.04896,0.01474,-0.015,-0.10985,-0.00772,-0.01501,-0.02958,0.07265,0.00745,0.00952,0.04222,-0.01033,-0.02454,-0.05503,-0.03632,0.03818,0.11512,0.14746,0.02937,0.03314,0.01843,-0.04538,0.04538,0.08383,-0.01632,-0.0323,0.09736,0.06562,0.08468,-0.06,-0.01304,0.12069,-0.16427,-0.03437,0.08432,-0.05064,-0.05186,-0.13889,0.02672,0.09652,0.02543,0.03407,-0.05334,0.03365,0.07301,0.00706,-0.05117,-0.00045,0.04171,-0.06481,-0.0049,0.05696,0.0546,0.03919,-0.0518,0.02081,-0.00327,0.04918,-0.03956,0.0187,0.10161,0.06749,0.02865,0.07448,0.05718,-0.01535,0.0083,0.05891,-0.00781,0.01684,0.03791,0.0143,0.05968,0.07516,0.02195,0.03444,0.09418,-0.04114,-0.02059,-0.10644,-0.02334,-0.09263,0.02953,-0.02341,-0.04919,-0.03339,-0.15186,0.01959,0.01292,-0.10615,0.07157,0.00851,-0.11044,0.02195,0.02845,-0.04717,-0.13199,-0.07691,0.00903,0.05339]},{"domain":"time_series","key":"exponential_trend_forecast","name":"Exponential trend fit and forecast","package":"time-series-ai999x","example":"Fit an exponential trend to [100, 112, 124, 140, 155] and forecast 1 period ahead.","v":[-0.05204,-0.01691,-0.02193,0.0038,0.0414,-0.0051,0.00368,0.02521,-0.01641,0.04327,-0.06511,0.06996,-0.01562,0.0449,0.10808,-0.02879,0.08183,0.0257,0.0682,-0.00762,-0.03144,0.01641,0.00629,0.01205,0.00352,-0.08057,-0.03751,0.00796,-0.07103,0.03981,-0.03165,-0.06944,0.0899,-0.05714,0.10267,-0.01258,-0.06004,-0.01722,-0.05499,0.08937,-0.03402,0.07561,-0.03636,-0.03844,-0.12842,-0.01633,0.03438,-0.01296,-0.04051,0.0212,-0.00183,0.06428,-0.01118,0.00767,0.0267,-0.06377,0.11388,-0.02695,-0.11158,-0.01689,-0.00969,0.06855,-0.0507,0.04438,-0.02256,0.0118,0.06331,0.00255,0.10251,-0.01301,0.10141,-0.06838,-0.10803,-0.18271,-0.02343,0.0428,0.06656,0.05034,-0.01219,0.01462,0.04884,-0.03709,-0.0113,-0.07055,0.08504,-0.04394,-0.04161,-0.00883,-0.03181,-0.08768,-0.01952,0.05195,0.13176,-0.06567,0.02525,-0.04166,-0.10615,-0.02926,0.03336,-0.065,0.01747,0.04578,0.01622,-0.03514,0.00412,-0.10211,0.0132,-0.03194,0.16518,0.0187,-0.00672,0.07877,0.05739,0.02845,0.10548,-0.01278,-0.18259,0.08312,0.07324,-0.02051,0.00863,0.06016,0.0353,-0.01903,-0.0861,0.08891,0.02969,-0.05743,-0.0492,-0.05638,-0.08212,-0.06451,-0.01411,-0.07954,-0.00056,-0.00653,-0.01574,-0.01437,0.02183,-0.04764,-0.00781,0.06419,-0.04802,0.05906,0.07377,0.01539,-0.02843,0.00955,-0.00296,0.13416,-0.06467,-0.05998,0.0182,-0.04158,-0.04145,-0.02138,-0.06872,0.08258,0.11021,0.08646,0.0279,-0.00735,0.03104,-5e-05,-0.01719,0.05407,0.05891,0.07728,-0.00465,-0.0163,-0.06482,-0.03215,-0.04228,0.1684,0.0191,0.06894,-0.01536,0.04767,-0.01158,0.11332,-0.10476,-0.08472,-0.04293,-0.04386,0.14401,-0.06636,0.08596,0.00162,-0.07082,0.01238,0.04471,0.0112,0.00351,-0.11615,0.06721,0.04622,-0.02426,-0.04291,0.04128,-0.03431,0.04823,-0.03479,-0.0326,-0.08661,0.06148,0.06702,0.06518,0.07138,0.0373,0.03816,-0.0361,-0.02458,-0.01811,-0.01586,0.0976,-0.00736,0.00941,-0.01701,0.06394,0.06764,-0.12116,-0.152,0.077,0.03595,0.05133,0.02334,-0.07864,0.06722,-0.11713,-0.06604,-0.00476,-0.05636,0.07237,0.0843,-0.00131,0.00625,0.17281,-0.02496,-0.0372,-0.07486,-0.05269,0.05486,-0.03922,0.00394,-0.0377,-0.18696,0.01435,-0.02328,-0.03839,0.03456,0.11578,-0.07081,0.09009,-0.06932,0.0656,0.01365]},{"domain":"time_series","key":"forecast_error_variance","name":"h-step forecast error variance of an ARMA model","package":"time-series-ai999x","example":"Find the 3-step forecast error variance of the ARMA(1,1) model with phi = [0.5], theta = [0.3] and sigma2 = 2.","v":[0.11134,0.03547,0.02422,-0.10308,0.07602,0.11479,0.12308,0.02132,-0.03951,-0.11818,0.05482,-0.03893,0.00112,0.06706,0.03641,-0.07514,0.15817,0.01818,-0.04112,0.03544,-0.08189,0.02931,-0.08812,0.04723,-0.0272,0.02783,0.05634,0.03051,0.02772,0.07558,0.045,0.00993,0.07113,0.06561,-0.09191,-0.08464,-0.01608,0.0388,-0.00146,-0.05198,-0.00347,-0.0633,-0.00963,0.03152,0.02302,-0.07907,0.06973,-0.03169,-0.03905,-0.04819,-0.02409,0.02094,0.00596,0.09886,0.01591,0.00952,0.08095,0.04708,0.02505,-0.03243,-0.02863,0.04519,-0.14946,0.07509,0.07108,-0.04104,0.06535,0.01698,-0.03781,-0.12394,-0.064,0.02886,-0.00722,-0.10112,0.09496,-0.01554,-0.02927,-0.05744,-0.08374,-0.05511,0.02297,-0.0046,-0.04141,-0.00531,-0.03765,0.02233,0.05818,0.01009,-0.01716,0.01035,-0.10285,-0.04945,-0.02421,0.04383,-0.02927,0.04282,-0.05934,-0.08675,-0.05749,-0.08709,0.00138,-0.01998,-0.06187,0.02688,-0.00722,-0.02559,0.00464,0.07604,0.0541,-0.03397,0.14985,0.13745,-0.07248,-0.05587,0.01467,-0.0816,-0.02425,-0.12484,-0.0109,0.04104,0.03697,-0.06239,0.05595,-0.03975,-0.00225,-0.00541,-0.07256,0.03332,0.03254,-0.04944,-0.03436,0.0367,0.01107,-0.00476,0.03067,0.03119,-0.05933,-0.09199,0.05565,0.03677,0.09451,-0.04163,0.01554,-0.04498,0.17587,-0.04123,0.00665,-0.03491,-0.0596,-0.02499,-0.04426,0.06481,-0.06071,0.01163,-0.014,0.00939,0.08311,0.15433,-0.03483,0.0589,-0.0274,0.06234,-0.04977,-0.01019,0.10066,-0.03318,0.00361,0.06739,-0.03954,-0.08069,0.03561,0.02183,0.07348,-0.05658,0.01529,-0.02397,-0.03074,0.05594,-0.00131,0.17445,0.02503,-0.04482,-0.02756,0.00347,0.06598,0.06197,0.06108,-0.05135,-0.06195,-0.00736,0.0332,-0.07161,-0.10745,-0.06988,0.09422,-0.03411,-0.02924,0.0911,-0.03944,0.08141,-0.00195,0.00382,-0.04761,0.06316,-0.01972,-0.0234,0.02806,0.00956,-0.14338,0.05708,0.01415,0.07376,0.03717,-0.01061,0.00047,-0.04737,-0.13173,-0.07524,0.08227,0.06869,0.04256,-0.06381,-0.01874,-0.02249,-0.01821,-0.01491,0.08581,-0.05065,0.0335,-0.00565,0.09512,-0.10126,0.0702,0.00114,0.03514,-0.02218,0.00177,0.02804,-0.03872,-0.10155,-0.04087,-0.04874,-0.11807,0.05341,0.05536,-0.02627,0.07359,0.11353,-0.06459,0.14277,0.01814,-0.09122,-0.05089,-0.16289,-0.03396,0.1226]},{"domain":"time_series","key":"holt_damped_trend","name":"Damped-trend Holt method","package":"time-series-ai999x","example":"Apply Holt's damped trend method with alpha = 0.5, beta = 0.3 and phi = 0.9 to [10, 12, 15, 16, 19, 21].","v":[0.0319,0.02946,0.033,-0.01957,0.02156,-0.00436,-0.01541,0.0195,-0.09443,0.04174,-0.01863,0.03044,-0.092,0.07618,0.10404,-0.02366,0.0126,0.01872,-0.07891,0.03017,-0.01245,0.0587,-0.09323,0.0081,0.03473,-0.03794,-0.04613,0.04384,-0.02189,-0.01884,0.01258,-0.10384,0.04673,-0.00734,0.14388,0.04259,-0.09842,0.02235,-0.02681,0.04808,-0.02842,-0.00157,-0.0965,-0.05143,-0.07507,-0.06416,0.102,-0.03174,-0.09153,-0.0014,0.04889,0.04744,-0.00266,0.00511,0.07677,-0.07502,0.09335,-0.02145,-0.01606,-0.01809,-0.01579,0.09236,0.0109,0.107,-0.01155,-0.0083,0.04252,0.06309,0.0413,-0.07437,-6e-05,0.02177,0.00834,-0.11233,0.0169,0.0146,0.00379,0.10094,-0.08134,-0.03487,0.05236,0.04783,-0.00433,-0.00926,0.15365,-0.07017,-0.02308,0.02019,-0.05283,0.04675,-0.0219,0.07522,0.11632,-0.07328,0.01652,-0.07498,-0.01363,-0.13677,0.00295,-0.08183,0.00896,-0.03062,-0.05195,-0.00988,-0.04783,0.00798,-0.1444,-0.00326,0.15024,0.06744,0.01245,0.05897,0.0407,-0.01151,0.02342,0.02192,-0.103,0.00482,-0.0173,0.01479,-0.01876,-0.04128,0.12076,-0.01787,-0.1413,0.08362,-0.01941,-0.06647,0.0556,-0.11805,-0.07657,-0.03827,-0.0529,-0.07536,-0.07996,0.02169,-0.07567,-0.02614,0.0115,-0.02274,-0.10391,0.00281,-0.03347,-0.00329,0.14519,-0.06905,-0.00579,0.02131,-0.06314,0.10079,0.02182,-0.10337,0.03312,-0.03356,-0.05965,-0.01571,0.03493,0.06325,0.00551,0.08114,0.02875,0.12827,-0.00453,-0.02706,0.00726,-0.02425,0.11471,0.03276,-0.02929,-0.06513,0.05504,-0.03056,-0.01621,-0.05304,0.01328,0.08719,0.0156,0.12583,0.10026,0.06077,0.01697,0.03001,0.0052,0.10506,0.20852,-0.13784,-0.00622,0.06128,-0.06918,0.04882,-0.00851,-0.02304,0.02651,-0.08862,0.03382,-0.02462,-0.05633,-0.09614,-0.0242,-0.03056,0.06063,-0.01682,-0.08461,-0.10565,0.09348,-0.01393,0.07641,0.06932,-0.05645,-0.06645,-0.00252,-0.03886,0.01835,0.0538,0.11146,0.01794,0.03903,0.05965,-0.03749,0.09631,-0.03204,-0.1046,0.05244,0.00292,0.079,0.0768,0.01327,0.02122,-0.0871,0.02686,-0.00918,-0.00844,0.05683,-0.05821,-0.0158,-0.07941,0.02099,0.00633,0.03001,-0.06572,-0.02557,0.04347,-0.06551,-0.00173,0.04278,-0.11708,0.07468,0.03763,-0.09108,0.10081,0.03149,-0.08528,0.08956,0.02291,0.08609,0.02053]},{"domain":"time_series","key":"holt_linear_trend","name":"Holt's linear trend method","package":"time-series-ai999x","example":"Apply Holt's linear trend method with alpha = 0.5 and beta = 0.3 to [10, 12, 15, 16, 19, 21].","v":[-0.00998,0.06718,0.05775,-0.0549,0.04306,-0.01063,-0.01914,0.03313,-0.07436,0.08497,-0.04069,0.03018,-0.04673,0.07732,0.08424,0.0216,0.06653,-0.00905,-0.02212,0.00285,-0.00782,0.03481,-0.09336,0.05828,0.00807,-0.01919,-0.03093,0.00631,-0.04622,-0.06773,0.00089,-0.06691,0.05494,-0.00514,0.13377,0.03473,-0.09905,0.03286,-0.06078,0.03772,-0.06102,-0.01094,-0.10716,-0.03644,-0.08046,-0.05267,0.08959,-0.02576,-0.11511,0.01242,-0.01347,0.0544,-0.00343,-0.01896,0.07658,-0.08932,0.1268,-0.04274,-0.05275,-0.02412,-0.04989,0.09022,0.00294,0.06739,0.01757,-0.0289,0.06495,0.02443,0.0541,-0.08505,-0.01627,-0.00738,-0.02166,-0.14876,-0.01677,0.05209,0.00607,0.12756,-0.02903,0.01597,0.02478,0.01978,0.04744,0.02444,0.12264,-0.08479,-0.03045,0.06576,-0.05163,0.02912,0.00494,0.08596,0.07756,-0.08344,0.0207,-0.08138,-0.05879,-0.14156,0.01325,-0.12015,-0.0099,-0.0222,0.0105,0.00569,-0.01835,-0.00667,-0.08353,-0.08411,0.2053,0.04562,0.03113,0.02037,-0.02189,-0.00581,0.06962,0.00379,-0.1087,0.01901,0.01797,0.00279,-0.02332,-0.05746,0.07328,-0.03359,-0.11739,0.08647,0.02057,-0.03816,0.09059,-0.11958,-0.05946,0.00021,-0.03573,-0.03872,-0.06822,-0.01947,-0.06729,-0.02774,0.0267,-0.09062,-0.08898,-0.01379,-0.07118,-0.02164,0.11647,-0.07498,-0.01731,0.05095,-0.08963,0.09104,-0.01921,-0.04912,0.062,-0.04691,-0.06701,0.00732,0.015,0.05357,0.03783,0.03678,0.02352,0.08152,0.0295,0.01655,0.02414,-0.05786,0.06673,-0.00492,-0.02604,-0.06318,0.01766,-0.03129,-0.01446,-0.00844,0.01125,0.0868,-0.01034,0.0702,0.06709,0.0357,-0.00556,0.0007,0.06943,0.08144,0.17643,-0.08856,0.03583,0.07829,-0.11961,-0.00447,0.01393,0.04106,-0.00029,-0.02347,0.04159,0.01249,-0.06054,-0.09623,-0.03235,-0.02124,0.06864,-0.00163,-0.12767,-0.08909,0.09518,0.01817,0.12336,0.12561,-0.04686,0.00475,0.00535,0.00774,-0.012,0.06402,0.07608,0.03822,0.11699,0.0252,-0.01664,0.09132,-0.06471,-0.10611,0.03759,0.0487,0.04399,0.06744,0.0182,0.03538,-0.07139,0.01406,-0.00054,-0.03473,0.04435,-0.05755,-0.00784,-0.10791,0.07091,-0.05375,-0.03281,-0.08483,-0.05042,0.02045,-0.06218,-0.00642,0.00978,-0.13187,0.11428,0.04345,-0.07284,0.12997,0.04291,-0.09814,0.052,0.0271,0.09265,0.04253]},{"domain":"time_series","key":"holt_update","name":"One update of Holt's method","package":"time-series-ai999x","example":"Update Holt's method with previous level 50, previous trend 2, new observation 55, alpha = 0.3 and beta = 0.1.","v":[0.03251,0.04792,0.04556,-0.07237,0.07338,0.01822,0.0219,0.01596,-0.02348,0.11886,0.0007,0.07272,0.03153,0.06297,0.05423,-0.0127,0.05436,-0.00664,0.05145,-0.00454,-0.01021,0.03341,-0.05836,0.05941,-0.0101,-0.07537,-0.07714,-0.04979,0.06101,-0.02943,0.05251,-0.04109,0.04397,-0.03213,-0.03326,0.04817,-0.1122,0.03345,-0.04191,0.02302,-0.03872,-0.00977,-0.13123,-0.03164,-0.05403,-0.0651,0.07437,-0.06713,-0.09978,-0.04381,0.06137,0.00891,-0.03117,0.00855,0.09475,-0.05281,0.05416,-0.03091,-0.07908,-0.06985,-0.06524,0.07048,-0.01977,0.03919,0.0925,-0.00379,0.03429,0.04442,0.04455,-0.09809,0.07193,-0.08121,-0.01363,-0.0387,-0.05398,-0.03315,0.02445,0.10948,-0.13479,0.0641,-0.00056,0.03155,0.03087,0.05982,0.07797,-0.06147,-0.01369,0.01942,-0.0106,0.00502,0.0298,0.08237,0.0191,-0.01,0.02605,0.0319,-0.10553,-0.06999,-0.03157,-0.14128,0.01948,0.01295,0.02264,0.03401,-0.08465,-0.06133,0.03734,-0.01741,0.22705,0.03752,0.07311,0.01407,-0.10131,-0.06598,0.10787,0.0449,-0.05224,0.05808,0.00696,-0.05081,0.00745,-0.04301,0.1162,-0.05203,-0.05953,0.04115,0.00857,-0.03562,0.03484,-0.16541,-0.07123,-0.04122,0.00098,-0.00491,-0.06287,-0.02614,-0.03149,0.03229,-0.01549,-0.09839,-0.05215,-0.02277,-0.06352,-0.06063,0.07715,-0.05693,-0.06746,0.0983,-0.09997,0.11316,-0.00458,-0.04876,0.07211,0.05395,-0.07902,-0.02269,0.06374,-0.01928,0.00669,-0.04684,-0.01658,-0.01137,0.05249,0.07231,-0.0351,-0.006,0.07749,-0.02181,-0.03927,-0.06903,0.0304,0.00816,0.00441,0.02541,-0.0162,0.09826,0.00083,0.02095,0.03804,0.05751,0.03195,-0.01071,0.08341,0.08342,0.1448,-0.16062,0.01742,0.06794,-0.17119,-0.08006,0.05235,0.02272,0.02085,-0.04559,0.02332,0.02649,-0.05916,0.03837,-0.07807,0.05075,0.05261,0.0378,-0.07567,-0.04821,0.1419,-0.05023,0.05829,0.0707,-0.04901,0.01389,-0.02949,0.03501,0.02718,0.08271,0.0268,0.05642,0.07572,0.05112,0.02829,0.05227,0.01017,-0.09095,-0.022,0.02526,-0.05953,0.05462,0.0521,0.0013,-0.02816,0.07073,-0.00382,0.01814,0.09139,-0.12894,-0.01453,-0.09297,0.01404,-0.08485,0.05005,-0.02847,-0.05908,-0.06407,-0.09072,0.03769,0.04281,-0.13199,0.12065,0.05246,-0.09219,0.06255,0.02404,-0.1073,-0.07943,0.0217,0.01556,0.09267]},{"domain":"time_series","key":"holt_winters_additive","name":"Holt-Winters additive method","package":"time-series-ai999x","example":"Apply the additive Holt-Winters method with m = 4, alpha = 0.5, beta = 0.3 and gamma = 0.2 to [30, 21, 29, 31, 40, 30, 39, 41, 50, 39, 48, 51].","v":[0.05603,0.01855,0.03705,-0.01704,0.07976,0.03156,-0.08929,0.01187,-0.02998,0.06159,-0.00179,0.03404,-0.01863,0.08574,0.06904,-0.04563,0.06848,0.04192,-0.0415,0.0774,-0.06021,0.02153,-0.06174,0.12471,-0.00599,0.05313,-0.04287,0.02728,-0.03485,0.00429,-0.01352,-0.07443,-0.0183,0.01856,0.14621,0.03261,-0.12519,0.02981,-0.00336,0.01456,-0.06462,0.01348,-0.08732,-0.01421,-0.02226,-0.02709,0.15636,-0.01524,-0.09842,0.00503,0.03469,0.04422,0.01723,0.01938,0.11571,-0.08693,0.10131,0.0023,-0.02337,-0.07374,-0.02959,0.15519,-0.03223,0.04705,0.05281,-0.04645,0.05684,-0.01079,0.02437,-0.11671,-0.0105,-0.04351,-0.07063,0.00663,-0.01877,0.07496,-0.03142,0.11999,-0.0191,-0.0379,-0.00017,0.02118,0.0283,-0.00903,0.13524,-0.07901,-0.04367,-0.03668,-0.04572,0.06294,-0.04273,0.03665,0.09737,-0.06386,0.03525,-0.07902,-0.00033,-0.11305,-0.01122,-0.0195,0.00944,-0.04683,0.03635,0.04784,-0.01707,-0.06292,-0.06683,0.01347,0.10234,0.06899,0.0142,0.02516,0.05053,-0.08339,0.05103,0.0804,-0.14668,0.03616,0.08969,0.05332,-0.04915,-0.03337,0.06251,-0.05389,-0.1493,0.01438,-0.01335,-0.08646,-0.02592,-0.12718,-0.03409,0.01568,-0.02211,-0.1329,-0.034,-0.04344,-0.11781,-0.07012,-0.02621,-0.06493,-0.07592,-0.05292,-0.09519,-0.02416,0.12148,-0.0807,-0.03554,0.02681,-0.07552,0.10499,0.00973,-9e-05,0.00221,-0.01035,-0.10409,0.06331,0.01262,0.06533,-0.00332,0.02541,0.03669,0.01438,-0.02597,0.01688,0.02409,-0.04094,0.05513,0.08997,0.04002,-0.00034,0.05854,0.02981,0.01895,0.05009,0.00143,0.10405,-0.03515,0.06705,0.04163,0.09017,0.0183,0.01397,-0.0122,0.02128,0.16647,-0.08342,0.05463,0.01011,-0.07719,-0.01717,0.04559,0.00265,-0.03394,-0.02768,0.05565,-0.01502,-0.05703,-0.05614,-0.04037,-0.01471,0.08632,-0.01302,-0.12114,-0.07745,0.06825,0.04545,0.02396,0.05391,-0.06978,-0.0419,-0.01737,0.00184,0.04843,0.01418,0.17256,0.05292,-0.01051,-0.01482,0.01239,0.11014,-0.0297,-0.13113,0.04146,0.00261,0.10497,0.05369,-0.01987,0.03716,-0.06693,-0.04799,0.01837,-0.0354,0.09768,0.07974,-0.01268,-0.11826,0.07582,0.00487,0.01641,-0.05328,-0.01435,0.02488,-0.06286,-0.0488,-0.00715,-0.038,0.11419,0.06881,-0.08261,0.13429,0.0484,-0.11523,0.05916,0.02303,0.02524,-0.04667]},{"domain":"time_series","key":"holt_winters_multiplicative","name":"Holt-Winters multiplicative method","package":"time-series-ai999x","example":"Apply the multiplicative Holt-Winters method with m = 4, alpha = 0.5, beta = 0.3 and gamma = 0.2 to [30, 21, 29, 31, 40, 30, 39, 41, 50, 39, 48, 51].","v":[0.05931,0.00888,0.03135,-0.01229,0.07686,0.03457,-0.09232,0.0007,-0.02893,0.05029,0.00101,0.04254,-0.02084,0.07982,0.07866,-0.02525,0.05803,0.02645,-0.04886,0.09832,-0.06278,0.04037,-0.04629,0.13491,-0.00314,0.0657,-0.03911,0.02193,-0.04481,0.01914,-0.01686,-0.07518,-0.01686,0.03363,0.12805,0.04706,-0.13275,0.04142,-0.01107,0.0185,-0.07044,0.03095,-0.06366,-0.01566,-0.0239,-0.0207,0.16414,-0.01194,-0.09089,-0.0094,0.03817,0.04178,0.01095,0.00571,0.1226,-0.07784,0.08379,0.0081,-0.03762,-0.06793,-0.02662,0.14059,-0.03623,0.02331,0.04934,-0.03785,0.03554,-0.00618,0.02919,-0.10885,-0.00504,-0.05373,-0.07909,0.00382,-0.01801,0.07178,-0.05675,0.1204,-0.02234,-0.06266,-0.00997,0.02857,0.02541,-0.0132,0.1311,-0.08268,-0.05496,-0.05124,-0.03946,0.0682,-0.04047,0.02194,0.10441,-0.07622,0.04689,-0.07158,0.00099,-0.10579,-0.0064,-0.00109,0.01706,-0.0485,0.03618,0.04204,-0.03192,-0.06642,-0.06754,0.02533,0.10454,0.07789,0.01226,0.01747,0.04415,-0.10062,0.03465,0.10486,-0.14777,0.04622,0.09344,0.05404,-0.04404,-0.03015,0.06964,-0.04828,-0.15758,0.01006,-0.03226,-0.08701,-0.04119,-0.09158,-0.04118,0.02942,0.00301,-0.13813,-0.02893,-0.04016,-0.1118,-0.06886,-0.02272,-0.06749,-0.07493,-0.05528,-0.08364,-0.01062,0.10567,-0.07293,-0.02562,0.01716,-0.07006,0.11169,0.01365,-0.01063,-0.00573,-0.00984,-0.09252,0.0496,0.01196,0.06054,0.00541,0.03749,0.03832,0.01277,0.00529,0.00447,0.02418,-0.0524,0.05613,0.07876,0.04521,0.01623,0.06641,0.03935,0.01922,0.04169,0.01884,0.09856,-0.02865,0.07293,0.05911,0.09192,0.0168,0.01947,-0.02756,0.01604,0.16923,-0.09281,0.04508,0.01797,-0.0907,-0.00391,0.04882,-0.00703,-0.02355,-0.0343,0.0515,-0.01327,-0.05004,-0.06544,-0.04995,-0.00469,0.08156,-0.02919,-0.10244,-0.087,0.06933,0.06411,0.00305,0.0519,-0.0744,-0.0346,-0.01904,-0.00165,0.03802,-1e-05,0.16253,0.04261,-0.01144,-0.01284,0.01456,0.11635,-0.0216,-0.14278,0.01988,0.0071,0.10035,0.05764,0.00478,0.03737,-0.05428,-0.05629,0.00172,-0.02132,0.08536,0.08601,-0.01254,-0.11188,0.06933,0.0053,0.03076,-0.05848,-0.02089,0.04423,-0.05229,-0.05988,-0.0192,-0.04105,0.10599,0.08216,-0.10363,0.13071,0.06221,-0.11605,0.06204,0.01407,0.02753,-0.04878]},{"domain":"time_series","key":"kalman_filter_constant_velocity","name":"Kalman filter for a constant-velocity model","package":"time-series-ai999x","example":"Run a constant-velocity Kalman filter with time step 1, process variance 0.1, measurement variance 1, initial position 0, initial velocity 1 and initial variance 10 for the positions [1.1, 1.9, 3.2, 4.0, 4.8].","v":[0.07867,0.09038,0.07738,0.03463,-0.04247,-0.06395,0.06807,0.09217,-0.01676,-0.1388,-0.00773,-0.02403,-0.03589,0.02074,0.07771,-0.05871,-0.01559,-0.00307,-0.02855,0.02248,-0.00482,-0.04493,-0.06233,0.02874,-0.09717,-0.01608,-0.01987,-0.07223,0.09205,-0.08499,0.03912,-0.03085,0.02395,-0.01721,0.07821,-0.07435,0.07022,0.1453,-0.07127,-0.05143,0.0763,-0.10688,-0.09229,0.01787,-0.03839,5e-05,-0.00748,0.01407,-0.04347,-0.03604,0.05725,-0.09571,0.07719,0.08468,-0.05466,-0.04351,0.14181,0.11679,0.08711,-0.0732,-0.06914,0.08255,-0.014,0.10268,-0.13972,0.03882,0.11012,0.02722,0.01714,-0.01506,-0.05669,-0.02374,0.03607,0.01135,0.02822,-0.00775,0.08655,0.05995,-0.00531,-0.05457,0.05549,-0.05358,-0.01204,0.00109,0.05726,0.07775,-0.02368,-0.01935,0.05698,0.02541,0.04277,-0.06333,0.00074,-0.0055,0.07469,-0.00645,0.09031,-0.06824,0.00995,0.00851,0.04711,-0.01856,-0.01652,0.00684,-0.0196,-0.01991,-0.08228,-0.05214,-0.01172,0.00043,0.03097,0.03023,0.00263,0.08009,-0.00737,0.08536,-0.02348,-0.09088,-0.01394,0.098,0.05116,-0.09973,0.05053,0.04857,-0.1252,-0.01138,0.03778,-0.04734,0.11864,-0.00347,-0.04337,-0.05107,-0.0898,0.05094,0.01058,-0.00468,0.01276,0.02261,0.15977,-0.10029,-0.06571,0.1138,-0.03496,0.04273,0.05669,0.02002,-0.0544,-0.01187,-0.01709,-0.03493,-0.08571,-0.13026,-0.12397,-0.09263,-0.02896,0.02054,-0.02555,0.03254,-0.06872,0.05622,-0.02471,-0.09507,0.11292,-0.05138,-0.0083,-0.00674,0.0555,-0.05246,-0.00958,-0.08399,0.00799,-0.10621,-0.1076,-0.10089,0.00564,0.05626,0.04753,-0.00126,0.0903,-0.0707,0.10187,0.00941,0.04319,-0.01963,0.04349,-0.12934,-0.0324,-0.05464,-0.02475,0.03821,0.03677,-0.02175,0.01516,0.05292,0.05652,-0.06085,0.03538,-0.04026,0.02567,-0.05363,0.00143,-0.08245,-0.10604,-0.00649,0.0576,-0.04583,-0.05217,-0.03901,0.13976,-0.06127,-0.00643,-0.02448,0.04927,-0.08921,0.07991,-0.02484,0.08343,0.06335,-0.12071,-0.06514,0.08428,-0.00206,0.00129,0.11349,0.0232,-0.01053,-0.05327,-0.0149,0.02378,-0.00266,0.05136,0.04026,0.04269,-0.03195,-0.08144,-0.02268,0.128,0.06028,-0.02823,0.11688,0.01153,0.02363,-0.00843,0.00074,0.01945,-0.02303,-0.0749,0.03314,-0.00329,0.13153,-0.02459,-0.0879,-0.01564,-0.06734,0.09106,-0.08955]},{"domain":"time_series","key":"kalman_filter_local_level","name":"Kalman filter for a random-walk (local level) model","package":"time-series-ai999x","example":"Run a Kalman filter with process variance = 0.5, measurement variance = 2, initial estimate = 10 and initial variance = 5 for the measurements [10.4, 11.1, 10.7, 11.9, 12.3].","v":[0.03845,0.03699,0.07422,0.03315,0.03326,0.05226,-0.07062,0.04142,-0.05292,-0.13204,0.0761,-0.04713,-0.02803,0.06239,0.19095,-0.06641,0.01115,0.01362,-0.07164,-0.05871,-0.07012,-0.04214,-0.04305,-0.00999,-0.10534,-0.0113,-0.07019,-0.04442,0.11056,-0.01606,0.06587,-0.02787,0.03886,0.00367,0.12916,-0.01908,-0.05473,0.09833,-0.07863,-0.09258,0.02771,-0.0473,-0.1299,0.0787,0.02944,-0.00422,0.0994,0.02169,-0.09901,-0.06667,0.00801,0.00593,0.09666,0.07755,-0.02548,-0.08781,0.06245,0.01951,0.05222,-0.01141,-0.04476,0.12095,0.00445,0.09248,-0.05875,0.00077,0.01262,0.04186,0.00502,-0.06228,-0.02876,-0.0121,-0.02149,0.09167,0.02986,0.04536,0.09485,0.02495,-0.0866,-0.07607,-0.00689,0.04992,-0.02895,0.076,0.05175,0.03088,-0.05828,0.08224,0.02112,0.01803,-0.00351,0.01119,-0.01665,-0.02781,0.08815,0.01594,-0.04891,-0.10599,-0.01624,-0.0329,0.09849,0.01839,-0.09323,0.02063,0.02807,-0.02542,-0.11089,-0.03168,0.05936,-0.07831,0.06294,0.0716,0.0723,0.05422,0.0282,0.09584,-0.02927,-0.06178,0.00035,0.05703,0.08289,-0.0442,0.06679,0.03318,-0.10429,-0.01318,0.03701,-0.07621,0.09447,-0.04811,-0.10318,-0.06028,-0.05925,-0.09594,-0.01755,0.10708,-0.07074,-0.00802,0.05912,-0.0601,-0.07368,0.08352,-0.12174,0.10403,0.0637,-0.07,-0.08836,0.02938,0.05614,-0.06099,0.00734,-0.01188,-0.09731,-0.04862,-0.08311,0.03212,-0.00898,0.07213,-0.05643,0.08837,-0.05127,0.06313,0.05321,-0.09355,0.02006,0.05298,0.03888,0.0733,-0.04934,-0.05537,0.0274,0.00683,-0.00955,-0.04262,-0.06927,0.0509,0.08258,0.06676,0.02589,-0.00369,0.04663,0.01363,0.02917,-0.02531,0.13151,-0.1067,-0.00326,-0.04292,-0.07137,0.12836,-0.0024,-0.00098,0.07377,0.04272,0.14719,0.0044,0.00414,-0.01766,0.04578,-6e-05,0.01935,-0.04835,-0.12222,-0.03064,0.12371,-0.11483,0.04746,-0.05276,-0.01333,-0.05914,0.07654,0.0437,0.03154,-0.04998,0.06308,-0.06772,0.01551,0.08454,0.00132,-0.02716,-0.00725,-0.00089,0.02472,0.0631,0.06289,-0.01955,0.03415,-0.03736,0.00876,-0.02136,-0.00034,-0.05216,0.05546,-0.02591,-0.10296,-0.04688,0.08452,0.01214,-0.05554,0.09422,-0.02791,-0.00407,0.0019,-0.061,0.02073,0.00732,-0.0236,0.08509,-0.04054,0.07773,0.0726,-0.14294,-0.06231,0.01078,-0.00279,-0.07982]},{"domain":"time_series","key":"kalman_steady_state_constant_velocity","name":"Steady-state Kalman gains of a constant-velocity model","package":"time-series-ai999x","example":"Find the steady-state Kalman gains of a constant-velocity model with time step 1, process variance 0.1 and measurement variance 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Kalman gain (random-walk model)","package":"time-series-ai999x","example":"Find the steady-state Kalman gain with process variance 1 and measurement variance 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Kalman filter step (random-walk model)","package":"time-series-ai999x","example":"Do one Kalman filter step with previous estimate = 10, previous variance = 4, process variance = 1, measurement = 12 and measurement variance = 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measurement update (scalar)","package":"time-series-ai999x","example":"Do a Kalman update with prior mean = 10, prior variance = 4, measurement = 12 and measurement variance = 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stationarity statistic","package":"time-series-ai999x","example":"Compute the KPSS statistic for level stationarity with 2 lags for [10.2, 10.8, 10.5, 11.3, 11.0, 11.9, 11.6, 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interpolation of a missing value","package":"time-series-ai999x","example":"Linearly interpolate the value at t = 2.5 from times [1, 2, 3, 4] and values [10, 14, 13, 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invertible?","v":[0.0245,-0.01702,0.06133,0.11303,-0.01661,-0.00669,-0.02784,0.04528,-0.04825,-0.05427,-0.0178,0.0408,0.01343,0.0579,0.05803,-0.02,0.02313,-0.01856,0.07544,0.04037,0.00709,0.01514,-0.0635,0.01848,-0.01109,-0.05697,-0.00996,0.08134,0.13696,0.05754,0.02772,0.07233,-0.02919,-0.04094,-0.09988,-0.09715,-0.09308,0.06699,0.02895,-0.03908,0.11115,-0.05653,0.09007,-0.04654,0.07164,0.0205,0.0952,-0.01057,0.0327,-0.03492,0.01084,0.02211,0.0274,0.09803,-0.1031,-0.02885,0.0297,0.04065,0.03978,0.11474,-0.01211,-0.07431,-0.13115,0.0159,-0.00111,-0.10508,0.00529,-0.03333,0.11894,-0.03631,-0.06452,0.03716,-0.01284,-0.04936,0.02444,-0.01229,-0.00249,-0.00682,0.05488,0.00566,0.02025,0.08678,-0.02253,0.06414,-0.00071,-0.00233,0.02803,0.01397,-0.04206,-0.10247,0.00338,0.05385,0.06619,0.06902,0.09536,0.03873,-0.05783,-0.06789,0.00834,0.04151,0.08905,-0.07182,-0.05021,0.03603,-0.09384,0.03536,-0.04666,0.05161,-0.07496,-0.01466,0.00159,0.12088,-0.03439,0.07678,0.00865,-0.10447,-0.06813,-0.14709,-0.02554,0.09833,0.11949,-0.06373,0.04111,-0.04254,0.09779,0.0426,0.04382,0.01231,0.07207,-0.02133,-0.07136,-0.00449,0.00738,-0.06646,0.05323,0.03065,-0.04778,-0.03177,-0.01362,-0.07119,0.13293,-0.04146,-0.02313,-0.04324,0.14133,-0.02112,0.00367,-0.02773,0.07673,-0.09869,0.03314,0.08515,-0.10199,-0.02051,-0.02312,-0.01508,-0.05131,0.13157,0.03139,0.11233,0.00423,0.01325,-0.10237,-0.15114,-0.03141,0.01272,0.02579,0.13138,0.01889,-0.01648,0.08537,0.02173,0.13527,-0.07195,0.02311,-0.09594,0.09616,0.00745,-0.07559,-0.01229,0.02196,-0.06875,0.00377,-0.02125,0.01977,0.00551,-0.01295,0.10878,-0.01452,-0.01856,0.04211,-0.08748,0.01988,-0.07649,-0.06122,-0.02635,-0.08195,-0.0072,0.01112,0.16727,-0.0054,-0.00664,-0.08451,-0.0451,0.06731,-0.10361,0.08285,0.02835,-0.09661,-0.0446,0.07635,0.04735,0.00454,-0.02136,0.09686,0.02772,-0.18178,0.01453,0.06681,-0.08432,-0.03107,0.01478,0.01603,-0.06731,0.04585,-0.05843,-0.02469,-0.11686,-0.06572,-0.00808,0.05994,0.01042,0.03051,-0.0758,0.006,0.00235,-0.12713,-0.05098,-0.08694,-0.07339,-0.01539,0.095,0.0201,0.05467,0.10066,-0.0113,0.0082,0.00302,-0.02991,-0.02916,0.00927,0.01621,-0.00849,-0.05462,-0.01887,0.01527]},{"domain":"time_series","key":"ma_theoretical_acf","name":"Theoretical autocorrelations of an MA(q) process","package":"time-series-ai999x","example":"Find the autocorrelations of the MA(2) process with theta = [0.5, 0.3].","v":[0.01917,-0.00432,0.00077,0.04488,-0.01866,-0.01802,0.08923,0.01705,0.02635,-0.05367,0.09109,-0.00314,0.01356,0.07425,0.02418,-0.0456,0.08428,-0.07268,0.06011,0.00751,0.03379,0.10408,-0.1117,-0.0706,-0.00214,0.05225,-0.00359,0.05744,-0.01798,-0.03957,0.07918,0.0206,0.03623,0.00845,-0.05092,-0.07979,-0.00676,0.08017,0.02438,-0.04766,-0.07374,-0.05609,-0.00389,-0.06618,-0.00012,0.04137,0.10735,-0.03936,0.01383,-0.02318,-0.00244,0.14703,0.08016,0.04542,0.01218,-0.09307,0.00382,0.04691,0.10675,0.05579,0.05365,-0.12269,-0.07146,0.05568,0.03464,-0.0797,0.07998,0.03283,0.01291,-0.06532,-0.09203,0.04179,-0.0262,-0.04737,0.07738,0.00505,0.14582,-0.04215,-0.0154,0.01922,0.0599,-0.01204,-0.10705,0.07616,0.0639,-0.02146,0.03337,0.04875,-0.00543,-0.10439,-0.02684,-0.02906,0.01359,0.0109,-0.06532,-0.01292,-0.03288,0.01327,-0.00853,0.02167,-0.00011,-0.18301,-0.01518,0.00022,0.00786,0.02348,-0.06999,0.10249,0.04818,-0.05683,-0.0621,0.08358,-0.0002,-0.04077,-0.03127,0.03836,-0.01721,-0.08423,0.0154,0.02778,0.07672,-0.02574,0.05403,0.0431,0.01175,-0.00397,0.02795,-0.04997,0.04094,0.03009,0.00395,0.02878,-0.01179,-0.05524,0.06377,0.06177,0.01616,-0.02299,-0.0958,0.05906,-0.03402,-0.11815,0.04813,-0.02215,0.18437,-0.07495,0.05836,0.07842,0.05543,-0.07616,0.06959,0.01316,-0.02115,-0.08587,-0.09774,-0.01634,-0.05498,0.17798,-0.11131,0.08452,-0.08612,-0.0278,-0.07222,-0.11593,0.04402,0.0485,-0.02126,0.08187,-0.00924,0.00579,0.0518,-0.0124,0.01209,-0.10472,0.05374,-0.01232,0.03544,-0.05738,-0.08301,0.11138,0.0676,0.07499,-0.02005,-0.04038,0.08091,-0.03042,-0.18155,0.00722,-0.03704,-0.00584,0.09251,-0.00213,0.02096,0.00413,-0.06815,-0.02631,0.03605,0.00863,0.00021,-0.028,-0.03359,-0.05315,0.0098,0.11627,0.03316,-0.09104,-0.00656,-0.04902,-0.01229,0.00812,0.0077,-0.08937,0.00018,0.07223,0.02002,0.06426,-0.20465,-0.06929,-0.03774,0.03729,0.06862,-0.05835,-0.00186,-0.00672,0.06175,-0.11611,0.14351,0.00025,-0.00386,-0.06538,-0.03685,0.02606,0.03833,-0.11621,0.00322,-0.05323,-0.01184,0.07742,-0.03223,-0.03846,0.02629,0.02132,-0.0304,0.00245,0.07946,-0.00767,0.13968,0.05115,-0.02598,0.14876,-0.00432,-0.01693,-0.00583,-0.05789,-0.05289,-0.09125]},{"domain":"time_series","key":"mann_kendall_test","name":"Mann-Kendall trend test","package":"time-series-ai999x","example":"Perform the Mann-Kendall trend test on [12, 14, 13, 17, 16, 19, 25, 21, 24].","v":[0.01509,-0.09632,0.02887,0.04572,-0.01519,0.00984,-0.07339,0.07427,0.01433,-0.0687,0.0104,-0.01648,-0.12639,-0.05263,0.05366,-0.01945,0.07915,-0.03355,-0.02503,-0.02291,0.02417,-0.07266,-0.09486,0.02803,-0.027,0.03802,-0.00883,0.00277,-0.05432,-0.07053,-0.10084,0.00092,0.01534,0.07657,0.00788,-0.0027,-0.03269,0.02181,0.07985,-0.11018,0.00388,0.00151,-0.03828,0.04971,0.05552,-0.07808,0.08988,0.05635,0.0522,0.07058,-0.06932,0.07596,0.07536,0.07396,0.00131,-0.1008,-0.02352,0.02508,0.01646,-0.00468,0.04124,0.01844,0.00411,0.05391,-0.04767,-0.02703,0.07656,0.07253,0.06124,-0.03367,-0.05264,0.03556,0.10675,0.14108,0.10851,0.01757,0.06958,-0.06955,0.09918,-0.13242,-0.10485,0.06485,-0.01791,-0.04403,0.0512,0.04103,-0.00322,0.11404,-0.09593,-0.03084,-0.11289,-0.05559,-0.03839,-0.00303,0.02402,-0.07629,0.07973,-0.02784,-0.02981,0.09539,0.08062,0.02216,-0.12918,0.04168,0.04957,0.03955,-0.15938,0.02395,-0.0327,0.05974,-0.11007,0.05779,0.03686,0.06833,0.03667,0.0046,0.07465,0.00116,-0.00535,0.09057,0.06227,0.03527,0.0621,0.0285,-0.15316,-0.01149,0.02045,-0.08817,-0.00393,-0.00453,0.03065,0.04488,-0.04119,-0.02052,0.04708,-0.03323,-0.04397,-0.02653,0.03326,0.0649,-0.09907,0.04508,-0.06398,0.11329,0.0494,-0.12332,-0.0485,0.08327,0.05261,0.00531,0.03431,-0.11352,0.00136,-0.03041,-0.02647,0.07927,0.07031,0.04787,-0.08315,-0.05434,-0.04435,-0.00699,-0.04736,-0.1435,0.07102,-0.02318,-0.11788,0.16347,0.04852,0.0361,-0.00466,-0.01673,0.04734,-0.05959,-0.00298,0.02706,0.03857,0.08885,-0.01251,-0.02089,-0.04605,-0.09456,0.0072,-0.02792,0.10469,0.04288,-0.0895,-0.02707,0.02632,0.12374,-0.02086,-0.06401,-0.02014,0.01184,0.04905,0.00822,-0.11591,-0.0089,0.08114,-0.1329,0.00408,0.02763,-0.07067,-0.0767,0.05746,0.05557,0.019,-0.03312,-0.0125,0.02842,0.01931,0.04074,-0.07663,-0.03383,0.02461,-0.07363,-0.03859,-0.04144,-0.15503,-0.02018,0.00519,-0.01247,0.08483,-0.01626,0.01442,-0.0116,0.01264,-0.04958,-0.11261,-0.03251,0.01049,-0.04758,0.03237,-0.06511,0.05833,-0.04153,-0.02912,0.1046,0.01346,0.02023,-0.04319,-0.00149,0.12689,0.0255,0.05493,-0.04317,-0.01513,0.12737,0.06738,0.06381,0.06418,0.01346,0.00174,-0.04812,0.03612,-0.10438]},{"domain":"time_series","key":"mean_absolute_error","name":"Mean absolute error","package":"time-series-ai999x","example":"Find the MAE for actual values [10, 12, 14, 13] and forecasts [11, 12, 13, 15].","v":[0.11382,-0.04964,0.10659,0.06192,0.09038,0.00602,0.07511,0.06733,0.01168,-0.02416,0.05662,-0.00702,0.13673,-0.05084,-0.06424,-0.03185,0.09817,0.01028,0.04312,0.05571,0.01435,0.03181,-0.00612,0.04711,-0.02877,0.0495,-0.01518,-0.04078,0.04021,-0.00374,0.09791,-0.03806,0.03578,-0.12063,-0.09104,-0.09625,0.02728,0.04526,0.06704,-0.00301,-0.0472,-0.00344,0.06175,0.07848,0.05665,-0.04799,-0.0225,0.01475,0.13394,-0.01158,-0.07143,-0.02292,0.03652,0.14551,0.11119,-0.15339,0.06284,-0.06277,0.00799,-0.05533,-0.05839,-0.05154,-0.11572,-0.03219,0.11298,-0.06463,0.02805,0.05143,-0.11747,-0.00626,0.10449,0.07864,0.00386,-0.11468,0.00121,0.06399,0.04252,-0.0358,-0.06771,-0.01032,0.02639,-0.05758,-0.0119,-0.05321,0.01165,-0.04965,0.08052,-0.02856,0.03691,-0.02464,-0.02622,-0.06171,0.02332,0.04941,-0.05381,-0.02399,-0.04627,0.00145,-0.12478,0.03806,-0.02063,-0.0982,-0.09059,0.03561,-0.13436,0.0779,-0.05865,0.01609,0.0103,0.06652,0.00364,-0.02684,-0.01134,-0.01857,-0.03625,0.01509,-0.07399,0.02561,0.11213,0.08879,0.13682,-0.05107,-0.0533,-0.13169,0.0517,0.00774,0.02038,-0.00784,-0.04529,0.02997,0.09031,-0.03786,-0.01657,0.0182,-0.0226,-0.10537,-0.01355,-0.07508,0.04861,-0.01735,-0.03561,-0.0324,0.08762,0.0803,0.05796,0.03804,0.00057,-5e-05,-0.02439,-0.12615,-0.05263,0.07205,-0.05503,-0.07867,-0.10251,0.02354,0.06457,0.08845,-0.07668,-0.0228,0.06164,0.00489,-0.06339,-0.04642,-0.03121,-0.04799,-0.01213,0.00814,0.09752,-0.05238,-0.04657,-0.12103,0.07403,0.04717,0.02801,-0.04097,0.05752,-0.09926,0.06331,0.10388,0.05612,-0.02697,-0.02879,0.03464,-0.01667,0.09604,-0.03497,0.09929,-0.06198,-0.0493,0.03984,-0.03572,-0.08619,-0.07265,-0.02211,0.11325,0.02517,0.1338,-0.10514,0.04622,0.10817,-0.01873,0.01275,0.0995,-0.05917,-0.0543,-0.0535,0.01142,-0.05789,0.06527,0.0339,-0.05014,-0.01359,0.02338,-0.07041,-0.0619,0.04452,0.00743,0.02427,-0.01791,0.00188,0.0655,0.00731,0.04314,-0.02585,-0.0901,0.02031,-0.05383,0.00267,0.0316,0.02949,-0.02386,0.06496,0.04336,0.05096,-0.00527,0.0571,-0.02575,-0.03505,-0.0838,0.046,0.028,-0.10685,0.07108,0.00264,-0.10058,0.07243,-0.01385,-0.05752,-0.03703,0.08022,0.0147,-0.08239,-0.09261,-0.0971,0.02978]},{"domain":"time_series","key":"mean_absolute_percentage_error","name":"Mean absolute percentage error","package":"time-series-ai999x","example":"Find the MAPE for actual values [10, 12, 14, 13] and forecasts [11, 12, 13, 15].","v":[0.12036,-0.02789,0.11209,0.08616,0.0716,0.00775,0.08701,0.04155,0.01601,-0.02585,0.06743,-0.01524,0.12777,-0.05878,-0.0549,-0.00818,0.11639,0.00124,0.03767,0.04867,0.04337,0.04689,-0.00393,0.02797,-0.04261,0.05038,-0.02999,-0.03896,0.02383,0.01433,0.07723,-0.03834,0.08134,-0.07601,-0.08818,-0.08936,0.02067,0.05642,0.09456,0.0068,-0.03823,0.01805,0.05792,0.08218,0.04319,-0.06098,-0.00411,0.01514,0.14655,0.00539,-0.06864,-0.01909,0.01135,0.1376,0.11642,-0.12575,0.06633,-0.04164,0.01378,-0.06907,-0.04488,-0.09201,-0.11378,-0.02176,0.0931,-0.07055,0.01366,0.04194,-0.10165,0.00226,0.09848,0.07706,0.04029,-0.15723,-0.01769,0.06052,0.03721,-0.02615,-0.09267,-0.0088,0.01451,-0.06413,0.00094,-0.07779,0.00581,-0.07199,0.05742,-0.05184,0.02543,-0.01931,-0.02892,-0.04135,0.0286,0.04143,-0.0483,-0.0308,-0.02773,0.00629,-0.08711,0.04727,-0.01816,-0.09524,-0.05448,0.01839,-0.1511,0.07383,-0.05734,0.02909,0.0128,0.07152,-0.00065,-0.02835,-0.00276,-0.03963,-0.06372,0.02557,-0.07252,0.02975,0.11532,0.07764,0.14386,-0.07366,-0.05007,-0.12195,0.01929,0.04147,0.02603,-0.02058,-0.06656,0.06063,0.09317,-0.03685,0.00211,0.01187,-0.03304,-0.09162,-0.01207,-0.10283,0.0253,-0.00204,-0.04893,-0.0514,0.11418,0.06897,0.07039,0.0259,0.02602,-0.03038,-0.04663,-0.0938,-0.07516,0.02897,-0.017,-0.06826,-0.08075,-0.0153,0.04261,0.08888,-0.06831,-0.03131,0.0591,0.01831,-0.05694,-0.05961,-0.00608,-0.06131,0.00811,-0.00121,0.1136,-0.05203,-0.0462,-0.13548,0.08235,0.02228,0.09721,-0.01617,0.06194,-0.06461,0.09848,0.08841,0.03762,-0.02564,-0.03339,0.0259,-0.01404,0.09506,-0.03752,0.10728,-0.08497,-0.05269,0.062,-0.03853,-0.07037,-0.07796,-0.06171,0.1104,0.02538,0.10457,-0.08558,0.05533,0.11683,-0.03516,0.02662,0.10817,-0.03504,-0.0723,-0.03975,0.00177,-0.07846,0.06438,-0.00828,-0.08541,-0.03939,0.00896,-0.04986,-0.03086,0.05416,0.04152,0.00701,-0.00792,0.01246,0.03027,0.01784,0.03543,-0.01784,-0.09248,0.01745,-0.0446,-0.00643,0.00042,0.04921,-0.01003,0.03562,0.02819,0.02702,0.0093,0.0406,-0.03018,-0.01836,-0.10292,0.02821,0.05334,-0.12067,0.06025,-0.01234,-0.09358,0.07504,-0.01708,-0.05433,-0.02463,0.04293,0.04486,-0.0709,-0.11215,-0.07237,0.05006]},{"domain":"time_series","key":"mean_absolute_scaled_error","name":"Mean absolute scaled error","package":"time-series-ai999x","example":"Find the MASE for training data [10, 12, 11, 14, 13], actual values [15, 14, 16] and forecasts [14, 15, 15].","v":[0.12057,0.01947,0.08208,0.06187,0.07003,0.03777,0.03035,0.07847,0.01362,-0.05012,0.06514,0.03784,0.13763,-0.03657,-0.04838,-0.01644,0.10221,0.03132,-0.0249,0.04802,0.02624,0.02311,-0.00797,0.052,-0.0405,-0.00706,-0.00175,-0.11229,0.05316,0.02499,0.10114,-0.04601,0.02207,-0.11209,-0.04541,-0.08601,0.00373,0.06029,0.04154,0.02453,-0.04918,0.01018,-0.00327,0.07346,0.08164,-0.01137,0.02904,0.02733,0.15747,-0.02553,-0.04906,-0.03993,0.00275,0.16392,0.14789,-0.15734,0.10495,-0.04949,0.03014,-0.02297,-0.05227,-0.03081,-0.0984,-0.02699,0.10743,-0.03174,-0.0028,-0.01274,-0.08649,-0.02425,0.14645,0.02522,-0.00435,-0.09659,-0.01788,0.09802,0.03055,-0.06712,-0.07131,0.01792,0.0346,-0.02756,-0.01498,-0.07349,0.02565,-0.00487,0.0034,-0.04526,0.04974,-0.03537,-0.00848,-0.01633,0.0127,0.08067,-0.01252,0.02778,-0.07178,-0.00272,-0.08347,-0.00742,-0.01696,-0.14582,-0.08265,0.02427,-0.12426,0.09706,-0.04171,0.02666,0.06456,0.0572,0.02163,-0.01009,0.0158,-0.10301,-0.02481,0.03403,-0.13934,0.07289,0.10162,0.09344,0.09564,-0.04037,-0.05687,-0.15121,0.08398,-0.05958,-0.00394,-0.01127,-0.04391,-0.0013,-0.00976,-0.06739,-0.03893,-0.05922,0.01099,-0.12861,-0.03565,-0.06935,-0.00501,-0.02094,-0.03912,-0.02302,0.04175,0.06443,0.08046,0.05812,-0.02101,-0.00815,-0.04704,-0.03576,-0.03535,0.05301,-0.0619,-0.03149,-0.14339,0.00953,0.06561,0.10283,-0.02156,-0.0096,0.04988,0.02423,-0.06988,-0.03163,-0.01958,-0.03272,-0.01735,0.06294,0.07344,-0.04267,-0.04263,-0.11356,0.09811,0.09777,0.05063,-0.03339,0.04672,-0.10702,0.03177,0.08613,0.12182,0.00301,-0.00474,0.03031,-0.05896,0.02838,-0.00359,0.04904,-0.06919,-0.07575,0.05081,-0.04826,-0.05907,-0.10285,0.02468,0.11618,0.04267,0.13225,-0.10345,0.11825,0.08112,-0.04553,-0.02831,0.08561,0.03872,-0.05772,-0.04603,0.00209,-0.0567,0.0303,-0.00993,-0.05788,0.01324,0.01616,-0.02793,-0.02547,-0.01751,-0.02277,0.04264,-0.01472,-0.02967,0.01295,-0.01338,0.04093,0.01208,-0.0008,-0.01314,-0.06718,0.00357,0.02401,0.02827,-0.04092,0.10225,0.11338,-0.01786,-0.00236,0.02052,0.00834,0.02045,-0.07924,0.03527,0.06223,-0.10854,0.05731,-0.01567,-0.07373,0.09156,0.00674,-0.06845,-0.02884,0.07223,0.02672,-0.03802,-0.05586,-0.08558,-0.02585]},{"domain":"time_series","key":"mean_forecast_error","name":"Mean forecast error (bias)","package":"time-series-ai999x","example":"Find the mean forecast error for actual values [10, 12, 14, 13] and forecasts [11, 12, 13, 15].","v":[0.10379,-0.08086,0.13636,0.01254,0.1038,0.00767,0.06482,0.0649,-0.00693,0.01382,0.088,0.00488,0.09803,-0.06512,-0.04321,-0.02888,0.04603,0.04904,-0.04518,0.055,-0.03514,-0.00762,0.01568,0.09704,-0.01349,-0.00988,-0.01726,-0.0954,0.08702,-0.01804,0.06367,-0.01567,0.06066,-0.14322,-0.04621,-0.07352,0.04214,-0.02627,0.02142,0.04191,-0.04476,0.01743,0.08772,0.08197,0.08163,-0.06013,-0.05962,-0.01474,0.08332,0.06438,-0.06639,-0.02506,0.05654,0.12042,0.09768,-0.02887,0.02701,-0.01023,-0.05535,-0.07374,-0.06021,-0.0046,-0.12067,-0.02775,0.12764,0.04295,0.03364,0.00216,-0.09938,-0.04494,0.06759,0.0218,-0.08033,-0.06456,-0.00233,0.06989,-0.02848,0.00519,-0.104,-0.06112,-0.00781,-0.0492,0.00173,-0.05806,-0.0149,-0.07813,0.05022,-0.01387,0.05892,0.00114,-0.03371,-0.06247,0.033,0.03616,-0.04623,0.0841,-0.06457,0.01383,-0.19279,0.04461,-0.035,-0.00446,-0.07754,0.05696,-0.07476,0.03429,0.0691,0.01942,0.0716,0.03324,0.02388,-0.03668,0.00448,-0.07845,-0.03674,0.03353,-0.04438,-0.00268,0.12357,0.0817,0.11283,-0.02611,-0.08804,-0.14914,0.01373,-0.01654,0.0622,0.01239,-0.0872,-0.02099,0.10151,-0.04906,0.06253,-0.01212,-0.01608,-0.0991,0.00627,-0.02429,-0.00809,-0.04782,-0.00649,0.04787,0.04657,0.01494,-0.00682,0.04756,0.01837,0.03881,-0.01659,-0.08931,0.00239,0.07601,0.06954,-0.07637,-0.0667,0.01944,0.08197,-0.0072,-0.09282,-0.00519,0.10513,-0.02845,-0.09024,-0.03434,-0.0094,-0.01022,-0.00463,0.01288,0.0547,-0.06569,-0.03923,-0.06401,0.02778,0.11907,0.01884,-0.02211,0.03305,-0.09207,0.02968,0.08672,-0.01078,-0.08938,0.01314,-0.0039,-0.00873,0.06354,-0.01429,0.11139,-0.04001,-0.03629,0.0231,-0.05652,-0.09388,-0.11794,-0.0101,0.09714,0.00192,0.14876,-0.07494,0.04934,0.10419,0.041,-0.00037,0.04948,-0.04187,-0.07385,-0.06937,0.06298,-0.01786,0.07347,0.01878,0.02505,0.00638,0.02775,-0.00138,-0.0611,0.0925,0.08589,0.09555,-0.01143,-0.0398,0.06451,0.01926,0.03201,0.00989,-0.10791,0.03398,-0.05752,0.00822,0.07177,-0.02261,-0.09437,0.02867,0.08443,0.00363,0.02675,0.0421,0.03479,-0.03528,-0.01841,0.00474,-0.01957,-0.09962,0.02146,0.00996,-0.1388,0.09093,0.01365,-0.08062,-0.09135,0.09125,-0.01795,-0.1608,-0.08865,-0.10825,0.03329]},{"domain":"time_series","key":"mean_squared_error","name":"Mean squared error","package":"time-series-ai999x","example":"Find the MSE for actual values [10, 12, 14, 13] and forecasts [11, 12, 13, 15].","v":[0.1182,-0.05984,0.12607,0.03432,0.08221,-0.01654,0.04221,0.0863,0.00667,-0.06624,0.08282,-0.05207,0.15416,-0.08379,-0.06899,-0.01375,0.11065,0.01711,0.02823,0.06446,-0.01694,0.01136,0.03438,0.05662,-0.04423,0.01849,-0.0513,-0.05526,0.00936,0.02439,0.07739,-0.04207,0.05217,-0.11487,-0.02742,-0.10273,0.07221,0.00798,0.06841,-0.00556,-0.00714,0.01774,0.04094,0.0924,0.023,-0.04115,-0.01866,0.01964,0.05796,0.00888,-0.08405,0.00619,0.03109,0.089,0.11134,-0.0903,0.09861,-0.04358,-0.03506,-0.03488,-0.01566,-0.03648,-0.13717,-0.00211,0.11694,-0.01196,0.04253,0.02397,-0.14622,0.00071,0.08916,0.02516,-0.0927,-0.05343,-0.03551,0.05824,0.01141,0.00763,-0.14106,-0.01383,0.00258,-0.05577,-0.00536,-0.03012,-0.0278,-0.10429,0.02438,-0.02684,0.0843,-0.02337,-0.03163,-0.07261,0.07307,0.02197,-0.06569,-0.05349,-0.0115,0.01979,-0.17157,0.02854,-0.02079,-0.0227,-0.07089,0.06032,-0.15549,0.04031,0.00669,0.02946,0.0499,0.0496,0.00769,-0.04184,-0.00541,-0.03202,-0.05435,0.04359,-0.05511,0.01687,0.11324,0.06629,0.10573,-0.01186,-0.0604,-0.15845,0.01421,-0.0297,0.00771,0.01604,-0.0633,0.03188,0.13392,-0.02386,-0.01639,-0.00648,0.01278,-0.07606,-0.03384,-0.03673,0.04273,-0.02467,-0.03626,0.00019,0.10139,0.07694,0.00991,0.0247,-0.00415,0.06731,-0.00563,-0.10916,-0.01777,0.06277,-0.04372,-0.06782,-0.09792,0.01671,0.05733,0.03616,-0.08617,0.06121,0.08948,0.02559,-0.03685,-0.02524,-0.00528,-0.01448,-0.04994,0.04831,0.05229,-0.06939,-0.07824,-0.04523,0.05183,0.09666,0.00672,-0.06614,0.06508,-0.05282,-0.02323,0.09608,-0.00039,-0.02056,-0.03389,-0.00587,0.03644,0.07397,-0.03896,0.06842,-0.08222,0.01276,0.04509,-0.04315,-0.07677,-0.0682,0.01248,0.12536,0.0028,0.13064,-0.05474,0.02963,0.1294,0.02122,0.00212,0.01908,-0.07149,-0.07925,-0.10723,0.04135,0.00125,0.06132,0.04732,-0.01377,0.02992,0.01233,-0.04923,-0.02434,0.05676,0.03392,0.08204,-0.01064,-0.03401,0.07159,0.00567,0.06169,0.03383,-0.08385,0.0482,-0.05382,0.01181,0.05405,0.0281,-0.03341,0.05217,0.05097,0.03568,-0.0152,0.07035,-0.01973,-0.00449,-0.06926,0.06107,-0.00365,-0.11932,0.03459,-0.05424,-0.13033,0.10384,-0.01279,-0.05529,-0.02935,0.04535,0.00193,-0.15208,-0.09197,-0.15265,0.06235]},{"domain":"time_series","key":"partial_autocorrelations_from_autocorrelations","name":"Partial autocorrelations from autocorrelations","package":"time-series-ai999x","example":"Find the partial autocorrelations from the autocorrelations [0.6, 0.3, 0.1].","v":[-0.04439,-0.04012,0.0149,0.01953,0.02429,0.06748,0.05163,-0.05597,0.05745,0.00961,0.03139,0.0179,-0.04699,0.02972,0.01908,-0.00235,0.02923,0.01541,0.02317,0.02222,0.0318,0.07966,-0.10348,-0.04866,0.02425,0.05668,0.0372,0.10179,0.08142,0.04848,-0.03227,-0.05835,0.05719,0.04193,0.05702,0.01667,0.04105,-0.02238,-0.07986,0.04301,0.02576,-0.13128,-0.08115,-0.10542,-0.0322,-0.00859,0.14514,-0.0379,-0.12002,-0.0498,0.06147,0.02753,0.01028,0.06344,-0.02688,-0.10111,-0.00792,-0.05082,0.094,-0.03978,0.04498,-0.03952,-0.01821,0.01393,-0.01495,-0.02369,0.05758,0.00209,0.02063,-0.15868,-0.03811,0.01186,0.00352,-0.1027,-0.00073,-0.02772,0.08581,-0.09149,-0.05914,-0.14953,0.02506,0.02144,-0.05828,0.07935,0.10249,-0.057,-0.01866,0.012,0.01793,-0.09504,0.00826,-0.0017,-0.06407,-0.02995,-0.10277,0.02327,0.05601,-0.02669,0.00649,0.03728,0.01382,-0.09094,0.06354,-0.07036,-0.0308,0.03461,-0.09493,0.07475,0.07869,0.08493,-0.0717,0.00839,-0.00704,-0.03317,0.00223,0.12052,0.02029,-0.01731,-0.03347,-0.04211,0.00728,0.03491,-0.03038,0.20333,-0.09745,0.08146,0.0167,0.03545,0.00601,0.00749,0.06677,0.00061,0.09449,0.02218,0.04189,0.09027,-0.01493,0.03944,-0.01192,0.14628,-0.00992,0.02609,0.05873,-0.08525,0.16667,-0.02486,0.01227,0.00197,-0.00313,0.0522,0.03657,-0.01789,0.01073,-0.07861,0.00029,-0.01377,-0.01205,0.09237,-0.02116,0.0851,-0.09553,0.00644,-0.05653,-0.11162,0.054,0.01369,-0.04627,0.16216,-0.01519,0.04953,0.0661,-0.00576,-0.02036,-0.05759,0.0037,0.11096,0.04983,-0.01765,0.00484,0.11219,-0.05845,0.03638,-0.01044,-0.00364,0.13192,-0.0364,-0.1412,-0.07025,-0.06054,0.02775,0.01874,0.08549,0.04928,-0.02167,-0.08331,-0.09512,-0.04432,0.00826,0.08716,-0.0609,0.00408,-0.09436,-0.04388,0.05844,0.00105,-0.04829,0.00439,-0.07878,0.07191,0.05867,-0.05174,-0.12622,-0.10717,0.02339,0.06264,0.0091,-0.0908,-0.00362,-0.04066,0.03911,0.07699,-0.06795,-0.04057,-0.0551,0.05332,-0.02248,0.12119,-0.03998,-0.02597,-0.10275,0.00955,-0.04851,-0.02278,-0.09118,-0.03397,-0.08768,-0.01813,0.11715,0.0484,0.02446,0.06646,-0.05698,-0.02937,0.00272,0.07419,-0.02033,0.10094,-0.01469,-0.04331,0.06088,-0.02011,-0.11809,-0.03634,-0.09229,-0.01821,-0.04599]},{"domain":"time_series","key":"penalised_change_points","name":"Multiple change points with a penalty (PELT)","package":"time-series-ai999x","example":"Find the change points with PELT and penalty 10 in [5, 6, 5, 12, 13, 12, 20, 21, 19, 20].","v":[-0.0199,0.0564,0.06226,0.04115,-0.09643,0.00478,-0.00475,-0.03115,-0.01046,0.01258,-0.04934,0.0045,-0.03911,-0.05328,0.01672,-0.11469,0.07118,0.00904,0.09368,0.07761,-0.0888,0.02286,-0.03281,-0.05707,0.02372,0.08721,-0.03016,0.07915,0.0598,0.00816,-0.06937,-0.04233,-0.02698,-0.00972,0.04432,-0.08027,-0.00682,-0.10636,-0.01939,0.00859,0.01814,0.10405,0.06447,0.02816,0.09535,0.08563,0.10127,0.0798,0.02103,-0.06625,-0.08361,0.04169,0.05015,-0.03742,0.04604,-0.06349,-0.10963,0.07514,0.00822,-0.03712,-0.04083,0.04941,-0.04955,0.01675,-0.01361,-0.07193,0.00572,0.06522,0.05968,0.1058,-0.05075,0.11635,0.04231,-0.01227,0.00049,0.04488,0.12393,0.06581,0.02662,0.0341,-0.01251,-0.01949,0.06223,-0.01106,0.06813,-0.04305,-0.05222,-0.0755,-0.08528,0.00499,-0.06813,0.04035,-0.03142,0.01674,-0.00179,-0.16477,-0.06834,0.06864,-0.04128,-0.00671,-0.02038,-0.0403,0.05196,-0.0391,-0.09029,0.09117,-0.07546,-0.06793,-0.13638,0.15596,0.01474,0.06303,0.10222,0.06059,-0.03298,-0.00843,0.06296,0.06547,0.05038,-0.00554,0.03985,0.1395,0.03664,0.16966,-0.05802,0.03782,-0.02126,-0.09038,0.17353,0.00502,0.02572,-0.04863,-0.09321,0.02074,0.05037,-0.08493,0.06035,0.03239,-0.0003,0.13297,-0.0548,0.0043,0.05619,0.0758,0.08924,0.03566,-0.02429,-0.02094,0.00607,-0.00461,-0.0573,-0.1344,-0.04554,-0.09134,-0.01196,-0.05789,-0.00515,-0.00216,0.01873,0.02739,-0.07148,0.00926,0.02531,-0.00222,0.02149,-0.02691,-0.00625,-0.05787,0.0134,-0.01663,-0.01152,0.02754,0.1391,0.00429,0.00099,0.02558,0.03752,0.03538,-0.07943,0.06745,-0.09854,-0.01825,-0.02571,-0.02012,-0.00043,-0.07093,-0.01372,-0.03768,0.05519,0.01282,-0.12065,0.06004,0.00877,0.07386,0.04421,0.06472,-0.04111,-0.12746,0.12321,-0.14315,-0.06236,0.04373,0.07056,-0.00567,0.04242,0.012,0.05858,-0.04893,-0.07836,0.08032,-0.04975,-0.04432,0.03009,-0.01207,-0.03867,0.02604,-0.07562,0.00363,-0.08017,0.04548,-0.07772,0.0296,0.07791,0.02034,-0.00745,-0.02876,-0.08388,-0.01043,-0.10255,-0.01478,-0.01805,-0.08473,-0.0091,-0.13531,0.05069,0.01399,-0.03724,-0.09764,0.02334,-0.04348,0.07181,-0.08823,0.00808,0.06388,-0.01436,-0.05466,-0.17223,0.0032,-0.01455,-0.00143,0.0677,-0.03004,-0.05312,0.00573,0.06354,-0.00158]},{"domain":"time_series","key":"pi_weights","name":"Pi weights (AR-infinity representation) of an ARMA process","package":"time-series-ai999x","example":"Find the first 5 pi weights of the ARMA(1,1) process with phi = [0.5] and theta = [0.3].","v":[0.07166,-0.00584,-0.04359,-0.02267,0.01134,0.10571,0.01448,0.00621,-0.07139,-0.09384,-0.06924,0.0462,-0.05995,0.08931,0.02421,-0.10445,0.01374,-0.00961,-0.08475,0.02614,-0.04249,0.0004,-0.10656,0.03842,-0.04892,-0.04528,0.08469,0.06863,0.09909,0.09324,0.00592,0.01856,0.0098,0.09708,-0.04932,-0.06755,-0.03525,0.0569,0.02558,-0.01286,0.01053,-0.07361,0.03247,-0.0257,-0.03646,0.01749,0.03545,-0.03881,-0.08948,-0.09158,0.01006,0.07451,0.02616,0.06038,-0.05455,-0.06872,0.0667,-0.02847,0.09899,0.07256,-0.06213,0.03207,-0.13725,-0.0214,0.002,-0.06882,-0.02184,-0.01569,0.07256,-0.03565,-0.11861,0.00631,0.00476,-0.14273,-0.00301,0.0318,-0.01311,0.00025,0.02952,-0.00195,-0.00442,0.03041,0.03717,0.06108,-0.00265,-0.007,0.0342,-0.03081,0.00406,-0.0615,0.00446,-0.04741,-0.01234,0.04756,-0.04542,0.01361,-0.02988,-0.05998,0.04961,-0.04653,0.01881,-0.08958,-0.0652,0.01723,0.04297,-0.06912,-0.02242,0.04857,0.02515,-0.0425,0.1179,0.04973,-0.12826,-0.01704,-0.00099,-0.10803,-0.0231,-0.12708,0.01917,0.06037,-0.03592,-0.04037,0.03139,-0.05731,0.11599,0.06042,-0.02821,-0.02541,0.07006,0.01396,-0.05883,0.03886,0.04025,-0.02768,0.06635,0.02051,-0.06126,-0.06919,0.03291,0.02703,0.13822,-0.10184,0.00308,-0.11333,0.14324,-0.0,0.02201,-0.01087,0.05024,-0.09112,-0.03967,0.13154,-0.08076,0.02069,0.03506,-0.02373,0.02913,0.05397,0.1027,0.1296,-0.03272,0.00235,-0.07513,-0.0433,0.16025,0.03427,0.06391,0.15663,-0.09889,0.06854,0.17019,0.05162,0.08544,-0.0834,0.00502,-0.01264,0.00208,-0.0044,-0.00442,0.13165,0.03104,-0.02027,0.00442,-0.05851,0.0503,0.08225,-0.01366,-0.02241,-0.02541,-0.02472,0.03244,-0.03427,-0.01538,-0.02984,0.02592,0.01211,-0.0193,-0.02413,0.08444,0.08417,-0.09097,-0.07437,-0.03546,0.05331,-0.03129,-0.08232,0.09497,-0.05127,-0.17684,0.06386,0.09641,0.04785,0.01908,-0.00773,0.10968,-0.01604,-0.16027,-0.10528,0.04503,0.04153,0.01445,-0.0275,-0.08975,-0.0463,0.04456,0.01077,-0.01853,-0.00816,0.05058,-0.00112,0.09684,-0.00601,0.03468,-0.05559,-0.02618,-0.03103,-0.00676,0.04385,-0.03239,-0.13451,0.02504,0.03377,-0.05834,-0.00348,0.06647,0.03645,0.03066,0.04467,-0.07203,0.11014,0.01403,0.02253,0.0219,-0.06913,-0.06419,0.06885]},{"domain":"time_series","key":"psi_weights","name":"Psi weights (MA-infinity representation) of an ARMA process","package":"time-series-ai999x","example":"Find the first 5 psi weights of the ARMA(1,1) process with phi = [0.5] and theta = [0.3].","v":[0.07195,0.0123,-0.04125,-0.04187,-0.0391,0.08045,0.10236,-0.02731,-0.08149,-0.06376,-0.0566,0.04593,-0.04756,0.08338,-0.01876,-0.04753,0.01456,0.02011,-0.10109,0.05894,-0.00696,-0.00879,-0.17235,0.08663,-0.04914,0.04584,0.07708,0.10331,0.07581,0.06041,0.05207,0.01767,0.03485,0.10663,-0.04462,-0.03205,-0.01324,0.08647,0.05907,-0.01898,-0.05497,-0.04072,0.05101,-0.00197,-0.01772,-0.05824,0.03238,-0.09849,-0.03385,-0.03437,-0.03881,0.06068,0.01394,0.07422,-0.02859,-0.01595,0.01109,-0.00893,0.09348,0.03775,-0.03958,0.00174,-0.12453,-0.01256,0.01271,-0.09312,-0.0299,0.01747,0.06113,-0.06042,-0.12681,0.03428,0.04153,-0.15711,0.08611,-0.016,0.00914,-0.04258,0.01091,-0.08189,0.00294,-0.00289,0.02941,0.06465,-0.012,-0.03276,0.07031,0.00626,-0.04634,-0.04475,-0.05316,-0.04218,-0.07165,0.04674,-0.05865,-0.0087,0.01652,-0.05979,0.06592,-0.00517,-0.00534,-0.09414,-0.04844,0.02726,0.0984,0.01344,-0.06787,0.0498,0.02713,-0.03981,0.0597,0.08271,-0.06671,-0.01729,-0.03006,-0.09319,-0.02808,-0.09343,0.01458,0.07731,-0.01687,-0.05529,0.04128,-0.0252,0.05688,0.05188,-0.07171,-0.04502,0.08702,-0.00919,-0.02535,0.02631,0.04495,-0.00282,0.07887,0.05675,-0.04785,-0.05828,0.02123,0.07982,0.13998,-0.09679,-0.04013,-0.10623,0.15804,-0.03637,0.04217,-0.07028,0.00907,-0.05404,-0.05497,0.09708,-0.0374,0.01805,-0.02956,-0.00656,0.05356,0.11034,0.0369,0.0901,-0.06329,0.01194,-0.0299,-0.0511,0.13105,0.03294,0.01276,0.10369,-0.06962,0.07052,0.11915,0.01196,0.03473,-0.10046,0.01904,-0.02981,0.02882,-0.02771,-0.00952,0.15305,0.00769,-0.04071,-0.02171,-0.05341,0.01622,0.09077,-0.0499,-0.06329,-0.04759,-0.02426,0.01812,-0.03063,-0.01285,-0.01495,0.01778,0.04445,-0.06602,-0.00877,0.08937,0.05682,-0.09135,-0.05892,-0.02068,0.11407,-0.0622,-0.01363,0.06996,-0.02585,-0.14979,0.09005,0.01161,0.0649,-0.01837,0.00486,0.04628,-0.04546,-0.1208,-0.17163,0.04884,0.07781,0.07006,-0.05291,-0.1234,-0.00556,0.01501,0.01373,0.07611,-0.04188,0.07108,0.01273,0.04286,-0.02111,0.07953,-0.04047,0.01582,-0.03885,-0.03178,0.07646,-0.04163,-0.12489,0.00419,0.02587,-0.08835,-0.01599,0.05066,-0.00531,0.08213,0.09417,-0.01046,0.14221,0.00825,-0.02728,-0.05167,-0.10284,-0.02964,0.09069]},{"domain":"time_series","key":"quadratic_trend_forecast","name":"Quadratic trend fit and forecast","package":"time-series-ai999x","example":"Fit a quadratic trend to [3, 5, 9, 15, 22, 32] and forecast 1 period 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mean squared error","package":"time-series-ai999x","example":"Find the RMSE for actual values [10, 12, 14, 13] and forecasts [11, 12, 13, 15].","v":[0.11638,-0.06688,0.12423,0.05561,0.05183,-0.02676,0.0104,0.08843,-0.02272,-0.06294,0.0962,-0.04573,0.15209,-0.08018,-0.05451,-0.00916,0.12696,-0.02201,0.02333,0.04511,0.00396,-0.00946,0.04606,0.07809,-0.00609,0.04494,-0.07526,-0.03629,0.03913,-0.01934,0.04955,-0.02065,0.06613,-0.12698,-0.05963,-0.0913,0.08237,0.05666,0.07097,-0.00694,0.02376,0.01634,0.0815,0.07658,0.01277,-0.04452,0.02768,-0.03027,0.01695,-0.00854,-0.07027,0.04858,0.04212,0.08517,0.09675,-0.13716,0.09087,-0.02621,-0.03182,-0.04315,-0.01108,-0.04055,-0.11337,-0.01254,0.11957,0.00476,0.01411,0.04404,-0.15703,-0.00119,0.0741,0.02128,-0.08104,-0.03574,-0.02363,0.05752,0.01669,-0.00445,-0.16837,0.00158,0.0168,-0.04439,0.01176,-0.08312,-0.00055,-0.08613,-0.00362,-0.00601,0.05651,-0.04098,-0.03394,-0.0386,0.0517,0.01346,-0.03347,-0.03682,0.00144,0.01591,-0.16101,0.03619,-0.00452,-0.02881,-0.07312,0.06844,-0.17792,0.01363,0.02351,0.04551,0.02969,0.06998,-0.06348,-0.07025,0.0125,0.01618,-0.05663,0.0642,-0.06527,-0.03052,0.10938,0.02774,0.15037,0.00888,-0.07715,-0.14445,-0.02764,-0.04509,0.02682,0.02962,-0.04828,0.03083,0.07664,-0.01952,-0.01871,0.0059,-0.00324,-0.07349,-0.04711,-0.03923,0.04494,-0.03196,-0.02075,0.02608,0.09742,0.09382,0.00481,-0.01294,0.01779,0.05229,-0.00679,-0.08732,-0.01652,0.04196,-0.05681,-0.06605,-0.08045,0.02542,0.04096,0.07359,-0.10745,0.04747,0.06148,0.0515,-0.02946,-0.01779,-0.06076,-0.00884,-0.04253,0.04289,0.06353,-0.05901,-0.07739,-0.03746,0.01777,0.11853,0.00724,-0.08635,0.0575,-0.05009,-0.03993,0.09225,-0.01456,-0.02469,-0.0427,0.00918,0.0747,0.04948,-0.05227,0.05682,-0.06905,0.01045,-0.02561,-0.06276,-0.04571,-0.06015,0.03335,0.11737,-0.05257,0.11863,-0.07112,0.06685,0.13953,0.01567,-0.01061,0.05266,-0.05506,-0.0857,-0.12588,0.03688,0.01211,0.05424,0.08885,0.02002,-0.00552,0.04827,-0.0667,-0.00711,0.01712,0.02358,0.06902,-0.0028,-0.0133,0.06696,0.01815,0.05282,0.06675,-0.06716,0.01908,-0.05784,0.00205,0.04183,0.0111,-0.02745,0.04672,0.07135,0.01248,0.00027,0.02421,-0.04574,0.00398,-0.03671,0.08169,-0.00174,-0.13248,0.02256,-0.04539,-0.10956,0.07446,0.01702,-0.05185,0.0255,0.0711,-0.00395,-0.14317,-0.09158,-0.13114,0.05813]},{"domain":"time_series","key":"rts_smoother_local_level","name":"Rauch-Tung-Striebel smoother (random-walk model)","package":"time-series-ai999x","example":"Apply the RTS smoother with process variance = 0.5, measurement variance = 2, initial estimate = 10 and initial variance = 5 for the measurements [10.4, 11.1, 10.7, 11.9, 12.3].","v":[0.02403,0.10907,0.13471,0.00173,0.01387,-0.06767,-0.03332,0.02973,-0.04243,-0.11322,0.02179,-0.02348,-0.04006,0.05931,0.15739,-0.05572,0.0412,-0.05464,-0.04583,-0.04362,-0.08233,-0.0235,-0.02031,0.01081,-0.1434,-0.01296,-0.03455,-0.06732,0.08408,-0.04377,0.0815,-0.02344,0.06107,-0.02744,0.11184,-0.03728,-0.00596,0.08292,-0.02132,-0.06751,0.05312,0.00781,-0.09007,-0.00539,-0.02068,-0.03439,0.06063,0.00195,-0.14782,-0.10527,0.00345,-0.03818,0.0423,-0.00888,-0.06639,-0.05773,0.11832,0.02073,0.05281,-0.0058,-0.02964,0.11386,0.0184,0.10461,-0.05644,0.06423,-0.01203,-0.00115,-0.05756,-0.0784,-0.06119,-0.03939,-0.0289,0.05651,0.01125,0.064,0.1464,0.12319,-0.08685,-0.03711,-0.01317,0.04531,0.00551,0.04773,0.04921,0.02698,-0.04739,-0.01041,0.06944,0.05825,-0.01406,-0.01354,-0.00084,0.00554,0.05661,0.00512,0.02386,-0.08733,0.03339,-0.01856,0.08078,0.09613,-0.03395,0.01712,-0.02884,-0.06994,-0.09058,-0.02478,0.05179,-0.04156,0.05796,0.01236,0.06184,0.01619,0.05147,0.0723,-0.03008,-0.09068,-0.01658,0.06471,0.11103,-0.07258,0.00847,0.08072,-0.12174,0.01078,0.02978,-0.09407,0.12245,0.01288,-0.08434,-0.03152,-0.1467,-0.08726,-0.0065,0.10533,-0.0627,-0.00806,0.00723,-0.0277,0.03334,0.06487,-0.03505,0.00617,0.12204,-0.02523,-0.02851,0.08741,-0.00709,-0.02308,-0.05799,-0.10813,-0.03364,-0.03995,-0.04641,0.02891,-0.07833,-0.00365,0.05842,0.04963,-0.05401,0.05161,0.02708,-0.09618,0.00185,0.03481,0.09322,0.048,-0.04369,-0.03124,0.01161,0.05378,0.01198,-0.05497,-0.03228,0.06334,0.06436,0.02796,0.04001,-0.05759,0.045,0.01515,0.08598,-0.01998,0.16323,-0.11837,-0.02662,0.05663,-0.05256,0.15152,0.02976,0.00215,0.09579,0.03944,0.15802,-0.01255,-0.03959,-0.03069,0.06597,0.01556,0.01331,-0.0831,-0.11788,-0.08068,0.05453,-0.10025,-0.01094,0.01453,-0.01479,-0.06532,0.0378,0.01193,0.01469,-0.0629,0.06357,-0.10729,0.03955,0.07296,-0.04453,0.02307,0.09413,-0.02199,0.02254,0.05211,0.03524,0.00303,-0.03376,0.01813,-0.00596,-0.01181,0.07944,0.01185,0.05054,-0.04703,-0.08477,-0.10195,0.03478,0.00987,-0.01472,0.11524,0.02563,-0.0167,-0.02471,-0.064,0.00768,-0.0031,-0.03102,0.07479,-0.07854,0.10664,0.04284,-0.14135,-0.02625,0.00891,0.01007,-0.06579]},{"domain":"time_series","key":"sample_autocorrelation","name":"Sample autocorrelation at lag k","package":"time-series-ai999x","example":"Find the lag 1 autocorrelation of [4, 6, 5, 8, 7, 9, 8, 10].","v":[0.01455,0.03786,0.00609,0.09762,-0.0092,-0.01225,-0.02056,-0.0499,0.03718,-0.01968,0.00098,0.02857,0.00546,0.02323,0.07671,-0.02557,-0.03096,0.04742,-0.10549,0.02896,0.05527,0.10313,-0.04448,-0.09133,0.12174,0.02435,0.00925,-0.02642,-0.03383,-0.01205,0.0586,-0.1138,0.0251,0.038,0.17609,-0.04713,-0.06037,-0.04234,-0.07603,-0.0227,0.04895,-0.03377,-0.12618,-0.06872,-0.06799,0.07956,0.05939,0.04678,-0.0518,0.01665,0.00516,0.0758,0.05837,0.01437,0.04446,-0.15897,0.07595,-0.02582,0.0135,0.05392,0.0491,0.01668,-0.04767,0.03649,-0.08439,0.05829,0.07834,-0.00589,0.025,0.00593,-0.00819,0.05876,0.02715,-0.09112,-0.02676,0.08997,0.04357,0.03866,0.00455,-0.04977,0.13607,0.01567,-0.10715,-0.00429,0.15296,-0.02693,-0.09016,-0.04084,0.00124,-0.04325,0.01321,0.08345,0.11901,0.0107,-0.02782,-0.07483,0.05475,-0.00954,0.0512,-0.00569,-0.03927,-0.11312,0.00487,-0.03686,-0.02299,-0.00991,-0.19968,0.04192,0.06046,0.02425,-0.06107,-0.01655,0.0689,0.01312,0.02666,0.09703,-0.01127,-0.00594,-0.04261,-0.01048,-0.05046,0.01829,0.04261,0.13659,-0.1034,0.07098,0.00466,-0.10224,0.09056,0.09065,0.08673,-0.02437,-0.04388,-0.04674,0.02877,0.03546,-0.01832,0.02526,-0.04135,0.12025,-0.1322,0.03588,-0.01955,0.04281,0.13798,-0.00647,-0.07203,0.0277,0.01622,0.00086,0.06668,-0.09731,-0.02816,-0.11861,-0.03052,-0.06365,-0.0427,0.07929,0.0127,0.06722,0.04608,0.12674,0.01548,-0.18198,-0.01194,0.0067,-0.02537,0.09062,0.02429,-0.00073,0.01674,-0.06919,-0.01793,0.01264,-0.0093,0.06112,0.00346,0.04439,-0.0135,0.00954,-0.05741,0.07465,-0.077,-0.00895,0.10754,-0.11782,-0.13143,-0.04189,-0.03054,0.13254,0.07252,0.05023,0.04339,-0.04622,-0.03248,-0.0543,0.00332,-0.06644,0.02625,-0.05986,-0.01117,0.00471,-0.00971,-0.04163,0.04485,0.00525,0.07854,-0.0103,-0.00026,-0.02455,-0.00805,-0.17711,-0.07604,0.02756,0.06466,0.026,-0.01776,0.00863,-0.069,0.02402,-0.04614,-0.06394,0.06013,-0.03188,0.08817,0.02897,0.0973,0.00909,-0.07951,-0.0389,-0.00622,-0.0616,-0.0186,-0.08781,-0.05635,-0.01057,-0.01192,0.05786,0.03472,-0.054,0.09295,-0.06882,-0.0002,-0.01241,0.04967,-0.04956,0.10324,-0.00154,0.0297,0.01203,-0.00939,-0.01051,0.05941,-0.01678,-0.06932,-0.09265]},{"domain":"time_series","key":"sample_autocovariance","name":"Sample autocovariance at lag k","package":"time-series-ai999x","example":"Find the lag 2 autocovariance of [4, 6, 5, 8, 7, 9, 8, 10].","v":[-0.00575,0.09363,0.01235,0.08925,-0.00326,-0.02091,-0.02165,-0.02125,0.04556,-0.04378,0.00324,0.02344,-0.02504,-0.00728,0.09952,-0.0274,-0.04415,0.03093,-0.13686,0.04958,0.06028,0.09422,-0.03304,-0.13039,0.12609,0.04404,-0.02165,-0.06764,-0.07573,0.00824,0.03152,-0.12128,-0.00715,0.05244,0.18645,-0.05434,-0.06078,-0.02518,-0.08528,-0.04623,0.05624,0.01366,-0.13209,-0.05002,-0.03596,0.05862,0.01287,0.0545,-0.04159,0.01688,0.03395,0.03703,0.04802,0.01263,0.04037,-0.0795,0.08947,-0.008,0.00917,0.02283,0.0514,0.04431,-0.06815,0.07921,-0.10238,0.06992,0.07973,-0.0222,0.0196,0.01923,-0.02679,0.06732,0.01461,-0.05521,-0.03285,0.08611,-0.01026,0.04906,0.02217,-0.04969,0.15299,0.0221,-0.11081,0.01701,0.1003,-0.00424,-0.09368,-0.01345,0.0017,0.00335,0.02779,0.09484,0.09747,-0.00529,-0.00603,-0.10622,0.04927,-0.0133,0.06038,-0.01865,-0.04706,-0.04445,-0.03145,-0.06792,0.00121,-0.00282,-0.21117,-0.00655,0.06194,-0.00193,0.00289,-0.02981,0.05784,0.05136,0.01433,0.07307,0.027,-0.06085,-0.03501,0.00042,-0.05534,0.02923,0.04006,0.09832,-0.07108,0.10817,-0.01814,-0.0804,0.10594,0.09638,0.07397,-0.01137,-0.08573,-0.02632,0.00754,0.01051,-0.02076,0.03948,-0.01084,0.10845,-0.13322,0.0476,0.01023,0.03987,0.08454,-0.0439,-0.07589,0.03675,0.02143,0.02432,0.0747,-0.12261,-0.00221,-0.12228,-0.01536,-0.06719,-0.02597,0.04688,0.01375,0.07585,0.02008,0.18144,0.02456,-0.13973,-0.02254,-0.01203,0.02364,0.06682,0.00343,-0.04314,-0.01891,-0.07579,-0.03645,-0.01066,-0.01692,0.02046,-0.02614,0.09701,-0.01155,-0.03673,-0.08582,0.03712,-0.06997,0.01885,0.09346,-0.12213,-0.10864,-0.04011,-0.00036,0.16956,0.03749,0.04072,0.0486,-0.04462,-0.06155,-0.04083,0.0122,-0.1023,0.00147,-0.0355,0.02673,0.00294,-0.04564,-0.0756,0.05208,0.00691,0.08502,-0.03037,-0.0149,-0.02741,-0.01541,-0.1586,-0.09788,-0.00532,0.0749,-0.00438,0.03331,0.01119,-0.06682,0.02262,-0.07948,-0.05967,0.04251,-0.01195,0.05687,0.04127,0.10874,0.03514,-0.04145,0.01375,0.01117,-0.02285,-0.03599,-0.10459,-0.04195,0.00269,0.001,0.04651,0.06896,-0.06778,0.1009,-0.08135,-0.01058,-0.00793,0.05939,-0.0665,0.06167,0.01648,0.06655,0.00613,0.00153,0.02069,0.04505,-0.01215,-0.04909,-0.06018]},{"domain":"time_series","key":"sample_partial_autocorrelation","name":"Sample partial autocorrelation at lag k","package":"time-series-ai999x","example":"Find the partial autocorrelation at lag 2 of [4, 6, 5, 8, 7, 9, 8, 10, 9, 12].","v":[-0.01052,0.03271,0.03731,0.06091,0.00894,0.01521,-0.01758,-0.0385,0.01469,0.00384,-0.01798,0.05115,-0.06908,0.04281,0.1098,-0.00759,-0.01303,0.0356,-0.07621,0.02927,0.02229,0.10575,-0.08804,-0.09688,0.09471,0.01566,-0.0104,0.04842,0.00232,0.02121,0.03124,-0.09391,0.03873,0.07593,0.15275,-0.02407,-0.01962,-0.03175,-0.09966,0.02069,0.05127,-0.05343,-0.09767,-0.10724,-0.05841,0.05662,0.07209,0.04357,-0.10696,-0.00419,0.02302,0.07037,0.0324,0.00243,0.029,-0.12227,0.06257,-0.04211,0.08052,0.03463,0.02254,0.00268,-0.02619,0.02885,-0.0741,0.00362,0.08564,-0.01266,0.03159,-0.05136,-0.04225,0.06109,0.0079,-0.10279,-0.01904,0.03118,0.0769,0.00376,0.00388,-0.11181,0.11091,0.00529,-0.0827,0.04094,0.14213,-0.03959,-0.05118,-0.00016,-0.001,-0.03323,0.01918,0.0762,0.05656,-0.03248,-0.01774,-0.03864,0.06504,-0.03242,0.03458,0.00621,0.00661,-0.08222,0.02966,-0.05087,-0.07329,0.0405,-0.18501,0.03305,0.07419,0.031,-0.06826,-0.01674,0.02992,0.03507,0.01675,0.08793,-0.00049,-0.02127,-0.08503,-0.02188,-0.0357,0.02355,0.026,0.17295,-0.11025,0.09744,-0.00696,-0.03677,0.092,0.05719,0.06273,-0.03931,0.00515,-0.02501,0.03628,0.07759,-0.0552,0.03239,-0.00721,0.10936,-0.08109,0.02711,0.01405,-0.00139,0.16984,-0.00793,-0.01107,-0.00184,0.00796,0.01855,0.05472,-0.09099,-0.04084,-0.09491,0.00312,-0.08217,-0.02947,0.08018,-0.00978,0.11695,0.00664,0.12772,9e-05,-0.19367,0.0393,-0.0073,-0.03433,0.13732,-0.01844,0.03296,0.04643,-0.02205,0.00606,-0.0558,-0.01902,0.10468,0.01114,0.03045,-0.01239,0.0647,-0.09541,0.03766,-0.06131,0.02136,0.12094,-0.12095,-0.11922,-0.06814,-0.05005,0.10718,0.04245,0.07738,0.03895,-0.00682,-0.04011,-0.07124,-0.04849,-0.07394,0.08297,-0.0583,0.00416,-0.02381,-0.04459,-0.04292,0.07192,-0.00476,0.0883,-0.04944,0.00098,-0.02685,-0.01815,-0.16937,-0.08087,0.04594,0.07848,0.02185,-0.04147,0.03863,-0.04811,0.02032,-0.00403,-0.05721,0.01909,-0.05914,0.05983,0.05842,0.09739,0.0111,-0.09893,-0.06418,0.01811,-0.06221,-0.04634,-0.13205,-0.05516,-0.05236,0.00403,0.03264,0.05458,-0.02554,0.05361,-0.06457,-0.03236,-0.01015,0.06154,-0.04966,0.07381,-0.02988,0.00431,0.04361,-0.04033,-0.04507,0.05675,-0.02262,-0.01193,-0.10804]},{"domain":"time_series","key":"seasonal_indices_additive","name":"Seasonal 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51].","v":[0.00333,0.06548,0.05812,0.02248,0.05958,-0.02067,-0.07848,0.03812,0.00165,0.07271,-0.02521,0.03761,0.0362,0.01259,-0.09229,-0.08401,0.04734,0.10057,-0.02596,-0.01002,-0.066,-0.0021,-0.04327,0.08412,-0.0104,0.01438,0.02139,0.03456,-0.13556,-0.1026,-0.05532,-0.05565,0.0304,-0.04388,0.13775,-0.12844,0.01444,-0.12458,0.01211,0.01478,-0.02614,0.01487,-0.05595,-0.03435,-0.01713,0.00593,0.01617,0.08964,0.02584,0.03224,-0.13377,0.08409,0.02235,-0.03226,0.08254,-0.14038,0.11106,-0.05916,0.03825,-0.03305,0.0423,0.15986,-0.00931,-0.02471,-0.02148,-0.06169,0.03602,-0.04737,0.13241,0.02998,-0.00989,-0.01774,-0.07588,-0.03443,-0.08647,0.09634,0.05947,0.07979,0.19613,0.03449,0.03209,-0.01164,0.0213,-0.00796,0.13216,-0.06016,-0.02324,-0.0706,-0.02633,-0.02608,-0.02206,0.07759,0.0271,0.00839,0.02793,-0.06491,0.01904,-0.00497,0.07241,-0.04156,-0.03581,-0.09609,0.06371,0.03533,0.02532,-0.04141,-0.0149,-0.03219,0.03888,0.01078,0.01196,-0.00585,0.13964,0.07309,0.03345,-0.03387,-0.0918,-0.04041,0.13547,0.07712,-0.12128,-0.05234,-0.01946,-0.06438,-0.05156,-0.05949,0.08151,-0.04966,0.03489,-0.06317,0.04577,-0.04456,-0.03906,-0.03071,0.01835,-0.0296,-0.08323,0.03353,-0.11844,0.05525,-0.03874,-0.04937,-0.02323,-0.05882,0.18176,0.04806,0.00735,-0.04407,-0.02223,0.01834,-0.05499,0.06725,-0.0408,-0.07157,0.0094,0.01683,-0.03937,0.0356,0.00819,0.0195,0.07909,-0.03364,-0.09176,0.00015,0.04505,-0.02842,-0.02034,0.08061,0.11795,0.00335,-0.02983,0.00718,0.06784,0.07341,-0.01828,0.01076,-0.14246,-0.05527,-0.03382,0.08497,-0.05051,-0.0248,-0.00044,-0.03182,-0.04079,-0.02008,0.12796,-0.06347,-0.01275,-0.05727,0.08657,0.07324,-0.07346,0.05493,-0.02694,-0.00075,-0.00616,-0.00867,-0.0231,-0.01895,0.021,0.03033,-0.07548,0.01175,-0.08428,0.00352,0.051,0.11295,-0.04382,0.04991,-0.01383,-0.00645,-0.05081,0.03297,0.13515,0.04715,-0.08455,-0.06586,0.02287,0.00298,-0.14324,0.04282,0.05447,-0.03351,0.06482,0.03151,-0.1375,0.02376,-0.03417,0.00397,0.05101,-0.03556,0.07113,0.09563,0.00669,-0.07279,0.11855,0.07964,-0.07119,0.03789,0.01341,-0.00342,-0.00999,-0.01928,-0.04891,0.01323,0.08164,-0.02515,0.04903,-0.01391,0.02111,-0.01296,0.01992,0.03219,-0.09265,-0.13792]},{"domain":"time_series","key":"seasonal_indices_multiplicative","name":"Seasonal 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51].","v":[0.02334,0.04024,0.05208,0.03865,0.0553,-0.00014,-0.09748,0.01778,0.00461,0.06176,-0.03069,0.09607,0.04768,0.02449,-0.01196,-0.0321,0.00224,0.05271,-0.08029,0.05242,-0.06986,0.09007,0.00472,0.10684,0.00373,0.05578,0.03403,-0.00893,-0.15396,-0.07347,-0.017,-0.05871,0.02369,0.00404,0.07144,-0.06927,-0.04338,-0.08169,-0.01382,0.04497,-0.06011,0.07276,-0.01198,-0.02784,-0.03426,0.01993,0.06228,0.0965,0.05659,0.00439,-0.09508,0.08976,0.00811,-0.05282,0.14018,-0.1272,0.08564,-0.02651,-0.02749,-0.03552,0.03366,0.09157,-0.03808,-0.08717,-0.00608,-0.0385,0.01199,-0.02468,0.13583,0.02318,0.02077,-0.05491,-0.09152,-0.03829,-0.06713,0.11253,-0.03747,0.07962,0.18364,-0.02873,0.00693,-0.00829,0.00175,-0.05037,0.14023,-0.0828,-0.03728,-0.1469,-0.02977,-0.00428,-0.00925,0.03829,0.06395,-0.03856,0.08476,-0.05084,0.01182,-0.0195,0.09134,0.00854,-0.01443,-0.13061,0.07911,0.01942,-0.00483,-0.06855,-0.0333,0.01418,0.0701,0.0272,-0.00041,-0.00404,0.12866,-0.02333,-0.00819,0.04781,-0.1276,0.01987,0.16041,0.07881,-0.0804,-0.07773,0.02858,-0.02942,-0.12198,-0.05668,-0.00489,-0.0538,-0.01911,0.01587,0.0005,-0.00808,0.0587,-0.09174,0.03577,-0.02795,-0.06323,0.01689,-0.11698,0.04615,-0.04421,-0.05345,-0.00211,-0.02805,0.13433,0.06716,-0.00131,-0.09179,-0.02712,0.06881,0.00143,0.00955,-0.04765,-0.07327,0.03063,-0.03983,-0.02256,0.01808,0.04371,0.06092,0.10222,-0.01917,0.00438,-0.07,0.02592,-0.07539,-0.02117,0.04138,0.13831,0.04468,-0.00961,0.05096,0.04782,0.06313,0.05082,0.01631,-0.1206,-0.01538,0.04086,0.08259,-0.02682,0.00834,-0.06547,-0.06765,-0.01315,-0.0682,0.10243,-0.02036,-0.0554,-0.02874,0.10105,0.0579,-0.02779,0.00126,-0.03682,0.00514,0.02933,-0.0108,-0.0634,0.03004,0.01905,-0.02619,-0.04562,-0.0262,-0.05232,0.05996,-0.01398,0.10099,-0.08221,0.03946,-0.00999,-0.01615,-0.0962,-0.00419,0.15456,0.03741,-0.08034,-0.01373,0.05207,0.03065,-0.11909,-0.01193,0.01065,-0.0394,0.06864,0.05174,-0.08186,0.01421,-0.02398,-0.0526,-0.01345,0.01317,0.03458,0.13458,0.00154,-0.07953,0.11637,0.05427,-0.02108,0.01155,0.01708,0.08768,0.00995,-0.05652,-0.09197,-0.00906,0.08723,0.03378,-0.02417,0.02117,0.08209,-0.02885,0.00663,0.01229,-0.08252,-0.15527]},{"domain":"time_series","key":"seasonally_adjusted_additive","name":"Seasonally adjusted series (additive)","package":"time-series-ai999x","example":"Seasonally adjust the quarterly series [30, 21, 29, 31, 40, 30, 39, 41, 50, 39, 48, 51] using additive decomposition.","v":[0.0138,0.06566,0.0069,0.0313,0.07335,-0.04117,-0.08115,0.0545,-0.03119,0.08851,-0.09555,-0.00151,0.00487,0.01284,-0.09493,0.00377,0.05805,0.1298,-0.04268,0.03152,-0.03864,-0.0045,-0.07365,0.09168,0.05073,0.01235,0.02907,-0.02695,-0.07847,-0.05339,-0.00711,-0.0594,-0.05406,-0.0306,0.16712,-0.06316,-0.03279,-0.0806,-0.02776,-0.0057,-0.04686,-0.00998,-0.05424,-0.05886,-0.0536,0.00855,0.04826,-0.0053,-0.0313,0.05345,-0.08801,0.07961,0.06197,-0.04,0.0821,-0.16776,0.09383,-0.08305,0.01505,0.00426,0.03628,0.06191,-0.00959,0.00254,-0.05305,-0.04951,0.03456,-0.02296,0.0882,0.00655,0.02413,0.02887,-0.05694,-0.09738,-0.06751,0.04692,0.13776,0.07913,0.18138,0.00256,0.02504,-0.02361,-0.04311,0.05469,0.14957,-0.02848,-0.01452,-0.09209,0.03626,-0.06121,-0.02041,0.10707,0.04748,0.03665,0.01074,-0.13406,-0.0269,-0.06335,0.1121,-0.06936,-0.00784,-0.04798,0.07211,-0.00061,0.03683,-0.05887,-0.1077,-0.04746,0.00498,0.03496,0.08827,0.03601,0.07134,0.13624,0.06405,-0.04011,-0.10665,-0.04053,0.09536,0.01732,-0.09325,-0.03593,-0.02837,-0.0298,-0.07771,0.03102,0.1012,-0.09358,0.07638,-0.07321,-0.01334,-0.06978,-0.05324,-0.02284,-0.01008,-0.0241,-0.03816,0.01861,-0.07443,0.06063,-0.01528,-0.06503,-0.00091,0.00721,0.15873,0.0401,-0.04103,0.00352,0.0186,0.03245,-0.08018,-0.00454,-0.06626,-0.11115,-0.03031,0.06956,-0.03623,-0.00223,0.06824,0.00846,0.0878,-0.0529,-0.02886,-0.04108,0.03413,0.00853,0.01836,0.17945,0.03803,-0.02702,-0.01053,-0.00097,0.05448,0.10358,-0.04536,0.01147,-0.09122,-0.05363,0.03402,0.07982,-0.01502,-0.05654,0.02241,-0.02893,0.07232,-0.0973,0.03263,-0.01321,0.04122,0.00697,0.12192,0.03551,-0.04288,-0.02137,0.01844,0.00127,-0.0437,-0.0294,0.03146,-0.01951,0.00814,-0.00582,0.0072,-0.03599,-0.08959,0.06314,0.0456,0.14662,0.05972,0.04463,0.004,-0.0932,-0.0583,-0.01665,0.05166,-0.01547,0.00778,-0.06159,0.02393,-0.0672,-0.08912,0.0315,0.08166,-0.03725,0.05989,0.01008,-0.11757,-0.00516,-0.03077,0.02498,0.07054,-0.05418,0.15191,0.00549,0.02301,-0.05487,0.07763,0.10517,-0.05483,-0.08154,-0.02839,0.00632,0.04788,-0.0215,-0.03228,-0.0178,0.0422,-0.04356,0.05712,-0.06126,0.06849,-0.01575,0.04435,0.00151,-0.0368,-0.14629]},{"domain":"time_series","key":"seasonally_adjusted_multiplicative","name":"Seasonally adjusted series (multiplicative)","package":"time-series-ai999x","example":"Seasonally adjust the quarterly series [30, 21, 29, 31, 40, 30, 39, 41, 50, 39, 48, 51] using multiplicative 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slope (Theil-Sen trend)","package":"time-series-ai999x","example":"Find Sen's slope of [12, 14, 13, 17, 16, 19, 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smoothing constant among candidates","package":"time-series-ai999x","example":"Which smoothing constant among [0.1, 0.3, 0.5] gives the smallest SSE for simple exponential smoothing of [20, 22, 21, 24, 23, 26]?","v":[0.001,0.09824,0.0509,0.01271,0.00163,-0.07224,-0.01078,0.04759,-0.05367,-0.05692,-0.07663,-0.04314,-0.00412,0.01931,0.00698,-0.01619,0.12262,0.02091,0.00206,0.04393,-0.00013,0.07847,-0.04495,0.01003,-0.04037,0.0013,-0.03265,0.02601,-0.06806,0.02254,-0.01015,-0.06593,0.07214,-0.00346,0.12014,-0.0425,-0.03635,-0.04342,-0.0263,-0.01462,-0.05758,0.05526,-0.10073,0.01299,-0.10415,-0.04006,0.0631,-0.00697,-0.02453,-0.00563,0.00505,0.05546,0.03485,0.00098,0.06575,-0.1659,0.13578,-0.03983,-0.02957,0.03051,0.02728,0.01749,-0.08025,0.10348,-0.04905,-0.04606,0.06417,-0.04856,-0.04497,0.02639,-0.00489,0.04986,-0.04735,-0.13375,-0.04409,0.125,0.1385,0.15429,-0.03042,0.02876,0.03822,0.05947,0.01872,0.03148,0.11972,-0.00228,-0.01356,-0.02691,0.05622,0.03818,-0.02791,0.07178,0.1107,-0.05263,0.00632,-0.09373,-0.01566,-0.06275,0.01648,-0.08368,-0.04942,0.06364,-0.00043,-0.00289,-0.04173,-0.03546,-0.1017,-0.05952,0.07387,0.0227,0.05228,-0.00227,0.04874,-0.0008,0.05247,-0.02058,-0.0747,-0.06154,-0.01854,0.04562,0.0012,0.00748,0.0583,-0.00282,-0.1548,0.05523,0.06842,-0.06662,0.06934,-0.0339,-0.01219,-0.01611,-0.17352,-0.02432,-0.0123,-0.02166,-0.16564,-0.02818,0.05155,0.044,-0.01336,0.02184,-0.00766,-0.0083,0.14546,0.01417,0.01654,0.09284,-0.00915,0.01529,-0.04951,-0.07798,-0.07241,-0.08247,-0.02776,-0.0155,-0.02879,0.07377,0.04367,0.05527,0.05369,0.00722,-0.00141,-0.02724,0.05976,0.00306,0.04498,0.01309,0.04681,-0.06689,-0.06212,-0.02414,0.06544,0.01136,0.06217,-0.00032,0.04308,0.0924,0.03525,0.03186,-0.04108,-0.04458,0.04478,0.05282,0.19103,-0.05758,-0.03131,0.05234,-0.096,0.09557,0.03534,-0.05161,0.01954,-0.02948,0.05996,0.02142,0.00205,-0.08933,0.0903,-0.08606,0.00385,-0.0037,-0.11452,-0.08846,-0.03822,0.00065,0.10022,0.16061,0.02239,-0.00739,-0.05567,-0.04436,0.03778,-0.06595,0.03614,0.02824,0.06193,-0.00105,-0.00301,0.03914,-0.13007,-0.05064,0.0961,0.02167,0.09519,0.05794,-0.04177,0.04867,-0.05431,0.00064,0.08467,0.02459,0.04868,-0.08273,0.00758,-0.11219,0.0655,-0.04727,0.00748,-0.14368,-0.02783,-0.00059,-0.05298,-0.02254,-0.04768,-0.11515,0.03824,-0.08291,-0.0971,0.11065,0.07922,-0.07938,0.08746,-0.05188,0.02717,-0.02919]},{"domain":"time_series","key":"simple_exponential_smoothing","name":"Simple exponential smoothing","package":"time-series-ai999x","example":"Apply simple exponential smoothing with alpha = 0.3 to [20, 22, 21, 24, 23].","v":[0.0621,0.0419,0.08558,0.01826,0.0173,-0.0579,-0.02019,0.0419,-0.08237,-0.00281,-0.0258,-0.00159,-0.03194,-0.01052,0.04274,-0.01397,0.09969,-0.03665,-0.01548,0.02985,0.00694,0.08449,-0.0456,0.1178,-0.0626,-0.01027,-0.07437,-0.0196,-0.06247,-0.00614,0.03003,-0.01631,0.10219,-0.01222,0.07138,-0.00639,-0.01606,0.01314,-0.03312,0.01833,-0.0896,0.03323,-0.12095,0.03747,-0.04755,-0.0592,0.04315,-0.02834,-0.03341,0.0029,-0.04376,0.05748,0.04875,0.0367,0.14376,-0.09547,0.16437,-0.05388,-0.04478,-0.01221,-0.0401,0.03345,-0.06358,0.06029,0.01704,-0.04371,-0.00487,-0.00148,-0.01853,-0.03062,-0.00551,0.01846,-0.07633,-0.1211,-0.08186,0.11856,0.03667,0.19371,-0.10663,-0.00197,0.0548,0.03766,0.10368,0.02506,0.07757,0.00128,-0.06051,0.03,0.09521,0.04626,0.01976,0.03044,0.079,-0.0602,-0.00272,-0.00922,-0.0169,-0.03308,0.03288,-0.10689,-0.02748,0.07595,-0.025,0.02439,-0.03913,-0.02113,-0.03427,-0.08454,0.21084,0.02317,0.05443,-0.07434,-0.07137,-0.08858,0.05996,0.02519,-0.07459,-0.07104,0.04095,0.01844,0.03559,-0.07534,0.04679,-0.09453,-0.11455,0.07363,0.02675,-0.06662,0.03425,-0.04772,-0.00055,0.03522,-0.07794,-0.03899,-0.00825,-0.03015,-0.07531,0.00514,0.07323,-0.044,-0.02661,0.01659,-0.0354,-0.06202,0.05434,-0.04674,0.03171,0.10552,-0.06847,0.03747,-0.04919,-0.05835,0.00984,-0.11287,-0.04608,0.00122,0.00333,0.08611,0.05037,0.01154,0.02062,0.07566,-0.00523,0.04995,0.03581,-0.04479,0.02206,-0.04621,-0.01039,-0.0763,-0.02323,-0.00331,0.03451,0.05139,0.08744,-0.02466,-0.00938,0.04079,0.04758,0.05196,-0.03077,-0.03002,0.09486,0.08414,0.12623,-0.05732,-0.04788,0.12085,-0.13284,0.00166,0.003,-0.06853,0.02885,-0.05662,0.04347,0.03558,-0.00439,-0.08638,-0.0123,-0.0455,0.05304,-0.01044,-0.19143,-0.07119,0.07785,-0.03971,0.08031,0.10731,0.00464,0.03983,-0.02536,0.01574,-0.02391,-0.02111,0.01616,0.02875,0.1534,-0.01835,-0.03449,0.08596,-0.07649,-0.0387,0.03512,0.06537,0.08998,0.04378,-0.02362,0.04733,0.05635,0.02536,0.03167,0.00674,0.02909,-0.0588,0.03437,-0.11547,0.05441,-0.07091,0.01952,-0.09223,-0.04879,0.03987,-0.14178,-0.00848,-0.01749,-0.10506,0.1435,-0.00215,-0.11566,0.08036,0.07488,-0.08293,-0.03762,-0.02497,0.03544,0.00424]},{"domain":"time_series","key":"simple_moving_average","name":"Simple moving average","package":"time-series-ai999x","example":"Find the 3-period simple moving average of [10, 12, 14, 13, 15].","v":[0.01989,0.01463,0.11385,-0.01006,0.06092,-0.07955,0.01241,0.05177,-0.03643,0.0298,-0.03708,-0.03065,0.00346,-0.07484,0.04511,0.01086,0.04868,-0.05298,-0.0966,0.05623,-0.02469,0.05689,-0.12318,0.02653,-0.02465,0.07201,0.00802,-0.08216,-0.06864,-0.05045,0.10487,-0.03692,0.03265,0.0487,0.03444,-0.07692,0.0171,-0.05154,-0.0074,-0.02253,-0.10607,0.01442,-0.04454,-0.01421,-0.06772,0.01322,-0.00655,0.03947,0.00457,0.07706,-0.12203,0.12993,0.03349,0.00289,0.1547,-0.11614,0.13727,-0.09733,-0.00346,-0.06151,-0.01244,0.00335,-0.10206,0.0507,0.07734,-0.02463,-0.02656,0.03462,0.06303,-0.00019,-0.04995,0.09089,-0.08152,-0.11095,-0.10522,0.12544,0.01189,0.18167,-0.01808,-0.02576,0.07767,0.00529,0.00513,0.01365,0.0803,-0.03618,-0.04427,-0.0039,0.03324,-0.02516,0.02409,0.09455,-0.01261,-0.00239,0.01359,0.02356,0.04051,0.03673,-0.00598,-0.02389,0.01303,0.0041,0.02754,0.06165,-0.00779,-0.02396,-0.09591,-0.05013,0.14827,0.06242,0.00507,-0.09571,-0.04305,-0.03846,-0.01509,0.03143,-0.10694,-0.03766,-0.01665,0.10865,0.03651,-0.10889,-0.03188,-0.03572,-0.04174,0.10354,0.06623,-0.07613,0.06358,-0.04391,0.05909,-0.01912,-0.02788,0.00533,-0.03101,-0.04357,-0.04602,0.07788,-0.04624,0.08947,-0.09599,-0.02796,0.01123,-0.01489,0.00404,-0.00194,-0.0397,0.04099,-0.03842,0.03836,-0.02447,0.01626,0.06564,-0.18446,-0.08435,-0.00104,0.06483,0.02505,0.03966,0.08902,0.06847,0.0584,0.00326,-0.01977,0.0128,-0.02674,-0.05426,-0.05067,0.08238,-0.10747,-0.01866,-0.01911,0.05354,0.05128,-0.00183,-0.04856,-0.01147,-0.03244,0.07072,0.18705,0.04886,-0.01871,0.0815,0.03091,0.0218,0.01275,-0.04695,0.10667,-0.03851,-0.05399,-0.01399,-0.02244,-0.05859,-0.04479,-0.03343,0.059,0.03408,-0.06652,-0.02468,0.05361,0.03266,-0.10015,-0.10324,-0.00583,0.04047,0.04046,0.02427,0.11542,-0.11446,-0.08508,0.07467,0.01944,-0.11101,0.0055,0.00994,-0.00608,0.10321,0.03283,0.0734,0.01574,-0.0497,0.07724,-0.0039,0.02573,0.01317,-0.06116,-0.04195,0.05261,0.06885,0.04824,0.07385,0.01698,0.00816,0.02333,0.08638,-0.1015,-0.00289,-0.01219,0.03657,-0.08023,0.00775,0.02118,-0.13769,-0.03998,0.05733,-0.09905,0.11123,0.05552,-0.08642,0.00677,0.01991,-0.08594,-0.04093,-0.02058,-0.05676,-0.13595]},{"domain":"time_series","key":"symmetric_mape","name":"Symmetric mean absolute percentage error","package":"time-series-ai999x","example":"Find the sMAPE for actual values [10, 12, 14, 13] and forecasts [11, 12, 13, 15].","v":[0.13205,-0.00769,0.14327,0.04042,0.04969,0.01416,0.08387,0.03045,0.03115,-0.08566,0.03761,-0.01315,0.12964,-0.0743,-0.04934,-0.00231,0.09755,0.06581,0.0386,0.03193,0.00486,0.06344,-0.06359,-0.00677,-0.05264,-0.01649,-0.03085,-0.0624,0.02975,0.02695,0.08138,-0.06786,0.08698,-0.11557,-0.02039,-0.10051,0.03854,-0.02521,0.08429,-0.00935,0.01317,0.02528,0.02955,0.10242,0.03464,-0.05678,-0.02226,0.03026,0.14812,0.00615,-0.08401,-0.03138,-0.03928,0.11665,0.17697,-0.13501,0.06949,-0.03087,-0.01539,-0.04512,-0.05293,-0.05241,-0.09539,0.00067,0.06943,-0.1039,-0.02315,0.01358,-0.07957,-0.0013,0.14511,0.02289,0.04694,-0.13826,-0.04354,0.07033,0.00427,-0.00734,-0.11478,-0.04116,0.02598,-0.0236,0.02074,-0.03402,0.04877,-0.05941,0.07582,-0.06038,0.01172,0.01229,0.00806,-0.04154,0.05168,0.10754,-0.02862,-0.0136,-0.03569,0.01289,-0.06885,-0.03216,-0.04074,-0.03663,-0.01481,0.03456,-0.13569,0.04229,-0.04839,0.02743,0.02417,0.03282,-0.01842,-0.01667,0.05493,-0.04167,-0.03763,0.03006,-0.10672,0.04926,0.06462,0.02939,0.09608,-0.05042,-0.03316,-0.08843,-0.01439,0.08552,-0.01949,-0.05105,-0.05181,0.04591,0.10617,-0.04973,-0.03551,0.02858,-0.03865,-0.07997,-0.09571,-0.10575,-0.00897,0.00378,0.01969,-0.09255,0.08075,0.0568,0.11151,0.04473,0.03141,0.00354,-0.10094,-0.03182,-0.03992,-0.01383,-0.02304,-0.10172,-0.03813,-0.04368,0.08071,0.10486,-0.06296,0.00681,0.08818,0.05577,-0.07499,-0.03292,0.00442,-0.0463,0.04713,0.00677,0.09437,-0.00055,-0.04328,-0.11215,0.1187,0.00802,0.06721,-0.0059,0.04923,-0.063,0.11892,0.04437,0.04301,-0.03939,-0.02631,0.06532,0.03409,0.0632,-0.0469,0.08576,-0.10933,-0.0148,0.09992,-0.02346,-0.05687,-0.04535,-0.04957,0.07814,0.03422,0.12827,-0.08459,0.03299,0.09429,-0.00623,-0.02155,0.06376,-0.04718,-0.05511,-0.05522,0.03733,-0.10085,0.05314,-0.01887,-0.08693,-0.01368,-0.0146,-0.01627,-0.00771,0.03089,0.04097,-0.00828,-0.00381,-0.01524,-0.03834,0.07188,-0.00032,-0.00904,-0.02899,-0.02789,-0.04516,-0.03646,-0.00095,0.03443,-0.01353,0.03743,-0.01215,0.01775,-0.02152,0.03333,-0.05583,-0.0371,-0.09451,0.10745,0.01229,-0.11388,0.0698,0.01182,-0.09514,0.09678,-0.03915,-0.05132,0.00161,0.04695,0.04217,-0.0986,-0.10317,-0.11054,0.07807]},{"domain":"time_series","key":"tabular_cusum","name":"Tabular 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11.9].","v":[0.11219,0.06,0.0444,0.04037,-0.0529,0.01173,-0.04742,-0.03509,-0.00402,-0.04332,0.01893,0.09868,-0.08535,0.12786,0.08689,0.00185,0.04628,-0.08911,0.07845,-0.06627,-0.01543,-0.00856,-0.12933,-0.06559,-0.03035,0.07995,-0.0729,-0.01651,-0.07161,-0.11564,-0.04504,-0.00117,-0.02962,0.04707,0.07165,0.0137,-0.04754,0.08982,0.08962,0.04329,-0.04583,0.01293,-0.11985,0.05583,0.02076,-0.06069,0.02142,0.09193,-0.04929,-0.07776,0.02173,0.03828,0.10559,-0.02314,0.11677,-0.01707,0.00333,-0.02816,0.04456,-0.00585,-0.04481,0.04536,0.00887,-0.02398,0.02872,-0.06666,0.07498,0.00509,0.01054,0.07426,-0.03294,0.1026,-0.04821,0.13038,0.00113,-0.06072,0.03573,0.02478,0.07934,0.03466,-0.01646,-0.03733,0.00759,-0.06089,0.08752,0.02699,0.01402,-0.05146,-0.01992,0.00052,-0.03657,0.15453,0.05408,0.03003,-0.00722,-0.11947,0.0383,-0.07892,0.02598,0.05182,-0.05396,-0.0296,-0.08303,-0.01567,0.06973,-0.03431,-0.11803,-0.04181,0.04431,0.02501,0.02852,0.02409,0.0878,0.10191,-0.05101,0.09916,0.04774,-0.02543,-0.07895,0.02933,-0.13185,-0.00503,0.07109,0.10856,-0.04952,0.01204,0.07388,-0.11857,0.07424,0.01797,0.01639,-0.05584,-0.16243,-0.07638,-0.00373,-0.04123,0.01583,-0.0359,0.08769,0.00265,-0.02289,-0.00848,0.09228,-0.01743,-0.05321,-0.00649,-0.08929,0.12251,0.01466,-0.06173,0.07297,-0.18934,0.04189,0.03864,-0.10473,-0.00084,0.02674,0.08458,-0.06079,-0.12724,-0.03123,0.04294,0.09151,-0.08546,-0.02391,0.0186,-0.08795,-0.0458,0.10551,0.04674,0.05229,-0.004,0.01853,-0.02245,-0.07631,0.05243,0.01589,0.09006,-0.02221,0.04821,-0.04512,-0.0144,0.06286,0.08305,0.07385,-0.02625,-0.07882,0.005,-0.00977,0.05573,0.07359,-0.04733,0.00468,-0.01111,0.02129,0.00293,-0.01032,-0.03008,0.05551,-0.12372,0.01769,0.09218,0.01151,-0.13799,-0.04771,0.02109,-0.04578,0.01457,0.08794,-0.07722,-0.0936,-0.00994,0.02812,-0.03069,-0.00387,-0.02992,-0.04366,0.02161,-0.12961,0.00375,0.03373,-0.04346,0.00085,-0.04887,-0.01532,0.02289,0.01346,0.03535,-0.09532,-0.03391,0.04764,-0.00826,-0.01163,-0.08494,0.08711,-0.02525,0.04625,0.04771,0.13634,-0.00833,-0.01913,-0.01375,-0.03559,-0.00382,-0.01345,-0.04776,-0.04081,0.00449,0.04944,0.07239,0.00108,0.12381,0.13379,0.00355,0.00202,-0.06662]},{"domain":"time_series","key":"trend_seasonal_regression","name":"Linear trend with seasonal dummy variables","package":"time-series-ai999x","example":"Fit a linear trend with seasonal dummies to the quarterly series [30, 21, 29, 31, 40, 30, 39, 41, 50, 39, 48, 51] and forecast 1 period 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change points in the mean (optimal segmentation)","package":"time-series-ai999x","example":"Find two change points in the mean of [5, 6, 5, 12, 13, 12, 20, 21, 19].","v":[-0.063,0.07606,0.02841,0.00813,-0.03863,-0.03264,0.01974,-0.03759,0.01159,-0.02608,-0.02697,-0.04099,0.00393,-0.09598,-0.04904,-0.13199,0.07614,0.01146,0.01662,0.06187,-0.08994,-8e-05,-0.00457,-0.01337,0.07404,0.10049,-0.04686,0.0994,-0.02276,0.00285,-0.04091,-0.03192,-0.08222,0.00595,0.12403,-0.07478,0.01598,-0.07941,-0.00615,0.02633,0.01511,0.10075,-0.00596,-0.00297,0.02951,0.05323,0.04773,0.06949,-0.01599,-0.06226,-0.08564,0.01783,0.06358,-0.00766,-0.01683,-0.04345,-0.04326,0.04514,0.01653,0.01257,0.00927,0.07978,-0.07059,0.01937,-0.02326,0.01248,0.03534,0.04251,0.05015,0.08154,-0.08782,0.12467,-0.00138,-0.01544,-0.06456,0.07501,0.05239,0.10653,0.01719,0.0422,0.07033,0.00528,0.02091,0.08233,0.0779,-0.04625,-0.03035,0.00731,-0.02123,0.04238,-0.12768,0.05171,-0.03269,0.01268,0.00071,-0.2058,-0.05074,0.10455,-0.02629,-0.01894,-0.05748,0.00155,0.04473,-0.02593,-0.08274,-0.00331,-0.08999,-0.04945,-0.10568,0.12431,0.02183,0.01124,0.13092,0.05101,-0.08672,-0.02452,0.01932,0.0382,0.06063,0.02171,0.03141,0.13471,0.05917,0.14486,-0.05077,0.02914,-0.02454,-0.11391,0.21297,-0.02553,0.05875,-0.08012,-0.11846,0.0456,0.06655,-0.12252,0.02133,0.04334,-0.02699,0.09716,-0.09838,-0.03262,0.05378,0.05944,0.05052,0.03844,-0.00647,-0.01603,0.02051,-0.02742,-0.06749,-0.08374,-0.03384,-0.12314,0.0104,-0.02203,-0.02398,-0.02475,0.09398,0.0507,-0.02257,0.00336,0.0711,0.00212,0.03365,0.01212,-0.03636,-0.03406,-0.02992,-0.00268,0.0111,0.03776,0.15403,0.0129,-0.03978,-0.0068,0.05034,0.04541,-0.0926,0.03965,-0.10129,-0.02655,-0.06057,-0.023,-0.06874,-0.01878,-0.05135,-0.01691,0.04289,0.00807,-0.13288,0.06416,0.02001,0.0765,0.08202,0.03857,-0.05225,-0.1396,0.08992,-0.14127,-0.05713,0.05705,0.01321,-0.04894,-0.00772,0.04537,0.05143,-0.0284,-0.07048,0.02845,-0.01352,-0.04091,0.02986,-0.01806,-0.03899,0.07089,-0.05589,-0.04677,-0.05192,0.07776,-0.05452,0.02097,0.05713,0.02102,-0.00754,-0.07437,-0.05376,0.02728,-0.04283,0.02302,0.033,-0.08165,-0.02821,-0.13607,0.05908,0.07264,0.01789,-0.10257,-0.00414,-0.05002,0.0433,-0.10599,0.01872,0.04761,0.05167,-0.0522,-0.13622,0.02564,0.02666,0.00721,0.10133,-0.05758,-0.0491,-0.05738,0.02911,0.01811]},{"domain":"time_series","key":"yule_walker_from_autocorrelations","name":"Yule-Walker 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0.2].","v":[0.03446,-0.01448,-0.03525,0.02907,0.00318,0.02394,0.01317,-0.03766,0.01908,-0.09909,0.00265,-0.06312,-0.01505,0.05401,0.02507,-0.03989,0.0189,-0.10199,-0.04541,-0.00401,0.00461,0.0168,-0.06677,-0.01449,0.04091,0.01,-0.04042,0.06768,0.05746,0.09022,0.0777,-0.04839,0.02154,0.05244,0.09495,-0.03108,0.02031,0.06533,-0.04605,-0.02634,0.05321,-0.09632,-0.08189,-0.05926,0.03545,-0.01155,0.12696,0.03001,-0.09462,-0.0051,0.11695,0.08975,0.04569,0.05564,-0.08001,-0.05438,-0.00788,-0.02388,0.03182,0.04164,0.10396,0.05199,-0.00681,0.0453,0.0068,-0.00101,0.04797,-0.0712,-0.03025,-0.20313,-0.08424,0.03376,0.05234,-0.0295,0.08697,-0.03024,0.02305,-0.0639,-0.05245,-0.11594,-0.04227,0.00657,-0.12618,0.05481,0.02466,0.01122,-0.01127,0.08098,0.01646,-0.02856,-0.07797,0.02269,0.0228,-0.02733,-0.04921,0.02374,-0.05911,-0.04143,0.02094,-0.01142,0.00455,0.00404,-0.01612,-0.0086,0.03113,-0.07328,-0.03713,0.10192,0.13823,0.01975,0.03853,0.03039,-0.09684,-0.0864,0.00287,0.04745,0.01964,-0.10911,0.0281,-0.09668,0.03594,-0.01051,0.07844,0.10548,-0.00842,0.04493,-0.0933,0.05755,0.02374,-0.01105,0.02389,0.01076,0.05702,-0.04326,-0.03141,0.07018,-0.0053,-0.0333,0.01625,0.094,0.05826,0.02562,0.00763,-0.01206,0.2216,-0.0616,-0.0956,0.05619,0.08842,-0.04427,0.05477,-0.01654,-0.03604,-0.02684,0.00889,-0.01287,-0.05458,0.09994,0.10569,0.12737,-0.04793,-0.0235,0.0289,-0.08303,0.11527,0.03859,0.01524,0.20873,-0.01101,0.03702,0.08018,0.07546,-0.05619,-0.13785,0.00674,0.03872,0.0424,0.04134,0.02475,-0.01668,0.01716,0.01933,-0.04528,-0.04132,0.11055,-0.02832,-0.13652,-0.05783,-0.01201,0.09241,-0.12836,0.02243,0.05715,0.00249,0.05415,-0.08905,0.01205,-0.02306,0.04302,-0.04887,0.0148,-0.07211,0.01902,0.03356,-0.00892,-0.09269,-0.05184,-0.10076,-0.04106,0.02845,0.00066,-0.00954,-0.03901,-0.03539,0.04776,-0.05114,-0.10161,-0.07743,-0.04009,0.03428,-0.03702,-0.07977,-0.00424,0.0683,0.04853,-0.01286,0.10607,0.04643,0.01281,-0.04619,-0.03794,-0.0794,0.00348,-0.0583,-0.10449,-0.0372,-0.00723,0.07029,0.04267,0.01725,0.05304,-0.05537,0.04783,-0.07041,0.11124,0.02894,0.0312,0.09903,-0.04349,0.12701,0.03415,-0.13009,-0.12164,-0.04083,-0.01421,-0.02309]},{"domain":"astronomy","key":"absolute_magnitude","name":"Absolute magnitude","package":"astronomy-ai999x","example":"Absolute magnitude: m = 8, d = 100 pc, A = 1","v":[0.01216,-0.09546,0.02272,-0.0038,0.10823,-0.05501,0.02344,0.00241,0.01847,-0.05705,-0.0565,-0.01045,-0.00794,0.0966,0.01978,0.05662,0.14562,-0.02399,0.05715,-0.06526,0.05956,-0.01373,-0.0506,-0.02725,0.02885,0.0517,0.07933,0.01679,0.01554,0.00725,0.08725,0.01392,-0.04118,-0.0841,-0.11999,0.02183,-0.04708,0.04187,0.01017,-0.01408,-0.09464,-0.04894,0.06597,0.04436,-0.01314,0.03944,-0.0197,-0.03382,0.03288,-0.03681,0.06131,0.02149,0.06878,0.07726,-0.04794,-0.14201,-0.07625,-0.07636,0.09518,-0.02763,-0.01392,-0.08292,-0.05921,-0.00246,0.036,-0.09947,0.00271,0.07508,-0.01141,0.1111,0.12928,0.04061,-0.06011,-0.05871,0.11993,0.02062,0.07281,-0.1573,0.01429,-0.03488,0.03552,-0.01508,0.03251,0.031,0.15731,0.07572,0.11171,-0.00368,-0.01449,-0.03258,0.04035,0.06261,-0.01455,0.0698,0.06196,0.05816,0.01644,0.00372,-0.04971,0.00588,0.01296,-0.10332,-0.13591,-0.06259,-0.05675,-0.00285,-0.12133,-0.12405,0.10783,-0.00373,0.02299,0.01471,-0.05827,0.01436,0.04239,-0.00596,0.03016,0.03436,-0.07248,0.00868,0.17216,-0.01982,-0.02385,0.02666,0.12378,-0.05845,-0.02807,-7e-05,-0.0043,-0.03598,-0.07347,0.062,-0.01675,-0.02382,0.00575,0.08177,-0.01152,-0.03045,0.05993,0.05063,-0.00545,-0.0028,0.05255,-0.09888,0.03146,0.00265,0.02735,-0.06552,0.01426,-0.10176,0.02421,-0.01355,-0.03085,-0.06028,-0.04733,0.076,0.00613,0.03004,-0.00738,-0.0509,-0.09719,-0.05387,-0.04804,0.00398,-0.09312,-0.05111,-0.0403,-0.1038,0.01632,-0.02479,0.0029,-0.05569,-0.01148,-0.06491,-0.02285,0.05028,0.08269,-0.14138,0.08567,0.07423,0.17165,0.0202,0.04378,0.0554,-0.01564,-0.00261,0.05402,-0.00327,0.00384,-0.16542,-0.05597,-0.0237,-0.02026,-0.01302,-0.02058,-0.00558,-0.00789,0.12874,-0.09576,0.00235,-0.03915,0.01977,0.0211,-0.05326,-0.06073,0.05965,0.03859,-0.11061,-0.01349,0.05075,-0.11869,0.02099,0.0191,-0.03039,-0.05027,-0.11631,-0.06912,0.05865,-0.01871,0.02202,0.19243,0.02505,-0.0316,0.04634,-0.10613,0.01195,0.02787,-0.04707,-0.03378,0.04258,0.06431,-0.01986,0.14026,0.0424,0.04436,0.00666,0.02827,-0.00354,-0.00297,0.03485,-0.01577,0.09869,-0.02695,0.10767,-0.04056,0.06286,-0.00419,-0.03963,-0.01606,-0.03377,0.07535,0.04216,0.0845,-0.01203,-0.07286,-0.04368]},{"domain":"astronomy","key":"age_at_redshift","name":"Age 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1","v":[-0.02287,0.02301,-0.07813,0.07784,0.06498,-0.01961,0.10767,0.07437,0.01797,0.00395,0.0213,-0.07276,0.02867,0.02655,-0.0386,0.01676,0.12838,0.03948,0.01277,0.02013,0.00988,-0.05324,-0.05686,0.06236,0.04338,-0.09399,0.06957,0.04084,0.05032,0.11191,-0.0316,-0.01737,-0.0866,-0.04596,-0.05015,-0.07235,0.07737,0.06904,-0.01225,0.05002,-0.03679,-0.00656,0.01356,0.01787,-0.05476,-0.07665,-0.02316,-0.04564,-0.01539,-0.01138,-0.04816,-0.05232,-0.04768,0.02032,-0.09875,0.01342,-0.03668,0.00146,-0.01772,0.06139,0.10789,0.0291,0.07661,0.11669,0.0227,-0.07565,0.00369,0.05363,0.01159,-0.01426,-0.03564,0.08267,0.08297,0.04753,0.0889,-0.02071,0.0869,-0.00732,0.07243,0.05775,0.0564,0.00473,-0.05944,0.06307,-0.04226,-0.00193,-0.04518,-0.10906,0.04538,0.15006,-0.11581,-0.02428,-0.0202,-0.06192,-0.07065,0.02813,-0.00949,-0.04933,0.05043,0.07014,-0.09752,0.01269,0.03109,-0.08292,-0.00606,0.12342,0.02948,-0.00899,0.04912,-0.04394,-0.06075,-0.01103,-0.03806,-0.06704,0.00932,0.13741,0.0043,0.00079,-0.00988,0.01565,0.04504,-0.07755,0.02298,0.06003,0.02201,-0.05224,0.00575,-0.11463,0.04389,0.03424,-0.03082,0.042,0.04661,-0.09085,0.01106,-0.1006,-0.05358,-0.00866,0.17433,0.00534,0.11806,-0.01187,-0.00539,-0.03975,-0.02717,0.12256,-0.08796,-0.04344,0.0378,0.04556,0.0577,-0.06402,-0.07672,-0.06511,0.07933,-0.11371,-0.04463,-0.01563,0.06365,0.04219,0.05929,0.00516,0.0008,0.05223,-0.07176,0.02838,-0.02594,0.04258,0.02528,-0.01692,0.08102,-0.04761,0.01035,0.00734,-0.03818,0.16939,-0.00337,-0.04952,0.12608,-0.00087,0.01862,-0.09252,-0.05094,0.01035,0.01174,-0.03824,-0.04017,0.01911,0.05671,-0.06883,0.09164,0.11583,0.00166,-0.1627,-0.09675,-0.02168,-0.00783,0.07115,-0.05843,-0.00052,-0.10219,0.03542,-0.00558,-0.10125,-0.08563,-0.00329,0.16641,0.04263,-0.04523,-0.06671,-0.06013,0.1222,-0.02936,-0.10166,0.07038,-0.04756,0.00961,0.04539,-0.12299,0.0163,0.03164,0.02945,0.00979,-0.19976,0.01096,-0.06228,-7e-05,0.02979,0.01948,-0.05786,0.05263,-0.03623,0.09606,-0.00421,0.07656,-0.03811,0.05159,0.00826,0.0033,-0.02575,-0.03875,0.04676,0.09224,0.04384,0.00092,0.05146,-0.07321,-0.06712,0.04587,-0.02399,0.02705,0.00038,0.07081,-0.02808,-0.10676,-0.08963]},{"domain":"astronomy","key":"airmass_extinction","name":"Airmass and atmospheric extinction","package":"astronomy-ai999x","example":"Airmass: zen = 60 deg","v":[0.06364,-0.03929,0.02328,0.03078,0.07485,-0.0204,-0.11231,-0.04676,0.06454,-0.0391,-0.00408,-0.14741,-0.02485,0.04336,0.12976,-0.03106,0.16834,0.01065,0.02581,0.0132,-0.04213,0.01615,0.0315,0.01777,0.04658,-0.02308,0.08586,0.04865,-0.02636,-0.01683,0.01141,0.00123,-0.14907,0.07779,-0.09599,-0.02088,0.03281,-0.0468,0.05567,0.02593,-0.07491,0.01915,-0.07863,0.05253,-0.01915,-0.00601,-0.02748,-0.09082,-0.07361,0.01142,0.03362,0.01526,0.10597,-0.01791,0.0094,-0.02106,-0.00512,-0.00546,-0.03167,-0.02503,-0.02183,0.05477,-0.03545,-0.02762,-0.08902,-0.00731,-0.00785,-0.01204,0.01713,0.07831,0.13073,-0.01058,0.16512,0.13683,0.11652,0.01102,0.08426,-0.04785,0.04037,-0.02893,0.00998,-0.04761,0.0062,-0.03549,0.05448,-0.01445,0.09044,-0.05111,0.12348,0.01788,0.03187,-0.05687,-0.12197,-0.01216,0.07704,0.02772,0.04785,0.03443,-0.05583,0.02145,0.02239,0.00274,-0.07261,-0.01025,0.03455,-0.0092,0.04875,-0.01634,0.06051,-0.14305,-0.01288,0.08401,0.04396,-0.02619,0.01441,0.03181,0.08516,-0.00617,-0.12562,0.07792,0.03253,-0.00772,0.02089,-0.01467,0.01165,-0.01908,0.02421,-0.027,-0.01752,-0.05697,-0.06412,-0.07552,0.02915,0.02079,0.00397,-0.05599,-0.05071,-0.09349,0.0996,0.02066,-0.01454,0.04911,0.05781,-0.06423,-0.00614,-0.02775,0.13017,0.09237,0.0011,0.01822,0.02155,0.02451,-0.03685,0.00112,-0.01274,-0.01193,-0.08683,0.05647,-0.05443,0.02484,0.0743,-0.06949,-0.04708,-0.0033,-0.05257,-0.03375,-0.0737,-0.13366,-0.0932,-0.01042,0.01823,-0.02023,0.0324,-0.00923,0.00019,0.01596,-0.05938,-0.09907,0.09395,0.06175,0.04513,0.08833,-0.02225,-0.08047,-0.03297,-0.0049,-0.11689,-0.1125,0.0413,-0.00987,-0.04617,-0.02605,0.00425,-0.16353,-0.06391,0.03538,0.06342,0.11871,-0.03723,0.03541,-0.05177,0.00538,0.01719,-0.04988,-0.00023,0.03177,0.09494,-0.03689,-0.0842,-0.05607,-0.13571,0.13144,-0.0504,0.05018,-0.05505,-0.0261,0.01498,0.20586,-0.03287,0.04456,0.05649,-0.06902,-0.03043,-0.03916,-0.07886,-0.04359,0.0744,-0.07318,-0.02447,0.05806,0.05999,0.03499,-0.01558,0.00388,0.05971,-0.08568,0.07394,-0.02157,-0.02259,-0.02012,-0.09114,0.08799,0.03284,0.00297,0.01595,0.105,0.08729,-0.06168,0.0282,-0.09584,-0.03317,0.11979,0.08628,-0.03942,-0.09746,-0.08106]},{"domain":"astronomy","key":"alfven_speed","name":"Alfven speed","package":"astronomy-ai999x","example":"Alfven speed: B = 5 nT, n = 5 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deg","v":[0.03448,0.0466,-0.09231,-0.01747,0.05648,0.07044,-0.05207,-0.08579,-0.00955,0.02323,-0.038,-0.0228,0.01193,0.15154,0.07084,0.04696,0.15127,0.06734,-0.09429,-0.03701,-0.14143,-0.02193,-0.07655,0.02175,0.03175,0.04476,-0.06473,-0.03187,0.03009,-0.04484,-0.06365,0.017,-0.05682,0.01875,-0.03018,0.04478,0.08563,-0.05308,-0.04509,-0.03235,-0.05098,-0.02051,-0.01772,0.06117,-0.05204,0.03412,-0.03151,-0.11016,-0.01501,0.02012,0.11199,-0.02868,0.09565,0.06105,-0.07725,-0.01532,-0.08092,-0.08626,-0.01062,-0.1138,-0.09276,0.0472,-0.00791,-0.11782,-0.00385,0.05772,0.01438,-0.11572,-0.13163,0.06182,-0.06395,-0.05808,0.08884,0.07844,0.10267,-0.09303,0.0043,0.07968,0.03865,-0.00502,-0.06038,0.03716,0.06851,0.03023,0.06887,-0.07321,0.01045,-0.06105,0.06808,0.03897,0.05142,-0.02552,-0.0756,-0.04886,-0.05283,0.10957,0.01147,0.0437,-0.07099,-0.0385,-0.02292,0.00649,0.018,-0.00966,0.05484,-0.01711,-0.01198,0.05198,-0.04608,-0.04185,0.11293,0.07893,-0.07331,0.07244,0.00988,0.11049,0.05098,0.01588,-0.10173,-0.04658,0.0352,-0.06524,0.06091,-0.09314,0.0538,0.10659,-0.04017,0.05957,0.02212,-0.04104,-0.05255,-0.10754,0.03824,0.06526,0.00418,0.02904,-0.06917,0.04764,-0.01055,-0.01434,0.02169,0.04602,-0.1186,-0.10364,0.03448,-0.02815,0.05963,0.08399,0.00941,-0.00253,0.00818,-0.06634,0.00525,0.03677,-0.00049,0.10009,-0.0897,0.0799,-0.05617,-0.07311,0.10104,-0.11516,0.04967,0.01675,-0.00777,-0.00165,-0.05642,-0.06825,-0.05964,0.0485,0.12572,-0.03363,0.04515,-0.08663,-0.10591,0.02821,-0.03395,0.01914,0.01027,-0.09968,-0.04418,0.0722,0.06091,-0.02459,0.04759,-0.11397,0.03598,-0.09053,0.03138,-0.02533,-0.05351,-0.03276,0.03674,-0.04002,0.00552,0.08251,0.03502,0.10082,-0.00561,0.04293,-0.06725,-0.02502,0.02303,3e-05,-0.13071,0.00349,0.11645,0.07036,-0.01043,-0.02334,4e-05,0.02846,-0.04009,0.16811,-0.03046,-0.12992,-0.02543,0.01993,-0.04229,-0.01086,0.00123,-0.05286,-0.04789,0.07428,-0.03723,-0.0123,0.06,0.02534,0.01031,-0.00414,-0.01399,-0.07032,-0.01029,0.0096,-0.04881,-0.04937,0.13039,0.0393,0.02974,-0.08285,-0.00262,0.05005,0.00366,-0.03972,-0.04381,-0.03241,0.18836,0.00432,0.02403,0.03154,0.05855,0.04365,0.06971,-0.05754,0.00847,0.04383]},{"domain":"astronomy","key":"angular_separation","name":"Angular separation of two sky positions","package":"astronomy-ai999x","example":"Angular separation: ra1 = 0 h, dec1 = 0 deg, ra2 = 6 h, dec2 = 0 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size","package":"astronomy-ai999x","example":"Angular size: D = 2 m, d = 1 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size of an object at a redshift","package":"astronomy-ai999x","example":"Angular size at redshift: z = 3, H0 = 70, Om = 1, D = 1 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bolometric magnitude and flux","package":"astronomy-ai999x","example":"Apparent bolometric magnitude: L = 3.0128e28 W, d = 100 pc","v":[0.0643,-0.10595,-0.02283,-0.00484,0.12835,-0.06981,-0.02415,-0.0602,-0.02677,0.03258,0.00437,-0.08701,0.0654,0.11531,-0.02035,0.04056,0.06628,0.06713,-0.00041,-0.05898,0.04577,-0.01692,-0.08063,0.01772,0.08059,-0.03817,0.12393,-0.04587,-0.02332,0.04197,0.09421,-0.0025,-0.02237,-0.12527,-0.03071,0.07457,-0.07685,-0.0384,-0.04534,-0.0431,0.02169,-0.07782,-0.01393,-0.02153,0.04132,-0.02967,0.01281,-0.07923,0.02438,0.03099,0.00899,-0.04723,0.08589,0.06965,-0.00308,-0.01455,-0.08983,-0.06043,0.01166,0.02106,0.06505,-0.00736,-0.08865,-0.02965,-0.01652,-0.05209,0.01101,0.02598,0.04817,0.02506,0.13729,0.01429,-0.10589,-0.07841,0.10392,0.06452,0.07934,-0.20935,-0.01977,-0.0298,-0.038,0.07144,0.00108,-0.06395,0.1263,-0.03409,0.0135,-0.10576,-0.02369,-0.03532,0.05562,0.02891,0.11246,0.06845,0.10331,0.065,-0.01789,-0.03315,0.02439,0.04306,-0.00969,-0.00421,-0.08483,-0.04674,0.0193,-0.12706,-0.08881,-0.13403,0.03299,-0.00349,0.04648,-0.04604,0.08197,0.01819,0.05345,0.0534,0.06096,-0.00242,-0.01306,0.04154,0.02949,-0.05011,-0.02559,-0.03721,0.12097,-0.07862,0.01628,0.02287,-0.03261,-0.01293,-0.00332,0.09204,0.03222,-0.03052,0.03207,0.01569,-0.01099,0.01169,-0.04738,-0.04141,-0.04649,0.0052,0.00825,-0.1195,-0.02568,-0.01104,0.02413,-0.03455,0.01315,-0.08695,0.10483,-0.02335,0.02069,-0.04505,-0.12611,-0.0315,-0.00285,0.04662,0.00693,-0.064,-0.00883,-0.15963,-0.07932,-0.05058,-0.14768,-0.0202,-0.03733,0.00462,-0.02563,-0.02552,0.03403,0.06274,-0.04187,-0.02628,-0.02786,0.02977,0.07106,-0.09824,0.08621,0.02119,0.13973,-0.05391,0.02152,0.00907,-0.00789,-0.04756,-0.01617,0.05621,0.01255,-0.16027,-0.03463,0.00457,0.00989,0.00618,-0.02724,0.02933,0.06699,0.10155,-0.07273,-0.01002,-0.10431,0.04545,0.06301,-0.10451,0.07497,0.05635,-0.0052,-0.08462,-0.0274,0.03688,-0.08663,0.02633,0.01797,-0.00183,0.01441,-0.03462,-0.08573,0.01849,0.07893,0.02643,0.13035,0.03139,-0.06557,0.14907,-0.00644,0.07443,0.02628,-0.04903,0.03902,0.13755,-0.01385,0.01004,0.08879,0.03955,-0.00134,-0.0093,-0.03356,-0.0136,-0.04472,0.00917,-0.01199,0.01918,0.0167,0.03873,0.00343,0.04057,0.06364,0.06234,0.10078,-0.03544,0.14905,-0.02468,0.06197,0.04028,-0.13306,0.09865]},{"domain":"astronomy","key":"apsis_speeds","name":"Speeds at periapsis and apoapsis","package":"astronomy-ai999x","example":"Apsis speeds: rp = 1 m, ra = 3 m, M = 1.4982e10 kg","v":[0.0868,-0.06481,0.01815,0.01809,0.04179,-0.10634,-0.08526,-0.02254,0.04737,-0.00752,-0.05425,-0.06146,0.05097,-0.03467,-0.02936,0.11065,0.06759,0.02574,-0.00083,-0.06852,-0.04504,-0.06343,-0.01713,0.03977,0.02636,-0.02435,0.08143,-0.02712,-0.01256,0.03596,-0.04334,0.10956,0.0237,0.00129,0.01385,-0.01488,0.00274,0.0596,0.00341,0.00886,0.00016,0.07427,0.02445,-0.01053,-0.09142,-0.03574,-0.05845,-0.09722,0.02128,-0.0182,-0.0079,0.0094,0.01151,0.12985,0.0195,0.013,-0.09495,0.0486,0.07332,-0.0725,-0.04053,-0.05135,-0.0473,-0.02723,-0.01669,0.00388,0.00111,-0.04297,0.02665,0.07577,0.04044,0.02449,0.02333,-0.1497,0.00326,0.08889,-0.06178,-0.04827,-0.013,0.03239,-0.12007,0.04187,-0.06727,-0.02243,0.00644,0.0258,-0.10834,-0.0978,-0.05142,-0.05666,0.06357,-0.0272,-0.00259,0.05277,-0.05001,0.0802,0.02765,0.11318,-0.01636,0.04133,0.00542,0.1041,0.07557,0.00846,-0.01187,-0.07585,-0.06276,-0.01723,-0.05624,-0.08109,0.05262,0.0836,0.00458,0.13576,0.00101,0.03207,0.01986,0.08462,0.00603,0.01556,0.16177,0.03993,-0.07143,0.0675,-0.10918,0.05617,0.00949,0.03331,-0.03928,-0.00047,-0.02925,-0.01432,-0.02853,-0.03829,0.05095,0.0539,0.07046,0.0777,0.00776,0.00437,0.05054,0.04524,0.07151,-0.0176,0.05366,0.02167,-0.09361,-0.09433,-0.0991,0.11883,-0.11718,0.01571,-0.027,-0.12873,-0.03348,0.03701,0.08205,-0.00977,0.01932,-0.09871,-0.05952,0.02069,-0.05561,-0.0456,-0.05678,-0.01331,-0.00786,0.04975,0.02895,0.13645,-0.02343,-0.0485,0.08364,-0.07933,0.03164,0.0583,0.00769,0.08417,0.0494,0.12034,0.02612,-0.05223,0.06611,0.0762,0.01601,0.05733,-0.10294,-0.00372,0.00123,-0.10292,-0.00267,-0.09072,0.00091,-0.03,0.01649,-0.0055,0.00199,0.062,0.11067,-0.11078,-0.02176,-0.02332,0.02224,0.07614,-0.10051,0.01034,0.01056,-0.11771,-0.07787,-0.10831,-0.16742,-0.08176,0.10876,-0.11269,-0.06076,-0.03734,-0.02348,-0.0315,0.07664,0.02498,-0.04545,-0.0293,0.01081,0.09722,0.09371,0.06162,-0.01634,0.10442,-0.0417,0.03671,0.13818,-0.01859,0.05793,0.00663,-0.03924,0.00179,0.00933,0.03433,0.05808,-0.08399,0.03845,0.13065,0.04358,-0.03487,-0.02353,0.01527,0.05408,-0.11902,0.03635,-0.10874,0.0576,0.10478,-0.07147,-0.08572,0.03038,-0.02338]},{"domain":"astronomy","key":"atmospheric_scale_height","name":"Scale height of an isothermal atmosphere","package":"astronomy-ai999x","example":"Scale height: T = 288 K, mu = 28.97 g/mol, g = 9.81 m/s^2","v":[-0.12172,0.00765,0.03855,-0.01116,0.04802,0.05974,-0.00548,0.06776,0.02961,-0.04584,0.1197,-0.05897,0.03672,0.03766,-0.05128,-0.1067,0.09652,0.08069,0.0753,0.11172,0.01918,-0.07882,0.04337,-0.00587,0.03769,-0.0578,0.10228,-0.04191,-0.05596,0.06344,-0.09576,0.06133,0.02275,-0.07901,0.01474,-0.01266,-0.06807,0.07394,0.00491,0.03337,-0.05065,0.03321,-0.05708,0.00586,-0.05563,0.05316,0.00866,-0.06324,-0.00879,-0.055,-0.07858,-0.08617,0.02917,-0.06155,0.01618,0.04641,-0.02916,0.05408,-0.0429,-0.00116,-0.15608,-0.08327,-0.01272,0.00021,0.0137,-0.0442,0.04431,0.08459,0.06919,0.07992,0.05233,0.05921,-0.02835,0.00369,-0.00353,0.10133,-0.04398,-0.0036,-0.06738,-0.05439,-0.00665,0.12595,-0.0591,-0.04264,-0.02904,-0.02032,0.06911,0.0192,0.05355,0.0511,0.08734,0.0505,-0.06037,-0.00221,0.00854,-0.01877,0.09657,-0.06289,0.00827,0.09357,0.02703,-0.21161,-0.06387,0.00721,0.02741,-0.00568,0.14465,0.05431,0.0642,0.02193,-0.00493,-0.05728,-0.00391,-0.04179,-0.05988,0.05344,-0.06882,0.04286,0.02079,0.00092,0.05516,0.01681,0.0412,-0.11294,0.04992,-0.06004,-0.08454,-0.03487,-0.09648,0.08042,-0.06046,0.03051,0.02285,0.02721,-0.11025,-0.00069,0.02898,0.02747,0.04893,0.10256,0.11101,0.0193,0.06788,-0.00194,-0.02997,0.01011,0.04835,-0.06713,-0.04334,0.03877,-0.03805,-0.09809,-0.03886,0.04802,-0.02209,0.00984,0.05071,0.04107,-0.06471,-0.00518,-0.02804,0.05401,0.15798,-0.14407,-0.15731,-0.00558,-0.09681,0.06489,0.00072,0.03658,0.04176,0.07588,0.04037,0.05656,-0.08353,-0.01987,0.04612,0.00781,-0.03721,0.10122,0.03871,-0.01426,0.00399,0.11566,-0.05138,-0.04748,0.02863,-0.03039,-0.03518,-0.08007,-0.01109,0.09582,0.05078,-0.05485,-0.01241,-0.04555,-0.054,0.04732,-0.05851,0.01439,-0.01275,-0.04492,-0.07515,-0.09049,0.06,-0.00987,-0.00676,0.06334,0.00749,-0.07905,-0.03053,0.1347,0.03177,-0.05265,-0.0526,0.0427,-0.01038,0.00415,0.02383,0.03646,-0.1277,-0.06061,0.06055,-0.08416,-0.03738,-0.04277,0.01351,-0.11784,-0.08271,-0.11736,0.15847,0.05343,-0.04991,0.0323,0.07306,-0.04045,-0.02888,-0.03283,-0.10405,-0.04811,-0.06029,-0.02541,0.01029,-0.01542,-0.00342,0.12972,0.12184,0.00973,-0.00136,-0.03663,0.00273,0.08505,0.00975,-0.00555,-0.03435,0.06872]},{"domain":"astronomy","key":"binary_star_masses","name":"Masses of a visual binary star","package":"astronomy-ai999x","example":"Binary star masses: P = 1 yr, a1 = 0.25 au, a2 = 0.75 au","v":[-0.00032,-0.12264,-0.02679,-0.03866,0.07804,-0.05752,0.04941,-0.05225,-0.02026,0.01826,0.13779,-0.01543,0.01529,-0.06022,-0.00423,-0.00726,0.0011,0.03945,0.05002,-0.10085,0.09011,0.03225,-8e-05,0.07225,0.01459,-0.0076,0.0488,0.08991,-0.0509,0.04403,-0.0194,-0.02847,-0.06758,0.00328,-0.00403,-0.06177,-0.13302,0.05465,0.0267,-0.04719,-0.04721,0.06956,-0.02045,-0.15901,-0.13676,-0.00182,-0.04955,0.05868,0.00933,-0.0125,-0.10946,0.13296,0.04471,0.02238,0.00436,0.04839,-0.04806,0.02338,0.1674,0.06249,0.00515,0.04848,-0.05637,0.04308,0.01704,0.07167,0.15095,-0.03611,0.02306,0.02749,0.00526,-0.0889,0.01668,-0.05875,-0.04068,0.00979,-0.13506,-0.02006,-0.029,-0.0927,-0.01253,-0.02013,0.03906,-0.03751,0.13559,-0.01787,-0.00599,0.06697,-0.04467,-0.02105,-0.05792,-0.02908,-0.00562,-0.04704,0.04256,0.01458,0.05437,0.1085,-0.18886,0.00545,0.05011,0.0474,0.02626,0.03632,0.01289,-0.06978,-0.02483,-0.08084,-0.05226,-0.0493,0.00113,0.00235,0.00147,0.03185,-0.02971,-0.04576,0.1408,0.02845,-0.05326,0.0741,-0.08781,0.02503,0.01337,0.06556,0.00209,0.09686,0.00286,-0.00718,-0.05607,0.077,0.02589,0.04542,-0.11251,0.00857,-0.06349,0.04202,-0.02089,0.09239,0.05866,-0.04707,0.00047,-0.00279,0.06944,-0.07772,0.01649,0.07854,-0.06094,0.00924,-0.0356,0.0882,-0.03483,-0.0483,0.01276,-0.09105,0.00116,0.07849,0.05875,-0.03016,0.00401,-0.03769,-0.00809,-0.04967,0.01503,0.0009,0.00462,0.02609,-0.07429,0.09418,0.06913,0.00047,0.01335,0.00863,0.03897,-0.13964,0.01749,0.06079,-0.02069,0.0056,-0.07114,0.09199,-0.05983,0.06678,0.0223,-0.04509,-0.07002,0.03087,-0.01223,-0.08211,-0.07964,-0.16267,-0.15615,0.11596,-0.01224,-0.01486,0.11977,-0.05926,-0.00578,0.00571,-0.00457,-0.02777,0.0432,0.0079,-0.03536,0.08338,-0.09443,0.08366,-0.07421,-0.03886,-0.14036,-0.04463,-0.03029,0.03025,-0.02657,-0.1051,0.05038,0.03516,0.00099,0.06319,0.0346,0.07467,0.06583,-0.01294,-0.06647,0.06648,0.02585,-0.04323,-0.00203,0.02362,0.11584,7e-05,0.03985,-0.12024,-0.04047,0.06232,0.10403,0.01144,0.03464,0.02375,0.02647,0.07851,0.06813,0.03238,0.11014,0.03649,-0.06904,0.0504,0.05086,-0.10432,0.07802,-0.02847,-0.05596,-0.04125,0.05317,-0.00963,-0.09502,-0.04098]},{"domain":"astronomy","key":"bolometric_magnitude_from_luminosity","name":"Absolute bolometric magnitude from luminosity","package":"astronomy-ai999x","example":"Absolute bolometric magnitude: L = 1 Lsun","v":[0.0551,-0.06824,-0.08426,0.01877,0.11825,0.02223,-0.05397,-0.0641,-0.03112,0.04098,-0.03189,-0.00942,0.03411,0.00525,-0.00918,-0.00712,0.06566,0.03875,0.00239,-0.02999,0.05277,-0.03264,-0.12858,0.08226,0.05797,-0.01811,0.13483,0.04585,0.00722,0.12579,0.01967,-0.05858,-0.02789,-0.05195,-0.01449,0.04021,-0.15688,0.02218,0.00924,-0.09201,0.05704,-0.0622,-0.07905,0.00126,0.15277,-0.02757,-0.01168,-0.05915,0.0484,-0.09346,-0.01898,-0.09363,0.11557,0.07991,-0.03549,-0.15855,-0.05442,-0.10736,0.04838,0.11912,0.08116,0.02886,-0.05489,-0.0109,0.03724,-0.05656,-0.0302,0.0158,0.08049,0.04012,0.02561,0.03027,0.00341,-0.08511,0.04056,-0.01872,0.07883,-0.0887,-0.01144,-0.01601,-0.029,0.05126,0.00104,-0.03502,0.08209,-0.02242,0.00628,-0.05803,-0.0154,-0.08074,0.08281,0.0478,0.03484,0.03337,0.115,-0.04026,-0.01121,-0.01286,0.03085,-0.01698,-0.03936,-0.09217,-0.04026,-0.07703,0.00529,-0.07231,-0.12929,-0.08993,-0.03369,0.05876,0.01962,-0.07,0.06945,-0.06392,0.00757,0.03866,0.04144,-0.04225,0.0508,0.09306,0.00537,-0.0837,0.01325,-0.07217,0.13809,-0.0424,0.09807,0.01231,-0.01311,-3e-05,-0.01823,0.09144,-0.10079,-0.01048,-0.02807,-0.11941,-0.01016,-0.01825,0.02155,0.00573,0.00071,0.00395,0.05076,-0.01523,-0.01096,-0.077,-0.02095,-0.07513,0.02074,-0.15794,0.02917,0.04442,-0.04897,-0.02582,-0.195,0.05277,-0.05376,0.0071,0.03191,-0.08716,-0.00317,-0.06458,0.02341,0.00169,-0.10394,0.02385,0.03564,0.11003,-0.01379,-0.00977,0.04618,0.00063,-0.0306,0.00571,-0.01684,0.00518,0.06876,-0.08342,0.10863,-0.08314,0.14512,-0.03051,-0.07674,-0.02986,0.00029,-0.0254,-0.00794,0.10177,-0.07439,-0.08123,-0.09062,0.02502,0.07343,0.06529,-0.02111,-0.00745,0.02636,0.06607,-0.04921,0.07586,-0.05746,-0.00983,0.04021,0.00373,0.10844,0.0758,0.03033,-0.04031,-0.08189,0.04539,0.02034,-0.01142,0.0104,-0.04951,0.02974,-0.04469,-0.07853,-0.03904,-0.01618,-0.00115,-0.00119,0.02068,-0.13157,0.07376,0.06828,0.10927,0.02861,-0.08619,0.01678,0.05027,0.02383,0.01307,0.04401,-0.02469,0.09747,0.05946,-0.04241,-0.00909,-0.01258,-0.02631,0.0199,0.07213,0.00954,0.07438,0.00219,0.08164,0.07042,0.02864,0.07721,-0.00645,0.09107,-0.0403,0.17486,0.07801,-0.04615,0.01944]},{"domain":"astronomy","key":"calendar_date_from_julian_date","name":"Calendar date from a Julian date","package":"astronomy-ai999x","example":"Calendar date from Julian date: jd = 2451545.0","v":[0.12356,0.03395,-0.00869,0.114,0.00032,-0.14684,0.1069,0.02887,-0.03663,0.09918,-0.08759,-0.04224,0.13452,-0.05797,-0.10394,-0.10568,0.00319,-0.08217,-0.17339,-0.02395,-0.01081,-0.01574,0.10609,-0.00117,0.00961,0.04506,-0.12958,0.07594,-0.04026,-0.08242,-0.10782,0.02466,0.01362,-0.01295,-0.00113,-0.09247,-0.01497,0.0348,-0.05381,-0.01159,0.0277,0.03184,0.02776,-0.15189,0.03777,-0.02541,-0.01173,-0.0511,0.0211,0.04033,-0.04859,0.05292,-0.03439,-0.02568,-0.07844,0.04466,0.05716,-0.03687,-0.07023,-0.03325,-0.04326,-0.05224,0.03595,0.00901,0.03036,0.01972,0.06308,0.07781,-0.12767,0.08703,-0.05271,-0.16852,0.02465,-0.0343,0.05794,-0.10053,0.08787,-0.01439,0.01648,-0.06756,-0.01126,-0.07788,0.05682,0.00266,0.05343,-0.05182,-0.06336,-0.02527,0.03456,-0.05452,-0.06373,-0.03349,0.09701,0.00874,-0.0578,-0.0138,0.03743,-0.10402,-0.0075,0.0722,0.09718,-0.03332,0.00411,-0.0763,-0.02963,0.08053,0.01169,0.03595,-0.00312,-4e-05,-0.00647,-0.00319,0.02093,-0.04034,0.10836,0.0686,0.07722,-0.03546,-0.01659,-0.02184,-0.08179,-0.07395,0.02041,-0.0481,-0.01658,-0.05838,0.07014,0.016,-0.04115,0.08604,0.04073,-0.07002,-0.02754,0.11084,0.08683,0.08072,-0.02608,0.03611,0.03258,0.10389,0.01143,0.02849,0.04985,-0.04842,-0.01362,0.10167,0.02888,-0.05866,0.03237,0.07544,0.01781,-0.19181,-0.00911,0.02961,0.00038,-0.02413,0.00863,-0.0479,0.01072,-0.05388,0.11599,0.06781,0.05571,-0.00909,0.05805,0.05035,-0.09962,0.0473,-0.00125,0.02282,-0.06624,-0.0342,0.11883,-0.1292,-0.05124,-0.05709,0.03292,0.0018,0.06024,-0.12111,0.00322,0.04462,0.03879,0.00562,0.03021,0.01671,0.10158,-0.07172,0.01224,-0.03175,0.0373,0.00487,0.04996,0.04343,-0.08748,0.02729,0.02792,0.05513,-0.09374,0.0122,-0.03743,-0.02648,0.02017,-0.06606,0.07125,-0.05793,-0.05495,0.07252,-0.0331,-0.02219,0.01008,-0.05585,0.05861,-0.01394,0.07993,0.0572,0.08765,0.01025,-0.02787,-0.03606,0.00313,0.06761,0.08097,0.02164,0.0969,0.05681,0.07329,-0.1096,-0.05683,-0.03479,0.02678,-0.04959,0.00875,0.04192,0.03815,-0.02543,0.07917,0.01346,0.05852,0.08303,-0.00516,0.01051,-0.08434,-0.01027,-0.06692,-0.01633,-0.08192,-0.1306,-0.00517,0.00105,0.07964,0.07394,-0.05404,-0.02692,-0.11382,-0.08807]},{"domain":"astronomy","key":"camera_pixel_scale","name":"Pixel scale and field of view of a telescope camera","package":"astronomy-ai999x","example":"Pixel scale: f = 2000 mm, p = 3.76 um, N = 6248","v":[0.08096,-0.06071,-0.02088,0.0439,-0.00489,0.01087,0.00756,-0.03035,-0.03589,-0.12608,0.03588,-0.07604,0.0198,0.00833,0.0022,0.01982,0.01803,0.1243,0.02723,0.09604,-0.06862,0.07432,-0.03255,-0.02899,-0.06233,-0.0481,-0.03877,-0.03119,0.08912,-0.03814,-0.05005,-0.08641,0.0333,-0.00359,0.0272,-0.13517,0.16013,0.08022,0.04814,0.11139,-0.00192,0.0005,0.08998,-0.15666,0.05491,0.06433,-0.00054,0.08926,-0.00175,0.06427,-0.00812,0.01783,-0.01356,-0.02486,0.02757,-0.03678,-0.03984,-0.01843,0.06347,-0.05306,-0.03177,0.06736,-0.09866,-0.00339,-0.05721,0.06519,-0.07279,-0.04142,-0.00749,0.02546,0.04417,-0.00884,0.04395,0.0652,-0.02452,0.02394,0.10646,-0.01376,0.05689,-0.05024,0.03181,-0.10224,0.05883,-0.08349,0.09627,-0.00306,0.04547,-0.07304,0.11279,0.07827,0.03897,-0.05927,0.04449,0.0223,0.00458,0.05089,0.08966,0.02912,0.03468,0.13598,-0.07612,0.023,-0.062,-0.06216,-0.018,0.01616,0.06388,-0.01399,-0.00846,0.04266,-0.11468,-0.0193,-0.10169,0.00352,-0.05032,0.03684,0.07024,0.0546,0.08017,-0.0257,-0.02423,-0.00921,-0.00198,-0.01028,0.04383,-0.08472,-0.09201,0.05568,-0.06237,-0.03559,-0.10176,-0.06635,-0.07389,0.00039,0.07453,0.04769,-0.04507,-0.01992,0.02085,0.02562,0.06059,0.01846,-0.01803,-0.07405,-0.03138,-0.02914,-0.0309,0.02962,0.04319,0.07753,0.02994,-0.07838,-0.06558,0.02294,0.02095,-0.03668,-0.02197,0.09892,-0.03739,0.03295,-0.02077,0.00719,0.02017,0.03615,0.01047,-0.01534,-0.06765,0.07136,-0.11391,0.05419,0.02394,0.03868,0.03717,-0.00683,0.11657,0.03762,-0.10395,0.02414,0.04464,-0.04641,-0.06256,-0.01936,0.03179,0.00703,-0.12393,-0.03,0.05615,-0.12963,0.05798,-0.04434,0.04256,-0.01893,-0.05168,-0.08465,-0.02374,0.11149,0.01452,-0.08585,-0.11019,0.00154,0.04152,-0.12651,0.09486,-0.0764,0.04596,-0.04011,-0.04181,0.07328,-0.03304,0.03482,0.02165,0.11421,-0.08762,-0.00468,-0.07861,0.01038,0.02103,0.06849,0.01056,-0.0086,-0.10208,-0.02109,-0.18698,0.14194,0.04221,0.03271,0.14855,0.00524,0.01384,-0.03249,0.02864,0.00477,-0.00211,0.046,-0.14858,0.00597,0.06346,-0.03462,-0.06754,0.03819,-0.05587,0.00211,-0.06675,-0.01731,-0.03594,0.16144,0.08357,-0.09704,0.01385,-0.11994,0.01994,-0.03025,-0.05923,-0.0041,0.04944,0.08511]},{"domain":"astronomy","key":"combined_magnitude","name":"Combined magnitude of two stars","package":"astronomy-ai999x","example":"Combined magnitude: m1 = 5, m2 = 5","v":[-0.06446,-0.0305,-0.01076,0.06027,0.06108,-0.10085,0.05979,-0.01936,-0.01338,-0.00758,0.03097,-0.03459,0.03425,0.03331,0.04277,-0.14205,0.03622,0.03584,0.07985,0.04208,0.09891,0.05732,0.03396,0.05626,-0.0071,0.03852,0.04778,-0.00188,-0.09885,0.01686,0.00131,-0.00027,-0.1081,-0.0382,-0.00359,-0.02056,-0.07339,-0.03692,0.00185,-0.02937,-0.0369,0.0882,-0.01251,-0.15315,-0.00038,0.02716,-0.02176,0.05098,-0.01779,0.03292,-0.094,0.09432,0.0701,0.02607,0.02938,0.02679,-0.09495,-0.07883,0.07897,0.04703,-0.01822,0.07809,-0.07162,-0.01423,-0.11361,-0.0146,0.08267,0.065,0.11853,0.057,0.12209,0.05582,-0.06875,0.04102,0.00821,0.0301,-0.03391,-0.09154,-0.01917,-0.01511,0.02084,-0.04456,0.09081,-0.06272,0.12166,-0.03181,0.10938,0.1269,-0.00906,0.06857,-0.04004,0.07417,-0.01462,0.06665,0.05728,-0.01744,0.01767,0.05134,-0.10545,-0.03344,0.01077,0.02971,-0.05753,0.0566,0.00341,-0.07866,-0.01558,-0.0776,-0.04089,0.04197,-0.00343,-0.02969,-0.01947,0.04808,0.01748,0.003,0.09767,0.00649,0.0032,0.09407,-0.06271,0.03798,0.04401,0.0448,0.15439,0.00232,0.01331,-0.00842,0.00896,-0.01489,0.0359,0.00312,-0.16312,-0.00218,-0.03477,-0.02693,-0.09352,0.07127,0.00486,0.02384,-0.13894,0.00638,-0.00711,-0.0618,0.09202,-0.02675,0.04257,0.01495,0.03441,-0.03282,-0.08867,0.07919,-0.07668,0.01727,-0.08191,-0.02208,-0.05034,-0.00982,-0.05099,0.02313,0.0357,-0.09242,-0.11742,-0.0002,-0.02565,0.05672,-0.07123,0.01927,0.01577,-0.03081,0.01371,0.05228,-0.00102,-0.14078,-0.05763,0.09746,0.07894,-0.14763,0.04299,0.00253,-0.02884,-0.01353,0.05499,-0.06413,-0.1324,0.01743,0.09631,-0.04585,-0.03253,-0.07965,-0.13524,0.11899,-0.01143,0.08963,0.04406,-0.05271,-0.0337,0.02658,-0.06564,-0.0674,0.04408,0.06514,0.04362,0.02707,-0.08787,0.1076,-0.0581,0.0312,-0.07624,0.08557,-0.05501,0.10139,-0.04716,-0.0581,-0.08922,-0.01801,-0.04869,0.07483,-0.07086,0.08248,0.07155,0.00947,-0.05056,-0.00355,-0.03591,0.04463,0.04358,-0.06622,0.02748,0.13502,-0.05652,0.04976,0.07649,-0.03152,0.1253,-0.00127,0.01081,0.00965,-0.05627,0.02405,0.07755,-0.03072,-0.02424,0.07749,-0.10657,-0.00061,-0.0009,-0.06357,-0.01223,-0.0805,-0.0588,0.0187,0.0483,0.01817,-0.13084,0.00334]},{"domain":"astronomy","key":"comoving_volume","name":"Comoving volume out to a redshift","package":"astronomy-ai999x","example":"Comoving volume: z = 3, H0 = 70, Om = 1","v":[-0.05831,-0.06402,-0.02184,-0.01652,0.02456,-0.03543,0.08082,0.0597,0.07704,0.01939,0.06786,0.00981,0.04205,-0.04166,0.03849,-0.03024,0.10964,0.0592,-0.07052,0.14597,0.0242,0.06804,-0.03495,0.00038,0.04322,-0.09463,0.02452,0.03629,-0.01951,-0.01581,-0.04723,-0.14275,-0.05686,-0.08385,-0.00668,-0.12772,0.05331,0.01973,-0.00402,0.09721,0.00253,0.02921,-0.15121,-0.04679,-0.05022,-0.0403,-0.04242,-0.04964,-0.10243,-0.07025,0.00219,-0.08428,0.00384,-0.07138,-0.02157,-0.01431,-0.00184,0.06757,0.02706,0.01126,0.07464,0.09747,-0.0353,0.07929,0.03624,-0.07292,0.12113,-0.07743,0.05953,0.10584,0.06935,0.06973,0.02708,0.06317,-0.04965,0.05629,-0.01289,-0.05606,0.09499,0.14286,0.0644,0.01788,-0.03705,-0.0491,-0.05848,0.09213,-0.02346,0.01906,0.07331,0.11439,0.02422,0.04834,-0.02306,-0.01356,-0.10881,0.07046,-0.02472,-0.08083,0.12689,0.025,-0.08657,-0.05457,0.08782,-0.10516,-0.00021,0.0092,0.01882,0.00277,0.07083,0.08501,-0.02399,0.03171,-0.03881,0.05853,-0.04066,0.07048,-0.00363,-0.02648,-0.01745,0.01027,-0.05111,-0.1137,-0.06189,0.04799,0.01725,-0.01143,0.01159,-0.03727,0.06138,0.03064,-0.03892,-0.00648,-0.01587,-0.04223,-0.05913,-0.06743,-0.05528,-0.00504,0.04529,-0.01727,0.01827,-0.02346,-0.02065,-0.07259,-0.03982,0.06804,0.01292,-0.14061,-0.00828,0.08743,0.09695,0.06932,0.07484,-0.0519,-0.01514,-0.04286,0.0166,-0.02769,0.07369,0.13184,0.13267,-0.0575,-0.02752,0.06277,-0.02555,0.10029,0.01445,-0.03268,-0.00332,-0.13686,0.04781,0.05239,-0.14339,-0.03643,-0.00057,0.16857,-0.0249,0.02272,0.08691,-0.09029,-0.0025,-0.0262,0.02713,0.04468,0.01935,0.02037,0.05579,-0.01104,0.06896,-0.07095,0.014,0.05349,-0.00694,-0.06201,-0.11263,0.0001,-0.00495,0.00867,-0.12971,0.03973,-0.04007,-0.02203,0.03443,-0.02412,-0.04715,0.06205,-0.00854,0.02382,0.01064,-0.06375,-0.09578,-0.02273,0.03767,-0.05425,-0.01151,0.00414,-0.03662,0.02659,-0.03928,-0.05474,0.03629,0.04753,-0.04468,-0.18324,0.03746,0.01433,0.01683,0.0831,0.01642,0.0134,0.03239,0.01845,-0.01289,-0.06771,0.05332,-0.06986,-0.02768,-0.03972,0.00415,-0.02145,0.0238,-0.06643,0.10601,0.02008,0.06477,0.08032,-0.02977,0.01253,0.11596,0.12987,-0.03097,-0.10414,-0.03675,0.05247,-0.12467,-0.0706]},{"domain":"astronomy","key":"cosmological_distances","name":"Cosmological distances at a redshift","package":"astronomy-ai999x","example":"Cosmological distances: z = 3, H0 = 70, Om = 1","v":[-0.08536,-0.0418,0.04071,-0.01505,0.03854,-0.06658,0.04645,0.07071,0.08215,-0.03904,-0.04041,-0.06064,0.05314,0.09996,-0.04733,-0.00875,0.12763,0.01529,-0.04125,0.04429,-0.04542,-0.02575,-0.00998,-0.07705,0.06595,-0.09513,0.07243,0.05942,0.01838,-0.03004,-0.01553,0.01863,-0.06043,-0.14422,-0.05093,-0.00982,0.0388,0.10318,-0.00726,0.01577,-0.05111,-0.01778,-0.03706,0.01948,-0.15756,-0.07124,-0.06459,-0.05384,-0.09314,-0.08431,0.00839,0.01722,-0.02152,-0.02229,-0.05363,-0.03129,-0.0751,0.10929,0.00031,-0.06717,0.12659,0.00927,-0.06376,-0.01354,0.05052,-0.06049,0.04246,0.04035,-0.02932,0.05342,0.03374,0.06203,-0.01034,0.07726,0.06364,0.06242,0.05597,-0.07755,0.03984,0.08027,0.02419,0.03025,0.04162,0.01187,0.0,-0.0018,-0.02405,-0.01406,0.02318,0.10414,-0.02334,0.05634,0.0684,0.01321,0.02975,0.03788,-0.00996,-0.06308,-0.02563,-0.0373,-0.05837,-0.02497,-0.04808,-0.04584,0.03697,0.09778,-0.01279,-0.02145,0.08094,0.06529,0.05369,0.00153,-0.0931,0.0719,0.06579,0.14425,0.00515,0.01425,-0.01162,-0.01008,0.03438,-0.0818,-0.03283,0.0875,0.08789,-0.0745,-0.01614,-0.00578,0.06979,0.02708,-0.05926,0.07529,0.01465,-0.02729,-0.02948,0.00903,-0.08322,0.01174,0.00396,-0.07711,0.03648,-0.00343,-0.01348,-0.09211,0.00758,0.1703,0.0534,-0.02609,-0.01171,0.05425,0.14871,-0.00545,-0.02696,-0.07503,0.04696,-0.13963,0.04894,-0.01776,0.02956,0.12074,0.04021,-0.08005,-0.05044,0.04873,-0.06325,0.00963,-0.05063,-0.13096,0.01997,-0.06181,0.05324,0.00639,-0.03369,-0.01788,-0.08632,0.07273,-0.09371,-0.0141,0.14264,0.04239,0.13124,-0.05907,-0.01575,0.03277,-0.05018,-0.00713,-0.01934,-0.0143,0.08057,-0.12472,0.02426,0.03455,-0.05723,-0.07229,-0.1079,0.0118,-0.01557,-0.01511,-0.05712,-0.07676,-0.06075,0.08924,0.03295,-0.19087,-0.07513,0.09061,0.07862,-0.02831,0.03751,-0.07339,-0.08753,0.04859,0.00843,-0.06827,0.03713,-0.05052,-0.03116,0.09724,-0.03759,-0.03654,0.08058,-0.03225,0.07706,-0.03486,-0.06132,-0.03555,0.08554,0.04315,0.05302,0.00726,0.04892,-0.00216,0.12041,-0.03484,-0.03738,-0.03892,0.01567,-0.03924,0.0139,-0.06056,0.04899,-0.02182,0.11012,-0.00431,-0.08873,0.08219,-0.08439,0.07021,0.10223,0.09722,0.09613,0.02383,0.01191,-0.04191,-0.10901,-0.01179]},{"domain":"astronomy","key":"critical_density","name":"Hubble parameter and critical density","package":"astronomy-ai999x","example":"Critical density: H0 = 70 km/s/Mpc, Om = 0.3","v":[-0.02418,-0.03875,-0.06735,0.00948,0.1027,0.03509,0.09347,-0.00326,0.07846,-0.0154,-0.05978,-0.00099,0.00949,0.08824,-0.02025,-0.0054,0.10551,0.04322,0.14779,0.11168,0.04717,-0.00642,-0.02272,-0.09582,0.01581,-0.11816,0.04505,0.09413,0.06116,0.02897,-0.11053,-0.01231,-0.104,-0.08928,-0.03109,-0.04911,0.0424,0.09494,0.03094,-0.06265,0.01675,-0.01147,-0.1694,0.04182,-0.08237,-0.03562,-0.08185,-0.10257,-0.02278,-0.06457,0.02164,-0.09894,0.01983,-0.04519,-0.0557,-0.06215,-0.0772,0.07634,-0.03836,-0.06818,0.07104,0.00247,0.0439,0.03834,0.05733,-0.07441,0.0009,-0.00855,-0.03404,0.03463,0.03168,0.05633,0.01176,0.02249,0.05717,0.01773,0.08657,-0.04537,0.04478,0.16227,0.06969,0.01529,-0.093,0.02449,-0.01968,0.02811,-0.035,-0.02913,-0.0551,0.104,-0.04905,0.0171,0.0018,0.00923,-0.0153,0.01371,-0.04517,-0.08128,0.00255,-0.0287,-0.08337,-0.02831,0.01682,-0.02351,0.012,0.09609,0.06971,-0.01172,0.0575,-0.01005,-0.07403,0.03156,-0.11496,0.02617,0.01398,0.09363,0.04783,0.09849,-0.06852,-0.02355,-0.00658,-0.07909,0.05835,0.08715,-0.01339,-0.02773,-0.02163,-0.05374,0.06901,-0.02864,-0.0456,-0.02908,-0.01362,-0.04548,-0.04247,-0.02916,-0.1308,0.01698,0.04304,0.01664,0.08249,-0.0498,0.04519,0.0313,0.02104,0.11982,-0.00512,-0.1,0.03562,0.03165,0.13494,-0.02957,-0.00432,0.0273,0.07346,-0.08175,0.08168,-0.01927,-0.04209,0.04565,0.14165,0.01515,0.04659,-0.00489,-0.05756,0.00328,0.02051,-0.03835,-0.0299,-0.06716,0.06752,-0.06457,-0.03126,-0.04499,-0.03672,0.13539,-0.00892,0.08509,0.13651,0.07586,0.0485,-0.06949,0.01994,0.03621,-0.03973,0.00347,0.01787,0.06189,0.06767,-0.02928,0.0473,0.04273,-0.06951,-0.08928,-0.01932,-0.02277,-0.01077,0.04291,-0.02707,-0.08424,-0.10203,0.08124,-0.0661,-0.03077,-0.05533,0.01215,0.10449,0.01671,-0.05612,-0.10174,-0.12206,0.12914,0.064,-0.07649,-0.02798,0.08744,-0.09018,0.08549,-0.09932,-0.02532,-0.0203,-0.05176,0.07006,-0.13652,0.01316,-0.00956,0.01775,-0.01771,-0.02197,-0.02243,0.06782,-0.02618,0.11256,-0.13829,0.04327,-0.02948,-0.01112,0.0227,0.04461,0.00887,-0.03591,-0.01674,0.06121,0.08832,-0.04134,0.08584,-0.06933,-0.00701,0.11495,0.01058,-0.02261,0.10221,0.01818,-0.00568,-0.06542,-0.00837]},{"domain":"astronomy","key":"culmination_altitude","name":"Altitude of a star at culmination","package":"astronomy-ai999x","example":"Culmination altitude: dec = 20 deg, lat = 50 deg","v":[-0.03962,-0.07197,-0.00054,0.04012,-0.01294,-0.05696,-0.05404,-0.12958,0.04094,0.05966,-0.0008,0.00405,0.02586,0.09082,0.04875,-0.07511,0.1327,-0.01391,0.0382,-0.10816,0.03475,-0.0394,-0.00935,-0.01622,0.02013,0.03738,-0.01666,-0.04955,-0.07435,-0.0415,-0.0756,0.06277,-0.06346,-0.04069,-0.01682,0.033,0.03603,-0.14533,0.01545,0.01124,-0.06534,0.02159,0.06587,0.04581,-0.05282,0.02052,-0.01519,-0.04868,-0.02552,0.08077,0.04659,0.00741,0.07294,0.02373,0.02315,0.01515,-0.06779,-0.02478,0.05394,-0.10165,-0.03315,0.05101,-0.0426,-0.09969,-0.04295,-0.00217,0.12384,-0.04914,-0.08673,0.02251,0.11284,0.06732,0.01679,0.09704,0.09005,0.01726,-0.10218,-0.0337,0.03151,0.03562,-0.05507,-0.08083,-0.02076,-0.0383,0.04387,-0.08696,0.11005,-0.00997,0.03578,0.06107,0.07771,0.13048,-0.05925,0.06375,-0.01294,0.07023,0.03472,0.05197,-0.0867,0.03431,0.00435,0.01301,-0.02232,0.07638,-0.01326,0.02732,0.02455,-0.00745,0.06258,0.01402,0.06401,0.07087,-0.05525,0.11074,0.03034,0.04452,0.09374,0.04214,-0.05393,-0.01859,0.01058,-0.04947,-0.05456,0.03645,0.0362,0.05085,-0.022,-0.02253,0.0005,0.05415,0.02508,-0.07935,-0.00831,0.0065,-0.10463,0.04287,0.01678,-0.03897,0.0298,0.03931,-0.03571,0.11726,0.02267,-0.1004,-0.02765,0.03094,0.07971,0.09226,0.05941,0.0565,0.03363,-0.08746,-0.05234,0.02974,-0.01653,-0.01732,-0.08346,0.01058,-0.11752,-0.00533,0.0884,-0.14236,0.00244,-0.00328,0.0022,-0.05303,-0.06925,-0.05734,0.08912,-0.02482,0.06523,0.08445,0.0198,-0.18991,-0.07463,0.13221,0.02831,-0.05559,0.1368,-0.03927,-0.06161,0.03283,0.1096,-0.03335,-0.00026,-0.02672,0.00253,-0.05513,-0.04574,-0.02597,-0.04681,0.04142,0.05038,-0.07474,0.02221,0.0341,0.05221,0.02745,0.08758,-0.04062,0.01227,0.02628,-0.03102,-0.0467,-0.16378,0.03629,-0.03933,0.0122,-0.039,-0.02998,-0.05275,0.00719,-0.0635,0.09109,-0.06843,-0.03282,-0.04354,0.17293,-0.10326,0.02099,0.00783,-0.02324,0.09269,0.01154,-0.0433,-0.01114,-0.05695,-0.09459,-0.03207,0.05681,-0.11782,-0.0597,-0.02468,-0.01089,0.02121,-0.06236,0.08785,-0.04311,0.01118,-0.0111,0.01382,0.08452,0.00529,-0.04477,-0.14181,0.01326,0.09398,-0.13406,0.0729,-0.02779,0.03862,0.11838,0.0084,0.11802,-0.09486,-0.03043]},{"domain":"astronomy","key":"debye_length","name":"Debye length","package":"astronomy-ai999x","example":"Debye length: T = 1e5 K, n = 1e18 m^-3","v":[-0.08133,-0.16166,0.06949,-0.11263,-0.03657,-0.10187,-0.04211,0.03735,0.00685,0.01655,0.04107,-0.03544,0.08733,0.0086,0.00303,0.03029,-0.00947,0.04844,-0.0409,-0.00247,-0.08745,-0.02762,-0.07259,-0.00549,0.03101,0.04102,-0.11914,0.0004,0.04451,-0.01178,-0.10012,-0.08802,0.06749,0.00021,0.09487,0.04227,0.03719,-0.07003,-0.0298,0.05815,-0.00058,0.03773,0.01144,0.09081,-0.07775,0.0032,-0.00712,0.02132,-0.05126,0.06695,-0.0761,0.03484,0.04497,-0.04657,-0.00756,-0.01916,-0.03122,0.08824,-0.03635,-0.04115,-0.00105,0.11362,0.06243,-0.00085,-0.107,0.05616,-0.01619,-0.06554,-0.06981,-0.01202,-0.02534,0.01488,-0.06509,-0.02784,0.04151,0.02364,0.1162,-0.01627,0.02,0.01719,0.01016,-0.02425,0.01217,-0.05749,0.03699,-0.07771,0.08641,-0.03613,0.04236,0.01052,0.07225,-0.02316,-0.04861,0.04794,0.02173,-0.06933,-0.06509,-0.0308,0.15079,-0.03769,-0.0094,0.06036,0.03151,0.01433,-0.08057,0.00817,-0.06327,0.00547,0.07004,-0.05052,-0.01734,-0.02774,-0.06748,-0.03414,-0.04095,-0.03709,-0.08666,0.04104,-0.01679,-0.03241,0.08658,0.12752,0.01622,0.04101,0.02325,0.03901,-0.02869,0.04919,-0.01129,-0.07404,0.05469,0.09766,0.02979,0.03504,-0.08152,0.12817,-0.01962,0.0347,-0.0908,-0.03715,-0.05528,0.02421,0.01405,-0.04875,-0.00588,-0.03615,0.03241,0.01574,-0.09991,-0.00998,0.12934,0.13082,0.01366,-0.00698,-0.03264,-0.09701,0.14411,0.07985,0.01279,-0.04848,-0.03858,0.12521,-0.08087,0.05878,-0.02733,0.00984,0.10112,-0.07209,-0.08604,-0.0086,0.01594,-0.00781,-0.01434,0.03501,0.01576,-0.01833,-0.08178,-0.07877,0.05749,0.07657,0.07232,0.0009,0.13621,-0.00016,-0.08127,0.06969,0.14476,-0.06281,0.03762,-0.06808,0.02542,0.03843,-0.06139,0.08382,-0.13073,-0.00578,0.02197,0.03146,0.09976,-0.11628,-0.02548,-0.10352,0.13087,-0.09088,-0.12238,0.03502,0.03003,0.02662,-0.04347,-0.0602,-0.01765,0.01423,0.02969,-0.03298,0.0432,-0.01572,-0.1649,0.05756,-0.07153,-0.03069,-0.06444,0.00373,0.0677,-0.02177,0.07781,0.00457,0.04139,-0.00196,-0.02006,0.08939,-0.03302,-0.05377,0.03701,0.01977,-0.05884,0.01118,-0.10357,0.07606,0.05127,0.00199,-0.03316,0.10867,-0.0215,-0.12809,0.04175,0.10166,0.02027,0.08708,-0.00393,-0.02438,0.07303,0.08097,-0.04773,-0.05414,0.06422,-0.13941]},{"domain":"astronomy","key":"debye_number","name":"Number of particles in a Debye sphere","package":"astronomy-ai999x","example":"Debye number: T = 1e6 K, n = 1e15 m^-3","v":[-0.08765,-0.1773,0.02334,-0.029,-0.00557,-0.04529,-0.03177,-0.00545,0.04401,0.03349,0.00612,-0.07569,0.04694,-0.0135,0.02319,-0.01432,-0.06068,-0.01159,0.08628,0.08754,-0.01983,-0.06116,-0.00208,-0.00461,-0.05506,0.02605,-0.01847,-0.01592,0.07752,-0.01094,-0.09187,-0.10986,0.11396,0.00046,0.06173,-0.00361,-0.01811,-0.01835,-0.03276,-0.01509,-0.02305,0.12928,0.04676,0.11375,-0.02681,0.03024,0.00526,0.10497,-0.01761,0.03662,-0.03767,-0.00908,0.07292,-0.03119,0.04712,0.02285,-0.11031,0.07352,-0.07554,-0.03357,-0.0048,0.14079,-0.01015,-0.07445,-0.07925,0.00635,-0.05962,-0.10225,-0.06218,-0.00331,0.02646,-0.01025,-0.08936,0.03793,0.07756,0.06033,-0.02348,0.0538,0.0547,0.00113,0.01328,-0.08134,-0.02615,-0.02214,0.04274,-0.04271,0.01765,-0.03529,0.05074,0.00862,0.06154,-0.0367,0.03112,0.008,-0.01518,-0.08436,-0.09595,-0.03795,0.13218,-0.08262,0.00145,0.05168,0.04416,0.03672,-0.08514,0.05165,0.0353,0.0235,0.09672,-0.03066,-0.00283,-0.05736,-0.06774,-0.041,-0.0495,-0.0394,0.00691,0.01129,-0.08643,-0.03277,0.04436,0.06728,-0.00387,0.07533,0.055,-0.04349,-0.01038,0.02673,0.0173,0.00108,0.0324,0.01556,0.04503,-0.00416,-0.07729,0.07975,0.05348,-0.02663,-0.09758,-0.01188,-0.09492,0.05484,0.00461,-0.01952,-0.01775,-0.02589,0.04032,0.07527,-0.15012,0.01005,0.14893,0.04804,0.00836,-0.02761,-0.04088,-0.0607,0.07325,0.08614,0.04396,0.02588,0.01429,0.08122,-0.07498,0.08957,-0.08331,0.05656,0.09538,-0.07927,-0.09759,0.02937,0.02612,0.06811,-0.05576,-0.00153,0.02565,-0.01037,-0.09079,0.0217,-0.02161,0.11735,0.12832,0.00773,0.17431,0.08615,-0.00655,-0.04395,0.10164,-0.01028,0.03664,-0.02895,-0.02022,0.04671,-0.06237,0.08203,-0.15344,0.05604,0.0161,0.05236,0.0197,-0.06394,-0.12768,-0.0755,0.11754,-0.03552,-0.02245,0.0824,-0.02951,-0.04695,-0.03633,-0.04325,0.03962,0.01695,0.06841,-0.04523,-0.01639,-0.10692,-0.17024,0.06659,-0.02295,0.0227,-0.05469,0.01619,0.12194,-0.06058,0.10099,0.00426,0.02678,-0.08011,-0.00679,0.05913,-0.04282,-0.05234,0.03516,-0.01683,-0.03613,0.02161,-0.16479,0.02507,0.0509,-0.00323,-0.03596,0.08618,0.02945,-0.02042,-0.00183,0.12776,-0.0443,0.08127,-0.03905,-0.06204,0.08194,0.03123,-0.07925,-0.03467,0.03886,-0.12173]},{"domain":"astronomy","key":"distance_from_distance_modulus","name":"Distance from the distance modulus","package":"astronomy-ai999x","example":"Distance from distance modulus: m = 10, M = 0","v":[0.01632,-0.09781,0.04584,-0.00211,0.09039,-0.07757,0.0234,0.03434,0.02255,-0.04173,-0.03842,-0.02173,-0.01704,0.0983,0.01431,0.0643,0.14154,-0.02828,0.0249,-0.07478,0.03369,-0.02067,-0.04947,-0.03693,0.02786,0.03815,0.05803,0.01811,0.00144,-0.025,0.07224,0.01539,-0.04176,-0.08651,-0.11187,0.01117,-0.02955,0.03369,0.00771,0.02654,-0.10584,-0.04183,0.08078,0.01895,-0.06699,0.04446,-0.04829,-0.04972,-0.00136,-0.02138,0.05924,0.05664,0.03883,0.02977,-0.04445,-0.11098,-0.07302,-0.05948,0.07889,-0.03345,0.01377,-0.05807,-0.08257,0.01018,0.01129,-0.06678,0.01574,0.10621,-0.01187,0.12821,0.12282,0.01493,-0.08411,-0.03396,0.13402,0.02561,0.06905,-0.16192,-0.00554,-0.03947,0.04485,-0.01694,0.02533,0.03359,0.15648,0.04367,0.08152,-0.01102,-0.00179,-0.00972,-0.00069,0.06456,-0.00393,0.06385,0.08531,0.09922,0.0366,0.01765,-0.08219,0.03164,0.0273,-0.07872,-0.11077,-0.04043,-0.06397,-0.0006,-0.09577,-0.12132,0.13613,-0.03386,0.04405,-0.00036,-0.06011,0.019,0.03146,0.02129,0.02685,0.03183,-0.07712,-0.00542,0.16332,-0.03105,-0.03966,0.05561,0.09903,-0.07603,-0.05019,0.00115,-0.05584,-0.0509,-0.06704,0.07718,-0.00028,-0.02422,0.03774,0.12007,-0.0214,-0.02989,0.05667,0.03868,0.00665,0.01507,0.04311,-0.1031,0.02707,0.02711,0.04311,-0.04353,0.00251,-0.07283,0.04937,-0.06053,-0.01468,-0.07514,-0.00936,0.02636,0.02002,-0.00192,-0.00718,-0.04907,-0.1126,-0.04914,-0.04704,0.0127,-0.05233,-0.05206,-0.05878,-0.11677,0.01533,-0.03119,0.01819,-0.01579,0.00399,-0.04243,-0.00821,0.06231,0.05464,-0.16832,0.08686,0.07638,0.14604,0.02123,0.0642,0.05698,-0.00721,0.00437,0.06311,-0.03874,0.0236,-0.17313,-0.03641,-0.01962,-0.02135,-0.00627,-0.00923,-0.00356,-0.01729,0.12845,-0.08637,-0.00896,-0.05683,0.03231,0.0325,-0.12532,-0.0899,0.06379,0.03693,-0.08654,-0.00571,0.01905,-0.10585,0.0345,0.0359,-0.03118,-0.0409,-0.10975,-0.03323,0.11513,-0.01578,0.02585,0.21361,0.03689,0.00964,0.03763,-0.08628,-0.00425,0.03052,-0.02505,-0.06481,0.0322,0.05036,-0.04598,0.12948,0.03286,0.05549,-0.00043,0.03186,-0.00886,0.01356,0.06723,-0.00258,0.09068,-0.02374,0.06011,-0.05449,0.05859,-0.00347,-0.02304,0.00086,-0.03629,0.0756,0.04757,0.041,-0.04806,-0.09386,-0.07791]},{"domain":"astronomy","key":"distance_from_flux","name":"Distance from luminosity and flux (inverse-square law)","package":"astronomy-ai999x","example":"Distance from flux: L = 1 Lsun, F = 1361 W/m^2","v":[0.03271,-0.02189,-0.01935,0.004,0.03863,-0.04869,-0.10817,-0.05496,-0.03928,0.01994,-0.01648,-0.07173,0.02529,0.10282,-0.02001,0.05672,0.00705,0.10613,-0.05665,-0.07656,-0.02709,0.04814,-0.01884,0.00598,0.04541,-0.03164,0.04284,-0.01737,-0.00697,0.06374,0.05103,-0.00784,-0.02353,-0.09052,0.02227,0.05334,-0.01346,-0.02728,-0.08511,-0.01887,0.00507,-0.07,0.02192,-0.07333,-0.07014,-0.02235,0.01448,-0.09606,0.00564,0.01696,-0.01425,0.01403,0.01925,0.02254,-0.11178,0.00471,-0.05036,0.0536,-0.02868,0.04564,0.14081,0.04576,-0.14217,-0.03641,-0.05743,-0.0144,-0.02061,0.0452,0.03642,0.00744,0.04433,-0.08818,-0.11024,-0.03554,0.11964,0.04208,0.06844,-0.11742,-0.07116,-0.06425,-0.023,0.02528,0.05459,-0.01626,0.09156,-0.01139,-0.05794,-0.05426,0.00111,-0.01376,0.00809,-0.01397,0.15356,0.06355,0.15378,-0.01206,0.04212,0.00903,0.00318,0.05214,0.04654,0.05385,-0.11209,-0.03425,0.00902,-0.13951,-0.04561,-0.13423,0.08902,0.03064,0.03586,-0.05471,0.05634,0.05658,0.06602,0.06031,0.09127,0.00235,-0.05664,-0.02281,-0.00493,0.0119,-0.0298,0.01797,-0.0159,-0.03849,-0.01318,0.02897,-0.08234,0.07764,0.03142,0.09293,0.05571,-0.08588,0.05275,0.04385,0.0195,0.03401,0.00399,-0.07275,-0.00921,0.08246,-0.03329,-0.18986,-0.01447,0.01409,0.0327,-0.00279,0.03569,-0.02063,0.04704,-0.09565,0.087,-0.05398,-0.06694,-0.07229,0.03113,-0.07851,0.07043,0.0103,-0.03931,-0.00872,-0.09474,-0.02457,-0.00899,0.01863,-0.02489,0.00541,-0.04147,-0.06648,0.02133,0.15993,-0.03265,-0.00017,0.0102,0.03159,-0.03125,-0.022,0.0684,0.01906,0.09642,-0.05084,-0.04327,0.03619,-0.01147,0.05686,0.0249,0.06182,0.00063,-0.07894,-0.02576,-0.0187,0.06053,-0.00899,0.01937,0.0332,0.10259,-0.01678,-0.11319,-0.08763,-0.04699,0.05618,0.08024,-0.22439,0.02517,0.00036,-0.10438,-0.07358,0.01848,0.00938,-0.01719,0.0913,0.10837,-0.07122,0.04621,0.01219,0.00021,0.09298,0.06877,0.03603,0.11053,-0.00231,-0.08496,0.11157,0.06519,-0.02522,0.03649,0.01805,0.11775,0.02729,-0.08255,0.00105,0.01245,0.01024,0.03942,0.00263,0.06646,-0.08942,0.02639,-0.02553,0.11319,0.05273,0.04725,-0.01508,-0.11127,0.04699,-0.05386,0.03544,0.15088,-0.04323,0.14885,-0.0365,-0.01574,0.04217,-0.11534,0.06674]},{"domain":"astronomy","key":"distance_unit_conversion","name":"Astronomical distance units","package":"astronomy-ai999x","example":"Distance conversion: d = 1 pc","v":[-0.1128,-0.04683,0.01997,0.01574,0.09381,-0.16193,-0.0286,0.00082,0.00059,-0.02786,-0.00474,-0.02596,0.02531,0.07289,0.05293,0.01212,0.03446,0.0826,-0.07208,-0.03335,-0.12246,-0.02169,-0.03054,-0.12225,0.05327,0.00607,-0.02472,0.03615,0.05204,-0.02411,0.0395,0.02616,-0.03508,-0.04349,-0.03221,-0.04277,0.00517,0.08788,-0.04406,0.05993,-0.06262,0.02226,0.09898,-0.08454,-0.10203,-0.03808,-0.09884,-0.01536,-0.04882,0.01327,-0.00294,0.09277,-0.05642,-0.04395,-0.05197,-0.07786,0.02621,0.06591,0.03047,-0.11888,0.07014,-0.06738,-0.12698,-0.05063,-0.02971,0.03044,0.01592,0.05184,-0.07944,0.1205,0.02373,-0.04484,-0.07325,-0.00769,0.07712,0.04003,0.14198,-0.09885,0.04519,-0.05002,-0.02849,-0.01923,0.06054,-0.01197,0.09414,0.0073,-0.03721,0.00397,0.05733,0.01206,-0.00322,0.05354,0.1231,0.06563,0.02941,0.02313,0.0363,-0.0084,0.00491,-0.00243,0.03821,-0.00905,-0.09744,-0.00791,-0.07921,-0.00679,-0.03161,-0.07144,0.08564,0.02656,0.03467,-0.05137,-0.098,0.06595,0.01576,0.12366,0.05832,0.07143,-0.02257,-0.06719,0.04345,0.08473,-0.05106,0.10748,0.03109,-0.03777,-0.05243,0.09671,0.01259,0.01326,-0.03787,-0.00061,-0.02666,-0.03693,0.03938,0.09315,0.0117,0.05786,0.05277,0.04904,0.06545,0.05746,0.06939,-0.14763,0.09126,0.07896,0.01158,0.00344,0.01723,0.07289,0.08175,-0.11869,0.00275,-0.07203,0.02907,-0.07717,0.04345,-0.08083,0.06476,0.03302,-0.0119,0.06105,0.05004,0.0418,0.05735,-0.01111,-0.05303,-0.03978,-0.07119,-0.00272,-0.03284,0.00288,0.05463,-0.00431,-0.00863,0.04777,-0.03902,-0.04356,0.05402,0.12022,0.0579,-0.05736,0.06598,0.14788,0.0071,0.01626,0.10739,-0.14722,0.01506,-0.05968,0.00551,-0.07633,0.00312,0.00887,-0.01766,0.01704,0.01417,-0.02278,-0.05436,-0.07114,-0.01113,-0.01277,0.04635,-0.20978,-0.01291,0.00429,-0.03741,-0.08299,0.09162,-0.0068,-0.04742,0.02871,0.00702,-0.1229,-0.01697,-0.0492,0.03707,0.13822,-0.06779,0.09428,0.04359,-0.05216,-0.05387,0.12295,0.01841,-0.07571,0.04627,0.00982,0.01345,-0.04963,0.01381,-0.02142,0.06019,-0.02457,-0.06141,0.03165,0.08301,-0.10994,0.05002,-0.01499,0.08108,0.03476,-0.01714,-0.02972,-0.13169,0.04665,-0.0342,-0.07316,0.04487,-0.03506,0.075,0.12065,-0.07158,0.01779,-0.03601,-0.07078]},{"domain":"astronomy","key":"effective_temperature","name":"Effective temperature of a star","package":"astronomy-ai999x","example":"Effective temperature: L = 1 Lsun, R = 1 Rsun","v":[0.09584,-0.14111,-0.00894,0.00028,0.0269,0.0081,-0.05351,-0.0601,0.05487,-0.01097,0.02438,-0.16138,0.02703,-0.02835,-0.05683,0.09549,0.0605,0.05801,0.0996,-0.05762,0.11358,0.0436,-0.09855,-0.00514,0.02707,0.01208,0.04147,-0.05247,0.07338,0.00055,-0.10641,0.00273,0.03982,-0.071,-0.04111,0.09826,0.00072,-0.01009,-0.08935,-0.03845,0.07633,-0.07415,0.0089,0.0708,-0.09458,0.03721,0.06224,-0.02518,-0.01448,0.0149,0.00524,0.05486,0.06874,-0.00854,0.00039,0.01845,-0.07077,-0.02315,-0.0778,0.08239,0.03438,-0.01944,-0.04335,0.01247,-0.05437,0.02633,0.02286,-0.01264,0.0496,0.03706,-0.05626,0.07938,-0.06294,-0.00305,-0.02756,0.06876,0.05545,0.06466,-0.16435,-0.1262,-0.03071,0.05191,0.09405,0.00747,0.04777,-0.09355,0.0412,0.03096,0.02918,-0.06451,0.06645,0.0441,-0.02161,-0.03944,-0.01435,-0.02613,-0.03602,0.08251,0.04625,-0.06384,0.00133,0.08069,0.07209,0.07247,0.01761,-0.08716,0.02782,-0.0859,-0.00723,-0.04028,0.12477,0.03109,0.06115,0.03128,-0.00063,0.02195,-0.03021,-0.0288,-0.02215,-0.09437,0.0088,0.08557,-0.02797,-0.0186,-0.00692,-0.05101,0.05078,-0.04637,-0.11432,0.00322,0.04839,0.06013,0.028,-0.02199,-0.06689,-0.02383,-0.01549,0.0729,-0.04968,-0.02521,-0.00286,0.04801,0.02788,0.03722,0.05543,-0.00857,0.05221,0.03284,-0.01866,-0.06144,0.01382,0.13079,-0.05767,-0.05802,-0.04329,-0.07069,-0.0426,0.03218,-0.03761,-0.08206,-0.07748,-0.07753,-0.08689,0.09004,-0.10253,0.06612,-0.05039,0.09741,-0.03627,0.01006,0.0538,0.05479,-0.03065,0.00021,-0.09416,0.07219,0.03884,-0.06125,0.10383,0.08769,0.06213,-0.03851,-0.00578,-0.12312,-0.01458,0.02661,-0.05842,0.0923,-0.14557,-0.04228,-0.09427,0.06671,-0.01677,0.0078,0.02286,0.015,0.06054,0.08865,0.04274,-0.01765,-0.07601,0.01786,-0.0228,-0.01981,-0.02761,0.02854,-0.02221,0.17936,-0.13432,-0.08928,0.00756,0.03799,0.01288,0.05279,-0.01938,-0.08444,-0.05228,-0.14051,0.04108,-0.00387,-0.04761,-0.0137,0.05261,-0.07799,0.13192,0.01269,0.0738,-0.05628,0.06142,0.07783,0.05507,-0.04458,0.03441,0.02258,-0.04083,0.04736,-0.01682,-0.06349,-0.03931,0.16116,0.08264,0.03912,0.08486,0.02249,-0.00658,0.11757,0.04186,-0.06447,0.0895,-0.03851,0.05613,-0.01772,-0.08207,-0.05563,-0.14055,-0.00063]},{"domain":"astronomy","key":"einstein_radius","name":"Einstein radius of a point-mass lens","package":"astronomy-ai999x","example":"Einstein radius: M = 0.5 Msun, D_l = 4 kpc, D_s = 8 kpc","v":[-0.03812,-0.10811,0.07716,-0.0439,0.02029,0.04095,0.04041,-0.03289,0.0837,-0.07931,-0.00883,-0.03939,0.04781,-0.00122,-0.04273,-0.0018,0.0465,0.10996,0.03776,-0.03905,-0.01111,0.06625,-0.04396,-0.01014,0.01047,0.04637,-0.05302,0.0089,0.03593,-0.01041,0.03973,-0.09383,-0.04064,-0.10205,0.04471,0.04139,-0.04638,0.07434,0.03111,0.00661,-0.03801,0.05775,-0.10234,-0.05664,-0.13078,-0.0079,-0.01932,-0.00884,0.06436,0.01219,0.01637,0.02643,0.03536,0.04178,-0.13501,0.06947,-0.03745,0.07103,-0.02339,0.03143,0.13773,0.08804,-0.0471,0.05604,0.03888,0.04032,-0.01374,0.02528,0.02528,0.06784,-0.03579,0.00431,0.09175,0.00158,0.03518,0.00489,0.06738,-0.05479,-0.1296,0.01551,0.05233,-0.0542,0.05566,0.01846,0.08121,-0.11133,0.05234,-0.0342,-0.13882,-0.00362,0.1192,-0.10058,0.0811,-0.04222,0.05563,-0.0192,0.02774,0.02993,-0.00242,-0.07735,0.04136,-0.00989,-0.05819,-0.04714,-0.05545,0.06574,-0.03178,-0.03839,-0.00812,0.02823,0.02417,0.05919,-0.01746,-0.01357,0.05003,-0.08875,0.08341,0.03414,-0.01044,0.03947,0.05041,0.01655,-0.02846,0.03059,0.07452,-0.10715,-0.02625,-0.00212,-0.05085,0.02815,0.02915,0.07468,-0.04865,-0.05063,0.0693,0.06407,-0.04856,0.12155,-0.06466,-0.03704,0.01611,0.03137,0.03942,-0.04074,0.07843,0.05735,0.13668,-0.0852,-0.026,0.07817,0.03745,0.00631,0.03104,-0.142,0.00127,0.09577,0.07334,0.09612,0.03482,0.01469,-0.04024,0.03317,-0.0966,0.01972,-0.01748,-0.01792,-0.08699,-0.01584,-0.03321,-0.01305,-0.04064,0.01014,-0.02141,-0.07353,-0.00809,0.00523,-0.14275,0.00195,0.03663,0.00035,0.05786,-0.01229,0.03255,-0.00034,-0.0073,0.06045,-0.05462,-0.00164,-0.01051,-0.20774,-0.00994,0.09313,0.03895,0.0102,0.03303,0.05729,0.00059,-0.10184,0.00903,-0.147,-0.0539,-0.11164,-0.02238,-0.07014,0.0494,-0.06403,0.05404,-0.05159,-0.07203,-0.0721,0.0126,0.16188,0.08152,-0.08121,-0.00267,0.01056,-0.00395,0.05301,0.00743,-0.08995,-0.02707,-0.04169,0.02467,0.06994,-0.04354,-0.10312,0.01828,0.00519,0.06144,0.02568,0.10533,0.03681,-0.08029,-0.14463,-0.08168,0.02105,0.06022,-0.13566,0.00631,-0.02198,0.1168,-0.06374,0.08177,0.02872,-0.11123,0.119,0.003,-0.00596,0.12163,0.08367,-0.03587,0.01548,0.11662,0.02953,-0.07007,0.0228]},{"domain":"astronomy","key":"escape_delta_v","name":"Departure burn from a circular orbit","package":"astronomy-ai999x","example":"Escape delta-v: M = 5.972e24 kg, r = 6678 km","v":[0.08821,-0.00199,-0.00195,0.02604,0.06204,-0.07682,-0.09711,0.01297,0.02548,0.02403,-0.02698,-0.01756,-0.02836,-0.08087,0.00062,-0.02148,-0.06487,-0.07563,0.00089,0.04182,-0.06237,0.04405,0.02913,-0.03457,-0.01584,-0.00422,-0.00345,-0.006,-0.02741,-0.01813,-0.04364,0.02456,-0.0365,0.03422,-0.00183,-0.05014,-0.01695,0.04259,-0.10897,-0.00127,0.12459,0.12268,0.05317,-0.10028,0.08163,-0.03229,-0.06007,0.01057,-0.10642,-0.01494,-0.05961,-0.04141,-0.03392,0.07482,-0.02807,0.04683,-0.07132,0.00569,-0.03452,-0.03124,0.00931,0.02345,0.08604,-0.08953,-0.02553,0.05391,0.0537,0.01527,0.03541,0.03632,-0.01777,0.06954,0.01267,-0.01116,-0.02247,0.03993,-0.16129,0.03401,-0.03546,-0.06735,-0.06183,-0.01982,-0.0835,0.0368,-0.0599,-0.02923,0.00165,0.01233,0.00104,0.02317,0.08288,0.03056,0.07211,-0.02757,-0.10768,0.03694,-0.00857,-0.03587,-0.00996,-0.04399,0.01648,-0.00228,0.05541,-0.08703,-0.04883,-0.06752,-0.0405,0.03988,-0.01147,0.08739,0.03728,0.07907,-0.06821,0.01279,0.00924,0.03974,-0.0048,-0.08611,0.10076,0.0045,0.04403,0.0121,-0.17522,0.05673,0.03658,0.11487,-0.02037,0.05305,-0.02051,0.08831,-0.03071,0.01041,-0.01687,-0.02458,-0.03159,-0.08433,0.06705,0.04914,0.05921,0.04366,-0.02028,0.0892,0.01915,-0.05994,0.0954,0.01938,0.0627,0.01981,-0.08639,0.1365,0.07854,-0.02206,0.00836,-0.0557,-0.16403,-0.04522,-0.07215,-0.06991,0.1117,-0.04783,0.02551,0.07792,-0.00193,-0.12634,-0.10496,-0.02823,0.00018,-0.02953,0.03977,0.14289,-0.00045,0.11639,-0.00621,-0.09712,0.07943,-0.0042,-0.06611,0.14607,-0.04717,0.03924,0.0354,-0.08223,-0.0125,-0.02068,0.06833,0.02913,0.02942,-0.08653,0.14489,-0.10123,-0.07636,-0.01631,0.03294,-0.05422,0.05138,-0.0733,-0.09095,0.00464,0.06306,0.00755,-0.03506,0.02586,0.1043,-0.00961,-0.05492,-0.00496,0.09338,0.07709,0.05358,-0.0347,-0.07809,-0.00541,0.17773,-0.05148,0.03764,-0.09203,-0.02522,0.01998,0.07365,0.10117,-0.07407,-0.00141,-0.06267,0.09652,0.07725,-0.01201,-0.01914,0.07387,0.05711,0.01827,0.02606,-0.03279,0.02979,-0.04008,0.00351,-0.054,-0.09202,0.04335,0.00639,-0.03917,0.03703,0.03407,0.16964,-0.08575,0.01024,0.02117,-0.08667,-0.04417,0.04953,-0.07766,-0.12524,0.08787,0.02699,0.06394,0.12528,0.01182]},{"domain":"astronomy","key":"flux_ratio_from_magnitudes","name":"Flux ratio from a magnitude difference","package":"astronomy-ai999x","example":"Flux ratio: m1 = 1, m2 = 6","v":[0.04862,-0.04148,-0.00667,0.11051,0.05212,-0.06294,-0.06429,0.00077,-0.03429,0.00267,-0.08736,-0.08937,-0.0423,0.11212,0.05625,-0.01576,0.0202,-0.00259,0.03302,-0.02406,0.0399,0.10852,0.05059,0.02183,-0.01135,0.01857,0.0272,-0.08491,-0.11401,0.0043,0.03683,0.08641,-0.09786,-0.07612,-0.06139,0.05882,0.00779,0.01806,-0.01951,-0.0764,0.00304,0.04385,0.0838,-0.11209,-0.00109,0.06042,0.01088,0.03169,-0.03591,0.12931,-0.01122,0.17021,-0.00732,-0.02009,0.01419,0.06959,-0.07137,-0.09112,0.02071,-0.04103,-0.01303,-0.04908,-0.04002,-0.03282,-0.0057,0.0024,0.08314,0.05552,0.01037,0.0382,0.17748,0.05949,-0.03414,0.04282,0.03223,0.0309,-0.0088,-0.11832,-0.00903,-0.10363,-0.01479,-0.00951,0.00085,-0.03838,0.1513,-0.02345,0.05935,0.03277,-0.0262,-0.00793,0.0345,0.01596,0.11229,-0.03052,0.12033,0.03876,0.00097,-0.02916,-0.03286,0.0221,0.00524,0.06975,-0.10333,-0.05119,-0.05811,-0.08783,0.05079,-0.02238,0.04498,0.02649,-0.05783,-0.05298,-0.02808,0.00952,0.00939,0.01724,0.07524,0.08588,0.00054,0.09782,-0.02328,-0.03122,0.06982,0.08695,0.10529,0.04146,-0.05075,0.02446,-0.05707,0.05497,0.00048,0.0363,0.00158,-0.02048,0.00096,0.00012,-0.07787,0.01256,0.03167,-0.04509,-0.11615,0.0614,0.01676,-0.13348,-0.00163,0.01246,0.03264,0.02282,0.02249,0.01549,-0.01349,-0.14618,-0.06894,-0.04546,-0.08688,-0.1276,-0.04736,0.02924,-0.03465,0.01722,0.12976,-0.10587,-0.09232,-0.14165,-0.00984,0.01563,-0.11726,-0.04389,0.02687,-0.00745,-0.04375,0.08756,-0.01567,-0.07126,-0.01678,0.12976,0.04386,-0.04812,0.04186,-0.04366,0.02494,0.00188,0.05488,-0.02747,-0.09521,-0.00572,-0.01263,0.10315,0.04545,-0.0855,-0.0358,0.10245,0.04507,-0.00151,0.0433,0.01245,0.03768,0.03015,-0.14457,-0.00406,0.01645,0.02726,0.10912,-0.11101,0.00717,0.09516,-0.0941,-0.06727,-0.09647,0.11908,-0.13216,0.06264,-0.05202,-0.03938,-0.00473,-0.09195,0.01835,0.13189,0.01519,-0.00886,0.10061,-0.0331,-0.07674,0.0642,0.01168,-0.00349,0.06675,-0.02307,0.08866,0.04556,-0.09375,0.09206,0.02848,0.05465,0.09727,-0.07505,0.03869,-0.02865,-0.05213,0.03143,0.0589,-0.03424,0.01156,0.02525,-0.07246,0.03524,-0.0279,-0.04288,-0.00104,-0.025,-0.03985,-0.00479,-0.00123,0.06215,-0.06779,-0.00368]},{"domain":"astronomy","key":"free_fall_time","name":"Free-fall time of a uniform cloud","package":"astronomy-ai999x","example":"Free-fall time: rho = 1e-17 kg/m^3","v":[0.02876,-0.06403,-0.05111,0.05831,-0.00566,0.07729,0.07909,0.01417,0.07654,-0.07636,0.05759,-0.05284,0.03724,-0.02497,0.00748,-0.07407,0.02448,-0.01322,0.02635,-0.02236,-0.05836,-0.04615,0.00814,-0.01526,0.11313,0.00794,-0.0305,-0.00707,-0.0758,-0.01004,-0.01472,0.04263,-0.03808,-0.09434,0.03627,0.00655,0.01796,0.01568,0.0029,0.11467,-0.02729,0.05474,-0.06308,-0.03049,0.00717,0.09833,-0.03116,0.0124,0.00889,0.06916,-0.08399,-0.03718,-0.07848,-0.0592,-0.10294,0.00932,0.01377,0.02539,0.00563,0.00678,0.01912,0.14017,-0.03412,0.05998,-0.01279,-0.06372,0.015,0.01321,0.00194,-0.03925,-0.01055,0.0914,-0.09144,-0.03886,-0.02391,0.0667,-0.01904,-0.03105,-0.10241,0.01959,0.01849,-0.05427,0.01139,-0.01802,-0.00085,-0.04191,-0.00298,0.01048,0.07858,0.04254,0.01336,0.0442,0.00068,-0.02303,-0.00329,0.10565,0.05442,-0.04922,-0.06011,0.0324,-0.01796,-0.06967,-0.05619,-0.03019,0.01192,0.0588,0.16471,0.0288,0.07425,-0.01006,-0.05103,-0.01603,-0.04495,-0.07729,-0.0361,0.02099,0.11623,0.06167,-0.0584,0.04795,-0.12124,-0.05007,-0.02791,0.06369,0.07572,0.05754,-0.09389,0.05339,-0.05498,0.08539,0.0736,-0.04156,-0.0106,0.02716,-0.05461,-0.04034,0.09882,0.01973,0.16007,-0.00279,-0.00365,0.08032,0.09201,-0.03007,-0.13476,0.05872,0.08927,-0.00511,0.01388,0.11078,0.10312,-0.13491,0.07048,-0.03886,-0.02411,0.0344,0.00892,-0.04451,-0.05578,0.05716,0.00195,0.11437,0.07373,0.04127,-0.08634,-0.01882,0.03439,0.06963,-0.03208,0.01933,0.08292,0.05477,-0.04181,-0.00809,0.01101,0.00555,-0.00653,0.10833,0.00048,-0.0013,-0.1744,0.05734,0.04781,0.02354,0.09118,0.04475,0.02975,0.00281,0.09679,0.06956,-0.14825,-0.05311,0.08284,-0.15205,-0.05306,0.00509,0.09302,-0.10188,-0.07542,0.00643,-0.088,0.01297,-0.04864,-0.1448,-0.06051,-0.03114,-0.0411,-0.03728,-0.08687,0.01411,0.08416,0.10168,0.01149,-0.11395,-0.14101,-0.00082,0.0486,0.10899,-0.01574,0.00623,-0.10751,0.02565,0.02332,-0.05525,0.04484,-0.00694,-0.00501,-0.02285,0.03723,-0.04456,0.05716,-0.07096,-0.14433,-0.05121,-0.04025,-0.00368,-0.12759,-0.07599,-0.10864,0.1446,-0.02022,0.00476,0.08408,0.04484,0.05114,0.02674,0.00875,-0.02209,0.00904,0.00803,-0.04539,-0.0323,-0.08067,0.01936,0.00439,-0.05244]},{"domain":"astronomy","key":"gyrofrequency","name":"Gyrofrequency (cyclotron frequency)","package":"astronomy-ai999x","example":"Gyrofrequency: B = 1 T, particle = proton","v":[0.09623,-0.00935,-0.01382,0.03424,-0.00588,0.07298,-0.01734,-0.05118,0.01963,0.05649,0.01061,-0.07316,0.0728,0.02121,0.04074,-0.06027,-0.13578,0.02316,0.00912,0.03313,-0.03172,0.038,-0.11778,0.02111,0.09294,-0.01971,0.03658,-0.10155,-0.01714,0.0855,-0.00649,-0.0378,0.04128,0.04285,-0.10289,0.04646,-0.06316,-0.01585,-0.06842,-0.01262,0.01881,-0.03593,0.03495,0.03398,0.04859,-0.03637,-0.02749,0.15341,0.02366,0.00835,-0.06196,-0.06519,0.03841,0.02075,-0.10128,0.05757,-0.09657,-0.06238,-0.07693,0.00962,-0.01289,0.06731,-0.00206,-0.07501,-0.0387,0.03672,0.02937,0.00933,-0.07112,0.01462,0.05135,0.07946,-0.09967,-0.10495,0.0387,0.00436,-0.03659,0.11964,0.07525,0.04074,0.10515,-0.02799,0.09254,0.03123,-0.16968,-0.05241,0.04706,-0.10369,0.19938,0.01116,0.11046,-0.15067,0.01253,-0.0218,-0.01571,-0.00363,-0.04167,-0.04811,0.05292,0.01263,-0.01663,-0.01491,-0.03453,-0.00337,0.06752,-0.10892,0.042,0.02595,0.09257,0.00984,-0.04953,0.02798,-0.00797,0.03777,-0.00921,0.00401,0.00323,-0.04843,-0.03773,-0.10115,-0.0568,0.04674,-0.07514,0.07395,-0.05324,-0.04831,-0.0203,-0.05913,0.00252,-0.02498,0.05022,-0.08417,-0.01847,0.00908,-0.02528,0.00479,-0.04323,0.01887,0.00521,0.0159,-0.07449,0.02837,-0.04215,-0.03861,-0.05676,-0.10403,-0.03663,-0.05505,0.03122,0.09715,0.20695,-0.04389,0.01452,-0.00105,-0.03181,-0.05637,0.1197,0.06749,-0.00546,-0.09884,0.01326,0.05069,0.09129,0.04857,-0.06496,-0.10836,0.06685,0.09754,-0.11963,0.08419,0.12041,0.0127,0.03049,0.06841,-0.01365,0.12983,-0.01163,0.10725,-0.10919,-0.08665,-0.03401,0.01449,0.03791,-0.05409,0.04541,0.02907,-0.00116,-0.02701,0.04051,0.00534,-0.06187,0.07126,-0.09995,-0.00913,-0.06129,-0.09079,-0.00459,0.01727,-0.05404,0.02964,-0.04105,0.02265,-0.01477,0.02277,0.00774,-0.02348,0.05263,0.10722,-0.07379,0.01008,0.04903,0.09394,-0.01761,0.01208,-0.05862,-0.09016,0.02032,-0.04116,0.10548,-0.09699,-0.17786,0.01866,0.02485,0.08064,-0.04034,0.01333,0.02066,-0.03876,0.0549,0.08528,0.014,-0.08496,0.00744,0.07241,0.09995,0.02151,0.06122,0.0158,-0.01636,-0.05749,0.00954,-0.01082,0.05381,0.00178,0.01949,-0.02113,-0.00325,-0.02944,0.06703,-0.06499,0.04527,0.01481,0.0078,0.08829,0.04036,-0.0982]},{"domain":"astronomy","key":"gyroradius","name":"Gyroradius (Larmor radius)","package":"astronomy-ai999x","example":"Gyroradius: B = 5 nT, v_perp = 400 km/s, particle = proton","v":[-0.00493,-0.13127,0.01432,0.04613,-0.0217,-0.00437,-0.03652,0.03447,0.06102,0.11241,0.02048,-0.12357,0.11924,-0.02998,0.02925,0.01237,-0.14833,0.01852,-0.06155,0.0404,-0.03644,-0.02872,-0.0818,-0.04811,0.07019,0.02808,0.00111,-0.14247,0.07542,-0.01594,0.03983,-0.03448,0.03118,0.01136,-0.07012,0.0206,0.02803,0.04364,-0.04996,0.052,0.16609,0.02226,0.14835,-0.0042,0.07689,0.06778,0.08187,-0.01075,0.01422,0.00517,-0.02734,-0.05513,0.03626,0.09811,-0.05813,0.01029,0.00136,-0.02739,0.04039,0.03718,0.04833,0.01251,0.05389,-0.12422,-0.08719,0.07124,-0.03456,0.0627,-0.05879,0.1001,0.07958,0.072,-0.06061,-0.14687,-0.01739,-0.01928,0.02071,0.09189,0.06857,0.07261,0.0456,0.02549,0.02149,-0.00907,-0.18899,-0.02647,-0.00411,-0.06529,0.13615,-0.04167,0.08675,-0.0349,0.02799,0.05418,0.0448,0.07716,-0.03229,0.01061,0.05967,-0.02936,0.00116,-0.05444,0.04167,0.04201,-0.05137,-0.09458,-0.02927,-0.03414,0.08682,-0.01723,-0.06976,-0.05497,0.01621,0.05782,-0.03032,0.02647,0.02519,-0.02937,-0.04218,-0.15346,-0.01643,-0.0054,-0.09219,0.07425,-0.09993,-0.04344,0.03788,0.05788,-0.01444,-0.01138,-0.00733,-0.07437,0.07276,-0.03904,-0.01978,-0.00396,-0.03963,-0.0014,-0.05479,0.05573,-0.02233,0.03898,0.01343,0.02679,0.03634,-0.04959,0.03588,-0.04568,0.01279,0.07884,0.05334,0.09592,0.0543,-0.01476,-0.00372,-0.11309,0.13495,0.06455,-0.01607,-0.10937,0.01839,0.09171,0.00696,-0.03443,-0.10359,-0.09045,0.05184,0.00772,-0.11729,0.08205,0.00105,-0.05971,-0.02152,-0.00693,0.02356,0.06496,0.04601,0.14881,-0.02357,-0.04874,0.01635,0.01828,0.08643,-0.01156,0.13185,-0.03333,-0.00976,-0.01825,-0.00982,-0.0854,-0.04725,0.04042,-0.06719,-0.00591,-0.0402,-0.10098,-0.1045,0.07654,0.03133,-0.00489,0.01011,0.00648,-0.01481,-0.011,-0.03932,-0.04001,0.02452,0.09167,-0.06647,-0.04462,0.00701,0.04989,0.08236,0.04817,-0.08375,-0.06595,-0.08034,-0.09636,0.04358,-0.01112,-0.11763,0.00648,0.01209,0.09379,-0.03341,0.08709,0.05032,0.02171,0.06685,0.02033,-0.09394,-0.0523,0.08058,-0.03217,-0.06363,-0.0638,-0.03083,0.06408,-0.04529,-0.06295,-0.00419,0.09253,-0.02127,-0.08893,-0.00386,-0.022,0.01905,0.02567,-0.10058,0.03031,0.08693,0.04549,-0.03018,0.10616,0.00248,-0.06881]},{"domain":"astronomy","key":"hohmann_transfer","name":"Hohmann transfer between circular orbits","package":"astronomy-ai999x","example":"Hohmann transfer: r1 = 6678 km, r2 = 42164 km, M = 5.972e24 kg","v":[0.01487,-0.02254,0.00541,0.07164,0.11311,-0.0407,0.00767,0.00236,0.10317,-0.01748,0.00419,-0.02166,0.03251,-0.03512,-0.0079,0.01298,0.02553,-0.04109,0.10099,0.05863,-0.0207,0.04996,-0.00498,-0.07033,0.01867,0.00052,-0.03403,0.00875,-0.06245,-0.0482,-0.00742,0.07614,-0.11262,0.06939,-0.02803,0.00425,-0.04115,0.11636,-0.01321,0.03906,0.09919,0.05645,-0.04636,-0.11121,-0.06099,-0.08281,-0.09142,4e-05,-0.06931,-0.0783,-0.07991,-0.00182,0.00151,0.09056,0.02441,0.0435,-0.00481,0.05749,-0.03252,-0.04065,-0.06655,-0.03242,0.05223,0.02407,0.04998,0.0201,0.13195,0.0863,0.08682,0.08493,0.01014,-0.02518,-0.0269,-0.0168,-0.02493,0.06288,-0.22892,0.12751,-0.06482,-0.06059,0.0182,-0.06977,-0.0638,0.04308,0.06235,-0.03876,0.00893,-0.00089,-0.03189,0.00485,0.04745,-0.05482,0.02348,-0.11667,-0.0873,-0.00979,0.05085,-0.02477,-0.13591,-0.02613,0.09031,-0.01801,0.03289,-0.04842,-0.08608,-0.11311,-0.1756,0.02523,0.00994,0.04368,0.02193,0.07995,0.05485,-0.00661,-0.084,-0.00053,-0.0171,-0.01243,0.05066,0.05397,-0.06023,-0.02281,-0.10267,0.12084,-0.04019,-0.0089,-0.01255,-0.00545,0.03695,0.03889,-0.03251,-0.04512,-0.06078,0.01027,-0.11109,-0.12006,0.01802,0.08986,0.13691,0.00994,-0.05688,0.00874,0.07161,-0.08143,0.07916,0.07768,-0.02497,-0.06398,-0.09856,0.04345,0.04409,-0.07937,-0.01921,-0.12335,-0.073,0.0357,0.02436,-0.03036,0.06728,0.01804,0.11794,0.13052,0.00935,-0.02278,-0.06857,-0.09811,0.00039,-0.03077,0.04442,0.07021,-0.02795,0.02249,0.00088,-0.08326,0.00609,0.00945,-0.02773,0.13335,-0.02273,-0.07791,0.056,0.01166,0.01052,-0.02425,-0.02682,0.01051,0.00454,-0.03724,0.11932,-0.06554,0.02953,0.10144,0.00163,0.07501,0.02011,-0.14312,-0.04032,-0.00414,-0.02684,-0.01305,-0.01107,0.03735,0.00989,0.00913,-0.04682,0.05273,0.11468,0.08552,-0.03408,-0.0771,-0.01217,-0.08359,0.09786,-0.04872,0.01369,-0.01731,-0.0219,0.04439,-0.01759,0.0367,0.05178,0.02085,-0.01742,-0.04833,-0.02517,0.00699,0.03834,0.10745,0.04325,0.03886,0.09281,0.07623,0.022,-0.05268,0.00711,-0.06044,-0.05557,-0.03527,-0.03821,-0.04771,0.05135,-0.11911,0.03285,0.00133,0.0383,0.02324,-0.02774,-0.04238,0.00959,-0.01151,-0.11683,0.1617,0.07546,0.02974,0.08117,0.09541]},{"domain":"astronomy","key":"inertial_length","name":"Inertial length (skin depth)","package":"astronomy-ai999x","example":"Inertial length: n = 5 cm^-3, particle = proton","v":[0.04646,-0.06567,-0.00623,-0.08375,0.00469,-0.00234,0.0224,0.09464,0.00172,0.02491,-0.03454,0.00457,0.02436,0.0043,0.00939,0.01877,-0.03761,0.06165,-0.02997,-0.0058,-0.04495,-0.03011,-0.04311,-0.0201,0.05143,0.025,-0.04041,-0.04556,0.05804,0.02529,-0.04488,-0.01843,0.02254,0.01066,0.0731,0.03009,-0.01784,0.06858,-0.04607,0.05934,-0.00072,-0.03784,-0.02527,0.13146,-0.08882,0.00404,-0.01892,-0.08947,-0.06736,-0.0141,-0.02147,0.04265,0.05282,0.13155,-0.13217,-0.02828,-0.02292,0.17316,-0.06735,0.00429,-0.05319,0.05374,-0.00334,-0.0303,-0.05729,0.0993,-0.00913,-0.04637,-0.02929,-0.03466,-0.07628,-0.04907,-0.07795,-0.02956,-0.01183,0.02006,0.22428,-0.04428,0.00733,0.00282,0.09693,-0.06789,0.03604,-0.05274,-0.01646,-0.07564,-0.00148,-0.04668,0.05437,-0.00076,0.07416,-0.0467,-0.10535,0.01654,0.07377,-0.00075,-0.03447,-0.03052,0.09274,0.03474,-0.01455,0.13115,-0.06018,-0.0264,-0.02596,-0.03124,-0.01629,-0.02758,0.07487,-0.05119,-0.01868,-0.01226,-0.10787,0.04639,-0.03541,-0.09661,0.00422,0.04349,-0.03842,-0.01643,0.11517,0.11424,0.03372,0.12811,-0.0051,0.02878,-0.06127,0.06983,0.02863,-0.09301,-0.0613,0.03687,0.02603,-0.0596,-0.0027,0.08095,-0.02677,-0.00599,-0.05459,-0.04264,-0.0891,0.06534,0.04357,-0.0877,-0.07566,-0.11781,-0.00909,0.05214,-0.04182,-0.0138,0.08597,0.17666,-0.06779,0.06108,-0.00904,-0.02751,0.14888,0.06775,0.02242,0.01994,-0.10389,0.07825,-0.02239,0.11549,-0.02614,0.05235,0.14713,0.00253,-0.11169,0.04791,0.00099,-0.00902,0.00724,0.03193,-0.00267,-0.06011,0.02345,0.10741,-0.01499,0.00304,0.00231,-0.03061,0.10368,0.05287,-0.07096,0.1286,0.0935,-0.0602,0.04193,-0.02746,0.01801,-0.0174,0.02575,0.01028,-0.1862,-0.06827,-0.01662,-0.04949,-0.00369,-0.07924,-0.02133,-0.01163,0.04338,-0.09215,-0.07943,-0.03414,0.01337,0.03399,-0.05228,0.09765,-0.0001,-0.0131,0.10223,-0.05978,-0.10388,0.02472,-0.08726,0.03117,-0.00405,-0.02532,-0.07284,0.00225,-0.00227,0.02297,0.09055,-0.03218,-0.06786,-0.05746,0.0326,0.00869,0.0088,-0.05726,-0.00791,0.00277,0.02589,-0.04525,-0.0766,0.11908,0.12789,-0.02233,-0.0623,0.04894,0.00858,-0.06418,0.10041,0.04338,-0.00469,0.04553,-0.00148,-0.00311,0.16874,0.08185,-0.04448,0.02584,0.01387,-0.07791]},{"domain":"astronomy","key":"julian_date","name":"Julian date of a calendar date","package":"astronomy-ai999x","example":"Julian date: year = 2000, month = 1, day = 1, hour = 12","v":[0.11142,0.06802,-0.03077,0.1202,-0.0111,-0.11109,0.13156,0.03704,0.01741,0.04801,-0.08669,-0.03555,0.09969,0.00872,-0.09039,-0.11669,0.09999,-0.07099,-0.08276,-0.00515,0.06262,-0.04718,0.08138,0.08162,0.04409,0.03736,-0.08144,0.08566,-0.01707,-0.06151,-0.0708,0.05149,0.00027,-0.06624,-0.00325,-0.09795,-0.04196,0.01864,-0.03095,-0.0248,-0.01919,0.01802,-0.02607,-0.08176,-0.01159,0.00477,-0.0309,-0.05648,0.0465,0.0163,-0.06109,0.05781,-0.00555,-0.00946,-0.105,0.04072,-0.02123,-0.05586,-0.08511,-0.01851,-0.0705,-0.05072,0.03444,0.06701,0.04697,0.0286,0.12604,0.0744,-0.09381,0.11313,-0.08389,-0.17044,0.06573,-0.03739,0.06937,-0.0919,0.15541,-0.00871,-0.00091,-0.05191,-0.00159,-0.10057,0.06383,0.01125,0.06758,-0.0137,-0.0007,-0.0481,0.02506,-0.06749,-0.09634,-0.03725,0.01952,0.02879,-0.06242,-0.02028,0.03103,-0.08647,-0.02645,0.03919,0.13196,-0.01924,-0.05674,-0.03357,-0.00576,0.04029,0.01228,0.03955,0.01874,0.02332,0.01728,0.00331,-0.00559,-0.01925,0.09765,0.0654,0.00255,-0.03023,0.00227,0.02494,-0.00984,-0.06328,-0.0153,0.0427,-0.00766,-0.13806,0.10412,-0.0552,-0.05539,0.05259,0.01242,-0.05526,-0.07972,0.05415,0.08681,0.04415,-0.00116,0.01202,0.01875,0.08327,0.06429,-0.00617,0.03049,-0.00423,-0.02459,0.09942,-0.0203,-0.06322,0.02552,0.08417,-0.01447,-0.16728,-0.02518,0.01259,-0.05543,0.05406,-0.00269,-0.05286,-0.0188,-0.08002,0.07392,0.00587,0.05848,0.02653,0.0708,0.04449,-0.10781,0.10921,0.00692,0.02529,-0.01397,-0.04267,0.17452,-0.07955,-0.07025,-0.0182,0.04143,-0.03503,0.02708,-0.05431,0.06052,0.00122,0.08431,-0.01937,0.01006,-0.02521,0.05707,-0.07821,-0.04625,-0.04479,0.06605,0.00502,0.01816,0.05243,-0.0413,0.037,0.02735,0.07263,-0.05829,0.01128,-0.095,0.0176,-0.01793,-0.07771,0.04398,-0.02986,-0.0273,0.04639,0.01516,-0.0287,0.03165,0.0379,0.06717,-0.00811,-0.00433,-0.02367,-0.02678,-0.04329,-0.03333,-0.07125,0.02918,0.08227,0.12026,-0.01215,0.02467,0.01509,0.05579,-0.15642,-0.08787,0.00827,0.07165,-0.11634,0.02245,0.05447,0.11052,0.00211,0.09004,0.01368,0.01762,0.07777,0.01121,-0.00712,-0.11916,0.03302,-0.02519,0.01571,-0.05942,-0.14387,0.04437,-0.01398,0.10445,0.09377,-0.03566,-0.0461,-0.12782,-0.09991]},{"domain":"astronomy","key":"kepler_position_at_time","name":"Position on an elliptical orbit at a given time (Kepler's equation)","package":"astronomy-ai999x","example":"Kepler's equation: M = 1.4982e10 kg, a = 1 m, e = 0.5, t = 3.14159265358979 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size from angular size","package":"astronomy-ai999x","example":"Linear size: theta = 90 deg, d = 1 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m^-3","v":[0.01775,-0.0763,-0.03059,-0.11073,0.04826,0.04005,0.06866,0.0094,0.03684,0.10036,-0.01628,-0.04752,0.10855,-0.0039,0.01469,-0.07209,-0.02502,0.01702,0.01251,0.00211,-0.08197,-0.00343,-0.08285,-0.0248,0.10211,-0.04861,-0.00943,-0.05678,-0.07842,0.00846,-0.10418,-0.02414,0.05193,-0.01872,0.03189,0.06669,-0.06612,-0.01864,-0.09992,0.07862,-0.05493,-0.08462,-0.13029,-0.0095,0.0856,-0.0818,-0.08881,0.0888,-0.06602,-0.01448,-0.00289,-0.07506,-0.05664,-0.07201,-0.08645,0.07688,-0.05998,0.00917,-0.09484,0.04287,0.06369,0.02186,0.06814,0.04075,0.01615,0.01043,-0.02831,0.0548,0.01152,0.0104,0.04609,0.02701,0.00937,-0.09247,0.02072,-0.04946,-0.04486,0.13045,-0.07168,-0.01861,0.03931,-0.00913,0.09095,0.01215,-0.08437,-0.25998,0.06111,-0.07644,0.05032,0.08441,0.06003,-0.03667,-0.06669,0.05333,0.09292,0.03656,-0.11574,-0.02291,0.03472,0.02656,-0.02366,0.04464,0.01254,-0.01587,-0.02133,-0.11038,0.08179,0.01889,0.08507,-0.01265,0.06093,-0.07349,0.01339,-0.01057,-0.00817,-0.0144,0.02452,0.02307,-0.04151,-0.05104,0.02909,0.00315,0.04852,0.02229,-0.05336,0.033,-0.03048,0.01915,0.04473,-0.06685,0.13131,0.05688,0.08576,0.04835,-0.10119,0.01136,-0.10579,0.0265,0.02313,-0.04157,-0.05709,0.00947,0.05059,-0.109,-0.01217,-0.09159,-0.02757,0.04037,-0.04365,-0.05889,0.14444,0.04831,0.05887,0.02673,0.01689,-0.10908,0.18475,0.01816,-0.07189,0.05905,-0.00877,0.06162,-0.02679,0.03377,-0.06794,-0.05605,0.04578,-0.02138,-0.07304,-0.01413,0.04463,0.05091,0.04796,0.05463,-0.0702,0.08934,0.03411,0.0067,-0.01984,-0.16242,0.01522,-0.00638,-0.11634,0.01375,0.03922,-0.03645,0.02564,0.02751,-0.00896,0.02672,-0.02056,0.02966,-0.00078,0.12551,-0.07783,-0.0822,0.01766,0.05272,-0.00307,0.06078,0.00819,0.00011,-0.11302,-0.02903,-0.07234,-0.06646,0.0439,0.15673,-0.11326,-0.03151,0.00681,0.04663,0.04864,0.06018,-0.01034,0.06005,0.01795,0.10874,0.09869,-0.13576,-0.05985,0.06579,0.00348,0.01811,-0.05116,0.1437,0.06325,-0.01251,0.02762,0.04079,0.0302,-0.07061,0.07472,0.01621,0.0547,0.0243,-0.00256,0.00669,-0.03749,0.00939,-0.0567,-0.058,-0.01174,-0.02635,-0.00536,0.03862,0.06838,0.03639,0.05406,-0.0371,-0.06638,0.013,-0.05541,0.02843,0.04403,-0.0448]},{"domain":"astronomy","key":"luminosity_from_bolometric_magnitude","name":"Luminosity from absolute bolometric magnitude","package":"astronomy-ai999x","example":"Luminosity from bolometric magnitude: M_bol = -5","v":[-0.03786,-0.11471,-0.05731,-0.00067,0.17648,-0.08317,0.00613,0.00108,-0.05233,0.05944,0.01721,-0.0857,0.0533,0.00502,0.0165,0.04279,0.05614,0.04228,0.01077,-0.04086,0.08635,-0.02609,-0.09387,0.00176,0.06691,-0.04121,0.13218,0.04733,-0.00761,0.03532,-0.01917,-0.01243,0.00255,-0.05758,-0.11113,0.01363,-0.13789,0.00547,-0.00923,-0.03452,0.06064,-0.00392,-0.06654,-0.03092,0.17765,0.0482,0.01756,-0.00128,0.02358,-0.07764,-0.01617,-0.07246,0.03244,0.01455,0.00762,-0.15688,-0.04778,-0.13861,0.10377,0.05444,0.06336,-0.01658,-0.02883,-0.00177,-0.01008,-0.01366,0.00158,0.0923,0.10665,0.1181,0.08768,0.01168,-0.06963,-0.03989,0.07327,-0.0026,0.06665,-0.11554,-0.04403,-0.02492,-0.05322,0.06612,0.0177,-0.05555,0.13813,-0.03914,0.01103,-0.04366,0.02162,-0.08303,0.12634,0.04499,0.06077,0.01206,0.14112,0.05206,-0.00264,-0.0561,0.05948,-0.07259,-0.05192,-0.0318,-0.03882,-0.10134,-0.04974,-0.07841,-0.07046,-0.13938,-0.02419,0.02897,0.02591,-0.0315,0.0638,-0.03639,0.01764,0.03971,0.0596,0.01046,0.01999,0.03529,-0.00746,-0.04634,0.08985,-0.05571,0.1331,-0.08297,0.05697,0.06098,0.01111,0.01451,0.01201,0.07849,-0.10104,0.0443,-0.01872,-0.08421,-0.04604,0.03141,0.02589,0.01463,-0.00704,0.05518,0.11487,-0.02554,0.01287,-0.0417,0.00593,-0.0781,0.00344,-0.12466,-0.00888,-0.02156,-0.07188,-0.02087,-0.15525,-0.02478,-0.06558,0.05697,-0.04082,-0.04486,-0.03604,-0.04785,0.02333,-0.01705,-0.0839,0.01987,-0.00984,0.04768,-0.04327,-0.02468,-0.04212,-0.02318,-0.00786,-0.03169,-0.01963,0.02953,0.07771,-0.07455,0.0663,-0.06906,0.08267,0.04363,-0.01687,0.01907,-0.02561,-0.06098,0.01904,0.0381,-0.06945,-0.09624,-0.09566,0.02242,0.08743,0.06473,-0.01043,-0.0201,0.01126,0.10316,-0.10219,0.10476,-0.02233,-0.04056,0.04123,-0.00681,0.04562,0.00749,0.00589,-0.01504,-0.09256,0.11972,-0.03103,-0.02288,-0.01464,-0.08494,-0.03726,-0.03373,-0.11306,0.06194,0.00025,-0.02677,-0.00087,0.04807,-0.12651,0.0634,0.02313,0.11084,0.06085,-0.13331,-0.04666,0.03478,0.02519,0.05751,0.05271,-0.05312,0.07678,-0.00326,-0.02164,-0.01918,-0.0539,0.01613,-0.00265,0.02068,-0.02873,0.04295,0.03549,0.0319,0.11884,-0.00562,0.00539,-0.00478,0.09318,0.03234,0.1533,0.03312,-0.05077,0.05403]},{"domain":"astronomy","key":"magnetic_pressure","name":"Magnetic pressure","package":"astronomy-ai999x","example":"Magnetic pressure: B = 1 T","v":[-0.02771,-0.01098,-0.13003,-0.09022,0.06887,0.10664,0.13499,-0.02757,0.00595,0.04562,-0.09693,0.0072,0.05554,0.05663,0.01705,-0.02119,-0.00626,0.0301,0.0748,0.12409,-0.09567,0.00071,0.03817,0.03565,0.08486,0.06883,0.10075,-0.03908,0.01029,0.06945,0.05847,0.03827,0.02798,0.06146,-0.03541,0.08728,0.02661,-0.00691,-0.02484,-0.04937,-0.00888,0.05219,0.09384,-0.01374,0.05362,0.01862,-0.02398,-0.01378,0.04993,0.04911,0.03521,-0.11007,-0.01299,0.07481,-0.02257,0.0235,-0.02819,-0.05149,0.06332,-0.01273,0.02232,-0.01377,-0.12525,-0.13876,-0.13366,0.03744,-0.03385,0.03909,-0.04895,0.00262,0.01655,0.02909,-0.08391,-0.06234,-0.03716,-0.08255,0.10278,-0.00177,-0.05968,-0.00943,0.05389,0.0118,0.04756,-0.10664,-0.05063,-0.11488,0.02264,-0.09402,0.0853,-0.0022,0.06074,-0.00526,-0.00584,-0.05826,0.03116,-0.01495,0.12047,-0.01007,0.09634,0.1248,0.03335,-0.07488,-0.06965,0.01001,-0.0635,-0.11155,-0.02834,-0.01534,0.01685,0.02241,-0.17276,-0.0299,0.01616,-0.00438,-0.02579,-0.11235,0.06507,0.04912,-0.09658,0.05421,-0.05888,0.10727,0.00022,-0.08298,-0.0484,0.02071,-0.01606,0.08171,0.10141,0.01116,-0.06754,0.02109,0.07595,0.01703,-0.01816,-0.02876,-0.03432,-0.07116,0.02473,0.05746,-0.09878,-0.01282,0.00768,-0.01876,0.02577,-0.04949,0.07743,-0.01547,0.00288,-0.03124,0.01307,0.00756,0.0713,0.0593,0.04022,-0.04293,0.03261,0.06273,-0.05555,-0.02305,0.10169,0.06037,0.03369,-0.13544,-0.11504,-0.07798,0.06368,-0.02996,-0.13822,-0.00389,-0.08668,-0.07826,-0.03295,-0.0884,0.00242,0.02597,0.04407,0.05976,-0.00741,0.09265,0.03545,0.05004,-0.08961,0.01258,0.01533,0.0598,0.11609,-0.0434,-0.05779,-0.03411,-0.06801,0.03168,0.06142,0.01619,-0.09247,-0.06385,-0.008,-0.06837,-0.12193,0.03453,-0.00342,-0.00724,-0.04194,-0.00694,0.05511,-0.07188,-0.03108,0.0035,-0.061,0.05139,-0.08042,0.0828,-0.02447,-0.04201,-0.00915,-0.00706,-0.03852,-0.09227,0.03929,-0.00271,-0.06174,-0.01412,-0.01133,0.07906,-0.0409,0.0104,0.04043,-0.05527,0.08162,0.09179,0.0784,-0.00911,0.07248,0.14529,-0.01788,0.06815,-0.03171,0.05976,-0.01344,0.04426,-0.07305,-0.02774,0.03866,0.05798,0.01532,-0.09212,0.03149,-0.00966,-0.01514,-0.08882,-0.0099,-0.013,0.05074,0.22153,-0.03269,0.03401]},{"domain":"astronomy","key":"magnitude_difference_from_flux_ratio","name":"Magnitude difference from a flux ratio","package":"astronomy-ai999x","example":"Magnitude difference: ratio = 100","v":[0.05731,0.01577,-0.00536,0.13402,0.03001,-0.04854,-0.10154,0.00062,-0.05952,-0.01714,-0.05935,-0.0749,-0.03388,0.13358,0.03672,-0.0118,-0.0276,0.00447,0.02149,0.00784,0.03912,0.13022,0.06165,0.02181,0.02596,-0.01552,-0.02368,-0.08747,-0.11533,0.03287,0.04423,0.08026,-0.10013,-0.09693,-0.03649,0.06518,0.0262,0.00926,0.00223,-0.07497,0.0261,0.01503,0.14082,-0.13509,0.03599,0.02975,0.0302,0.004,-0.02712,0.0895,-0.00131,0.14086,-0.01803,-0.03152,0.00439,0.07667,-0.06481,-0.06442,-0.00261,-0.05373,0.00633,-0.07878,-0.00402,-0.02408,-0.01071,0.00386,0.08365,0.05736,-0.01143,0.03,0.18571,0.06629,0.00833,0.05344,0.02145,0.03399,-8e-05,-0.09631,-0.01753,-0.10575,-0.0272,0.00653,-0.00618,-0.04048,0.10216,-0.02009,0.07183,-0.00205,-0.01589,-0.03566,0.02382,-0.01132,0.13156,-0.01479,0.10241,-0.00635,-0.00246,-0.0385,0.00943,0.04071,-0.00135,0.11046,-0.09612,-0.06023,-0.06976,-0.10123,0.07671,-0.0131,-0.02247,0.03583,-0.09042,-0.04277,0.03104,0.00995,-0.0052,-0.00778,0.03272,0.08086,-0.00502,0.09228,-0.03442,-0.02197,0.0447,0.08384,0.06129,0.04032,-0.04201,0.00374,-0.0771,0.04614,-0.00377,0.01817,0.02195,-0.06574,-0.01084,-0.00206,-0.05457,-0.02326,0.02654,-0.08098,-0.07707,0.06389,0.01588,-0.09745,-0.00046,0.00785,0.01952,0.00677,0.01899,0.04638,0.00446,-0.1886,-0.05339,-0.02608,-0.05037,-0.15155,-0.01722,0.02709,-0.00989,-0.00201,0.18162,-0.09978,-0.09752,-0.18721,0.0291,0.0263,-0.09447,-0.0076,0.02751,-0.0117,-0.08127,0.08847,0.00596,-0.01537,-0.0198,0.1177,0.04801,0.0129,0.04524,-0.03731,0.00439,-0.00979,0.00408,-0.01743,-0.05571,0.00304,-0.02225,0.13364,0.04916,-0.05558,0.04008,0.09561,0.06131,-0.02796,0.03491,0.0073,0.03759,0.01025,-0.14087,0.01761,0.03178,-0.00393,0.15561,-0.09251,-0.00916,0.04151,-0.0939,-0.06662,-0.06172,0.1334,-0.13679,0.05238,-0.01269,-0.01734,-0.02312,-0.08022,0.03856,0.1266,0.00925,-0.04458,0.06368,-0.03803,-0.06133,0.06393,0.04113,-0.01672,0.06184,0.00799,0.09513,0.04482,-0.1139,0.08244,0.00434,0.06754,0.07363,-0.07666,0.03771,-0.04207,0.00226,0.02499,0.06083,-0.02772,0.03047,-0.00772,-0.03485,0.01587,-0.04436,-0.07754,0.00146,-0.07701,-0.0027,-0.02045,0.01624,0.06587,-0.02409,0.01068]},{"domain":"astronomy","key":"orbit_from_state","name":"Orbital elements from position and velocity","package":"astronomy-ai999x","example":"Orbit from state: M = 1.4982e10 kg, r = 1 m, v = 1.2 m/s","v":[0.07438,-0.0523,0.01317,-0.03427,-0.01127,-0.13463,-0.06098,-0.04234,0.06913,-0.06634,-0.01158,-0.08303,0.01604,0.01284,0.00792,0.08465,0.01037,0.03755,-0.02401,-0.01065,-0.02825,-0.03057,0.0382,0.02777,-0.00414,-0.06409,0.09336,0.01649,-0.00344,0.01376,0.05824,0.09017,-0.02613,-0.01198,0.10363,-0.02779,0.02463,0.08546,-0.11586,0.05618,0.05004,0.01323,0.04884,-0.05634,-0.05237,-0.01346,-0.06898,-0.08064,-0.03851,-0.08765,-0.04708,-0.01564,0.0653,0.15187,0.02593,0.04248,-0.06859,0.10739,-0.02353,-0.05912,-0.05797,-0.01118,-0.05585,-0.05278,-0.02364,-0.0019,0.08999,-0.06043,0.01148,0.02448,0.01878,-0.03337,0.12672,-0.07261,0.00938,0.09831,-0.02365,0.02337,0.01275,-0.02343,-0.1017,0.04884,-0.06998,-0.03318,0.00388,-0.03139,-0.00816,-0.02545,-0.01039,0.03067,0.0669,-0.08034,-0.0184,0.03212,-0.12194,0.05654,-0.01457,0.06035,-0.07172,0.01648,0.01366,0.08448,0.08402,-0.06836,0.02788,-0.16543,-0.10452,0.02474,-0.13166,-0.06301,0.06204,0.11231,0.07243,0.06361,0.06716,-0.00128,0.01807,0.00052,0.02807,0.06742,0.03419,0.0595,-0.02991,0.05814,-0.09742,0.02953,-0.00237,0.05268,-0.02851,0.03957,-0.04156,0.01204,0.05273,-0.00666,0.08138,-0.01863,0.05182,0.10255,0.03733,-0.04214,-0.03278,0.08969,-0.02403,-0.06114,-0.02718,0.00417,-0.04484,-0.08433,-0.11431,0.13911,-0.02904,0.00487,-0.01395,-0.08832,-0.10834,-0.00635,0.03222,-0.03186,0.0721,-0.01029,0.01032,-0.03157,-0.11825,-0.04077,-0.0634,0.07946,0.02132,0.03398,0.01731,0.08158,-0.06476,-0.02806,0.04835,-0.05305,0.0303,-0.01696,-0.05158,0.07306,0.01443,0.10738,0.09632,-0.01532,0.01446,0.03599,0.05488,0.06741,-0.07142,-0.04874,0.11371,-0.14899,0.00884,-0.10703,-0.00429,-0.01406,-0.01769,-0.04387,-0.07721,0.01971,0.07344,-0.0431,-0.01483,-0.0297,0.06332,0.00877,-0.04652,-0.01805,-0.01201,-0.06384,-0.01364,-0.15024,-0.06832,0.03395,0.17914,-0.0092,-0.07418,0.04287,-0.04021,-0.00197,0.07344,0.0756,0.011,-0.11553,-0.05473,0.15577,0.05199,-0.00672,0.06316,0.11626,0.06193,0.06233,0.06835,-0.00052,0.03201,0.03087,-0.07886,-0.03982,-0.00528,0.02064,0.07497,-0.08256,0.06987,0.01909,0.13105,-0.09355,-0.07429,0.03753,0.01249,-0.07613,0.05495,-0.13474,-0.00684,-0.00927,-0.08105,-0.02332,0.06231,0.0041]},{"domain":"astronomy","key":"parallax_distance","name":"Distance from parallax","package":"astronomy-ai999x","example":"Parallax distance: p = 0.1 arcsec","v":[0.01641,-0.07304,0.0234,0.00946,-0.01912,-0.02671,-0.09494,-0.0324,0.04485,0.01411,-0.00032,-0.03541,-0.06912,0.0682,-0.02919,0.04309,0.03262,0.11526,-0.02546,0.02419,-0.10028,0.08189,-0.00722,-0.05556,0.01016,-0.00742,-0.01428,0.00934,0.0989,0.04263,-0.06338,-0.03702,-0.0235,0.01739,-0.07093,-0.02295,-0.00392,-0.03482,-0.03227,0.01661,-0.01009,-0.03452,0.12495,-0.04525,0.002,-0.03835,0.05534,0.04943,0.01233,0.03261,-0.01683,0.08238,-0.06947,-0.04059,-0.02917,-0.02214,0.00692,0.02458,0.03964,-0.1216,0.08656,-0.05316,-0.09022,-0.01458,-0.09744,0.0344,-0.05894,-0.05744,-0.0871,0.03623,0.02646,-0.02458,0.03968,-0.07419,0.02264,0.00207,0.09963,-0.13779,-0.06013,-0.0769,-0.02776,-0.03976,0.16703,0.02665,0.0602,-0.00455,-0.02782,-0.01848,0.01421,0.06643,-0.11701,0.02596,0.0311,0.05693,-0.03985,0.01208,0.02456,0.02214,-0.00546,-0.02009,-0.00611,0.01724,-0.06844,0.11248,0.02367,-0.05696,0.00785,-0.07564,0.08936,0.04912,0.12624,0.01349,-0.03855,-0.0189,0.03962,-0.04055,0.05642,0.05472,-0.03828,-0.01397,-0.03614,0.02317,-0.03477,0.07406,-0.03012,-0.05247,-0.07778,0.09095,-0.02724,0.03278,0.01566,-0.0502,0.03793,-0.03275,-0.03187,0.15186,0.00893,0.06942,0.00641,0.08829,0.10115,0.00667,0.03578,-0.06668,0.22208,0.05054,-0.00906,-0.02461,0.01759,0.07714,0.01523,-0.05495,-0.03021,0.03432,0.11858,-0.15206,0.06704,-0.15088,0.08014,-0.01565,0.00687,0.06645,-0.06018,0.02567,-0.02735,-0.06147,-0.12152,0.05072,-0.06758,0.00137,-0.00639,0.08249,0.13461,-0.02708,0.02708,0.06792,-0.02361,0.04468,0.00566,0.09257,0.04096,-0.06125,0.03665,0.06181,0.06671,0.03205,0.06631,-0.24215,-0.04091,-0.06884,0.04268,-0.10108,-0.00942,-9e-05,0.08632,0.03216,0.00593,0.03522,-0.02572,-0.09344,-0.01602,-0.05528,0.03719,-0.0336,0.01457,0.01477,0.01607,-0.12689,0.04882,0.02044,-0.00243,0.00707,0.05323,-0.07071,0.02531,-0.05735,-0.03668,0.1064,-0.03208,0.07813,0.09803,-0.09211,-0.08284,0.06027,-0.0239,-0.08768,0.04015,-0.01295,0.08387,-0.02864,0.03395,-0.01251,0.07535,-0.01862,-0.01449,-0.00449,0.00427,-0.02393,-0.02239,-0.09021,0.06112,0.09041,0.01275,0.05826,-0.12983,0.09508,-0.06468,-0.1311,-0.01941,-0.11492,0.03809,0.05615,-0.04847,-0.01461,0.04252,0.05845]},{"domain":"astronomy","key":"plane_change_delta_v","name":"Delta-v of a combined plane change","package":"astronomy-ai999x","example":"Plane change: v1 = 3 km/s, v2 = 4 km/s, di = 90 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temperature of a planet","package":"astronomy-ai999x","example":"Equilibrium temperature: T_star = 1000 K, R_star = 2 m, a = 4 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beta","package":"astronomy-ai999x","example":"Plasma beta: T = 1e5 K, n = 5 cm^-3, B = 5 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frequency","package":"astronomy-ai999x","example":"Plasma frequency: n = 1e12 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deg","v":[0.00517,-0.04477,0.00424,0.01023,0.0153,0.02481,0.02519,-0.08753,0.03577,0.00978,-0.0213,0.0232,-0.01209,0.1281,0.14247,-0.01345,0.05198,-0.02442,-0.06172,-0.0417,-0.13359,-0.01279,-0.00272,-0.02951,0.00707,0.05173,-0.01515,0.0385,0.04359,-0.06076,-0.07241,-0.00105,-0.08729,0.01999,-0.05448,0.0151,0.04192,0.01237,-0.01192,-0.04367,0.02649,0.00202,0.08934,-0.00303,-0.06492,0.04414,-0.01862,0.06235,0.002,0.10034,0.07971,0.01903,0.07021,0.02552,-0.02132,-0.06395,-0.03418,0.0272,-0.01016,-0.03685,-0.05797,0.09584,-0.10165,-0.19827,0.05106,0.03879,-0.00089,-0.07809,-0.12246,0.03162,-0.05202,-0.06885,0.1336,0.02957,0.05597,-0.13816,-0.01015,0.04922,0.05478,-0.0454,0.03092,-0.07671,0.05764,0.03089,0.10179,0.00171,0.05212,-0.0332,0.07205,0.11746,-0.05931,0.00621,-0.0053,-0.03521,-0.0462,0.10491,0.13406,0.01098,-0.13602,0.01291,-0.01346,-0.05783,-0.00971,-0.03418,0.04185,-0.01765,0.00902,0.14039,-0.05373,0.0082,0.0337,0.05191,-0.07239,0.05343,0.05808,0.02799,0.14335,-0.0233,-0.07472,0.02839,0.04728,-0.06375,-0.02634,-0.03772,0.01767,0.03249,-0.05143,0.04128,0.03408,0.04295,-0.02294,-0.08686,-0.02384,-0.01027,0.0152,0.03038,-0.0841,0.04058,0.03278,-0.04371,-0.13705,0.04551,-0.06288,-0.07261,0.04553,0.07291,0.07784,0.08422,-0.00602,-0.01094,-0.04129,-0.06947,0.07176,0.01161,0.00604,0.09705,-0.06499,0.04868,0.03189,0.00479,0.15502,-0.08257,0.0024,0.021,0.01378,-0.05425,-0.03369,-0.11249,-0.01646,0.02881,0.04627,-0.00639,0.05811,-0.12761,-0.00916,0.11984,-0.03605,-0.04167,0.01138,-0.18386,-0.01183,0.03959,0.04767,-0.0578,0.0597,-0.04012,0.05157,-0.10421,0.05959,-0.14223,0.0286,0.03893,0.02437,-0.04777,-0.00887,0.08909,0.02672,0.06871,-0.01492,-0.04092,-0.04943,0.00063,0.07563,-0.06644,-0.0894,0.15643,-0.01597,0.01457,-0.01379,0.0009,-0.01151,0.00033,-0.10319,0.07532,0.05376,-0.07519,-0.00049,0.03646,-0.04865,-0.04683,0.04814,-0.07513,-0.03635,0.06919,-0.05624,0.01426,0.08816,-0.03572,0.06036,8e-05,0.00832,-0.02454,0.02775,-0.02739,-0.10755,-0.02284,0.08527,-0.06357,-0.01282,-0.01507,-0.03157,0.02312,0.04224,0.09157,-0.1257,0.06583,0.07364,0.0103,0.09744,0.06224,-0.09836,0.00408,-0.03014,-0.13396,0.02344,-0.03632]},{"domain":"astronomy","key":"radial_velocity_semi_amplitude","name":"Radial-velocity semi-amplitude of a star","package":"astronomy-ai999x","example":"Radial velocity semi-amplitude: M_star = 1 Msun, m_p = 1 Mjup, P = 11.86 yr","v":[0.06409,-0.10572,-0.10147,-0.01691,0.11221,-0.0816,0.01512,-0.03288,0.04298,0.0101,0.00085,-0.13025,0.06153,-0.01225,-0.00694,0.01769,0.06893,-0.02526,-0.00707,-0.02963,0.17005,0.05689,-0.01078,0.10314,-0.05653,0.0789,0.13714,0.00625,-0.04131,0.03084,-0.02367,-0.01345,-0.02222,0.00527,-0.03804,-0.03714,-0.09762,0.07389,-0.04509,0.03629,0.01809,-0.07739,-0.04149,-0.03189,-0.07409,0.08483,-0.046,0.05084,0.03642,-0.14883,-0.0962,0.08363,0.07209,0.02884,0.04945,0.04054,-0.01654,-0.05796,0.14909,0.03185,0.01086,-0.05364,-0.10372,0.14106,0.09591,0.01667,0.12331,-0.07726,0.01421,-0.0248,0.06943,-0.03276,0.0478,-0.02563,0.05377,0.02613,0.05858,-0.06682,-0.04068,-0.09252,0.00299,0.01652,0.04109,-0.09637,0.08899,-0.09262,0.03511,0.03488,-0.05532,-0.04958,0.0031,-0.06812,0.00571,-0.06089,-0.01341,0.03309,0.04722,0.04084,-0.01538,0.00096,0.00632,0.04419,0.07579,-0.00684,0.01127,-0.08876,-0.0453,-0.04644,0.05076,-0.02747,0.10049,0.07619,-0.06368,-0.05989,0.01173,-0.07207,0.03441,0.03618,-0.01035,0.06815,-0.0071,0.03409,-0.04926,0.10969,0.00679,0.05981,0.00143,-0.10503,-0.06686,0.05682,-0.03926,0.02242,0.0076,0.00258,-0.00964,0.00192,-0.05294,0.07968,0.09897,0.02135,-0.04625,0.04048,0.01899,-0.06465,0.03895,-0.02373,-0.04661,-0.04712,-0.0685,0.03455,-0.03835,-0.03556,-0.07844,-0.10593,-0.09037,0.13895,0.12822,0.00925,-0.01888,-0.10258,-0.10734,-0.07257,-0.04136,0.05907,-0.06564,0.04069,-0.06578,0.0717,0.01178,0.03269,-0.05088,0.00136,-0.05593,-0.07897,-0.02193,0.15983,-0.00471,-0.0657,0.01078,0.0034,0.11081,0.01256,0.10482,0.00201,-0.04266,-0.04414,-0.05236,-0.06529,-0.01857,-0.12302,-0.12912,0.08199,-0.00811,-0.07292,0.05411,-0.00766,0.062,0.14123,0.06002,0.03247,-0.0205,0.00252,-0.08795,0.1048,-0.02432,0.05556,-0.0647,-0.06207,-0.09138,-0.04005,-0.10815,-0.01869,0.01836,-0.01148,-0.02426,-0.07157,-0.0883,-0.02486,0.03628,0.0466,0.07018,-0.00886,-0.01676,0.02961,-0.00524,-0.06553,0.02579,-0.02286,0.10342,0.03593,0.01974,0.04377,0.04227,0.06569,0.1077,-0.05473,-0.03001,0.03994,-0.04411,0.05396,0.04272,-0.00021,0.10911,-0.02016,0.02574,0.04684,0.04446,-0.03963,0.07557,0.007,-0.07916,0.01569,0.0357,-0.02133,-0.11918,0.00707]},{"domain":"astronomy","key":"rayleigh_resolution","name":"Diffraction limit of a telescope (Rayleigh criterion)","package":"astronomy-ai999x","example":"Rayleigh criterion: lam = 550 nm, D = 2.4 m","v":[-0.00035,-0.06774,0.05053,0.10798,-0.07688,0.10092,0.01604,-0.12915,0.06086,-0.09327,0.0538,0.02582,0.05229,0.06017,-0.00917,-0.09094,0.01976,0.04013,0.00893,-0.02409,-0.06903,0.07718,-0.06037,-0.06973,-0.0091,-0.00922,-0.07724,0.0473,0.02311,0.05625,0.00078,-0.03323,-0.03134,-0.04457,-0.02592,-0.07244,-0.04071,-0.01713,0.03058,0.11729,0.03326,0.00406,0.03624,-0.06667,0.03576,-0.01559,0.08641,0.04515,0.06597,0.04638,-0.02175,0.00276,0.00637,0.04067,0.01008,0.02433,0.00809,-0.02398,-0.05584,0.05755,0.07005,0.1186,0.01798,0.11898,0.01567,0.02944,-0.09542,0.0026,-0.05008,0.04087,0.03529,0.14148,0.09786,0.04178,0.01795,0.02489,-0.03212,-0.00864,-0.14563,-0.0101,0.00048,0.00676,0.08345,-0.04971,0.10686,-0.05123,0.03683,-0.03726,-0.02433,0.06737,-0.07568,-0.0251,0.08864,-0.04254,0.01754,-0.04724,0.01405,0.04504,-0.02211,0.01838,-0.09843,0.06224,0.02552,-0.04425,0.08197,0.13174,0.01133,0.01414,0.10493,0.00776,-0.09234,-0.14272,-0.05301,-0.09417,-0.0739,0.08584,-0.00209,0.03277,0.10426,0.01964,0.03545,-0.04017,0.02783,0.07143,0.03257,-0.04679,-0.10591,0.05434,-0.06075,-0.0329,0.00576,-0.07063,0.07128,-0.01444,0.02808,0.05304,-0.01481,0.03855,0.096,0.05652,-0.02559,-0.0164,-0.01063,-0.06431,0.15542,0.0279,0.1267,-0.08269,-0.00139,-0.01237,0.06477,0.02786,-0.05256,0.02057,0.06969,-0.04656,-0.00322,0.08021,-0.00045,-0.0025,-0.06747,0.12473,-0.1307,0.00905,-0.00886,-0.00627,-0.0253,-0.06985,-0.02194,-0.0113,0.02497,0.06789,0.01394,-0.11181,0.04923,-0.00525,-0.07578,-0.06053,0.05111,-0.14486,-0.09305,0.00648,-0.01793,-0.01863,-0.06079,-0.05762,0.02196,-0.07842,0.08146,-0.07186,-0.13456,-0.02467,0.03982,-0.09074,0.05374,0.07003,-0.02724,-0.00652,-0.01295,-0.08822,-0.0088,0.00979,0.0152,-0.06644,0.04591,-0.03595,0.09967,0.02001,-0.05946,-0.09594,0.00667,0.11634,-0.08357,0.02375,-0.06977,0.03428,-0.00924,0.03659,0.04136,0.00689,-0.13878,-0.01529,0.04051,0.07385,0.04547,-0.06815,0.05328,0.03322,0.09848,-0.00172,-0.01078,0.04923,-0.01431,-0.06017,-0.05585,-0.01336,0.03288,-0.13017,-0.10271,-0.05451,0.01068,0.05102,0.04133,-0.06143,-0.10771,0.19929,-0.05133,-0.06312,-0.04936,-0.03699,-0.11008,0.02083,0.03357,-0.02546,0.04473,0.04196]},{"domain":"astronomy","key":"recession_velocity_from_redshift","name":"Radial velocity from a Doppler redshift","package":"astronomy-ai999x","example":"Radial velocity from redshift: z = 1","v":[0.01766,0.0067,0.03304,0.11084,0.01682,-0.00674,0.01848,0.12968,0.02676,-0.00426,0.04395,0.0095,-0.01032,0.02678,-0.0502,-0.00128,-0.02768,-0.05374,-0.14728,-0.02002,0.08999,0.01896,-0.06437,-0.03241,-0.03618,0.02519,0.01013,-0.07249,0.0669,0.02429,0.01639,-0.02767,0.02843,-0.08181,-0.06325,-0.02089,-0.01256,0.03337,-0.03528,0.01376,-0.01728,0.04227,0.04331,-0.11438,-0.00054,0.0035,0.04269,-0.08147,-0.1144,-0.14293,0.03952,-0.0213,-0.05165,-0.08526,-0.02847,0.00747,-0.04238,0.0625,0.00233,-0.05154,0.06276,0.02741,0.1183,0.07371,0.07915,-0.01481,-0.01244,-0.00679,-0.06754,0.08633,0.05198,0.09249,0.07246,-0.02061,0.04065,-0.05616,-0.05516,-0.02172,0.05007,0.02948,0.16133,0.10791,-0.02553,-0.03232,-0.02505,0.00039,-0.10137,-0.06004,0.01664,-0.0018,0.02913,0.05006,0.06968,0.04168,0.09966,0.13594,0.05304,-0.03444,-0.1021,0.01707,0.00594,-0.09533,0.04426,-0.01433,0.04956,0.06633,0.05641,-0.02126,0.08888,0.07669,-0.04364,-0.02215,-0.11515,-0.09048,0.04968,0.11593,-0.00874,-0.02918,0.0159,-0.02061,0.04882,-0.19945,-0.02809,0.05701,0.00728,0.07142,0.061,0.01739,0.00491,0.0208,-0.05972,-0.01534,-0.05722,-0.05372,-0.05777,0.00401,-0.011,0.01637,0.02119,-0.0483,0.03956,0.10958,-0.00833,-0.09313,0.05097,0.06598,0.01818,-0.04697,-0.08642,0.11496,0.08012,-0.0308,0.15527,-0.10055,-0.09188,-0.1165,0.06345,-0.04746,-0.03723,-0.07876,0.02016,-0.11538,-0.02518,-0.02437,-0.08765,0.00702,-0.08841,0.03993,0.02921,-0.03924,-0.01189,0.04346,0.00513,0.00646,-0.00611,0.15899,-0.03988,-0.03547,0.05225,-0.05609,-0.01958,-0.05615,0.02556,-0.03133,0.05694,0.00053,0.05434,0.04557,0.02076,-0.02348,-0.11937,0.00522,0.05078,-0.04641,0.03267,-0.07164,0.03662,0.10524,0.07899,0.0126,-0.10219,0.02214,0.07734,-0.11809,-0.0687,0.12429,-0.03447,0.06596,-0.00403,0.03616,0.02651,0.05808,-0.02591,0.04107,0.10051,-0.05365,-0.01741,0.08254,0.02349,-0.02648,0.11554,0.01497,0.03126,-0.06329,-0.07092,-0.00033,0.0279,0.04494,0.06985,0.01802,-0.07576,-0.01721,-0.01064,0.01094,-0.01469,-0.04195,-0.0511,0.07456,0.05688,0.06652,0.01985,0.03068,0.1228,-0.01389,-0.02694,-0.07822,-0.15444,0.01839,0.02475,0.06499,-0.13991,0.0055,-0.07303,-0.04096,-0.08031,-0.03452]},{"domain":"astronomy","key":"redshift_at_lookback_time","name":"Redshift at a given lookback time","package":"astronomy-ai999x","example":"Redshift at lookback time: t = 8 Gyr, H0 = 70, Om = 0.3","v":[0.01967,0.01141,-0.07991,0.0808,0.07309,0.04157,0.12664,0.05622,0.05119,-0.02962,0.05167,0.00839,0.02191,0.07035,-0.00234,-0.01801,0.10469,0.03749,0.02415,-0.00355,-0.02628,-0.03794,-0.1074,-0.00535,0.05349,-0.11887,0.04329,0.01965,0.0593,0.15485,0.01253,-0.04162,-0.03659,-0.0413,0.02024,-0.07456,-0.00035,0.06301,-0.09038,0.06338,-0.08705,-0.00896,-0.00091,-0.01022,-0.0831,-0.03287,-0.07883,-0.09244,-0.03519,0.062,-0.07064,-0.00663,-0.09115,-0.02926,-0.06235,0.00923,-0.02226,0.01875,-0.00024,0.00284,0.07265,0.1242,0.06542,0.15246,0.0643,-0.11089,0.10495,-0.00256,0.02985,-0.00094,-0.04445,0.01791,0.04257,-0.01557,0.0389,-0.06127,0.0133,0.00273,0.01881,0.11547,0.06734,-0.014,-0.04614,0.00973,0.00833,-0.0205,-0.07758,-0.09285,0.06619,0.16623,-0.07784,0.00162,0.06174,-0.05212,0.00189,0.03815,0.02993,-0.08047,-0.07166,0.12948,-0.03725,0.01676,-0.04203,-0.10081,-0.03111,0.09786,-0.03087,-0.01157,0.05309,-0.04768,-0.06513,0.00473,-0.11919,-0.03932,0.04187,0.12028,-0.05212,-0.01599,0.00308,0.03485,-0.06116,-0.05326,-0.00548,0.02848,0.06064,-0.03163,0.01083,-0.02498,0.04812,0.11799,-0.01118,0.01833,-0.02015,-0.10715,0.06834,-0.05376,-0.05144,0.02551,0.16304,-0.00292,0.08379,0.03292,0.00483,-0.10442,-0.11499,0.07519,-0.02373,-0.04129,0.02593,0.1116,0.11518,-0.04296,-0.01226,-0.05246,-0.04094,-0.10472,-0.0286,0.00957,0.02644,-0.00482,0.03173,0.04638,0.01808,0.08325,-0.09825,0.00198,-0.01927,0.04896,-0.00045,-0.08441,0.09735,0.06349,-0.05778,0.01187,-0.04444,0.16234,0.01983,-0.06591,0.07274,0.00425,-0.07872,-0.10497,0.02447,0.00329,0.01524,0.05551,0.06636,0.03909,0.02953,-0.06531,-0.00102,0.11325,-0.01526,-0.12393,-0.09039,0.0441,0.04896,-0.00226,-0.05739,0.0455,-0.03307,0.03014,0.00959,-0.10872,-0.03064,0.04375,0.1035,0.00316,-0.09228,-0.01108,0.00207,0.10298,-0.04168,-0.09845,0.0327,-0.069,0.04565,0.06311,0.00621,0.00828,0.03376,0.01937,-0.04863,-0.17194,0.047,-0.06849,0.04675,0.05865,0.05653,-0.05735,-0.01378,-0.12019,0.01254,0.01137,0.02027,-0.04248,0.01759,0.00804,0.02411,0.01474,0.03494,0.07387,0.08264,0.00668,-0.01697,0.00613,-0.05582,-0.02067,0.05347,0.03171,-0.01379,-0.03602,0.06101,0.01993,-0.15304,-0.07378]},{"domain":"astronomy","key":"redshift_from_wavelengths","name":"Redshift and radial velocity from a spectral line","package":"astronomy-ai999x","example":"Redshift from spectral line: lam_obs = 1312.56 nm, lam_rest = 656.28 nm","v":[0.04969,0.00186,0.04722,0.07571,0.02304,0.07117,0.02431,0.03581,0.03474,-0.01309,0.00398,0.06479,0.02654,0.02417,-0.06405,-0.0351,-0.00562,0.03558,-0.04729,-0.0598,0.08243,-0.01543,-0.10826,0.02891,0.00308,-0.02712,0.02849,-0.11459,0.04898,0.03447,-0.00603,-0.09185,0.01675,-0.07983,-0.02803,-0.08007,0.05293,0.09184,-0.04424,-0.01394,-0.0127,-0.0318,0.0738,-0.06108,-0.04855,0.03151,0.00485,-0.05229,-0.06626,-0.04922,-0.01486,-0.00065,-0.02888,-0.03927,0.04348,-0.0424,-0.04766,0.06536,-0.0261,0.03524,0.09867,0.05825,0.16669,0.12841,0.10487,-0.00952,0.01675,-0.00177,0.00507,0.0502,0.09333,0.10981,0.14476,0.02835,0.02568,0.0015,-0.01854,-0.03813,0.08285,0.00326,0.17875,0.12103,0.03882,-0.02271,0.01953,-0.05036,-0.09697,-0.04094,-0.00171,0.01897,-0.02288,0.05993,0.03428,-0.00607,0.06801,0.04068,0.01362,-0.04595,-0.06726,-0.03198,0.01502,-0.02478,0.03933,-0.06871,0.04382,0.07628,-0.01857,-0.0716,0.03152,0.02243,-0.08077,-0.06606,-0.15516,-0.08413,0.05351,0.12046,-0.03601,0.00072,0.06282,-0.01805,0.00061,-0.16176,-0.03653,0.02811,0.05444,0.06797,0.10808,0.02652,-0.01158,0.01212,-0.06012,0.02682,0.00974,-0.01217,-0.01204,0.0142,-0.03231,-0.0169,0.05325,-0.03231,-0.04273,0.10247,-0.06225,-0.11031,0.02284,0.06187,-0.0088,-0.07321,-0.09322,0.03535,0.07923,0.02352,0.08191,-0.02436,-0.04917,-0.06542,0.06316,-0.02266,-0.00085,-0.11822,-0.03697,-0.12898,-0.05036,0.02742,-0.11191,0.00589,-0.05159,0.02266,0.00042,-0.06184,0.05944,0.0398,0.02012,0.03776,0.00332,0.12359,0.00198,-0.15449,0.04077,-0.11305,-0.05116,-0.01634,-0.01311,-0.06522,-0.00752,0.00798,0.00917,-0.01385,0.06299,-0.04178,-0.14643,0.07116,0.05879,-0.07045,0.02716,-0.05989,0.03261,0.07176,0.00768,-0.02909,-0.03225,0.11087,0.02198,-0.13592,-0.09154,0.0472,0.01449,0.07647,-0.11394,-0.02301,-0.01988,0.10619,-0.09403,0.06114,0.11252,-0.02043,-0.04125,0.07734,0.02815,0.01367,0.03866,-0.01752,0.09594,0.01907,-0.00451,0.02751,0.01002,0.06872,0.08828,-0.05841,-0.00897,-0.02974,-0.02086,-0.03561,-0.07528,-0.0794,-0.03655,0.01166,-0.06185,0.05087,0.04321,-0.04277,0.12066,0.00613,0.01036,-0.01822,-0.11057,0.01169,0.07953,0.10875,-0.14646,-0.05227,-0.11388,-0.02192,-0.073,0.01135]},{"domain":"astronomy","key":"rise_set_hour_angle","name":"Rising and setting of a star","package":"astronomy-ai999x","example":"Rising and setting: dec = 0 deg, lat = 45 deg","v":[0.0646,-0.0074,-0.10296,-0.01063,0.01585,0.11171,0.0469,-0.10471,0.09307,0.02551,0.0154,-0.02848,-0.03482,0.18241,0.10298,0.0467,0.08819,0.04403,-0.02128,-0.07802,-0.0227,-0.10238,-0.0709,-0.03717,0.11004,0.02739,-0.01028,-0.01146,0.03609,0.01005,-0.04718,0.05742,-0.0574,0.01058,-0.03398,0.02468,-0.00506,-0.03462,-0.02553,0.04942,0.01595,-0.06622,0.00407,0.06378,-0.03087,0.07786,0.00423,-0.1036,0.07555,0.04743,0.13294,-0.00161,0.1107,0.07151,-0.06377,0.01612,-0.0922,-0.0471,-0.00756,-0.0185,-0.02761,0.13378,-0.03016,-0.0589,0.04819,-0.00734,0.02797,-0.0999,-0.06387,-0.00421,-0.02322,-0.0194,0.02348,0.06823,0.10589,-0.06391,-0.09515,0.03528,0.01001,0.02826,-0.05644,-0.02587,-0.002,-0.03684,0.09282,-0.09745,0.04036,-0.07156,0.01003,0.02015,0.02385,0.03471,-0.08764,-0.04935,-0.05263,0.09068,0.04364,0.04481,-0.11833,0.00668,-0.00285,-0.01004,-0.00999,0.00522,0.02482,-0.01638,0.08863,0.02875,0.0585,-0.07386,0.07981,0.04959,-0.00951,0.05181,0.06156,0.10808,-0.0057,0.06328,-0.09468,0.02342,0.04907,-0.03824,-0.02887,-0.06666,0.06905,0.03451,-0.05882,0.00555,0.03456,0.01245,-0.03976,-0.08781,0.0576,-0.02586,0.05435,0.05369,-0.05729,-0.01518,0.04567,0.01558,0.02659,0.08382,-0.02555,-0.14086,-0.01281,-0.06245,0.01267,-0.00122,-0.00595,0.04543,0.01198,-0.03682,0.0522,-0.00044,-0.10538,0.11472,-0.08416,0.07029,-0.07347,-0.10915,0.10172,-0.09455,0.00933,0.00183,-0.00836,-0.04112,-0.02409,-0.02325,0.01912,0.05158,0.135,0.01887,-0.00805,-0.1144,-0.15094,0.07364,-0.03437,0.05179,0.10991,-0.06383,-0.07041,0.04229,0.09351,-0.05346,0.044,-0.12021,0.0196,-0.03966,-0.03056,-0.07352,-0.10547,0.00245,-0.01874,-0.15529,0.03612,0.06784,0.03431,0.09392,-0.02346,0.0292,-0.04134,0.09464,-0.02882,0.02291,-0.12802,0.11582,0.0556,0.08501,-0.09325,-0.04307,-0.06729,0.08081,-0.07883,0.09428,-0.04089,-0.06467,-0.08921,0.00387,-0.05828,-0.00364,0.00073,0.00246,-0.00337,-0.03052,-0.02342,0.00079,0.04164,-0.05016,0.01298,0.01455,-0.01615,-0.1452,-0.02682,-0.06236,-0.02598,-0.01637,0.09365,-0.00639,-0.00257,-0.01639,-0.0554,0.11889,-0.02401,0.03446,0.00977,0.02472,0.1312,-0.08176,0.02998,0.02227,0.04764,0.00354,0.07777,-0.09029,-0.00937,0.04007]},{"domain":"astronomy","key":"saha_hydrogen_ionization","name":"Ionization fraction of hydrogen (Saha equation)","package":"astronomy-ai999x","example":"Saha equation: T = 10000 K, n = 1e20 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radius","package":"astronomy-ai999x","example":"Schwarzschild radius: M = 1 Msun","v":[-0.07782,-0.00795,0.02021,0.07825,0.11364,0.03498,0.06951,-0.00075,0.03443,-0.10094,0.03502,0.06109,0.11455,-0.07655,0.01799,-0.02439,0.01026,0.04757,0.06329,0.01937,0.04408,-0.01808,0.01105,-0.02075,0.01801,-0.02001,0.01628,-0.06251,-0.04878,-0.04751,-0.09614,-0.02261,-0.07738,-0.09419,-0.0008,-0.08434,-0.12353,0.11822,-0.03231,-0.07899,0.0171,0.13346,-0.10408,0.01031,-0.01216,0.07598,-0.00827,0.04233,0.06485,0.03135,-0.0404,0.01023,0.04695,-0.01062,-0.0003,-0.01498,-0.06406,0.0839,0.0408,0.11775,-0.01258,-0.0363,0.03381,0.07369,0.13503,0.07553,0.03286,0.08776,-0.0029,0.09484,0.04903,-0.0231,-0.03631,0.01753,-0.05927,0.02523,-0.0725,-0.02678,-0.18727,0.11354,0.04943,-0.00209,0.01123,-0.06074,0.00657,-0.10313,0.04291,0.06894,0.09771,-0.06238,0.10496,-0.01086,0.09383,-0.02304,0.06228,0.01618,-0.00095,-0.00896,-0.06527,-0.07075,0.06408,-0.16685,-0.08598,0.05396,-0.12681,-0.01484,0.03724,-0.02319,-0.0413,0.06137,-0.1892,0.06579,-0.04951,0.00195,-0.01571,0.02949,0.12883,0.03904,0.03141,0.01419,-0.03964,-0.00449,-0.03102,-0.01495,0.0391,-0.05807,0.0023,-0.01346,0.03359,0.03831,-0.02689,0.10734,-0.16278,0.02676,-0.0141,-0.07549,-0.00613,0.02939,-0.01017,-0.03192,-0.02189,0.01528,0.06809,0.00207,0.0162,0.03691,0.0486,-0.03404,-0.05166,0.0521,0.05922,-0.09517,-0.07405,-0.07546,-0.04978,0.04293,-0.01033,0.02736,0.02724,-0.04106,0.03038,0.07524,0.0604,-0.09096,-0.09377,0.03076,-0.06333,0.05449,-0.00399,0.02108,0.00569,0.00907,-0.02197,-0.01612,-0.06289,0.01978,-0.05781,-0.0628,-0.03336,0.03745,0.00265,0.04952,0.08218,0.0224,0.02726,0.01288,0.02443,0.04489,-0.06371,-0.16698,-0.06285,0.04839,0.07043,-0.06278,0.04783,-0.00249,0.04346,-0.00107,-0.07256,-0.01545,0.0072,0.02257,-0.05617,0.02681,-0.00701,-0.02789,0.03416,0.02085,-0.09229,-0.02912,-0.01915,0.07601,0.08993,-0.17066,-0.02067,0.00387,-0.08088,-0.00845,0.04331,0.0285,-0.06539,0.05995,-0.02095,-0.03013,0.02175,0.05069,-0.05335,-0.07019,-0.00606,-0.02394,0.05925,0.05442,-0.02543,-0.15784,0.06586,0.00754,0.00376,-0.12639,-0.06293,0.01335,0.0267,-0.07671,-0.03444,0.06588,-0.04382,0.10872,0.03135,-0.04909,-0.01678,0.13815,-0.05202,0.07951,0.08074,0.12713,-0.06048,0.05657]},{"domain":"astronomy","key":"sidereal_time","name":"Greenwich and local mean sidereal time","package":"astronomy-ai999x","example":"Sidereal time: jd = 2451545.0","v":[0.01375,0.0371,-0.06164,0.07141,0.01762,-0.01553,0.12591,0.05961,-0.00164,0.10276,-0.07809,-0.06965,0.0751,-0.00785,-0.04495,-0.03453,0.12309,0.00212,-0.03962,-0.01916,-0.06066,-0.11437,0.05213,0.08348,0.06651,0.0291,0.00012,-0.02622,0.0652,0.01849,-0.0389,0.00271,-0.03914,0.01618,0.06985,-0.08694,0.04862,0.06454,0.01137,-0.03328,0.01705,-0.17262,-0.1246,0.08324,-0.04505,0.01338,-0.01652,-0.06605,0.06863,-0.00463,-0.0335,0.0546,0.10421,0.07777,-0.11946,-0.06515,-0.02062,-0.01043,-0.08845,0.07327,-0.07376,0.02265,-0.03915,0.04325,0.06292,0.08254,0.07004,-0.02621,-0.08192,0.03652,-0.09301,-0.14491,0.03369,0.02906,0.00293,-0.08766,0.08836,-0.01704,-0.05275,-0.03131,0.02096,-0.00716,0.10008,-0.0024,0.00235,-0.04128,0.00095,-0.05915,0.01601,-0.02149,-0.03712,-0.02878,-0.07235,-0.07215,-0.02016,0.05816,0.05447,-0.02388,-0.02631,-0.0037,0.08508,0.03605,-0.01525,-0.05385,0.11549,-0.01583,-0.00028,-0.03438,-0.01668,0.0148,0.05971,-0.03266,0.07765,0.00865,0.0688,0.07933,-0.02004,0.02449,-0.06674,0.02628,0.07577,-0.02969,-0.08565,-0.02242,-0.03776,-0.1181,0.06263,-0.01013,-0.02345,0.07233,-0.04327,-0.06579,-0.06079,0.03587,0.10468,0.07278,-0.04597,0.00359,0.00255,-0.04747,0.08604,-0.01602,0.05411,-0.0146,-0.026,0.00448,-0.00304,-0.11984,0.01473,0.02434,-0.09051,-0.03632,0.04922,0.01256,-0.10384,0.14638,0.04683,0.02163,-0.06516,-0.08015,0.11955,-0.05519,0.03778,-0.01943,-0.02218,0.03006,-0.03183,0.09737,0.00226,0.09547,0.00708,-0.03367,0.15166,-0.02296,-0.07627,0.06508,0.05392,0.0033,0.05057,-0.12792,0.00626,0.00062,-0.00462,-0.09434,0.01764,0.02121,0.0283,-0.00616,-0.06932,-0.06111,0.00802,0.03988,0.06445,-0.02665,0.03102,0.03338,0.06171,0.07593,-0.06692,-0.00429,-0.10117,0.0294,-0.08362,-0.0353,-0.03215,-0.0502,0.05851,0.0128,-0.03621,-0.00453,0.01849,0.11574,0.00735,-0.01477,0.02632,0.00466,-0.04327,-0.02945,-0.02196,-0.10793,-0.11615,0.01754,0.0036,-0.01146,0.01572,-0.09584,0.03866,-0.13507,-0.03155,-0.06663,0.11724,-0.12647,0.01283,-0.04003,0.09193,0.0113,0.13093,0.02413,-0.0014,0.06731,0.03886,0.06332,-0.08031,0.04303,0.12983,0.02088,0.13693,-0.13849,0.09043,-0.0386,0.08269,-0.03555,-0.04358,-0.08742,-0.08286,-0.03805]},{"domain":"astronomy","key":"stellar_luminosity","name":"Luminosity 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K","v":[-0.00718,-0.18916,-0.0003,-0.05423,0.05731,-0.09024,-0.03631,-0.02097,0.02621,0.03061,0.08446,-0.18803,0.04457,-0.03746,0.01787,0.10722,0.01688,0.04248,0.06444,-0.10884,0.15176,-0.03005,-0.08141,-0.09771,0.04122,-0.02027,0.06435,-0.04214,0.02865,-0.03958,-0.06281,0.02372,0.01554,-0.08887,-0.08179,0.06725,-0.02056,-0.0122,-0.08166,-0.01391,0.11519,0.00185,-0.03677,0.01564,-0.04554,0.08867,0.05533,0.01894,-0.03266,-0.02485,-0.00548,0.05085,0.01349,-0.03607,0.00477,-0.06212,-0.03424,-0.06364,0.04164,0.12458,0.09611,0.01286,0.00398,0.02893,-0.07004,0.02169,0.01766,0.07767,0.10908,0.09847,-0.02602,0.03685,-0.14484,0.05359,0.01384,0.05461,0.02413,0.0035,-0.18235,-0.09496,-0.05777,0.05782,0.0731,-0.00045,0.12575,-0.09313,0.0094,0.03075,0.01934,-0.09602,0.10459,0.06786,0.02451,-0.06769,0.10081,0.03273,-0.06517,0.03523,0.06371,-0.10508,-0.03089,0.05325,0.04857,-0.00195,-0.05693,-0.05162,0.02428,-0.13433,-0.02511,-0.07914,0.06765,0.00337,0.07218,0.00626,0.0408,0.04853,0.08115,-0.0148,-0.04298,-0.10453,-0.04591,0.02949,0.03943,-0.00824,0.00453,-0.04133,0.03647,-0.00336,-0.07566,0.04756,0.05779,0.08133,-0.01031,0.02152,-0.09694,-0.0123,-0.0189,0.04021,-0.014,0.01077,-0.00196,0.12096,0.0993,2e-05,0.03762,0.03134,0.03454,0.02899,-0.05326,-0.06769,0.01816,0.01946,-0.08168,-0.03074,-0.07141,-0.11845,-0.05482,0.0625,-0.07817,-0.05345,-0.08483,-0.01831,-0.0391,0.06114,-0.10112,0.08613,-0.05556,0.05372,-0.04647,-0.02564,-0.0001,0.05427,-0.04227,-0.0365,-0.03254,0.06912,0.0242,-0.00517,0.10346,0.03162,0.01508,0.05219,0.00171,-0.05845,0.00639,-0.07148,-0.01085,0.06527,-0.09887,-0.07556,-0.14357,0.08618,0.04249,0.05298,0.06205,-0.00344,0.03871,0.11955,-0.01381,0.01426,-0.00992,0.01882,-0.00526,-0.04699,0.02817,-0.017,-0.08165,0.17288,-0.1125,-0.01493,0.01473,0.02134,0.04324,-0.05303,-0.01171,-0.03303,-0.0591,0.03262,0.01568,-0.03443,0.00265,0.00868,-0.02109,-0.04786,0.06591,0.05835,0.0735,-0.10266,0.01065,0.01069,0.04709,-0.02022,0.00772,-0.05483,-0.00749,0.02163,-0.01658,-0.08343,-0.06297,0.12942,0.07439,0.03164,0.02028,0.01288,-0.03546,0.09152,0.05257,-0.05163,0.01527,0.00834,0.07737,0.00343,-0.05472,-0.01429,-0.11674,0.071]},{"domain":"astronomy","key":"stellar_radius","name":"Radius of a star from luminosity and temperature","package":"astronomy-ai999x","example":"Stellar radius: L = 1 Lsun, T = 5772 K","v":[0.05795,-0.14077,-0.03597,-0.02429,-0.0361,0.0054,-0.04824,-0.06961,0.04428,-0.00173,0.04812,-0.10072,0.02025,0.01209,-0.03575,0.04921,0.02272,0.03796,0.01082,-0.11461,0.10068,-0.04125,-0.07538,-0.03205,0.01815,0.01364,0.09959,-0.08272,8e-05,-0.01873,-0.00154,0.00694,-0.03029,-0.0576,0.00018,-0.02443,-0.03477,0.03071,-0.0997,-0.03481,0.07684,-0.05239,-0.00701,0.05846,-0.06502,0.08689,0.04784,0.02626,-0.02043,-0.0422,-0.0244,0.07474,0.12103,0.032,-0.04596,-0.00882,-0.01979,-0.05778,-0.00821,0.16325,0.10373,0.0517,-0.02905,0.02994,0.02773,0.0338,-0.00784,-0.0221,0.0465,0.00799,-0.05829,0.04011,-0.13825,0.00314,-0.02678,0.00805,-0.00404,0.04668,-0.16664,-0.05236,-0.00277,0.05201,0.07523,0.01752,0.10383,-0.08017,0.00725,0.0593,-0.04705,-0.10619,0.04583,0.05939,-0.01141,0.00028,0.07963,-0.00573,-0.06685,0.08177,-0.05947,-0.07987,-0.01145,-0.00802,0.08551,0.06126,0.00274,-0.07542,-0.01085,-0.0867,0.06599,-0.02193,0.09919,-0.04352,-0.02795,0.01243,0.02377,0.00993,0.09513,-0.05844,-0.04777,-0.08444,0.00197,0.02193,-0.08453,-0.00444,-0.01749,-0.02028,0.05982,-0.01919,-0.06152,0.01812,-0.03711,-0.00354,0.06558,-0.00236,-0.11946,0.00207,-0.03869,0.01515,0.00781,-0.03286,0.00863,0.07281,0.02477,-0.03892,0.02787,0.01532,0.06047,0.04329,-0.03641,-0.08778,0.10301,0.05225,0.00194,-0.03283,-0.08467,-0.02445,0.02527,-0.01732,-0.0016,-0.06377,-0.09289,-0.0114,-0.09377,0.08596,-0.10224,0.09009,0.02696,0.06958,-0.00928,-0.00674,0.06991,0.11195,-0.09015,-0.02185,-0.10359,0.05561,0.00447,-0.02473,0.13098,0.04227,0.09017,0.04748,0.01642,-0.11047,0.04074,-0.03602,0.05037,0.08587,-0.09833,-0.10614,-0.15128,0.07976,-0.00341,0.04759,0.09191,0.0142,0.0509,0.14032,0.01045,0.00239,-0.03859,0.08247,-0.02797,-0.04005,-0.02059,0.01008,-0.04026,0.11234,-0.08886,-0.10656,0.08609,0.01724,0.09957,0.00649,-0.01266,-0.06497,-0.08582,-0.10334,0.02683,0.05862,0.09691,0.04159,-0.04028,-0.02185,0.12446,0.00733,0.06674,-0.02322,0.09508,0.04632,-0.06727,-0.04159,0.03844,-0.03937,-0.0523,-0.00187,-0.04267,-0.02568,-0.0654,0.11841,0.12961,-0.00156,0.02545,-0.0336,-0.12772,0.12715,-0.0184,0.01176,0.03284,0.03257,0.05836,-0.05563,-0.05162,0.04182,-0.16357,0.03044]},{"domain":"astronomy","key":"telescope_magnification","name":"Telescope magnification, exit pupil and true field","package":"astronomy-ai999x","example":"Telescope magnification: f_obj = 1200 mm, f_eye = 25 mm, D = 200 mm, afov = 52 deg","v":[0.11278,-0.09285,0.06855,-0.0122,0.06009,0.08315,0.03116,-0.06265,0.01346,-0.15798,0.09119,-0.1013,0.08877,-0.0746,0.01046,-0.03962,0.00378,0.11677,0.12504,0.05137,-0.0663,0.14963,-0.04935,0.02015,0.04778,0.10344,0.04667,-0.03238,0.07017,0.06129,0.02922,-0.06647,-0.00912,-0.01733,0.00286,-0.09219,0.03563,0.01593,0.05915,0.04065,-0.03011,-0.07628,-0.05436,-0.06489,0.06589,-0.0093,0.01974,-0.02276,0.08224,0.0143,0.00654,-0.01341,-0.00124,0.05522,-0.02967,0.00876,-0.00658,-0.14406,-0.01873,-0.10402,0.04339,0.09896,-0.12078,0.03971,-0.05513,-0.01662,-0.0034,-0.02532,-0.04785,0.02582,0.11351,0.09778,0.00032,0.01901,0.00164,-0.07616,-0.03044,0.03271,-0.02516,0.05162,0.01725,-0.11237,0.11699,-0.00066,0.03865,-0.02236,0.0541,-0.09965,0.07,-0.00434,0.02031,-0.05186,-0.02344,-0.02063,-0.08672,-0.02208,-0.05187,0.00951,0.0469,0.00306,-0.00551,0.0511,-0.03881,-0.06505,-0.00549,0.0605,0.00227,-0.02085,0.07483,0.01977,-0.04877,0.04112,-0.02162,-0.01457,-0.02229,0.00137,-0.01956,0.05125,0.09761,-0.07099,0.02711,0.0595,-0.06646,0.01731,0.0939,-0.05663,-0.02507,0.01742,-0.01277,0.00842,-0.03506,-0.056,-0.05301,-0.0059,0.06305,0.00438,-0.10249,0.03549,-0.02641,-0.02066,0.00848,-0.00616,0.01455,-0.00109,0.03874,-0.02157,0.03013,-0.00625,0.07766,0.1102,0.03557,0.1069,-0.17369,-0.05907,-0.0512,0.02483,-0.02331,0.17795,-0.09038,0.01449,0.04629,0.02154,-0.01695,-0.00173,-0.05838,-0.03001,-0.05255,-0.0347,-0.03216,0.07014,0.00386,-0.01432,-0.02089,0.04783,-0.02823,0.04761,-0.05099,0.04547,0.0675,-0.08093,-0.02078,-0.07741,-0.01827,0.00408,-0.12,0.02773,0.02048,-0.03323,-0.02238,-0.05221,0.05332,0.10422,-0.08621,-0.09088,-0.06144,0.0658,-0.02753,-0.07015,-0.12615,0.04088,-0.03691,-0.04613,0.0416,0.03533,0.07423,0.05084,0.05711,0.0466,-0.06293,-0.04948,-0.05988,0.0777,-0.07748,0.0252,-0.08627,-0.10371,-0.01312,0.00213,0.09586,-0.04988,-0.06917,0.02253,-0.11851,0.06262,-0.02862,-0.03588,0.15253,0.0197,-0.00133,-0.03752,0.09956,0.03904,-0.01598,0.0225,-0.02469,-0.0459,0.02019,-0.0301,-0.12494,0.01054,-0.05307,0.15014,0.05745,0.07355,0.03636,0.13849,0.00759,-0.06964,0.08008,-0.17951,0.02061,-0.03784,0.10826,-0.06446,0.02301,0.02718]},{"domain":"astronomy","key":"thermal_speed","name":"Thermal speed of plasma particles","package":"astronomy-ai999x","example":"Thermal speed: T = 1e6 K, convention = rms, particle = proton","v":[-0.09393,-0.09179,0.08938,-0.03183,-0.0351,-0.03336,0.00116,0.01678,-0.04082,0.03436,0.01577,-0.04082,0.03642,-0.04644,0.09391,-0.0097,-0.09323,-0.05749,0.0252,0.02944,0.04059,-0.03479,0.04265,-0.00997,-0.01286,0.05693,-0.03071,-0.02425,0.12417,0.0058,-0.02225,-0.07061,0.0774,0.01474,-0.02637,0.0111,0.02478,-0.04507,-0.06103,-0.04226,0.05053,-0.00324,0.08806,-0.01055,-0.02053,-0.03279,0.08862,-0.03628,-0.01444,-0.01249,-0.0651,-0.03212,0.06135,-0.0254,0.02464,-0.08807,0.01579,0.08421,0.03941,0.03908,0.02197,-0.03372,0.0009,-0.10534,-0.08387,0.08906,-0.04527,-0.00352,-0.05918,0.05877,-0.0649,-0.00073,-0.08232,-0.08177,-0.0101,0.06942,0.07265,0.05539,0.05645,0.00179,0.07038,-0.09689,0.01868,0.10876,-0.12165,-0.08253,0.05874,0.05054,0.01171,-0.03919,0.10406,0.05497,0.02936,-0.00063,-0.01171,-0.00346,0.04051,-0.01687,0.13385,0.01636,0.00438,0.0336,0.05,-0.07235,-0.06524,-0.09133,0.03351,0.07231,0.01043,-0.00642,-0.04034,-0.00893,0.07587,-0.04537,-0.04936,-0.00659,0.03254,-0.05026,-0.07316,-0.10786,0.1178,0.10366,0.01906,0.08075,-0.04548,-0.07912,0.02691,0.00222,-0.05088,-0.01194,0.0028,-0.06774,-0.02835,0.00995,-0.03236,0.01432,0.01275,0.013,-0.08133,-0.09025,-0.01163,0.06744,0.11207,0.04979,-0.09358,-0.02273,-0.04632,0.10056,-0.19146,0.03999,0.10193,0.08564,-0.03651,0.00242,-0.11632,-0.00312,0.08782,-0.01304,-0.12031,-0.03157,-0.0259,0.08087,-0.01753,-0.03801,-0.08613,0.02827,-0.0265,-0.06059,-0.06797,0.0502,-0.03151,0.08215,0.0031,0.06174,0.0238,0.00272,0.0633,0.10118,-0.1143,0.03222,0.16672,-0.00481,0.05748,0.05532,0.00784,-9e-05,-0.03132,-0.03593,-0.0452,0.03796,-0.05346,-0.01782,-0.07676,0.0187,-0.01268,-0.02059,-0.00764,0.04107,0.02049,-0.00883,0.01462,-0.13215,-0.00087,0.03661,0.00497,0.01573,-0.06383,0.15065,0.03167,-0.04969,0.10863,0.1421,0.0589,-0.06147,0.00603,0.01615,-0.14532,0.05247,-0.00613,0.03795,-0.10908,-0.06507,0.08196,-0.09924,0.05953,-0.03395,-0.03287,-0.06398,0.09651,0.00691,0.04059,0.05454,0.10743,-0.00552,0.06685,-0.07433,-0.07585,0.08107,0.05024,-0.02467,-0.00033,0.11534,-0.08422,0.08713,0.01155,0.01513,-0.03258,0.00708,0.06983,-0.02987,0.05598,0.05832,-0.2028,-0.04906,0.00141,-0.08499]},{"domain":"astronomy","key":"time_of_flight","name":"Time of flight between two points of an elliptical orbit","package":"astronomy-ai999x","example":"Time of flight: M = 1.4982e10 kg, a = 1 m, e = 0.5, nu1 = 0 deg, nu2 = 180 deg","v":[0.11035,-0.00091,0.01175,-0.01698,0.07526,-0.04893,0.05851,-0.06312,0.11678,-0.08074,0.14558,-0.04394,0.05137,0.04841,0.04348,0.06575,0.01787,0.04617,0.08554,0.02966,0.02511,0.02127,0.01712,0.06761,0.0577,0.00831,0.01471,0.02852,0.0608,0.00606,0.04333,-0.02711,-0.01886,0.02857,0.1385,-0.00759,-0.00858,0.04277,-0.0346,-0.02873,0.04662,-0.01366,-0.05778,-0.08611,-0.07874,-0.0339,0.03564,-0.07956,0.00543,-0.11197,-0.13614,0.00281,-0.02075,0.1118,0.00179,0.02618,-0.02566,0.1086,-0.06561,-0.09377,-0.04877,0.05337,-0.04218,0.07956,0.02452,0.01107,0.16141,-0.08624,0.04586,-0.02279,-0.07644,-0.14621,0.07878,-0.02384,-0.01046,-0.03194,0.0304,0.01743,-0.11407,-0.02321,-0.03434,-0.07212,0.01343,-0.01431,-0.0059,-0.02873,0.00935,0.02005,0.0371,-0.06108,-0.02109,-0.08023,-0.00474,-0.11689,-0.15446,0.02616,-0.0283,0.02446,-0.10815,0.06588,0.10186,0.08634,0.001,-0.05184,-0.03475,-0.1702,-0.13604,0.05465,-0.0156,-0.05657,0.04029,0.09256,-0.00303,-0.07029,0.07713,-0.05756,0.02163,0.0543,0.03407,0.16892,-0.08212,0.11157,-0.01614,0.07044,-0.01452,-0.04535,0.00592,0.00884,-0.01335,0.05371,-0.03311,-0.05784,0.0034,-0.05476,-0.03569,-0.05506,0.09246,0.12734,0.02309,0.02887,-0.0426,0.0605,0.00141,-0.04997,-0.0998,-0.00828,-0.03714,-0.0523,-0.08427,0.08762,0.03815,-0.04325,-0.00522,-0.03181,-0.15944,0.08964,0.01732,-0.05536,0.11444,-0.04339,0.0006,0.0277,-0.06627,0.09902,-0.00506,0.0703,0.015,0.13847,0.00723,0.06901,-0.00711,-0.01104,0.05565,0.08287,-0.00228,0.04571,-0.11166,0.02393,-0.07183,0.04563,0.10295,-0.05961,0.00753,-0.01902,-0.02616,0.10916,-0.05642,-0.00993,0.04339,-0.05372,0.06303,-0.06643,-0.00113,0.0037,-0.00798,-0.02837,0.06889,-0.02848,-0.01131,-0.00039,0.06503,0.03109,0.04244,0.04156,0.08282,0.02914,0.08055,-0.00305,0.00321,-0.05286,-0.00281,-0.05083,0.11115,0.01487,-0.02185,-0.02515,-0.02981,-0.06473,0.01192,0.00815,0.01755,-0.04453,-0.03339,-0.00608,0.03881,-0.13375,0.07343,-0.06393,0.01833,-0.02407,0.01969,-0.06529,-0.01566,-0.04189,0.05093,0.03046,-0.03843,-0.02695,0.05427,-0.02832,0.04217,-0.13882,0.07944,0.06147,0.05687,-0.03466,-0.06163,-0.11158,0.04809,-0.09624,0.02712,-0.05063,0.06669,0.02063,-0.01671,-0.04776]},{"domain":"astronomy","key":"transit_depth","name":"Transit depth","package":"astronomy-ai999x","example":"Transit depth: Rp = 1 Rjup, Rs = 1 Rsun","v":[0.01558,-0.11503,-0.03771,0.01742,0.07293,0.03791,-0.0375,-0.09749,-0.04532,-0.04897,0.02477,-0.10859,-0.05336,-0.03315,-0.00072,0.02086,0.0534,-0.02648,0.00643,-0.00598,0.08239,0.01147,0.03915,0.02041,0.04489,0.0118,0.06628,0.01335,-0.01163,-0.02007,-0.01656,0.0678,-0.04573,-0.02208,-0.06818,0.08564,-0.05239,0.01339,-0.13498,0.12655,-0.05257,0.00383,0.09598,-0.10968,-0.02687,0.0608,-0.02789,-0.03086,-0.04166,0.04142,-0.0328,0.03225,0.00874,-0.03265,-0.02414,0.08977,-0.00477,-0.07784,0.01682,0.02666,-0.03226,0.01373,-0.03958,-0.03276,-0.04044,0.0095,0.08847,0.05864,0.04297,-0.04237,0.09051,0.01025,0.04938,0.02987,-0.06919,0.07983,-0.14609,0.0589,-0.03466,-0.00055,0.05123,-0.10631,0.00631,-0.01542,0.15479,-0.0705,0.08025,-0.03582,0.00982,0.08266,0.02589,0.02675,0.07523,0.00399,0.02843,0.00123,0.06487,-0.03951,-0.04197,0.01908,0.03281,0.06683,0.03887,0.01341,-0.05317,0.05723,0.02125,0.011,0.11917,-0.0622,0.00206,0.09635,-0.01899,-0.07006,0.01356,-0.02973,0.05043,-0.03505,0.01513,-0.00759,-0.02466,0.0246,-0.07118,0.16923,0.00294,0.07067,-0.02909,-0.00838,-0.0728,0.13283,-0.04295,-0.05785,0.13606,-0.03129,-0.07601,-0.0171,0.02724,0.02065,0.01681,0.08977,-0.08171,0.06411,0.0238,-0.12372,-0.05656,-0.04027,0.07341,-0.08564,-0.08294,0.06976,0.05602,-0.08073,0.01268,-0.04844,-0.05876,0.07073,0.01357,0.0654,-0.08436,-0.04574,0.01719,0.05434,-0.04882,-0.01219,-0.06384,-0.08449,0.014,-0.05432,-0.03165,0.0725,0.01685,0.08654,-0.05726,-0.15502,0.00318,0.06141,-0.04415,0.08027,0.01003,-0.01944,-0.01248,0.05839,0.08974,-0.12387,-0.01187,-0.05026,0.09029,0.11079,0.05522,-0.03051,-0.1337,0.15756,-0.00486,-0.04543,-0.05567,-0.03252,0.03434,0.07727,-0.01673,0.08156,-0.05701,0.12031,-0.03544,-0.08024,0.01058,-0.03494,-0.04782,0.005,-0.18485,0.03648,-0.10681,0.03988,-0.0102,-0.03836,-0.03582,-0.01301,0.0461,0.07013,0.06745,0.05406,0.06962,-0.00605,-0.07933,-0.06881,0.06563,0.00989,0.02316,-0.00171,0.12626,0.03586,-0.06446,0.03629,-0.03097,0.03085,0.05316,-0.05523,-0.11999,-0.02633,-0.05711,0.10731,0.01572,-0.03386,0.09691,-0.12403,-0.0519,0.11381,-0.00842,-0.06271,-0.01822,-0.02739,-0.09563,0.01167,0.01682,0.05993,-0.02373,0.00352]},{"domain":"astronomy","key":"transit_duration","name":"Transit duration","package":"astronomy-ai999x","example":"Transit duration: P = 6.283185307179586 s, a = 2 m, Rs = 0.9 m, Rp = 0.1 m, i = 90 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hybrid frequency","package":"astronomy-ai999x","example":"Upper hybrid frequency: B = 1 T, n = 1e18 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energy from two rate constants","package":"chemistry-ai999x","example":"k1 = 1.0e-3 s^-1 at T1 = 300 K and k2 = 5.0e-3 s^-1 at T2 = 320 K. What is the activation energy?","v":[-0.06702,-0.15119,0.09678,0.04925,-0.06449,-0.06523,-0.06025,-0.0172,0.00243,-0.02251,0.01246,0.04148,0.01608,-0.05678,0.11767,-0.05825,0.04845,0.00336,-0.01958,0.01546,0.08071,0.01592,0.06764,0.00647,0.00633,0.09209,0.11514,0.00121,-0.00309,0.05086,-0.02332,-0.00036,-0.03691,0.04411,0.03009,0.01756,0.03179,0.0863,-0.01288,-0.03948,0.02206,-0.00237,-0.08782,0.0013,-0.07529,-0.00328,-0.026,0.06784,0.0488,0.02888,-0.00944,0.06748,0.02834,0.07689,0.00129,-0.05327,0.09042,0.07725,-0.04691,0.12182,-0.02209,0.01348,-0.04616,0.00789,-0.06971,0.08328,-0.02793,0.07609,-0.092,-0.02434,0.03551,-0.02771,0.01885,-0.18279,0.01822,0.03157,-0.02922,0.05434,0.03768,-0.10009,0.01602,-0.03864,-0.04475,0.12986,-0.08996,0.04409,0.00115,0.04503,-0.07122,-0.01174,-0.01483,0.00855,0.09637,-0.04417,-0.10135,-0.05432,-0.04675,-0.0759,0.09053,-0.0203,0.00224,0.09434,-0.02925,0.17392,-0.07774,0.00196,-0.03824,-0.00142,-0.03109,0.02514,0.11558,-0.06432,0.00796,-0.04346,0.00153,-0.06382,-0.0213,0.00518,0.01086,0.09914,-0.0065,-0.03343,0.04492,-0.08091,0.00976,-0.04888,-0.0055,-0.00387,-0.0923,-0.02261,0.03659,-0.08685,-0.02459,-0.02145,0.04881,-0.12762,-0.05849,-0.0118,0.03623,-0.01429,-0.04348,0.13466,0.07098,0.14428,-0.02689,0.08315,-0.0945,0.01492,0.04864,-0.04182,-0.07999,-0.00157,0.03047,-0.05478,0.04098,0.02613,0.08021,-0.03734,0.06895,-0.0841,-0.02169,-0.12898,-0.04484,0.02613,-0.06048,0.11539,-0.16008,0.00937,-0.02041,0.04172,0.08468,0.02399,0.06455,0.02846,-0.03469,-0.04958,0.02647,0.07269,0.01791,-0.02753,-0.01023,-0.1171,-0.10958,-0.03643,-0.12052,0.07967,-0.10053,-0.08644,-0.06365,0.11684,-0.03398,0.07966,0.00233,0.08911,-0.0152,-0.03434,-0.06065,0.09744,0.07744,-0.03343,0.03011,-0.03995,0.02255,-0.03828,-0.02665,0.00303,0.00954,-0.00038,-0.03058,-0.02567,0.06172,0.0302,-0.13682,0.05702,0.00205,0.05409,-0.06222,-0.04262,-0.00078,0.01221,-0.04881,0.01382,0.0961,0.02948,-0.09524,0.07218,0.05589,-0.01381,-0.00059,0.01091,0.11934,-0.01866,-0.01582,-0.04184,0.00731,0.04392,0.11687,0.04965,-0.07701,-0.02103,-0.08294,-0.00213,0.06199,0.03713,-0.0541,0.04069,-0.01822,-0.06559,0.12061,0.00771,-0.06382,0.16357,-0.10303,0.02493,0.05063,-0.04157]},{"domain":"chemistry","key":"arrhenius_k2","name":"Arrhenius equation: rate constant at another temperature","package":"chemistry-ai999x","example":"A reaction has k = 1.2e-3 s^-1 at 300 K and Ea = 75.0 kJ/mol. What is k at 350 K?","v":[-0.03871,-0.14693,0.06586,0.07724,-0.06408,-0.08358,-0.04894,0.01994,0.0298,-0.00359,0.03195,0.00918,0.05895,-0.02374,0.14852,-0.03294,0.02501,-0.04213,0.02517,0.04738,0.0871,-0.01972,0.09815,-0.03521,0.00413,0.06779,0.06782,-0.05394,0.01067,-0.00136,0.04595,0.04535,-0.00628,0.02145,0.01482,0.0283,0.07434,0.09596,-0.01779,-0.00614,0.05031,-0.03222,-0.0851,0.0158,-0.08936,0.01644,-0.00194,0.05788,0.06729,0.04026,-0.01552,0.10245,0.0213,0.02276,0.06464,-0.06733,0.07823,0.06875,-0.06664,0.0958,-0.02953,-0.04842,-0.00229,0.00977,-0.05912,0.05402,-0.00613,0.08017,-0.09519,-0.00768,0.05591,-0.01786,0.02791,-0.15175,-0.01636,0.03867,-0.00416,0.00838,0.03969,-0.08409,0.04436,-0.07107,-0.06612,0.08275,-0.06844,0.0396,0.00546,0.06253,-0.09286,-0.0102,0.03051,0.02187,0.09842,-0.05903,-0.0882,-0.02209,-0.10096,-0.06137,0.12074,-0.04901,0.01867,0.08711,0.0081,0.1679,-0.10109,0.02407,0.04679,-0.0034,0.00617,0.02209,0.08406,-0.0768,0.02269,-0.04513,-0.00074,-0.03005,-0.04188,0.03685,-0.00111,0.0541,-0.03991,-0.0832,0.06605,-0.05582,0.05585,-0.07517,-0.00485,-0.01227,-0.11956,-0.03539,0.03337,-0.08382,-0.02551,-0.03016,0.0237,-0.13689,-0.04374,-0.00869,0.00721,-0.03408,-0.02756,0.15893,0.08692,0.13195,-0.01421,0.08153,-0.11558,-0.02064,0.0284,-0.0388,-0.05861,-0.03353,0.00764,-0.05177,0.07323,-0.05084,0.04177,-0.01185,0.06314,-0.11364,0.03503,-0.14689,-0.03623,-0.01302,-0.03757,0.08946,-0.15341,-0.02803,0.01761,0.04319,0.04733,0.01974,0.02784,0.0403,-0.02384,0.00618,0.0253,0.05551,0.03172,-0.01421,-0.00335,-0.11457,-0.06863,0.00151,-0.11668,0.0001,-0.12397,-0.08258,-0.10121,0.08435,-0.02084,0.10137,-0.00305,0.01439,-0.01022,-0.01954,-0.0235,0.10102,0.04978,-0.05427,0.04659,-0.07559,0.01121,0.00198,0.01986,-0.00432,0.00684,0.00944,-0.01621,-0.00319,0.02787,0.05746,-0.13566,0.07211,0.03304,0.06795,-0.02513,-0.01848,-0.05597,0.01789,-0.09877,-0.02217,0.09791,0.03761,-0.06025,0.05865,0.0201,-0.05065,0.02741,-0.00917,0.0887,-0.02057,-0.02305,-0.05339,-0.00672,0.06076,0.11318,0.03321,-0.11833,0.01288,-0.08642,-0.00805,0.02942,0.04751,-0.03077,0.06278,-0.00081,-0.08768,0.07554,0.05208,-0.08394,0.19087,-0.11239,0.04326,0.06168,-0.02792]},{"domain":"chemistry","key":"arrhenius_rate_constant","name":"Arrhenius equation: rate constant","package":"chemistry-ai999x","example":"A reaction has a pre-exponential factor of 1.0e13 s^-1 and Ea = 100 kJ/mol. What is the rate constant at 500 K?","v":[-0.01381,-0.10288,0.01481,0.07002,0.01139,-0.04678,-0.10542,0.02678,-0.03144,0.02569,0.0281,-0.00502,0.05211,-0.03594,0.1473,-0.00317,0.05156,-0.02659,0.027,0.11263,0.05821,0.0055,0.07108,0.02688,0.02186,0.07525,0.0568,-0.08076,0.0264,0.0717,0.02686,0.02153,-0.01729,0.03595,-0.02799,0.03837,0.06316,0.08043,-0.06973,0.02597,0.00215,-0.0318,-0.06256,-0.01507,0.00267,0.0007,-0.00906,0.04169,0.0008,-0.03439,0.03853,0.02209,0.00482,0.05454,0.07854,-0.0073,0.0511,0.06295,-0.10942,0.09066,-0.01451,-0.02541,-0.01314,0.03592,-0.0548,0.01645,-0.06827,0.05746,-0.14907,-0.02522,0.07255,-0.03067,-0.01556,-0.13205,-0.04173,0.03363,0.04313,-0.04213,0.03123,-0.09075,0.01663,-0.02976,-0.06084,-0.00997,-0.04601,-0.03265,-0.04975,0.04342,0.03941,-0.05019,-0.03987,0.05929,0.04528,-0.09837,-0.08484,0.01879,-0.11182,-0.07652,0.14175,-0.11352,-0.00165,0.11495,0.045,0.11533,-0.02496,0.04835,0.05568,-0.0992,0.09887,0.03473,0.14062,0.04397,0.02581,-0.04628,0.06933,-0.04698,-0.11939,0.01512,0.03975,-0.012,-0.02721,-0.0377,-0.02742,-0.07257,0.01924,-0.08291,-0.05987,0.01742,-0.14072,-0.05811,0.02234,-0.0517,0.07641,-0.07485,0.05222,-0.03318,-0.06118,-0.0541,0.04275,-0.00743,0.06935,0.11016,0.07549,0.18895,-0.07123,0.07933,-0.02674,-0.00131,-0.02892,0.00077,0.03451,0.01723,0.07318,0.01326,-0.01061,0.00383,0.01318,0.03964,0.08175,-0.05387,-0.02473,-0.12572,0.01707,0.04466,-0.01711,0.09141,-0.07421,0.04982,-0.08914,0.05895,-0.01157,0.09868,0.05469,0.18867,-0.05528,0.03142,0.00665,0.09627,-0.00022,0.06584,-0.04407,-0.08842,-0.10143,-0.00595,-0.08668,0.02085,-0.06827,-0.0901,-0.12323,-0.00396,0.06753,-0.05234,-0.04266,-0.07741,-0.01311,-0.02792,-0.07061,0.10872,-0.01827,0.06517,0.03054,-0.07579,0.0721,0.04504,0.04803,0.0014,0.02977,0.04704,0.06923,0.01733,0.02088,0.03573,-0.08293,0.01518,-0.02429,-0.00916,-0.00909,-0.0557,0.02041,0.06671,-0.08203,-0.04404,0.04147,0.02441,-0.05996,-0.06647,0.06042,0.00163,0.03461,-0.08186,0.06135,-0.04272,0.02319,0.08923,-0.0344,0.033,0.08533,-0.03695,-0.12263,-0.00126,-0.11852,0.0299,0.02971,-0.07315,-0.03836,0.03787,0.01404,-0.09653,0.05642,0.08789,0.00664,0.08705,-0.05766,0.02482,0.06641,-0.12968]},{"domain":"chemistry","key":"atoms_of_element","name":"Atoms of an element in a mass of compound","package":"chemistry-ai999x","example":"How many atoms of oxygen are in 10.0 g of CO2?","v":[-0.04697,0.04734,0.04328,-0.05274,0.06451,-0.02364,0.02201,-0.06058,-0.01019,0.03937,0.02338,-0.03929,0.05456,0.00674,0.0062,-0.01171,-0.07776,0.05234,0.07598,0.09644,0.02091,-0.06002,0.05983,-0.00454,-0.07009,-0.00288,0.04968,-0.11162,-0.05267,0.07549,-0.06501,-0.01779,-0.00159,-0.03243,0.06147,-0.10846,0.06869,-0.05672,0.01065,-0.18788,0.03249,0.06418,-0.06268,0.06287,0.02482,0.07118,-0.15082,0.07895,-0.03717,0.06899,0.01814,0.04857,0.00419,0.06243,0.06974,-0.02631,-0.02037,-0.02614,0.01778,-0.08735,-0.06157,-0.03981,-0.03769,0.0423,0.12047,0.08211,0.07162,0.00257,0.0889,0.01556,-0.02218,-0.10644,0.02525,0.02866,0.03075,0.05697,-0.03757,-0.05267,0.07768,0.08167,0.0812,-0.13683,0.12219,-0.00139,-0.01327,0.06541,0.05809,-0.07345,0.06537,-0.01113,0.06712,-0.10976,0.01038,0.0112,-0.01065,-0.02156,-0.09485,-0.05399,-0.00902,0.01568,0.03844,-0.08128,-0.03923,-0.17092,0.00348,0.02179,0.00562,-0.07565,0.00771,-0.14323,-0.06646,0.00254,0.09179,-0.05186,-0.08113,-0.01649,0.01034,0.03689,-0.034,0.01842,-0.06166,0.01515,0.02979,-0.04631,0.07458,0.17596,0.01207,0.05344,0.06113,0.01568,-0.02578,0.15854,-0.03048,0.06119,0.01518,0.01794,-0.03678,-0.01347,0.05767,0.02609,-0.0319,0.06002,0.07054,-0.05241,-0.04865,-0.08754,0.05462,0.00282,-0.05853,0.06817,-0.04242,0.03364,-0.08816,-0.10671,-0.00655,-0.02768,0.02554,0.01993,0.05576,0.02481,0.02218,0.03235,0.01805,-9e-05,-0.05875,0.03487,0.15062,-0.0361,-0.02238,-0.09872,-0.07547,-0.07287,-0.07156,0.03699,-0.00169,0.0566,0.0105,-0.0164,-0.11349,0.02467,-0.00501,0.20042,-0.03462,0.07908,-0.09106,-0.01313,0.00059,-0.05434,-0.05513,-0.01258,-0.08457,0.02036,-0.03611,-0.03395,-0.08077,-0.0214,0.03753,0.06455,-0.14755,-0.00766,0.02447,0.01338,-0.04208,-0.00456,-0.03339,-0.03478,0.03649,-0.01992,-0.05615,0.0123,-0.05094,-0.07089,0.04252,0.03361,0.03831,-0.06198,0.01437,0.08263,0.04401,0.02787,0.03501,0.01242,-0.10222,-0.04086,0.04979,0.12207,0.05053,-0.0074,-0.03892,0.05063,0.03571,0.10178,-0.02426,-0.01533,0.00709,-0.12304,-0.05024,0.0062,-0.06,-0.15865,-0.00062,-0.07487,-0.09911,-0.00179,0.04406,0.01238,0.0635,-0.04149,0.04602,0.04202,-0.0783,0.10008,0.07729,0.0818,-0.00418,0.03761]},{"domain":"chemistry","key":"balance_equation","name":"Balancing a chemical equation","package":"chemistry-ai999x","example":"Balance the equation C3H8 + O2 -> CO2 + H2O.","v":[0.06537,0.08912,-0.05929,0.16333,0.11394,0.00509,-0.01018,0.00389,-0.03235,0.04119,0.06189,-0.02496,-0.16017,-0.06387,0.00503,-0.02382,0.06707,0.06451,0.13896,-0.05313,-0.11775,-0.02536,0.0671,-0.01217,-0.03569,0.02469,0.02811,-0.01417,-0.08145,0.10057,-0.00226,-0.04126,0.03043,0.05742,-0.04976,-0.0207,0.10094,0.00377,-0.00578,-0.09637,0.00662,-0.04066,0.01342,-0.05742,-0.00305,0.00853,-0.06828,-0.019,-0.06996,0.08681,0.15758,0.12292,-0.08207,0.00852,0.04082,-0.0014,-0.12703,-0.05073,-0.0027,0.02328,0.04588,0.02462,-0.01538,0.06301,0.03187,0.01402,-0.02365,-0.18551,0.1077,-0.06031,-0.05455,-0.03438,-0.0866,0.07929,-0.01234,-0.04268,0.01153,0.0213,0.12018,0.00948,-0.01272,-0.06388,0.01946,0.05298,0.01768,0.14154,0.05562,0.02699,0.05489,0.11481,0.00122,-0.08546,0.02027,-0.00752,-0.08222,-0.01115,-0.06849,-0.04702,-0.04823,0.01236,-0.05667,0.02586,0.04041,-0.06491,0.01536,-0.06516,-0.07232,0.00753,-0.01072,-0.08856,-0.01202,-0.00797,0.08705,-0.05869,0.05151,0.00616,0.05411,0.0212,-0.03794,0.05399,-0.01598,0.06086,0.11569,-0.03462,-0.01573,0.15209,0.03932,0.04307,0.00941,-0.06531,-0.03296,0.06376,-0.00517,-0.03981,-0.09401,-0.03988,-0.13431,0.00272,-0.06183,0.08771,-0.01866,0.02502,0.03442,-0.00141,-0.03478,0.06949,-0.00985,0.0994,0.02867,0.0243,0.07057,0.06431,-0.12916,-0.02377,-0.0098,-0.02157,-0.02942,-0.01325,-0.03718,0.03443,0.0078,0.06351,-0.00312,0.0662,0.00668,0.03061,0.02433,0.0766,-0.08329,0.0844,-0.01932,0.14889,-0.0535,0.04455,-0.02713,-0.08455,-0.03528,-0.02955,-0.05455,-0.00372,0.0266,-0.0343,-0.06905,0.11433,-0.16828,0.02133,0.00598,0.0127,0.0202,0.06826,-0.01404,-0.02286,-0.00554,-0.02146,-0.05905,-0.08932,-0.01489,0.01052,-0.11548,-0.06308,0.07089,-0.05515,0.00733,0.0425,-0.07271,-0.00724,-0.06853,0.01321,0.05179,-0.02858,0.04912,-0.02256,0.0156,0.00498,0.01462,0.00636,0.05001,0.06073,-0.08576,0.06981,0.05415,0.01606,-0.13484,0.02673,-0.00177,0.01855,-0.02633,0.05024,0.05405,0.10662,0.0119,-0.02972,0.05171,-0.05027,-0.01744,-0.10275,-0.16255,0.08245,-0.04018,-0.14544,0.03965,-0.02894,-0.0387,0.01678,0.01696,0.02373,-0.00743,-0.08337,-0.05733,0.11733,0.00873,0.06446,0.00262,0.07489,-0.0215,0.07336]},{"domain":"chemistry","key":"beer_lambert_absorbance","name":"Beer-Lambert law: absorbance","package":"chemistry-ai999x","example":"A 1.00 cm cell holds a 2.0e-5 M solution with molar absorptivity 15000 L/(mol·cm). What is the absorbance?","v":[0.04981,0.09947,0.00371,0.01747,0.09068,0.04691,0.04128,0.05547,0.05006,0.02278,0.0282,-0.06717,0.06669,0.00769,-0.00458,0.02403,0.07927,-0.04883,0.0964,-0.04284,-0.05048,-0.03058,-0.1823,0.00976,0.00571,0.06132,0.02951,0.03302,-0.01749,0.10682,0.10198,0.01455,0.02373,0.06797,-0.02487,-0.00591,0.02098,-0.00794,0.09696,0.0475,-0.02657,0.0386,0.09881,0.05801,0.02904,-0.00334,-0.05492,-0.03697,0.04615,-0.03211,0.03337,-0.02908,0.0864,-0.04254,-0.0478,0.0058,0.0231,-0.02198,-0.01097,0.07632,0.06722,-0.06246,0.10022,0.00214,-0.09199,-0.09475,-0.14006,0.01607,-0.0313,0.00022,0.03909,0.05571,0.09032,-0.08541,0.10919,-0.01184,0.12398,-0.11761,0.01845,0.05915,-0.02422,0.05472,0.02397,0.0433,0.11344,0.02723,-0.00639,-0.14395,0.03607,0.01419,0.05193,0.05262,-0.07003,0.03518,0.00732,0.07073,-0.08205,-0.01575,0.05466,0.04922,0.05648,0.02383,0.04837,-0.08245,-0.04575,0.10041,-0.14611,-0.06489,0.0671,-0.01787,-0.0147,0.02438,-0.01184,-0.09025,-0.0573,-0.03031,-0.0804,-0.00811,-0.00023,0.09742,0.03288,-0.05479,-0.08644,0.03167,-0.00423,0.02384,0.07688,0.03071,-0.04794,0.02127,0.03968,0.02618,-0.00128,-0.04326,0.01548,-0.00168,-0.0608,-0.0854,0.00074,0.0994,-0.01703,0.02557,0.07898,-0.01624,-0.0125,-0.11351,-0.02798,-0.11064,-0.0538,-0.06732,-0.03213,0.0829,-0.04977,-0.07656,-0.06111,0.01131,-0.01696,-0.01214,0.06659,-0.15245,-0.06629,-0.00269,-0.04751,0.00182,-0.00745,-0.00681,-0.01775,-0.01698,-0.12167,-0.10574,0.02531,-0.12319,-0.02491,0.00973,0.07329,-0.1342,-0.06908,-0.09455,0.10085,-0.03636,0.09575,0.03913,0.01454,-0.01587,-0.10773,0.17752,0.09302,0.08572,-0.08054,-0.02423,0.01553,0.076,-0.0267,-0.09526,-0.0297,-0.07044,-0.08667,-0.00031,-0.02326,0.08455,0.05811,-0.02142,0.06213,0.04459,-0.00063,0.01871,0.11354,-0.04958,-0.11473,0.04846,-0.11617,-0.05607,-0.01067,0.02742,-0.01626,-0.0086,0.06219,0.0455,-0.03306,-0.03521,-0.02037,-0.0376,-0.02778,0.02991,-0.0421,0.08326,0.05758,0.05854,0.01163,0.00874,0.03741,0.07877,0.02208,-0.0021,0.01079,0.02962,-0.02201,-0.09681,0.08862,-0.03711,-0.09542,0.08681,-0.01655,-0.04405,0.0026,-0.02717,0.12539,0.02407,0.00668,-0.08981,0.03375,-0.01864,0.06305,-0.04173,-0.0382,-0.13126]},{"domain":"chemistry","key":"beer_lambert_concentration","name":"Beer-Lambert law: concentration","package":"chemistry-ai999x","example":"A solution has an absorbance of 0.450 in a 1.00 cm cell; ε = 1.25e4 L/(mol·cm). What is its concentration?","v":[-2e-05,0.13325,-0.00467,-0.07084,0.11077,0.00748,0.01472,0.12647,0.03862,0.04075,0.01463,-0.09404,0.04381,0.06876,-0.02697,0.05878,0.00998,-0.01709,0.06484,-0.07044,-0.04163,0.02681,-0.17407,-0.02343,0.05248,0.06071,-0.00065,0.04435,-0.00444,0.09112,0.10086,-0.01473,0.02426,0.04427,0.03506,0.01118,-0.00125,0.00754,0.12112,0.06484,0.01113,0.0536,0.10631,-0.00686,0.07665,0.02066,0.02108,-0.02148,-0.01737,-0.12234,0.02363,-0.00517,0.06174,-0.12469,-0.10889,0.04405,-0.00204,0.01273,-0.06083,0.03257,0.09398,-0.03542,0.10044,0.03631,-0.0748,-0.0655,-0.10197,-0.03002,-0.04184,-0.0172,0.0115,0.04959,0.03969,-0.07558,0.14721,0.02256,0.14289,-0.14925,0.01207,-0.00041,-0.04451,0.09476,-0.0283,-0.01831,0.13991,0.0264,0.00239,-0.12211,0.04594,-0.03093,0.07404,0.03205,-0.06847,0.05776,-0.01267,0.10232,-0.10353,-0.01906,0.0798,0.02005,0.06771,0.07189,0.0928,-0.06395,-0.03146,0.02073,-0.14079,-0.02987,0.06879,0.01785,0.02639,-0.00773,-0.01186,-0.06947,0.00662,-0.00986,-0.08614,0.02693,0.01043,0.10397,0.06495,-0.05034,-0.03514,0.06968,0.00143,0.03171,0.04913,0.00247,-0.02838,-0.06359,0.05416,0.05697,0.05642,-0.09584,0.03537,0.0348,-0.07171,0.01118,-0.05715,0.0168,0.06769,0.04105,0.0732,-0.03564,-0.02147,-0.11941,-0.0302,-0.06404,-0.07464,-0.04597,-0.03558,0.08788,-0.04818,-0.06079,-0.00542,-0.02733,0.0056,-0.04565,0.06809,-0.10523,-0.04714,-0.01751,-0.04272,-0.00245,0.01824,0.0409,-0.02263,0.02108,-0.10419,-0.13342,-0.01523,-0.08354,-0.05084,0.04305,0.01487,-0.17426,-0.04933,-0.08099,0.13084,-0.0404,0.13276,-0.01375,-0.0046,-0.0158,-0.02729,0.16105,0.07652,0.09065,-0.05376,-0.00023,0.05988,-0.01286,0.016,-0.10449,0.01312,-0.09338,-0.09808,-0.07678,0.01179,0.03841,0.03266,-0.0423,0.06871,-0.01,-0.00083,0.03653,0.10728,-0.0019,-0.00914,0.05356,-0.08042,-0.05441,0.01521,0.02535,0.00406,0.02626,0.04701,0.01041,-0.02534,-0.02443,-0.07414,-0.03831,0.00848,0.07592,0.00589,0.04295,0.04502,0.04824,0.02041,-0.002,-0.03426,0.08353,0.03922,-0.06091,0.00328,-0.00334,-0.02806,-0.07967,0.0423,0.00568,-0.0906,0.07184,0.01679,-0.06475,-0.0257,-0.01118,0.06462,0.04251,-0.02634,-0.06529,0.01942,-0.11128,0.05238,-0.06008,-0.01582,-0.08639]},{"domain":"chemistry","key":"boiling_point_elevation","name":"Boiling-point elevation","package":"chemistry-ai999x","example":"What is the boiling point change of a 0.50 mol/kg aqueous solution of a nonelectrolyte (Kb = 0.512 K·kg/mol)?","v":[0.07627,-0.02272,-0.01936,0.01387,-0.04857,0.00877,0.03264,0.06205,0.0564,-0.06579,0.10763,-0.02827,-0.03938,-0.04409,0.03903,-0.08163,-0.0425,0.06087,0.02965,0.12815,0.10019,-0.05242,-0.22963,-0.03901,-0.00084,-0.05376,0.11169,0.04117,0.07214,0.04543,-0.02583,0.0008,-0.08386,-0.0908,-0.04044,0.06909,0.06035,-0.0265,0.01456,0.01691,0.02406,0.11235,0.07004,-0.00162,0.05468,-0.0264,0.09715,-0.1344,0.00832,0.04594,0.0204,-0.03416,0.06406,0.03652,0.05646,0.00173,-0.10638,-0.0221,0.00917,-0.02927,0.01327,0.07712,0.0042,-0.04644,-0.04936,0.06253,0.00788,0.02615,0.07025,0.03104,0.00901,0.02642,-0.04979,-0.02434,0.02985,0.07434,0.0286,-0.16441,-0.05566,-0.00674,-0.09321,-0.05298,-0.04276,-0.08946,-0.02204,-0.02743,-0.04692,-0.05767,0.06318,0.09953,-0.01195,0.02041,0.05788,0.0054,-0.05936,-0.03307,-0.10308,-0.10622,0.0482,-0.08009,0.04704,0.02284,0.0086,0.0324,-0.03725,0.08429,0.05496,-0.02321,-0.01049,0.02489,0.16659,0.057,-0.01015,-0.03693,0.02991,-0.05606,0.01933,0.11102,-0.01807,0.01071,0.04363,-0.03163,-0.06093,-0.04066,0.02883,0.05744,0.00532,0.01681,0.04613,-0.05457,0.00268,-0.04715,-0.09029,0.04875,0.03185,0.02065,0.088,0.05956,-0.08703,-0.02839,-0.09548,0.19281,-0.06015,0.21375,-0.02263,-0.08518,-0.04329,0.06676,0.04159,0.0421,-0.01781,-0.08573,-0.00795,0.00088,0.02543,-0.08175,0.01822,-0.07751,0.00476,-0.13136,-0.11431,-0.11402,0.05541,0.07935,0.06162,-0.03796,-0.08342,0.02589,-0.00968,-0.02066,0.02239,0.00429,0.01856,0.05077,0.04746,-0.03539,-0.11771,-0.01613,-0.05259,0.10833,-0.01217,-0.02147,-0.01995,-0.07834,-0.02893,-0.0748,0.04509,-0.05482,-0.02953,-0.05703,-0.07774,0.011,-0.03298,-0.05892,0.0812,0.02736,-0.09304,-0.02158,0.11357,0.02436,-0.01096,0.01258,0.12628,0.03774,0.01601,0.03699,0.04519,0.0613,-0.02585,-0.00895,-0.02776,-0.01973,-0.12494,0.08296,0.0242,0.06501,-0.06065,-0.00851,0.02289,0.00056,-0.14319,-0.00375,0.07038,0.0102,-0.02135,0.08066,0.04264,-0.05862,-0.03355,-0.00821,0.0045,-0.06108,-0.00752,-0.02474,-0.02304,0.14035,-0.10527,-0.01839,-0.05934,-0.00804,-0.02384,-0.01181,-0.00423,-0.0136,0.05037,-0.06701,0.06289,-0.00838,-0.02625,-0.0806,-0.00823,0.07349,0.04768,0.01434,0.10712,-0.0346]},{"domain":"chemistry","key":"boyle_final_pressure","name":"Boyle's law: final pressure","package":"chemistry-ai999x","example":"A gas at 1.00 atm occupies 4.00 L. What is the new pressure if it is compressed to 1.00 L at constant temperature?","v":[-0.04047,-0.03223,-0.10082,-0.15475,0.0206,0.09488,-0.03825,0.00608,0.00469,0.08323,-0.03132,0.04264,0.05155,0.02026,0.04465,0.04789,0.11266,0.11016,0.09178,0.116,-0.01401,0.01804,-0.01507,0.11657,0.02846,-0.03058,-0.01463,0.05237,-0.02461,0.02693,0.07153,0.02583,-0.01139,0.01984,-0.01369,0.10001,0.03763,0.02204,-0.02698,0.12096,0.0746,0.00087,-0.0172,-0.08725,-0.01159,-0.01687,0.05432,-0.0889,-0.04365,-0.10754,0.11934,-0.07689,-0.0101,-0.05234,-0.00143,0.01624,0.08435,-0.00309,0.04743,0.07443,0.06223,0.01735,-0.12958,-0.02139,-0.05541,-0.01423,0.03333,-0.07924,0.03294,-0.00111,-0.0122,-0.09165,-0.04437,0.01644,-0.06179,-0.03324,0.06307,-0.01751,-0.04107,0.00589,-0.01792,-0.00684,0.1121,-0.02409,-0.05893,0.01792,-0.01762,0.00684,0.10751,0.00702,0.09115,0.00749,-0.06937,-0.01791,-0.01191,0.11329,0.06548,-0.0041,0.13392,-0.03581,0.06449,0.04584,0.02144,0.00858,-0.0792,-0.01399,-0.02572,-0.03969,0.07558,0.09119,-0.01588,-0.03034,-0.02991,-0.03083,-0.09081,-0.03055,0.07763,0.06362,0.04678,-0.14979,-0.07088,0.05913,0.02415,0.00157,-0.09887,0.05143,0.03874,-0.0294,0.08863,0.00255,-0.01021,-0.02715,0.07247,-0.02461,-0.06867,-0.13479,-0.02402,0.06441,0.0805,-0.07491,-0.06576,0.10927,-0.01485,0.01218,0.13988,0.02305,0.04779,-0.01076,0.01779,0.0397,-0.02282,0.02601,0.01029,0.02348,0.09138,-0.0382,-0.02974,-0.02415,0.04709,-0.09116,-0.09817,0.01382,0.12763,0.01996,0.00483,-0.02809,0.06991,-0.0387,-0.04588,-0.12572,-0.11155,0.05785,-0.06684,0.02786,0.09016,0.01624,-0.11882,-0.02338,0.07901,-0.03335,-0.06553,0.03105,0.11328,0.01705,-0.0538,-0.1052,-0.0043,-0.08979,-0.07471,-0.03461,-0.10077,0.06609,0.00043,-0.01202,0.11364,-0.00892,-0.05617,-0.15721,-0.12731,-0.05294,0.00109,0.0202,-0.02941,-0.07909,0.10659,-0.02805,-0.0889,-0.00096,0.09632,0.01128,0.05311,-0.10519,0.00047,-0.07358,0.00693,-0.05085,0.12663,0.03965,-0.10477,0.00251,0.00547,0.02648,-0.05422,-0.00619,0.03271,-0.01494,0.04261,0.00118,-0.00335,0.03143,-0.00286,-0.07124,-0.00236,0.00163,-0.0396,0.00189,-0.01863,-0.02802,0.04063,-0.00912,0.05187,-0.0903,0.08266,0.04968,0.03608,-0.0831,-0.01397,-0.02641,-0.0895,-0.04432,0.03047,-0.00998,-0.13029,0.08796,0.07801,0.06177]},{"domain":"chemistry","key":"boyle_final_volume","name":"Boyle's law: final volume","package":"chemistry-ai999x","example":"A gas occupies 2.00 L at 1.00 atm. What is its volume when compressed to 3.00 atm at constant temperature?","v":[-0.03871,-0.0407,-0.10441,-0.13356,0.01576,0.07475,-0.04341,0.0233,0.00963,0.06805,-0.0175,0.03421,0.02933,0.00877,0.05397,0.05634,0.10236,0.11766,0.08086,0.11604,-0.00934,0.03568,-0.02448,0.11029,0.02199,-0.05661,-0.00209,0.05255,-0.03429,0.02779,0.0643,-0.00079,-0.02812,0.02693,0.00177,0.06917,0.02798,0.02147,-0.00912,0.13011,0.05679,-0.00911,0.00188,-0.1035,-0.01377,-0.02854,0.0642,-0.0801,-0.06326,-0.12218,0.14008,-0.0777,-0.04222,-0.04857,0.01532,0.03472,0.07472,-0.00478,0.04767,0.08046,0.06164,0.03483,-0.1271,-0.00123,-0.05426,-0.04019,0.06247,-0.09429,0.04118,0.02897,0.01768,-0.08929,-0.05258,0.01425,-0.06418,-0.02272,0.04009,-0.0263,-0.0072,0.00298,-0.03287,-0.02001,0.07969,-0.0388,-0.05697,0.04793,-0.0057,0.00921,0.10897,0.00568,0.09595,-0.0128,-0.06261,-0.02398,-0.03583,0.11134,0.06555,-0.01219,0.14447,-0.03697,0.05338,0.0504,0.04174,0.0157,-0.09492,-0.01594,-0.03437,-0.02541,0.06266,0.09973,0.00702,-0.03548,-0.02972,-0.00276,-0.11685,-0.03683,0.05825,0.04542,0.03057,-0.1479,-0.07727,0.04547,0.00927,-0.00553,-0.10094,0.06436,0.05025,-0.02406,0.10058,0.00677,0.00522,-0.04445,0.05802,-0.00943,-0.07818,-0.11315,-0.02057,0.06232,0.08429,-0.063,-0.04652,0.11869,-0.01058,-0.00146,0.1436,0.00724,0.0128,-0.03398,0.0085,0.05188,-0.03646,0.02913,0.02433,0.00871,0.08444,-0.00214,-0.03094,-0.03372,0.06058,-0.08292,-0.08977,0.00267,0.13795,0.00904,0.00266,-0.01892,0.04709,-0.03515,-0.04588,-0.13774,-0.13444,0.09192,-0.08654,0.02343,0.08157,0.01739,-0.11615,-0.03057,0.05852,-0.03265,-0.05654,0.04303,0.1193,0.03241,-0.03788,-0.09662,0.00992,-0.09762,-0.04185,-0.01016,-0.09374,0.05668,-0.01077,0.00761,0.12194,-0.01548,-0.0529,-0.15796,-0.11604,-0.04428,0.01336,-0.00444,-0.00042,-0.07469,0.08169,-0.04457,-0.10096,-0.0134,0.10428,0.00166,0.03062,-0.13077,0.01494,-0.09648,0.00901,-0.05159,0.1102,0.03294,-0.0796,-0.01692,0.01682,0.02055,-0.05847,-0.03378,0.01762,-0.0041,0.04511,0.0295,-0.00276,0.03684,-0.00313,-0.05495,-0.00684,0.00071,-0.0222,-0.01042,-0.01413,-0.03009,0.05793,-0.00768,0.07349,-0.07769,0.09158,0.06575,0.04803,-0.07365,-0.01643,-0.02427,-0.08736,-0.04099,0.04463,-0.03205,-0.12752,0.07117,0.06343,0.0601]},{"domain":"chemistry","key":"buffer_ph","name":"Buffer pH (Henderson-Hasselbalch)","package":"chemistry-ai999x","example":"What is the pH of a buffer that is 0.10 M acetic acid and 0.15 M sodium acetate (pKa = 4.76)?","v":[0.05689,0.05806,-0.04337,-0.00404,0.04784,-0.06767,0.08733,-0.00857,-0.05615,-0.00437,0.02592,0.02963,0.00647,-0.01222,-0.04573,0.01237,-0.09369,-0.1095,0.13739,-0.04976,0.08938,0.01563,-0.02443,-0.08149,0.03787,0.06187,0.07052,0.03082,0.1066,-0.00731,-0.01597,-0.10015,0.0497,-0.01746,-0.09039,-0.00535,-0.0018,0.03505,-0.03606,-0.10562,-0.01134,-0.02324,-0.13846,-0.10883,0.05587,0.00184,0.01222,-0.02151,-0.03722,0.01182,0.04067,-0.00475,0.11634,-0.02165,-0.08299,-0.09098,-0.03736,-0.03311,-0.08811,-0.01418,0.01767,-0.07052,-0.02957,0.04765,0.01095,0.03043,-0.0729,0.02858,-0.06873,-0.04256,0.06678,0.0433,-0.05036,0.01499,0.01138,0.01326,-0.02774,-0.05324,0.01077,-0.04853,0.08615,-0.00724,0.00154,0.07922,-0.01957,-0.02307,0.13796,-0.09926,0.09199,0.0336,-0.02527,-0.09636,0.03397,0.12847,0.02199,-0.04049,0.03195,0.03014,0.10132,-0.03336,0.0529,-0.01008,0.0527,0.08102,-0.07501,-0.02237,-0.07946,0.05506,-0.02931,0.05882,0.09117,-0.02922,-0.00108,0.01302,0.04044,-0.0802,0.06207,0.02452,0.02106,-0.02288,-0.00313,0.05767,0.11062,-0.09435,-0.14739,-0.01526,-0.02248,-0.09028,0.06101,-0.0153,0.0068,-0.12261,0.0656,-0.02795,-0.01154,0.02491,-0.03457,0.0525,0.02433,-0.07868,0.03125,-0.03694,0.07907,-0.03144,0.03287,0.01691,-0.04165,0.0043,-0.01498,-0.03267,-0.00949,0.03521,0.02537,0.04122,0.03881,-0.01686,0.09019,-0.1008,-0.04205,-0.0356,-0.01099,0.03462,0.05143,-0.06074,-0.14921,0.07396,0.0262,-0.05311,0.06183,0.01135,0.0821,0.07175,0.1104,-0.09867,0.04145,0.06359,-0.02061,0.03863,0.06109,-0.03885,0.03095,-0.04127,0.01876,-0.02667,0.00688,0.06418,-0.0517,-0.06761,0.01689,0.01301,0.12461,0.02002,-0.01994,-0.12844,-0.08124,-0.06293,-0.12568,0.09605,0.01194,0.06217,0.00735,-0.02357,0.10236,0.05595,0.02042,-0.0706,-0.03396,-0.05116,0.05188,0.03142,0.00726,-0.04352,0.03499,0.00178,0.15965,0.06383,-0.04714,0.01508,-0.08844,-0.17516,0.14426,-0.00537,0.06947,0.06361,-0.0091,0.08287,-0.01993,-0.0017,0.1068,-0.05829,-0.07849,0.03749,0.07915,-0.10354,0.02508,-0.00819,0.02894,-0.01808,-0.0133,0.10195,0.15606,0.00779,-0.16035,0.06505,-0.06693,0.01172,-0.04788,0.03579,-0.02256,-0.15233,0.03543,0.01583,-0.01311,0.02292,-0.01021,0.02274]},{"domain":"chemistry","key":"calorimetry_heat","name":"Heat from a temperature change","package":"chemistry-ai999x","example":"How much heat is needed to warm 50.0 g of water from 20.0 °C to 80.0 °C (c = 4.184 J/(g·°C))?","v":[0.05544,0.05271,-0.07936,-0.04259,-0.0188,0.031,0.03079,-0.04441,-0.01203,-0.06279,-0.04247,0.08405,-0.00358,-0.00398,0.01006,-0.04152,-0.03552,-0.02362,-0.01313,0.00646,-0.00868,0.01637,-0.14218,-0.01979,-0.12437,0.01657,0.01103,0.00445,-0.06822,0.07374,-0.0327,0.07167,-0.04608,0.01895,-0.00496,0.03303,-0.04096,-0.11374,-0.00654,-0.11283,0.02008,0.02728,0.10248,0.03352,0.02558,-0.03005,-0.04186,0.01605,0.06535,0.04252,-0.07055,-0.05381,0.12348,0.02534,-0.00145,-0.05284,0.0574,0.03242,0.08864,-0.01746,-0.0445,-0.12927,0.01937,0.09359,0.02579,0.08551,-0.14987,0.03236,-0.05016,0.01786,0.03696,0.00475,-0.04735,-0.00021,0.06242,0.03028,0.00074,-0.01348,0.10123,-0.01231,-0.0529,-0.08085,0.0367,0.00245,-0.0619,0.05351,-0.04591,-0.09016,0.05565,0.0482,0.09129,-0.05864,0.08682,0.08286,-0.02306,0.0145,-0.01877,-0.02942,0.03362,0.07548,0.05689,-0.05211,-0.1721,-0.06592,-0.13313,0.06404,0.0424,0.07839,-0.07178,0.05221,-0.05747,0.06701,-0.03114,-0.01788,0.05239,0.03911,0.06429,-0.05004,0.10454,0.12839,-0.06121,0.01697,0.07807,-0.14222,-0.01604,0.05161,0.05471,-0.06328,-0.03565,0.07393,0.08696,0.08244,0.02265,-0.01887,0.16352,-0.10817,0.12724,0.01796,-0.07366,-0.06449,-0.00441,0.05065,-0.00062,-0.05849,-0.04195,0.02137,0.03034,0.01166,0.03641,-0.059,0.13689,-0.10342,-0.07536,-0.0179,-0.12435,0.03002,-0.0948,-0.08596,0.01465,-0.00759,-0.03869,0.0808,0.02505,0.07332,-0.02147,0.02072,-0.0332,0.05311,0.02741,0.00326,0.07637,-0.02639,-0.05723,0.04992,-0.14185,-0.07573,-0.01807,0.00358,-0.00808,0.03504,0.00973,0.12112,-0.02669,-0.03432,-0.0856,0.01804,0.01474,0.07325,0.01002,-0.03047,-0.06594,0.04783,0.07903,0.11878,0.06552,-0.03745,0.00307,0.0471,-0.01798,-0.00904,0.02272,-0.0166,0.13579,-0.15203,-0.01763,-0.0344,-0.03165,-0.01482,-0.03159,-0.15586,0.04672,-0.11047,0.00988,-0.01793,0.08704,-0.0152,0.00783,-0.09667,0.06771,0.03612,-0.00621,0.06819,-0.06394,0.0624,0.04319,0.0345,0.02168,0.06486,-0.0696,0.08323,-0.01347,-0.01674,-0.02527,0.00648,0.06581,-0.04128,0.0552,0.04218,-0.06028,0.01179,-0.01988,-0.08262,-0.03126,0.0149,-0.10192,-0.03182,0.08054,-0.00442,0.07733,-0.08551,-0.04736,-0.02509,0.06736,0.02953,0.03336,0.07108]},{"domain":"chemistry","key":"charles_final_volume","name":"Charles's law: final volume","package":"chemistry-ai999x","example":"A balloon holds 2.50 L at 25 °C. What is its volume when heated to 75 °C at constant pressure?","v":[0.0009,-0.06551,-0.08621,-0.04755,-0.02495,0.01605,-0.02408,0.01676,0.07807,0.0832,0.00226,-0.03235,-0.00137,0.02381,0.06054,-0.02108,0.02957,0.04684,0.09324,0.11188,0.04782,0.10268,-0.07163,0.03807,0.02133,-0.12791,0.06627,-0.03725,-0.01793,-0.01778,0.03269,0.03424,-0.00645,0.04239,-0.00175,0.04999,0.01258,-0.03709,0.00203,0.02748,0.08689,-0.00271,0.02176,-0.09112,-0.04282,-0.10199,0.05425,-0.02627,-0.01323,-0.06745,0.07438,-0.04313,-0.0038,-0.12164,0.04854,-0.03882,0.09636,0.02596,0.02277,0.06368,0.01493,-0.00138,-0.07337,0.04353,-0.03526,0.00645,0.07461,-0.0407,-0.01235,0.11284,0.05645,-0.01457,-0.07232,0.00193,-0.00852,0.0033,-0.01909,0.03834,0.03169,0.04232,-0.00232,-0.01634,0.0034,0.00271,-0.03225,0.155,-0.03929,-0.00526,0.09303,0.01857,0.13735,-0.09859,0.00249,-0.02935,-0.10308,0.08572,-0.01518,-0.03045,0.14535,-0.05263,0.05875,0.02064,0.00313,0.02499,-0.15285,-0.00388,0.03845,-0.02528,0.05107,0.05236,0.03475,-0.1008,-0.03087,0.03986,-0.08271,0.02467,0.06883,0.03497,0.01711,-0.04404,-0.07372,-0.02961,0.075,-0.05713,0.00515,0.05895,0.11805,-0.08664,0.02637,0.08672,0.10032,-0.05538,0.01555,-0.03252,-0.04857,-0.1675,0.02855,0.08528,0.03191,-0.03958,0.01189,0.13626,-0.00914,0.01387,0.00149,0.06999,-0.05242,0.00186,0.0148,0.01538,0.02177,-0.08071,-0.0258,-0.08335,0.01355,-0.06995,-0.02635,-0.0765,0.05405,-0.11339,-0.08992,-0.06679,0.04061,-0.00526,0.0158,0.05592,-0.01682,-0.07634,0.03965,-0.06892,-0.05314,0.15514,-0.09011,0.04624,0.00086,-0.03897,-0.14028,-0.0256,0.09719,-0.06969,-0.0375,-0.01189,0.12591,-0.02081,-0.07568,-0.10736,0.01232,-0.0537,-0.03583,0.03468,-0.07034,0.06056,0.0599,0.05131,0.1445,0.05537,0.01899,-0.06847,-0.12167,-0.02276,-0.0453,-0.06811,0.07614,-0.07108,0.08219,-0.03471,-0.05541,-0.00251,0.11624,-0.0829,0.04543,-0.08993,-0.06528,-0.04012,0.11332,0.02154,0.08104,-0.00962,-0.0834,-0.00737,-0.08769,0.0892,0.05255,-0.05161,-0.01313,0.05228,0.08771,0.04336,-0.0378,0.00913,0.00196,-0.07805,-0.01552,-0.09032,0.05302,0.0256,0.00081,-0.07329,-0.02963,-0.00477,0.08343,-0.08162,0.06532,0.0589,0.07561,-0.0384,0.02723,-0.01847,0.00938,-0.07408,0.03885,-0.00298,-0.16415,0.03522,0.05089,0.04263]},{"domain":"chemistry","key":"clausius_clapeyron_enthalpy","name":"Clausius-Clapeyron: enthalpy of vaporization","package":"chemistry-ai999x","example":"P1 = 100 torr at T1 = 300 K and P2 = 400 torr at T2 = 340 K. What is the enthalpy of vaporization?","v":[-0.08598,-0.03876,-0.02187,0.01508,-0.13001,-0.04836,0.07509,0.0554,0.02313,0.04284,-0.0865,0.0193,-0.12567,0.08016,0.0287,0.00982,-0.01293,0.01591,-0.02238,0.04364,0.02394,0.06898,0.00355,-0.00389,-0.02184,0.03729,0.07813,-0.01733,-0.04412,0.03497,0.00499,0.0314,-0.04535,0.00034,0.01081,0.19211,-0.00289,0.02185,-0.0309,0.11518,0.02866,0.05639,0.09694,-0.00239,-0.07343,-0.03118,0.02007,0.00607,-0.02348,0.0925,-0.01414,-0.00383,-0.10704,-0.01103,-0.00075,0.0232,0.03437,0.01755,0.07675,0.03632,0.00224,-0.00641,-0.02786,-0.01899,-0.08719,-0.02498,-0.08324,0.05267,0.10771,-0.07835,-0.09933,0.03795,0.05494,-0.06314,0.10685,-0.01334,-0.06731,-0.01504,0.03076,-0.09563,-0.05319,-0.13343,0.00519,-0.02274,0.00458,-0.07744,-0.19376,0.06355,-0.026,0.02319,0.01304,-0.00116,0.06281,-0.12663,-0.06822,-0.09017,0.063,-0.08454,0.05727,0.00282,0.03696,-0.01178,-0.0495,0.0366,-0.01418,-0.04884,0.0069,0.10063,0.018,-0.03137,0.04604,-0.02882,-0.0203,-0.06713,-0.08829,0.01211,0.03191,0.02385,0.0359,0.04788,0.03266,-0.02501,-0.04367,0.06584,-0.02789,0.10015,-0.04838,0.03919,-0.01171,0.0433,0.00299,-0.06629,0.0107,-0.08908,0.09563,0.00973,0.08732,0.00846,-0.03199,0.00119,-0.00825,0.02795,0.11814,0.06701,0.14784,0.05688,-0.09233,-0.0006,-0.00018,0.09908,-0.05676,-0.1827,0.04159,-0.01302,0.05269,0.03665,-0.03216,-0.02185,0.09925,0.01757,-0.04116,-0.05328,-0.01003,-0.00482,-0.15634,0.02665,-0.15717,0.02773,0.04366,-0.0328,-0.06287,0.03575,-0.04424,-0.03705,0.0018,0.00875,-0.01501,0.13411,0.068,0.04866,0.05764,-0.02083,-0.05446,0.0297,-0.02024,-0.02658,0.0116,-0.014,-0.0368,0.107,-0.02891,0.10543,0.0276,0.041,0.04236,-0.03188,-0.07622,-0.01642,0.02543,-0.04781,0.0573,0.01134,0.09496,-0.03786,0.00812,0.0669,-0.01654,-0.05941,-0.0332,-0.05624,-0.02846,0.02259,-0.05432,0.02857,0.0842,0.00771,-0.0268,-0.00289,0.09063,0.01479,0.01857,-0.06179,0.10704,-0.00842,-0.1743,-0.03331,0.07684,0.11161,-0.089,0.01346,0.0,-0.05106,-0.078,-0.01393,0.05945,0.03301,-0.00642,0.02265,-0.09126,0.11398,-0.01666,0.00981,0.13713,0.04411,-0.01243,-0.1487,0.00066,0.02151,0.06406,-0.09968,-0.10513,0.06466,0.03353,0.06844,0.07665,0.1053]},{"domain":"chemistry","key":"clausius_clapeyron_pressure","name":"Clausius-Clapeyron: vapor pressure at another temperature","package":"chemistry-ai999x","example":"Water has a vapor pressure of 23.8 torr at 25 °C and ΔHvap = 43.9 kJ/mol. What is its vapor pressure at 50 °C?","v":[-0.04012,-0.02696,-0.03554,-0.08033,-0.11337,-0.04262,0.05422,0.0684,-0.01767,0.01684,-0.08976,-0.02218,-0.1046,0.00738,0.04769,0.00235,-0.01145,-0.00356,-0.05801,0.05836,-0.04447,0.07879,-0.02001,0.01009,0.00279,0.03236,0.07251,-0.04937,-0.02194,0.05556,0.0169,0.06743,-0.06473,-0.00036,0.0326,0.16853,0.01342,0.0135,-0.05986,0.12071,0.04535,0.05304,0.10857,-0.00068,-0.03023,-0.04474,0.02826,-0.02473,-0.06053,0.07568,0.03935,-0.03335,-0.11851,-0.01676,-0.02645,-0.02082,0.00961,-0.00967,0.06655,0.02808,0.03026,-0.00575,-0.0591,-0.00104,-0.06918,0.00656,-0.11436,0.04732,0.07883,-0.04686,-0.10668,0.04322,0.04434,-0.021,0.12004,0.00651,-0.0656,-0.00803,0.05194,-0.092,-0.08418,-0.08584,0.03717,-0.00045,-0.02628,-0.08803,-0.2171,0.04652,0.02566,0.05733,0.00582,0.02012,0.07224,-0.14022,-0.06228,-0.0562,0.04855,-0.04785,0.07771,0.00109,0.03488,0.04536,-0.05855,0.04118,0.00507,-0.03588,0.06932,0.10939,0.05495,-0.05898,0.04962,-0.08446,-0.03684,-0.06627,-0.08444,0.02467,0.04282,0.02622,0.03069,0.04379,0.00026,-0.01502,-0.07501,0.02284,-0.04252,0.14253,-0.0318,0.07075,-0.01042,0.03199,0.00808,-0.04689,0.07084,-0.10097,0.08539,0.02616,0.05174,0.05685,-0.04338,-0.02523,-0.00455,0.09107,0.11559,0.02595,0.11285,0.03783,-0.09958,0.01119,0.00791,0.10515,-0.06545,-0.15374,0.06131,0.01137,0.03197,0.06194,-0.03526,-0.03124,0.10437,0.02177,-0.04807,-0.03595,0.03755,0.0167,-0.13298,0.01236,-0.13945,0.04042,0.05542,-0.04185,-0.07344,0.08531,-0.03937,-0.0235,0.01991,-0.00515,-0.04116,0.12357,0.07102,0.04476,0.03247,0.01503,-0.05132,0.01456,-0.03684,-0.01643,0.02199,-0.03162,-0.04249,0.13458,-0.04488,0.10433,0.04209,0.02267,0.06507,-0.03631,-0.06797,-0.00611,0.052,-0.028,0.02799,0.02716,0.08781,-0.09348,-0.01366,0.02777,-0.01146,-0.05932,-0.03312,-0.07694,-0.02144,0.01953,-0.07302,0.00528,0.09676,-0.00371,0.00999,-0.06338,0.08079,-0.0192,0.00039,-0.01576,0.0736,0.042,-0.12265,-0.01007,0.09155,0.10583,-0.05759,0.02386,-0.00615,-0.05092,-0.06583,-0.00328,0.02983,0.03511,-0.01873,0.0571,-0.08773,0.1111,-0.06304,-0.02521,0.13124,0.00571,0.00861,-0.13219,0.00251,-0.00402,0.09092,-0.12867,-0.07725,0.04291,6e-05,0.09821,0.04832,0.07091]},{"domain":"chemistry","key":"combined_gas_final_pressure","name":"Combined gas law: final pressure","package":"chemistry-ai999x","example":"A gas at 1.00 atm and 300 K occupies 3.00 L. Find the final pressure if V2 = 1.50 L and T2 = 450 K.","v":[-0.04177,-0.03072,-0.03339,-0.03943,0.00371,0.06475,-0.07803,-0.06773,0.04158,0.02545,-0.03537,0.0123,0.01014,0.07577,0.0611,0.01934,0.08082,0.0777,0.17915,0.14628,0.02901,0.06855,0.07211,0.0759,-0.00824,-0.03948,0.02816,0.00824,-0.0351,0.02627,-0.00251,-0.06426,-0.01733,0.02962,-0.02719,0.14402,-0.04972,0.06064,0.0005,-0.01187,0.03946,0.00108,-0.02842,-0.01097,-0.08765,-0.00549,-0.0081,0.06958,-0.00496,-0.10752,0.0214,-0.03237,0.06763,-0.05249,0.05142,0.07268,0.02283,-0.00705,0.0595,0.03449,0.00349,-0.03359,-0.12451,-0.0984,-0.05532,-0.08172,0.09455,-0.03638,-0.00275,0.0297,0.02276,-0.05947,-0.0726,-0.01936,-0.02591,-0.00721,0.03971,0.09694,-0.00069,0.05235,0.02636,-0.03553,0.0827,0.05613,0.0161,0.02267,-0.03763,-0.00693,0.03822,0.0023,0.04786,0.00577,-0.03947,-0.03789,-0.02488,-0.00168,0.0377,0.06054,0.09321,-0.14412,0.10946,0.04667,-0.02915,0.09525,-0.09928,-0.06398,-0.10998,-0.06258,0.10828,0.10341,0.03023,0.01327,-0.03431,0.0127,-0.08083,-0.05367,0.06984,-0.01664,0.04409,-0.10524,-0.06605,0.07083,-0.01469,0.00597,-0.02041,-0.01229,0.07027,-0.09032,0.11383,0.09139,0.03637,-0.05956,-0.10439,-0.00637,-0.07177,-0.10775,0.01255,0.06325,0.02961,-0.07369,-0.08987,-0.02615,-0.03512,0.06175,0.11213,0.05902,-0.05779,0.03348,-0.00918,0.04918,-0.02929,0.00047,-0.07495,-0.02082,0.0362,0.05127,0.00576,-0.03101,0.09228,-0.07456,-0.05762,-0.10335,0.01059,0.03701,-0.08489,0.0383,0.03907,0.00097,-0.02785,0.00462,-0.01799,0.11451,-0.01425,0.11107,0.03389,0.06293,-0.14834,-0.04736,0.00421,0.01131,0.03905,-0.01975,0.0869,-0.04924,-0.0941,-0.07605,0.00398,-0.05524,-0.03917,-0.03145,-0.03567,0.13465,-0.0593,0.0689,0.12274,0.05177,-0.08261,-0.12474,-0.09979,-0.02965,-0.03369,0.0152,0.11264,-0.02026,0.03606,0.00785,-0.03534,-0.01983,0.0591,-0.07454,0.01184,-0.06483,-0.00612,-0.05266,0.03634,-0.06829,0.01206,0.00883,-0.03783,-0.03918,0.04659,0.00636,0.06644,-0.0831,-0.06757,-0.04706,0.04072,0.03033,-0.06289,0.0567,0.05695,-0.10772,-0.0141,-0.05006,0.07113,-0.0241,0.0351,-0.09361,0.08398,0.03641,0.11265,-0.13036,0.13383,0.12259,-0.06261,0.0176,0.00792,-0.02771,-0.01633,-0.12992,0.01123,-0.02015,-0.12299,0.01511,-0.01766,0.06823]},{"domain":"chemistry","key":"combined_gas_final_temperature","name":"Combined gas law: final temperature","package":"chemistry-ai999x","example":"P1 = 1.00 atm, V1 = 2.00 L, T1 = 300 K, P2 = 2.00 atm, V2 = 1.50 L. Find the final temperature.","v":[-0.05005,-0.0631,-0.02114,-0.03819,-0.01906,0.06509,-0.08456,-0.05727,0.04301,0.02249,-0.02181,-0.00347,0.01684,0.05363,0.05936,0.01617,0.07546,0.07371,0.18599,0.14705,0.03191,0.08068,0.06181,0.06497,0.00306,-0.0472,0.03341,0.02079,-0.04676,0.03143,-0.00855,-0.0658,-0.01795,0.04782,-0.00897,0.13738,-0.05735,0.04656,0.0129,-0.02448,0.03613,-0.00299,-0.01223,-0.00886,-0.08301,-0.02157,0.02916,0.07137,-0.02507,-0.08992,0.01336,-0.02003,0.06609,-0.06124,0.0619,0.05651,0.03848,0.01823,0.06508,0.04149,0.0005,-0.01168,-0.10524,-0.06912,-0.05525,-0.08977,0.1,-0.03754,-0.00243,0.03177,0.02628,-0.05889,-0.04654,-0.01913,-0.02727,-0.0043,0.02281,0.09746,0.02522,0.05406,-0.00466,-0.0403,0.07528,0.03554,0.02121,0.04879,-0.04551,0.0028,0.02494,-0.01118,0.05803,0.00104,-0.02901,-0.03731,-0.03184,0.01101,0.04362,0.0538,0.10327,-0.12985,0.11376,0.05104,-0.02025,0.09564,-0.10078,-0.07844,-0.12106,-0.06215,0.1018,0.10748,0.01799,0.0078,-0.0033,-0.00591,-0.0871,-0.04368,0.05893,-0.02586,0.03729,-0.11179,-0.06658,0.0473,-0.00697,-0.00186,-0.03285,-0.0068,0.07435,-0.09775,0.09041,0.09386,0.0323,-0.04527,-0.09575,-0.03642,-0.08286,-0.11326,0.01113,0.06917,0.00727,-0.08413,-0.05891,-0.01169,-0.01351,0.05785,0.09735,0.06455,-0.06247,0.02407,-0.002,0.06114,0.00725,0.00249,-0.05732,-0.02031,0.0269,0.0533,0.00237,-0.03213,0.09127,-0.05737,-0.05722,-0.11331,0.00013,0.03437,-0.08381,0.0533,0.02535,-0.00074,-0.03035,-0.003,-0.01425,0.13833,-0.03488,0.11132,0.02199,0.05845,-0.1369,-0.02389,0.0065,0.00037,0.05451,-0.03016,0.08835,-0.04879,-0.10094,-0.07059,-0.00196,-0.03851,-0.02396,-0.03223,-0.03291,0.13041,-0.05373,0.08408,0.12496,0.04011,-0.07177,-0.12686,-0.10228,-0.03513,-0.02381,-0.00226,0.11461,-0.02365,0.04456,0.01545,-0.03742,-0.02479,0.06937,-0.11381,0.03038,-0.06967,-0.00936,-0.04734,0.06234,-0.0485,0.00574,-0.00302,-0.03191,-0.02868,0.03884,0.0187,0.0753,-0.09766,-0.06305,-0.05029,0.0514,0.02616,-0.06994,0.06852,0.05928,-0.11413,-0.02063,-0.08126,0.05844,-0.02887,0.02881,-0.08981,0.09227,0.0309,0.12862,-0.11458,0.13389,0.12932,-0.06008,0.01099,0.0114,-0.03375,-0.04046,-0.12289,0.0221,-0.01352,-0.13365,0.01484,-0.00407,0.06584]},{"domain":"chemistry","key":"combined_gas_final_volume","name":"Combined gas law: final volume","package":"chemistry-ai999x","example":"A gas occupies 4.00 L at 1.00 atm and 300 K. What is its volume at 2.00 atm and 400 K?","v":[-0.04772,-0.06335,-0.03758,-0.06026,-0.00253,0.06715,-0.08126,-0.04958,0.05982,0.03249,-0.02106,0.02656,0.02251,0.05037,0.06431,0.01332,0.08809,0.09299,0.15462,0.14748,0.01492,0.0854,0.03761,0.06748,-0.01732,-0.05556,0.03784,0.03468,-0.05263,0.0044,0.00191,-0.07873,-0.03454,0.03281,-0.00598,0.09265,-0.03394,0.0162,0.02585,0.00381,0.05296,0.01621,-0.02834,-0.02576,-0.07568,-0.01387,0.02342,0.05383,-0.03629,-0.10724,0.0168,-0.05307,0.07022,-0.0781,0.04214,0.07052,0.05369,0.00787,0.04924,0.04067,0.00681,0.01377,-0.11339,-0.06811,-0.06311,-0.07872,0.08778,-0.06515,0.00301,0.05654,0.04056,-0.08105,-0.06973,-0.01236,-0.02842,0.00639,0.0224,0.08857,0.02388,0.06694,0.00295,-0.01421,0.06515,0.02469,0.00523,0.08369,-0.03919,0.01106,0.06475,-0.01263,0.07141,-0.01005,-0.03416,0.00563,-0.03569,0.03839,0.02522,0.05222,0.12729,-0.12541,0.10859,0.03462,-0.00622,0.06677,-0.12581,-0.08992,-0.09855,-0.03781,0.09642,0.11312,0.02397,0.00345,-0.01813,0.00695,-0.09354,-0.02482,0.0691,-0.01549,0.0625,-0.13265,-0.05214,0.0716,-0.01855,-0.0022,-0.04171,-0.01258,0.05946,-0.10003,0.10833,0.08008,0.03603,-0.07161,-0.08554,-0.03422,-0.06391,-0.12552,0.0103,0.08033,0.03206,-0.06808,-0.0436,0.00449,-0.04464,0.04701,0.10355,0.06095,-0.03948,0.03032,0.00532,0.05941,-0.00445,0.00981,-0.04274,-0.02604,0.03687,0.04894,0.01208,-0.03814,0.10726,-0.06746,-0.04846,-0.10821,0.02134,0.03751,-0.05571,0.0554,0.03289,0.00219,-0.05624,-0.03557,-0.00753,0.12468,-0.05859,0.11287,0.04013,0.02661,-0.14653,-0.04225,0.03249,-0.02072,0.02703,-0.01842,0.11334,-0.0455,-0.07941,-0.0851,0.01216,-0.03676,-0.01494,-0.02869,-0.06142,0.10539,-0.04654,0.08954,0.1117,0.04975,-0.07118,-0.1208,-0.11896,-0.0154,-0.03832,-0.00202,0.09864,-0.02656,0.05035,0.00868,-0.0615,-0.04469,0.07733,-0.10941,0.02251,-0.09058,0.00396,-0.06038,0.03265,-0.05436,0.01193,-0.00298,-0.01724,-0.01305,0.04113,0.0222,0.05625,-0.08983,-0.04175,-0.00712,0.04437,0.03911,-0.06387,0.06216,0.03546,-0.10204,-0.02969,-0.06736,0.05193,-0.00252,0.02836,-0.10564,0.07796,0.00339,0.13,-0.12274,0.12689,0.11277,-0.04484,0.00223,0.00761,-0.02552,-0.04122,-0.11066,0.03198,-0.03138,-0.15186,0.01421,0.00767,0.06862]},{"domain":"chemistry","key":"common_ion_solubility","name":"Molar solubility with a common ion","package":"chemistry-ai999x","example":"What is the molar solubility of CaF2 in 0.10 M NaF (Ksp = 3.9e-11)?","v":[-0.10832,0.07704,-0.06111,-0.02814,0.08488,-0.11437,0.05731,0.18499,0.02923,-0.0158,0.08258,-0.03669,0.04019,-0.05001,0.07967,0.04377,-0.10947,-0.17777,-0.0914,0.01632,0.04836,0.05519,-0.02549,0.04346,-0.03578,0.10594,-0.00026,-0.00257,0.00538,0.03799,0.03341,-0.00974,0.02053,-0.02572,-0.02348,0.03271,-0.01811,-0.03439,-0.00582,0.002,0.03856,-0.06162,-0.01737,-0.10526,0.04424,-0.01719,-0.02211,0.01641,-0.02048,0.03741,0.00473,0.13416,0.03392,-0.059,-0.03565,0.16589,-0.12751,0.03107,-0.06959,0.09617,0.02157,-0.06111,-0.03566,-0.075,0.08901,-0.05156,-0.08314,0.04652,-0.04082,-0.00092,0.06843,0.01691,-0.02625,-0.00779,-0.10174,0.11218,0.03006,-0.08293,0.03596,-0.08675,-0.0682,0.00362,0.08244,-0.00033,-0.01496,0.06242,-0.05111,0.07588,0.1254,0.05108,0.07372,0.03814,-0.05333,0.00304,0.04043,-0.04484,-0.09526,-0.02385,0.02642,-0.09372,0.0706,0.03912,0.01171,0.00921,0.04567,0.13399,0.0586,0.02492,0.11693,0.02992,0.14405,-0.08136,-0.03821,-0.05727,0.06141,0.0586,-0.0281,-0.01358,-0.02525,0.00497,0.07722,-0.09754,0.12822,0.0134,0.02751,0.01946,0.04447,0.01492,-0.0631,-0.10978,0.01304,0.01021,-0.03151,0.01034,-0.02294,0.05569,-0.01059,0.08423,-0.00616,-0.0406,0.07019,0.02301,0.03778,0.0198,-0.06049,-0.0749,-0.02387,-0.07791,-0.02131,-0.04069,-0.04326,0.02635,-0.03068,0.0823,-0.01349,-0.12839,-0.05395,-0.04739,0.03383,0.0517,-0.06819,-0.00432,0.09794,-0.05768,-0.07172,0.04362,0.09474,0.04943,0.04234,0.06913,0.11314,-0.00778,0.01695,-0.02275,-0.03992,-0.09968,0.01698,-0.04761,-0.09955,-0.04111,0.06632,0.06183,-0.12541,0.03604,-0.04473,-0.09125,0.03728,0.05103,-0.00533,-0.01802,0.00875,0.0276,0.00145,-0.0654,-0.04875,-0.05211,-0.06719,0.00789,-0.03941,0.08921,0.07376,0.01511,0.06208,-0.03293,0.03759,0.04048,-0.1061,0.05393,-0.02183,0.06304,-0.03307,-0.02585,0.05202,-0.09822,-0.09948,0.02771,0.05163,-0.03312,-0.00028,-0.03876,0.0075,-0.05006,-0.0556,0.10875,0.03402,0.05495,0.11566,-0.11877,-0.03163,0.03476,-0.11529,-0.06535,0.07463,-0.07442,0.04499,-0.03368,-0.0676,-0.0682,-0.02456,0.07326,-0.0481,0.05801,-0.00893,-0.04669,0.03019,0.05026,0.05526,-0.00826,-0.04613,0.05507,-0.02439,0.00198,0.07392,-0.06841,-0.09036,-0.06073]},{"domain":"chemistry","key":"consecutive_first_order","name":"Consecutive first-order reactions (A -> B -> C)","package":"chemistry-ai999x","example":"For A -> B -> C with k1 = 0.10 s^-1, k2 = 0.050 s^-1 and [A]0 = 1.0 M, what is the concentration of the intermediate B after 10 s?","v":[-0.04701,0.02827,0.04547,0.02381,0.02813,-0.01811,-0.02894,0.05225,0.04617,0.02819,0.04627,0.06217,-0.07802,0.07015,0.20448,-0.0147,0.02484,-0.06382,0.12892,0.02188,0.05221,-0.06412,0.06027,0.11946,-0.04117,0.0275,0.08032,0.06354,-0.06761,0.02348,0.06126,-0.01034,-0.07406,0.06051,0.01888,0.16898,-0.04482,0.08249,-0.03335,-0.03559,-0.02913,-0.01297,-0.10643,0.0322,-0.04233,-0.02428,-0.05983,0.06314,-0.10074,0.03075,-0.04083,0.08426,-0.05047,0.01846,0.01714,0.06137,0.05824,0.06668,-0.0094,-0.01958,-0.04974,-0.05404,0.07952,-0.07714,-0.063,-0.00445,0.14423,0.01257,0.03291,-0.13185,0.01345,0.00563,-0.04744,-0.02759,-0.09716,0.00693,-0.03832,-0.00377,-0.01626,-0.04372,0.05247,-0.13745,0.05701,-0.02746,-0.00113,0.06311,-0.00111,-0.0571,-0.06551,0.04183,0.06185,-0.02465,0.03494,-0.07722,0.02713,0.01856,0.11458,0.02113,-0.02434,0.04729,0.01529,0.00335,-0.01713,0.0498,0.09133,0.05694,-0.1029,-0.00699,0.09075,0.01202,0.03541,0.0237,-0.00266,-0.05937,0.01805,0.04427,-0.00662,0.00407,-0.02564,0.08681,-0.0134,-0.00859,0.07904,0.09255,-0.07362,0.07104,0.00711,0.00517,-0.00203,-0.02024,0.01281,-0.04248,0.00375,-0.07817,-0.01146,-0.12053,0.02843,-0.00453,0.02052,-0.16943,-0.1611,0.05668,0.08837,-0.03054,-0.11189,0.03317,-0.06367,0.11922,-0.01734,-0.04049,-0.08622,-0.0823,-0.03861,-0.04684,0.10854,-0.01571,0.03845,0.01968,0.06856,-0.11811,-0.0105,-0.01599,-0.02739,-0.04526,-0.0005,0.05442,-0.0419,-0.06326,-0.0254,0.08015,0.02891,0.07672,0.01157,-0.01974,0.05994,0.02697,-0.08841,-0.05688,-0.08994,-0.07997,0.00227,0.01151,-0.02841,-0.03717,-0.15675,0.03529,-0.07886,-0.01009,-0.02677,-0.06357,0.01424,0.08212,0.00129,0.01218,-0.0257,-0.02681,-0.02364,0.04737,0.00595,-0.10602,0.012,0.04051,-0.0495,0.01894,0.12751,0.05266,-0.00265,0.0035,0.03457,0.10204,-0.04702,-0.05911,-0.13715,0.13417,-0.04119,-0.02088,0.05982,-0.03196,-0.15835,0.08092,0.06872,-0.06255,-0.00107,0.03604,-0.01751,-0.01401,-0.02204,0.0593,0.09516,-0.05516,0.0075,-0.02163,-0.10646,0.02832,0.05047,-0.06316,0.1485,-0.01703,0.06746,0.05938,-0.01954,0.01222,-0.10774,0.01172,-0.04484,0.05973,0.02366,-0.06493,0.03078,0.11617,-0.04831,0.04836,0.04659,0.03434,-0.00554,-0.02028]},{"domain":"chemistry","key":"crossover_temperature","name":"Temperature at which dG = 0","package":"chemistry-ai999x","example":"For ΔH = 178 kJ/mol and ΔS = 161 J/(mol·K), above what temperature is the reaction spontaneous?","v":[0.00165,-0.01588,-0.09673,0.11092,-0.11011,0.03377,0.0985,0.04136,0.01919,0.01682,0.00046,0.03073,-0.16211,0.02872,0.11265,-0.07775,0.01859,-0.04177,-0.01537,0.04962,-0.05362,0.00257,-0.05524,-0.05486,-0.0327,0.06453,0.03917,0.06077,0.00992,0.06167,-0.04509,0.05438,0.03028,-0.01242,-0.0325,0.09223,-0.11387,-0.08728,-0.0034,0.02192,-0.00634,-0.0332,0.11431,0.02762,0.04243,-0.02661,0.14505,-0.02229,-0.02697,0.02657,0.06852,-0.04455,-0.00201,-0.0088,-0.06294,0.05846,-0.05643,0.08634,-0.00272,-0.01663,-0.07886,0.09166,0.08173,0.04872,0.03397,-0.04933,-0.07186,0.02786,0.02398,-0.0129,-0.05101,0.07593,-0.06691,0.08832,0.10531,-0.04732,-0.0972,-0.02698,-0.06017,-0.09015,-0.02215,-0.01937,-0.0196,0.02522,0.06957,0.06295,-0.15418,0.05836,-0.04777,-0.05606,-0.01198,-0.02469,0.03945,0.03805,-0.03977,0.02479,-0.02411,-0.00719,0.02882,-0.00165,0.00333,0.0135,-0.00076,-0.02271,-0.01625,0.04803,0.03141,0.12436,-0.07144,0.08943,0.01097,0.0755,0.02566,-0.09846,0.02228,-0.00632,-0.08418,-0.06352,0.01748,0.05725,0.10775,0.05986,-0.05195,0.01999,-0.02812,-0.02878,-0.00056,-0.04861,-0.04515,-0.03616,-0.03251,0.0156,0.00295,-0.08475,0.1452,0.06432,0.12722,-0.0103,-0.02824,-0.09024,0.07704,0.03988,-0.0617,0.02133,-0.01368,-0.02699,0.03654,-0.05442,-0.00842,-0.00914,0.07194,-0.19363,-0.00633,0.03484,-0.03987,0.0318,0.06718,-0.04755,0.04019,-0.0939,0.02247,-0.04385,-0.01341,-0.02876,-0.03617,0.0682,-0.03938,-0.02634,0.0434,-0.03675,0.13183,0.06279,0.02456,-0.00056,-0.07292,-0.02783,-0.02305,0.10872,0.07843,0.07463,0.14207,-0.06007,-0.14351,0.01219,0.00762,-0.02955,0.06329,0.07448,0.03152,-0.03239,0.02927,0.00921,0.02064,-0.07845,0.02636,-0.05337,-0.10232,-0.00217,-0.0617,0.05658,-0.11398,-0.0411,0.18612,-0.08941,-0.03615,0.04104,0.04536,0.01087,-0.09256,-0.0431,0.09088,0.07138,-0.03245,0.05,0.0425,0.00114,-0.04417,-0.03235,0.00273,0.00342,0.00946,0.0426,0.10928,-0.05389,0.00225,-0.02853,0.02786,0.01496,-0.03201,0.07301,0.01125,-0.10658,-0.03014,-0.09292,0.06707,0.08153,-0.05907,0.04952,-0.04326,0.16136,0.00798,0.10785,0.07214,0.05943,-0.05271,-0.03584,-0.0572,-0.00811,0.01525,-0.12392,-0.14143,0.00345,0.02504,-0.00326,0.03986,-0.04012]},{"domain":"chemistry","key":"dalton_mixture","name":"Partial pressures in a gas mixture","package":"chemistry-ai999x","example":"A mixture of 2.0 mol N2, 1.0 mol O2 and 0.50 mol Ar has a total pressure of 3.5 atm. Find the partial pressures.","v":[-0.14269,0.15629,-0.07244,-0.01988,0.06459,0.08875,0.01464,-0.05172,0.06201,-0.04995,0.02485,0.00704,-0.08622,-0.04817,-0.03233,-0.07474,0.0255,0.02368,0.07962,0.18391,-0.09901,-0.02741,0.0223,0.01148,0.04145,0.07081,-0.00452,0.03225,0.01844,0.11475,-0.00786,-0.06974,0.05835,0.02331,-0.01446,0.01234,-0.02254,0.01408,0.02281,0.02976,-0.03438,0.01549,0.00388,-0.03915,0.00693,0.00484,-0.07423,0.01671,-0.06081,0.05041,-0.01285,-0.05839,-0.09516,-0.05852,-0.02731,0.08623,-0.04857,-0.1282,0.08521,-0.05208,-0.0113,-0.01203,-0.08429,-0.14467,-0.01285,-0.10503,0.0097,-0.07943,0.02458,0.02407,-0.12785,-0.05314,-0.01637,-0.00882,0.00395,0.05544,0.0086,0.0382,0.05221,0.00465,0.05181,0.03053,0.12559,0.03675,0.09586,-0.00716,-0.04291,0.07089,0.04625,0.00373,-0.04021,0.0013,-0.15238,0.03028,-0.02448,-0.02301,-0.02539,0.07401,-0.0573,-0.02341,0.02759,0.04793,0.04018,0.00834,0.03034,-0.01375,0.02054,0.016,0.05414,0.04957,0.02597,-0.11223,-0.03095,0.04255,-0.10543,-0.02965,0.04546,0.02002,0.07306,-0.01187,-0.08393,0.09852,-0.05176,-0.06053,0.05669,0.03102,0.07764,-0.01062,0.07495,0.0042,0.01477,0.00648,-0.03262,0.04117,-0.05546,0.01298,-0.10177,0.07939,0.00058,0.14193,-0.10578,-0.05322,-0.09547,0.02783,0.06319,0.07256,0.09204,0.04927,-0.0366,0.07091,-0.13343,0.09248,-0.01836,0.04904,0.09319,0.0274,0.02175,-0.02726,0.07459,0.01047,-0.04504,-0.0833,-0.02437,-0.01235,0.11777,0.00516,-0.00696,0.0737,0.01821,0.01959,0.05429,-0.00783,0.07104,-0.08167,0.02073,0.01944,-0.01613,-0.14472,0.05584,0.1151,-0.10477,0.01427,-0.00511,0.01514,-0.14149,0.0857,0.15182,-0.08365,-0.01712,-0.05658,-0.07197,0.12266,-0.04485,0.15924,-0.05211,-0.00836,-0.11172,-0.03377,-0.04204,0.02549,-0.00687,-0.01976,-0.02691,0.05326,-0.09471,-0.0123,0.02184,0.0144,0.06176,0.02566,-0.00463,0.06872,-0.05041,-0.04057,-0.01428,-0.05539,0.03908,-0.01263,-0.03707,-0.02789,0.04253,0.07513,-0.08692,0.00857,-0.04642,-0.15051,0.04647,0.01995,0.02772,-0.05145,0.06975,-0.02494,-0.00997,0.05543,0.05631,-0.04656,-0.02204,0.04342,-0.02529,-0.09535,0.08624,-0.07086,0.06264,0.09399,0.00329,0.0426,-0.02363,-0.0169,-0.00258,-0.08182,-0.06192,-0.03098,-0.07992,-0.00405,-0.04807,-0.07899]},{"domain":"chemistry","key":"degree_of_unsaturation","name":"Degree of unsaturation","package":"chemistry-ai999x","example":"What is the degree of unsaturation of C6H6?","v":[-0.03682,0.08489,-0.08901,0.07967,-0.04948,0.01267,0.06284,-0.01114,0.0528,0.0623,0.07492,0.00132,0.01204,0.14373,-0.06502,0.01208,-0.02734,-0.0236,0.0396,-0.03495,-0.00287,-0.11888,-0.02046,-0.10979,-0.01288,-0.01044,0.00469,-0.04532,-0.07211,-0.02796,-0.11306,0.01929,0.02804,-0.0701,-0.05949,-0.03052,0.11921,-0.12368,0.0764,-0.05164,0.10116,-0.1333,-0.01186,0.02983,0.07502,-0.00062,-0.03087,0.02494,0.03355,0.00349,0.05931,-0.00224,-0.06679,0.09883,0.04437,-0.00728,-0.11354,-0.00928,-0.0996,-0.04997,0.03582,0.09662,-0.04016,-0.03275,-0.01907,0.00351,-0.02136,0.02634,-0.07497,-0.00016,-0.05594,0.03443,-0.13339,0.18448,-0.08726,0.04026,-0.05203,-0.00934,0.02899,-0.02691,-0.03043,0.01758,-0.00084,-0.02687,0.04747,0.0386,0.02946,-0.12456,0.0784,-0.01293,0.02869,0.04623,0.05068,0.0138,0.01903,0.08628,-0.06497,-0.06268,0.06468,-0.01876,-0.03045,0.07238,0.10527,-0.00934,0.07297,0.02805,0.08547,-0.02279,-0.04047,-0.05454,0.01623,-0.00487,-0.03017,0.01226,-0.00686,0.00103,0.01189,-0.09872,-0.05035,-0.08667,-0.01225,-0.07019,-0.0737,0.09698,0.02136,0.1108,0.10917,0.0198,-0.07152,-0.07725,-0.11455,0.0587,-0.01922,-0.01317,0.11147,0.0969,-0.03591,0.05331,0.06453,0.03632,0.02386,0.09605,0.07102,0.00049,0.0999,-0.00495,0.04413,-0.04423,-0.01736,-0.01073,-0.06757,0.02113,-0.05312,0.01,-0.0239,-0.05617,-0.01955,0.02444,0.05239,-0.00334,0.01315,-0.10005,-0.06762,-0.02886,0.00021,0.11533,0.05314,0.02583,0.06189,0.05238,0.06505,-0.06826,0.05269,0.0386,0.04244,-0.00831,0.02722,0.11358,0.03025,0.00462,-0.06638,-0.00049,0.04471,-0.03627,0.02013,0.01747,0.03838,-0.01809,-0.0259,-0.07334,-0.02796,-0.0497,-0.05569,-0.06083,-0.04396,-0.1507,0.05251,0.0317,-0.06202,-0.02484,-0.0216,0.09695,0.13182,-0.02801,-0.04309,-0.14121,0.09661,-0.008,0.02376,0.0655,0.08379,0.02859,0.0997,0.01236,0.00992,0.0332,0.10867,0.08461,-0.05702,0.01699,-0.00116,0.02028,0.04193,-0.01623,-0.01311,-0.09752,-0.01882,-0.08628,-0.08902,-0.00061,0.09044,0.01594,-0.01179,-0.07011,0.03387,-0.09047,-0.0999,0.10472,0.12203,-0.01784,0.07185,-0.07181,-0.04708,-0.06507,-0.10365,-0.07063,-0.03714,-0.10611,0.07439,-0.1313,0.03536,-0.00353,0.05753,0.04358,-0.04143,0.05072]},{"domain":"chemistry","key":"delta_g_from_cell_potential","name":"Gibbs energy from a cell potential","package":"chemistry-ai999x","example":"A cell has E° = 1.10 V and n = 2. What is ΔG°?","v":[0.09546,0.01531,0.02125,0.07133,0.01044,0.08278,0.08243,0.03634,-0.08577,0.04984,-0.03469,-0.03655,-0.04066,-0.05001,0.01131,0.00732,0.00912,0.07825,0.09173,0.05791,-0.01674,0.06721,-0.05456,0.03447,-0.11469,0.07205,-0.00678,-0.02999,-0.03741,0.11275,-0.04667,-0.02791,0.05492,0.07381,-0.07668,0.06946,-0.01759,-0.07135,-0.03754,-0.03627,0.01903,-0.02064,-0.02317,0.03906,-0.00083,0.08313,-0.10799,-0.02521,-0.00893,0.07419,0.04114,-0.03787,0.05362,-0.02187,0.01153,-0.04068,-0.01878,-0.06198,-0.1181,0.01632,-0.02513,0.04274,0.00058,-0.11113,0.0897,0.05339,-0.03874,-0.02524,-0.01576,0.0396,0.01219,0.05124,-0.12488,-0.01987,0.04798,0.07757,0.03552,-0.05306,-0.15665,0.04145,0.00658,0.06247,0.03176,0.06774,-0.02295,-0.03107,-0.00042,0.02624,0.0658,-0.0479,0.01066,0.03749,0.0069,0.05114,-0.05748,0.13525,-0.1961,0.0074,0.05351,-0.0274,0.0178,0.08581,0.11282,0.0354,-0.10743,-0.0262,0.02734,-0.05113,0.00081,-0.04142,0.00951,0.05872,-0.07527,-0.05717,0.05446,-0.02892,-0.10809,-0.07912,0.06723,-0.02512,0.0631,0.00831,-0.02952,0.04817,-0.06107,-0.13403,-0.06792,0.14069,-0.01747,-0.04873,0.04436,-0.02931,0.08746,-0.01069,0.06827,0.07119,-0.05154,-0.00577,0.05599,-0.07035,0.05873,0.02696,-0.14051,-0.04917,0.0401,-0.1268,-0.05007,-0.02999,0.08169,-0.00989,0.04175,-0.02088,-0.01381,-0.01688,-0.0678,0.05757,0.11786,-0.06518,0.13766,-0.08735,-0.04832,-0.0003,0.00492,0.1004,0.01857,0.00168,-0.01045,0.05865,-0.09667,-0.08519,-0.00833,0.02477,0.06707,0.0862,-0.01977,-0.02275,-0.12126,-0.13617,-0.04052,0.02234,0.04972,-0.07963,-0.06825,0.01845,0.00022,-0.01763,0.00382,-0.07484,-0.02245,-0.14835,0.00501,0.10495,-0.02215,0.09337,0.03377,0.06679,-0.08928,0.1268,0.02447,0.0629,-0.08886,-0.02745,0.11976,0.05748,-0.03264,-0.13207,0.08257,-0.03792,-0.01778,-0.05957,0.08512,0.09352,-0.05944,0.07273,0.02568,-0.05033,-0.00385,-0.09049,0.0337,-0.10282,0.09952,0.05337,-0.01214,0.07136,0.05017,-0.02914,0.08627,0.01519,-0.00133,0.09024,-0.0758,0.03978,-0.0114,0.01906,-0.00527,0.04507,-0.04244,0.05217,0.06272,0.01938,-0.04827,0.03507,0.00166,-0.02002,-0.01499,-0.04972,0.00603,-0.05947,-0.0373,-0.04884,-0.03613,0.01344,-0.01625,0.05032,0.01454,-0.04869]},{"domain":"chemistry","key":"delta_g_from_k","name":"Standard Gibbs energy from the equilibrium constant","package":"chemistry-ai999x","example":"K = 1.0e5 at 298 K. What is ΔG°?","v":[0.0482,-0.00265,-0.02926,0.11001,-0.07232,0.06148,0.05347,-0.00873,-0.05506,-0.00473,0.00277,-0.00594,-0.13544,0.02478,-0.00105,-0.05768,0.03278,0.05313,0.02519,0.01335,-0.05478,0.00046,-0.01442,0.01558,-0.00822,0.03745,0.05799,-0.04977,-0.01185,0.02734,-0.0227,-0.007,0.02027,0.02233,-0.06673,0.11508,-0.04867,-0.03143,-0.05037,-0.16288,-0.0008,-0.08538,-0.08412,0.06639,-0.01508,0.06745,0.03114,-0.0436,0.1391,0.10097,0.0143,-0.00981,0.12273,0.12785,0.04937,-0.05468,-0.05291,-0.04854,0.02778,0.06155,-0.09179,0.0286,-0.0637,-0.11164,0.04119,0.00503,-0.12785,-0.01906,0.05808,-0.05474,-0.00313,0.00431,-0.14307,0.0015,0.07007,-0.06308,-0.04933,-0.03236,-0.07168,0.08086,0.02658,0.06889,0.02819,0.13291,-0.01283,-0.002,-0.06942,0.02773,-0.00237,0.06609,0.00862,-0.01837,0.06356,0.10829,-0.02601,0.01095,-0.1002,-0.00631,0.07094,-0.13687,0.07128,0.04362,0.00893,0.06028,-0.01947,-0.06412,0.00909,-0.00625,-0.02619,-0.01814,-0.01559,0.08051,0.03816,-0.07218,0.01921,0.01693,-0.02463,-0.06494,-0.01657,-0.03288,0.05685,0.1007,0.04968,-0.10674,-0.06329,-0.10158,0.03957,0.02976,-0.05146,-0.07846,-0.00816,-0.03845,0.00894,0.02463,0.11754,0.01927,-0.05703,-0.00096,0.02879,-0.04524,-0.01972,0.05572,-0.13081,0.0583,-0.02759,-0.03548,-0.0208,-0.07741,0.06745,-0.04438,0.03835,0.00082,0.03467,0.0368,0.00689,-0.00051,0.20528,-0.06848,0.01041,-0.16901,-0.09215,0.06941,-0.01948,0.09583,-0.03,-0.04794,0.00767,-0.01153,-0.09326,0.01898,0.0656,-0.00987,0.03259,0.03153,0.00974,-0.10958,-0.04584,0.06901,0.01591,0.03257,0.0966,-0.05594,-0.09905,0.02944,0.03785,-0.08713,-0.01073,-0.03267,-0.00184,-0.11275,-0.03495,0.14724,0.01203,0.05336,0.00881,0.02459,-0.04705,0.16264,-0.05046,0.01445,-0.07667,-0.02023,0.09132,0.011,-0.0278,-0.15365,0.01423,0.0045,-0.07543,-0.08447,0.02121,0.13761,-0.03265,0.0473,0.07469,-0.00614,-0.07907,-0.09304,-0.02823,-0.02038,0.07787,0.07124,-0.05104,-0.0037,0.02089,0.01542,0.0678,-0.01451,-0.00899,0.09533,0.00938,-0.03111,0.01859,-0.07745,0.0067,0.07039,0.04654,0.0735,-0.00526,-0.01512,0.01041,0.05045,-0.03855,0.05319,0.02612,0.05561,-0.01383,0.00895,-0.01872,-0.04821,-0.0221,0.15849,-0.11452,0.04116,0.02221,-0.01547]},{"domain":"chemistry","key":"delta_g_nonstandard","name":"Gibbs energy change at non-standard conditions","package":"chemistry-ai999x","example":"ΔG° = -33.0 kJ/mol, T = 298 K and Q = 100. What is ΔG?","v":[0.0469,0.11813,-0.02467,0.04056,-0.07942,-0.06895,-0.02529,0.06236,-0.13678,-0.08402,-0.00896,-0.03227,-0.08083,0.01952,0.0068,-0.0706,0.05333,0.03668,-0.00545,0.03182,-0.03681,0.02655,-0.03112,-0.03032,-0.07883,0.07956,0.02183,-0.02853,-0.07299,0.07139,-0.02634,0.10977,0.04662,0.003,-0.1125,0.11878,-0.09794,-0.05408,0.00371,-0.11229,-0.04441,-0.04234,-0.02927,0.0447,-0.00841,0.05237,0.04401,0.00445,0.01558,-0.02056,-0.02361,-0.027,0.06218,0.00928,-0.01136,0.10709,-0.02983,0.02804,-0.02623,-0.03813,-0.06983,-0.02526,-0.0487,-0.0713,0.05365,-0.03761,-0.07913,0.01388,-0.0174,0.07954,-0.01127,0.01428,-0.12586,0.01946,0.13673,-0.11758,0.02219,0.07472,-0.05419,0.04506,-0.00063,0.0222,0.01916,0.13462,-0.01445,0.01751,-0.02999,-0.02676,0.02565,-0.01385,-0.0634,-0.06551,0.15435,0.09881,-0.04667,0.03606,-0.03366,0.07878,0.08451,-0.0999,0.06329,0.04473,-0.02399,0.09916,-0.01005,-0.03414,-0.00887,0.07031,0.04328,-0.06391,-0.0156,0.0883,0.06848,-0.08069,0.00122,-0.00851,-0.05848,-0.02311,0.03266,-0.05546,0.02803,0.1057,-0.03653,-0.02382,-0.01126,-0.07263,0.01976,0.03043,-0.01703,0.00333,-0.04398,-0.05214,-0.04125,-0.0063,0.17026,0.02476,-0.00385,0.0182,-0.09599,-0.09022,0.01141,-0.00119,-0.08998,-0.00826,0.04565,-0.0279,0.08427,-0.08084,0.08459,-0.01494,0.0499,-0.09977,-0.04343,-0.02728,0.04053,0.00047,0.0822,-0.12441,0.01905,-0.0861,0.0111,-0.0205,0.0655,0.00065,0.02172,0.00099,0.0097,0.01015,-0.0937,-0.09743,0.02231,0.07355,-0.00665,0.04308,-0.03544,-0.08651,-0.00664,-0.01399,-0.02703,0.08503,0.06251,0.04867,-0.10376,-0.02371,0.06593,-0.14518,-0.04997,0.00525,0.05923,-0.04874,0.00675,0.0397,-0.03546,0.04133,0.02456,0.0257,-0.06756,0.14799,-1e-05,0.01132,-0.14213,-0.02169,0.19454,-0.09073,-0.07216,-0.0785,0.03482,0.02663,-0.00718,-0.0365,0.08835,0.04554,0.02572,0.07338,0.05599,-0.06844,-0.11524,-0.06276,0.05361,-0.04313,0.14746,0.02537,0.04481,0.03944,0.04576,-0.06542,0.07314,-0.01485,0.02259,0.09113,-0.01366,0.03102,0.00071,-0.04026,0.10091,0.08418,0.0756,0.04458,0.04678,0.01311,0.05345,0.02994,0.02307,0.01401,-0.0915,-0.02212,-0.05349,0.06307,0.02338,-0.09567,-0.1628,0.09292,0.00239,0.00298,0.01408,0.02825]},{"domain":"chemistry","key":"dilution_final_concentration","name":"Dilution: final concentration","package":"chemistry-ai999x","example":"25.0 mL of 6.0 M HCl is diluted to 500 mL. What is the new concentration?","v":[0.05824,0.07948,0.0142,-0.14089,0.03778,-0.05572,-0.03358,0.12416,0.0154,-0.01494,0.03277,-0.014,-0.04678,0.01077,0.06988,-0.07761,-0.0499,0.05372,0.00959,0.03257,0.00715,0.12765,-0.10986,-0.02185,0.02747,-0.07448,-0.02773,0.06428,-0.04414,0.03216,-0.01446,-0.04225,-0.02179,-0.02627,-0.01732,0.03585,-0.08161,0.02546,0.10974,0.0708,0.03362,0.05682,-0.00363,-0.10385,0.10841,0.00256,0.06599,-0.04845,-0.16088,-0.12423,0.06938,-0.01812,-0.00675,-0.14415,-0.03853,0.14093,0.00683,-0.03868,-0.12857,-0.0017,0.11132,0.07372,0.07551,0.06022,-0.01478,0.01227,0.03251,-0.11538,0.04991,0.07374,0.05898,-0.06738,-0.04913,0.09844,0.03857,0.03187,-0.06908,-0.04937,-0.07875,-0.03352,-0.02932,0.00164,0.00435,-0.08855,0.01607,0.09221,-0.06384,-0.07307,0.02446,-0.07288,0.04749,0.00714,-0.01979,0.02501,-0.04951,0.13346,-0.01609,-0.0087,0.05904,-0.08202,0.05348,0.04468,0.085,0.00282,-0.03678,0.03085,-0.02005,0.02974,0.04247,0.07499,0.06651,-0.03774,-0.07998,0.00934,-0.04191,0.10519,-0.01108,0.00869,0.07871,0.00016,0.02087,-0.03575,0.07521,0.01642,-0.08804,0.13978,0.06979,-0.03877,0.01969,-0.04601,0.01253,-0.03523,-0.04667,0.00659,-0.04341,0.00091,0.01693,0.132,0.01341,-0.08957,0.02476,0.13818,-0.02378,0.01471,-0.00309,-0.04427,-0.00795,0.03128,-0.03449,0.05759,-0.00269,-0.03847,-0.06327,0.00641,0.03193,-0.08201,-0.00613,-0.0619,0.02356,-0.01429,-0.00269,0.04228,0.05337,-0.01644,0.0986,0.03262,-0.00092,-0.03138,-0.03318,-0.15765,-0.00626,0.06109,-0.05521,-0.02569,0.04113,-0.06333,-0.08353,-0.06312,0.0476,-0.12938,0.06764,0.03626,-0.0228,-0.04009,0.04516,-0.07407,-0.00966,0.06362,0.05967,0.01005,-0.02111,-0.0908,0.02805,-0.09446,0.06375,-0.05551,-0.06509,-0.10884,-0.06325,-0.0086,-0.02028,0.01518,0.06394,-0.11353,0.04808,0.01507,-0.0658,-0.06758,0.06037,0.01188,0.05917,-0.14916,0.05036,0.03036,0.00359,-0.11968,0.11227,0.0558,-0.06506,-0.09395,-0.03391,-0.05475,0.05784,0.0099,0.09653,0.06417,0.02925,0.01076,0.07608,0.01937,-0.03123,0.10738,0.05215,-0.06958,0.0112,-0.05358,-0.01758,-0.07678,0.12063,-0.03269,0.12949,-0.00346,-0.00735,0.0112,0.00567,0.01079,0.0305,0.0332,-0.00215,-0.10129,-0.02318,-0.11375,-0.02385,0.01438,0.08446,0.04047]},{"domain":"chemistry","key":"dilution_volume","name":"Dilution: volume of stock needed","package":"chemistry-ai999x","example":"What volume of 12.0 M HCl is needed to prepare 500 mL of 0.100 M HCl?","v":[0.05086,0.04925,0.02201,-0.09199,0.04995,-0.02177,0.04472,0.10269,0.04267,-0.02075,0.05045,-0.01549,0.01396,0.04965,0.02055,-0.06255,-0.04193,0.09112,-0.09353,0.03232,-0.07199,0.08822,-0.11963,-0.10066,0.04687,0.01954,-0.01779,0.0386,-0.02581,0.02933,-0.08023,-0.15746,-0.0335,0.03068,-0.03402,-0.04607,-0.02588,-0.01683,0.13801,0.13958,0.04006,0.09041,-0.01352,-0.01599,0.07386,0.04844,0.02652,-0.04705,-0.02941,-0.03382,0.06232,-0.00877,-0.07863,-0.08569,-0.04355,0.11507,-0.04938,-0.01262,-0.07765,0.04018,0.03986,0.1098,-0.02564,0.10314,-0.06396,0.01161,-0.01234,-0.14263,0.08435,0.1094,-0.00191,-0.01729,-0.0605,0.0541,0.05717,0.06487,-0.10968,-0.03166,-0.03375,0.03018,0.02401,0.07993,-0.08247,-0.03766,-0.00574,0.10497,-0.09438,0.08213,-0.00049,-0.00011,0.05035,0.02818,0.01293,-0.04268,-0.04962,0.09994,-0.05458,-0.0498,-0.04203,-0.02504,-0.03735,-0.01195,0.09145,-0.10146,-0.06458,-0.0495,-0.04793,0.01141,0.05276,0.05653,-0.01702,-0.06635,-0.13827,0.04016,-0.06109,0.01936,-0.00409,0.06489,-0.00042,0.03764,0.06167,0.01206,0.12263,-0.03671,-0.02977,0.03622,0.00537,0.03018,0.0878,-0.05681,-0.05347,-0.03838,-0.08175,0.02013,0.02594,0.05035,0.07551,0.0466,0.06321,0.08314,0.01313,0.09572,-0.03254,-0.0369,-0.02586,-0.12758,-0.03613,-0.00282,-0.00458,-0.02184,0.02856,0.00535,0.05766,0.09516,-0.0639,-0.01401,-0.03289,-0.00627,0.08101,-0.04292,-0.03359,0.05765,-0.03849,0.07399,0.0119,0.04442,0.02209,-0.04452,-0.04987,-0.10407,-0.04563,0.09468,-0.11227,-0.09866,0.08065,-0.08293,-0.00325,0.0306,0.04553,-0.03834,0.06678,-0.00257,0.09701,0.02147,0.11204,0.01518,0.13863,0.14032,0.06596,-0.00301,-0.06879,-0.08885,-0.01173,-0.08424,-0.03045,-0.08728,0.03066,-0.02651,-0.09298,0.02041,0.06352,0.00263,0.07186,-0.02292,-0.00032,-0.03032,-0.07479,-0.11215,-0.05789,0.05871,-0.03525,-0.16245,0.04089,-0.04357,0.01656,-0.06043,0.0453,0.00138,0.04716,-0.01276,-0.04934,-0.01176,-0.0487,-0.07647,0.05713,0.05749,0.05401,0.0657,0.05724,0.08131,-0.02593,0.08477,-0.03998,-0.10587,-0.0445,-0.02798,-0.01479,0.00786,0.04124,-0.06378,0.0697,-0.05433,-0.07719,-0.07466,0.06729,0.07124,0.05854,0.03731,-0.05097,-0.06024,-0.0898,-0.06784,0.04109,-0.08306,0.03751,0.01183]},{"domain":"chemistry","key":"electrolysis_mass","name":"Mass deposited in electrolysis (Faraday's law)","package":"chemistry-ai999x","example":"What mass of copper is deposited from a Cu2+ solution by a current of 2.00 A flowing for 30.0 min?","v":[-0.03595,0.11911,-0.05283,-0.0401,0.06412,0.01318,0.10439,0.00124,-0.03986,0.11121,-0.02017,0.00561,0.12696,-0.03362,-0.00757,0.12122,-0.04614,-0.06521,0.04846,0.07444,0.036,0.05616,-0.00918,-0.00817,-0.05453,0.10985,-0.01632,-0.00852,-0.0178,0.01494,-0.021,-0.07026,-0.06246,0.01368,0.09187,0.03856,-0.05932,-0.05543,-0.0012,-0.1355,-0.05808,0.06487,-0.09455,0.0289,-0.12227,0.05572,-0.08667,0.06346,0.07572,-0.04874,-0.04397,0.02129,0.00362,-0.03938,0.07486,0.0092,-0.04974,0.04023,-0.05068,0.05045,0.03961,0.00047,0.02137,-0.12686,0.02219,0.13123,0.05967,-0.01773,0.05546,-0.00654,0.02931,-0.12818,-0.01002,-0.03688,0.05131,0.04464,0.15913,-0.06998,-0.06384,-0.02754,0.00963,-0.08503,0.07598,0.05636,0.02651,0.02364,0.06898,0.08214,0.07055,0.02106,0.03549,-0.08423,-0.04283,0.05793,0.07811,-0.01302,-0.12141,-0.02789,-0.07719,-0.0065,0.12383,-0.06944,-0.1081,-0.06171,-0.04146,0.10052,0.01525,0.06834,0.00236,-0.06659,-0.05014,0.10126,-0.00075,0.04407,0.05212,-0.0737,-0.00179,-0.02386,-0.03315,0.0929,0.02197,-0.03129,0.09297,0.11078,-0.03939,0.02379,-0.1259,0.07188,0.03434,0.08006,-0.02139,0.06911,-0.05176,-0.0194,0.04141,0.02531,-0.03527,0.00956,-0.01095,-0.04914,0.01563,-0.08823,-0.01118,-0.04606,0.00031,-0.05789,-0.01807,0.04396,0.00435,0.07416,0.05,-0.01097,-0.02228,-0.0174,-0.08908,0.01594,0.01977,-0.02292,0.04181,-0.00388,-0.01886,0.05511,0.07994,0.08503,-0.1204,-0.03817,0.00264,0.03128,-0.12022,-0.06456,-0.10484,0.017,0.03953,-0.00151,-0.07324,0.02498,-0.05248,-0.11356,-0.14691,0.12207,0.08634,0.12626,-0.0113,-0.02584,-0.08961,0.12281,-0.02758,-0.03438,0.01216,-0.12833,-0.05827,0.08841,-0.03896,0.03054,0.02485,0.05059,-0.02908,0.11039,-0.02626,-0.02358,-0.044,-0.0043,-0.04199,-0.04118,-0.045,-0.05744,-0.02658,-0.04582,-0.08008,-0.04895,0.04227,0.0806,0.0489,-0.04032,0.08352,-0.03089,-0.09062,-0.01205,-0.02149,-0.00925,0.04049,0.01494,-0.06622,-0.02035,-0.02893,0.0022,0.03958,-0.02888,-0.03557,0.08849,0.0375,0.07039,-0.04239,0.00933,0.07328,0.00641,-0.06808,-0.00557,-0.01068,-0.04875,-0.08822,-0.08527,-0.01821,-0.02263,0.01023,0.02072,0.12179,-0.0609,-0.02541,0.12931,-0.04226,0.04,0.12505,0.08389,-0.05925,0.03792]},{"domain":"chemistry","key":"electrolysis_time","name":"Time for electrolysis (Faraday's law)","package":"chemistry-ai999x","example":"How long must a current of 5.00 A flow to deposit 10.0 g of Ni from a Ni2+ 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formula from percent composition","package":"chemistry-ai999x","example":"Find the empirical formula of a compound with 40.0% C, 6.71% H and 53.3% 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What is the enthalpy of reaction?","v":[0.03826,0.09801,-0.04137,0.04144,-0.00071,-0.0464,0.06987,0.10516,0.00764,0.02933,0.01214,0.00547,-0.02996,0.05745,0.06243,-0.02702,-0.0114,0.05157,-0.09176,0.01425,0.08456,0.05304,-0.07953,-0.06971,-0.03935,0.10599,0.07707,0.0361,-0.10158,0.01126,-0.02401,0.03109,0.01028,0.02413,0.0544,0.10706,-0.02795,0.00295,0.05177,0.02783,0.01266,-0.02133,0.11547,-0.01474,0.03597,-0.00057,0.04954,0.03835,0.02534,0.0799,0.00679,0.04007,-0.01793,0.08352,-0.03672,0.1106,0.06544,0.01203,0.03739,-0.0168,-0.02287,-0.05704,0.08039,0.14125,0.01412,-0.06136,-0.16885,0.01231,0.003,0.04029,-0.01291,0.01456,-0.05883,0.01299,0.08567,0.07726,-0.07149,-0.01477,-0.00429,-0.06378,-0.10053,-0.14179,-0.0149,-0.0016,0.0419,0.03496,-0.10671,-0.00786,0.04431,-0.01171,0.06722,-0.08206,0.10985,0.02445,-0.15566,0.01351,-0.06474,-0.07473,-0.02776,-0.01512,0.06743,-0.01461,-0.08879,0.01266,-0.05917,0.06719,-0.0441,0.05843,-0.06937,0.05151,0.0481,0.05321,0.00245,-0.0304,-0.02507,0.0026,0.0515,-0.03945,-0.0103,0.1303,-0.01638,-0.05872,0.07975,-0.02003,0.00334,0.1297,0.07081,0.0029,0.03257,0.01315,0.00223,0.00736,-0.03749,-0.04981,0.09692,-0.03115,0.09925,0.00822,-0.0539,0.00289,-0.03562,0.0216,0.05214,-0.03047,-0.00019,0.00239,-0.02319,-0.05669,-0.00672,-0.09742,0.02705,-0.15869,-0.02319,0.01277,-0.08749,0.00014,-0.0744,-0.12717,0.06666,0.03017,-0.01643,-0.00319,-0.02597,0.0258,-0.07596,0.03621,-0.11425,0.00386,0.02533,-0.05492,0.02266,0.02943,-0.05762,-0.01932,-0.14601,-0.04495,0.00506,0.03395,0.00114,0.03764,0.04132,0.05628,-0.14985,-0.05394,-0.09139,-0.066,-0.0272,0.02932,0.05029,0.01625,-0.02566,-0.03765,0.08079,0.06013,0.0502,-0.10236,-0.13424,0.00597,-0.09254,-0.03168,0.03126,-0.03033,0.19025,-0.13808,-0.07664,-0.02524,0.05392,0.09136,-0.10247,-0.1186,0.0613,-0.13208,-0.04286,0.03198,0.05715,-0.00626,0.06777,-0.04588,0.05626,0.07198,0.02637,0.08797,0.07615,0.04923,-0.06322,0.04613,0.0077,0.06666,-0.03066,0.06483,-0.04725,-0.02477,0.00614,-0.049,0.03186,-0.03215,-0.04104,0.06019,-0.09412,0.09234,-0.02543,0.01244,-0.04706,-0.00657,-0.0707,-0.04305,0.07966,0.00221,0.00046,0.00182,-0.13157,0.04265,0.10937,0.08994,0.03909,0.03092]},{"domain":"chemistry","key":"equilibrium_ice","name":"Equilibrium concentrations (ICE table)","package":"chemistry-ai999x","example":"For N2O4 ⇌ 2 NO2, Kc = 4.6e-3. Initially [N2O4] = 0.10 M and [NO2] = 0. What are the equilibrium concentrations?","v":[0.00309,0.04064,-0.04034,-0.03791,0.08352,0.04176,-0.00035,0.04068,0.051,-0.06157,-0.01979,-0.04635,-0.19596,-0.03765,0.0956,-0.11152,0.01771,-0.05283,0.11675,-0.0212,-0.03397,0.02468,0.02883,0.01987,0.03466,0.05512,0.03049,-0.00728,-0.00703,0.02483,0.06592,-0.04912,0.06744,-0.03975,-0.01505,0.04561,0.00736,0.09694,0.01366,-0.05463,0.05094,-0.06967,-0.05778,-0.01222,0.05015,0.05708,0.01421,-0.00291,-0.06639,-0.07174,0.03257,0.14576,0.04061,-0.07819,0.01793,0.04035,0.09486,-0.04762,0.00059,-0.05173,-0.00422,0.01214,-0.08606,-0.03236,0.04895,-0.06467,-0.05269,-0.16374,0.02925,0.02852,0.00996,-0.0691,-0.07987,0.01733,-0.05682,0.066,-0.04551,-0.04968,0.09103,-0.02887,0.03737,-0.02936,0.08188,0.03119,0.03439,0.0702,0.01061,-0.0462,-0.02278,-0.03696,0.10499,-0.02626,-0.04478,-0.01199,-0.09398,0.03457,-0.04773,0.02637,0.07103,0.01151,0.05109,0.00781,0.08012,0.00153,0.0498,0.01607,-0.1428,0.03876,0.11753,-0.08574,0.1188,-0.0033,0.05547,-0.08024,0.02533,0.06551,0.02876,0.02303,-0.01861,0.09247,-0.0113,0.01951,0.0888,-0.05856,0.01212,0.1037,0.07429,0.01131,0.0125,-0.00542,0.02655,0.00157,-0.02244,0.01828,-0.10348,-0.04736,-0.03946,0.1434,0.12232,0.04456,-0.01027,0.03972,0.00619,-0.01279,-0.07165,0.00947,0.07052,0.0701,0.05961,-0.04854,-0.02111,0.0881,-0.129,0.02943,0.09382,-0.03157,0.08312,-0.05268,0.02891,0.00629,-0.01605,-0.03395,-0.04119,0.0116,0.04898,-0.0517,0.04284,-0.05676,-0.04637,0.08985,0.07769,0.00223,-0.12095,-0.02579,0.04373,-0.1262,-0.04621,-0.02491,0.03804,-0.05737,0.05961,0.058,-0.17711,0.01401,-0.1345,-0.00885,-0.05365,0.00521,0.06822,0.01488,0.00704,0.01426,-0.00211,-0.01998,-0.09929,-0.07641,-0.05416,-0.036,-0.13907,-0.00433,0.02221,-0.04038,0.03711,-0.0347,-0.06716,-0.00897,-0.0488,-0.0898,-0.01376,0.09673,0.07811,-0.10986,-0.01812,0.08647,-0.0063,0.03257,0.05652,0.00042,-0.15827,-0.07186,0.02044,-0.00841,-0.08763,0.09735,0.03442,-0.01603,-0.07685,-0.02464,0.11321,0.03024,0.04908,-0.0075,-0.05161,-0.10823,-0.06754,-0.06171,-0.06291,0.0168,0.01895,-0.03911,0.10809,0.05659,-0.03684,0.05738,-0.03459,0.02154,0.06587,-0.09122,-0.02454,0.06987,-0.10724,0.12792,-0.03156,0.04383,0.02467,0.07856]},{"domain":"chemistry","key":"first_order_concentration","name":"First-order integrated rate law","package":"chemistry-ai999x","example":"A first-order reaction has k = 0.0150 s^-1. If [A]0 = 0.800 M, what is the concentration after 60.0 s?","v":[0.02223,0.06111,-0.02776,-0.03956,0.0658,-0.07962,-0.02965,0.04333,0.04227,0.01416,-0.07284,0.03772,-0.07874,-0.01123,0.14901,-0.02738,-0.01799,-0.04982,0.0335,0.05064,0.00586,0.03019,-0.0046,0.06581,-0.0913,0.03769,0.03383,0.08284,0.0058,-0.08904,0.03368,0.09779,0.14525,0.00365,-0.04361,0.08942,-0.0074,0.06139,-0.00042,-0.01228,0.04812,4e-05,-0.07125,0.01426,-0.0052,0.04196,0.0017,0.09256,-0.04114,-0.07137,-0.10341,0.10728,-0.02069,-0.16825,0.04227,-0.01765,0.08077,0.02857,-0.05824,-0.07772,0.03315,-0.02501,0.08953,0.02236,-0.00608,-0.01697,0.01246,-0.03177,0.01567,-0.02389,-0.02509,-0.09028,-0.06318,-0.0397,0.03843,-0.01608,0.08662,-0.03787,-0.02743,-0.15401,0.04179,-0.01388,0.10175,-0.00398,0.03675,0.03152,-0.02452,-0.01671,-0.05165,0.04986,0.05021,-0.10204,0.00538,-0.11742,0.02049,0.12526,0.08948,0.06971,0.06662,0.01952,-0.00285,-0.02892,0.06549,0.06893,0.037,0.06714,0.01391,0.01995,0.17388,-0.0061,0.05018,-0.03834,-0.03985,-0.00681,-0.00229,0.14382,-0.04649,0.02609,0.05801,0.11042,-0.02341,-0.02543,0.03482,0.09194,-0.03625,-0.01875,-0.02639,-0.00106,-0.08457,-0.00477,0.07867,-0.01783,0.02646,-0.02558,0.06536,-0.1172,0.02513,0.04667,0.03944,-0.0831,0.00233,0.0657,-0.02063,-0.02746,-0.12446,0.03011,0.00753,0.09785,-0.03354,-0.00194,-0.08248,-0.13302,-0.08885,-0.0106,0.06834,-0.12583,0.01414,0.03618,0.06009,-0.11586,-0.01603,-0.0657,-0.06401,-0.04675,0.03837,0.05953,-0.0087,-0.02792,0.03648,0.0182,0.01055,0.04433,0.01366,-0.02267,0.10818,-0.01381,-0.07695,-0.07514,0.03661,-0.12577,-0.00764,-0.01758,0.01768,-0.03947,-0.08768,-0.01225,-0.04936,-0.08125,-0.06492,-0.04115,0.02893,0.01181,0.04549,0.00155,0.04692,0.02428,-0.02712,-4e-05,0.00179,-0.13404,-0.09304,-0.00573,-0.10399,-0.09723,0.17782,0.03751,0.10022,-0.08242,0.02328,0.08538,0.07718,-0.00079,0.00772,0.09954,0.01374,-0.07961,0.02253,0.02237,-0.18182,-0.02448,-0.06309,0.0065,0.08255,0.02311,-0.03647,-0.0282,0.07354,-0.03365,0.158,-0.00104,0.00979,-0.00229,-0.06701,-0.09673,0.04712,-0.01717,0.04229,-0.08377,-0.05214,0.04622,-0.06053,-0.0147,-0.09801,0.05082,0.01664,0.01481,0.04209,-0.01463,0.08823,0.09324,-0.04819,-0.01541,-0.00418,-0.00403,-0.00222,0.0068]},{"domain":"chemistry","key":"first_order_half_life","name":"Half-life of a first-order reaction","package":"chemistry-ai999x","example":"What is the half-life of a first-order reaction with k = 0.0250 s^-1?","v":[0.07423,-0.04392,-0.05129,0.09057,0.13336,0.01566,-0.06025,0.03528,0.062,-0.01468,-0.03907,0.10465,0.00517,-0.0119,0.09116,-0.06188,0.04403,0.01479,0.06569,0.06986,0.03292,0.09089,0.06239,0.00456,-0.10374,0.024,0.07174,0.06516,-0.06743,-0.0201,-0.01141,0.18871,0.0477,0.03482,-0.08735,-0.04932,0.00729,0.02928,0.00151,0.02648,-0.04823,0.04297,-0.05122,0.00985,-0.02577,0.06262,-0.02778,0.13307,-0.02896,-0.00195,-0.04386,0.13929,-0.03078,-0.00487,0.08618,-0.03743,0.04147,0.08205,0.00512,-0.05395,-0.04686,-0.05098,0.04025,0.11478,-0.00972,0.01393,0.07788,0.00223,0.04231,-0.0337,-0.00784,-0.00189,-0.14651,-0.05519,0.04103,0.05418,-0.00634,-0.04026,0.04211,-0.19524,0.00522,0.02721,0.01041,0.00892,0.06202,-0.00811,0.00117,-0.01102,-0.04849,0.06027,0.04134,-0.12653,0.05057,-0.12529,0.00533,0.06788,0.00652,0.04759,0.02515,0.07738,-0.04224,-0.01483,0.02676,0.08929,-0.01942,0.05103,0.03866,-0.11964,0.04102,-0.07046,0.06493,-0.09125,0.04724,-0.01632,-0.05581,0.01182,-0.09578,0.01612,-0.02638,0.0343,0.02005,-0.05722,0.0349,0.05025,-0.06371,-0.10662,-0.06742,0.02252,-0.13388,-0.04814,0.08401,-0.01228,0.06802,0.01795,0.08007,-0.12413,0.0051,0.05364,0.01925,-0.00534,-0.00111,0.05133,0.01758,0.05758,-0.08411,0.02218,-0.01622,0.04603,0.02991,-0.04413,-0.02671,-0.01364,-0.03388,0.02614,0.07727,-0.07589,0.0636,0.0623,-0.03108,-0.10881,-0.00226,-0.10317,-0.16753,-0.15134,-0.04736,0.00187,-0.07764,-0.03695,0.07577,-0.0169,-0.06841,0.05175,0.05635,0.01821,-0.00801,-0.03624,-0.00064,0.03757,0.00636,-0.10547,0.01453,-0.01683,0.0194,-0.01953,-0.02991,0.01395,-0.01361,-0.15169,-0.06833,0.04888,-0.05035,0.07013,-0.04215,-0.00209,0.04114,0.0392,-0.04395,0.09529,0.01614,-0.10471,-0.01962,-0.00807,-0.02168,0.04242,0.06503,-0.01726,0.14141,-0.05332,-0.07576,-0.0043,-0.01133,0.09975,0.02541,0.06401,0.01032,0.00623,-0.12838,0.02477,-0.14149,0.02309,-0.10117,0.0262,0.0808,-0.09783,-0.0157,-0.01534,0.00378,-0.00905,0.12748,-0.00653,0.03128,0.04758,-0.0617,0.03359,0.04421,0.05999,0.01856,-0.00657,-0.09852,0.04256,-0.11424,0.0345,-0.10197,0.00116,-0.00535,0.06604,-0.02106,-0.10474,-0.0119,0.07175,-0.10229,0.07563,0.00168,0.01498,-0.01919,-0.00618]},{"domain":"chemistry","key":"first_order_time","name":"Time to reach a concentration (first order)","package":"chemistry-ai999x","example":"A first-order reaction has k = 0.0300 s^-1. How long does it take for the concentration to fall from 0.500 M to 0.100 M?","v":[0.0132,0.07069,-0.01304,0.03216,0.04143,-0.02938,-0.01377,-0.01977,0.04429,-0.04773,0.04011,0.0713,-0.00362,0.02188,0.10608,-0.03824,0.00185,-0.01883,0.06153,0.02988,-0.02735,0.01576,0.01675,-0.0135,-0.01164,0.04192,0.01026,0.07344,-0.02248,0.0028,0.04734,0.0617,0.03502,-0.00977,-0.03776,0.04988,0.00576,0.06784,0.04842,0.09769,0.03311,0.06181,-0.1143,0.00834,0.01546,0.09165,-0.00244,0.1122,0.07734,0.03213,-0.13522,0.13035,-0.09248,-0.09495,-0.00555,-0.02235,0.06708,0.04616,-0.0141,-0.08719,-0.05638,0.02249,0.03722,0.02836,-0.0445,-0.05976,-0.01739,-0.00899,0.02314,-0.00449,-0.02874,0.00087,-0.16569,-0.07942,0.04341,0.02361,-0.0088,-0.08446,0.0351,-0.12294,0.04642,0.04574,0.02872,-0.02051,0.00504,0.02868,-0.00245,0.01814,-0.02716,0.05214,0.07197,-0.05671,0.03344,-0.14417,0.03004,0.10079,0.12769,0.04571,-0.03916,0.11085,-0.00173,-0.03463,0.01134,0.0001,0.02338,0.10773,-0.03866,-0.00627,0.16871,-0.0074,0.00393,0.0082,-0.06404,-0.02859,-0.0389,0.03217,-0.11587,0.05837,0.00513,0.18797,0.05041,-0.00457,0.07227,0.04257,0.01571,-0.02826,-0.0689,0.01266,-0.06024,-0.01486,0.05458,0.00056,0.01887,0.01183,0.13833,-0.06733,0.04617,0.04179,0.16006,-0.01889,-0.05894,0.05257,0.04455,-0.00774,-0.18385,-0.04227,0.01035,0.0532,0.02997,0.00167,-0.02723,-0.11003,-0.05872,-0.01507,0.09264,-0.0864,-0.00058,0.05498,0.02756,-0.11833,0.01837,0.00813,-0.10827,-0.03086,-0.02461,0.00635,-0.00692,-0.02313,0.04485,0.05397,0.02336,0.06713,-0.0352,0.02134,0.06432,-0.07461,-0.01457,0.05394,-0.03,-0.10009,-0.12658,-0.03985,0.07245,-0.04017,-0.10164,0.05286,0.01593,-0.0782,-0.11163,-0.00093,-0.0351,-0.02091,-0.01212,-0.0081,-0.01786,0.00975,0.0189,-0.04755,-0.00888,-0.06071,-0.05155,0.03422,0.01009,-0.03169,0.12271,-0.01624,0.13425,-0.15104,-0.06259,0.09614,-0.03088,-0.01508,-0.02754,0.01419,-0.04119,-0.06248,-0.09224,-0.00425,-0.13861,-0.01246,-0.10076,0.03232,0.05519,-0.05205,0.00529,-0.07759,0.01586,0.03993,0.11337,-0.06711,0.00498,0.01243,-0.15872,-0.10236,-0.00102,0.00638,0.03848,-0.00419,-0.09271,0.06683,-0.11173,0.02474,-0.08417,0.00533,0.01926,0.0983,0.04454,-0.04601,-0.0054,0.09856,-0.08504,0.01583,0.01469,-0.04082,0.06471,-0.02471]},{"domain":"chemistry","key":"freezing_point_depression","name":"Freezing-point depression","package":"chemistry-ai999x","example":"What is the freezing point change of a 0.50 mol/kg aqueous solution of a nonelectrolyte (Kf = 1.86 K·kg/mol)?","v":[0.11156,-0.02612,-0.02555,-0.06756,-0.05974,0.0326,0.02595,0.08767,0.00496,-0.08187,0.08339,-0.00417,-0.06906,-0.07595,0.02594,-0.16881,-0.06301,-0.04234,-0.02728,0.15785,0.05098,0.06769,-0.17645,-0.0207,0.02311,-0.06617,0.05113,0.01879,0.11553,-0.03478,-0.05662,0.04635,-0.04533,-0.05655,-0.15758,0.08066,0.06667,-0.03722,0.03617,0.0678,0.00058,0.05552,0.03552,-0.05305,0.09225,-0.00662,0.06525,-0.07677,-0.00163,0.04496,0.00543,0.02271,-0.01049,-0.00422,-0.00596,-0.06548,-0.15854,-0.07209,0.01723,-0.10864,0.02725,0.11019,-0.03212,-0.00357,-0.05477,0.06108,-0.03676,-0.01217,-0.00533,0.0233,0.02375,0.05579,-0.0659,0.03233,0.03516,0.05391,0.00679,-0.12045,-0.10088,0.00078,-0.05242,-0.03648,0.05206,-0.05167,0.02222,0.01719,-0.08461,-0.00295,0.09647,0.06969,-0.00804,-0.01569,0.02697,0.00377,-0.06104,0.02197,-0.07827,-0.01,0.02606,-0.0932,0.049,0.0394,0.04188,0.04718,-0.00831,0.10211,0.15931,0.0624,-0.02075,0.01806,0.1286,0.03022,-0.02189,-0.052,0.02193,-0.00692,-0.00763,0.07725,0.02783,0.07135,0.07682,-0.02757,0.00316,0.05511,0.03842,0.04676,-0.03414,0.10732,-0.07485,-0.08174,-0.01886,-0.02042,-0.02681,0.01659,0.06521,0.06321,0.08855,0.08174,-0.06314,-0.05519,0.0035,0.11894,-0.12192,0.12367,-0.09881,-0.10905,0.04501,0.03192,0.033,-0.04268,0.01523,-0.13609,-0.04327,0.02669,-0.0038,-0.01569,0.0493,-0.05769,-0.12104,-0.10284,-0.07458,-0.04162,0.09032,0.06168,0.05829,-0.08025,-0.02223,0.03077,0.03955,-0.00275,0.07611,0.02513,0.08538,0.14221,0.02659,-0.03721,-0.09597,-0.01879,9e-05,0.03244,-0.02585,0.05005,0.03471,-0.06263,-0.00763,-0.02867,0.06831,0.01336,0.05004,0.00258,-0.05173,-0.00665,-0.01485,-0.10246,0.07622,0.07202,-0.03646,-0.02679,0.00672,0.05346,-0.04254,0.07208,0.05267,-0.06152,-0.01251,0.01195,0.02739,0.04163,-0.06359,0.01777,0.10057,0.0095,-0.08772,0.04321,-0.02699,0.00464,0.00521,0.04449,0.01537,-0.02685,-0.10726,0.01173,0.06509,0.01949,0.03728,0.10207,0.04295,-0.04125,-0.04898,0.07196,-0.03789,-0.11393,-0.00929,-0.02382,-0.0176,0.1028,-0.12862,-0.04832,-0.15754,0.04648,-0.02225,-0.0418,-0.01317,-0.02928,0.01112,-0.02074,0.04643,0.01737,-0.04882,-0.027,-0.05361,0.03334,0.00506,-0.00441,0.02396,-0.10377]},{"domain":"chemistry","key":"gas_density","name":"Density 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K?","v":[0.0179,-0.06852,-0.14213,-0.02384,0.00579,0.0417,0.05429,0.008,0.08782,0.02444,-0.11545,-0.02613,0.04399,0.1437,0.02817,-0.02875,-0.00304,-0.04664,0.05716,0.08457,-0.01359,-0.03155,0.0498,-0.08751,0.03657,0.07909,-0.00603,0.03269,-0.07763,-0.03791,0.05108,-0.00471,0.01837,-0.05201,0.02182,0.15185,0.03871,0.03387,-0.02122,0.01015,-0.0008,0.08595,-0.01658,0.06788,-0.03233,0.04756,-0.06838,0.01713,0.04047,-0.00319,0.02223,0.0008,0.00385,-0.02078,-0.03986,0.02362,0.06011,0.06058,0.04538,0.01261,0.01042,-0.08739,-0.01364,-0.09355,-0.0434,-0.09606,-0.01968,-0.00467,-0.09806,0.02572,-0.11803,-0.08345,-0.04987,-0.05573,0.10172,0.03297,0.1355,-0.0569,-0.01697,0.03491,0.10459,0.00125,0.08211,0.0535,0.03473,-0.06455,0.02865,0.00565,0.0405,0.01815,0.0107,-0.00248,0.00375,-0.05292,-0.00291,0.00166,0.02867,0.04132,0.03751,0.03135,-0.0317,-0.06128,-0.02122,0.11979,0.03962,-0.05844,0.07088,0.10257,0.08803,-0.08605,-0.11163,-0.02553,-0.032,-0.01325,-0.08625,-0.02861,0.12878,0.10329,-0.05679,-0.08302,-0.08682,-0.02132,0.03571,-0.06479,-0.05215,-0.03315,-0.07015,0.00444,0.08511,0.00703,-0.07382,-0.05455,0.01188,-0.03171,-0.01368,0.06002,-0.08359,0.01201,-0.00119,0.03257,-0.0729,0.02946,0.0562,0.0086,0.11957,0.12609,0.06535,0.03211,0.0076,-0.01974,0.09741,-0.02796,0.04351,0.02811,0.13366,-0.09525,0.06432,-0.01735,-0.04239,0.0063,-0.02844,0.02876,0.00998,-0.09485,0.05973,0.03671,0.10238,-0.02832,-0.09782,-0.05144,-0.051,-0.04747,-0.066,-0.03051,-0.01229,0.0382,-0.0519,0.03202,0.11767,0.16541,0.0672,0.08219,-0.02982,0.08882,-0.01209,0.0025,0.03202,-0.01397,-0.06408,-0.00762,0.01378,0.00755,0.02836,-0.03454,0.01621,0.08644,0.09737,0.02786,-0.06007,-0.0926,-0.09551,0.05447,0.03459,-0.10055,-0.03394,-0.04033,-0.09365,0.01049,0.05222,-0.06187,0.12192,0.00172,0.07986,-0.08836,0.00488,0.08535,-0.03585,0.0814,-0.06032,0.02278,-0.02886,0.02635,0.03678,0.01485,-0.04404,-0.01683,0.0558,-0.06085,-0.12253,0.02094,0.05294,0.027,-0.02562,-0.06156,-0.08777,-0.04114,-0.03418,-0.06916,-0.03832,0.07749,0.06902,-0.06351,0.07769,0.00543,-0.07022,-0.01116,-0.02128,0.00776,-0.06534,-0.09772,-0.03325,0.10788,-0.24761,0.05989,-0.07163,-0.04955]},{"domain":"chemistry","key":"gay_lussac_final_pressure","name":"Gay-Lussac's law: final pressure","package":"chemistry-ai999x","example":"A tyre is at 2.20 atm at 20 °C. What is the pressure when it warms to 45 °C at constant volume?","v":[-0.03308,-0.02927,-0.02491,-0.16616,-0.05259,0.07983,-0.01536,-0.00577,0.03134,0.02244,-0.08108,-0.04503,0.05971,0.05498,0.06561,0.0546,0.05255,-0.01633,0.07646,0.09604,0.0593,-0.00011,-0.02207,0.07733,0.03033,-0.00017,0.01437,-0.05737,0.04302,0.06225,0.15745,0.0513,-0.02845,0.03571,-0.04442,0.23795,-0.02808,-0.00315,-0.05866,0.02893,0.05441,-0.04,0.03105,-0.00102,-0.07725,-0.01401,0.04088,0.01077,0.04999,0.01608,0.00248,-0.05114,0.05126,-0.05809,0.08432,0.0203,0.06896,-0.01481,0.00304,0.11598,-0.06839,-0.07023,-0.10195,-0.13881,-0.08918,-0.00496,-0.00542,0.02615,-0.03505,-0.02121,-0.02728,0.01005,-0.06608,-0.06423,-0.06536,-0.02653,-0.01375,0.08548,0.02434,0.00382,0.05715,-0.06338,0.14793,0.07508,-0.03466,0.00111,-0.04756,0.03695,0.09873,0.03114,0.06452,0.06081,-0.01361,-0.06142,-0.0248,-0.00505,0.10146,0.01418,0.02563,-0.10641,0.05956,0.03514,-0.02253,0.07618,-0.07798,0.10695,-0.03905,-0.00483,0.08479,0.03398,-0.03243,-0.00902,-0.0307,-0.04175,-0.04353,-0.03285,0.08163,0.01888,-0.03122,-0.06702,-0.09955,0.03132,0.06302,-0.07713,-0.02977,0.01857,0.06009,0.02061,0.01422,0.03538,0.04915,-0.07634,0.05245,-0.02312,-0.08759,-0.16709,0.0509,0.03991,0.01984,0.00298,-0.09339,0.07377,0.05165,0.01796,0.07407,0.08434,-0.0315,0.02588,0.01438,0.02375,0.06032,-0.01628,-0.05278,-0.01828,0.09086,-0.13036,-0.0039,-0.01029,0.01211,-0.05426,-0.09618,0.0305,0.0761,0.0218,-0.04707,-0.02685,0.05715,-0.08227,-0.03825,0.02331,-0.02537,0.03043,-0.01408,0.0451,-0.05664,0.05541,-0.10035,0.00943,0.03821,0.11771,-0.02854,-0.01185,0.06381,-0.00243,-0.11314,-0.08829,0.01325,-0.04503,-0.08281,0.0108,-0.08059,0.09124,-0.06356,0.07002,0.0697,0.04993,0.0306,-0.11777,-0.08544,-0.05347,0.02572,0.0241,0.03601,-0.03693,0.09861,-0.04528,-0.02049,0.06187,0.08251,-0.10205,0.05506,-0.01624,-0.07335,-0.07157,0.06044,0.00626,0.12992,-0.00973,-0.11848,0.00793,-0.0105,0.05766,-0.0182,-0.02167,-0.06902,-0.02544,0.06906,-0.03036,-0.06825,0.0081,0.10616,-0.09359,-0.02032,0.01308,0.05958,0.04261,0.03393,-0.0436,-0.06597,0.02381,0.01708,-0.06363,0.11201,0.06933,-0.03828,-0.04715,-0.01211,-0.09015,-0.0891,-0.1403,0.02479,0.05724,-0.15732,0.05669,0.03826,-0.00412]},{"domain":"chemistry","key":"gibbs_free_energy","name":"Gibbs energy change (dG = dH - T dS)","package":"chemistry-ai999x","example":"For a reaction ΔH = -92.2 kJ/mol and ΔS = -198.7 J/(mol·K). What is ΔG at 298 K? Is it spontaneous?","v":[0.05711,0.00517,-0.06488,0.1178,-0.02942,0.03018,0.10895,-0.01143,-0.06582,-0.02723,-0.03698,0.02071,-0.14183,0.06525,0.06318,-0.07043,-0.04273,0.0422,0.01004,0.0609,-0.04361,0.01359,-0.02881,-0.02495,-0.05462,0.04481,0.0417,0.01477,-0.01954,0.10166,-0.07878,0.01596,0.01814,0.00779,-0.03514,0.10894,-0.17838,-0.0706,-0.01642,-0.02993,-0.02543,-0.04102,0.03477,0.07436,0.05441,0.01204,0.07616,0.01128,0.02745,0.04544,0.04628,-0.05475,0.04785,0.07975,-0.02675,0.03301,-0.07193,0.00964,-0.00092,0.00725,-0.06059,0.08156,0.02546,-0.02099,0.00563,-0.06212,-0.13146,0.04325,0.04498,-0.02532,-0.03969,0.07427,-0.15468,0.06189,0.11773,-0.06631,-0.05655,-0.00583,-0.10023,-0.0279,-0.03466,0.02203,0.0118,0.07015,0.04356,0.00176,-0.14154,0.01871,-0.04066,0.02659,-0.08086,-0.0831,0.05311,0.0305,-0.01736,0.00147,-0.08823,-0.00688,0.10585,-0.08195,0.0438,0.04004,-0.02747,0.02212,-0.03228,-0.02274,0.01301,0.06424,-0.04419,0.03284,-0.01012,0.09466,0.0088,-0.04994,0.00903,-0.02298,-0.10308,-0.06382,0.06833,0.03721,0.12293,0.12173,-0.03847,0.0181,-0.02698,-0.07458,-0.02384,-0.01089,-0.0265,-0.05872,0.00142,-0.03751,-0.02951,-0.03571,0.1851,0.11636,0.07267,-0.01254,-0.02809,-0.0436,0.03703,-0.0112,-0.10335,0.01893,0.05644,-0.05405,-0.04378,-0.0683,0.03784,-0.01086,0.05929,-0.19545,-0.01821,0.02927,-0.05628,0.09766,0.11543,-0.05779,0.06455,-0.08257,0.01267,0.00564,-0.00687,0.01109,-0.05913,-0.00421,-0.00265,0.06957,-0.02596,0.03499,0.11011,0.04102,0.01946,0.0752,-0.02773,-0.08215,0.01172,0.08768,0.05549,0.05396,0.13585,-0.05247,-0.10084,0.02873,0.03682,-0.05645,0.07413,-0.01569,0.01143,-0.10307,-0.03249,0.05103,0.00176,-0.00781,0.0307,-0.00524,-0.10834,0.05707,-0.03104,0.03137,-0.1122,0.00185,0.17436,-0.09213,-0.03107,-0.06137,0.01787,-0.04339,-0.10169,-0.07957,0.0631,0.10677,0.0008,0.03336,0.03349,-0.06944,-0.11841,-0.0657,0.02825,-0.02681,0.09019,0.04374,0.06905,-0.0162,-0.01802,-0.05003,0.02839,0.03608,-0.02504,0.09639,-0.01528,-0.07655,-0.0276,-0.05278,0.08165,0.07157,-0.00057,0.02003,-0.02972,0.09918,0.05412,0.07669,0.04466,0.09335,-0.01601,-0.03504,-0.01493,0.01703,0.04008,-0.1412,-0.06756,0.04573,-0.01379,0.04212,-0.00062,0.01061]},{"domain":"chemistry","key":"graham_molar_mass","name":"Graham's law: molar mass of an unknown gas","package":"chemistry-ai999x","example":"An unknown gas effuses 1.50 times as fast as O2. What is its molar mass?","v":[-0.01364,0.11392,-0.00128,0.14466,0.06036,0.06667,0.0038,-0.02404,0.07796,-0.00282,-0.01947,-0.02212,0.08072,-0.01158,-0.0163,0.03446,0.01586,-0.08264,1e-05,0.0824,0.10524,0.04052,0.07711,-0.02256,-0.04171,0.00182,0.07849,-0.01596,-0.12059,0.02842,0.06194,-0.03297,-0.02328,0.04116,-0.05973,0.07987,-0.0023,0.04509,0.02395,-0.0361,0.04672,0.04133,-0.0132,-0.08276,-0.02341,0.05576,-0.03199,0.0427,0.09547,0.01419,0.01931,0.09982,0.02651,-0.02594,0.00528,0.11173,-0.00776,-0.05813,-0.00039,-0.0817,-0.03656,-0.24549,-0.00511,-0.10811,0.01516,-0.06124,0.07707,0.01138,-0.03483,0.0377,0.04238,-0.0437,0.02903,-0.0815,0.04974,0.10022,0.05294,-0.05604,0.04157,-0.04756,-0.02478,0.0373,-0.05566,0.1007,-0.11735,0.04242,-0.04798,0.03259,0.06751,-0.04715,0.0216,0.01203,-0.04297,0.07291,0.01725,-0.03639,-0.04248,0.03241,0.02342,-0.00966,0.05636,0.018,-0.00806,-0.00714,0.06793,-0.01645,0.145,0.03623,-0.02283,0.0527,-0.00342,-0.0503,0.0333,0.09876,-0.08227,0.02814,-0.13114,0.05056,0.09235,-0.04628,0.05133,-0.08594,0.01754,0.08562,0.06154,-0.06139,0.10064,-0.05993,-0.12871,-0.06943,-0.01137,0.00402,-0.01563,-0.01756,-0.02914,-0.03534,-0.02772,0.13021,0.0831,-0.07163,0.02223,0.02482,0.01777,0.0748,0.06509,0.02322,0.04458,-0.07261,0.02765,0.06981,-0.07448,-0.02801,-0.06251,-0.07701,0.00219,-0.07412,0.03244,0.02434,0.05973,-0.06204,-0.00355,-0.25938,0.02855,-0.0805,0.05806,0.10995,-0.05285,0.06365,0.0946,-0.06238,-0.0019,0.07565,0.11155,0.00349,-0.02342,0.06221,0.0078,-0.04923,0.04683,0.0204,-0.02666,-0.02218,-0.01199,-0.00571,-0.09884,0.06604,-0.06855,-0.05612,-0.06402,-0.03277,-0.06121,0.07628,-0.05777,-0.04315,0.12722,0.06087,-0.06477,0.03216,-0.01755,0.05286,-0.00769,-0.05646,0.00853,0.03299,-0.0884,0.02647,0.03011,0.03858,0.05151,0.01041,-0.09822,0.0818,-0.01708,-0.06454,-0.03506,-0.10923,-0.06354,0.00814,0.06057,0.02465,-0.03555,0.01371,0.07103,0.02046,-0.136,-0.15549,0.01823,0.00233,-0.03689,-0.08294,0.0352,0.0433,0.01755,0.03318,0.02302,-0.12672,-0.03886,0.0572,-0.11616,-0.04717,0.00222,0.04128,0.02536,-0.03966,-0.0135,0.06397,-0.01025,0.00033,0.04467,0.01191,-0.04275,-0.04668,-0.05778,-0.01295,-0.08876,-0.03525]},{"domain":"chemistry","key":"graham_rate_ratio","name":"Graham's law: ratio of effusion rates","package":"chemistry-ai999x","example":"How many times faster does H2 effuse than O2?","v":[0.01202,0.05987,0.01397,0.11805,0.02697,0.02137,-0.10183,-0.02574,0.05479,-0.04568,-0.07173,-0.03357,0.01248,0.05313,-0.00027,-0.00107,-0.06732,-0.02945,0.03017,0.07551,0.02755,0.05027,0.12178,-0.07067,-0.02851,-0.02198,-0.04174,-0.03276,-0.13546,0.1371,0.01395,0.05175,0.00884,0.05162,-0.06782,0.10256,0.06277,0.04916,-0.00633,-0.07289,0.06355,0.0841,-0.00672,-0.0411,-0.08422,0.00914,-0.01996,0.01745,-0.02349,0.05434,0.04619,0.10702,0.00744,-0.04078,0.0111,0.09436,0.05718,-0.04176,-0.05999,-0.12511,-0.04122,-0.164,0.03059,-0.14228,-0.03992,-0.00426,0.11954,0.01705,-0.0298,0.05175,0.01856,-0.02944,-0.00497,-0.05296,-0.00692,0.02309,-0.04548,0.03566,0.03614,-0.08416,0.00357,-0.01213,-0.07384,0.0787,-0.09903,0.06412,-0.05638,0.01822,0.04846,-0.01594,0.00837,0.0334,0.06098,-0.01653,0.05407,-0.02297,0.0126,0.03613,0.03266,-0.03434,0.00355,0.10173,-0.00427,-0.00195,0.0384,-0.06879,0.16707,0.00191,0.02588,-0.05957,-0.01967,-0.07004,0.05927,0.0572,-0.05662,0.00578,-0.10051,0.1336,0.09378,-0.05469,-0.02309,-0.00742,0.03444,0.11388,0.00738,0.03516,0.02034,0.00911,-0.11692,-0.02823,0.02509,-0.09594,-0.05746,-0.00049,-0.01103,-0.00357,0.0055,0.10485,0.01652,-0.09247,0.01355,0.12106,0.01399,0.06284,0.06418,0.06497,0.03528,0.06751,0.03239,0.13263,-0.06773,-0.12742,-0.09012,-0.05958,0.03022,-0.14941,0.04476,0.01247,0.07005,-0.07809,0.09446,-0.18702,-0.0065,-0.10009,0.11412,0.05612,-0.07849,0.04607,0.07746,-0.05059,-0.01976,0.11803,0.01966,0.06231,0.02089,0.0325,-4e-05,0.03206,0.06445,0.04025,-0.1326,-0.0389,0.00124,-0.03562,-0.0728,0.07609,-0.08491,-0.03831,-0.06142,0.05184,-0.06699,0.02787,0.01019,-0.03334,0.0904,0.01202,0.00119,-0.05332,-0.04799,-0.00022,0.04766,-0.01523,0.03763,0.00895,-0.01976,0.05385,-0.05947,-0.00452,0.04107,0.07603,-0.09944,0.00654,-0.04739,-0.0078,-0.05949,-0.1185,-0.01922,0.08438,0.02389,0.02205,-0.07972,-0.02991,0.11981,-0.03071,-0.01994,-0.13839,-0.01479,0.01947,0.04506,-0.04173,0.01161,0.03089,-0.06205,0.03058,0.08934,-0.02915,-0.02029,0.07049,-0.0104,-0.05707,-0.01915,-0.00758,0.03611,-0.04185,-0.02315,0.0546,-0.08251,-0.08238,0.06972,-0.04202,-0.04415,-0.00774,-0.13417,0.02879,0.00013,0.01629]},{"domain":"chemistry","key":"heat_from_reaction_mass","name":"Heat of reaction for a given mass","package":"chemistry-ai999x","example":"How much heat is released when 10.0 g of CH4 burns? ΔH = -890 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atom transition wavelength (Rydberg)","package":"chemistry-ai999x","example":"What is the wavelength of light emitted when an electron in hydrogen falls from n = 3 to n = 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gas law: amount","package":"chemistry-ai999x","example":"How many moles of gas are in a 5.00 L flask at 2.00 atm and 300 K?","v":[-0.20792,-0.042,-0.12073,0.03913,-0.05605,-0.05418,-0.02825,-0.06485,0.08962,0.06042,-0.00521,-0.04271,0.08182,0.03729,-0.02568,0.0067,0.03402,0.05045,0.05297,0.17224,-0.05515,-0.02413,0.02924,-0.07923,-0.03053,0.04592,0.06833,0.0096,-0.00739,0.06148,-0.01602,-0.10156,-0.00563,0.03477,-0.03022,0.01505,-0.02279,0.02635,0.03335,-0.01983,0.04239,0.0696,0.11891,0.03581,0.02536,0.02071,-0.03204,0.03542,0.05913,0.06655,0.04447,-0.03463,-0.01004,-0.07001,0.02147,0.01116,-0.02845,0.0247,0.06725,-0.04514,-0.07893,-0.05083,-0.15805,-0.07162,-0.02979,-0.07627,-0.05267,-0.03545,-0.06192,0.06087,-0.0993,-0.0867,-0.06001,0.04075,0.09732,0.05294,0.0424,0.05895,0.11971,-0.01362,0.00541,0.03268,-0.00265,0.06084,0.04735,0.09958,-0.09926,0.05985,0.03836,0.0194,0.09524,-0.00443,-0.02791,0.05043,-0.01275,0.05023,0.02101,0.05307,0.03681,0.05726,0.03844,0.00683,-0.00535,0.02377,-0.06954,-0.03894,0.01986,0.00634,0.09228,0.02774,-0.09043,-0.12093,-0.03714,0.01591,-0.08984,-0.0266,0.07756,0.00828,0.02011,0.0072,0.10449,0.03082,0.04866,-0.14851,0.03225,-0.13714,0.08975,0.03053,0.04977,0.06983,-0.03437,-0.02699,0.00506,0.04288,-0.01773,-0.02887,-0.0721,0.05461,0.00483,0.13009,-0.03743,0.02139,0.02034,-0.00775,0.02371,0.06692,0.01267,0.02808,-0.03793,-0.02804,0.07479,0.03099,0.01979,0.03061,-0.00744,0.03091,-0.00614,0.02659,0.15636,-0.0147,-0.03784,-0.10271,-0.06317,-0.0535,-0.08028,0.07711,0.05047,0.02134,-0.10976,-0.05721,-0.03833,0.03117,-0.06544,0.03701,0.03095,-0.02993,-0.11196,-0.01843,0.08128,0.12704,0.09293,0.0039,0.07627,0.02647,-0.10543,0.02646,0.0435,0.0211,-0.0252,-0.01759,-0.07729,0.1,-0.03627,0.0945,-0.08398,0.06625,-0.0181,-0.00225,-0.12017,0.0942,0.03477,-0.07062,0.08271,-0.01796,0.03753,0.03652,-0.03556,-0.04743,0.09168,-0.1036,0.05814,-0.00321,0.04511,-0.10026,0.05427,0.00835,-0.03365,0.00523,-0.05655,-0.06643,-0.07744,0.09347,0.01016,-0.01303,-0.07221,-0.04703,0.10082,-0.07691,-0.14686,-0.04798,0.00499,-0.00113,0.04707,-0.04835,-0.00436,0.02606,-0.09048,0.00461,-0.06567,-0.11385,0.04074,-0.04695,0.02795,-0.01134,-0.00576,0.04317,0.01441,-0.01186,-0.10223,-0.08352,0.03995,-0.01235,-0.14092,0.06129,-0.0536,-0.10095]},{"domain":"chemistry","key":"ideal_gas_pressure","name":"Ideal gas law: pressure","package":"chemistry-ai999x","example":"What is the pressure of 2.0 mol of gas in 10.0 L at 300 K?","v":[-0.13006,-0.05002,-0.14097,-0.13007,-0.03584,0.04326,0.00538,0.01298,0.02815,0.08352,-0.0781,-0.02459,0.04373,0.04296,0.01319,0.00518,0.03191,0.13476,0.02813,0.14634,-0.03217,-0.03639,-0.04743,0.00825,0.01684,0.07878,0.04739,0.03394,0.0913,0.0384,0.04826,0.03538,0.0826,0.0085,-0.0326,0.06991,0.04693,0.00604,-0.05663,0.07966,0.06699,0.00868,0.0426,-0.00068,0.05035,-0.03801,-0.00696,-0.1031,0.01819,-0.03506,0.09723,-0.10461,-0.12481,-0.10353,-0.03272,-0.0152,0.0207,-0.01726,0.03917,0.05435,0.02014,-0.01483,-0.17902,-0.00449,-0.05132,-0.05171,-0.00148,-0.07983,-0.06776,0.08212,-0.13042,-0.06945,-0.03136,0.00068,-0.02599,-0.00699,0.09306,-0.02549,-0.02952,-0.05172,0.02072,0.08978,0.12885,0.03239,-0.01859,-0.01062,-0.03223,0.00267,0.02285,-0.00435,0.05561,0.04715,-0.07739,-0.02176,0.01641,0.1487,0.00044,0.07365,0.08807,0.00856,-0.0005,0.0304,0.07979,0.05653,0.00885,0.00627,0.03794,-0.02661,0.12122,-0.07558,-0.03074,-0.10949,-0.01439,0.00463,-0.05273,-0.05384,0.06766,0.05195,-0.02668,-0.04714,-0.04849,0.02054,0.02111,-0.12335,-0.028,-0.09254,0.06196,0.03628,0.01675,-0.00798,-0.10297,-0.07975,0.0901,0.01414,-0.04647,0.01462,-0.07922,0.12495,0.0591,0.06796,-0.01363,0.07664,-0.05205,-0.01092,0.12776,0.0212,0.07159,0.00782,-0.02984,-0.0252,0.02555,0.07392,0.00038,0.10444,0.0555,0.00835,0.01222,-0.03079,0.10238,-0.00787,-0.08063,0.00283,0.03253,-0.03764,-0.05666,0.09627,0.08508,0.02604,-0.08182,-0.13204,-0.10109,-0.00335,-0.03741,0.10438,-0.01099,-0.03828,-0.00789,-0.04837,0.08129,0.11948,0.00711,0.04869,0.03201,0.01039,-0.00262,-0.02946,0.06729,-0.10517,-0.10591,0.01643,-0.0142,0.01864,-0.01867,0.03769,0.0123,0.05051,-0.06257,0.05858,-0.06007,0.09773,-0.01226,-0.01415,-0.03763,-0.0902,-0.00648,0.00054,-0.06565,0.056,0.13792,0.01504,0.11052,-0.00362,0.04623,-0.04646,0.02518,-0.02421,0.09814,-0.03312,0.01501,-0.092,-0.06986,0.02412,-0.03398,-0.01324,-0.05475,-0.09523,0.11004,-0.10208,-0.06384,0.00729,0.04432,-0.02657,0.0065,0.05339,-0.02072,0.03419,-0.04847,0.02407,-0.05763,0.0083,0.00491,-0.08605,0.08325,-0.03934,0.01355,-0.06227,-0.02973,-0.06721,-0.05278,-0.07172,0.05643,-0.04195,-0.17876,0.03845,-0.06908,0.003]},{"domain":"chemistry","key":"ideal_gas_temperature","name":"Ideal gas law: temperature","package":"chemistry-ai999x","example":"At what temperature does 2.00 mol of gas occupy 50.0 L at 1.00 atm?","v":[-0.11852,-0.04905,-0.09225,-0.05212,-0.09008,-0.04595,-0.01186,0.00076,0.06539,0.08801,-0.05248,-0.01284,0.07196,0.02548,0.0202,0.0066,-0.01951,0.06759,0.02096,0.06302,-0.02259,0.00943,-0.12184,-0.06308,0.00722,0.00984,0.05908,0.01219,0.06795,0.03662,0.04963,0.02434,0.05055,-0.00692,-0.02217,0.01415,0.00589,-0.05591,-0.02707,-0.005,0.01041,-0.0039,0.06838,0.02038,0.02094,-0.0627,0.03605,-0.03484,-0.00398,-0.04932,0.06464,-0.08312,-0.10992,-0.16018,-0.03352,0.02658,0.03715,0.03286,0.00134,0.0317,0.01203,-0.04042,-0.08524,0.02315,-0.03735,-0.06278,0.02265,-0.07631,-0.09395,0.1069,-0.11365,-0.05237,-0.03949,-0.00762,0.02529,-0.01462,0.03249,0.01438,0.01201,-0.05899,0.04666,0.07043,0.10561,0.07842,0.01849,0.07756,-0.06245,-0.04005,0.02357,-0.0362,0.10305,0.05995,-0.07178,0.00474,-0.00877,0.16255,-0.01726,0.03538,0.02272,0.01951,-0.05347,0.01633,0.07007,0.01658,-0.01607,-0.01825,0.0479,0.00047,0.08839,-0.0425,0.0034,-0.10438,0.00621,0.02423,-0.02442,-0.0158,0.05653,-0.00086,-0.0674,-0.00938,-0.01099,-0.00877,0.02074,-0.15241,-0.01017,-0.04166,0.13785,-0.00236,-0.02456,0.04028,-0.03077,-0.04536,0.06546,0.00656,-0.02645,-0.00278,-0.06275,0.15729,0.00083,0.02246,0.0696,0.08859,-0.01778,-0.01379,0.07668,0.06115,0.03926,0.02135,-0.0502,-0.02714,0.07531,0.04309,0.01898,0.06159,-0.00875,0.01889,0.00478,-0.0275,0.08461,-0.0203,-0.07781,-0.06496,-0.01495,-0.04173,0.01062,0.13795,0.06379,-0.01657,-0.0443,-0.14405,-0.04154,0.05605,-0.0339,0.11169,-0.08491,-0.05733,-0.00951,-0.06115,0.11619,0.06589,0.06411,0.03592,0.04742,0.02104,-0.03937,-0.03285,0.06281,0.00376,-0.07585,0.06283,0.00432,-0.00621,-0.00193,0.12344,0.03105,0.03567,-0.01039,0.11079,-0.02551,0.12806,-0.03924,-0.04461,0.00792,-0.12218,-0.04784,0.02276,-0.01024,0.09712,0.13615,-0.07333,0.16008,-0.01399,0.02792,-0.01675,0.05114,-0.01475,0.09767,-0.00464,0.04708,-0.11055,-0.09371,0.0837,-0.01331,-0.03886,-0.03952,-0.08686,0.15444,-0.07075,-0.10699,0.00597,0.03047,-0.05359,0.03576,0.02562,0.00548,0.00188,-0.02608,0.01428,-0.044,0.03842,0.05469,-0.08626,0.09869,-0.06604,-0.04924,-0.02801,0.00631,-0.05905,-0.00454,-0.10576,0.06497,-0.09973,-0.24647,-0.00852,-0.10482,-0.06445]},{"domain":"chemistry","key":"ideal_gas_volume","name":"Ideal gas law: volume","package":"chemistry-ai999x","example":"What volume does 1.00 mol of gas occupy at 1.00 atm and 273.15 K?","v":[-0.13104,-0.10439,-0.09906,-0.06837,-0.042,-0.04716,0.02427,0.02304,0.05556,0.10843,0.00748,-0.01294,0.06143,0.01151,0.0093,0.00793,-0.01633,0.09198,-0.0479,0.11137,-0.01448,0.02783,-0.08613,-0.03415,-0.00555,0.00877,0.05678,0.0455,0.02097,-0.00176,-0.00246,-0.03607,0.03238,-0.00298,0.02318,-0.06095,0.04488,-0.07831,0.00586,0.08174,0.06227,0.04343,0.04901,-0.03709,0.05375,-0.04589,0.04414,-0.05392,-0.03809,-0.08496,0.07768,-0.11789,-0.10867,-0.13479,-0.07626,0.00102,0.05906,0.00911,0.01433,0.05286,0.06332,0.00113,-0.10142,0.07068,-0.04104,-0.03991,0.04694,-0.09555,-0.03953,0.13597,-0.04774,-0.08422,-0.03188,-0.01014,0.00409,0.01333,0.05386,-0.0122,0.02317,-0.01306,-0.00829,0.10207,0.01786,0.03108,-0.0018,0.10557,-0.01675,-0.01208,0.04802,-0.00107,0.05813,-0.00147,-0.05899,0.0748,-0.02362,0.17144,-0.04104,0.02625,0.10842,0.03049,-0.04213,0.0077,0.0924,-0.02003,-0.04619,-0.05903,0.03711,0.01115,0.0624,-0.02235,-0.00017,-0.15093,-0.01027,0.05971,-0.05708,-0.03674,0.03616,0.04228,0.01132,-0.05048,0.04345,0.01944,0.04933,-0.12784,-0.04545,-0.05069,0.07969,-0.00516,0.00707,0.04182,-0.00934,-0.06408,0.06189,0.0045,-0.02982,0.02044,-0.05185,0.1326,0.00595,0.04866,0.09818,0.09499,-0.01621,-0.04062,0.07768,0.05327,0.03387,-0.00742,-0.01014,-0.00298,0.03578,0.08689,0.09987,0.03621,-0.0149,0.04258,0.01854,-0.0169,0.09262,-0.04595,-0.0524,-0.07439,0.02029,-0.06358,0.03119,0.14385,0.03543,0.00879,-0.05999,-0.16129,-0.10089,0.10037,-0.12503,0.05401,-0.00373,-0.07697,0.01348,-0.07728,0.14173,-0.00645,0.01415,0.03964,0.08812,0.02072,0.00847,-0.03811,0.08786,-0.04106,-0.03602,0.04582,-0.0491,-0.00441,0.02569,0.10205,0.02496,0.03455,-0.02786,0.06489,-0.03775,0.06362,-0.02253,-0.0658,-0.0032,-0.08521,-0.04196,-0.011,-0.06988,0.01976,0.13597,-0.05845,0.12445,-0.06754,0.06207,-0.06552,0.0191,0.01647,0.05494,-0.00653,0.0341,-0.10069,-0.07624,0.08321,-0.01398,-0.04767,-0.00256,-0.04519,0.11702,-0.02016,-0.0697,-0.00048,-0.01918,-0.00786,-0.02226,-0.04246,0.01421,0.00176,-0.05231,-0.04202,-0.0272,-0.07724,0.10503,-0.06941,0.10133,-0.0599,0.00617,-0.07509,-0.00833,-0.04344,-0.0042,-0.04645,0.1036,-0.12025,-0.21315,-0.01242,-0.0958,-0.03409]},{"domain":"chemistry","key":"k_from_cell_potential","name":"Equilibrium constant from a standard cell potential","package":"chemistry-ai999x","example":"A cell has E° = 0.46 V with n = 2 at 298 K. What is the equilibrium constant?","v":[-0.02902,-0.06022,0.00874,0.03353,0.00564,0.08092,0.01336,0.13148,-0.02925,0.06435,0.03348,-0.08572,-0.0081,0.00712,0.04541,0.03622,0.02022,0.02267,0.04635,-0.02163,-0.05055,0.01616,-0.03783,-0.0484,-0.02191,-0.0176,-0.00291,-0.0685,0.02715,0.03746,-0.02394,-0.03133,0.11186,-0.0075,-0.02099,0.06145,0.08022,-0.04013,-0.05903,0.01841,0.11072,-0.04652,-0.00755,0.00852,-0.08556,0.06927,-0.0369,-0.05305,0.01425,0.08832,-0.00768,-0.00623,0.01725,-0.09869,0.05768,-0.18842,0.06079,-0.00645,-0.0426,0.0742,-0.02318,0.06173,0.0113,-0.0104,0.10486,0.15909,-0.02173,-0.04731,0.01302,0.04167,-0.00427,0.02529,-0.07843,-0.05498,-0.01435,0.11243,0.00017,-0.06661,-0.05877,0.05139,-0.00604,0.01058,0.03044,0.1027,-0.01318,0.00326,0.10844,0.06954,0.0554,-0.05131,0.10612,0.07831,-0.01557,0.02835,-0.09238,0.12427,-0.22556,-0.05955,0.01314,0.01491,0.03337,0.08892,0.15622,0.01312,-0.12768,-0.00026,-0.05719,-0.06042,-0.02338,-0.11955,0.06393,0.01795,0.00216,-0.09536,0.08313,0.0037,-0.00585,0.05229,-0.03659,-0.01326,-0.04999,-0.03236,0.11449,-0.01412,-0.04553,-0.04747,-0.00096,0.10188,-0.05065,-0.02038,0.04643,-0.03255,0.06775,-0.00094,-0.05989,-0.04542,-0.08278,0.03699,0.05459,-0.00765,0.06811,0.10347,-0.04143,-0.05469,-0.04824,-0.08224,-0.02394,0.01981,0.03647,-0.03234,0.05395,0.0666,-0.04124,-0.03056,0.01746,-0.05614,0.12207,-0.05323,0.05855,-0.12724,-0.05747,0.00648,-0.05196,0.0795,0.00373,-0.00573,-0.00701,-0.0415,-0.05107,-0.07354,-0.05238,-0.01783,0.0054,0.00038,-0.03126,0.00823,-0.12313,-0.07048,0.00047,-0.03269,-0.01002,-0.06784,-0.08537,-0.00515,-0.02344,0.08637,-0.03362,-0.01394,-0.0193,0.00407,0.04478,0.13254,0.0508,0.06567,-0.02536,0.01544,-0.00838,0.0995,-0.04292,0.01142,0.0006,-0.0649,0.02881,0.11493,-0.02234,-0.11196,0.12333,0.04486,-0.0111,-0.06628,0.07937,0.0805,-0.09002,0.0383,0.08017,0.12891,0.04125,0.00759,-0.08043,-0.09526,-0.05118,-0.01642,-0.03,0.04452,0.05987,0.05503,0.0273,-0.06284,-0.01783,-0.01809,-0.00156,0.03498,0.01795,-0.07284,-0.10339,0.04407,-0.07513,0.02594,-0.04522,-0.01145,-0.09952,-0.02815,-0.00183,0.00205,0.02598,-0.05656,0.02351,-0.15952,-0.08978,0.0456,-0.01209,0.17578,0.00614,0.06659,0.01966,-0.03041]},{"domain":"chemistry","key":"k_from_delta_g","name":"Equilibrium constant from the standard Gibbs energy","package":"chemistry-ai999x","example":"ΔG° = -33.0 kJ/mol at 298 K. What is the equilibrium constant?","v":[0.03116,-0.03985,-0.05868,0.07692,-0.03858,0.04358,-0.00012,0.06833,-0.0655,-0.00735,0.01615,-0.04289,-0.12835,0.01362,0.05334,-0.07456,-0.00503,0.04919,0.02152,-0.00595,-0.06716,0.01138,0.01069,-0.0429,0.02661,-0.00489,0.02077,-0.04737,0.02925,0.00845,-0.0343,0.01028,0.05635,-0.00749,-0.03017,0.0771,-0.0166,-0.0168,-0.0609,-0.09844,0.02468,-0.11528,-0.062,0.02742,0.00691,0.03254,0.05121,-0.04819,0.07701,0.05676,0.02881,-0.00597,0.06466,0.09472,0.0278,-0.12741,-0.01614,-0.05429,0.02923,0.07573,-0.04651,0.03546,-0.05736,-0.04573,0.05832,0.05074,-0.13709,-0.01895,0.03003,-0.00074,0.00149,-0.03111,-0.15453,-0.03694,0.05609,-0.06373,-0.06172,-0.09156,-0.03197,0.03326,0.00279,0.08301,0.04058,0.15956,-0.01999,-0.00093,0.0081,0.02272,-0.00772,0.04871,0.00724,-0.01415,0.079,0.11068,-0.00407,0.0515,-0.14857,-0.03829,0.09501,-0.122,0.06301,0.09555,0.04125,0.09085,-0.00934,-0.01965,-0.00824,-0.01741,0.00757,-0.10134,0.04653,0.04619,0.09002,-0.11522,0.02036,0.01665,-0.02811,0.01975,-0.04809,-0.03874,0.01935,0.07187,0.07838,-0.11295,-0.0685,-0.08291,0.06494,0.01043,-0.10388,-0.09563,-0.00833,-0.05251,0.03448,0.02477,0.08134,0.00956,-0.1003,0.04322,0.05051,-0.03423,0.02003,0.11691,-0.12053,0.02217,-0.04946,-0.0227,-0.02886,-0.07909,0.05655,-0.07389,0.0364,0.02052,0.0121,0.01786,0.04628,-0.03219,0.19121,-0.06965,0.00222,-0.16187,-0.0616,0.04997,-0.00423,0.08679,-0.02037,-0.02081,0.02071,-0.04565,-0.06452,0.03322,0.04105,-0.00202,0.02265,0.03867,0.00847,-0.10381,-0.02209,0.07372,0.01675,-0.02735,0.03273,-0.03708,-0.12489,0.02538,0.06305,-0.04236,-0.00405,-0.01599,-0.003,-0.03315,-0.01064,0.16213,0.02962,-0.0023,-0.01887,0.00665,-0.05226,0.18667,-0.01804,0.02109,-0.04635,-0.01791,0.05456,0.00357,-0.00544,-0.19514,0.05235,0.02731,-0.06692,-0.0813,0.04008,0.14833,-0.05037,0.01588,0.1004,0.07227,-0.04242,-0.03308,-0.07317,-0.04747,0.00594,0.01454,-0.02901,0.00585,0.00044,0.04228,0.066,-0.05351,0.00232,0.02242,0.01873,-0.03244,0.02809,-0.12779,-0.02397,0.04433,0.04722,0.05989,-0.04856,0.01487,0.0019,0.05724,-0.01707,0.06245,0.0367,0.04085,-0.01045,-0.05366,-0.00451,-0.02841,-0.02345,0.24382,-0.08122,0.06078,0.03051,-0.02203]},{"domain":"chemistry","key":"ka_from_ph","name":"Ka from the pH of a weak acid","package":"chemistry-ai999x","example":"A 0.10 M solution of a weak acid has a pH of 2.87. What is its Ka?","v":[0.08353,0.00504,-0.0686,0.00524,0.06942,-0.02872,0.02498,0.10615,-0.02239,-0.09361,0.00709,-0.02719,-0.03301,0.02341,0.04077,0.03855,-0.03895,-0.06994,-0.00049,-0.057,0.05437,-0.03367,-0.06692,-0.08928,-0.02731,0.09643,0.18759,0.02349,0.0793,-0.00677,-0.06768,0.0005,0.00304,0.00651,-0.06628,-0.05141,0.04056,0.05592,-0.04383,-0.04092,0.00558,-0.03982,-0.0985,-0.01733,0.00024,0.02737,-0.00567,-0.04147,0.09103,0.12204,0.10962,0.04222,0.08098,0.06303,-0.07476,-0.08107,0.02151,-0.06351,-0.00387,-0.01156,-0.02004,-0.04922,-0.02279,0.12132,0.05236,0.01416,-0.08319,0.00687,-0.08463,-0.05064,0.02347,0.04582,-0.02246,-0.06425,-0.03504,0.04576,0.02016,-0.10649,-0.01823,-0.05768,0.02315,-0.01744,-0.02473,0.06973,-0.03993,-0.00978,0.07194,-0.0577,0.05772,-0.02021,-0.05848,-0.07758,-0.02893,-0.03601,-0.02513,-0.05917,0.01554,-0.07949,0.06179,0.04747,0.00985,-0.00533,0.03848,0.06915,-0.07867,0.05181,-0.07589,0.00013,-0.04911,0.10407,0.11055,-0.1088,0.04247,0.04213,-0.02671,-0.08585,0.01457,0.06315,-0.01261,0.06914,0.05141,0.10672,0.09975,-0.13254,-0.07676,-0.00016,0.07167,-0.02686,0.01975,-0.09685,-0.04352,-0.09059,0.01272,0.07134,-0.0317,0.00099,-0.08887,0.04842,0.12536,0.03622,-0.00522,0.05024,-0.01688,-0.02468,-0.04304,0.00659,-0.07025,-0.01781,-0.00871,-0.08603,-0.05563,0.02004,0.06268,0.01886,-0.01003,-0.00346,0.0741,-0.10484,-0.00031,-0.08566,-0.0733,-0.01434,-0.1423,-0.02003,-0.11753,0.06589,-0.00396,-0.04871,0.00576,-0.02838,0.02022,-0.03354,0.11383,0.0076,-0.01507,-0.02783,-0.02462,0.03457,0.068,-0.00309,0.03899,-0.0347,0.01583,0.03551,0.00257,0.08531,-0.02625,-0.06525,0.05443,0.08609,0.08468,0.02535,-0.0818,-0.07967,-0.07932,-0.06324,-0.03038,0.11604,-0.01795,-0.05139,0.04243,-0.02062,0.02243,0.11179,-0.04367,-0.08259,0.02057,-0.09706,-0.01033,-0.04177,0.03639,-0.0087,0.02434,-0.03981,0.11745,0.10699,-0.01606,0.07331,-0.19355,-0.17546,0.08253,0.02965,-0.00102,0.06526,-0.04814,0.09897,-0.02945,-0.02265,0.12207,-0.04594,-0.02515,0.12002,0.05168,-0.13724,0.0322,0.02203,0.08259,0.05748,-0.03253,0.07729,0.10413,0.04044,-0.08779,0.04646,-0.05104,0.05438,-0.03086,0.02595,-0.00858,-0.09889,0.00884,0.08995,-0.00102,0.03354,0.02171,-0.03298]},{"domain":"chemistry","key":"kc_from_kp","name":"Kc from Kp","package":"chemistry-ai999x","example":"For PCl5(g) ⇌ PCl3(g) + Cl2(g), Kp = 1.8 at 523 K. What is Kc?","v":[-0.03301,0.03696,-0.13493,-0.02749,-0.00509,0.00033,0.03743,0.04449,0.02479,0.02174,-0.0263,-0.07578,-0.03848,0.05086,0.00095,-0.0127,0.03679,-0.00703,0.12981,0.12149,-0.09702,-0.01753,0.08142,-0.02102,0.08857,0.07608,-0.00204,-0.05938,0.06914,-0.01471,0.05169,-0.06588,0.00912,-0.00203,-0.06856,0.19074,-0.05584,0.07199,-0.03364,-0.08043,0.08427,-0.02325,0.02591,0.04445,0.04498,0.06801,0.03113,-0.01034,0.08742,-0.01607,0.11852,0.07292,0.04021,0.00621,0.04725,-0.0544,-0.06038,-0.01824,0.01975,-0.0285,-0.02703,-0.0854,-0.16373,-0.12695,-0.04879,-0.03556,-0.12395,-0.08717,-0.06234,-0.02961,-0.02857,-0.00998,-0.02335,0.03834,0.0333,0.06487,-0.02521,-0.04081,0.0895,0.01008,-0.01249,-0.05771,0.05887,0.08936,0.04122,-0.02193,-0.02566,-0.09485,-0.01124,-0.01029,0.07968,0.06464,-0.00582,0.09964,0.01741,-0.01875,-0.00136,0.01376,0.08681,-0.02201,0.07263,0.06907,0.02309,0.06457,-0.01744,0.13316,-0.08125,0.01979,0.06838,0.0407,0.09168,-0.01148,0.00669,-0.05058,-0.02525,0.02626,0.09135,0.0697,-0.0244,-0.00929,0.02513,0.04731,0.05234,-0.08671,0.05311,0.03105,0.04424,-0.03877,0.03873,-0.01016,-0.05129,-0.09112,0.01072,0.053,-0.06262,-0.03989,-0.06,0.06291,0.0575,0.11862,-0.07562,0.01506,0.04684,-0.0306,0.02608,0.00583,0.00349,-0.04917,-0.03018,0.07577,0.04486,0.03863,-0.03498,0.06481,0.09723,0.00299,0.13101,-0.03077,0.03845,-0.09455,-0.05546,-0.09907,0.00907,-0.09036,-0.12375,-0.02228,0.10669,-0.06954,-0.04313,0.02508,0.00443,-0.0026,-0.0056,-0.04059,0.07832,0.02346,-0.08134,0.08241,0.07376,0.04635,0.04242,0.00934,-0.10779,-0.00658,-0.06421,-0.08629,0.03291,-0.06734,-0.05872,-0.03418,0.02551,0.12987,-0.03887,-0.05236,-0.11805,0.01755,-0.07349,0.0068,-0.07175,-0.00027,0.03161,-0.03477,0.1036,-0.02035,-0.02584,-0.05691,-0.02688,-0.09921,0.03859,0.00754,-0.05851,-0.02031,-0.02672,-0.02071,0.11545,0.07068,-0.05631,0.05401,-0.11791,-0.10743,-0.00967,-0.03572,-0.00766,0.09367,-0.05827,-0.0388,-0.0088,-0.03795,0.02698,0.00097,0.04433,-0.04104,0.02133,-0.14765,-0.12591,-0.05024,-0.09978,0.05912,-0.02787,-0.03726,0.03747,-0.03681,0.0209,0.01899,0.04734,0.00438,-0.04911,-0.06484,-0.02365,0.00335,-0.05988,0.18258,-0.10683,0.12684,-0.0451,-0.01708]},{"domain":"chemistry","key":"kp_from_kc","name":"Kp from Kc","package":"chemistry-ai999x","example":"For N2(g) + 3H2(g) ⇌ 2NH3(g), Kc = 0.50 at 400 K. What is Kp?","v":[-0.04481,0.02043,-0.16088,-0.05523,-0.01193,0.05288,-0.00368,0.03421,0.03194,0.00801,-0.04695,-0.0682,0.0002,0.06001,-0.01304,-0.02915,0.05209,0.01921,0.09714,0.11473,-0.11981,-0.05265,0.05511,-0.01983,0.07546,0.07686,-0.0163,-0.04599,0.05956,-0.01032,0.04786,-0.03181,0.0123,0.0208,-0.06358,0.16704,-0.04815,0.0631,-0.01726,-0.03836,0.10151,-0.004,-0.02091,0.03622,0.03945,0.04232,0.03321,-0.0565,0.0668,-0.01877,0.08954,0.04835,0.03277,-0.021,0.04574,-0.09585,-0.02967,-0.00428,0.01153,0.00534,-0.03439,-0.06317,-0.17176,-0.13989,-0.06472,-0.01638,-0.13297,-0.03857,-0.06586,-0.00842,-0.09165,-0.04595,-0.00875,-0.01125,-0.00789,0.01635,-0.01635,-0.035,0.07103,0.05413,-0.00094,0.02007,0.0628,0.11012,0.00157,-0.04186,0.00487,-0.07474,-0.00054,0.02891,0.06618,0.08194,0.0285,0.14163,0.04111,-0.01201,-0.03893,0.05439,0.09058,-0.04373,0.09239,0.07727,0.07503,0.08223,-0.00222,0.06551,-0.06637,0.04993,0.09182,-0.02237,0.07614,-0.04656,-0.00489,-0.06195,-0.03564,-0.00853,0.11505,0.10229,0.0077,-0.05426,0.003,0.0275,0.07481,-0.10339,0.02642,-0.01135,0.02632,-0.01002,0.02978,-0.05267,-0.08537,-0.1035,0.00576,0.05606,-0.05034,-0.04542,-0.10944,0.09236,0.05198,0.10445,-0.07675,0.01283,0.00466,-0.03173,0.03475,0.03237,0.03977,-0.03997,-0.02297,0.06336,0.07467,0.0793,-0.04155,0.08214,0.09855,-0.00686,0.14879,-0.0371,0.05119,-0.05246,-0.03938,-0.11489,0.03792,-0.05936,-0.08547,-0.00867,0.1067,-0.05248,-0.0725,0.00259,0.0286,-0.05293,0.02226,-0.06656,0.07476,0.00587,-0.06442,0.08664,0.06803,0.04303,0.02433,0.0126,-0.10476,0.00272,-0.07612,-0.03184,0.0452,-0.04582,-0.09198,-0.04627,-0.01691,0.13549,-0.02983,-0.0073,-0.11166,0.01165,-0.06954,0.01316,-0.05629,0.02388,0.04864,0.04399,0.07349,-0.02655,0.01667,-0.03905,0.01285,-0.05283,0.05598,-0.01894,-0.01738,-0.01237,-0.0461,-0.02379,0.09603,0.07723,-0.0384,0.00322,-0.10077,-0.09924,-0.01179,-0.02828,-0.01321,0.09999,-0.06379,-0.02436,0.03356,-0.07256,0.00012,0.00849,0.01908,-0.05941,0.03062,-0.12742,-0.12601,-0.00325,-0.11355,0.05094,-0.05686,-0.06081,0.02422,-0.03832,0.01922,0.01223,0.01014,-0.03991,-0.03224,-0.05239,-0.04241,-0.00634,-0.03855,0.18227,-0.13574,0.13029,-0.02762,-0.02353]},{"domain":"chemistry","key":"ksp_from_solubility","name":"Ksp from molar solubility","package":"chemistry-ai999x","example":"The molar solubility of PbI2 is 1.5e-3 M. What is its Ksp?","v":[-0.07585,0.03308,-0.09738,0.00591,0.11605,-0.09456,0.05484,0.11514,0.04871,-0.05619,-0.0011,-0.05527,0.03772,-0.04389,0.06373,0.05482,-0.10876,-0.16595,-0.0787,0.01035,0.0137,-0.00532,-0.0208,0.05208,-0.06847,0.06589,0.12933,-0.03258,0.02786,0.0578,0.01622,-0.01191,-0.03357,-0.021,-0.02078,-0.00849,-0.00913,-0.05292,-0.03246,-0.00273,-0.03333,-0.05874,-0.01279,-0.00555,0.01639,0.03858,-0.0554,0.03083,0.07321,0.10439,0.01447,0.12065,0.02542,-0.0211,0.01084,0.11782,-0.11624,-0.05947,-0.00599,0.04666,-0.02674,-0.0852,-0.08365,-0.07001,0.04426,-0.0144,-0.14318,-0.00416,-0.02403,0.00949,0.09259,0.01725,-0.01845,6e-05,-0.03226,0.13836,0.11451,-0.109,0.03975,-0.12972,-0.15426,0.00147,0.07532,-0.03519,0.04662,0.03978,-0.0535,0.08818,0.11739,0.07276,0.03055,0.01134,-0.04725,0.01866,0.03144,-0.04152,-0.09935,-0.07454,0.04687,-0.05326,0.06371,0.01245,0.0474,0.02698,-0.01846,0.12445,0.03989,-0.01201,0.10304,0.10942,0.12021,-0.09795,-0.04487,-0.03909,0.03838,0.01152,-0.08016,0.013,-0.06026,0.05724,0.14707,-0.07272,0.10527,0.00786,0.0655,-0.00937,0.01264,0.05332,-0.07132,-0.0758,0.01055,0.0337,0.01269,0.04916,-0.01823,0.05201,0.02792,0.06766,-0.0076,0.01032,0.02706,0.00075,-0.03807,0.02379,-0.07386,-0.11463,-0.0313,-0.09719,-0.0231,-0.05,-0.05297,0.05012,-0.08828,0.0359,-0.01075,-0.09575,-0.02664,-0.04301,0.02403,-0.01101,-0.09704,0.00145,0.00505,-0.02159,-0.0949,0.00013,0.05008,0.08451,0.02096,0.08092,0.07472,-0.00421,0.03819,-0.00586,-0.00845,-0.07564,0.07125,-0.09334,-0.05545,0.05978,0.10959,0.0646,-0.10717,0.05226,-0.02163,-0.05571,0.05492,-0.00318,0.00274,-0.01409,-0.02558,0.03153,-0.0181,-0.05826,-0.03535,0.0151,-0.02586,0.0588,0.00812,0.05072,0.07331,0.00037,0.10132,0.04552,0.04003,0.00532,-0.08773,0.01039,-0.04873,0.06133,-0.05153,0.01345,0.02821,-0.10836,-0.07853,0.00813,-0.07586,-0.01775,-0.006,-0.02391,0.04119,-0.03598,-0.0016,0.11479,-0.00315,0.07533,0.04659,-0.09205,0.00329,0.08601,-0.12382,-0.02766,0.09188,-0.08547,-0.03137,0.0038,-0.0732,-0.04481,-0.11281,0.09313,-0.05191,0.03052,-0.0212,-0.0279,0.01973,0.08495,0.09294,-0.00089,-0.05556,0.04086,-0.01943,0.00157,0.10215,-0.04502,-0.09134,-0.08]},{"domain":"chemistry","key":"ksp_molar_solubility","name":"Molar solubility from Ksp","package":"chemistry-ai999x","example":"What is the molar solubility of CaF2 (Ksp = 3.9e-11)?","v":[-0.07827,0.03757,-0.07574,0.02433,0.11589,-0.07772,0.04317,0.11485,0.0494,-0.04753,0.01725,-0.06037,0.04972,-0.05431,0.0662,0.039,-0.12574,-0.15599,-0.10028,0.0168,0.01037,0.00361,-0.03746,0.02433,-0.04467,0.0604,0.12341,-0.01365,0.02546,0.04826,0.00255,-0.00071,-0.02303,-0.05754,-0.03847,-0.00381,-0.0129,-0.0391,-0.03238,-0.01614,-0.00065,-0.06725,0.005,-0.0029,0.02462,0.00845,-0.04115,0.02416,0.06831,0.10522,0.01184,0.11031,0.02191,-0.01712,0.00848,0.10479,-0.10465,-0.03121,-0.02178,0.07646,-0.00529,-0.07041,-0.0597,-0.06594,0.04201,-8e-05,-0.1542,-0.01867,-0.06053,-0.00947,0.07836,0.01796,0.00902,0.00099,-0.0287,0.15942,0.08685,-0.08368,0.03088,-0.12957,-0.11269,-0.0024,0.07542,-0.0294,0.03752,0.0437,-0.06236,0.09891,0.13147,0.04962,0.06386,0.04519,-0.058,0.01282,0.04415,-0.04634,-0.13014,-0.07412,0.01756,-0.04196,0.07332,0.02584,0.04409,0.01893,-0.01223,0.13206,0.03946,0.00471,0.08602,0.07346,0.13814,-0.09753,-0.01865,-0.0205,0.05168,0.00499,-0.09442,0.03095,-0.05653,0.05716,0.15218,-0.09464,0.09517,0.02021,0.04027,0.04668,0.02609,0.05563,-0.06615,-0.07358,-0.00295,0.04555,0.02772,0.02396,-0.03018,0.03583,0.00132,0.08933,-0.022,-0.01014,0.03488,0.00852,-0.04103,0.05677,-0.06178,-0.11395,-0.00767,-0.13858,-0.00983,-0.04471,-0.03902,0.06671,-0.07937,0.05613,-0.01254,-0.1085,-0.02563,-0.0656,0.02558,-0.01057,-0.06773,-0.02537,0.0292,-0.06511,-0.09221,-0.0186,0.0778,0.0957,0.04625,0.06248,0.06553,0.00158,0.03296,-0.00386,-0.01203,-0.06886,0.08647,-0.10813,-0.02794,0.03088,0.11173,0.0518,-0.13227,0.0294,-0.00277,-0.05066,0.06155,-0.00814,0.01319,-0.01193,-0.01622,0.00683,-0.01034,-0.09185,-0.02342,0.00482,-0.02068,0.03968,-0.00711,0.04406,0.09267,0.02183,0.0709,0.00337,0.04193,0.01606,-0.06634,0.04717,-0.05435,0.05869,-0.02865,0.02335,0.01859,-0.09591,-0.04569,0.02179,-0.02758,-0.02863,0.00687,-0.02602,0.00692,-0.04942,0.01512,0.12108,0.00959,0.06985,0.03917,-0.10663,-0.00287,0.07534,-0.13743,-0.02489,0.06834,-0.08932,-0.02819,0.02227,-0.11402,-0.05052,-0.14122,0.08615,-0.0408,0.05159,-0.00488,-0.02947,0.00601,0.06638,0.07068,-0.01661,-0.02319,0.06907,-0.04843,-0.01843,0.10382,-0.05706,-0.10512,-0.06606]},{"domain":"chemistry","key":"limiting_reagent","name":"Limiting reagent and theoretical yield","package":"chemistry-ai999x","example":"For H2 + O2 -> H2O, 4.0 g of H2 react with 16.0 g of O2. Which is the limiting reagent and what mass of H2O forms?","v":[0.01143,0.03306,0.05456,0.04004,0.06836,0.00974,0.01017,-0.00318,0.00291,0.19053,-0.00713,0.09454,0.02331,-0.04277,0.08183,-0.00115,-0.07113,0.00202,0.0723,0.03751,0.01454,0.06668,0.0925,-0.01158,-0.09713,0.09824,-0.00369,0.02415,-0.10012,0.00852,-0.0762,-0.0504,-0.01591,-0.0017,0.01368,0.03234,0.00309,0.06712,-0.04798,-0.08288,0.04817,0.02722,0.00255,0.00745,0.0232,-0.01052,-0.07344,0.13092,-0.03019,0.11722,0.03013,0.07117,-0.09255,0.02118,0.06148,0.11385,-0.0063,-0.02687,0.02121,0.03005,0.01215,-0.08526,0.00509,0.00054,0.01057,0.02141,-0.00931,-0.08434,0.14301,-0.08549,0.02607,-0.10945,-0.00091,-0.01139,-0.02544,0.06621,0.0176,-0.09196,0.04011,-0.00707,-0.04457,-0.17769,0.08228,-0.01837,0.03543,0.10598,0.02975,0.04997,0.06352,0.03844,0.01267,-0.04118,0.06569,0.01544,0.06989,-0.02433,0.04094,-0.03265,-0.04508,0.0527,0.03051,-0.02064,-0.07654,-0.08671,-0.00905,0.04635,-0.04397,0.00782,-0.0693,-0.09904,-0.0729,0.04577,0.08039,-0.06441,-0.05763,0.00265,0.02061,0.00991,0.00262,0.07503,-0.02956,-0.04937,0.06698,0.00473,0.00364,0.1935,0.0163,0.06597,0.01986,0.03395,-0.04206,0.12356,0.02288,-0.01076,-0.00859,-0.07861,-0.03596,-0.00623,-0.0903,-0.04517,-0.08215,0.08209,0.09013,-0.03148,-0.03943,0.00538,0.08864,0.00027,0.04036,-0.0,0.0306,-0.0169,-0.10055,-0.04596,-0.02248,-0.1198,0.0072,0.00782,-0.02222,-0.00533,0.04162,0.07241,0.01688,-0.09316,-0.09817,0.00697,-0.03132,-0.0119,-0.02746,-0.03022,-0.09222,0.14637,-0.01122,-0.0856,0.06435,0.03513,0.03307,-0.10821,-0.04453,-0.00372,-0.09519,0.04016,-0.06209,0.02338,-0.16769,0.03447,-0.06509,-0.0727,0.01192,-0.04501,-0.07547,0.04597,0.00147,-0.00108,-0.00047,-0.08062,-0.10335,0.03732,-0.11486,-0.09521,0.08687,-0.04138,-0.05177,-0.08818,-0.02247,0.01792,-0.0091,0.04615,-0.09675,-0.00317,-0.00619,-0.06667,-0.00841,0.04099,0.05457,0.00924,0.02337,0.12839,-0.00059,0.06146,0.02043,0.03704,-0.09765,0.0142,0.0075,0.06147,-0.09082,0.07603,0.06887,0.01762,-0.01285,0.0585,-0.12653,-0.02324,0.05921,-0.12031,-0.03765,0.05884,-0.08978,-0.08816,-0.01509,0.02241,-0.06672,0.00126,-0.02336,0.02285,0.09347,0.05384,-0.05099,0.13414,-0.08729,0.07188,0.10451,0.08908,-0.02513,0.03954]},{"domain":"chemistry","key":"mass_from_moles","name":"Mass from moles","package":"chemistry-ai999x","example":"What is the mass of 2.50 mol of NaCl?","v":[-0.06853,0.0482,0.01961,-0.02188,0.07443,-0.10801,0.08047,-0.00273,0.02003,0.08693,0.04687,0.01992,0.04699,-0.01724,0.08559,-0.00463,-0.00718,0.02831,0.0233,0.10364,0.04638,-0.01134,-0.11909,-0.04659,-0.03839,0.07544,0.05107,-0.06094,-0.02758,0.04481,-0.06444,-0.03961,-0.0185,-0.01658,0.01308,-0.0541,0.03012,0.00497,0.02935,-0.09414,-0.04972,-0.0091,0.03631,-0.01216,0.11565,0.04891,-0.12276,0.04669,-0.00141,-0.03481,0.01169,0.06396,-0.11155,-0.00642,0.01449,0.07774,-0.10577,-0.05566,-0.03508,-0.03571,0.03463,-0.09518,0.0082,0.09646,0.12302,0.0403,-0.01627,-0.06363,0.00511,0.05627,-0.1,-0.09757,-0.02829,0.12187,0.10572,0.06107,0.04912,-0.0874,-0.01517,-0.04346,-0.01919,-0.09507,0.14145,0.02582,0.02082,0.01548,-0.04945,-0.07724,0.05358,-0.05695,0.02626,-0.0751,-0.02452,0.00369,-0.03659,0.09966,-0.08222,-0.008,0.00971,0.02714,0.03909,-0.02529,-0.00116,-0.04378,0.03785,0.13806,0.09351,-0.00803,0.0484,-0.08951,0.01155,-0.02521,-0.04853,-0.0388,-0.06238,0.00693,0.07605,-0.05178,-0.118,0.10756,-0.00066,-0.08613,0.02471,-0.07074,0.03766,0.00513,0.05898,-0.00108,-0.06127,0.00512,-0.06971,0.15186,0.03434,0.05944,0.10138,0.01216,-0.05338,0.09103,0.05351,0.01721,0.07174,0.05092,0.05594,-0.03335,-0.00157,-0.06873,0.04039,0.01452,-0.07705,-0.04042,0.02639,-0.02224,-0.12827,-0.04826,-0.091,0.01963,-0.04024,-0.05404,0.08653,0.07096,-0.01776,0.04541,0.07689,0.00842,0.05358,0.05306,-0.00639,0.06331,-0.02318,-0.1265,-0.08054,-0.08658,0.02959,0.06773,-0.08032,-0.00226,0.02937,-0.08508,-0.13382,0.00948,0.07842,0.17423,0.0154,0.08418,0.00868,-0.0303,-0.0498,-0.04837,-0.01048,0.0064,-0.03863,-0.0347,-0.03305,5e-05,-0.03086,-0.0339,-0.01807,0.12099,-0.14765,0.07017,-0.05241,0.00874,-0.00468,-0.114,0.00181,-0.04029,0.04667,0.0317,0.0421,0.00556,0.02002,-0.00479,0.10778,-0.03612,0.03313,-0.11174,0.10514,0.02226,0.09039,-0.10024,-0.00893,0.00357,-0.08083,-0.02769,0.04358,-0.01735,0.04294,0.00625,-0.11463,-0.0173,0.06353,0.08284,0.05125,0.09026,0.03317,-0.06498,-0.05858,-0.01795,-0.12708,-0.06525,-0.05716,-0.10157,-0.04829,-0.02133,-0.02585,0.01455,0.13736,-0.00664,0.00512,0.04703,-0.01026,-0.05346,0.03075,0.02218,-0.07988,-0.00296]},{"domain":"chemistry","key":"mass_of_element","name":"Mass 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Fe2O3?","v":[-0.01014,0.11535,0.08653,-0.07092,0.06782,0.0328,0.01359,-0.05483,0.0102,-0.00636,0.04247,0.01982,0.04506,-0.03469,0.03341,-0.03898,-0.09586,0.06383,0.01331,0.07449,0.01061,-0.00012,0.047,-0.01837,0.00233,0.03498,-0.05701,-0.16619,-0.01942,0.02774,-0.08644,-0.00727,0.01599,-0.02003,0.02771,-0.07572,-0.00378,-0.09682,0.01556,-0.13388,0.04302,0.04443,-0.08187,0.02931,0.04505,0.08667,-0.11925,0.07758,-0.04992,0.02844,-0.04947,0.04014,-0.03929,-0.00681,0.0457,0.06928,0.02363,-0.02976,0.03209,-0.08408,0.01017,-0.05936,0.00893,-0.0275,0.0732,0.10314,0.10964,0.00663,0.11963,0.01239,-0.02373,-0.1119,0.01007,-0.01407,0.00665,0.07252,-0.01671,-0.06947,0.02635,0.03686,0.11931,-0.15411,0.16758,-0.01358,-0.00593,0.01546,0.07403,-0.00202,0.08406,0.03553,0.02241,-0.08234,0.01374,-0.00901,0.04855,0.02859,-0.10347,-0.00777,-0.02889,0.00116,-0.01023,-0.07585,-0.03225,-0.11841,-0.07102,-0.01991,0.06872,-0.02493,-0.04339,-0.04526,-0.09552,0.06694,0.07565,-0.04415,-0.06865,-0.0593,0.06559,0.07071,-0.00197,-0.00584,-0.14957,0.07879,0.00092,-0.03267,0.04685,0.17736,0.02411,0.03434,0.0112,0.05071,0.02083,0.14607,-0.03691,0.05465,0.00555,0.02157,-0.01971,0.03953,0.00966,0.02443,-0.0282,0.03155,0.02707,-0.05874,-0.04527,-0.03909,0.09609,0.0386,-0.03204,0.07748,-0.03035,-0.02301,-0.05749,-0.09167,0.00221,-0.09889,0.00925,-0.04737,0.01015,-0.003,0.05789,0.02356,0.03753,-0.0541,0.05902,0.01211,0.08973,0.02392,0.0238,-0.08361,-0.03759,-0.07322,-0.03688,0.01144,-0.0054,0.12711,0.00051,-0.09589,-0.10255,-0.00107,-0.1086,0.20821,-0.02745,0.04399,-0.11266,0.02974,0.01719,-0.06507,-0.03986,-0.05206,-0.10453,0.02848,-0.04508,0.02078,-0.03186,0.00358,-0.01433,0.02404,-0.12928,-0.02902,-0.01954,-0.00015,-0.11772,-0.06428,-0.05969,-0.11218,0.03935,0.00921,-0.05988,0.00175,-0.04705,1e-05,0.00811,0.01092,0.08059,-0.05111,0.06164,0.11959,0.02081,0.03337,-0.00011,-0.00025,-0.0842,0.00162,0.05866,0.07242,0.03154,0.00175,-0.0034,0.01639,0.09831,0.08463,-0.08211,0.0003,0.04637,-0.10462,0.01775,-0.06241,-0.01927,-0.07103,0.00996,-0.14563,-0.05934,0.03843,0.05322,-0.02158,0.03275,-0.02299,0.06161,0.03673,-0.10997,0.07983,0.03798,0.1237,-0.00641,0.04199]},{"domain":"chemistry","key":"mass_percent","name":"Mass 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H2SO4?","v":[0.03984,0.05446,0.08938,-0.05351,0.03776,-0.01179,0.05376,-0.02257,-0.01188,0.02778,0.02525,0.00992,0.07637,-0.00987,0.00833,0.03387,-0.0549,0.09701,-0.01117,0.03829,0.07325,-0.06,-0.0315,-0.04206,-0.04033,0.02599,-0.03306,-0.13305,-0.02639,0.08294,-0.03523,-0.05666,0.06684,0.01441,0.00675,-0.10016,0.01647,-0.09778,0.08657,-0.11049,0.04365,0.02622,-0.10706,0.06055,0.04506,0.10865,-0.0857,0.05834,0.01195,0.07927,-0.06542,0.03758,0.01418,0.05132,0.05563,0.05466,0.00646,0.00931,0.04488,-0.12058,-0.00667,-0.10637,0.01421,-0.00597,0.10218,0.04638,0.0332,-0.00664,0.04888,0.02518,-0.00406,-0.05866,0.09282,-0.10512,-0.05055,0.04819,-0.00998,-0.0846,-0.00939,0.08054,0.0693,-0.05899,0.13582,-0.03002,-0.04591,0.00687,0.00153,-0.05891,0.04559,-0.00656,0.04998,-0.01724,-0.03157,0.04,0.00169,0.00116,-0.09406,0.02354,0.0286,0.08731,-0.01194,-0.08066,0.07405,-0.13875,-0.05611,-0.00352,0.00772,-0.06274,-0.02355,-0.07724,-0.04438,0.07124,0.08905,-0.02265,-0.09812,-0.06893,0.03043,0.04874,-0.02275,-0.00131,-0.05854,-0.03404,-0.01411,-0.07523,0.09482,0.13348,0.06902,0.04171,-0.01783,0.00471,0.01843,0.14542,-0.07926,0.0433,0.00462,0.03296,-0.02538,0.02396,0.04887,0.01804,-0.04776,0.00906,0.01132,-0.02077,0.02591,-0.07601,0.09301,-0.03785,-0.05776,0.09234,-0.06566,0.0468,-0.06485,-0.03598,-0.00966,-0.04946,0.05775,0.02041,0.08656,-0.01059,0.07301,0.00398,-0.01832,-0.0406,0.01015,0.03082,0.12495,0.01385,0.04412,-0.10232,-0.03538,-0.0986,-0.03572,-0.05202,0.05221,0.12779,0.02912,-0.08262,-0.05239,-0.02712,-0.07339,0.1814,0.00051,0.01831,-0.12669,0.02807,0.06856,-0.06218,-0.12504,-0.11781,-0.03976,-0.00374,-0.08584,0.02927,-0.07187,-0.05246,-0.00698,0.06095,-0.09179,0.00313,0.01063,-0.01204,-0.02525,0.06205,-0.13795,-0.1315,0.0572,-0.03224,-0.10574,0.02625,-0.10533,-0.05074,0.06522,0.05446,0.08689,-0.03879,0.0505,0.10621,0.04063,-0.03725,0.03972,-0.07088,-0.10393,-0.03775,0.09936,0.07835,-0.03298,0.01821,-0.06349,0.03662,0.12165,0.04132,-0.04349,0.06839,-0.03732,-0.09782,-0.03277,0.02989,0.00236,-0.10005,0.0423,-0.06706,-0.07506,0.00451,-0.01428,-0.00773,0.06327,-0.01265,0.06769,0.0656,-0.10148,0.05839,0.01595,0.02941,-0.04563,0.07053]},{"domain":"chemistry","key":"mean_speed","name":"Mean speed of gas molecules","package":"chemistry-ai999x","example":"What is the mean speed of CO2 molecules at 300 K?","v":[-0.07173,-0.05424,0.04927,0.13575,-0.05815,0.03368,-0.05859,-0.04045,0.02151,0.05017,0.02028,-0.05763,0.02772,-0.0103,0.02074,-0.04629,-0.05576,-0.10244,-0.02424,0.01806,0.01188,-0.0429,0.12111,-0.03403,0.04148,-0.01065,0.11812,-0.09058,0.0457,0.03387,0.04397,0.00773,0.04019,-0.04967,-0.02974,0.02051,0.01535,-0.04574,0.03272,0.01078,-0.13114,0.0696,0.07423,0.07465,0.00588,-0.01651,0.01839,-0.0295,0.11182,-0.03594,0.00408,-0.07992,-0.01479,-0.01839,0.1,-0.0228,0.06645,0.07055,0.00809,-0.08288,0.00343,-0.07699,-0.05204,-0.12638,-0.02773,-0.03133,-0.00912,-0.01072,0.01712,0.01115,-0.10853,0.00466,-0.12643,-0.03071,0.06186,0.12721,-0.03184,0.00944,0.07882,-0.00153,0.09844,0.00352,-0.04608,0.13024,-0.07594,0.04388,0.04115,-0.02125,-0.02581,0.01949,0.06456,0.06488,0.05489,0.00866,0.00664,0.0308,0.08641,-0.00053,0.06558,0.01163,-0.03543,0.01292,-0.04273,-0.04689,0.05508,-0.02307,0.06911,0.02557,0.02655,-0.01468,0.01241,-0.03963,0.16834,-0.04032,-0.08345,0.06295,-0.04096,0.01316,-0.0462,-0.06533,0.12723,-0.03718,0.01021,-0.03163,-0.05155,-0.07846,0.02953,-0.03446,-0.08242,0.01278,-0.02103,0.00518,0.01559,0.00506,-0.00314,-0.08699,0.11076,0.08914,0.04373,-0.03674,0.05919,0.05915,0.11917,0.084,-0.05916,0.08971,-0.05573,0.05968,-0.07618,0.04626,-0.00136,-0.0534,0.05624,-0.07957,-0.02648,-0.05058,0.02576,-0.0592,-0.0592,-0.03079,0.0425,-0.06671,0.01016,-0.13674,-0.02546,0.11255,0.01083,-0.07874,-0.00807,0.04334,0.02077,0.02715,0.06642,0.02993,-0.07793,-0.10755,0.10069,0.04322,0.02123,0.01586,0.08122,0.00758,-0.02179,0.12445,-0.07534,0.00997,-0.10642,-0.01854,-0.04526,0.07134,-0.07467,-0.02946,-0.01413,-0.09593,-0.00231,0.02852,0.01872,0.08949,-0.09232,0.00188,0.03086,-0.00903,0.03092,-0.06682,0.0111,0.0448,-0.03072,0.02307,0.03313,-0.06561,0.08871,0.09499,-0.00813,-0.07692,0.00166,-0.01507,0.02397,0.11332,0.00026,0.08101,-0.21655,-0.01375,0.06232,-0.0815,-0.05243,-0.10047,0.03135,0.02749,0.00687,-0.09261,0.08129,0.02393,-0.01638,0.07517,0.03595,-0.00298,-0.03138,0.04159,-0.02139,-0.014,0.04151,0.09486,-0.0635,0.00358,-0.02098,0.00478,0.03206,-0.02749,0.03463,-0.06459,0.01404,0.05606,-0.26014,-0.10471,-0.11124,0.01715]},{"domain":"chemistry","key":"molality","name":"Molality of a solution","package":"chemistry-ai999x","example":"What is the molality of a solution of 10.0 g of NaCl dissolved in 500 g of water?","v":[0.01386,0.00272,0.02392,-0.03301,0.01568,-0.0449,0.05812,0.13194,0.09167,-0.02835,0.06149,0.07269,0.02815,-0.0,0.07479,-0.17524,-0.12353,0.0377,-0.07795,0.08215,0.074,-0.00528,-0.11094,-0.10855,-0.02168,-0.01198,0.0523,0.08564,0.02578,0.02889,-0.07811,-0.03274,-0.04325,-0.05017,-0.01047,-0.01747,-0.01377,-0.0652,0.07168,-0.03005,0.01337,0.06988,0.00984,0.05149,0.09298,0.04366,-0.0109,-0.04317,-0.01588,0.07409,-0.05741,0.03784,0.02894,-0.0203,0.06778,0.10083,-0.12287,-0.0998,0.03757,-0.11609,0.04339,-0.02227,0.0946,-0.00082,0.01649,0.03947,0.01523,-0.02501,0.01946,0.07754,-0.02322,-0.00231,-0.02538,-0.07399,0.05542,0.09356,0.06596,-0.1898,-0.07014,-0.02458,-0.09655,-0.00986,0.00153,-0.07074,-0.03801,0.04988,-0.04381,-0.00462,0.13379,0.0436,0.0226,-0.01352,0.01967,0.0253,0.0047,0.00549,-0.1472,-0.06292,-0.04847,-0.00835,0.07007,-0.0219,0.03758,0.00214,0.02846,0.02571,0.07777,0.00762,-0.03798,0.02958,0.0519,-0.05042,-0.00051,-0.0687,-0.01717,-0.02272,0.03735,0.0443,-0.03361,0.12874,-0.03259,-0.07131,0.05045,-0.02697,0.00927,0.0778,0.11772,0.0635,-0.06209,-0.12861,-0.00627,0.08591,-0.15892,0.07111,0.0155,0.0413,0.03245,0.1572,-0.07935,-0.02896,-0.08292,0.10458,-0.10206,0.08662,-0.03211,-0.1211,-0.02719,0.08174,-0.01735,-0.0631,-0.06287,-0.09712,-0.12783,0.04614,-0.0123,-0.14274,-0.03713,-0.1368,0.00055,-0.03974,0.00372,0.00632,0.00351,-0.00567,0.02555,0.06899,-0.09026,0.08312,0.02299,-0.06424,0.04197,-0.07932,0.09643,0.00757,-0.02907,-0.10022,0.02051,-0.0902,-0.04221,0.05708,0.03733,0.09647,-0.04055,-0.03474,-0.01453,-0.01042,0.02583,0.03951,0.03989,-0.02422,-0.06149,-0.0479,0.01276,-0.05533,0.02794,0.01662,0.0122,0.00695,0.00251,0.08784,0.03693,0.03923,0.06688,-0.01407,-0.00299,0.00476,0.03233,0.00881,-0.08684,0.03509,0.01196,-0.06934,0.01509,0.01132,0.0719,-0.04219,0.05162,0.0376,0.10025,-0.04165,-0.07797,-0.05009,0.01435,0.12992,0.01896,0.12623,-0.06105,-0.06213,-0.01377,0.06295,0.02633,0.01751,0.02858,0.00364,-0.01831,0.02379,-0.08651,-0.01391,-0.10266,-0.07038,0.08018,-0.02297,-0.05857,-0.03924,-0.02241,-0.00203,0.10232,-0.00199,-0.04727,-0.08428,-0.0337,0.04011,0.09109,-0.00886,0.00963,0.00307]},{"domain":"chemistry","key":"molar_mass","name":"Molar mass of a formula","package":"chemistry-ai999x","example":"What is the molar mass of Ca(OH)2?","v":[-0.07945,0.08053,0.03013,0.06127,0.10175,-0.05066,0.11739,0.05302,0.05304,0.07906,0.05515,0.00974,0.10618,0.009,0.01877,0.05684,0.03614,-0.04149,-0.01502,0.07921,0.09521,-0.06955,-0.10363,-0.00601,-0.04009,0.03549,0.06377,-0.06159,-0.05917,0.01068,0.02706,0.01327,-0.00453,-0.00846,-0.02608,-0.04164,0.01979,-0.00926,0.05772,-0.09058,-0.04785,-0.07012,-0.00968,-0.00244,0.07078,0.02015,-0.09683,0.03635,0.05896,-0.01393,-0.02069,0.09047,-0.06842,0.00594,0.00175,0.10111,-0.14221,-0.07707,-0.05874,0.01545,0.00192,-0.19232,0.01194,0.01889,0.07711,-0.03817,-0.06757,-0.04022,-0.01181,-0.01666,-0.04057,-0.02142,-0.02173,-0.00437,0.07477,0.03711,0.06793,-0.14028,-0.01629,-0.05334,-0.04172,0.01238,0.08811,0.00964,0.03263,0.05375,0.02857,-0.01999,0.05192,-0.04474,0.00959,0.00157,-0.03808,0.1176,-0.00839,0.02427,-0.10194,-0.04836,-0.03279,0.03884,0.04668,-0.09036,-0.00063,-0.02482,0.00255,0.10642,0.05458,0.04581,0.0154,-0.00869,0.04204,-0.0372,0.03133,0.01859,-0.05956,0.02299,-0.04866,-0.03142,-0.09335,0.00952,0.0836,-0.1394,-0.01079,-0.02891,0.05396,0.00635,0.03695,-0.05953,-0.10278,-0.05723,0.00438,0.2093,0.10523,0.02179,0.0713,-0.0313,-0.09173,0.07626,0.06805,0.00735,0.12812,-0.04884,0.10682,-0.00047,0.01457,-0.01374,0.04414,-0.09652,-0.06423,0.00161,0.02757,0.00215,-0.08259,-0.12032,-0.05832,0.02368,0.00342,-8e-05,0.07505,0.01492,-0.00844,-0.05741,0.10539,-0.05846,0.01627,0.09619,-0.013,0.06551,0.07946,-0.13086,0.01307,-0.03054,0.02167,0.07575,-0.10406,-0.03925,0.10829,-0.09879,-0.07168,-0.07296,0.10494,0.12505,-0.05259,0.05844,-0.00889,-0.04266,-0.06734,-0.00933,-0.06164,-0.05632,0.02022,0.00511,-0.043,-0.04079,0.00864,-0.02325,-0.06043,0.12839,-0.03241,0.02695,-0.02974,-0.00254,0.00493,-0.0516,-0.04642,-0.01685,0.08625,0.08072,0.08261,-0.07173,-0.07597,0.05884,0.0882,-0.05702,0.01245,-0.04037,0.04301,0.02767,0.08701,-0.0176,-0.00046,0.02387,-0.02566,0.03761,-0.07254,-0.09739,0.07043,-0.01754,-0.0891,-0.05404,0.05546,0.05441,0.06303,0.00276,0.05218,-0.13139,-0.09873,0.04937,-0.14054,-0.02271,-0.01468,0.00085,-0.02498,-0.02086,0.00089,-0.01873,0.10316,-0.00046,0.03971,0.07631,-0.03694,-0.03291,0.07073,0.0166,-0.13655,-0.00688]},{"domain":"chemistry","key":"molar_mass_from_freezing_point","name":"Molar mass from freezing-point depression","package":"chemistry-ai999x","example":"Dissolving 2.00 g of a nonelectrolyte in 100 g of water lowers the freezing point by 0.372 °C (Kf = 1.86 K·kg/mol). What is the molar mass of the solute?","v":[-0.00148,0.00197,0.01524,-0.04415,0.03538,0.01097,0.06425,0.07784,0.05028,-0.02684,0.10489,0.03161,0.05056,-0.1163,0.01143,-0.10107,-0.03293,-0.06825,-0.06693,0.1734,0.03824,0.08891,-0.15599,-0.03284,-0.01562,0.00672,0.0699,-0.01405,0.01404,-0.06119,-0.0833,-0.02814,-0.09966,-0.01505,-0.1122,0.02861,0.02492,0.01748,0.07829,-0.01541,-0.03549,0.06902,-0.02896,-0.07485,0.0439,0.05688,0.02028,0.02689,0.10199,0.06854,-0.04023,0.07627,-0.02003,0.01778,0.02277,0.00307,-0.19931,-0.09809,0.0339,-0.0708,0.0726,-0.02077,-0.07185,0.03123,0.01572,0.01624,-0.04968,-0.04751,0.04084,-0.02128,0.03795,0.00555,-0.05655,0.00103,0.07239,0.13094,0.00236,-0.14757,-0.06299,-0.01466,-0.05314,-0.03247,0.08935,-0.00847,0.05554,0.03078,-0.06415,0.07561,0.14875,0.0379,0.02117,-0.03051,-0.05772,0.03022,-0.01732,-0.02757,-0.06867,0.0153,-0.00871,-0.01688,0.07045,-0.03053,-0.03255,0.01662,-0.00034,0.14095,0.15143,0.07094,-0.0666,0.04552,0.10362,0.03413,-0.08197,0.00779,-0.01513,-0.01198,-0.04941,0.01833,-0.00087,0.13775,0.1118,-0.11138,0.00241,0.04173,0.06594,0.00566,-0.03749,0.06656,-0.10856,-0.04715,-0.0017,0.07998,-0.0379,0.08209,0.08948,0.04036,0.00831,0.07503,-0.0144,-0.03453,0.00653,0.02186,-0.06884,0.10309,-0.03433,-0.06679,0.04342,-0.02678,0.02824,-0.07578,-0.00491,-0.13085,-0.03811,-0.03121,-0.06512,0.01024,-0.0038,-0.03409,-0.0613,-0.06877,-0.08023,-0.06539,0.07716,0.04222,-0.01153,-0.05516,-0.04731,0.05229,0.05146,-0.03993,0.05081,0.01234,0.04328,0.07054,0.01215,0.00996,-0.03874,-0.081,-0.02402,-0.00626,0.01883,0.12411,0.03201,-0.05559,-0.03215,0.02387,0.04486,0.01436,0.03254,-0.04765,-0.09352,0.06455,-0.03696,-0.02788,0.10789,0.03553,-0.06849,0.02693,-0.03329,0.06821,-0.03194,-0.04848,-0.01864,-0.05312,-0.07506,0.03329,0.0212,0.00395,-0.09591,-0.04416,0.02853,0.01019,-0.05832,-0.10433,0.02334,-0.01555,-0.00366,0.04518,0.03436,0.00987,-0.10834,0.06605,0.0035,0.00808,-0.03822,0.03597,0.03566,-0.0057,-0.11516,0.0193,-0.00397,-0.0162,-0.01558,0.00338,0.03187,0.02953,-0.13644,-0.00319,-0.22106,0.01555,-0.02981,-0.00575,-0.01573,-0.02308,0.0642,0.01672,0.16206,0.07097,-0.05675,0.05483,-0.08834,0.02072,0.11096,-0.01357,-0.03627,-0.10841]},{"domain":"chemistry","key":"molar_mass_from_gas_density","name":"Molar mass from gas density","package":"chemistry-ai999x","example":"A gas has a density of 1.25 g/L at 1.00 atm and 273 K. What is its molar mass?","v":[-0.06956,-0.00616,-0.06559,0.07742,0.04682,-0.04238,0.10326,-0.00183,0.15242,0.06816,-0.02562,0.03671,0.10441,0.08523,0.03222,0.0321,0.02957,-0.08074,0.03972,0.07686,0.07441,-0.00892,-0.03891,-0.0628,-0.00152,0.07501,-0.00418,0.07875,-0.12936,-0.07411,0.07613,-0.02438,-0.06108,-0.04693,0.02707,0.08723,-0.03588,0.04515,0.05777,-0.04657,-0.04304,0.08096,0.04984,-0.01151,0.0071,0.06372,-0.06512,0.05374,0.10924,-0.02901,-0.07561,0.05945,0.02496,-0.04919,-0.03406,0.14239,-0.0248,-0.02035,0.03109,0.04303,0.02473,-0.20128,0.02341,-0.03658,0.06631,-0.11781,-0.05929,-4e-05,-0.04889,0.03364,-0.03708,-0.03821,-0.04508,-0.08483,0.18416,0.06167,0.1602,-0.07261,-0.02685,-3e-05,-0.00782,0.03838,0.02198,0.01667,0.03183,-0.0188,-0.00807,0.05273,0.01398,-0.01728,-0.01895,-0.011,-0.05825,0.04571,0.02016,0.00454,-0.05396,0.03823,-0.00281,0.05501,0.04993,-0.10167,-0.05331,0.06588,0.02235,0.00917,0.08194,0.15591,0.02911,0.04109,-0.07759,-0.05264,-0.10811,0.02395,-0.10508,0.02303,0.02811,0.05406,-0.01912,-0.02701,0.06898,-0.07889,-0.0325,-0.03026,0.00448,-0.09357,-0.00872,-0.07153,-0.02221,-0.00393,0.02361,0.10866,0.06028,-0.02412,0.02046,0.03324,-0.07354,-0.00722,0.03623,0.02346,0.02377,-0.03799,0.0807,0.02666,0.08877,0.07711,0.06414,-0.04836,0.01382,-0.05441,0.06844,-0.00745,0.02279,-0.08655,0.01791,-0.01531,-0.00031,0.00477,0.00032,-0.00273,-0.05624,-0.07552,0.0445,-0.12996,0.08191,0.08426,-0.00596,-0.00648,0.01492,-0.12516,0.03536,-0.04869,-0.00863,-0.03307,-0.08412,0.05799,0.03045,-0.12219,0.04334,0.06742,0.17625,0.05446,-0.0137,0.0276,-0.02153,0.0085,0.00791,0.07823,-0.03305,-0.14205,-0.01461,0.05292,-0.02051,0.00857,0.06587,0.06237,-0.01661,0.06521,-0.0009,-0.01064,-0.12378,-0.04936,-0.00726,-0.06594,-0.02195,0.00158,0.03654,0.01311,0.03723,-0.10041,0.0325,0.08697,0.0457,-0.09938,-0.00506,-0.00086,-0.03144,0.02526,0.0073,0.0272,-0.01627,0.07857,0.03219,0.03396,-0.10484,-0.10468,0.06176,-0.07589,-0.12307,-0.07864,0.02984,0.04725,0.02622,-0.085,-0.04658,-0.10674,-0.07022,-0.03279,-0.1054,0.07592,0.02767,-0.01575,0.05825,-0.02766,-0.02397,0.00734,0.06981,0.10656,-0.01559,-0.02521,-0.03627,-0.01546,-0.0945,0.00489,-0.1067,-0.10074]},{"domain":"chemistry","key":"molar_mass_from_gas_sample","name":"Molar mass from a gas sample","package":"chemistry-ai999x","example":"A 1.00 g sample of a gas occupies 0.500 L at 1.00 atm and 300 K. What is its molar mass?","v":[-0.19061,0.04251,0.00597,0.06216,0.03168,-0.03163,0.07986,-0.01971,0.10699,0.09351,0.0232,0.08279,0.11751,-0.0363,0.01974,0.05717,0.06469,0.04855,-0.02513,0.12885,0.07006,0.03592,-0.03617,-0.02299,-0.02048,0.05362,0.05367,-0.02646,-0.03714,-0.02959,0.04954,-0.06748,-0.04802,0.02287,-0.00827,-0.01717,-0.08627,0.00779,0.07419,-0.03145,0.01323,0.04008,-0.00916,-0.03217,0.0226,0.04216,-0.06237,0.06565,0.07865,-0.01541,-0.02034,0.01017,-0.01625,-0.07397,-0.01203,0.12562,-0.01551,-0.05355,0.04922,0.03486,-0.00029,-0.17077,-0.0889,0.02028,0.03824,-0.07982,-0.04379,-0.04602,-0.02494,0.04734,-0.00925,-0.06052,0.01757,-0.05814,0.10235,0.08305,0.09793,-0.05169,0.01776,0.00047,-0.00964,0.0409,0.0533,0.04683,0.01403,0.02888,-0.04883,0.02206,0.06057,-0.0219,0.08961,-0.02578,-0.08965,0.11556,0.0171,0.06395,-0.02953,0.05051,0.03478,0.05522,0.05501,-0.09867,-0.02802,-0.03465,-0.0747,0.01213,0.03452,0.1045,-0.01094,0.06781,-0.01434,-0.08456,-0.06195,0.03317,-0.09436,0.00568,-0.03438,-0.00115,-0.00984,-0.0268,0.10925,-0.03237,-0.03638,-0.07366,0.08314,-0.07723,0.06658,-0.07667,-0.04267,0.02887,0.05258,0.14719,0.02943,0.01542,0.0293,-0.02301,-0.07301,0.07176,0.0215,0.03943,0.04138,-0.04976,0.03794,0.00527,0.07916,0.03957,0.02154,-0.0667,-0.05086,-0.02904,0.03078,0.0033,0.03084,-0.07507,-0.0727,0.07174,-0.01961,0.02406,0.06834,0.00196,-0.02505,-0.10462,0.0557,-0.1032,-0.02427,0.10559,-0.0093,0.01351,0.03517,-0.13518,-0.00495,0.00676,-0.02699,0.05313,-0.07533,0.0107,0.01879,-0.17375,-0.00245,-0.03247,0.09635,0.13473,0.06241,-0.00267,-0.07651,0.01723,0.01213,0.02287,-0.05275,-0.09865,-0.03649,0.12253,-0.09138,0.05948,0.00721,0.03433,-0.11727,0.07026,-0.01653,0.10799,-0.06242,-0.1044,-0.06931,-0.04848,-0.02858,0.03519,0.04623,0.0004,0.04916,-0.14779,-0.03048,0.01989,0.03457,-0.10991,0.06039,-0.04021,-0.02667,-0.00435,0.05477,-0.04485,-0.02768,0.10774,-0.02102,-0.00013,-0.14711,-0.10189,0.06242,-0.00184,-0.1139,-0.05527,0.06983,0.02472,0.01589,-0.04293,0.02517,-0.09935,-0.08557,0.01048,-0.10743,-0.00489,0.02412,-0.0548,0.06819,-0.00597,0.05764,0.00119,0.12069,0.05528,0.0065,0.01571,-0.01958,-0.07203,0.00695,0.01133,-0.15941,-0.06505]},{"domain":"chemistry","key":"molar_mass_from_osmotic_pressure","name":"Molar mass from osmotic pressure","package":"chemistry-ai999x","example":"A solution of 1.00 g of a protein (a nonelectrolyte) in 100 mL of water has an osmotic pressure of 2.50 torr at 25 °C. What is the molar mass of the protein?","v":[-0.05978,0.00137,0.00076,-0.09917,0.03632,-0.01217,0.11522,0.09921,0.05838,0.02015,0.06954,0.02333,0.07149,-0.02735,0.08212,-0.02329,-0.00764,0.10434,-0.02499,0.11516,0.09806,-0.01795,-0.1749,0.02499,-0.00233,0.03582,0.0543,-0.04302,0.00773,0.00378,-0.03259,-0.03869,-0.05971,-0.01386,-0.10156,0.00784,0.02237,0.00675,0.10159,0.03362,0.0407,0.12819,-0.03125,0.00314,-0.02804,0.07936,0.03567,-0.0145,0.12828,0.06754,-0.02338,-0.03543,0.03926,-0.0553,0.03436,0.07045,-0.10132,-0.05836,0.04631,-0.03064,0.06938,-0.05413,0.00374,0.0392,0.05057,0.00808,0.02052,-0.089,0.05559,0.00641,0.00799,-0.02941,-0.06377,0.00509,0.04852,0.10439,0.09563,-0.1346,-0.08886,0.05576,-0.1058,0.06125,0.04727,0.0103,0.01615,0.00458,-0.05391,0.10907,0.18235,-0.02229,0.05097,0.00362,-0.03149,0.02444,-0.06948,0.08352,-0.03124,-0.01296,0.01947,0.06497,0.10738,-0.07094,0.04869,-0.01713,-0.02249,-0.03762,0.0079,0.06116,0.00648,0.07618,-0.0053,-0.01074,-0.03706,-0.00267,-0.06167,-0.07956,-0.06289,0.062,0.0055,0.03352,0.13726,-0.01654,-0.1379,0.01546,0.00793,-0.05112,-0.01276,0.01357,-0.11502,-0.03355,-0.05832,0.04149,-0.00459,-0.0622,0.02776,0.03033,-0.0662,0.0372,0.00201,-0.01271,-0.02484,0.03876,-0.03882,0.052,0.03756,-0.06324,-0.00408,-0.02841,0.02932,0.0035,0.01652,-0.00217,0.01928,-0.0023,-0.0822,0.03845,0.00262,0.02138,0.02599,0.0238,-0.05231,-0.10736,0.08231,-0.01659,-0.05199,0.07529,-0.06538,0.04194,0.00946,-0.1561,-0.06942,-0.00568,-0.01148,0.10895,0.06324,0.04537,0.00165,-0.0585,0.02594,0.03272,0.13801,0.14264,0.0387,-0.05345,-0.04689,-0.002,0.05212,0.0211,-0.03855,-0.10856,-0.00132,0.03207,-0.03421,-0.1167,0.09459,0.03031,-0.10909,-0.02665,-0.06144,0.08531,-0.03232,-0.02836,-0.07099,0.02776,-0.06824,0.05611,0.08247,0.04552,-0.06874,-0.01949,-0.01007,-0.05858,0.04457,-0.06127,0.0152,-0.02095,-0.02786,-0.06378,0.07851,0.00131,-0.07086,0.0753,0.00979,-0.02466,-0.10214,-0.09268,0.01276,-0.01818,-0.01516,-0.00179,0.06303,0.10325,0.01524,0.00484,0.01559,0.00983,-0.17667,0.0173,-0.2008,-0.03465,-0.03444,-0.03785,0.0649,-0.0221,0.09782,-0.07683,0.15572,-0.00294,-0.06269,0.00922,-0.00345,-0.05295,0.10233,-0.01041,-0.08292,-0.06425]},{"domain":"chemistry","key":"molarity_from_mass","name":"Molarity from a dissolved mass","package":"chemistry-ai999x","example":"What is the molarity of a solution made by dissolving 5.85 g of NaCl in 250 mL of solution?","v":[-0.0483,0.1119,0.01132,-0.05306,0.12114,-0.09217,0.05888,0.17248,0.07648,0.0023,0.09809,-0.02118,0.02934,-0.03898,0.05515,-0.0582,-0.06007,0.03943,-0.07357,0.0687,0.0199,0.06961,-0.14081,-0.04115,0.01178,0.01425,0.06592,0.05621,-0.03304,0.00313,-0.02446,-0.07339,-0.06454,0.02483,0.03629,-0.05977,-0.05678,-0.03314,0.15582,0.02088,-0.02994,-0.00767,0.02951,-0.06464,0.09452,0.03357,-0.00133,-0.01251,-0.03535,-0.04363,0.00793,0.03028,-0.02042,-0.09509,-0.01835,0.13201,-0.09782,-0.09003,-0.07307,-0.04297,0.07826,-0.02351,0.04636,0.10196,0.0436,-0.03833,-0.01557,-0.09261,0.00917,0.09883,0.02971,-0.00122,-0.03076,0.05434,0.14731,0.09707,0.03461,-0.16948,-0.01842,-0.04777,-0.10418,0.00858,0.00436,-0.07556,0.05261,0.08812,-0.03192,-0.06289,0.08796,-0.0769,0.07827,-0.0809,-0.07671,0.03793,-0.09665,0.07998,-0.07963,-0.03685,0.04069,0.00888,0.06308,-0.03932,0.09077,-0.03512,-0.0074,0.05318,0.00777,0.04532,-0.01994,0.1175,0.08875,-0.05089,-0.06579,0.01139,-0.04639,0.03887,-0.02582,-0.01581,-0.00293,0.11275,0.07753,-0.06481,0.04029,0.00226,0.05139,0.05831,0.09628,-0.02865,-0.01437,-0.09543,0.05369,0.1026,-0.07037,-0.0057,0.02766,0.02236,-0.00711,0.12705,0.01398,-0.00366,0.04544,0.04623,-0.01171,-0.00601,-0.04024,-0.10343,0.00369,-0.01006,-0.07312,-0.06471,0.0021,-0.00526,-0.06473,-0.03453,-0.05679,-0.01359,-0.0518,-0.04788,0.08076,0.00382,-0.01736,-0.06982,0.03894,-0.02373,0.07591,0.06348,-0.03658,0.01999,0.01959,-0.18453,0.02407,-0.00097,-0.02286,-0.00986,-0.01217,-0.05449,-0.00789,-0.13437,0.01273,-0.08119,0.14049,0.09637,-0.05767,-0.03795,0.01013,-0.00908,0.03579,0.13195,0.03818,-0.03146,0.00805,-0.0542,-0.06651,-0.08385,0.04688,-0.05372,-0.03337,-0.06115,-0.03223,0.05949,-0.00248,-0.0026,0.08893,-0.04849,-0.02096,0.00778,0.03248,-0.01099,0.0068,-0.01954,0.00929,-0.09613,0.06482,-0.06528,0.02123,-0.08673,0.09361,0.02333,-0.0013,-0.09868,-0.05955,-0.0268,0.04214,0.02737,0.01063,0.04193,0.0009,-0.01412,0.00883,0.03444,0.01596,0.06425,0.09833,-0.07896,-0.02129,-0.06353,-0.1379,-0.02864,0.0073,-0.03918,0.0994,0.00393,-0.01321,-0.01914,0.04471,0.0267,0.13519,0.04499,-0.01501,-0.03554,-0.04856,-0.09246,0.13479,-0.03119,-0.0226,0.01717]},{"domain":"chemistry","key":"mole_fraction","name":"Mole fraction in a solution","package":"chemistry-ai999x","example":"What is the mole fraction of solute in a solution of 20.0 g of C6H12O6 dissolved in 100 g of H2O?","v":[-0.00396,0.08598,0.02826,-0.01978,0.04673,0.01428,-0.011,0.07879,0.10385,-0.09844,0.11098,-0.0373,0.01639,-0.03937,0.02672,-0.13572,-0.09625,-0.05089,-0.12178,0.06373,0.00597,0.02137,-0.01062,-0.11825,0.04469,0.01904,-0.05299,-0.04503,-0.0501,-0.01021,-0.09104,-0.05213,-0.02882,0.02919,-0.02112,-0.04533,0.01429,-0.03735,0.09404,-0.05332,-0.01228,0.1033,0.02428,0.05428,-0.00571,0.07995,0.01751,0.04087,-0.03742,0.13164,-0.0594,0.11397,-0.02495,-0.05059,0.05849,0.17575,-0.10367,-0.10231,-0.03179,-0.10426,0.06554,-0.00125,0.05784,-0.04821,0.01401,0.02392,0.04965,-0.07242,0.05998,0.03885,-0.04166,-0.07128,-0.02471,-0.00995,0.06581,0.18347,-0.01249,-0.09632,0.02257,0.03045,-0.00593,-0.02356,0.02247,-0.04147,0.06814,0.05717,-0.02035,0.11626,0.1526,0.05165,-0.02221,-0.06373,-0.0183,-0.01646,0.00157,-0.02678,-0.07532,0.03356,-0.06195,-0.07797,-0.03348,0.04966,0.05914,-0.02441,0.04577,-0.0357,0.09341,0.03542,0.00655,0.14495,0.02281,-0.00849,-0.03844,-0.03199,-0.01887,-0.03388,0.10087,0.06452,0.00798,0.05495,-0.03013,-0.04864,-0.02102,0.06526,0.00176,0.0645,0.0542,0.03041,-0.03385,-0.01247,-0.02085,0.09662,-0.08762,0.01264,-0.01291,0.08759,-0.00909,0.16377,-0.07243,-0.01282,-0.04744,0.03707,-0.06325,0.07026,-0.03584,-0.06043,0.00622,0.08086,-0.02148,-0.01553,-0.10017,-0.17811,0.00188,0.00629,-0.02376,-0.12303,-0.05029,-0.08238,0.02679,-0.05993,-0.03482,-0.07364,-0.02146,0.01156,0.11549,-0.00022,-0.04853,0.09006,0.07521,-0.06113,0.08487,-0.03202,0.04469,-0.0639,0.07159,0.01514,0.00405,-0.09515,-0.00613,0.02151,-0.04093,0.14945,0.01032,-0.04043,-0.12607,0.03855,0.06877,0.10203,0.04593,-0.05385,-0.09252,-0.07862,-0.05059,0.02128,0.06637,-0.00584,0.05676,-0.09061,-0.10837,0.00777,0.04184,-0.03143,-0.04288,-0.00907,-0.01054,-0.04857,0.03577,-0.00262,-0.06386,0.04781,-0.05885,-0.01545,-0.03431,-0.05369,0.07018,-0.04113,0.12569,0.03053,0.00896,-0.00091,0.01842,0.02665,0.01583,0.05072,0.05739,0.04287,-0.0236,0.00887,0.04346,0.01639,0.02441,0.03945,-0.07482,-0.04334,0.06519,-0.01673,-0.0593,-0.06678,-0.05392,-0.10374,0.05082,-0.09431,-0.0349,-0.0163,0.0416,0.00295,0.06866,0.03857,-0.0536,-0.03988,-0.11757,0.02257,0.1023,-0.06557,0.02036,0.01763]},{"domain":"chemistry","key":"molecular_formula","name":"Molecular formula from the empirical formula","package":"chemistry-ai999x","example":"A compound has the empirical formula CH2O and a molar mass of 180.16 g/mol. What is its molecular formula?","v":[0.00224,0.06378,0.0369,0.12884,0.0314,0.01554,0.0669,-0.01525,0.04,-0.01596,0.05963,0.02891,0.02811,0.16238,0.04089,0.02981,0.04063,-0.05905,0.05755,0.03275,0.05919,-0.01307,-0.05158,-0.05888,0.00982,0.0994,0.00881,-0.03307,-0.13192,0.08653,-0.04812,-0.04031,0.07135,0.04899,-0.09803,-0.05053,0.01713,-0.05226,0.01192,-0.03746,-0.07476,-0.02798,0.00297,0.01078,0.01128,-0.03066,0.00659,0.0395,0.08304,0.07083,0.00102,0.07489,-0.0804,0.10826,0.06141,0.1132,-0.13027,-0.0536,-0.06318,-0.06348,0.00728,-0.15948,0.03714,0.02131,-0.01902,-0.04392,-0.01518,-0.01324,0.0049,0.03598,-0.02833,-0.00693,-0.0478,0.04662,0.06156,0.05394,0.04375,-0.08615,-0.0246,-0.04436,0.01368,0.01589,0.03086,-0.02829,0.0283,0.03411,-0.0724,-0.0281,0.07071,-0.10186,-0.08666,0.08165,-0.04648,0.00526,-0.01986,0.01462,-0.09362,-0.0918,0.02568,0.13459,0.02354,-0.00682,0.08713,-0.0481,0.0005,0.00084,0.06278,-0.00189,0.04632,-0.02204,-0.04743,-0.05325,0.04757,-0.00116,-0.11884,0.06698,-0.08288,-0.07262,-0.05162,0.03162,0.03875,-0.09349,-0.04071,-0.03416,-0.0231,0.10735,0.10638,-0.00301,-0.13422,0.03779,-0.11648,0.18405,0.06121,-0.02445,0.09666,-0.0201,-0.08147,0.05102,0.05115,0.01389,0.09378,0.00201,0.14398,0.03069,0.03318,0.03889,0.00955,-0.0845,-0.02079,0.01563,0.02825,0.02766,-0.1326,-0.05408,-0.04086,-0.05961,-0.04,0.01229,0.03996,-0.0134,-0.0913,-0.10981,-0.01778,-0.00786,-0.03755,0.12062,-0.07081,0.05481,0.04088,-0.06233,0.01343,-0.00057,0.09893,0.11437,0.02073,-0.05935,0.0694,0.0384,-0.11824,0.0631,0.03161,0.01346,-0.02966,0.01705,0.02802,0.04255,-0.05917,-0.03488,-0.078,-0.02996,-0.04381,-0.06207,-0.02139,-0.05797,-0.03167,-0.06722,-0.0357,0.07853,-0.09565,0.03322,-0.01817,0.00372,0.01762,0.11822,-0.04268,-0.01696,0.09695,0.00071,0.09057,-0.05286,-0.11597,0.02199,0.05426,-0.07037,0.01655,-0.0435,0.08652,0.04415,0.05717,0.03701,-0.0216,0.10245,-0.00092,0.02912,-0.04305,-0.10759,0.02533,0.0533,-0.05385,-0.07284,0.02658,0.09943,0.01203,0.09933,0.07733,-0.12386,-0.06636,0.06716,-0.10826,-0.00745,-0.01781,0.01874,-0.05511,-0.04632,-0.05061,-0.03994,0.05007,-0.00738,-0.06348,0.00702,-0.00358,-0.02776,0.14068,0.00178,-0.07874,-0.01145]},{"domain":"chemistry","key":"moles_from_mass","name":"Moles from a mass","package":"chemistry-ai999x","example":"How many moles are in 36.0 g of H2O?","v":[-0.05373,0.12536,0.03977,0.02154,0.11777,-0.08149,0.05046,-0.04391,0.00364,0.06216,-0.00174,0.01387,0.05765,-0.07644,0.0611,0.00351,-0.01702,0.02282,0.0135,0.13079,0.00739,0.01257,-0.0106,-0.02648,-0.05733,0.07724,0.05813,-0.08376,-0.0651,0.04857,-0.10525,-0.05641,-0.06809,-4e-05,0.00992,-0.08096,-0.00308,0.01398,0.03862,-0.13542,-0.02835,0.03688,0.01017,0.01957,0.03907,0.07914,-0.14804,0.10569,0.00157,0.0425,0.02024,0.04184,-0.04067,0.03008,0.03382,0.05078,-0.07175,-0.08441,-0.03612,-0.05342,0.01248,-0.11769,-0.06508,0.03919,0.10265,0.07234,-0.02661,-0.00486,0.03174,0.04231,-0.02891,-0.11838,0.00583,0.1127,0.10685,0.07725,0.05198,-0.05915,0.03521,-0.00139,-0.01345,-0.12964,0.10087,0.01931,0.01981,0.04997,-0.06662,-0.07283,0.11426,0.04446,0.03741,-0.13083,0.03489,0.04434,-0.01122,0.02087,-0.0903,-0.00975,0.03567,-0.00795,0.04629,-0.05707,-0.06172,-0.13485,0.00621,0.09172,0.09297,-0.0118,0.0447,-0.04916,-0.04102,-0.01411,-0.05022,-0.04281,-0.08454,0.00467,0.04992,-0.03641,-0.07886,0.06524,0.00217,-0.01507,0.01837,-0.02859,0.08819,0.04226,0.02855,0.03406,-0.02784,0.04856,-0.02245,0.18133,0.02519,0.08042,0.12358,0.02386,-0.02994,0.03591,-0.01212,-0.0039,-0.03924,0.05799,0.02851,-0.01605,-0.0416,-0.06882,0.02078,0.01549,-0.07474,-0.03747,0.02178,-0.04769,-0.12957,-0.06714,-0.09001,-0.03875,-0.05161,-0.01852,0.08055,0.0377,0.01195,0.08409,0.06264,-0.00367,-0.02961,0.0073,0.00154,-0.01934,-0.03422,-0.08488,-0.04293,-0.08846,-0.00331,0.02872,-0.03099,-0.01788,-0.01246,-0.06192,-0.17417,0.01981,0.05919,0.18757,0.02921,0.07135,-0.01629,-0.00445,-0.04326,-0.04566,-0.03765,0.00296,-0.05671,0.02202,-0.09402,-0.02452,-0.0417,0.02353,-0.00483,0.05282,-0.18395,0.04599,-0.05398,-0.00667,0.00874,-0.10435,0.02418,-0.01219,0.04709,-0.03882,0.00364,-0.01774,-0.03867,-0.03081,0.07806,-0.04025,0.06416,-0.12759,0.02232,0.01261,0.07383,-0.01986,0.0188,0.02429,-0.10665,-0.02981,0.03912,0.04767,0.06607,0.07258,-0.09183,-0.00147,0.04605,0.10594,0.04224,0.04716,0.04136,-0.04512,-0.06149,-0.01607,-0.11258,-0.10386,-0.04362,-0.0921,-0.07209,8e-05,0.02836,0.03768,0.13907,0.0778,-0.01843,0.03346,-0.06795,-0.00881,0.12371,0.0593,-0.04256,0.01683]},{"domain":"chemistry","key":"moles_from_particles","name":"Moles from a number of particles","package":"chemistry-ai999x","example":"How many moles are 3.01e23 molecules of CO2?","v":[-0.0925,0.02865,-0.03987,0.0416,0.05783,-0.01083,-0.04759,-0.04311,-0.01479,0.01097,-0.04968,-0.02482,-1e-05,-0.07718,-0.00475,-0.05562,-0.0303,-0.04204,0.09641,0.11798,-0.01363,-0.02046,0.04424,-0.00175,-0.07724,0.00623,0.11068,-0.01578,-0.00513,0.05887,-0.12655,-0.05992,-0.05824,-0.05998,0.01762,-0.09785,0.00039,0.03397,0.02368,-0.04738,-0.00353,0.06369,0.13566,0.04106,0.06671,0.01865,-0.08126,0.10624,-0.03684,0.06674,0.06204,-0.03906,-0.02512,-0.04094,0.06249,0.03287,-0.07195,-0.04176,0.01557,-0.09597,-0.0352,0.01606,-0.11963,-0.02542,0.04027,0.05845,-0.03136,0.04851,0.04055,0.06934,-0.04871,-0.17591,-0.05271,0.13065,0.11933,0.03216,-0.05696,-0.00623,0.03156,0.01923,0.0055,-0.1222,0.06406,0.0409,0.06228,0.03605,-0.05675,-0.07524,0.06834,0.03921,0.04428,-0.13116,0.0805,0.06247,-0.0231,-0.02303,-0.03166,-0.05465,0.05463,-0.05452,0.04006,-0.02163,-0.02474,-0.03594,0.00826,0.06534,0.10868,-0.03002,0.1185,-0.0435,-0.01423,-0.06126,-0.08439,-0.03476,-0.03404,-0.00406,0.09313,-0.05775,-0.00308,0.02624,-0.00167,0.02978,0.05688,-0.05014,0.05937,-0.08347,0.00205,0.07722,0.04165,0.08223,0.00719,0.04508,-0.00262,0.04384,0.02472,0.02698,0.00809,-0.03831,-0.01056,0.07028,-0.0699,0.05274,0.0043,-0.00799,-0.12776,-0.08376,-0.01392,0.11581,-0.12173,-0.0375,0.03724,-0.04257,-0.09254,-0.02968,-0.04681,0.01963,-0.00641,0.0023,0.09323,0.09494,0.01803,0.07203,-0.00649,0.03681,-0.05933,-0.00257,0.05173,-0.02472,-0.12622,-0.04289,-0.01272,-0.09831,-0.04516,0.05219,0.00185,-0.06482,-0.04177,0.0886,-0.09146,0.09046,0.13466,0.03467,0.04279,0.08986,0.01016,-0.02551,-0.00584,-0.00075,-0.00531,0.05194,-0.05773,-0.03479,-0.03815,-0.0198,-0.14915,0.06788,0.00786,0.02598,-0.16884,0.04141,-0.01528,-0.01762,0.03383,-0.04992,0.07707,0.08714,-0.04052,-0.12932,0.07819,0.0434,0.02651,-0.04836,0.11508,0.0131,0.04764,-0.13554,-0.0456,0.00742,0.01197,-0.01575,-0.00105,0.01576,-0.01363,-0.07081,0.11797,0.09867,0.13329,-0.06458,-0.0663,-0.05885,0.01741,0.06736,0.09886,0.05869,-0.01934,0.03157,-0.06215,-0.01229,-0.09462,-0.14094,-0.04685,-0.03379,-0.08879,0.06809,-0.00527,0.1159,0.0113,0.05951,-0.05046,-0.02332,0.01559,-0.01599,-0.01504,0.04229,0.03399,0.01212]},{"domain":"chemistry","key":"nernst_potential","name":"Nernst equation","package":"chemistry-ai999x","example":"E° = 1.10 V, n = 2, Q = 0.010 at 298 K. What is the cell potential?","v":[0.00618,0.04126,0.00984,0.03719,-0.01377,0.00972,0.0365,0.11788,-0.08203,0.01577,-0.00142,-0.08331,0.02624,-0.0409,0.04672,0.04567,0.07497,-0.00069,-0.00144,0.01049,-0.03734,0.01602,-0.05322,-0.02601,-0.12246,0.05881,0.00877,-0.0472,-0.05122,0.07431,-0.00304,0.0537,0.10211,0.04864,-0.09975,0.08031,0.05237,-0.06566,-0.01286,0.03058,0.04623,0.02569,-0.04166,0.04683,-0.11965,0.07532,-0.07531,-0.0576,-0.04165,0.06586,0.00941,-0.01994,0.03694,-0.18844,0.04889,-0.0266,0.05345,0.06136,-0.10127,-0.00841,-0.03179,-0.00656,0.03144,-0.06477,0.09929,0.11491,0.05639,-0.07179,-0.0374,0.10921,0.01441,0.01845,-0.02125,-0.01788,0.04603,0.07711,0.07538,0.02308,-0.03076,0.06063,-0.03737,-0.04228,0.00613,0.06777,-0.02987,0.01987,0.08904,0.06037,0.1002,-0.10588,0.07716,0.05229,-0.00592,0.02385,-0.11622,0.13623,-0.1404,0.00415,-0.05046,0.06809,0.04385,0.02365,0.16242,0.02686,-0.12472,0.00596,-0.05396,-0.01942,0.03296,-0.12855,0.01338,0.05446,-0.03168,-0.07839,0.07579,0.01517,-0.02157,0.02203,0.00684,-0.01814,-0.01525,-0.03908,0.05321,0.03739,-0.05877,-0.09286,-0.00489,0.14581,0.00532,0.01299,0.02264,-0.03304,0.01511,-0.03512,-0.017,-0.02387,-0.03628,0.006,-0.05487,-0.06169,0.00647,0.0175,-0.04189,-0.06884,0.02088,-0.09792,0.05883,0.04984,0.06539,0.00727,0.0903,0.03666,-0.07611,-0.02533,-0.02022,-0.01428,0.03359,-0.05075,0.09842,-0.05796,-0.08435,-0.05321,0.02119,0.04563,0.06205,0.02084,-0.05328,0.00823,-0.1102,-0.18671,-0.09217,0.06104,-0.01452,-0.02427,-0.04634,0.04506,-0.16634,-0.17178,-0.04556,0.09121,0.05509,-0.02076,-0.05891,-0.01424,-0.05392,0.06354,-0.08594,-0.01749,0.01258,-0.02635,0.07392,0.03501,0.00758,0.09203,0.02239,0.05165,0.0007,0.06998,-0.04462,0.04157,-0.05671,-0.10215,0.13862,0.07289,-0.08921,-0.06184,0.07391,0.01541,0.01959,-0.02636,0.10209,0.0102,-0.02995,0.07936,0.02172,0.02908,0.01953,-0.02868,0.04845,-0.09517,0.0756,-0.00061,0.02273,0.06404,0.1201,0.00035,0.04453,-0.0547,-0.00375,0.06986,-0.02646,0.08477,0.02127,0.01355,-0.01522,0.04901,-0.06747,0.00938,0.0235,-0.01304,-0.07377,0.01184,0.01542,-0.06328,-0.05992,-0.12959,0.01205,-0.07601,-0.08094,0.02157,-0.06823,0.09074,0.07326,-0.00898,0.0018,-0.04766]},{"domain":"chemistry","key":"osmotic_pressure","name":"Osmotic pressure","package":"chemistry-ai999x","example":"What is the osmotic pressure of a 0.100 M glucose solution (a nonelectrolyte) at 25 °C?","v":[0.02836,0.00648,-0.08868,-0.15887,-0.04801,-0.00645,0.07354,0.09594,0.06676,-0.04894,0.01077,-0.04616,0.00375,0.00726,0.04568,-0.03522,-0.00726,0.09001,-0.00898,0.06967,0.01131,-0.03795,-0.18928,-0.00344,0.04536,0.02091,0.04891,-0.03335,0.07792,0.07841,0.06303,0.04066,-0.02223,-0.00175,-0.1623,0.08942,0.04169,0.04712,0.05298,0.04079,0.04359,0.09817,-0.01496,0.05202,-0.07402,0.06223,0.04855,-0.13537,0.03793,0.05882,0.06677,-0.07813,0.04753,-0.06212,-0.00331,0.03989,-0.0502,-0.05172,-0.00312,-0.06947,0.06634,0.0011,-0.00103,-0.03188,-0.0467,-0.0321,-0.02981,-0.08069,-0.00645,-7e-05,-0.07278,0.04684,-0.07255,0.0781,0.04325,-0.00675,0.04912,-0.07603,-0.09492,0.04114,-0.07853,0.11797,0.00545,0.03683,0.02761,-0.03658,-0.12375,0.05292,0.12875,-0.03573,0.04875,0.06922,-0.00529,0.00839,-0.10505,0.09734,0.01407,-0.00297,0.01925,0.01465,0.06576,-0.01887,0.14031,0.01787,0.06621,-0.05249,-0.01977,0.07283,0.08868,0.04031,0.00614,-0.02743,-0.01194,-0.02823,-0.02549,-0.02212,-0.03996,0.0831,0.03613,-0.00734,0.11812,0.05172,-0.14132,-0.01656,-0.07024,-0.02769,-0.01971,0.05472,-0.07715,-0.05488,-0.12306,-0.082,0.03041,-0.04142,-0.02891,0.07913,-0.07418,0.00201,0.01244,0.0428,-0.09549,0.03631,-0.06123,0.05328,0.01007,-0.03218,-0.00414,0.03267,0.03974,0.0971,0.01895,0.02208,0.0314,0.0593,-0.01853,0.0177,0.02255,0.02656,0.0127,0.03106,-0.07567,-0.09649,0.06305,-0.02429,-0.00252,0.03132,-0.02108,-0.01631,0.00881,-0.13332,-0.01404,-0.00547,-0.02576,0.11597,0.05286,-0.00031,-0.02796,0.04973,0.11413,0.09722,0.147,0.06936,-0.03978,-0.04849,-0.04333,-0.04001,0.03102,0.02911,-0.07651,-0.00958,0.05347,-0.06505,-0.0617,-0.14579,0.04038,0.08011,-0.06927,-0.09002,-0.03848,0.07183,-0.01461,0.069,0.01883,0.02493,-0.05983,0.10883,0.05559,0.0468,-0.04826,0.0214,0.05257,-0.07931,0.05126,0.02275,-0.00397,-0.00586,0.01711,-0.05643,-0.00027,-0.00461,-0.04755,-0.00995,0.07498,0.02368,-0.08668,-0.07623,0.08524,-0.04034,0.03937,0.0255,0.01557,0.08956,0.06121,0.05133,-0.04878,0.09566,-0.18317,0.04457,-0.10505,-0.04848,-0.05662,-0.01747,0.08981,-0.04257,0.02967,-0.10917,0.04558,-0.04988,-0.0902,-0.14648,0.01526,0.00892,0.03951,0.00039,-0.02963,-0.07337]},{"domain":"chemistry","key":"partial_pressure","name":"Partial pressure (Dalton's law)","package":"chemistry-ai999x","example":"The mole fraction of O2 in air is 0.21. What is its partial pressure at a total pressure of 1.00 atm?","v":[-0.10824,0.12916,-0.11974,-0.08154,0.03164,0.10328,-0.01875,-0.03281,0.06494,-0.01601,-0.00166,0.00577,-0.04403,0.00043,-0.02371,-0.05997,0.01754,0.02239,0.01674,0.14006,-0.15182,-0.04896,0.0413,-0.00379,0.00571,0.06678,-0.08306,-0.03153,0.06466,0.08963,0.04165,-0.00659,0.06477,0.05752,-0.04267,0.06758,-0.02213,-0.01424,-0.01916,0.07608,-0.00613,0.00528,0.01517,-0.03675,0.02566,0.01993,-0.04052,-0.02957,-0.0353,0.02819,0.02246,-0.06562,-0.11583,-0.10606,0.03903,0.06325,-0.01595,-0.13075,0.06329,-0.06037,-0.0113,-0.023,-0.09204,-0.1089,-0.07269,-0.11169,-0.04396,-0.04593,-0.0055,0.02758,-0.11315,-0.08145,0.00103,-0.01157,-0.00283,0.03946,0.08234,-0.02239,0.03779,0.02441,0.02382,0.04099,0.11491,0.0463,0.10355,-0.05717,-0.01351,0.09434,0.07667,0.02874,-0.02913,-0.00271,-0.12822,0.01375,0.00874,0.01278,0.02641,0.09874,-0.06092,-0.00654,0.00735,0.02147,0.10183,0.02084,0.00059,0.01675,0.07921,0.06951,0.06972,0.06498,-0.05348,-0.09303,-0.02461,0.00988,-0.09064,-0.03487,0.08229,0.09908,0.06662,-0.06787,-0.07475,0.08325,-0.05445,-0.01785,0.0232,0.01881,0.04349,0.04165,0.0576,0.02656,-0.04242,-0.00641,0.08517,0.00223,-0.07719,0.03512,-0.05661,0.03579,0.01861,0.14612,-0.11019,-0.0413,-0.02656,-0.01867,0.02787,0.0583,0.18676,0.00609,-0.04949,0.09551,-0.10634,0.06791,0.04193,0.09198,0.12919,-0.03756,0.01484,0.00516,0.05475,-0.0286,-0.04425,-0.05808,-0.03412,-0.04758,0.07106,-0.04715,0.06328,0.02616,-0.01427,-0.02184,-0.00027,-0.0229,0.10616,-0.08379,0.0632,0.07211,-0.008,-0.12021,0.10022,0.15579,-0.07511,0.04929,-0.00288,0.02926,-0.1525,0.05203,0.12898,-0.09437,-0.02229,-0.06052,-0.05453,0.08204,-0.05112,0.08128,-0.06797,0.01594,-0.0677,-0.04167,-0.01483,0.03745,0.0413,0.0173,-0.06339,0.04461,0.01829,-0.02808,0.00875,-0.01211,0.04767,0.04143,-0.01969,0.04158,-0.06643,-0.0573,-0.00695,0.01008,0.05609,0.0222,-0.06601,0.00041,0.0682,0.03336,-0.08272,0.05855,-0.02522,-0.15274,0.06956,-0.01601,0.07205,-0.03187,0.01188,-0.03285,-0.033,0.05386,0.02867,-0.01646,-0.04194,0.01577,-0.04378,-0.06019,0.00695,-0.14046,0.04294,0.03717,0.02981,-0.00641,-0.03159,-0.03309,-0.04376,-0.09079,-0.08238,0.00913,-0.07974,0.0569,-0.00906,-0.08836]},{"domain":"chemistry","key":"particles_from_mass","name":"Number of molecules in a mass","package":"chemistry-ai999x","example":"How many molecules are in 10.0 g of CO2?","v":[-0.04877,0.06253,0.04897,0.02867,0.0408,-0.07945,0.02937,-0.0787,-0.00103,0.01038,0.03093,0.0195,0.03349,-0.07652,0.08805,-0.04639,-0.03906,0.03457,0.01314,0.10838,-0.01035,-0.00574,0.01222,-0.04404,0.00629,0.04383,0.04096,-0.11504,-0.03712,0.09007,-0.11119,-0.03846,-0.05953,-0.0597,-0.01325,-0.0716,0.00686,0.05745,0.03361,-0.12595,-0.04372,0.07016,0.02831,0.05449,0.0512,0.07472,-0.1385,0.08916,0.00742,0.01568,0.04059,0.05391,-0.06182,0.00987,0.02757,0.03959,-0.03571,-0.03233,-0.04942,-0.04069,0.03116,-0.08556,-0.07561,0.04907,0.04846,0.07184,-0.00389,-0.01692,-0.00209,0.02562,-0.05882,-0.15432,0.005,0.1568,0.09732,0.07482,0.02798,-0.05798,-0.00045,0.01977,0.05118,-0.12151,0.1165,-0.00526,-0.0061,0.05094,-0.06014,-0.08699,0.09482,-0.00572,0.04661,-0.09726,0.09409,0.01038,-0.02786,0.07806,-0.06147,0.01005,0.06487,-0.03339,0.03712,-0.01388,-0.10213,-0.09406,0.01497,0.07184,0.16015,-0.04552,0.05241,-0.07813,-0.04126,0.00271,-0.01092,-0.05882,-0.09613,0.03213,0.09534,-0.04042,-0.06852,0.01991,-0.03714,-0.00414,0.01441,-0.03155,0.01891,0.0888,-0.01173,0.04015,-0.02738,0.04045,-0.05911,0.14469,0.01457,0.0752,0.14012,0.00171,-0.01515,0.06321,0.02747,-0.01608,0.00136,0.05921,0.097,-0.00338,-0.02622,-0.07336,0.01502,0.03662,-0.06266,0.00038,0.02065,-0.09217,-0.06867,-0.05734,-0.0884,-0.05174,-0.02941,-0.06441,0.05182,0.03945,0.03598,0.09405,0.07907,-0.00324,-0.00348,0.02411,0.05379,0.00499,-0.07381,-0.07362,-0.04731,-0.09208,-0.01423,0.09527,-0.04453,-0.01919,-0.01162,0.00936,-0.18576,0.02195,0.05481,0.17018,0.02718,0.10013,-0.02214,-0.03632,-0.05592,-0.10375,-0.03827,0.04691,-0.05579,-0.02081,-0.05669,-0.06982,-0.05497,-0.00504,-0.00766,0.05811,-0.20321,0.01169,-0.04094,0.01244,-0.02075,-0.14072,0.03358,-0.03199,0.00895,-0.05529,-0.0021,0.00202,-0.01734,-0.02443,0.08215,-0.05318,0.05932,-0.08552,0.08191,0.03461,0.08141,-0.00282,-0.05194,0.02115,-0.08493,-0.06075,0.0613,0.02174,0.06423,0.05417,-0.10579,-0.00903,0.08868,0.09894,-0.03333,0.07116,0.02011,0.0107,-0.00347,-0.03005,-0.05929,-0.08132,-0.06136,-0.07671,-0.08172,0.00878,-0.00525,0.03627,0.11005,0.0276,-0.01129,0.01756,-0.04777,-0.00384,0.04949,0.09036,-0.02147,0.04323]},{"domain":"chemistry","key":"particles_from_moles","name":"Number of particles in an amount","package":"chemistry-ai999x","example":"How many molecules are in 0.250 mol of water?","v":[-0.05079,-0.00309,-0.06052,0.02155,0.05295,-0.10196,0.00991,0.0024,0.00167,0.02815,0.00789,-0.00824,-0.00077,-0.04151,0.03402,-0.03318,-0.07747,-0.00086,0.01982,0.09737,0.02566,-0.04503,-0.11234,0.0074,-0.06617,-0.00282,0.10096,0.02795,0.08394,0.04381,-0.07495,-0.01609,-0.01735,-0.05475,0.00182,-0.11812,0.04944,0.02876,0.02709,-0.02873,-0.02657,0.01549,0.15866,0.02248,0.10525,-0.0337,-0.02052,0.03885,-0.03552,-0.01782,0.071,-0.04034,-0.10469,-0.06388,0.02165,0.02408,-0.09301,-0.02925,-0.04033,-0.06515,-0.00196,0.0628,-0.06635,0.07115,0.00653,0.03548,-0.07769,-0.02812,-0.00538,0.0841,-0.09502,-0.13217,-0.04727,0.13106,0.1553,0.01153,-0.02743,-0.01086,-0.03408,-0.04949,-0.01254,-0.0564,0.07615,0.07043,0.05136,0.01942,-0.06374,-0.0959,0.03912,-0.02617,0.00468,-0.09569,-0.01114,0.06184,-0.04387,0.08021,-0.07218,-0.03882,-0.01468,-0.00188,0.03008,0.02328,0.07346,-0.00188,0.05432,0.07481,0.14028,-0.01505,0.11284,-0.09401,0.02923,-0.1209,-0.05858,-0.05118,-0.02286,-0.02175,0.08505,-0.07965,-0.04078,0.07383,0.0329,-0.05604,0.03477,-0.04832,-0.00838,-0.09728,0.05954,0.05614,-0.03878,-0.00091,-0.03706,0.02512,0.08142,0.02973,0.04626,0.03106,-0.00265,0.04654,0.021,0.04705,0.03676,0.10071,-0.00605,-0.01312,-0.05052,-0.07713,0.01297,0.0869,-0.12125,-0.05327,0.02923,-0.01887,-0.06014,0.00777,-0.06597,0.04391,-0.03899,-0.05023,0.1009,0.07708,-0.02964,0.06815,0.03998,0.04094,0.01627,0.05535,0.01186,0.03947,-0.08478,-0.12708,-0.0107,-0.08996,0.01384,0.12339,-0.04571,-0.10668,0.03993,0.02924,-0.02239,0.03673,0.12209,0.03934,0.03634,0.10102,0.04096,-0.0467,-0.01371,0.02512,0.03456,0.06344,-0.076,-0.10237,-0.03386,0.03318,-0.10135,-0.03054,-0.01289,0.06366,-0.08851,0.07967,-0.0464,0.05155,0.00883,-0.09494,0.05048,0.0521,0.03089,-0.01766,0.08562,0.0157,0.13887,-0.00374,0.10171,0.04495,0.00528,-0.13733,0.09153,0.01168,0.04903,-0.10698,-0.01019,0.02129,0.01149,-0.05218,0.1233,0.0164,0.12967,-0.11184,-0.04703,-0.10249,-0.00683,0.04151,0.13638,0.08129,0.01075,0.06199,-0.11498,0.01399,-0.07933,-0.10852,-0.05277,-0.05405,-0.06283,0.02086,-0.03819,0.06197,0.01589,0.00833,0.00663,-0.05071,0.02802,-0.08669,-0.08787,-0.03842,0.00668,-0.04778]},{"domain":"chemistry","key":"percent_yield","name":"Percent yield of a reaction","package":"chemistry-ai999x","example":"For CaCO3 -> CaO + CO2, 100.0 g of CaCO3 gave 50.0 g of CaO. What is the percent yield?","v":[0.0967,0.02614,0.0836,0.03538,0.0056,0.0073,0.02008,-0.00269,0.00295,0.11312,0.06278,0.10289,0.12226,-0.04139,-0.00348,0.04834,-0.03151,-0.02295,0.0334,-0.00158,0.12029,0.03633,-0.01994,-0.07131,-0.06873,0.10282,-0.06124,-0.03031,0.00355,0.03314,-0.00711,-0.08584,0.03514,-0.02756,-0.07247,-0.00703,0.00343,0.01866,-0.00932,-0.12619,0.04105,0.02171,-0.06891,0.12362,0.0351,-0.01199,-0.02852,0.04219,0.06461,0.12924,-0.01411,0.03309,-0.02312,0.05977,0.04783,0.09483,-0.03202,0.0174,0.00222,-0.05435,0.02762,-0.16234,-0.00976,-0.04302,0.04537,-0.02282,-0.10058,-0.06305,0.03972,-0.02316,0.10008,-0.06447,0.06304,-0.10138,-0.0644,0.07226,0.06303,-0.09872,-0.0565,0.0748,-0.0191,-0.09853,0.07005,0.00011,0.01652,0.07267,0.07829,0.02814,0.06084,-0.01919,-0.00236,0.00937,0.03611,0.18255,0.06648,-0.01558,0.01331,0.02637,-0.0514,0.0596,0.01247,-0.06414,-0.03488,-0.03799,-0.04851,0.05007,-0.09053,0.01548,-0.08266,-0.035,-0.06338,0.07871,0.10675,-0.05558,-0.04033,0.005,-0.02274,0.01553,0.03983,0.02027,0.08009,-0.05034,0.04125,-0.09588,0.01848,0.12078,0.01306,0.05119,-0.04353,0.0421,-0.0278,0.08814,-0.02444,0.00451,0.0097,-0.03901,-0.04432,0.00287,-0.03221,-0.01184,-0.10178,0.03394,0.06349,0.08474,0.00121,-0.04017,0.09053,-0.00797,0.08339,0.01537,0.03929,0.0003,-0.02519,0.02545,-0.02505,-0.09092,0.05602,-0.01132,-0.04951,-0.0906,0.01911,0.09706,0.0042,-0.09548,-0.12382,-0.04086,0.01306,0.01501,-0.00353,-0.06014,-0.05342,0.00232,0.00662,-0.08873,0.08055,0.08044,0.088,-0.14507,0.01092,0.02181,-0.12167,0.01218,-0.07924,-0.02339,-0.15014,0.04127,-0.01465,-0.06495,-0.0724,-0.10488,-0.05376,-0.02021,-0.03124,0.02989,-0.03206,0.00247,-0.06079,0.07004,-0.10192,-0.05747,0.08166,-0.00573,-0.01513,0.03836,-0.11678,-0.09815,-0.01416,0.01124,-0.12607,-0.02225,-0.00264,-0.14102,0.03665,0.0392,0.04145,-0.01984,0.02904,0.12976,0.04648,0.04195,0.04302,-0.0157,-0.04774,0.0352,0.04469,0.03795,-0.12137,0.09172,-0.00068,0.01735,0.02982,0.02432,-0.14258,0.02805,-0.00612,-0.09043,-0.03766,0.08783,-0.05095,-0.09535,0.07194,0.05438,-0.03808,0.02252,-0.10031,0.00236,0.07899,0.04521,0.00318,0.13292,-0.04751,0.05224,-0.01776,0.02557,-0.06631,0.05468]},{"domain":"chemistry","key":"ph_diprotic_acid","name":"pH of a diprotic acid","package":"chemistry-ai999x","example":"What is the pH of 0.10 M H2CO3 (Ka1 = 4.3e-7, Ka2 = 4.8e-11)?","v":[0.06984,-0.05319,0.02688,0.02912,0.08101,-0.03977,0.02472,0.10407,-0.04784,-0.02936,-0.04195,0.03066,-0.02424,-0.01185,0.01416,0.07074,-0.1063,-0.03163,0.05866,-0.0068,0.07864,0.03314,0.06097,-0.07968,-0.08437,0.09868,0.10691,0.05238,-0.0623,0.00902,-0.08095,-0.00131,-0.01146,-0.00024,0.00583,0.04121,0.02701,0.0057,-0.04115,-0.03783,-0.02426,0.12622,-0.10389,-0.07676,-0.05535,0.00626,0.01963,0.08586,0.01372,0.08984,0.02281,0.11811,0.06877,-0.00488,0.00802,0.02396,-0.01253,-0.01146,-0.0266,-0.00496,-0.01428,-0.07564,-0.02337,-0.09053,-0.02039,-0.01923,-0.00645,0.00481,0.02971,-0.1102,0.01008,-0.03135,-0.03303,-0.093,-0.04599,0.02617,-0.14252,-0.0792,0.04119,-0.08886,0.01006,-0.0888,0.03654,0.06446,-0.04549,-0.02866,0.03565,-0.01146,0.01487,0.09313,0.0249,-0.09029,0.06057,-0.04914,0.08839,-0.15643,0.03368,-0.06458,0.00983,-0.04606,0.02192,-0.02083,0.00214,0.065,-0.12894,0.07823,-0.06624,0.0431,0.01102,0.02002,0.08587,-0.11537,0.05325,0.00362,-0.04604,-0.0896,0.00827,0.05478,0.0226,0.02356,-0.02488,0.06464,0.08537,-0.03865,-0.04311,0.02726,-0.07843,0.01228,0.04924,-0.00746,0.03142,-0.07776,-0.02752,0.02984,-0.02475,0.03956,-0.05004,0.06979,0.06366,-0.04403,-0.06607,0.03785,0.00489,-0.05348,0.05181,0.05888,-0.04636,0.00539,0.03743,0.04544,-0.06991,-0.00184,-0.02038,0.03912,0.07754,-0.08721,0.04417,-0.10292,-0.00701,-0.01042,0.0066,0.01938,-0.06739,-0.03436,-0.11297,0.01216,-0.05293,-0.02836,0.00102,0.04574,0.04186,0.07071,0.0923,-0.14245,0.04537,-0.04874,0.00713,0.09438,-0.01254,-0.05639,0.03667,0.01007,0.004,0.05259,-0.06359,0.11309,0.03159,-0.04365,-0.00077,0.08335,0.05373,0.12286,-0.06483,0.04498,-0.08375,-0.1271,-0.09012,0.09886,0.00357,-0.19429,0.03478,0.02216,0.05777,0.09861,0.04741,0.04437,-0.09313,-0.05224,-0.03246,-0.00244,-0.00452,-0.04422,0.01599,-0.05127,0.07392,0.05018,-0.03231,0.10712,-0.1864,-0.12295,0.10117,-0.00273,0.08479,0.01455,-0.06396,0.17578,0.02861,-0.05431,0.09029,0.00076,-0.00674,0.06729,-0.04327,-0.14214,0.0817,0.01143,0.09839,0.04448,0.04185,0.0446,0.11254,0.03785,-0.03013,0.02957,-0.06118,-0.02503,-0.06298,-0.02113,-0.04701,-0.05767,-0.01333,0.09354,-0.00164,-0.01675,0.00906,0.01421]},{"domain":"chemistry","key":"ph_from_hydronium","name":"pH from the hydronium concentration","package":"chemistry-ai999x","example":"What is the pH of a solution with [H+] = 1.0e-3 M?","v":[0.01614,0.05877,-0.06034,-0.10287,0.13842,-0.06507,0.0616,0.14169,-0.08334,-0.05112,-0.05157,0.0243,0.01636,0.03598,0.00503,0.04659,-0.08667,-0.01034,0.04886,-0.03732,-0.01799,-0.05515,-0.13897,-0.13472,-0.02632,0.04464,0.02444,0.02091,0.06656,-0.03827,0.0364,0.0593,0.06147,-0.09125,-0.06108,0.01574,0.02204,-0.00372,-0.05909,-0.01069,-0.03302,-0.06052,-0.18855,0.00102,0.06893,-0.03118,-0.03378,-0.07155,-0.11283,0.06425,0.12949,-0.04228,0.09075,0.00885,-0.03811,-0.06537,-0.0441,-0.08437,-0.08028,-0.08728,-0.00108,-0.05722,0.03718,0.07445,0.10518,-0.0101,-0.03445,-0.08156,0.05928,-0.02011,-0.02874,0.03171,0.02294,-0.12246,0.04639,0.03854,0.06271,0.00642,0.07957,-0.06063,0.02011,-0.03108,0.03503,0.07569,0.00463,-0.0405,0.05762,-0.09078,-0.02759,0.00338,0.00839,-0.03922,-0.0592,0.04638,-0.03728,0.03004,-0.01116,-0.08126,-0.00696,0.06036,-0.02619,-0.08433,0.07181,-0.06424,-0.09892,-0.00283,-0.11241,0.06741,-0.01514,-0.00663,0.05633,-0.07363,0.09078,0.01242,0.06469,-0.0063,0.0339,0.11387,0.03292,-0.05198,0.01267,0.01486,0.02757,-0.16224,-0.01637,0.05208,0.03972,0.01685,0.08554,-0.08084,0.05171,-0.03227,0.02583,0.07246,-0.05542,0.07967,-0.08196,0.0999,0.06677,0.00611,0.07371,0.08489,-0.04294,-0.07375,0.00458,-0.03209,-0.05577,-0.00684,-0.01814,-0.01164,-0.01453,0.08375,-0.00639,0.07465,-0.01059,0.03446,0.06602,-0.05411,0.0631,0.05661,0.0113,-0.03737,0.02502,-0.07675,-0.01445,-0.02102,-0.05487,-0.07027,-0.02253,-0.07515,0.0161,-0.03544,-0.02766,0.04663,-0.04462,-0.03726,0.04495,-0.07018,0.132,-0.01371,0.04903,0.05767,-0.0199,0.03912,0.0056,0.01445,0.07571,-0.02801,0.05522,0.00522,0.05427,-0.00896,-0.06864,0.01391,-0.01874,-0.07252,-0.07545,0.08972,-0.01743,0.00818,0.06109,0.0101,0.1346,0.09768,-0.09511,0.05535,0.0874,0.10842,0.02322,0.04552,0.12172,0.02433,0.11398,-0.01431,-0.00301,-0.04855,-0.03497,0.04701,-0.1017,-0.20667,0.10296,0.0061,-0.0584,0.0218,-0.02597,0.09214,0.03661,-0.02484,0.05213,0.01983,-0.07774,0.0159,0.15358,-0.06913,-0.0431,-0.04876,-0.12442,0.06088,-0.06591,-0.01871,0.02434,0.00844,-0.07918,0.00082,-0.05847,-0.09693,-0.01367,0.01329,0.02355,-0.03636,0.07163,0.0246,-0.01026,-0.01403,-0.00304,0.00872]},{"domain":"chemistry","key":"ph_from_hydroxide","name":"pH from the hydroxide concentration","package":"chemistry-ai999x","example":"What is the pH of a solution with [OH-] = 1.0e-4 M?","v":[-0.03764,-0.02232,-0.11272,-0.04648,0.10212,-0.03645,-0.02145,0.08017,-0.07787,-0.0048,0.00803,-0.02004,0.07987,-0.02552,0.00309,-0.02868,-0.04865,-0.05672,0.0797,-0.02088,-0.06592,-0.1029,-0.05616,-0.08812,-0.05599,0.05861,0.05859,-0.06271,-0.02483,0.03676,0.05572,-0.04315,0.013,-0.05105,0.00758,0.08846,0.07654,-0.00701,-0.03817,0.01967,-0.05534,-0.02188,-0.21887,0.01297,0.03231,0.06647,-0.08199,0.0684,-0.08586,0.10317,0.08719,0.06379,0.08975,-0.00358,0.03696,-0.02504,-0.06092,-0.12879,-0.0302,-0.08578,-0.00957,-0.03501,0.02462,0.03848,0.1656,-0.00028,0.05077,-0.1311,0.03853,-0.06123,-0.03601,-0.00599,-0.01455,-0.0727,0.01062,0.06387,0.08415,-0.03419,0.15916,-0.08611,0.01538,-0.02437,0.00748,0.01185,0.0251,-0.03108,0.06616,-0.03981,0.02398,0.09059,0.03328,-0.01865,-0.04272,0.03466,-0.01965,-0.05198,0.02803,-0.03423,-0.04343,-0.01641,-0.02489,-0.10179,0.04963,-0.08095,-0.04815,0.03766,-0.17166,0.09483,0.03271,0.0106,0.07473,-0.04652,0.08334,0.02609,0.0115,-0.02677,0.00689,0.03224,0.05265,-0.0382,0.0153,0.05504,0.01056,-0.08266,0.0178,0.02396,-0.08032,0.0052,0.04066,0.02933,0.01277,0.0448,0.01329,0.05729,-0.05331,0.10457,-0.05093,0.04166,0.09265,-0.0166,-0.08498,0.05118,0.01273,-0.02862,-0.09516,-0.10658,0.01846,-0.06222,-0.00687,0.0079,-0.06592,0.10691,-0.03948,0.01582,0.00471,-0.00571,0.04848,0.03481,0.1138,0.09665,-0.0315,-0.00806,0.02841,-0.03495,-0.11688,-0.06041,0.0122,-0.09956,-0.09,-0.03669,-0.00971,0.00862,-0.03154,0.07642,-0.01748,-0.05202,0.04859,0.01117,0.03065,-0.01099,-0.00969,0.02033,-0.02732,0.07379,-0.06606,-0.04634,0.05946,-0.0578,0.06872,-0.01557,0.03112,0.05081,-0.11608,-0.03602,-0.07839,0.00572,-0.02717,0.09676,-0.03673,0.02454,0.08463,-0.02491,0.19188,0.03816,-0.07935,0.05692,0.02992,0.07221,-0.00585,0.10156,0.03933,-0.00739,0.0874,0.0503,-0.0239,-0.06827,-0.11546,0.01692,-0.05436,-0.08491,0.16563,0.04189,-0.06592,0.04464,0.01317,0.12345,0.0629,0.01287,0.03396,0.08284,-0.11001,0.02453,0.0609,-0.03619,-0.05255,-0.08335,-0.15182,0.03514,-0.10517,-0.02321,-0.04406,0.0427,-0.00783,-0.0343,-0.01251,0.05384,0.00768,0.03626,-0.0618,0.0508,0.06619,-0.00199,0.07442,-0.03554,-0.0043,-0.03128]},{"domain":"chemistry","key":"ph_salt_of_weak_acid","name":"pH of a salt of a weak acid","package":"chemistry-ai999x","example":"What is the pH of 0.10 M sodium acetate (Ka of acetic acid = 1.8e-5)?","v":[0.01423,-0.01145,0.01929,-0.07337,0.08817,-0.09156,0.04055,0.06328,-0.07097,-0.08406,-0.00999,0.06858,0.12525,0.00364,0.07111,-0.0429,-0.19904,-0.02868,0.00833,-0.03976,0.07357,-0.03487,-0.08132,0.00449,-0.007,0.06731,0.06741,-0.03387,0.06624,0.04588,-0.06102,-0.05358,0.00785,-0.11307,-0.02167,0.0107,0.10392,-0.11163,-0.03184,0.02546,0.02509,-0.02332,-0.07835,-0.04533,0.10249,-0.01076,0.01447,-0.0137,-0.03517,0.09797,0.01758,0.00334,0.0523,-0.02151,0.00592,-0.01188,-0.06904,0.0526,-0.00502,0.00548,-0.03462,0.00433,-0.00122,-0.03544,0.11606,0.06406,-0.12222,-0.01174,-0.08445,-0.06373,0.03054,0.02081,0.01084,-0.04609,-0.13527,0.0922,-0.00978,-0.09785,-0.02348,0.00019,-0.03206,0.00391,0.04746,0.05454,-0.11763,-0.03047,0.06625,0.01099,0.16275,0.03389,-0.03376,-0.03993,0.08893,0.04257,0.05499,-0.06695,-0.10197,-0.12843,0.04435,-0.01462,0.05357,-0.03259,0.07163,0.09289,-0.09345,0.09619,-0.00294,0.02833,0.02685,-0.02284,0.08644,-0.08964,0.0093,-0.00336,0.07346,-0.10928,-0.05905,0.09291,-0.04346,0.04551,0.00784,0.01152,0.06232,-0.11264,-0.04075,0.06667,0.0816,8e-05,-0.04735,-0.0999,-0.0147,-0.06802,0.02983,-0.00281,-0.08037,0.06274,0.04868,0.02931,0.0047,0.01769,0.0352,0.06123,-0.06334,-0.03195,-0.03272,-0.17871,-0.0407,0.03196,-0.06602,-0.03954,0.06176,0.03385,0.04597,0.09381,0.01836,-0.12506,0.14074,-0.02215,0.01204,0.06206,-0.01584,0.07109,-0.0474,-0.03548,-0.11549,0.04083,-0.02863,-0.00742,-0.01027,0.0879,0.04651,0.02961,0.08847,0.06381,-0.0261,0.00914,-0.00808,0.01348,-0.00903,0.00367,-0.03892,0.01122,-0.03582,-0.04597,0.03744,0.06802,0.07722,-0.03426,0.05826,0.02735,0.04987,0.03513,-0.01031,-0.12168,-0.07309,-0.00775,0.0168,0.13875,0.01557,0.02281,0.02298,0.09854,0.02772,0.02506,0.05041,-0.00959,-0.07314,0.00106,-0.00286,-0.0061,-0.02753,-0.06518,0.03441,-0.0091,0.15481,0.05038,-0.09619,0.02876,-0.10443,-0.11274,-0.02053,0.02194,0.0619,0.03784,0.06984,0.13097,-0.05598,-0.02054,0.11194,0.06732,-0.08779,-0.04254,0.06504,-0.11263,-0.04039,-0.05237,0.0219,-0.06648,-0.08468,0.03062,0.10023,-0.05441,-0.0435,0.01828,-0.0119,0.03831,0.01761,-0.06522,-0.01169,-0.00328,0.03904,0.0827,-0.03193,-0.03247,-0.04164,-0.01267]},{"domain":"chemistry","key":"ph_strong_acid","name":"pH 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HCl?","v":[0.06196,0.04796,-0.00074,-0.08067,0.09956,-0.03852,0.07292,0.14767,-0.02071,-0.08181,0.03272,0.01711,-0.01221,0.11008,0.0462,0.00506,-0.09163,0.0233,0.05864,-0.03802,0.02938,-0.02845,-0.0967,-0.12256,0.06701,0.06905,0.0848,0.09243,-0.01211,0.04979,-0.03604,-0.04156,0.02325,-0.0536,-0.11053,0.02786,-0.02916,0.01457,0.02974,0.12278,-0.01016,0.04536,-0.01276,-0.03147,0.0348,0.02918,0.07999,-0.05346,-0.07039,0.08649,0.08157,-0.00062,0.0997,0.04734,-0.123,0.0986,-0.12104,-0.04779,-0.01666,-0.10521,0.01114,-0.01532,0.10624,0.02793,0.05704,0.01845,0.02944,-0.13951,0.05423,-0.07991,-0.05203,0.06881,-0.07397,0.01809,0.10471,0.07466,-0.0796,-0.03092,0.02237,-0.03181,-0.02441,-0.0842,-0.06695,-0.02305,-0.01691,0.02829,-0.09828,-0.03375,0.04184,-0.04217,-0.01479,-0.0379,-0.01139,-0.06394,-0.03058,-0.04691,0.05615,-0.03834,0.00019,0.09062,0.02588,-0.05441,-0.01499,-0.05422,-0.01556,-0.03242,-0.03181,0.08168,-0.00371,0.15403,0.00589,-0.02877,-0.00222,0.08054,0.0344,0.02389,-0.04223,0.02727,-0.02798,0.08003,0.00352,0.03386,0.05677,-0.05328,-0.08309,-0.02555,0.05947,0.01037,-0.00043,-0.04226,-0.08144,-0.02748,-0.0178,-0.02628,-0.06012,0.10737,0.0349,-0.01212,0.00136,-0.00576,0.0519,0.10095,-0.0664,-0.04482,-0.01977,-0.06871,-0.10846,0.03539,-0.06039,-0.00855,0.00875,-0.0332,0.07895,0.1297,-0.06628,0.01363,-0.02413,-0.08455,0.10707,0.06061,-0.00145,-0.03514,-0.05808,-0.04328,-0.07554,-0.03584,-0.05633,-0.03944,0.00581,-0.04243,0.08108,-0.03849,-0.01744,0.01416,0.00582,0.02849,0.01705,0.0667,0.04981,0.10014,0.04589,0.06045,0.00327,0.0075,0.03137,0.07842,0.10277,0.10177,0.09663,0.00147,0.08185,-0.04484,-0.04486,-0.15861,-0.04675,-0.11866,-0.13511,0.01182,-0.12365,-0.08129,0.04494,0.07715,0.10297,0.12171,-0.0214,0.06414,-0.01083,-0.02074,-0.04663,0.02805,-0.03818,-0.02084,0.03606,-0.04573,0.01976,-0.02117,0.0049,0.01047,-0.14745,-0.20628,0.0603,0.01116,0.06524,-0.0333,0.0373,0.08644,-0.01291,-0.01384,0.04788,-0.01729,-0.05854,-0.00683,0.05381,-0.07387,0.00375,0.02674,0.01559,0.01772,-0.08146,0.03647,0.03068,0.10431,-0.10522,-0.01978,0.01439,-0.03428,0.0411,0.01726,-0.09348,-0.00335,0.02448,-0.02467,0.10952,-0.03394,0.07087,-0.03552]},{"domain":"chemistry","key":"ph_strong_base","name":"pH 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of a weak acid","package":"chemistry-ai999x","example":"What is the pH of 0.10 M acetic acid (Ka = 1.8 × 10^-5)?","v":[0.12852,0.00242,-0.04569,-0.00325,0.04838,-0.02245,0.04235,0.08384,-0.06998,-0.06365,-0.01455,0.03861,0.01584,0.00279,0.0073,0.08479,-0.04551,-0.08501,0.06741,-0.0777,0.10764,-0.05075,-0.09945,-0.08894,-0.05296,0.08921,0.09708,0.00512,0.09584,-0.00702,-0.02413,-0.02004,0.07309,-0.04006,-0.10201,-0.03383,0.00252,-0.00947,-0.03993,-0.05695,0.00323,-0.06285,-0.14,-0.01307,0.00895,0.00666,-0.01566,-0.05561,0.04515,0.11046,0.06271,0.00688,0.1589,0.06557,-0.04777,-0.04448,-0.03932,-0.05655,-0.03207,-0.01824,0.00873,-0.08064,-0.0118,0.0535,0.03833,-0.007,-0.05783,-0.01917,-0.11458,-0.04919,0.03067,0.08189,0.02681,-0.12546,-0.09162,0.01164,0.03924,-0.05869,-0.04445,0.01645,0.04199,-0.01073,0.02493,0.08454,-0.03635,-0.02206,0.07617,-0.10035,0.04153,-0.04903,-0.03046,-0.07082,-0.03331,0.01829,0.02292,-0.09824,-0.01465,-0.05856,0.08854,0.03835,-0.01246,-0.0608,0.06813,0.02179,-0.07694,0.00805,-0.06308,-0.01152,-0.01682,0.09293,0.12264,-0.03527,0.03851,0.05438,0.00863,-0.08945,-0.04295,0.05106,0.00956,0.03823,0.01653,0.07346,0.09101,-0.17787,-0.06069,0.04381,0.03327,-0.00931,0.00344,-0.07322,0.01907,-0.04743,0.01941,0.04953,-0.03907,0.04396,-0.09557,0.0227,0.09802,0.02089,0.03245,0.01329,-0.03707,-0.01721,0.02565,-0.01084,-0.06097,-0.00785,-0.00803,-0.06209,-0.06597,0.07393,0.0637,0.05475,-0.00226,-0.0064,0.07128,-0.076,0.0529,-0.08498,-0.03841,-0.02265,-0.08189,-0.03327,-0.11701,0.05505,0.07215,-0.03975,0.06201,-0.03226,0.05522,-0.02874,0.08571,-0.02031,-1e-05,0.03264,0.01711,0.00175,0.0797,-0.03679,0.05746,0.01317,0.03539,-0.00333,-0.0413,0.07333,0.00793,-0.04185,-0.01908,-0.00227,0.10136,0.02398,-0.10767,-0.05454,-0.12582,-0.07567,-0.05136,0.12541,0.0047,-0.04247,0.01593,0.02663,0.05879,0.15475,-0.04593,-0.06805,0.00395,-0.09685,-0.02326,-0.02793,0.00942,-0.03865,0.04355,-0.01983,0.10186,0.08765,-0.01125,0.05688,-0.2135,-0.20094,0.11969,0.01682,0.03013,0.0259,0.02962,0.07481,-0.02712,-0.00037,0.11122,-0.02901,0.01256,0.05976,0.06411,-0.096,-0.00749,-0.01152,0.05533,0.08686,0.01063,0.04426,0.15176,0.07077,-0.10562,0.02671,-0.05572,0.03152,-0.00665,0.04232,0.03958,-0.09052,0.05014,0.05776,-0.05867,-0.03265,-0.01589,0.01144]},{"domain":"chemistry","key":"ph_weak_base","name":"pH of a weak base","package":"chemistry-ai999x","example":"What is the pH of 0.10 M NH3 (Kb = 1.8 × 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of a photon from its wavelength","package":"chemistry-ai999x","example":"What is the energy of a photon of wavelength 500 nm?","v":[-0.01868,0.02796,-0.0139,0.08201,0.04209,0.00694,0.00478,0.00318,-0.03855,-0.02391,0.00617,0.0166,0.04733,0.00335,-0.06227,0.02863,0.01655,0.0209,0.00609,-0.02944,-0.08765,-0.01374,-0.19612,0.05511,0.00317,-0.02139,-0.00985,-0.02367,-0.08338,0.06107,0.09908,-0.01035,-0.06251,-0.00441,0.02927,-0.05974,0.12598,0.02159,0.01802,-0.00761,-0.0879,0.02038,0.09591,0.00342,0.04638,0.06804,-0.12794,0.06983,-0.00092,0.08904,0.02421,0.01612,-0.08095,0.01703,0.00281,0.02084,-0.06682,-0.05958,-0.07241,-0.01775,0.07261,-0.00058,0.06364,0.10734,0.01812,-0.01964,-0.06418,-0.02011,0.05384,-0.02264,-0.01059,0.11539,-0.00753,-0.02095,0.15288,0.09681,0.01632,-0.05819,0.051,-0.07631,0.02293,0.11071,0.04333,0.02028,-0.00019,-0.10714,-0.0453,-0.04505,-0.0017,-0.00924,-0.01272,-0.03732,-0.02181,-0.01412,-0.07598,-0.05448,-0.07275,0.02621,0.00873,0.11195,-0.01352,0.11218,-0.00716,0.03361,-0.04211,-0.01349,-0.01208,-0.03681,0.03986,-0.00677,-0.00584,-0.15857,-0.11683,-0.04917,-0.03466,0.07239,-0.02907,-0.05645,0.08031,0.05826,-0.04636,-0.01683,-0.0704,-0.05607,0.08189,-0.03997,0.08759,0.00165,-0.13808,-0.01344,0.0188,0.08504,0.0911,-0.00517,0.04438,0.08042,0.02909,0.05043,0.13762,0.10237,-0.00573,0.11861,-0.04676,-0.03956,0.02527,0.01619,0.02202,-0.00374,-0.03399,-0.07922,0.13691,0.01328,-0.01798,0.04374,0.02338,0.05994,-0.03809,-0.00335,0.09474,0.0062,-0.08467,-0.00076,0.00812,0.07132,-0.00144,0.00138,-0.12435,0.14228,-0.0765,-0.06178,0.16192,0.0355,0.07548,0.07778,-0.10418,-0.07704,0.05986,-0.12835,0.04624,-0.03788,-0.02494,0.01383,-0.0922,0.02089,-0.08794,-0.01797,-0.0059,0.0273,0.02137,-0.028,-0.0997,-0.09241,0.04425,0.05859,-0.0122,-0.00825,-0.04513,0.0247,0.02584,-0.03743,0.03407,0.02819,0.15963,-0.01526,-0.01156,-0.08424,0.04157,0.05345,-0.03596,-0.04487,-0.03918,0.04317,-0.03056,-0.0286,-0.00057,-0.04949,-0.0254,0.01783,0.13023,-0.05509,-0.11225,0.03424,0.02837,0.11579,0.0377,-0.06847,0.0947,0.02085,0.06731,-0.09963,-0.00867,0.05835,0.03227,0.15461,-0.02846,-0.01023,-0.00495,-0.10524,-0.07872,-0.08509,-0.00063,-0.04389,-0.01524,-0.10834,-0.06013,-0.02202,-0.00211,-0.00396,0.03423,0.03208,-0.0076,-0.06994,-0.11391,0.00823,-0.06396,-0.04515]},{"domain":"chemistry","key":"photon_wavelength","name":"Wavelength of a photon from its energy","package":"chemistry-ai999x","example":"What is the wavelength of a photon with an energy of 3.0e-19 J?","v":[0.03507,0.02262,-0.00752,0.04655,0.03801,-0.00293,0.04777,-0.09242,-0.05341,-0.02309,-0.01822,0.00859,0.02658,-0.01979,-0.06526,-0.02184,0.01081,0.06467,0.01503,-0.03606,-0.07289,0.09552,-0.16846,0.03467,0.02383,0.01797,-0.0385,-0.01349,-0.06132,0.07794,0.05195,-0.00217,-0.08501,-0.00081,0.06153,-0.06233,0.13172,-0.02576,-0.02072,-0.02926,-0.05721,-0.03182,-0.00855,-0.0234,0.06156,0.01955,-0.08375,0.0434,-0.052,0.12403,0.08024,-0.01464,-0.08333,0.03513,0.01745,0.03522,-0.00768,-0.02101,-0.06046,0.01239,0.06759,0.02468,0.08285,0.09511,0.01282,0.00198,-0.00892,-0.00231,0.04435,-0.02628,0.00615,0.11228,0.04806,-0.05083,0.05415,0.06049,-0.02293,0.00322,0.03116,-0.09657,0.04782,0.11467,0.03883,0.03864,-0.0344,-0.09286,-0.01896,-0.10495,0.04556,0.00161,-0.01605,-0.03906,0.03083,-0.06888,-0.06656,-0.05107,-0.0113,0.00585,0.05507,0.08507,-0.05331,0.13161,0.04869,0.01274,-0.07775,0.01752,-0.06614,-0.08993,-0.02473,-0.04782,-0.02371,-0.14461,-0.0815,-0.13019,-0.01963,0.05275,-0.00225,-0.05315,0.0942,0.0554,-0.10046,0.06515,-0.03125,-0.07638,0.04667,0.08009,0.11302,0.03606,-0.08414,0.03572,0.03327,-0.0099,0.11557,-0.01437,0.03386,0.06578,0.02911,0.0854,0.12553,0.06922,-0.07743,0.09764,-0.04035,-0.07514,0.0243,0.01066,0.01895,-0.00943,-0.03498,-0.08078,0.10775,0.03453,-0.04283,0.08818,0.02941,0.08132,0.02511,0.00335,0.07893,0.0135,-0.05787,0.06125,-0.04261,0.11898,-0.09065,0.01143,-0.068,0.07663,-0.09939,-0.0014,0.12264,0.04771,0.02465,0.00664,-0.12586,-0.11317,0.03126,-0.09958,0.08205,-0.09671,-0.04863,0.009,-0.09582,0.00462,-0.09688,-0.01317,-0.0033,-0.00876,0.05096,0.01365,-0.09734,-0.05951,0.11765,0.08541,-0.02781,0.0058,-0.04087,0.02493,0.02053,-0.03345,0.08098,0.01845,0.12815,-0.09396,0.01294,-0.08566,-0.00134,0.06529,-0.05144,-0.02518,-0.04258,0.00385,-0.04861,0.0153,0.0474,-0.03909,0.0104,0.01915,0.12971,-0.01221,-0.12293,-0.01095,0.04264,0.05464,0.07108,0.02532,0.09765,0.02123,0.12528,-0.05812,0.02198,0.08688,0.04343,0.10835,-0.01699,-0.03543,-0.06326,-0.01752,-0.05955,-0.09103,-0.01336,-0.09156,-0.01099,-0.08401,-0.10949,-0.01271,-0.0605,-0.03387,0.04061,0.01367,-0.0587,-0.06216,-0.12608,0.03045,-0.0364,0.01606]},{"domain":"chemistry","key":"raoult_vapor_pressure","name":"Vapor pressure of a solution (Raoult's law)","package":"chemistry-ai999x","example":"What is the vapor pressure of a solution of 50.0 g of C12H22O11 in 500 g of H2O if the vapor pressure of pure water is 23.8 torr?","v":[-0.0283,-0.03707,0.02154,-0.0443,-0.00416,0.0212,0.09222,0.14069,0.02196,-0.03109,0.09426,-0.03516,-0.00661,-0.04752,0.00533,-0.09266,-0.03506,-0.01051,-0.15489,0.10689,-0.03563,-0.01433,-0.06798,-0.04286,0.01057,0.08936,0.10533,0.04791,0.01517,0.01726,-0.05876,-0.03376,-0.02865,0.00216,-0.00407,0.02577,0.08777,-0.01588,0.05516,0.05635,0.08032,0.13145,0.06305,0.05289,-0.03688,0.02896,0.06298,-0.0515,0.00998,0.10289,0.02561,0.00979,-0.01115,0.04269,0.00687,0.03508,-0.10924,-0.10014,0.04453,-0.05641,0.08202,0.05538,-0.04427,-0.02319,-0.00997,0.03313,-0.02687,-0.07396,0.09143,-0.02344,-0.02086,-0.00873,0.07984,-0.02961,0.10931,0.12136,0.02902,-0.15652,-0.03327,-0.01375,-0.03774,-0.01556,-0.00716,-0.08574,-0.03427,-0.01155,-0.06277,0.09499,0.17309,0.05912,0.01763,-0.01712,-0.03938,-0.07145,-0.01519,-0.02859,0.07688,0.06848,-0.00734,-0.00399,0.01614,0.02255,0.03477,0.00371,0.05495,-0.02399,0.07551,-0.00091,0.01346,0.06177,0.06635,-0.03744,-0.03961,-0.06797,-0.01834,-0.06949,0.05061,0.06245,-0.01261,0.06579,0.04787,-0.06339,-0.03618,-0.0136,0.02327,0.06843,0.00737,0.10369,0.0215,-0.05325,-0.03549,0.02508,-0.11528,-0.02979,0.01442,0.07716,-0.01384,0.10785,-0.04844,-0.01101,-0.13294,0.08772,0.00284,0.07664,0.07428,-0.0494,-0.01473,0.05509,0.02916,0.0036,-0.11231,-0.10893,0.0455,0.08068,-0.01398,-0.04554,-0.08671,-0.08088,0.04298,-0.086,-0.08452,-0.04144,0.01332,0.0371,-0.05713,-0.03527,-0.08978,0.11534,0.04312,-0.13009,-0.06349,0.01702,0.01502,-0.09602,0.14733,-0.02257,-0.03308,-0.01922,0.05955,0.10837,-0.02826,0.11892,-0.00172,-0.0481,-0.09706,0.04611,0.08423,-0.04676,-0.03751,-0.02671,-0.10311,-0.03366,-0.03589,-0.0637,0.0989,-0.03073,-0.00839,-0.0875,-0.02069,-0.00397,0.01703,-0.0423,0.01432,0.01953,-0.07321,0.02995,-0.01486,-0.03985,-0.0735,0.01419,0.00085,-0.02837,-0.0209,-0.08878,0.08697,-0.02635,0.08557,-0.03879,0.02555,-0.05191,-0.00117,-0.01892,0.03714,0.04755,-0.0299,0.03931,-0.07797,-0.00081,-0.0082,0.06635,0.04829,0.02155,-0.06475,0.0076,0.00571,0.0995,-0.20082,0.02441,-0.10859,-0.06694,-0.0025,-0.01582,0.05603,-0.01912,0.04903,-0.09053,0.08143,0.00219,-0.05942,-0.04069,-0.09988,-0.0116,0.17699,-0.00892,0.06552,0.09253]},{"domain":"chemistry","key":"reaction_enthalpy_from_formation","name":"Reaction enthalpy from enthalpies of formation (Hess's law)","package":"chemistry-ai999x","example":"Using enthalpies of formation CH4 = -74.8, O2 = 0, CO2 = -393.5, H2O = -285.8 (kJ/mol), find ΔH° for CH4 + 2 O2 -> CO2 + 2 H2O.","v":[0.10035,0.07596,-0.04543,0.04259,0.09965,0.0251,0.06142,0.08263,-0.06522,-0.02423,0.00099,-0.0096,-0.1243,0.04991,0.03427,0.0415,0.01012,0.12567,-0.00536,-0.06492,-0.1021,0.01279,0.02585,-0.06199,-0.0434,0.02944,0.08693,-0.038,-0.11316,0.0753,-0.05001,-0.01113,0.09031,0.05783,0.06697,0.04292,0.0053,0.05014,-0.00746,0.02909,-0.04402,-0.04927,-0.00987,-0.04723,0.04065,0.01503,-0.00603,-0.03576,-0.01591,0.04051,0.05212,-0.04219,-0.09825,0.0793,-0.02881,-0.07137,-0.03853,0.0437,0.08159,0.03147,0.02084,0.0769,0.07533,-0.013,0.02536,-0.03336,-0.17125,-0.02403,0.07262,-0.00475,-0.11901,0.06982,-0.09926,-0.00483,0.011,-0.03024,-0.03376,-0.0043,0.05713,-0.04857,-0.15197,-0.08531,-0.05263,0.03268,0.14026,0.01473,-0.04587,-0.06362,-0.0489,-0.02863,-0.04181,-0.04214,0.01035,0.04675,-0.05041,-0.04239,-0.10648,-0.13756,0.01617,-0.01519,-0.02154,-0.04475,0.06748,-0.09222,-0.01272,-0.0446,-0.03489,0.03348,-0.0335,-0.07502,0.06004,-0.00462,0.06526,-0.04523,-0.03694,0.09083,0.01408,0.01135,0.02357,0.07678,-0.0224,0.03909,0.05296,-0.06908,-0.02317,0.03712,0.05954,0.06428,-0.04626,-0.03752,-0.0759,0.04321,-0.00237,-0.07071,0.04453,0.02314,-0.05635,-0.00074,0.01493,0.08671,0.12473,0.03624,0.0399,-0.01607,-0.0059,0.09874,-0.04937,-0.01526,0.02545,-0.10194,0.04962,-0.03244,-0.06473,0.03455,-0.05841,0.06208,0.04396,-0.02914,0.02598,-0.02699,-0.00751,0.08778,0.00857,0.02594,-0.01031,-0.00042,-0.05725,-0.00072,0.02546,0.04628,0.03664,0.11667,-0.00951,0.00993,-0.10531,-0.11261,0.00926,0.14149,0.04851,-0.02696,0.06047,0.00997,-0.16799,0.09238,0.03938,0.04531,-0.01909,-0.01054,0.0251,0.06147,0.04134,-0.00376,0.10727,-0.00493,0.00799,-0.07287,-0.03263,-0.00568,-0.16582,-0.07937,-0.00412,-0.04586,0.16588,-0.02246,-0.16841,-0.10291,-0.02377,0.02722,-0.00854,-0.07307,0.08241,-0.00704,0.01393,-0.00147,-0.00074,0.09238,-0.09154,-0.05787,0.05473,0.02603,0.06763,0.0494,0.02982,0.01103,0.07136,2e-05,0.01495,0.12753,0.04861,-0.00031,0.03241,-0.01383,-0.01371,-0.08575,0.04712,-0.1451,0.0058,0.13831,-0.11624,0.04511,-0.06266,0.12051,-0.02357,0.04147,-0.06235,-0.04717,-0.01457,-0.06482,0.05759,-0.01801,-0.0013,0.10085,0.00338,0.07617,0.0009,0.06625]},{"domain":"chemistry","key":"reaction_order_from_rates","name":"Reaction 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If [A]0 = 0.20 M, what is the concentration after 30 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yield from one reactant","package":"chemistry-ai999x","example":"For CH4 + O2 -> CO2 + H2O, what mass of CO2 is produced from 16.0 g of CH4?","v":[0.02128,0.07731,0.03199,0.03521,0.07511,0.03943,0.02967,0.00012,0.01452,0.13926,0.02601,0.08952,0.03555,-0.0507,0.0395,0.0088,-0.04541,0.01885,0.10716,0.05857,0.02501,0.05445,0.04478,-0.03523,-0.10075,0.11776,-0.00188,0.00058,-0.09285,0.01218,-0.05321,-0.09063,-0.00119,0.02886,-0.01167,-0.00654,0.00714,0.05852,-0.03461,-0.15233,0.0378,0.0178,-0.05362,0.01156,-0.02131,0.02379,-0.09986,0.07659,0.01692,0.12007,0.02519,0.04377,-0.05262,0.05733,0.07629,0.05764,-0.05997,-0.02524,0.02186,-0.02563,0.01337,-0.09482,-0.02455,-0.00826,0.06276,0.03573,-0.00932,-0.09927,0.1415,-0.03372,0.02914,-0.09342,-0.02906,0.02388,-0.01729,0.08685,0.02506,-0.11213,0.0414,0.01303,-0.03231,-0.15864,0.08851,-0.03464,0.04076,0.1037,0.04752,0.03944,0.0874,0.01633,0.01439,-0.03797,0.054,0.05635,0.03635,-0.03694,0.02567,-0.00807,-0.04828,0.08279,0.02183,-0.06186,-0.07208,-0.11617,0.00029,0.02759,-0.07879,0.01876,-0.09343,-0.08431,-0.07674,0.08466,0.08198,-0.04028,-0.05237,-0.00713,0.01747,-0.041,0.02508,0.06932,-0.01115,-0.02531,0.06327,-0.04757,0.03398,0.16319,0.02588,0.04861,-0.00859,0.05677,-0.07559,0.15959,-0.0239,0.00353,0.00154,-0.04003,-0.0681,0.00636,-0.0801,-0.0018,-0.11997,0.07235,0.05825,0.00858,-0.04088,-0.01814,0.09241,-0.01193,0.05442,-0.00471,0.04232,0.01139,-0.12126,-0.01212,-0.05145,-0.07489,-0.01372,0.00466,-0.04784,-0.01808,0.0173,0.06505,0.00418,-0.06405,-0.10427,-0.00854,-0.00249,0.00866,-0.03741,-0.03809,-0.07857,0.09366,0.01318,-0.0652,0.05624,0.04744,0.02762,-0.10458,-0.06101,0.02978,-0.11811,0.10162,-0.09904,0.006,-0.15897,0.05531,-0.02019,-0.08445,-0.02463,-0.06156,-0.04162,0.04581,-0.03671,-0.0083,-0.00105,-0.05809,-0.06273,0.01661,-0.16924,-0.07863,0.07831,-0.03598,0.00037,-0.01914,-0.04665,0.00773,0.03421,0.03969,-0.07038,0.01245,0.00364,-0.07573,0.0083,-0.02662,0.07431,-0.01524,0.01137,0.08123,0.03266,0.09101,0.04521,0.01968,-0.10626,0.01708,0.03822,0.0214,-0.07066,0.10497,0.0339,0.00155,-0.0039,0.0801,-0.11933,0.00027,0.06554,-0.11533,-0.0818,0.08947,-0.08924,-0.11142,-0.00491,0.01095,-0.04039,0.00524,-0.04713,0.01125,0.07911,0.05964,-0.03575,0.12673,-0.06931,0.0636,0.12987,0.08959,-0.03623,0.02554]},{"domain":"chemistry","key":"titration_equivalence_volume","name":"Titration: equivalence-point volume","package":"chemistry-ai999x","example":"What volume of 0.100 M NaOH is needed to neutralize 25.0 mL of 0.150 M HCl?","v":[-0.03626,0.06984,-0.01329,-0.0362,-0.01495,0.00439,-0.03604,0.11089,0.03998,-0.03917,0.02256,0.00658,-0.11381,-0.0248,0.00062,-0.09291,-0.0035,0.01179,-0.01201,-0.06438,-0.00326,0.0088,-0.08894,-0.11529,-0.01074,-0.00561,0.00033,-0.02056,-0.10488,0.00354,-0.03828,-0.11191,-0.02598,-0.04934,0.04442,-0.02421,0.04394,-0.03003,0.16187,0.07441,0.09419,0.06419,-0.00121,-0.1034,-0.03457,-0.02611,0.0149,-0.00318,-0.10131,0.0751,0.07306,-0.02451,-0.12109,-0.07646,-0.00174,0.09947,-0.0791,-0.02504,-0.09869,-0.04825,0.00983,0.02788,0.00154,0.14952,-0.08958,-0.08487,0.05302,-0.1242,0.06301,0.12948,-0.03475,0.04787,0.07669,0.01301,-0.01271,0.00834,-0.10464,-0.04937,0.10027,0.0923,-0.04342,-0.05088,-0.06936,-0.00914,-0.03087,0.1124,-0.06372,-0.03338,-0.03269,-0.00833,0.02008,0.04674,0.02744,-0.02457,-0.01837,-0.02635,-0.10882,-0.08869,0.01518,0.06312,0.02057,-0.1264,0.05676,-0.08535,0.00294,-0.04546,-0.02277,0.07548,0.00214,-0.03636,0.00726,-0.06213,-0.07511,-0.01008,-0.08148,0.00723,-0.05697,0.00847,0.07823,0.13928,0.00939,0.03322,0.1078,-0.12443,0.08215,0.13477,0.06249,-0.05442,0.02365,0.00531,-0.05188,0.0387,-0.08195,0.00377,-0.03986,0.06223,0.0189,0.05794,-0.09604,0.00703,-0.04163,0.15843,-0.01101,0.03418,-0.06283,-0.07739,0.05576,0.0199,-0.03486,-0.02402,0.01831,0.06664,0.07532,0.04444,-0.04476,-3e-05,0.02845,0.05302,0.09577,-0.04076,0.02005,0.03048,-0.06391,0.11234,-0.01349,0.01825,-0.11513,0.02471,-0.0014,-0.07373,-0.01358,0.03937,-0.0447,-0.11295,0.07679,-0.0103,0.04998,0.13331,-0.00945,-0.00239,-0.0676,-0.04464,0.01421,-0.08596,0.00196,0.11151,0.09296,0.07498,0.11023,0.06311,0.01599,-0.01484,-0.04452,-0.00148,-0.02957,0.05634,-0.03862,0.0139,-0.04472,0.00452,0.08494,-0.0984,0.11558,-0.05131,0.03229,-0.03668,-0.06219,-0.12725,-0.03305,-0.00685,-0.04545,-0.0562,0.03642,0.03236,0.05197,-0.15375,-0.02453,0.00529,-0.00964,-0.06542,-0.02653,0.0173,0.00861,-0.02243,0.11047,0.071,0.05327,0.02597,0.06894,0.02071,0.03034,-0.01636,-0.05491,-0.02651,0.02376,-0.01796,0.00909,-0.04422,0.04408,-0.08961,0.12319,0.07582,0.04943,-0.06447,0.08121,0.07213,0.01173,0.02831,0.00946,0.07255,0.04561,-0.0187,0.04578,-0.02073,0.05056,0.03115]},{"domain":"chemistry","key":"titration_ph_strong_acid_strong_base","name":"pH during a strong acid - strong base titration","package":"chemistry-ai999x","example":"25.0 mL of 0.100 M HCl is titrated with 0.100 M NaOH. What is the pH after adding 10.0 mL of base?","v":[0.00507,0.03184,-0.04342,-0.13965,0.07852,0.01947,0.00325,0.01265,0.00323,0.03421,0.0016,0.01,-0.02163,0.03131,-0.01064,-0.08281,-0.02354,0.02137,0.10054,-0.02505,0.05794,-0.05171,-0.0274,-0.07018,0.08324,-0.06694,0.05693,0.06054,-0.09178,0.02467,-0.0966,-0.13899,-0.00385,-0.05278,-0.01319,0.08381,0.00208,-0.08386,0.01332,0.15648,-0.0285,0.04588,-0.07007,-0.14167,0.04716,-0.04386,0.02362,0.02835,-0.09143,0.00821,0.01173,-0.01663,-0.00451,-0.11977,-0.02463,0.09256,-0.07327,-0.04459,-0.0154,0.00587,0.01593,0.03277,0.08102,0.05908,-0.01379,-0.01752,0.1285,-0.07902,0.17092,0.02358,-0.03744,0.01427,-0.03699,0.10845,-0.03944,0.00677,-0.11812,0.02027,0.04173,0.04101,-0.01484,-0.12065,-0.01318,-0.08451,-0.06898,0.04464,-0.05855,0.024,0.08502,-0.02601,-0.02863,-0.0502,0.0661,0.03837,-0.00895,-0.04782,0.00941,0.02482,0.09716,-0.06393,-0.00893,-0.09708,-0.06194,-0.03781,-0.04574,-0.04128,-0.05906,0.06304,0.01718,0.05652,0.01516,0.01581,-0.01212,0.10242,-0.03423,-0.00725,-0.0246,-0.049,0.0192,0.04008,-0.11695,0.02472,0.06799,-0.11768,-0.06114,0.06364,0.03949,-0.06582,0.02587,0.01218,-0.05025,-0.04371,0.05073,0.0069,-0.10743,0.02673,0.10281,0.00108,-0.04127,-0.05639,0.04544,0.09084,0.01216,-0.00711,-0.05239,-0.15976,0.01298,0.08954,-0.09574,0.0248,-0.01548,0.0366,0.10072,0.04663,-0.03709,-0.00184,0.00724,-0.0291,0.00713,0.05024,0.0136,0.00274,0.00026,-0.00779,-0.05467,0.0372,-0.09243,-0.09724,-0.03544,-0.0599,0.0582,0.05794,0.00406,-0.0804,0.04025,0.17331,-0.0483,0.05074,-0.07917,0.09376,-0.03591,0.00208,0.07996,-0.01158,0.07161,0.05108,0.0471,0.01054,0.06416,-0.00043,0.02781,-0.03456,0.00369,-0.0624,-0.04561,-0.04239,-0.1289,0.03558,-0.12326,0.00685,0.05369,0.03714,0.09069,0.04442,0.06655,0.01857,-0.11116,-0.04706,0.04063,0.03744,-0.14399,0.01587,0.00059,0.06119,0.09175,-0.01063,-0.05382,-0.0256,-0.05358,-0.12618,0.06537,0.0405,0.08367,-0.05761,0.07867,0.12772,0.006,0.08016,0.05269,0.03529,-0.04934,-0.08707,-0.06699,-0.05506,0.05819,0.00901,0.11001,-0.03914,-0.06105,0.06464,0.11567,0.01341,-0.05237,0.00413,0.06131,0.05497,0.01583,0.09069,-0.01825,0.07107,0.03313,-0.1083,0.05598,0.01397,0.04363,-0.02696]},{"domain":"chemistry","key":"titration_ph_weak_acid_strong_base","name":"pH during a weak acid - strong base titration","package":"chemistry-ai999x","example":"25.0 mL of 0.100 M CH3COOH (Ka = 1.8e-5) is titrated with 0.100 M NaOH. What is the pH after adding 12.5 mL of base?","v":[0.03965,0.03132,-0.06073,-0.09284,0.0729,-0.0188,0.02531,0.07082,-0.02691,-0.00124,0.00692,-7e-05,-0.03945,0.00346,-0.01953,-0.08157,-0.06194,-0.0449,0.10947,-0.02895,0.075,-0.0767,-0.04785,-0.07399,0.04337,-0.03932,0.08989,0.07455,-0.02857,-0.00734,-0.09683,-0.12523,0.05835,-0.04496,-0.02617,0.06358,0.02879,-0.083,-0.03039,0.06399,0.0108,0.00916,-0.10979,-0.15312,0.03866,-0.06173,-0.01603,0.01104,-0.03207,0.03754,0.02852,-0.01516,0.04661,-0.10372,-0.02004,0.01989,-0.08429,-0.04368,-0.01186,0.03409,0.02365,0.01217,0.01383,0.04793,0.01294,-0.01473,0.06935,-0.06321,0.08707,-0.01562,-0.02456,0.04168,0.00198,0.07177,-0.08119,-0.01411,-0.04946,-0.01567,0.02174,0.04876,0.0108,-0.11944,-0.04628,-0.04813,-0.1118,0.02297,0.04185,-0.01894,0.13421,0.00069,-0.02628,-0.11099,0.07918,0.06929,-0.01517,-0.08692,-0.01247,0.00307,0.12615,-0.08419,-0.01931,-0.10612,-0.02823,0.02707,-0.07119,-0.00676,-0.08623,0.05788,0.00324,0.04182,0.07935,-0.03464,0.01967,0.11223,-0.00425,-0.03721,-0.01008,-0.01129,0.03655,0.04115,-0.09991,0.0469,0.10606,-0.16904,-0.08315,0.08766,0.04299,-0.09605,0.0307,-0.01294,0.0102,-0.05002,0.03825,0.00618,-0.06063,0.00031,0.0511,0.05012,-0.0141,-0.06372,0.05182,0.06489,0.02241,-0.0174,-0.04181,-0.11384,0.01714,0.08789,-0.08311,-0.0274,-0.01972,0.06832,0.10855,0.04843,-0.0364,-0.00243,0.03636,-0.05901,-0.02106,-0.0059,-0.03188,-0.01278,0.00078,-0.03026,-0.09427,0.087,-0.0502,-0.06565,-0.00195,-0.05406,0.0737,0.05562,0.05468,-0.08464,0.04292,0.14071,-0.07212,-0.00261,-0.06369,0.01551,-0.03814,-0.00554,0.10887,-0.01561,0.01975,0.07908,0.03975,-0.00371,0.03632,-0.02523,0.05652,0.00368,-0.00399,-0.05962,-0.0749,-0.06942,-0.11642,0.07846,-0.03864,-0.02821,0.01386,0.05808,0.1013,0.04627,0.09609,0.00903,-0.10223,-0.05482,0.1023,0.02181,-0.10594,-0.00939,0.01353,0.03718,0.1481,0.03315,-0.06437,-0.00909,-0.13981,-0.14569,0.09945,0.05406,0.09032,-0.00203,0.04884,0.14406,-0.00982,0.02952,0.12123,0.07583,-0.03208,-0.04845,-0.01005,-0.13904,0.0564,0.01189,0.09708,-0.01198,-0.00959,0.05692,0.15914,-0.03652,-0.06089,0.02853,0.03045,0.04223,0.02247,0.06496,0.03157,0.03474,0.06314,-0.07878,0.0172,0.00754,0.02814,0.02061]},{"domain":"chemistry","key":"van_der_waals_pressure","name":"Van der Waals equation: pressure","package":"chemistry-ai999x","example":"Using the van der Waals equation, find the pressure of 2.00 mol of CO2 in 5.00 L at 300 K (a = 3.640 L^2·atm/mol^2, b = 0.04267 L/mol).","v":[0.02259,-0.13651,-0.0365,-0.02428,-0.01889,0.11278,0.00078,-0.00363,0.0584,0.04355,-0.08508,0.00526,0.02372,-0.12833,-0.06777,-0.07854,0.05608,-0.03687,0.01042,0.14363,-0.01493,-0.0449,0.01128,0.07808,0.07423,-0.01792,0.12443,-0.00397,0.08146,0.08809,0.00343,-0.02059,-0.01126,0.01569,0.04685,0.02938,0.01223,0.07362,-0.01774,-0.05391,0.13489,0.01324,0.14485,0.00237,-0.02096,-0.03066,-0.0276,-0.11331,0.09783,0.07309,0.15269,-0.05237,-0.00056,-0.06383,-0.0539,-0.02886,-0.01931,0.05459,0.02511,0.03532,0.06111,0.00709,-0.16778,-0.01219,-0.02155,0.05123,0.01423,-0.06576,-0.13308,-0.06389,-0.06507,0.00756,0.05284,0.07986,-0.02279,-0.07528,-0.04176,-0.04894,-0.03468,0.04939,0.04275,0.03709,0.00329,-0.04845,-0.08607,0.00451,-0.06983,0.02182,0.04619,0.00058,0.05961,0.0746,-0.01496,0.03325,-0.05246,-0.02042,0.04234,0.01664,-0.06069,0.02238,0.00881,-0.0121,-0.01862,0.14217,-0.00199,0.00396,0.02658,-0.08452,0.06259,-0.02273,-0.00035,-0.11111,-0.0647,0.02246,-0.10835,-0.08092,0.02551,0.02567,0.02753,0.01685,0.08784,-0.03813,-0.06469,-0.17555,-0.01139,-0.01767,0.01621,0.06872,-0.0196,-0.01988,-0.08623,0.02207,-0.01859,-0.03153,-0.14582,-0.01402,-0.0294,0.03282,-0.03476,0.00819,-0.07963,0.00751,-0.04899,0.04157,0.10252,0.02882,0.01093,0.03838,-0.01087,-0.00831,0.03029,0.06937,0.13952,0.0565,0.02484,0.08025,0.08887,-0.02779,0.03282,-0.01404,0.00759,-0.14711,0.00254,-0.03824,-0.07263,0.0709,0.10231,0.11714,0.02229,-0.07932,-0.01825,0.10682,-0.07239,0.02885,0.04198,-0.06304,-0.0486,-0.06988,0.10946,0.01223,0.08106,0.04429,-0.01734,-0.02144,0.00727,0.03865,0.01059,-0.06646,-0.05556,-0.023,-0.12506,0.04837,-0.02329,-0.0316,0.01962,0.08701,0.00575,-0.03996,0.00338,-0.03024,0.02535,-0.01759,-0.05265,-0.10173,-0.08144,0.09576,-0.13479,-0.05294,0.0644,-0.06222,0.10728,-0.04002,-0.02757,-0.00917,0.09799,0.08986,0.05379,-0.05077,-0.00319,-0.01637,0.0066,0.07154,0.04258,0.04547,0.01014,-0.05336,0.07503,-0.01922,-0.03838,0.03755,0.09954,-0.01524,-0.01071,0.08155,-0.02285,0.06645,-0.14416,0.0766,-0.04919,0.01812,0.0215,0.02898,0.07532,0.01175,0.03322,-0.04409,-0.08115,0.01168,0.01734,-0.06238,0.04489,-0.07099,-0.12864,0.10243,-0.03879,-0.01479]},{"domain":"chemistry","key":"vant_hoff_k2","name":"Van 't Hoff equation: K at another temperature","package":"chemistry-ai999x","example":"K = 1.8e-5 at 298 K and ΔH° = 50.0 kJ/mol. What is K at 350 K?","v":[-0.03802,-0.04095,-0.03961,0.04761,-0.08903,-0.02723,0.00065,0.12653,0.02445,0.0075,0.03971,-0.05039,-0.14545,0.03449,0.09635,-0.04534,0.01986,0.02263,0.04535,-0.06708,-0.01942,0.03923,0.0091,-0.0922,0.00146,-0.00019,0.03121,-0.06281,0.01203,-0.05148,-0.03812,0.04804,0.05257,-0.05559,0.00932,0.07437,0.07913,0.07026,-0.008,0.01421,0.04052,-0.01388,0.00032,-0.03095,-0.10881,0.02132,0.07155,-0.01099,0.07611,0.11476,-0.02874,0.08728,-0.01378,-0.02531,0.04838,-0.1964,0.08572,0.0427,0.05341,0.05905,-0.08063,0.00816,-0.03824,0.07816,0.05771,0.08169,-0.04845,0.03528,0.04184,-0.01183,-0.00809,-0.00759,-0.06903,-0.07706,0.021,0.00591,-0.07876,-0.04364,0.0586,-0.00873,-0.062,-0.0957,0.00494,0.1153,0.01972,-0.00791,-0.01966,0.06964,-0.063,0.03316,0.07832,-0.09412,0.09387,-0.02501,-0.12881,-0.02287,-0.08306,-0.07178,0.09935,-0.00974,0.05492,0.03013,0.06449,0.0965,-0.05042,-0.02158,-0.05703,0.04447,0.00865,-0.02289,0.09064,-1e-05,0.07087,-0.07266,-0.02667,0.02646,0.01264,0.11271,-0.00487,0.01183,-0.03983,-0.02547,0.08167,-0.0694,0.01425,0.00098,0.04673,0.00916,-0.07634,-0.05731,-0.00152,-0.02187,0.01638,-0.06042,0.01231,-0.05528,-0.02582,0.06562,0.05917,-0.01699,-0.00508,0.1101,-0.00799,0.056,-0.00877,0.0473,-0.04616,-0.00498,0.04058,-0.06022,0.01992,-0.06325,0.0248,-0.03778,0.06821,-0.01547,0.08097,-0.07756,-0.01361,-0.14142,-0.03104,-0.03755,-0.08154,0.06313,-0.0422,0.02987,-0.11465,-0.12406,0.04439,-0.00232,0.00272,0.00278,0.00544,-0.03996,-0.01151,-0.01751,-0.07331,0.04944,0.02959,-0.04874,0.05556,-0.04139,-0.13259,-0.00356,-0.0533,-0.01633,-0.00525,-0.01872,-0.00716,0.09038,0.04544,0.19333,0.09999,0.07646,-0.01442,-0.01718,-0.03577,0.0901,-0.05119,-0.07685,0.03634,-0.05366,0.07758,0.00448,0.00639,-0.03439,0.08848,0.01683,-0.06682,-0.06923,0.04507,0.03462,-0.11868,0.07749,0.11249,0.15691,-0.00458,0.03588,-0.0907,-0.03413,-0.05715,0.04399,0.08283,-0.03514,-0.04666,0.05325,0.06328,0.00405,-0.0297,0.00108,0.03792,-0.01758,-0.01418,-0.14478,0.00999,0.04208,0.02527,0.01872,-0.1396,0.05984,-0.01041,-0.04731,-0.02029,0.10484,-0.01274,-0.07823,0.00301,-0.06767,0.0236,0.00527,-0.09404,0.25463,-0.05159,0.08039,0.04327,-0.01084]},{"domain":"chemistry","key":"vibrational_wavenumber","name":"Vibrational wavenumber of a diatomic molecule","package":"chemistry-ai999x","example":"What is the vibrational wavenumber of HCl if its force constant is 516 N/m?","v":[0.06539,-0.03811,0.0632,0.0118,0.00063,-0.05184,-0.01626,-0.01809,-0.0217,-0.11702,0.05109,-0.03496,-0.01329,-0.08703,-0.01211,-0.04233,-0.00102,-0.03312,-0.06439,0.01054,-0.082,-0.04385,-0.05994,0.07822,-0.00917,-0.05926,0.04199,-0.05449,0.02813,0.0392,0.07967,0.01262,-0.02965,0.02162,-0.04045,-0.11499,0.10738,0.03678,0.0203,-0.08663,0.03227,-0.06935,0.05293,-0.02514,0.0246,-0.03022,-0.1385,0.06954,0.01047,-0.02383,-0.06126,0.0084,-0.08373,-0.0787,-0.01753,-0.03093,-0.13806,-0.05812,-0.0517,0.08514,0.10502,-0.02094,-0.00612,0.07436,0.06928,-0.01161,-0.07706,0.06316,-0.04453,0.00362,0.1173,-0.05585,-0.03154,0.04154,0.0887,0.02838,-0.14836,-0.00673,0.01915,-0.03443,-0.04155,0.03714,0.06415,-0.05985,-0.01555,-0.06458,-0.04825,-0.11141,0.04603,0.04437,0.0101,-0.03658,0.09105,0.03659,-0.0586,-0.03006,-0.06206,-0.03574,0.09605,-0.02127,0.01623,0.05204,-0.0211,0.01963,0.0096,0.00455,0.02785,0.0385,0.04375,0.0092,0.10443,-0.13679,-0.02957,-0.0841,-0.09434,0.11932,-0.08013,-0.1159,0.06218,-0.05303,-0.05394,-0.0936,-0.03021,-0.14583,0.00309,0.06286,-0.05357,-0.08312,-0.01897,0.01537,0.03173,0.14401,0.06912,0.03656,0.05899,-0.03905,-0.07144,-0.00378,0.08646,0.07587,0.02223,0.03796,0.11424,-0.06425,0.07789,0.04672,-0.02023,-0.01146,-0.05553,-0.04386,-0.0,-0.05727,0.05074,0.02227,-0.03012,0.02153,0.1993,-0.07011,0.10668,-0.04158,-0.02099,-0.06392,0.06024,-0.00215,0.01244,-0.0028,0.07206,-0.00271,0.04539,0.02548,0.05928,0.0255,0.10268,0.12625,-0.07883,-0.0613,0.03145,0.01103,0.02593,-0.18097,0.03154,0.03327,-0.08781,-0.0214,-0.06341,-0.04899,0.00046,-0.06673,0.00169,0.10354,-0.0743,0.01147,-0.05919,0.03033,-0.04969,-0.10465,-0.01998,0.15231,0.0009,0.02091,0.06093,0.00116,-0.06154,-0.01227,-0.00775,-0.00846,-0.04029,0.05146,0.03926,-0.09025,0.04592,-0.00425,-0.04762,0.04158,0.10313,0.03469,-0.01158,0.06265,0.01989,-0.01999,-0.09213,0.09708,-0.02266,0.09314,0.04172,0.01523,0.15178,0.04756,-0.0075,-0.09495,0.08453,-0.00085,0.07233,0.05687,-0.01064,0.01152,0.00179,0.08318,-0.07591,-0.00392,-0.01686,0.00493,-0.04086,-0.05918,0.02358,0.00351,-0.0462,0.09775,0.10598,0.04339,0.01488,0.05571,-0.08604,0.05294,0.00262,0.01397]},{"domain":"chemistry","key":"zero_order_concentration","name":"Zero-order integrated rate law","package":"chemistry-ai999x","example":"A zero-order reaction has k = 0.0020 M/s. If [A]0 = 0.50 M, what is the concentration after 100 s?","v":[-0.01349,0.10042,-0.03635,-0.09438,0.04672,-0.06774,0.01388,0.03131,0.07126,0.02824,0.02078,-0.05479,-0.05311,-0.0703,0.1394,-0.01405,0.03202,-0.04479,-0.02457,0.06146,-0.02887,-0.08151,-0.06691,0.06674,-0.05487,0.01993,0.11164,0.15357,0.01948,-0.02254,0.04564,0.02335,0.04699,0.01505,-0.05954,0.12935,-0.0023,0.06369,0.06812,-0.057,0.03963,-0.01752,-0.05779,-0.05848,-0.01122,0.0028,0.04456,-0.03783,-0.04852,-0.10674,-0.04448,0.02952,0.03267,-0.13442,-0.03195,0.02546,-0.00629,0.04887,-0.05018,-0.02146,0.02863,-0.00636,0.11335,0.05618,-0.00022,0.02473,0.00951,-0.05298,-0.09497,-0.04694,0.07946,-0.08742,0.0087,0.02403,0.06069,-0.04693,0.07629,-0.02759,-0.06912,-0.20007,0.00054,0.0295,0.0502,-0.06371,-0.0189,0.05628,-0.03866,-0.05774,-0.04329,-0.03558,0.03021,-0.00437,-0.07375,0.02864,0.00256,0.10691,0.14673,0.05778,0.03934,0.02955,0.04992,-0.00556,0.0441,0.0139,0.05702,0.13424,-0.04709,-0.00437,0.05788,0.0457,0.03627,0.01208,-0.00466,-0.05738,-0.01319,0.13681,-0.0436,-0.07123,0.00163,0.16997,0.04158,0.0082,0.03884,0.04038,0.02563,0.00407,0.05265,-0.04574,-0.05476,-0.03305,0.06908,0.01281,0.00762,-0.02027,0.01282,-0.13303,0.09253,0.0213,0.09427,-0.0613,0.01219,0.1091,0.03092,0.07189,-0.11396,0.03027,-0.01063,0.07403,-0.05073,0.01293,-0.02255,-0.04441,-0.07901,0.01366,-0.00336,-0.10309,0.02709,0.06629,0.0406,-0.12356,-0.04754,-0.08735,0.00711,-0.07268,0.03041,0.04132,0.02095,-0.05799,0.05379,-0.07142,0.06709,-0.03191,0.06739,0.00784,0.03781,-0.06137,-0.07218,0.00749,0.08076,-0.05828,0.04111,0.05255,-0.10603,-0.07787,-0.03556,-0.0052,-0.1039,0.0032,-0.03858,-0.04814,0.13197,-0.06843,-0.01732,-0.05362,0.04072,-0.03447,-0.09067,-0.06302,-0.03162,-0.08095,-0.12846,-0.079,0.01554,-0.12491,0.04839,0.09463,0.09659,-0.03536,0.01661,0.05992,0.05276,-0.05047,0.07684,0.06379,0.01607,-0.10392,0.07351,-0.01663,-0.15815,-0.0397,0.01487,-0.0038,0.03863,0.0271,0.06549,-0.05913,0.03704,-0.05923,0.0801,-0.02626,0.02222,-0.02851,0.00991,-0.05595,0.0447,0.01227,-0.0832,0.02234,0.02362,0.02752,-0.00743,0.1307,-9e-05,0.0597,-0.0013,0.01936,0.05446,-0.03299,0.07559,0.09068,-0.02893,-0.08128,0.06044,-0.12196,0.00592,-0.06377]},{"domain":"classical_physics","key":"uniform_motion","name":"Motion at constant velocity","package":"classical-physics-ai999x","example":"A bus travels a distance of 16600 m in an elapsed time of 0.48 h. What is the constant speed?","v":[0.00097,0.01672,0.04731,-0.0083,0.03205,-0.09209,0.11495,0.0226,0.07463,-0.02673,0.0235,-0.01287,0.03857,-0.02112,0.01657,0.01443,-0.12181,0.02021,-0.08163,0.05328,-0.13022,0.01342,-0.03034,-0.08461,0.05157,-0.04717,0.06609,-0.05033,0.09312,-0.00295,0.15312,0.0472,-0.03884,-0.00632,-0.07736,-0.00386,0.08249,0.02204,-0.031,-0.04664,-0.05786,-0.06766,-0.01545,-0.04947,-0.15398,-0.05557,-0.01276,-0.08246,0.05743,-0.10435,0.09767,-0.0882,-0.18657,-0.0462,0.06034,-0.05249,0.07583,0.12035,-0.02075,-0.07186,0.08109,-0.10682,-0.01832,-0.05362,-0.0639,-0.03382,0.06269,0.05571,0.01786,0.06515,-0.00683,-0.07035,-0.0271,-0.03031,0.10311,-0.02192,0.05598,-0.10589,-0.02247,0.00755,0.04439,0.01902,0.01879,0.16143,-0.04596,0.03447,-0.0006,-0.08538,0.01933,0.02442,-0.02433,-0.02371,-0.05369,0.05923,0.04011,0.00841,0.07173,0.06118,-0.01151,-0.04596,0.02709,-0.02343,-0.02007,-0.14928,-0.09758,0.05272,0.02495,-0.01612,0.02519,-0.04648,-0.00338,-0.03889,-0.02301,0.03857,-0.01601,0.11598,-0.05811,0.08574,-0.05303,0.00803,0.01878,0.0168,-0.05002,-0.01056,0.06966,-0.02677,-0.00192,0.10021,-0.02243,-0.01454,-0.02934,0.07138,0.01938,0.07494,0.00139,0.00453,0.03585,0.06114,-0.00618,-0.00071,-0.00601,0.18768,0.01651,-0.03485,-0.07805,0.05058,-0.0402,0.05587,-0.01917,0.14504,0.03721,-0.08188,-0.01661,-0.09799,0.00827,-0.02081,0.08768,-0.0712,0.008,-0.10982,0.01417,-0.02773,-0.00721,-0.01997,0.04986,-0.04794,-0.03724,-0.10898,0.03966,0.03316,-0.00465,-0.09449,0.0547,0.01486,-0.03942,-0.07145,-0.04351,0.03005,0.17976,0.07523,0.06436,-0.01511,0.05161,0.02129,0.02727,-0.01434,-0.04844,-0.1019,-0.02983,-0.03078,-0.10282,-0.09453,-0.05831,0.04948,0.01998,0.05454,0.0865,0.0648,0.05402,0.06332,-0.00823,-0.01279,-0.00277,-0.1091,-0.05325,0.05526,-0.01864,-0.01839,0.10746,0.00381,-0.00987,-0.08885,0.01533,-0.05897,0.05938,0.00536,0.0417,0.06207,-0.05893,0.0107,-0.06123,-0.03626,-0.14033,0.02257,0.04052,-0.01567,0.02846,0.07796,0.02784,-0.0471,0.04409,0.01569,0.08625,0.00866,-0.01144,0.05809,-0.01005,-0.01494,-0.03711,-0.06133,0.00735,0.04531,-0.13421,0.00273,0.11251,-0.07821,-0.01643,-0.06882,0.09379,0.02822,0.12861,0.0085,-0.11875,0.0032,-0.00925,0.07194]},{"domain":"classical_physics","key":"velocity_time","name":"Velocity under constant acceleration","package":"classical-physics-ai999x","example":"A scooter has an initial velocity of 2.97 m/s and accelerates at 3.5 m/s^2 for 7.92 s. What is the final velocity?","v":[0.03877,0.00944,0.05265,0.04231,-0.02764,-0.00034,0.02823,0.03053,0.01607,-0.06281,0.03566,0.00631,0.05422,-0.11106,-0.0206,-0.01058,-0.07498,0.01288,0.11077,0.06577,0.10316,-0.02122,-0.0995,0.09338,0.01479,-0.06053,0.05991,0.0065,-0.01916,-0.00289,-0.02847,0.01929,-0.00217,0.00517,-0.07105,-0.0871,0.05682,0.00105,0.01949,0.00421,-0.00818,-0.08393,-0.06545,-0.08885,-0.06812,0.01536,0.03032,0.00683,-0.01368,-0.10315,0.10011,-0.07084,-0.05079,-0.02191,0.05456,0.07229,0.03615,0.02926,-0.03509,0.00132,0.00586,0.01024,0.05103,0.05794,-0.01961,0.02062,0.09024,0.04673,0.01083,0.0391,0.0492,-0.00742,-0.01068,-0.03451,0.01909,-0.05507,0.14886,0.00157,-0.11503,0.01223,0.04357,0.02195,0.06634,0.00628,-0.0419,0.07838,0.00811,-0.14918,0.0231,-0.042,0.0698,-0.0696,-0.0388,-0.00477,-0.05906,0.02108,0.04687,0.01901,0.05363,-0.01516,0.02187,0.05102,0.05029,-0.03568,-0.05292,-0.04376,0.02974,-0.00513,0.07451,0.10192,-0.01312,0.07167,-0.09918,-0.01567,0.01425,0.05492,-0.03804,0.01523,-0.00888,-0.01308,-0.03227,0.01896,0.06541,0.03288,-0.03091,0.11787,0.01538,-0.02597,0.09138,0.00356,0.03418,0.05152,-0.07648,-0.03298,-0.00309,-0.15045,-0.02037,0.06314,0.05523,-0.02282,0.0279,0.1281,0.09688,0.04769,0.05116,-0.03544,-0.00233,0.13653,-0.02499,0.06337,-0.04764,-0.03698,-0.13093,-0.1627,-0.05759,0.02992,-0.09382,-0.01255,-0.07731,-0.1056,-0.06543,-0.03448,0.10574,0.08715,-0.00139,-0.01415,0.02854,-0.02176,0.08547,-0.04373,0.00064,0.06846,-0.03718,0.02865,-0.01072,0.03436,-0.08438,-0.11705,0.0505,-0.09436,0.02239,-0.03574,0.01464,-0.01397,-0.00642,-0.02376,-0.1027,-0.04606,0.0098,-0.04899,-0.06428,0.00615,-0.10776,0.04774,0.06089,-0.04875,0.05779,-0.06248,0.0376,0.00809,-0.07749,0.01997,0.03862,-0.05328,-0.01654,0.08373,-0.07954,-0.01947,0.20668,-0.00196,0.00738,-0.06402,-0.02547,-0.09602,0.02408,-0.02686,0.08765,0.02478,-0.16537,0.01294,-0.01763,-0.04991,-0.00463,0.07044,0.05443,-0.01205,-0.10919,0.05417,-0.03714,-0.0332,-0.07869,-0.00578,0.05252,-0.03275,0.03343,0.0279,0.03286,-0.00414,0.14913,0.10543,0.10662,0.07003,-0.11437,0.10655,0.10026,-0.13725,0.0371,-0.06695,0.12427,-0.11769,-0.05511,0.04733,-0.07531,-0.07706,0.09164,0.0288]},{"domain":"classical_physics","key":"displacement_time","name":"Displacement under constant acceleration","package":"classical-physics-ai999x","example":"A train starts moving at 3.82 m/s and accelerates at 2.49 m/s^2 for 0.123 min. How far does it go?","v":[0.01913,0.0142,0.02043,0.04374,-0.03371,0.00014,0.09483,-0.06835,0.05792,-0.03469,-0.08314,0.01064,0.01668,-0.00029,-0.06757,0.01591,-0.05212,0.01444,-0.00488,0.00968,-0.00941,-0.07011,-0.1128,-0.0082,-0.0474,0.00595,0.02832,-0.02299,0.00488,-0.05677,0.06988,0.03728,0.04166,-0.02655,-0.03234,-0.04792,0.06465,0.0247,-0.04479,-0.02446,-0.04105,-0.14349,-0.09587,-0.08019,-0.19033,0.0065,0.03296,-0.00485,0.05428,0.01333,0.07879,-0.04141,-0.02931,0.01067,0.0501,0.00859,0.08647,0.11564,-0.01592,-0.09235,0.01317,-0.03059,-0.00854,0.04705,-0.05836,0.05305,0.04066,0.0347,-0.03247,-0.02553,-0.01968,-0.0535,0.03055,-0.08074,0.01607,0.04756,0.09332,-0.00523,-0.12147,0.06305,0.11158,0.09285,0.0663,0.08463,-0.08474,0.08123,-0.00611,-0.12073,0.04639,-0.03211,0.00019,-0.05694,0.01015,0.0803,-0.01042,-0.02268,0.00415,0.03229,0.05077,0.01566,0.02596,0.0065,0.01424,-0.10962,-0.08248,-0.02488,0.0284,-0.00498,0.04915,0.08963,-0.03075,0.0035,-0.11347,0.00211,0.06696,0.09599,-0.10685,0.02194,-0.03862,0.10801,0.0142,-0.01364,0.07394,-0.0186,-0.00532,-0.01799,0.02918,0.02064,0.08608,0.01944,-0.01382,0.00568,-0.03203,0.00775,-0.0119,-0.05048,0.00721,0.05787,0.03646,-0.03012,-0.00407,0.10633,-0.01527,-0.02508,-0.01768,0.03448,0.0374,0.0932,0.00386,0.05027,-0.04396,-0.10557,-0.07932,-0.15975,0.00525,-0.02869,0.02649,-0.03783,-0.04113,-0.03392,-0.01686,-0.05719,0.0614,0.15961,-0.10184,-0.01081,0.05958,-0.05682,0.07734,0.02844,0.02397,-0.0047,0.02902,0.07454,-0.01073,-0.03118,-0.03222,-0.12866,0.09429,0.0411,0.11873,-0.05883,-0.03326,0.0278,-0.0127,-0.06762,-0.05741,-0.04872,0.01032,-0.13716,-0.01072,-0.09369,-0.05652,0.0517,0.06067,0.00015,0.05603,-0.02299,-0.03116,0.00363,0.01135,0.06752,-0.0362,-0.09457,0.03007,0.10459,-0.04868,-0.05126,0.16196,-0.03003,0.0228,-0.0836,0.04871,-0.063,0.12016,-0.00649,0.0931,-0.05369,-0.15312,0.02805,0.05226,-0.01623,-0.04239,0.13455,0.01636,-0.03034,-0.11458,0.0833,-0.0292,-0.01062,-0.06619,0.03246,0.06435,-0.00285,-0.02005,0.10916,0.07726,0.02949,0.06331,0.02116,0.08934,0.02938,-0.17894,0.09344,0.06651,-0.12408,0.01413,-0.06149,0.10588,-0.08156,0.04383,0.03294,-0.07614,-0.07525,0.08308,0.01227]},{"domain":"classical_physics","key":"velocity_displacement","name":"Speed after a displacement under constant acceleration","package":"classical-physics-ai999x","example":"A driver enters a zone at 30.7 km/h. The car accelerates at 3.75 m/s^2 for a displacement of 24.9 m. What is the final speed?","v":[0.05871,0.04659,0.03357,-0.08742,0.04043,0.12436,-0.02271,-0.05643,-0.02057,-0.0647,-0.04437,-0.04397,-0.03272,-0.02129,0.00813,0.02401,-0.07132,-0.03818,0.02206,0.04761,0.02185,-0.01497,0.01956,0.09266,-0.09257,-0.04038,0.05173,0.00814,-0.0435,-0.05646,0.00715,-0.07652,0.00421,0.01842,0.02089,0.03195,0.05109,0.03755,-0.06588,0.04343,-0.11148,-0.10745,-0.02244,-0.05705,-0.07051,0.04438,0.03127,-0.01265,0.07661,-0.05299,0.10286,-0.03924,0.02856,0.01097,0.06253,0.07094,0.03845,0.05741,-0.00305,0.01828,0.0694,-0.11674,0.03842,-0.10941,-0.13054,0.06134,0.0756,0.10991,-0.01071,0.03839,0.03178,-0.02623,0.00347,0.00639,-0.02778,0.04546,0.12326,-0.00421,-0.00331,0.07603,-0.00075,0.10175,0.00843,0.10923,-0.05608,-0.00708,0.03744,-0.10123,0.02079,-0.0132,0.00122,0.01277,0.03942,0.04551,-0.07202,-0.02658,0.00907,0.00054,0.13862,-0.11621,0.06659,0.01197,0.03092,-0.1485,-0.13132,0.013,-0.05138,0.00639,0.01064,0.10332,-0.02731,0.03868,0.01396,0.00148,-0.0148,0.06152,-0.05017,-0.01854,-0.01194,-0.02736,0.03739,-0.0091,0.03265,0.03229,-0.01405,0.05589,0.00443,0.05354,0.01333,-0.07108,-0.04498,-0.02558,0.00074,-0.03513,-0.12809,-0.01443,0.00755,0.05625,0.00178,-0.11959,-0.09513,0.10355,-0.00179,0.03231,-0.01451,0.04224,0.02322,0.09643,-0.13136,0.02067,-0.04553,0.04303,-0.15446,-0.09532,0.03227,-0.00416,-0.01854,-0.00323,-0.08517,-0.08788,0.00345,-0.0334,0.03191,0.05011,-0.06037,-0.06327,0.05572,-0.08,0.0789,0.0438,-0.07785,-0.00628,0.10239,-0.02337,-0.05998,0.07799,-0.00662,-0.04572,0.08647,-0.00022,0.1719,-0.0168,-0.03041,0.03832,0.01745,-0.07551,-0.06055,0.01151,0.01275,-0.01991,0.0822,-0.06496,-0.04391,-0.04247,0.03519,-0.00182,-0.0553,-0.06193,-0.10977,0.00872,0.07129,0.05462,0.08932,0.04707,0.07043,0.04462,-0.08704,0.04994,0.15247,-0.04412,-0.03749,-0.09714,0.03967,-0.0725,0.06314,0.00199,0.02293,0.02581,-0.16798,0.02368,0.05711,-0.09325,-0.00857,0.09471,0.05224,0.09522,-0.09891,0.14483,0.01371,-0.04579,-0.08167,0.0738,0.10826,0.00225,-0.00694,-0.00822,0.03548,0.08539,0.00371,0.09473,0.03782,0.05734,-0.09322,0.04137,0.04066,-0.02561,-0.04032,-0.03311,0.024,-0.02432,-0.06243,0.06736,-0.1218,-0.10839,0.06671,0.0105]},{"domain":"classical_physics","key":"average_velocity_displacement","name":"Displacement from the mean of initial and final velocity","package":"classical-physics-ai999x","example":"A dog runs from 2.71 m/s to 15.1 m/s in 3.87 s. How far did it go?","v":[0.07784,0.0133,0.08557,0.07928,0.02515,-0.06945,0.03918,-0.00754,0.0172,-0.08839,-0.01802,-0.0628,-0.03243,0.05892,0.03454,-0.00276,-0.1768,0.00401,-0.0841,0.00921,-0.08139,0.01067,-0.05161,-0.02924,-0.03274,-0.01318,0.03868,-0.07941,-0.00967,-0.00526,0.07821,0.02677,-0.03581,-0.00155,-0.05674,-0.03399,0.00503,0.00221,-0.00567,-0.07153,-0.10818,-0.05384,0.03034,-0.04167,-0.14321,0.01704,-0.00963,0.01666,-0.03471,-0.08976,0.06496,-0.02058,-0.10337,-0.01197,0.13784,0.0297,0.06736,0.1164,-0.04293,-0.07839,-0.00613,-0.09693,-0.00801,-0.03346,-0.0609,0.00256,0.0557,0.01786,-0.01736,0.10734,0.04545,-0.03353,-0.00218,-0.09655,0.07118,0.09284,0.05845,0.03515,0.01592,-0.02274,0.02973,0.13079,0.00291,0.1345,-0.06701,0.05919,-0.0128,-0.1198,0.04139,-0.02969,0.01111,-0.03974,0.02411,0.00373,0.06346,-0.05503,0.01051,-0.02863,-0.03534,-0.00034,0.05824,0.04065,0.0031,-0.08691,-0.03703,0.00192,0.00129,0.03391,0.04488,0.00751,-0.02642,-0.0299,-0.00657,0.01279,-0.05733,0.15464,-0.05326,0.0131,0.01246,0.02407,0.02413,-0.0448,-0.00737,0.01874,-0.00595,0.01847,0.07552,0.02869,0.09626,0.08107,0.01818,0.00988,-0.05226,0.04171,0.00031,-0.04672,0.0728,0.07742,0.04441,-0.00213,0.00272,0.11051,0.03036,-0.04608,-0.07279,0.06617,-0.06188,0.07164,0.04169,0.06832,0.02296,-0.10632,-0.07673,-0.15325,0.01706,-0.04194,0.02643,-0.04764,-0.0269,-0.04082,0.08206,-0.06226,0.00688,-0.02276,-0.02773,-0.00506,-0.01795,-0.06516,0.0389,0.06409,0.06997,0.00226,0.10705,0.05108,-0.03635,-0.13226,0.03215,-0.02493,0.11846,-0.03912,0.07284,-0.05691,-0.0398,-0.01874,-0.02864,-0.02563,0.00409,-0.03074,0.12921,-0.04442,-0.03925,-0.13269,0.00899,0.04337,0.07578,0.04551,0.07748,-0.02469,0.01245,0.10365,-0.01591,0.05408,0.09788,-0.13058,-0.01165,0.08596,-0.02691,-0.044,0.09259,-0.04337,0.01756,-0.08067,0.02461,-0.07572,0.02974,-0.10789,0.09327,-0.00112,-0.08746,0.00255,0.0065,-0.02351,-0.03619,0.04717,0.00167,-0.01425,-0.04874,0.10571,0.04341,-0.04358,0.00824,0.08908,0.01716,0.00217,0.00953,0.01897,0.05311,0.02823,0.01852,-0.03808,0.15681,-0.02844,-0.12784,0.03772,0.08852,-0.18619,-0.022,-0.13458,0.06946,-0.16227,0.05855,0.03295,-0.10728,-0.11338,0.00943,0.05992]},{"domain":"classical_physics","key":"newton_second","name":"Net force and acceleration","package":"classical-physics-ai999x","example":"A box has a mass of 4310 g. It accelerates at 1.03 m/s^2. What is the net force?","v":[-0.02494,-0.04648,0.08132,-0.10646,0.00793,0.05712,0.04788,-0.12433,-0.02832,0.10057,-0.00755,0.05088,0.0463,-0.06745,-0.04595,-0.02002,0.00864,0.15283,0.08953,0.04285,0.02528,-0.01173,-0.01033,0.00487,-0.12819,0.07329,-0.04498,0.01988,-0.07014,-0.12658,-0.06421,-0.01204,0.07143,0.01271,-0.06216,-0.00211,0.03707,-0.03759,-0.00264,0.03047,0.03295,-0.01406,-0.09401,0.01107,-0.01511,0.11608,0.02009,0.01691,0.09114,0.09363,-0.05292,-0.07509,-0.00491,0.09033,0.04158,-0.03461,-0.07581,-0.0203,0.08248,-8e-05,0.06298,-0.00093,-0.02648,-0.00031,0.07818,0.0895,0.02982,0.03846,0.04067,-0.09218,-0.00833,-0.06462,0.00958,-0.13481,-0.0568,0.03437,0.02509,-0.1228,-0.11483,0.00908,-0.11107,-0.06136,0.04763,-0.00929,-0.06435,0.04865,0.00625,-0.05779,-0.00386,-0.0607,-0.06058,-0.05574,0.04712,-0.02714,-0.01619,0.00377,0.00958,0.05607,0.11363,-0.02653,-0.00607,-0.04711,-0.02827,-0.07239,-0.06695,0.01826,0.10712,-0.07409,0.02058,0.08531,-0.04945,0.02458,-0.04046,-0.02861,0.06559,-0.0879,0.09852,0.06234,0.0039,0.06719,-0.06913,0.08618,0.09588,-0.05026,0.02436,-0.00236,-0.01849,0.05447,-0.02289,-0.08797,-0.03337,0.04311,-0.06781,0.0394,-0.1534,-0.06584,-0.07535,0.07144,-0.03875,-0.05057,-0.02028,0.01908,-0.01292,0.02354,0.03468,0.01917,0.08453,0.04336,0.01129,-0.07501,-0.00774,0.0464,-0.15139,-0.032,-0.0324,0.00617,-0.04147,-0.03405,-0.07258,-0.01578,0.00218,-0.01921,0.05755,0.0629,-0.10102,0.04106,0.07329,0.00984,0.00526,-0.02669,-0.07589,-0.01544,-0.02365,0.14401,0.07697,0.11328,-0.00345,-0.11144,-0.10185,0.08043,-0.00703,0.01685,0.09,0.00272,-0.00735,0.02711,-0.07872,-0.06883,-0.07211,-0.08437,0.03866,0.12405,-0.07013,0.0161,-0.02854,-0.00194,-0.03263,0.0538,-0.11788,0.00546,0.00984,0.00377,-0.04693,0.06252,-0.0354,0.10359,-0.01598,0.01026,0.08629,0.04428,-0.09094,0.02616,-0.05494,-0.11344,0.06176,-0.05871,0.01164,0.1139,-0.05985,-0.02451,0.00463,0.05035,-0.02092,0.11473,0.00503,0.0059,-0.03912,0.02725,0.01043,0.05289,-0.04461,0.04581,-0.06418,0.07735,-0.00776,-0.00309,0.12363,-0.05727,0.02688,0.10515,-0.04443,-0.03961,-0.12714,0.04359,0.08916,-0.10829,0.13945,0.01024,0.04782,0.05421,0.00327,0.08261,0.01998,0.0683,-0.06422,0.06338]},{"domain":"classical_physics","key":"weight","name":"Weight in a uniform gravitational field","package":"classical-physics-ai999x","example":"A box weighs 56.8 N and has a mass of 4.73 kg. What is the gravitational acceleration?","v":[-0.00062,0.03464,0.00423,-0.02538,0.04471,0.10795,0.07896,-0.15499,0.01504,-0.00755,-0.04152,0.11566,0.06068,-0.02044,-0.01197,-0.11024,-0.07465,0.06823,0.01068,0.05584,0.0538,-0.06072,-0.01925,0.06914,-0.04731,0.09284,0.04147,-0.02883,-0.06045,-0.04466,0.00035,0.05163,-0.01595,0.02123,0.03752,-0.02842,-0.03126,0.0805,0.04729,-0.09385,0.01201,0.0187,-0.14549,0.0481,-0.04324,0.13305,-0.04458,-0.00895,0.0644,0.05356,-0.06106,0.00957,0.08699,-0.01041,0.02004,-0.00413,-0.08942,-0.06755,-0.09589,0.13352,-0.03339,-0.01967,-0.01059,0.02515,0.10611,0.1082,0.00737,-0.00086,0.05344,-0.00324,0.05631,-0.02732,0.09057,-0.09741,-0.03264,0.0501,0.00209,-0.0785,-0.09309,0.04268,-0.10259,0.04412,0.04257,-0.02397,-0.11425,0.109,0.05261,-0.07088,0.0838,0.04325,-0.03646,-0.05843,-0.01019,0.01112,-0.00762,0.04488,0.01028,0.06509,0.02928,-0.0231,0.02003,-0.08957,-0.08972,0.00831,0.02152,-0.08032,0.14005,-0.02893,-0.05154,0.04531,-0.0872,0.03289,-0.11936,-0.05352,0.05096,-0.04338,0.07035,0.00715,0.03501,0.00391,-0.09155,0.03906,-0.03448,-0.12578,0.03774,-0.05919,-0.00158,-0.03796,-0.04012,-0.04466,0.10089,0.07063,0.06046,-0.01587,0.01201,-0.01515,0.00573,-0.00235,0.00129,-0.0257,0.02733,-0.04543,-0.04169,0.04003,-0.00881,-0.13549,0.09752,0.01117,0.05234,-0.07574,0.07329,0.00955,-0.01963,-0.06168,-0.04726,0.0335,0.0345,-0.10798,-0.03798,-0.05135,-0.04077,0.01403,0.07297,0.00324,-0.055,0.08961,0.09651,0.08557,0.0069,-0.03083,0.04808,0.02108,-0.04694,0.05317,-0.02181,0.12554,-0.05093,-0.17047,-0.11543,0.01914,0.07319,0.05208,0.02795,-0.01805,0.12468,-0.01242,-0.03378,-0.03456,-0.1036,-0.06093,-0.04187,0.1616,-0.02935,0.00605,-0.05657,0.05715,6e-05,0.02928,-0.09341,-0.00205,-0.10709,-0.03508,-0.18577,-0.05251,0.02898,0.03714,0.01766,-0.06704,-0.02366,-0.04367,-0.0164,0.16081,-0.02356,-0.09226,0.0761,-0.01281,0.09776,-0.02871,-0.00035,0.04343,-0.08366,0.05005,-0.02191,0.07536,0.05378,-0.05029,-0.06549,-0.01239,0.03927,0.02023,0.01325,0.08842,-0.06679,-0.00621,0.07508,0.03988,0.03339,0.03086,-0.01831,-0.00745,0.01991,-0.03199,-0.04441,0.02241,0.01217,0.01621,0.09721,0.07669,0.06511,-0.00442,-0.00503,-0.08222,0.01067,0.09679,-0.03436,0.0185]},{"domain":"classical_physics","key":"net_force_friction","name":"Net force with an opposing friction force","package":"classical-physics-ai999x","example":"A student pushes a desk with an applied force of 22.9 N. The friction force is 5.39 N. What is the net force?","v":[0.07966,-0.03353,0.0267,-0.09548,-0.01736,0.00099,0.00704,-0.0826,-0.08621,0.07254,-0.05262,-0.05638,-0.00348,-0.04268,-0.02292,-0.11404,-0.03394,0.02632,0.0371,0.00528,-0.07322,0.03423,0.05958,-0.0027,-0.12136,-0.03632,-0.02101,-0.03116,-0.03522,-0.07203,0.08211,0.06676,0.06059,-0.02542,-0.11388,0.00992,0.12717,-0.17665,-0.05522,0.03785,0.05362,-0.06492,0.05459,0.01019,0.00592,-0.00458,-0.04567,-0.01558,0.05648,0.04565,-0.01159,-0.01508,-0.081,0.04502,0.00922,-0.04336,-0.10841,-0.01522,0.12133,-0.02094,0.02725,0.05198,-0.03127,-0.03935,0.05583,0.01616,-0.00195,0.0407,-0.02481,0.01012,0.00359,-0.01885,-0.05628,-0.05861,-0.04175,0.05941,-0.03382,-0.05812,-0.03269,-0.05872,-0.09129,-0.08755,0.0499,-0.00796,0.02264,0.03436,0.04071,-0.04854,0.01185,-0.01571,-0.14046,0.05326,0.03084,-0.01377,-0.08604,-0.02034,-0.00718,0.04215,0.07859,-0.07495,-0.00991,0.00938,-0.00691,0.04037,0.01189,0.09178,0.03253,-0.10987,0.12222,-0.08572,0.03869,-0.03832,0.02933,-0.0289,0.03133,-0.05919,0.11845,0.01676,0.04095,0.05213,-0.03666,0.09498,0.0348,-0.06877,-0.0046,0.01883,-0.03726,0.16271,0.03819,-0.0469,-0.0005,-0.01778,-0.09576,0.00985,-0.1866,0.02019,0.0252,-0.0115,0.02499,-0.0169,-0.05599,-0.04166,-0.07947,-0.07888,0.05959,0.00605,0.07641,-0.01913,-0.03607,-0.08656,-0.03514,0.05853,-0.13364,0.05838,5e-05,0.01339,0.00856,-0.02152,-0.02286,-0.0475,0.02054,0.00849,-0.04503,0.04495,-0.0349,0.00138,0.09428,-0.05377,0.00563,-0.02636,-0.07599,0.00129,0.07161,0.15433,-0.00275,0.07307,0.13058,-0.0503,0.02531,0.10803,-0.0411,-0.08084,0.0874,-0.01551,-0.01693,0.03982,0.01692,-0.02864,-0.00831,0.06042,0.10996,0.05755,-0.0304,-0.00998,-0.01793,0.07145,-0.02368,0.06497,-0.04286,-0.05941,0.06253,0.04738,0.02025,0.07966,-0.06538,0.04915,0.00674,0.11002,0.12855,0.00903,-0.08348,0.02072,-0.08846,-0.03135,-0.07475,-0.06334,0.04032,0.11497,-0.07273,-0.07421,0.05741,0.06354,0.02733,0.06275,0.05093,0.06968,-0.0034,0.0347,0.04907,0.08566,-0.04756,0.06142,0.01355,0.11692,-0.01499,-0.07633,0.11872,-0.0632,-0.07599,0.06997,-0.11713,-0.06151,-0.11102,0.09685,0.1518,-0.07572,0.04839,-0.05551,0.04876,-0.06667,-0.00621,0.07354,0.00754,0.08503,-0.07429,0.05397]},{"domain":"classical_physics","key":"kinetic_friction","name":"Sliding friction","package":"classical-physics-ai999x","example":"A sled moves over snow. The normal force is 138 N. The friction force is 32 N. What is the coefficient of friction?","v":[0.04075,0.00974,-0.00229,-0.03326,-0.0117,-0.08003,0.00114,0.04214,-0.01569,0.04445,-0.04376,-0.02534,-0.01257,-0.0255,0.01728,-0.09859,-0.03479,-0.05294,-0.02917,0.05811,-0.08211,0.06825,0.05399,-0.01573,-0.04287,-0.0923,0.01438,-0.03072,-0.00974,-0.10614,0.12157,0.07746,0.07632,0.00696,-0.07364,-0.06598,0.16979,-0.17672,-0.01263,-0.04036,-0.00287,0.01545,0.02318,-0.01402,0.06479,0.00699,-0.03476,0.0467,-0.06195,-0.02089,0.01118,0.05389,-0.05236,-0.03201,-0.01957,-0.02994,-0.14568,0.03489,0.03012,-0.05944,0.03919,0.05843,-0.1184,-0.09756,0.09149,0.02195,0.03675,0.0459,0.05466,0.07303,-0.04713,-0.10294,0.01263,0.05047,0.03098,0.03414,-0.06491,-0.00925,-0.00701,-0.07815,0.00683,-0.01129,-0.03518,-0.01357,0.09771,0.07528,-0.04744,-0.05017,0.10559,0.00986,-0.0911,-0.05882,0.01477,-0.09443,0.01196,0.02035,0.0324,0.01231,0.04447,-0.076,-0.00608,0.01762,-0.03219,0.10242,0.0033,-0.04413,0.11013,0.01705,0.16123,-0.08368,0.00661,0.00208,0.01573,-0.10694,0.04158,-0.04343,0.1523,-0.07331,0.03429,0.02591,-0.04327,0.05238,0.06823,-0.07972,-0.06927,-0.04855,-0.09123,0.12262,0.01072,0.04737,0.02973,0.03538,-0.06418,-0.06658,-0.07836,0.0977,0.11591,0.0183,-0.09794,0.03012,0.0117,-0.04415,-0.04698,0.00331,-0.01775,-0.01243,0.07381,0.06487,-0.11062,-0.07138,0.02351,-0.0053,-0.1098,0.08776,-0.06699,-0.04601,0.01707,-0.08398,-0.00801,-0.06427,0.01554,0.06251,0.03609,0.01258,0.11819,-0.00648,-0.0053,-0.01877,0.00161,-0.04258,0.00643,0.08337,0.00662,0.13015,-0.08958,-0.00184,0.04729,-0.04494,-0.00104,0.01569,0.01261,-0.04034,-0.00017,-0.02743,-0.0143,0.02347,-0.04724,0.0058,0.02504,0.19493,0.14581,0.01301,0.04164,-0.03332,-0.01645,-0.02829,0.07429,-0.02697,0.0005,0.03202,0.09832,0.06858,0.08747,-0.0491,0.04296,0.03205,-0.00775,0.11999,0.17637,-0.01286,0.02193,0.02576,-0.08316,-0.10826,-0.10464,-0.03891,-0.00335,0.12425,-0.0293,-0.01608,-0.10102,-0.06583,0.01175,0.08077,-0.00027,0.06634,0.0297,0.0361,-0.02394,0.00132,-0.11538,0.03095,-0.03172,0.05874,0.07363,-0.00301,0.07983,0.00505,-0.08876,0.07113,-0.08766,-0.00443,-0.03651,0.00958,0.05586,-0.02012,0.0288,-0.06059,0.03015,-0.06562,-0.01535,0.02675,0.01535,0.11632,-0.02492,0.00618]},{"domain":"classical_physics","key":"normal_on_level","name":"Normal force on a level surface","package":"classical-physics-ai999x","example":"A bag lies on a desk. The weight is 108 N. What is the normal force?","v":[-0.00573,-0.02519,0.01037,-0.14205,0.00379,0.05145,-0.03805,-0.01693,-0.02248,0.03997,-0.02027,0.03212,-0.00489,0.03204,0.01543,-0.08534,-0.02991,0.02099,-0.03252,0.01426,-0.06447,-0.04522,0.00177,0.08151,-0.07936,0.00557,-0.01978,0.08837,-0.0221,-0.15175,0.14992,0.09165,0.14267,0.07303,-0.02263,-0.03103,0.09779,-0.02066,0.04262,0.00171,0.05943,-0.03162,0.01224,0.04068,0.03275,0.04094,-0.0678,-0.02918,-0.05471,0.07425,-0.05853,-0.08746,-0.02345,0.00657,0.0218,-0.14989,-0.11026,0.04297,0.01144,0.01062,-0.02933,0.07026,-0.07503,-0.05371,0.05027,0.06599,0.02005,-0.00362,0.08489,0.07314,-0.05378,-0.07704,0.06407,-0.01237,-0.02427,-0.07118,-0.09972,-0.04576,-0.02149,-0.01013,-0.07248,-0.03769,-0.04309,-0.03934,-0.03009,0.06739,-0.01588,-0.02517,0.06343,0.00208,0.01143,-0.02023,-0.0149,-0.04013,0.03053,0.06633,0.09643,0.03319,-0.01747,-0.06445,-0.04995,-0.02546,-0.0708,-0.02972,0.01975,-0.0925,0.12056,-0.05373,0.12331,-0.15481,-0.11452,-0.01911,0.02109,-0.11416,0.01886,-0.06337,0.18417,-0.01247,0.04242,0.03384,-0.05818,0.06975,0.01888,-0.2011,0.00097,-0.01966,-0.04431,0.06759,0.04457,-0.01782,0.01967,0.04834,-0.00261,-0.01571,0.00467,0.01318,-0.01396,0.03243,-0.0546,0.04072,0.03234,0.04268,-0.04803,-0.02111,-0.03329,-0.01438,0.12939,0.07579,-0.03168,-0.11099,0.07907,0.07875,-0.05951,0.17384,-0.02124,-0.0718,0.04137,-0.08812,0.00234,-0.06365,0.04461,0.08214,0.03737,-0.02274,0.04907,0.05737,0.00143,-0.00873,-0.06657,-0.10202,-0.02387,-0.03423,-0.06165,0.14645,-0.02336,0.07153,-0.00381,-0.07642,-0.09083,0.02864,0.02596,-0.02783,-0.01146,-0.03092,0.06069,-0.02413,-0.06408,-0.01174,-0.12377,0.00201,0.14631,0.03701,-0.03041,-0.00765,-0.06152,0.02619,0.00642,0.03352,-0.04614,0.05478,0.02657,-0.00148,-0.07614,-0.08752,0.07496,0.06067,0.03558,0.09893,0.02808,0.03759,-0.01025,0.08086,-0.08299,-0.09316,-0.01116,0.00654,0.12326,0.05603,-0.03931,-0.01697,0.00999,0.01058,-0.06397,0.07004,0.10824,0.05819,-0.00476,-0.04032,-0.02464,0.0345,-0.09615,0.11802,0.03294,0.11638,0.00323,0.04514,0.08346,-0.02883,-0.03751,-0.01417,-0.06728,-0.01138,-0.05203,0.00223,0.01894,-0.06248,0.03904,0.05358,0.03025,0.03558,0.08028,0.00578,-0.00996,0.13521,-0.03283,-0.01666]},{"domain":"classical_physics","key":"momentum","name":"Linear momentum","package":"classical-physics-ai999x","example":"A puck has a mass of 1.07 kg and a momentum of 9.87 kg*m/s. What is the velocity?","v":[-0.06034,0.03921,-0.00369,-0.05828,0.03454,-0.11966,0.11801,0.01473,-0.05114,0.09168,-0.04761,-0.01446,0.0751,-0.04387,-0.00695,-0.00493,-0.06372,-0.04168,-0.00241,0.07329,0.09185,0.02629,-0.00724,0.04156,-0.03796,0.02108,0.07465,-0.05932,0.01617,-0.01202,0.0161,0.01063,-0.04523,0.0337,-0.13556,-0.00677,-0.04309,-0.04916,-0.00362,-0.04631,-0.05941,-0.13487,0.0528,0.0765,-0.0452,0.05311,-0.01309,0.03552,0.03381,-0.07345,-0.03844,0.00276,-0.0992,-0.00567,0.11734,0.04593,-0.02101,-0.05149,0.01758,-0.00595,-0.0827,-0.05572,-0.05117,-0.01534,-0.00927,0.00983,0.08067,-0.06465,0.01134,0.10423,-0.01289,-0.03826,-0.03057,-0.03175,0.13386,0.07749,0.17965,-0.09351,-0.01121,-0.10031,-0.09083,-0.06547,0.05061,-0.03209,0.03875,-0.02597,0.00577,-0.01907,-0.06663,0.00959,0.00232,-0.03649,-0.12743,-0.11122,0.02427,-0.00241,0.08528,0.03483,0.09452,-0.02091,-0.00042,0.03695,-0.05178,-0.07627,-0.0122,0.0338,0.07615,-0.00718,-0.02503,0.08742,-0.01851,0.01672,0.05273,-0.03494,-0.06705,0.00982,0.00768,0.08275,0.02641,-0.02264,-0.04964,0.01785,-0.00987,0.13697,0.00501,-0.10928,0.02141,-0.0244,0.0921,0.07834,0.01684,0.05583,0.13544,-0.02336,0.05139,-0.07271,-0.00333,0.05959,0.03621,-0.017,0.07145,0.03812,0.13207,-0.06432,-0.03648,-0.00387,-0.04838,0.01246,-0.04342,-0.02544,-0.06004,0.05185,-0.10848,-0.08378,0.01005,0.0257,-0.03519,0.03712,-0.01074,0.0078,0.03066,-0.00701,0.09145,-0.09155,-0.00155,0.02086,-0.0268,-0.14026,-0.05356,-0.0375,-0.12935,0.01634,-0.0314,-0.0381,-0.01183,0.06974,0.0338,-0.08851,0.00035,0.00149,0.20424,-0.01725,0.12544,0.05087,-0.0229,0.00188,-0.02488,-0.12186,-0.01167,-0.0423,-0.05552,0.10141,-0.09911,-0.03609,0.0087,0.02836,-0.03416,0.01797,0.1012,0.02316,-0.08417,-0.07307,0.00334,0.00588,-0.0069,0.11214,0.0347,0.05019,0.09316,0.08426,-0.01482,0.06059,0.06202,-0.12033,0.02906,-0.09662,-0.02926,0.13333,-0.00078,-0.04463,0.00602,-0.05384,-0.03654,0.12273,-0.01455,0.04421,-0.03207,0.04282,0.01733,-0.00739,0.01617,0.14697,0.05421,0.00525,0.02632,-0.09574,0.03457,-0.05435,-0.07044,-0.03083,0.00412,0.05294,-0.00063,0.07289,0.09535,-0.08033,0.12837,0.05164,0.02959,0.08002,-0.0906,-0.02431,0.03844,-0.03893,-0.09045,0.01287]},{"domain":"classical_physics","key":"impulse","name":"Impulse of a constant force","package":"classical-physics-ai999x","example":"You apply a force of 6.85 N to a toy car for 2.55 s. Calculate the impulse.","v":[0.10167,0.05142,-0.01377,-0.06845,-0.06975,-0.03273,0.08053,-0.11011,-0.02388,0.06599,-0.04385,-0.01707,0.01838,-0.01092,-0.02606,-0.05024,-0.12659,0.07822,0.00525,0.10328,-0.02255,0.01418,-0.03613,0.07141,0.02234,0.08083,0.03108,0.09747,0.02952,-0.03482,0.11914,0.05155,-0.03277,0.0605,-0.06792,0.07574,-0.05459,-0.00908,-0.00781,0.00237,0.04461,-0.10017,-0.00224,0.05654,0.02043,-0.04267,0.00325,-0.03529,0.11914,0.07772,-0.06617,-0.0582,-0.17453,0.03527,0.01742,0.05631,-0.0675,0.03366,-0.04956,-0.04278,-0.0528,0.1014,-0.13079,-0.00571,-0.04542,-0.04792,0.07443,0.02281,0.00598,-0.03052,-0.00084,-0.09004,-0.08617,-0.12408,0.0382,0.05757,-0.05502,-0.04085,-0.06408,-0.10653,-0.09229,-0.0302,0.02648,0.05856,0.02418,-0.00046,-0.05532,-0.14045,-0.07651,-0.03291,-0.09124,-0.02094,0.00593,-0.06895,-0.04274,-0.07206,0.01173,-0.01824,0.09991,0.00371,0.02396,0.11451,0.05294,-0.04888,-0.0299,0.12856,-0.03608,-0.06699,0.06351,-0.09706,-0.03822,-0.02537,0.05906,-0.01198,-0.00224,0.0087,0.014,0.04513,0.02228,0.02775,-0.19457,0.00299,0.07639,-0.01382,-0.06105,0.05445,-0.06508,0.05887,0.11249,0.07299,-0.06905,-0.0441,0.00544,0.02683,-0.05276,0.02178,0.08263,0.09926,0.01646,0.05587,0.06895,0.07517,-0.00921,-0.05505,-0.03158,-0.00915,-0.04546,-0.02499,0.05507,-0.01529,0.05288,-0.0468,-0.13055,-0.05835,-0.06337,0.02792,0.05357,0.04042,-0.00523,0.00077,0.02449,0.03895,0.04807,0.10859,-0.12223,0.04662,0.10576,-0.02614,-0.05426,0.07085,-0.01282,0.01501,-0.00401,0.10687,-0.02648,-0.02833,0.03683,0.06339,0.08959,0.07559,0.02699,-0.06224,0.04874,-0.11799,-0.04889,0.02616,0.01068,-0.0582,-0.05339,-0.01201,-0.02263,-0.00467,-0.00352,-0.05909,-0.03986,0.10972,-0.03084,-0.05409,-0.02437,0.10209,-0.0286,0.01389,0.06162,-0.02737,-0.08728,0.1324,-0.01838,0.08052,0.02818,0.11062,-0.10149,0.00878,-0.01176,-0.04081,0.02538,-0.07538,0.12127,0.03288,0.0088,-0.0346,0.0129,0.03125,-0.0071,0.00883,0.00353,0.03413,0.09566,0.00617,0.05263,0.00753,-0.06997,0.01675,-0.02065,0.02978,-0.02189,-0.00066,-0.08472,-0.05084,-0.01026,0.06965,-0.10636,0.0278,-0.06514,0.04283,0.16269,-0.09746,0.04992,0.07622,0.0407,-0.01051,0.015,0.00052,-0.05087,0.01067,-0.1297,0.07651]},{"domain":"classical_physics","key":"work","name":"Work by a constant force","package":"classical-physics-ai999x","example":"A lawn mower is pushed with a force of 13.1 N. The handle makes an angle of 110 deg with the horizontal displacement of 209 cm. How much work is done?","v":[0.15013,-0.00945,0.02352,-0.03228,-0.0247,0.13696,0.00843,-0.15242,-0.05439,-0.04373,-0.09881,-0.04342,0.04493,-0.00834,0.01818,-0.01505,-0.12404,0.02609,-0.02761,0.00814,-0.10836,0.14071,0.06512,0.0287,-0.09881,0.02246,-0.01971,0.11744,-0.06833,-0.03734,0.09855,0.03221,-0.01359,0.04496,-0.04033,0.03642,-0.09286,-0.03757,-0.04474,0.00032,-0.08895,-0.03703,0.03215,0.01291,0.03016,-0.06793,-0.02607,-0.03249,0.05207,-0.04143,0.04,-0.01446,-0.05014,0.04268,0.04949,0.00918,-0.12309,0.1182,-0.07745,0.00942,0.11403,0.05693,-0.12057,-0.05957,0.06428,-0.00944,0.03739,-0.04967,-0.1733,-0.03062,0.03681,-0.01095,-0.00473,-0.0438,0.00128,0.08119,-0.01819,0.00692,-0.0172,-0.0541,-0.10547,0.03723,0.01693,-0.01353,0.00165,-0.06121,0.02648,-0.06616,0.05297,0.0101,-0.02852,-0.00305,0.09682,-0.04659,-0.07715,-0.04465,-0.02118,0.08667,0.02453,-0.02407,0.05483,-0.02159,-0.0035,-0.0205,-0.02367,0.0965,0.03167,-0.05244,0.03752,-0.07794,-0.03072,-0.00818,0.12177,-0.05312,0.00836,0.09129,-0.0138,-0.10342,0.03241,0.03169,-0.00666,-0.04262,0.05921,-0.10404,-0.00501,-0.03545,0.02222,-0.02227,-0.01059,0.07075,0.00831,-0.00359,0.00665,-0.00516,-0.08926,0.10371,0.07634,-0.00469,-0.00288,-0.12584,-0.02182,-0.11789,-0.1081,-0.03511,0.0548,0.04451,0.0112,0.01278,-0.00549,-0.11557,0.05662,0.00872,-0.16667,0.02828,0.03076,-0.01068,0.06758,-0.04603,0.08697,-0.0202,0.10824,-0.0866,-0.04554,0.07883,-0.1083,-0.03003,0.07433,-0.06533,-0.04049,0.02406,0.05134,0.05487,0.06109,0.17012,-0.03413,0.0185,0.10327,-0.01058,0.05605,-0.04555,0.07244,-0.06745,0.00874,-0.04911,0.04737,-0.04827,-0.03959,-0.05328,-0.03177,0.01588,0.03347,-0.01708,0.01088,0.05021,-0.01352,0.09514,-0.04654,0.07585,-0.07487,-0.03413,0.05504,0.11755,0.02165,-0.05316,0.01938,0.04669,-0.04446,0.07839,0.09435,0.00431,-0.03004,-0.02403,-0.06668,0.04528,0.07881,-0.0493,0.0868,-0.03745,-0.02004,-0.08882,0.04201,-0.05768,0.04671,0.0461,0.03815,0.04848,0.10539,0.09224,0.09872,0.07353,-0.08772,0.12182,0.03426,0.07498,-0.08423,-0.05484,0.06755,-0.02644,-0.08112,-0.03405,-0.1071,0.00134,0.04049,0.06346,-0.01214,0.00017,-0.03025,0.06541,0.03218,-0.10079,0.03718,0.03201,-0.00875,0.01261,-0.03186,0.04757]},{"domain":"classical_physics","key":"kinetic_energy","name":"Translational kinetic energy","package":"classical-physics-ai999x","example":"A toy car has a mass of 550 g. Its kinetic energy is 2.8 J. What is its speed?","v":[0.08348,-0.02873,0.05381,-0.07553,0.06232,-0.0883,0.05541,-0.08485,-0.05677,-0.0042,-0.02425,-0.06547,0.03324,-0.08446,0.06254,-0.09067,-0.07074,-0.07419,-0.06838,0.02088,0.02584,0.17375,0.06264,-0.01023,-0.11722,0.0936,0.17143,-0.03009,-0.02062,-0.0101,-0.01915,-0.04714,-0.08838,0.06353,-0.02337,-0.03178,-0.03384,-0.02236,0.01666,-0.11609,-0.08329,-0.03515,-0.02167,0.03812,-0.04986,0.08491,-0.07552,0.08452,0.08571,-0.01572,0.04572,-0.0673,-0.09988,-0.0451,0.12728,0.01629,0.06408,-0.0522,-0.01063,0.01334,-0.01025,-0.14089,-0.03496,-0.01199,-0.00833,0.05327,-0.04041,-0.01683,0.02828,0.15236,-0.02804,-0.07218,-0.02699,-0.08651,0.07572,0.07123,0.09251,-0.02404,0.01187,-0.05962,-0.02351,-0.00423,0.00241,0.07559,-0.04888,-0.04109,0.04753,-0.09995,-0.0191,-0.01979,-0.02771,-0.05525,-0.00204,-0.05231,-0.03071,0.06424,-0.03374,-0.01039,0.11613,0.02392,-0.01424,0.05217,-0.07463,0.00353,-0.15527,0.00463,0.12137,0.0465,-0.04947,0.00502,0.05311,0.05634,0.09322,-0.10904,-0.0429,-0.04288,0.05189,-0.05939,0.02951,0.04761,-0.06559,-0.02926,0.03003,0.01702,0.04821,0.00796,0.04516,-0.05092,-0.03873,0.01729,0.0213,-0.02815,0.07303,0.05832,0.07126,-0.0362,0.02242,0.11676,0.02113,0.04689,-0.02591,0.03385,0.04885,0.04933,-0.02498,0.0583,-0.08803,0.04834,-0.01588,-0.05073,-0.0347,0.06886,-0.07999,-0.13731,-0.0345,0.02962,0.01439,-0.01759,-0.03699,-0.12074,0.07028,0.0258,-0.02221,-0.00294,-0.03887,0.0664,-0.09673,-0.13069,-0.00751,0.08159,-0.10408,-0.00712,0.08207,0.06109,-0.06346,-0.05187,0.00465,-0.02578,0.00243,-0.06486,0.14585,0.01159,0.01998,-0.01163,-0.04259,-0.02326,-0.03414,-0.08651,0.02626,0.0836,-0.03534,0.01654,-0.03069,0.08387,0.01765,-0.00327,0.02688,0.11338,0.07482,0.0696,-0.02183,-0.03552,0.04899,-0.07846,-0.01876,-0.04738,0.03202,-0.02909,0.04552,-0.02722,0.00522,0.03135,-0.03853,-0.06404,0.0763,-0.01633,0.02747,0.00018,0.06157,-0.0443,-0.07235,-0.08387,-0.03096,0.0989,-0.05194,0.08056,-0.02374,0.036,0.01316,0.00803,0.01726,0.1971,0.02849,0.09723,0.01837,-0.11133,0.02075,-0.03798,-0.06095,-0.01929,-0.00935,-0.03534,0.11133,0.07875,-0.00964,0.01021,0.09182,0.00375,0.11773,0.04629,-0.08736,0.04179,-0.08932,-0.04858,-0.07288,0.05092]},{"domain":"classical_physics","key":"gravitational_pe","name":"Gravitational potential energy near the surface","package":"classical-physics-ai999x","example":"A crate with a mass of 4.59 kg is raised to 10.9 m. Its potential energy is 0.66 kJ. What is the gravitational acceleration?","v":[0.01925,0.03142,0.0361,0.02262,0.02306,0.10534,0.08186,-0.10657,-0.04752,0.01658,-0.06933,0.02898,-0.02348,-0.00773,-0.06085,-0.09957,0.00062,0.06464,0.00091,0.03688,0.03818,0.04226,0.04614,0.03478,-0.08834,0.08268,0.0822,0.02239,-0.06713,-0.04063,-0.12158,0.04783,-0.05852,0.04236,-0.01542,0.05336,0.00494,0.0664,0.03911,-0.11603,-0.03413,0.04702,-0.11148,0.08982,-0.01566,0.17254,-0.06984,0.01835,0.07247,0.05851,-0.01698,0.02124,0.07705,0.00279,-0.05405,-0.02255,-0.04311,-0.03299,-0.14922,0.05625,-0.02703,-0.07297,0.03789,-0.03556,0.04712,0.06275,-0.00538,-0.0086,-0.00241,0.09502,0.13403,-0.00519,0.0485,-0.06831,-0.01522,0.19849,-0.01972,-0.01947,-0.08794,-0.00092,-0.1063,0.06209,-0.03707,-0.06831,-0.09794,-0.00089,0.09265,-0.09679,-5e-05,0.05579,-0.00784,0.10407,0.01861,0.05671,-0.11401,0.14107,0.06527,0.02446,0.05104,0.01276,0.0801,-0.08634,-0.00976,0.09151,-0.05606,-0.04743,0.0896,-0.02244,-0.13393,-0.00818,0.01373,0.0609,-0.01802,-0.01042,0.05418,-0.03233,0.0115,-0.07585,0.01295,-0.04912,-0.02283,-0.04989,-0.01623,-0.06289,0.04415,-0.04456,-0.00052,0.01526,0.02344,0.07682,0.10568,0.02224,0.10766,-0.04216,0.06458,0.09395,0.07564,0.03508,0.0691,-0.08449,0.00882,-0.0701,0.02983,-0.02284,0.0607,-0.14115,0.0209,-0.01847,0.12252,0.03125,-0.06798,-0.02581,0.02954,-0.0405,-0.0837,0.07647,0.02506,-0.08949,-0.03563,-0.07367,-0.03439,0.03152,0.12296,0.03677,-0.02785,0.05147,0.01289,0.0777,-0.01274,0.01515,-0.01511,0.03814,0.05898,-0.05016,0.02655,0.01023,-0.12156,-0.05759,0.05168,-0.00739,0.02621,-0.03132,0.00454,0.0363,0.0819,-0.06662,-0.04806,-0.12117,-0.07807,-0.06745,0.00764,0.08222,0.04159,0.07057,0.03508,-0.04967,-0.08969,0.05066,-0.05483,-0.04326,-0.06333,-0.00632,-0.11498,-0.03575,0.00906,-0.14906,0.00191,-0.10051,0.0493,-0.03065,-0.02156,0.06568,-0.03008,-0.0506,0.01481,0.00049,0.09124,-0.07615,0.07443,-0.0462,-0.03013,-0.01577,0.03289,0.09939,-0.07981,-0.01944,-0.05493,0.02179,-0.02551,-0.03702,-0.00442,0.12048,-0.02458,-0.01466,0.03906,0.02704,-0.00529,-0.01324,-0.03129,0.02122,-3e-05,-0.01907,0.06332,0.05152,-0.07688,-0.0586,0.03227,-0.00089,0.11851,-0.04005,-0.07138,-0.0887,0.01359,-0.01647,0.05116,0.10554]},{"domain":"classical_physics","key":"spring_force","name":"Force of a linear spring","package":"classical-physics-ai999x","example":"A door stopper uses a spring that pushes back with 3.98 N when compressed by 2.47 cm. What is the spring constant?","v":[0.02296,-0.02035,0.06093,-0.18128,-0.00564,0.10687,-0.0271,-0.00054,-0.05758,0.02658,-0.09186,-0.04866,0.10044,-0.03778,0.08083,-0.04913,-0.04475,0.02424,-0.01108,0.00155,-0.09339,0.0117,0.01717,0.03898,0.02984,0.06469,0.03519,0.05496,0.05607,-0.15931,0.11231,0.0431,0.0231,0.00673,-0.03593,0.00936,0.03077,0.01079,-0.11037,0.07015,-0.00021,-0.0716,0.00993,0.10301,0.0958,0.06996,-0.04953,0.00413,0.0616,0.04989,-0.00585,-0.02571,0.00313,-0.03119,0.00437,-0.03653,-0.11845,0.00384,0.03399,0.13109,0.0266,0.02176,-0.104,-0.04216,-0.08433,-0.04808,-0.03097,0.06284,-0.04845,0.00857,0.10585,-0.04559,-0.06062,-0.08141,-0.12295,0.08284,-0.10506,-0.04682,0.03272,0.01009,-0.02642,0.00235,0.0338,-0.01936,-0.04717,-0.01876,0.00364,0.01433,-0.01946,-0.00975,-0.04955,0.06245,0.10115,-0.00492,-0.01607,-0.06744,-0.0533,-0.04516,0.06398,-0.00449,0.05602,0.03626,0.01476,0.03049,-0.0235,0.08643,0.14489,-0.05029,0.04194,-0.04413,-0.02264,-0.04426,-0.02557,-0.03865,-0.02195,-0.04029,0.06309,0.01897,0.03433,-0.05508,-0.06328,0.04168,0.00461,-0.08635,-0.02231,-0.05656,0.04268,0.03195,0.04681,-0.00932,-0.09018,0.01247,0.03208,0.04176,-0.01236,0.07364,0.00629,-0.00419,0.07293,-0.05377,-0.0428,-0.08229,-0.03853,-0.11231,0.03743,0.07079,0.05772,-0.041,-0.02922,-0.06729,-0.04794,0.02663,0.01043,-0.03217,0.00441,-0.06619,0.08609,-0.01218,-0.0312,-0.05325,0.00058,0.03433,0.01017,0.07327,-0.09792,-0.05987,0.12529,-0.15324,-0.10801,0.13014,-0.10747,-0.09608,-0.00402,0.19143,0.01874,-0.05837,-0.0396,0.01567,0.07188,-0.01644,-0.01846,-0.06856,0.03828,-0.0288,0.01145,0.04327,0.05496,-0.02333,-0.10709,-0.04525,-0.00099,0.02887,-0.0702,0.01605,-0.04235,0.00876,-0.02278,0.08796,-0.19372,0.09099,0.13409,0.12599,-0.06794,-0.05558,0.00205,0.02104,-0.00237,0.11224,0.04613,0.05902,-0.0149,-0.02138,0.01162,0.01255,0.02259,-0.05622,0.06637,0.14138,-0.04953,0.01434,-0.01507,0.03779,0.00044,0.09527,0.10055,0.05109,0.0839,-0.00479,-0.00795,0.01303,-0.04568,-0.00215,-0.01171,0.02839,-0.1757,-0.02062,0.0813,0.02095,-0.07005,0.0148,-0.11409,-0.04928,-0.059,-0.00836,0.04254,-0.06123,0.0113,-0.00128,0.01985,0.05777,0.03607,0.11176,-0.00587,0.05972,-0.08069,0.01683]},{"domain":"classical_physics","key":"spring_energy","name":"Energy stored in a linear spring","package":"classical-physics-ai999x","example":"A toy spring is stretched by 0.0912 m and stores 2.3 J of energy. What is the spring constant?","v":[0.05844,-0.04005,0.02277,-0.15458,-0.03366,0.11618,0.00164,0.0096,-0.05,0.02106,-0.08895,-0.05231,0.06379,0.00981,0.03834,-0.01751,-0.01038,-0.02558,-0.07029,-0.01975,-0.05285,0.0392,-0.04342,0.0526,-0.05694,0.13003,0.13971,0.08473,0.05601,-0.09894,0.04945,0.03143,-0.02042,0.07644,-0.03767,0.00457,0.00741,-0.00983,-0.03144,-0.07896,-0.06043,-0.00755,-0.02675,0.08735,0.03709,0.08808,-0.07766,-0.02098,0.0683,0.0389,0.00158,-0.00654,-0.02988,-0.04845,-0.03361,-0.0537,-0.08396,-0.00974,-0.10992,0.09735,0.00561,-0.02249,-0.05884,-0.04797,-0.06845,0.0197,-0.11767,-0.01745,-0.05804,-0.01997,0.07313,-0.03555,-0.02163,-0.04076,-0.0895,0.16287,-0.01184,-0.00555,-0.00139,0.01861,-0.05643,0.06193,-0.01602,-0.03794,-0.03826,-0.12454,0.03605,0.01533,-0.02789,0.02578,0.00444,0.10957,0.0846,0.05274,-0.10246,0.02353,-0.03362,-0.05708,0.04708,0.02501,0.03173,0.06009,0.02571,0.08224,-0.11202,-0.02465,0.1212,-0.04204,-0.10321,-0.01549,0.04295,-0.03056,-0.02246,-0.03061,-0.00612,-0.05772,-0.02233,-0.05105,0.07444,-0.01428,-0.05233,-0.02548,0.04625,-0.01622,-0.04459,-0.11248,0.04775,0.0112,-0.01403,0.09646,0.01002,0.01163,0.14241,0.05458,0.08935,0.1254,0.04336,0.02736,0.06633,-0.04076,-0.00459,-0.10508,-0.01368,-0.04532,0.05168,0.10922,-0.00631,-0.02554,0.07105,-0.05762,-0.08238,0.02443,0.10429,-0.10816,-0.04087,-0.04661,0.05337,-0.09108,0.03175,-0.11253,-0.02784,0.01797,0.06289,0.18195,0.03666,-0.05522,0.02668,-0.04423,-0.10288,0.16809,-0.04872,-0.03605,0.07724,0.03832,-0.0096,-0.09717,-0.04851,-0.07091,0.14664,-0.1007,-0.00121,-0.09176,0.02093,0.00301,0.02634,0.03868,0.03809,-0.04257,-0.05628,-0.03985,-0.00974,-0.03052,0.0528,0.08903,-0.006,-0.05934,-0.0223,0.06118,-0.08898,0.0261,0.13494,0.10294,-0.02002,-0.08541,0.02279,-0.07817,0.01599,0.00531,0.02962,-0.00663,0.08391,-0.00595,-0.03629,0.05218,0.03958,-0.02993,0.02666,-0.04381,-0.04492,-0.0332,-0.02312,0.00072,-0.02638,0.17232,0.05882,0.03143,0.08292,0.01146,-0.01446,-0.03422,-0.06177,0.0018,0.04851,0.07252,-0.12678,-0.02308,0.01993,0.07902,-0.10653,-0.02994,-0.07608,-0.01374,0.06879,0.01668,-0.042,-0.09485,0.01896,-0.00521,0.06039,0.01461,0.02341,0.01283,-0.04301,0.00548,-0.03479,0.05686]},{"domain":"classical_physics","key":"power_energy","name":"Average power","package":"classical-physics-ai999x","example":"A large fan transfers 1470 J of energy in 17 s. What is the average power?","v":[0.02128,-0.08933,0.01386,-0.03458,0.05449,0.05094,0.05086,-0.07437,-0.0414,0.02494,-0.01856,-0.08106,0.04617,-0.04911,0.00715,-0.02877,-0.03173,-0.06009,-0.03844,0.04433,-0.07305,0.07803,-0.00499,-0.03248,-0.02334,0.06961,0.06095,-0.01335,-0.03584,0.12855,0.08735,0.01542,-0.05653,0.09646,-0.01601,0.00938,0.01893,-0.09686,0.02823,-0.01166,-0.13517,0.01756,-0.06388,-0.00703,0.00594,0.01052,-0.03245,-0.06522,0.06256,-0.04315,-0.00771,-0.02551,-0.07205,0.05628,0.00747,-0.10876,0.09067,0.00056,-0.07236,-0.06092,0.10029,-0.02485,-0.06261,0.03031,0.02851,-0.00677,-0.12258,-0.04081,0.10709,-0.00746,0.06022,0.03709,-0.14022,-0.07148,0.02517,0.10557,0.04958,0.11685,-0.04475,-0.00978,-0.12166,-0.0564,0.02008,0.02685,-0.05796,-0.15801,0.07321,-0.18134,0.01309,-0.12748,0.0211,-0.03523,-0.05967,8e-05,-0.10931,-0.00632,0.11946,0.10277,0.02074,0.05886,0.02031,0.0971,0.04279,-0.03801,-0.08077,0.06465,0.04804,-0.04027,0.10059,0.01836,0.00428,0.01555,0.03236,-0.03703,0.00876,0.01939,-0.04361,-0.03206,0.03368,0.0068,-0.02461,-0.03315,-0.00207,-0.04075,-0.05823,-0.07868,0.00695,-0.01813,-0.04688,0.10794,0.03637,-0.0539,0.00935,0.01072,-0.01943,0.01003,0.09016,0.00495,-0.05177,0.02673,0.04542,0.00181,0.05712,-0.07052,-0.00851,0.1471,-0.11981,0.00817,-0.01264,0.05922,-0.02641,0.05473,-0.03393,-0.03895,0.00647,0.0545,0.0123,-0.0995,0.10121,0.02389,0.1072,0.04299,0.0271,0.12176,-0.06199,0.04769,-0.01681,0.10264,-0.00991,-0.02952,0.02645,-0.0218,-0.04611,0.08968,-0.0845,-0.02134,0.06047,0.03972,0.04707,0.02114,-0.00849,-0.03288,0.02137,-0.03781,-0.05404,-0.0026,-0.11405,-0.04318,-0.08947,0.01608,-0.06085,-0.06322,0.01482,0.12916,0.01097,0.10366,0.01313,-0.03839,0.0822,0.0181,0.05575,0.03399,0.00285,0.00731,0.03173,0.00136,0.01199,-0.1213,0.05267,-0.04162,0.00226,-0.02935,-0.05173,-0.10298,0.14384,-0.01022,0.00036,-0.11851,0.0708,-0.05542,0.109,0.07628,-0.03146,0.03806,0.02413,-0.17355,0.05935,0.02905,0.10423,0.02836,-0.04237,0.09884,0.0021,0.0989,-0.03312,0.04779,0.01983,-0.14408,0.03217,-0.01409,-0.02194,0.01204,-0.06187,0.05839,-0.0212,-0.04108,0.0733,-0.05492,0.0778,-0.07107,0.05512,-0.00653,0.02147,0.08392,-0.07341,-0.02686]},{"domain":"classical_physics","key":"power_force_speed","name":"Power of a force on a moving body","package":"classical-physics-ai999x","example":"A cart moves at a speed of 2.11 m/s while being pushed by a force along the motion of 94.3 N. What is the power?","v":[-0.02799,-0.10021,0.02698,-0.13187,0.02635,-4e-05,-0.01303,-0.05977,-0.08764,0.00336,-0.12263,-0.05705,0.03617,-0.10733,0.01871,-0.07279,-0.0847,-0.01169,0.04639,-0.00296,-0.04488,0.10022,0.11758,0.00392,-0.09964,0.08292,0.02652,0.03825,-0.04061,0.008,0.13139,-0.01348,-0.01705,0.06738,-0.08647,0.03249,0.04863,-0.09731,-0.00658,0.03587,-0.00324,-0.04532,0.03129,-0.05173,-0.01344,0.02784,-0.00465,-0.03101,0.10197,-0.02268,0.03511,-0.03609,-0.11557,-0.03155,0.0648,-0.07439,-0.03355,0.01049,0.05041,-0.04472,0.10789,-0.04927,-0.05739,-0.10611,-0.02752,-0.00594,0.05279,-0.02292,0.02293,0.01098,-0.0054,-0.00361,-0.11826,-0.10367,-0.00506,0.08491,0.04844,-0.00876,-0.03175,-0.00561,-0.08891,-0.06543,-0.04263,-0.06429,-0.06669,-0.06105,0.04403,-0.10667,0.05131,-0.03942,0.03305,0.02181,-0.0097,-0.02328,-0.05275,0.05357,0.03956,0.16215,0.12948,-0.04697,-0.03048,0.02653,0.01642,-0.08081,-0.08922,0.0393,0.04794,-0.04064,0.04773,0.01982,-0.03636,0.00739,0.08734,-0.02496,-0.01155,-0.0105,-0.00262,-0.00523,0.04278,-0.07853,0.03461,0.04654,-0.01216,0.00735,0.00459,-0.00416,-0.02989,0.07188,-0.02449,-0.00181,0.02768,0.00548,0.02114,-0.00966,-0.04931,0.12075,0.07242,0.0152,-0.04662,-0.03877,-0.0141,0.06993,0.04255,-0.05391,0.04382,0.0083,-0.05423,-0.02977,-0.04841,-0.04673,-0.05429,0.11017,-0.14844,0.0216,0.06999,-0.04322,0.02778,-0.05072,0.06858,-0.01208,0.08553,-0.07307,0.02655,0.05172,-0.06143,0.00499,0.0162,-0.02552,-0.0623,-0.04834,-0.08012,0.003,-0.00498,0.13733,-0.07412,0.04986,0.13606,-0.00501,0.04995,0.05536,0.08058,-0.05811,0.10839,0.0254,0.02489,-0.06803,-0.08239,-0.08425,-0.16742,0.06297,0.04062,-0.04002,-0.08494,0.0383,0.00797,0.13277,-0.0482,0.01897,-0.0034,-0.00832,0.10062,0.02993,-0.0091,-0.02991,-0.02363,0.13999,-0.06415,0.03464,0.12942,0.02251,-0.08073,0.03418,-0.01055,-0.09112,0.16159,-0.00708,0.00321,0.05903,0.00984,-0.00786,0.05402,-0.02856,-0.04874,0.08013,0.02928,-0.00523,0.03982,0.08129,0.11428,0.0799,-0.09238,0.11052,-0.01557,0.09947,-0.05628,-0.04091,0.11784,-0.10701,-0.07672,0.02672,-0.10943,-0.00554,-0.06452,0.04624,0.04624,-0.01942,0.04756,0.02733,0.07936,0.05707,0.02005,-0.02578,-0.04144,0.11107,-0.01981,0.05004]},{"domain":"classical_physics","key":"centripetal_acceleration","name":"Centripetal acceleration","package":"classical-physics-ai999x","example":"What is the centripetal acceleration of a satellite orbiting at 4.81 m/s with an orbital radius of 1.41 m?","v":[-0.03481,0.00756,-0.01783,0.06585,-0.0568,-0.04762,-0.01689,0.00864,0.06403,0.042,-0.03704,-0.07374,0.09078,-0.06507,-0.08363,-0.04003,-0.01176,0.06096,0.04191,0.02667,0.03915,-0.06475,-0.09483,-0.08556,-0.16192,-0.03908,0.10589,-0.05353,-0.0098,-0.07042,0.04384,0.08754,0.02832,0.00293,0.00624,-0.09135,0.06628,0.06868,0.0187,0.09956,0.09949,-0.01961,-0.06191,0.07632,-0.00903,0.16396,0.12693,0.01665,-0.01168,0.03664,0.02734,-0.10141,0.01512,0.05553,-0.07549,-0.04938,0.00531,-0.03528,-0.02058,0.03882,0.10148,0.00411,0.03136,0.03148,-0.0422,0.00291,-0.03842,0.00642,0.00882,0.07995,-0.05314,0.08057,0.05999,-0.02679,-0.06881,-0.03071,-0.0037,0.00979,-0.14062,0.1278,-0.00847,0.09267,0.01357,-0.0275,-0.04125,0.00317,-0.00075,-0.08477,0.00156,-0.12132,0.059,-0.00098,0.03455,0.03051,-0.07225,0.04321,0.00382,0.06023,0.08148,-0.11396,-0.08715,-0.07132,0.17974,-0.02575,-0.01079,-0.0305,0.02071,-0.06735,0.06077,0.0632,-0.09288,0.02889,0.00703,-0.01497,-0.00183,0.09512,0.09471,0.05419,-0.02203,0.02912,0.00487,-0.04542,-0.00457,0.01053,-0.07962,0.06954,0.06065,0.02675,-0.01349,-0.07822,-0.03449,-0.1055,-0.02222,-0.02351,-0.05601,0.09809,-0.08384,0.00131,-0.06959,0.04672,-0.06139,0.07931,0.08005,0.0457,0.1155,0.03254,0.12588,0.00483,-0.16008,0.14788,-0.02866,0.1366,-0.04364,-0.03762,0.03023,0.00712,0.03653,0.03358,-0.06278,-0.06113,-0.0496,0.01812,0.01623,-0.06726,-0.06374,-0.05361,0.00749,-0.02498,0.10242,0.00168,-0.10359,-0.06017,0.03039,-0.00603,-0.01419,0.04262,-0.05767,0.06636,0.02229,0.07713,0.0696,0.01608,0.01717,0.0055,0.07608,0.02043,-0.06902,-0.00471,-0.0786,-0.11972,0.01973,0.04076,-0.03924,-0.04818,-0.03632,-0.07652,-0.0268,0.05422,0.05218,0.06657,0.01897,-0.00329,-0.0089,0.08942,0.00155,0.03118,-0.02311,0.00534,0.08109,0.03216,-0.02711,-0.07192,0.05666,-0.05262,-0.04278,-0.04751,-0.12278,0.01881,-0.02077,0.13552,-0.05622,-0.05349,0.05634,0.12004,0.06921,0.01452,-0.05908,0.11162,-0.00722,0.05954,-0.05473,0.05286,0.01172,0.00799,-0.07457,-0.02865,-0.01478,0.00131,0.02973,0.05482,-0.02074,0.00789,-0.08508,-0.07762,0.00418,-0.04231,-0.09592,-0.04498,-0.04699,-0.00055,-0.08951,0.14521,-0.01657,0.02814,-0.07171,-0.05692]},{"domain":"classical_physics","key":"centripetal_force","name":"Centripetal force","package":"classical-physics-ai999x","example":"If the speed is 6 m/s, the radius of the circle is 3.61 m, and the centripetal force is 8.8 N, what is the mass?","v":[-0.02628,-0.01206,0.04497,-0.02298,0.00558,-0.00628,0.02558,-0.01085,0.04304,0.0367,0.00759,-0.06402,0.09595,-0.09255,0.00761,-0.0798,-0.08925,0.06558,0.0319,0.01965,-0.02117,0.03886,0.07225,-0.08899,-0.15465,-0.01625,0.04707,-0.0888,-0.07478,-0.13929,0.02099,-0.01222,0.01198,0.00826,-0.02825,-0.02252,0.03036,0.02097,0.01547,0.05367,0.06748,0.0299,0.00451,0.07656,0.01811,0.16445,0.04312,0.07257,0.02167,-0.01562,-0.05466,-0.06909,-0.0527,0.03346,0.02347,-0.00362,-0.03737,-0.03419,0.03663,0.07759,0.12437,0.00775,-0.0127,0.0031,0.00088,-0.04523,0.02624,-0.00881,0.0086,0.09631,0.00749,-0.02188,-0.00657,-0.06958,-0.02281,0.02508,-0.0882,-0.01193,-0.04356,0.08033,-0.05204,-0.01725,0.05894,-0.06422,-0.01389,-0.03115,0.01887,-0.05251,-0.01191,-0.06544,0.00434,-0.01789,0.04617,-0.04681,-0.01816,0.03246,-0.01273,0.07828,0.08582,-0.07255,-0.05781,-0.06795,0.04889,-0.05543,-0.04983,0.01776,0.06023,-0.09426,0.0391,-0.02943,-0.13639,0.04972,0.11554,-0.0374,-0.03823,0.04466,0.14705,0.03271,0.0029,0.02322,-0.07637,-0.02224,-0.00808,-0.00383,-0.04766,0.06978,0.05765,0.02652,-0.03422,-0.02606,-0.08736,-0.0185,-0.02947,0.00577,-0.05805,0.09744,-0.01103,0.02102,-0.00614,-0.05215,-0.04864,0.08577,0.12796,-0.00372,0.0928,0.01875,0.10356,-0.05797,-0.07931,0.1058,0.04949,0.12709,-0.09567,0.00749,0.01065,-0.07807,0.03187,0.01992,-0.07267,-0.03018,0.04077,0.06825,-0.00867,-0.10664,-0.05666,0.01842,0.00605,-0.04948,0.00931,0.03552,-0.15604,-0.05051,0.00935,0.04942,-0.01267,0.05688,-0.05662,0.05903,-0.03544,0.08683,0.03883,0.10969,0.08766,-0.01755,0.01626,0.02247,-0.05108,-0.06191,-0.09362,-0.09568,0.0346,0.13659,-0.07811,-0.02838,-0.00654,-0.00498,-0.07545,0.06405,-0.01026,0.07152,0.05045,-0.0098,-0.03134,0.06525,-0.091,0.01454,-0.03625,0.08047,0.02273,0.03552,-0.06209,-0.02687,0.09986,-0.08753,-0.03308,-0.08999,-0.03982,0.08188,0.07506,0.10266,-0.10214,0.03871,-0.01745,0.0474,0.0084,0.05829,-0.00279,0.1377,-0.0091,0.09992,-0.0463,0.10331,-0.07428,0.09024,-0.07533,-0.07095,0.04292,-0.06872,-0.04993,0.07886,-0.14718,-0.05569,-0.05462,-0.05251,0.01884,-0.05565,-0.02707,0.02147,-0.11279,0.08111,-0.11356,0.12405,0.04206,0.10398,-0.13721,0.04643]},{"domain":"classical_physics","key":"tangential_speed","name":"Speed on a circle from angular speed","package":"classical-physics-ai999x","example":"Find the speed of a satellite orbiting at a radius of 0.979 m if its angular velocity is 2.07 rad/s.","v":[0.0279,0.00417,-0.01786,-0.00195,-0.05832,-0.00864,-0.09643,-0.05082,0.0465,-0.03095,-0.03734,-0.05586,0.13211,-0.03902,-0.02389,-0.00254,-0.13845,-0.10754,-0.03369,-0.02208,-0.06552,0.01538,-0.00797,-0.08151,-0.0507,-0.02784,0.19079,-0.04123,0.0334,-0.0579,0.04162,0.05667,-0.02346,-0.03523,-0.05958,-0.07795,0.04927,-0.00774,-0.0798,0.0252,-0.06218,-0.10146,0.03799,0.07269,-0.06104,-0.07086,0.03051,0.08533,-0.04265,-0.1081,0.01262,-0.07813,-0.03203,0.0386,0.02444,0.03209,0.01664,0.0003,-0.08329,0.08128,0.06992,0.00083,-0.07016,-0.08066,-0.06224,-0.05247,-0.00095,-0.03774,-0.01104,0.09772,-0.07219,0.02971,0.00392,0.03008,0.06401,-0.02753,0.02764,0.09477,0.00047,0.1131,0.00223,0.07267,0.09355,0.07591,-0.02131,-0.04244,0.05011,0.02251,-0.03855,0.0331,0.03566,-0.00944,0.00165,-0.05467,-0.06197,-0.00788,-0.03085,0.0054,0.11762,-0.08941,-0.10594,-0.03279,0.07723,-0.11481,0.02039,0.01236,0.03903,0.02431,0.05794,0.0324,-0.00377,-0.00833,0.00532,0.04923,-0.03795,0.11283,-0.02149,-0.02143,0.05611,-0.07346,0.03791,-0.06097,-0.16,0.0154,0.02029,0.04303,0.07279,0.03349,-0.04257,-0.03974,-0.057,0.01054,0.01729,0.04866,-0.02292,0.06032,-0.04184,0.02938,-0.0009,-0.013,-0.10183,0.11165,-0.04878,0.00508,-0.03285,-0.00336,0.00861,0.04227,-0.14712,0.04091,0.09416,0.13303,-0.06175,-0.10761,-0.03059,-0.01546,0.00515,0.02562,-0.03755,-0.04943,0.06414,0.02871,-0.04403,-0.10418,-0.01861,-0.04877,-0.04188,-0.10111,-0.01753,0.0461,-0.0422,-0.01991,0.03782,0.04031,-0.1095,0.04306,-0.00482,0.06508,0.12168,-0.05393,0.11511,-0.0158,0.04868,0.02565,0.04126,0.0258,-0.07179,-0.0528,-0.03093,-0.03866,-0.05843,0.1078,-0.07546,-0.05506,-0.00896,0.02828,-0.0755,0.12598,0.0985,0.1249,0.01149,0.01134,-0.04531,-0.01593,0.02512,0.12215,-0.02256,0.10403,0.07206,-0.00413,0.11176,0.03598,0.04386,0.04459,-0.07535,-0.13583,0.00217,-0.04636,0.02254,0.02561,-0.1224,-0.0734,-0.01203,0.07752,0.04124,0.0689,0.07201,0.12868,0.11602,0.0888,-0.02547,0.13515,0.02005,0.0308,-0.04084,-0.07477,-0.02151,-0.05221,-0.09683,-0.09496,0.02065,0.05017,0.05981,-0.04378,-0.07124,0.04511,-0.03365,0.04376,0.04107,0.05074,-0.04989,0.05939,-0.00932,-0.03935,-0.05167,0.05871]},{"domain":"classical_physics","key":"angular_frequency","name":"Angular frequency and frequency","package":"classical-physics-ai999x","example":"A metronome ticks at a frequency of 0.542 Hz. Find the angular frequency.","v":[0.08791,0.02391,-0.06671,-0.02018,-0.02853,0.00073,-0.09323,-0.04771,0.00917,-0.02315,-0.05447,-0.01847,0.0897,0.02802,-0.04441,-0.03378,-0.04304,-0.04317,0.03706,-0.02226,-0.1145,0.0051,-0.0493,0.00762,-0.0077,-0.08849,0.12823,-0.05076,-0.00626,0.00841,0.01925,0.08746,-0.04278,0.00846,-0.11456,-0.03753,0.02669,0.0133,-0.04915,0.00758,-0.14446,-0.14581,-0.03148,0.06483,-0.01912,-0.05485,-0.07358,0.19583,-0.03205,-0.05196,0.00858,-5e-05,-0.08747,0.01234,-0.0805,-0.00392,-0.07222,-0.06523,-0.21533,0.01716,0.06507,0.00135,-0.07983,0.0647,0.10315,0.00335,0.01647,-0.02744,-0.08964,-0.04596,-0.01571,0.01614,-0.00509,0.02341,0.07925,-0.00406,0.01587,0.01375,-0.01132,0.03635,0.03693,0.021,0.15882,0.05254,0.00939,-0.11253,0.05996,-0.05791,-0.00954,0.03622,0.03927,-0.14056,-0.03051,-0.08846,-0.11491,-0.05037,-0.0685,-0.03583,0.08575,0.0092,-0.09617,0.09688,-0.03519,-0.07818,0.04193,0.04697,0.11992,0.06085,0.03529,0.05343,-0.00885,-0.07655,-0.01923,0.00108,0.01104,0.08757,0.07201,0.00436,0.0184,-0.01772,-0.07217,-0.03905,-0.01809,-0.00991,0.00832,0.02773,-0.01209,-0.10836,0.0418,-0.02446,0.01456,0.04364,0.00062,0.06122,0.00241,0.12166,-0.1022,0.00134,0.07999,0.07656,-0.06087,0.08167,-0.07946,-0.05441,-0.05515,0.00267,-0.00737,-0.01227,0.02144,0.04093,0.16166,-0.02199,-0.1009,-0.04621,0.04467,0.02872,-0.04483,0.07647,-0.00785,-0.01252,0.03491,0.0051,0.04541,0.06189,-0.00034,-0.07794,-0.02328,0.06335,0.00624,-0.03128,0.08308,0.07233,0.13908,0.20278,-0.08188,0.07573,0.00438,0.00617,0.01713,-0.08019,-0.00378,0.02522,-0.04253,0.02389,-0.0084,-0.00827,-0.10153,0.00236,0.04003,-0.01885,0.01556,0.0782,-0.11836,-0.07765,-0.02279,0.04128,0.01564,0.05288,-0.0392,0.00838,-0.01385,-0.00554,0.0102,0.0714,-0.01194,-0.00368,0.00907,0.08763,0.03649,-0.05841,0.08824,-0.00317,-0.03045,0.07119,-0.07843,-0.0217,0.01572,-0.02701,0.07388,-0.14364,-0.08177,-0.00971,0.03062,0.05758,-0.01276,-0.00347,0.1044,0.0172,0.05625,0.04907,0.08421,0.08459,-0.017,0.15626,-0.04601,0.07418,-0.02756,-0.06965,-0.03858,-0.0181,0.02099,-0.04138,0.07539,-0.02378,-0.05476,-0.02376,-0.04464,-0.05607,0.1144,-0.04304,-0.01849,0.0205,0.0222,-0.05233,0.01397,0.05306]},{"domain":"classical_physics","key":"period_frequency","name":"Period and frequency","package":"classical-physics-ai999x","example":"If a wave has a frequency of 1.68 Hz, what is its period?","v":[0.05351,0.06741,-0.08062,0.07575,0.02132,-0.02131,0.05967,0.03676,0.0192,0.09307,-0.05663,-0.01988,0.08023,0.00181,0.00198,0.00848,-0.03543,-0.00355,0.09368,-0.04449,-0.09008,-0.03626,-0.05103,-0.02291,0.00891,-0.07573,0.02859,-0.09753,0.0443,0.03086,0.03418,0.11617,-0.01498,0.03549,-0.08637,-0.10087,0.07218,-0.02199,-0.03256,0.03224,-0.0507,-0.08738,0.02077,0.05332,-0.02157,0.04906,-0.14662,0.19152,-0.00319,-0.04182,-0.0321,0.00762,-0.15508,-0.0716,-0.03387,-0.06395,-0.0356,-0.08319,-0.17579,-0.02553,-0.00632,-0.03533,-0.08247,0.11455,0.0973,0.00686,0.02213,-0.0369,-0.01816,-0.00922,0.05505,0.00018,-0.02358,-0.10043,0.07546,0.02262,0.00809,-0.05698,0.08477,-0.00366,0.06861,0.01077,0.08367,0.01643,0.0629,-0.06443,-0.01672,-0.11935,0.01519,-0.01889,-0.02036,-0.14131,-0.10914,-0.06747,-0.00549,0.01143,0.01833,0.00448,0.02366,0.10146,-0.02966,0.13181,-0.0252,-0.02503,-0.08748,0.04124,0.14951,0.01605,0.08504,-0.02019,-0.0343,-0.11742,-0.02066,-0.03584,0.04545,0.08292,-0.04403,0.08913,-0.01766,0.03838,-0.09484,-0.02552,-0.02227,-0.02756,0.0012,0.06656,-0.03712,-0.0942,0.02574,0.08233,0.02981,0.08669,0.00249,-0.00685,0.07879,0.08646,-0.04304,0.04829,0.08399,0.09041,0.03381,0.08669,-0.03387,-0.06784,-0.07652,-0.0188,-0.0219,-0.02815,0.0103,0.09941,0.07949,-0.12385,-0.06349,-0.03935,0.08089,0.03718,0.0169,0.04732,-0.01094,-0.05118,0.00531,0.00056,0.01591,0.05822,-0.02651,-0.01678,0.01915,0.12344,0.06558,-0.06621,0.05886,0.03737,0.10971,0.2087,-0.04152,0.03427,0.04804,-0.01076,0.04507,-0.00871,-0.0544,0.02933,0.05785,0.00598,-0.04233,-0.03286,-0.00028,0.00504,-0.03505,-0.01354,0.00054,0.01409,-0.06319,-0.09295,0.03632,0.0797,0.09174,0.0327,0.00742,0.0988,-0.02362,0.0022,-0.01985,0.00215,-0.06141,0.02788,-0.0426,-0.03456,-0.04366,-0.02376,0.05369,-0.09767,-0.054,-0.00381,-0.00988,-0.01975,-0.04596,0.03134,0.10362,-0.16663,-0.11897,0.0127,0.00579,-0.01851,0.02885,0.00856,0.04459,0.01193,0.04224,0.00406,0.0381,-0.00423,-0.04833,0.09346,-0.06136,0.11836,-0.00535,-0.07615,-0.00819,0.05837,0.0024,-0.04339,0.02775,-0.05483,0.02348,-0.08597,0.05077,-0.1296,0.06449,-0.09314,0.05748,-0.00317,-0.01526,-0.03887,-0.03013,-0.03071]},{"domain":"classical_physics","key":"density","name":"Mass density","package":"classical-physics-ai999x","example":"A brick has a mass of 11 kg and a volume of 1.59 L. What is its density?","v":[0.03318,-0.04048,-0.02917,-0.0793,0.09514,-0.064,0.08811,-0.01991,0.04703,0.07035,-0.00545,0.11528,0.10509,0.04031,0.09138,-0.01361,-0.05265,-0.00013,-0.00635,0.03619,0.04285,0.05277,-0.0599,-0.02297,0.01236,0.05214,-0.03505,-0.00096,-0.1461,-0.07443,-0.02104,-0.04488,-0.06998,-0.07731,0.0467,-0.01545,0.05814,-0.04246,0.03045,-0.01652,-0.00583,0.07668,-0.02288,-0.04828,0.00651,0.03212,-0.08712,0.01981,-0.01217,-0.0976,-0.00597,-0.00267,-0.05579,-0.06219,-0.04393,0.04359,0.07598,-0.00097,0.03799,0.07995,0.10303,-0.09117,0.05221,0.10752,0.05941,-0.00523,0.09543,-0.02163,0.04866,0.16171,0.04905,-0.09505,-0.03679,-0.03818,0.10726,0.08861,0.14456,-0.11356,-0.06222,0.02637,-0.05157,-0.03589,0.02931,-0.08237,-0.01295,0.05261,0.05812,-0.00969,0.05017,0.0221,-0.01932,-0.12687,0.00792,-0.04327,-0.03093,0.07117,-0.08311,0.0203,0.11685,0.03629,0.00169,-0.03592,-0.08402,-0.05764,-0.04787,-0.02876,0.09717,0.11971,-0.00159,-0.06043,-0.05753,-0.02784,-0.05493,-0.00648,-0.07198,-0.01108,0.13143,0.1222,-0.06404,0.00391,-0.01463,-0.01688,0.02421,0.00231,-0.03025,0.03221,-0.0884,-0.08841,0.06656,0.03189,0.04746,0.14883,0.04939,-0.029,0.08336,0.09976,-0.04925,-0.03135,-0.02035,-0.03003,0.00282,0.05072,0.0842,-0.05238,-0.01624,-0.0146,0.05683,0.00957,0.03205,-0.03467,0.05195,0.00818,-0.01699,-0.15737,0.02262,-0.01103,-0.04959,-0.06543,-0.06398,0.00283,0.01161,0.12421,0.04855,-0.0794,0.09752,0.05284,0.03312,-0.0753,-0.01599,-0.11741,-0.08916,-0.02031,-0.13658,-0.03347,0.02018,0.06272,0.02421,-0.08437,-0.01457,0.02971,0.07646,0.15579,0.07606,0.04507,0.06545,-0.01777,0.04036,0.02599,-0.02448,-0.05125,-0.05149,-0.02178,0.03573,-0.00323,0.06729,0.04859,0.06987,0.04737,-0.06138,-0.02003,-0.13719,-0.05332,-0.01722,-0.02872,-0.01924,-0.06004,-0.04609,-0.06408,-0.01217,0.04428,0.0088,-0.08518,0.02508,-0.1189,-0.01923,0.02478,-0.00364,0.04963,0.02549,0.02774,-0.02757,0.03847,-0.06227,-0.04677,0.08415,0.06367,-0.03456,0.04445,-0.02763,0.00649,0.02754,0.11091,-0.07075,-0.09255,0.02236,-0.0749,0.00882,-0.17625,-0.04247,0.05436,0.01814,-0.08333,0.016,-0.03934,0.03112,-0.07011,0.12341,0.09207,0.03591,0.04433,-0.05694,-0.03716,-0.02674,0.00415,-0.03496,0.02383]},{"domain":"classical_physics","key":"pressure_force","name":"Pressure of a force on an area","package":"classical-physics-ai999x","example":"A weight presses on a cushion with a force of 422 N. The contact area is 0.0332 m^2. What is the pressure?","v":[-0.01865,-0.02354,-0.02113,-0.16007,0.02417,0.03332,-0.01829,0.02466,-0.1027,0.04027,-0.04162,-0.02576,0.01892,0.03981,-0.01076,-0.03848,0.03601,0.04404,0.00018,0.15666,-0.05616,-0.04239,0.16717,0.04748,-0.0289,0.05949,-0.01262,0.0826,0.03551,0.00995,0.10235,0.08939,0.11342,0.04227,-0.0652,0.05453,0.09494,-0.01213,-0.01584,0.02666,0.15755,0.05591,0.00615,0.00971,0.03402,0.00284,-0.06161,0.01296,-0.02773,0.01531,0.05924,-0.06246,-0.04151,0.03806,-0.00474,-0.02548,-0.03522,0.00828,0.06002,0.04089,0.05789,0.01028,-0.1931,-0.02983,-0.01182,-0.01496,0.00946,0.12231,0.01238,0.05589,-0.05236,-0.1485,-0.05482,-0.04273,-0.05675,-0.00754,-0.01185,-0.07229,-0.03835,-0.04816,-0.03212,-0.01253,0.05697,-0.06702,-0.03995,-0.02156,0.02365,-0.03412,0.06465,0.01025,-0.00925,-0.02958,0.01241,-0.08089,0.02753,-0.00051,0.13353,0.05496,0.08193,-0.00021,-0.0095,0.07365,-0.04838,0.04279,0.01318,0.02065,0.03602,-0.0652,0.08959,-0.08959,-0.0581,-0.02648,-0.01709,-0.07029,-0.01592,-0.06327,0.11762,0.04225,0.02156,-0.03645,-0.10458,0.08017,0.04176,-0.07651,-0.04395,-0.03604,-0.13916,0.06456,0.12685,-0.00122,-0.01064,0.0641,0.04631,-0.03513,-0.07879,0.02183,0.03638,-0.01261,0.03873,0.08207,-0.03885,0.00297,0.00596,-0.06404,0.02048,-0.01964,0.13881,-0.01081,-0.04358,-0.00115,0.04856,0.06274,-0.07795,0.14771,0.04611,-0.0475,-0.01921,-0.04989,-0.00167,-0.02142,0.01541,0.10487,0.07479,-0.07937,-0.06711,0.0426,-0.0245,0.03661,-0.0538,-0.1412,-0.13306,-0.01231,0.0611,0.15552,0.03022,-0.00804,0.00478,0.03301,-0.02549,0.10276,0.00224,0.00697,-0.07879,-0.08621,-0.0197,0.00364,0.00642,-0.08576,-0.12893,-0.01888,0.07735,0.08128,-0.03975,-0.0536,-0.05826,0.05155,0.01311,-0.0579,-0.04104,0.0496,0.11377,-0.05753,-0.03771,-0.08201,0.05909,0.02514,-0.10104,0.01352,0.03467,0.10399,-0.00874,0.00301,0.01016,-0.10912,-0.04503,-0.05266,0.10175,0.00319,0.0018,-0.05478,0.00407,-0.03667,-0.08407,0.01998,0.06492,0.00582,-0.00344,-0.04873,0.08519,0.01326,-0.07006,0.11818,-0.00625,0.09191,0.00037,0.07098,-0.01094,-0.05002,-0.10599,-0.00808,-0.05615,-0.03062,-0.00071,0.01129,0.0155,-0.09322,0.02673,-0.0668,-0.04086,-0.09716,-0.03064,0.0257,-0.0394,0.13149,0.01469,0.10683]},{"domain":"classical_physics","key":"hydrostatic_pressure","name":"Pressure of a column of fluid","package":"classical-physics-ai999x","example":"Gravity is 6.87 m/s^2 and the depth is 2630 mm. The gauge pressure measured is 42100 Pa. What is the fluid density?","v":[0.04394,0.05524,-0.08205,-0.06162,0.02183,0.14292,0.15938,-0.01325,0.02777,-0.00484,-0.00724,-0.00195,0.03452,0.04348,0.00495,-0.07386,0.02962,0.04894,0.00919,0.04865,0.05787,-0.0525,-0.03929,0.01089,0.00167,0.0864,-0.01456,0.05703,-0.14857,0.05173,-0.00627,0.08747,-0.03997,-0.1051,0.01925,0.10692,0.08018,0.09565,0.02295,0.04738,0.00702,0.07562,-0.06139,-0.00589,-0.04565,0.12506,-0.06325,-0.0528,0.00634,0.04263,0.01138,-0.03049,0.08047,0.02147,-0.14327,0.05823,-0.03086,-0.00851,-0.08007,0.16516,0.08217,-0.06117,-0.01644,-9e-05,-0.05334,-0.00567,0.01381,-0.02797,0.00875,0.03357,0.00808,-0.05453,0.03506,0.01528,0.09816,0.05951,0.06531,-0.03904,-0.14637,-0.0224,0.01274,0.12114,0.02924,-0.02418,-0.01035,-0.03932,-0.00511,-0.07872,0.0676,0.06222,-0.07521,-0.03628,-0.06185,-0.01073,-0.0384,-0.01493,0.0525,0.02057,0.05157,-0.02172,-0.02488,-0.04515,-0.03146,0.07125,0.08519,-0.03892,0.08647,0.04353,0.00306,-0.04254,-0.09214,-0.02028,-0.04114,0.0299,-0.08997,-0.02863,0.10689,0.0521,0.00884,-0.10107,-0.14222,-0.01612,-0.06153,-0.01043,-0.0774,-0.03246,-0.14308,0.00779,0.12626,0.01462,0.0543,-0.07469,0.10278,-0.03914,0.03961,0.10279,0.00695,0.00486,-0.03178,-0.11584,-0.08281,0.06305,-0.05237,0.0373,0.06257,-0.08661,0.01139,-0.04183,0.0577,-0.00072,0.03263,-0.08858,-0.04408,0.02918,0.02045,-0.02063,0.02345,-0.05043,-0.10152,-0.07383,-0.08848,0.15795,0.07805,-0.07446,-0.0603,0.02316,0.02687,-0.01144,0.02645,-0.04014,-0.0231,-0.03246,0.03474,-0.01277,0.01877,0.077,-0.03395,0.00136,0.02047,0.15602,0.01533,-0.00091,-0.04398,0.0022,0.14692,-0.01553,0.03046,-0.09104,-0.0957,-0.08063,0.01823,0.07851,-0.01965,-0.08642,-0.00492,0.09417,0.04722,0.04998,-0.06706,-0.0857,-0.14971,0.04218,-0.06326,-0.03005,0.06015,-0.1272,-0.12856,0.00235,-0.04321,0.04609,0.05342,0.08006,0.00827,-0.07508,0.01328,-0.04279,0.00713,-0.06336,0.01729,0.00822,0.12373,-0.08497,0.06976,-0.00317,-0.04119,-0.03076,-0.0276,-0.00921,-0.01974,-0.00923,0.04337,0.03379,0.03471,-0.09751,-0.01264,0.09586,-0.01876,-0.01438,0.04685,0.03904,0.0592,-0.06104,0.04856,-0.0018,0.07183,-0.03888,0.00468,0.03873,0.01914,-0.08666,-0.0348,0.02227,-0.00194,0.04658,0.06632,0.05156]},{"domain":"classical_physics","key":"ohm","name":"Voltage across an ohmic resistance","package":"classical-physics-ai999x","example":"A circuit shows a current of 3740 mA and a voltage of 9720 mV. What is the resistance in the circuit?","v":[0.10174,-0.01441,-0.02289,-0.09523,-0.00622,-0.05462,0.16365,-0.04415,-0.04937,0.06824,-0.01231,-0.09426,0.06337,-0.07913,0.0588,0.02124,-0.12226,-0.05082,-0.06647,0.09202,0.04653,0.01021,-0.01888,0.00988,0.01239,0.03557,0.03316,-0.04821,0.05227,-0.01036,-0.04676,0.03703,-0.06496,0.0582,-0.06999,-0.03572,0.04971,-0.08912,0.02981,0.09498,-0.00082,-0.00334,-0.02127,-0.02364,-0.03713,-0.06524,-0.0317,0.10406,0.03493,-0.04665,0.06627,-0.01283,-0.0866,-0.08016,0.08883,0.0458,0.03715,-0.05101,-0.05618,0.03683,0.10216,-0.04458,-0.03298,-0.03642,0.05594,-0.00793,0.09408,0.12103,-0.07544,0.09562,-0.00813,-0.00281,0.03657,-0.06776,-0.0064,0.06133,0.05782,-0.05587,-0.02602,0.00899,-0.05452,0.0171,-0.07564,0.0305,0.03137,0.04292,0.089,-0.03895,0.00079,-0.03208,0.03419,-0.01712,-0.04976,-0.00132,0.04654,0.15684,-0.0327,-0.00072,-0.02791,0.02367,0.02125,-0.07137,0.09139,-0.11623,0.01295,-0.05365,0.08624,0.11631,-0.03243,-0.03687,-0.00748,-0.01823,-0.08426,-0.01255,-0.02823,0.07227,0.04756,-0.01275,-0.04301,-0.08433,0.03262,0.04396,0.04857,-0.00415,-0.00905,0.01675,-0.08007,-0.01856,-0.01094,0.12339,-0.05373,0.0289,0.08874,-0.00534,0.02055,0.04866,-0.02811,-0.02946,-0.00331,0.00059,-0.07047,-0.02559,-0.02654,-0.02476,0.08554,-0.06641,0.09978,-0.06468,-0.05121,0.02035,-0.01449,0.07897,-0.05941,0.01359,0.04972,-0.01615,-0.09162,0.05268,0.0845,-0.04009,0.00418,0.06389,0.12237,-0.09652,-0.07763,-0.03615,-0.09226,-0.14996,-0.12424,-0.19241,-0.12083,0.01668,-0.03738,0.06594,-0.07068,-0.07911,-0.08908,-0.14664,0.11266,-0.05862,0.02505,0.03052,0.05852,0.06052,-0.0443,-0.06949,-0.0666,-0.00707,-0.0371,0.04014,0.05594,0.02956,-0.01944,-0.0456,0.05893,-0.0315,-0.03609,0.14335,-0.00709,0.16078,-0.03762,-0.04306,0.02481,0.0271,-0.1002,-0.02116,-0.05974,0.04679,0.03688,0.01116,0.01187,0.09279,-0.02745,0.04477,-0.01737,-0.03038,-0.03279,0.00702,-0.04757,0.04303,-0.02544,0.05372,-0.00193,0.0707,0.02918,0.02943,-0.0359,0.10969,0.10806,0.0157,-0.04758,0.0456,0.01554,0.03434,0.01486,-0.04705,-0.10221,-0.01849,-0.03053,-0.02072,-0.04845,-0.00643,0.00218,-0.08834,0.06895,-0.03938,0.06865,0.0242,0.00874,0.16699,0.05401,-0.06909,0.06484,0.14862,-0.0079,0.03294]},{"domain":"classical_physics","key":"electric_power","name":"Electric power","package":"classical-physics-ai999x","example":"A drill operates on 25.6 V and draws a current of 3.91 A. What is the electric power?","v":[0.02227,-0.06373,-0.05326,-0.10278,-0.03142,-0.09545,0.07798,0.03897,-0.13808,0.00633,-0.02863,-0.12147,0.07718,-0.10821,0.00336,-0.0537,-0.11608,-0.09889,-0.01397,0.08292,0.00733,0.11658,0.03034,-0.00992,-0.0843,0.05148,0.03597,0.02072,-0.05129,0.02823,0.0308,-0.02286,-0.05915,0.02921,0.0037,-0.07392,0.05138,-0.0926,0.05641,-0.07451,-0.01061,-0.0287,-0.00809,-0.0412,0.01825,-0.00293,-0.01984,-0.02115,0.03343,-0.11313,0.04208,-0.0147,-0.07566,-0.02641,-0.05764,-0.04806,-0.01827,-0.07736,-0.11409,0.00986,0.10087,-0.03762,-0.03015,-0.0312,-0.05875,0.05877,0.01266,0.05014,-0.04935,0.04513,0.07468,0.04633,-0.01499,-0.05849,0.00225,0.048,0.13362,-0.06364,-0.05748,-0.01904,-0.05735,0.00138,0.03058,-0.00945,-0.06739,-0.12865,0.12314,-0.14951,0.03323,-0.07734,0.07657,-0.05848,-0.0754,0.0411,-0.07536,0.04976,-0.01738,0.04885,0.01306,-0.01849,-0.07284,0.00904,0.12132,-0.0632,-0.02781,0.03728,0.07448,-0.02236,0.12406,-0.03712,0.09129,0.04213,0.03137,0.10692,-0.0053,-2e-05,-0.02481,-0.04766,-0.00036,-0.10807,0.04508,-0.01336,-0.01875,-0.01205,-0.03544,-0.04043,-0.04422,0.00078,-0.00688,0.09166,0.03482,-0.00949,0.05903,0.01002,0.02602,0.11544,0.0475,0.03286,-0.07263,-0.04099,0.04601,0.01108,0.00368,0.02023,0.14856,-0.0146,-0.0374,-0.06064,0.00964,0.02139,-0.03276,0.19265,-0.03904,0.10115,0.0158,0.04884,0.00638,-0.02843,0.07238,-0.02394,0.02982,-0.06961,0.05458,-0.0306,-0.01396,0.03992,-0.02156,0.06094,-0.05757,-0.10398,-0.07059,0.02494,-0.05933,0.08452,-0.08851,0.04818,-0.00412,-0.11337,0.11253,-0.05433,0.05883,-0.00827,0.02813,0.05628,-0.01449,-0.03664,-0.02585,0.0034,-0.10033,0.03768,0.07887,-0.03694,-0.02743,0.09542,0.05723,0.04387,0.07953,0.02594,0.10574,0.02245,0.00967,-0.00608,0.07829,0.01617,-0.04864,0.01364,-0.06157,-0.06304,0.15546,-0.04718,0.01046,0.01455,0.09768,-0.08543,0.12732,-0.01341,-0.0874,-0.07332,-0.00245,-0.13501,0.05002,0.02297,-0.04967,0.07256,0.10547,-0.08375,0.05185,0.00113,0.07658,0.03333,0.01783,0.09156,0.05838,0.0323,0.01021,-0.02326,0.02495,-0.10554,-0.05849,-0.01903,0.03959,-0.0059,0.03137,0.04681,-0.03113,0.00594,0.0041,-0.01636,0.09683,0.04415,0.01984,-0.1448,0.06837,0.10875,-0.04133,0.02507]},{"domain":"classical_physics","key":"charge_current","name":"Charge carried by a steady current","package":"classical-physics-ai999x","example":"A steady current of 1.41 A carries 88.8 C of charge. For how long does this flow last?","v":[-0.02164,0.14987,-0.10034,-0.0313,0.01631,-0.07011,0.10939,-0.00122,-0.10802,0.03981,-0.05811,-0.04315,0.08388,-0.01249,0.0218,0.06138,-0.16431,-0.04131,-0.03571,-0.012,0.04279,0.06067,-0.08608,-0.04544,-0.06623,0.04721,-0.08872,0.08495,0.02559,-0.00597,0.04379,-0.00323,0.03526,0.04143,-0.00282,0.04978,-0.02259,-0.03832,0.06526,-0.05136,0.01826,0.04028,-0.01749,0.09245,-0.0465,-0.00676,-0.03683,0.07547,0.14079,-0.10095,-0.08709,-0.05767,-0.02883,-0.11335,-0.02715,0.0016,-0.0273,0.02597,-0.05305,-0.05641,0.02664,-0.0554,-0.07287,-0.06876,-0.02174,-0.00644,-0.02258,0.12952,-0.0341,-0.00409,-0.0799,-0.00212,-0.02619,-0.08949,0.01391,-0.09019,0.1125,0.01745,-0.09544,-0.00564,-0.0232,-0.12634,0.06144,0.15421,-0.00491,0.03153,0.00546,-0.06314,9e-05,-0.00799,0.00233,-0.12289,-0.03087,0.09219,0.02282,-0.01566,-0.06073,-0.00421,-0.0181,-0.05307,0.03266,-0.07889,-0.01579,-0.02748,0.01308,0.02884,0.03572,0.06311,0.1607,-0.04137,0.00369,-0.01802,0.03521,0.04986,0.09763,0.07617,0.13298,0.11574,-0.09765,0.0315,-0.06327,0.07832,0.07572,0.03644,-0.03859,0.0039,-0.04011,-0.00147,0.01937,0.12999,-0.00385,-0.00019,-0.0169,-0.01737,0.08389,0.02098,0.02467,0.07985,-0.10773,-0.05488,-0.00631,-0.03226,-0.04542,-0.09299,-0.0467,0.03126,0.02113,0.07468,0.06798,0.05956,0.00938,-0.01915,-0.01722,-0.06364,-0.10376,0.06275,-0.03359,-0.04737,0.00346,-0.02292,0.03636,0.03072,0.11572,0.0204,-0.0941,-2e-05,-0.04521,-0.0254,-0.13561,0.01089,0.06186,-0.0023,0.04473,0.0169,-0.11469,0.02334,-0.09345,-0.08073,0.01667,0.10538,0.0096,0.01283,0.05541,0.00676,0.00325,0.08882,-0.07405,0.00447,-0.05888,-0.05673,-0.06066,-0.04354,0.03294,0.05846,0.0058,0.06406,0.02642,0.02263,0.07571,0.00149,-0.00036,0.05239,0.07436,-0.0614,0.02431,0.03058,0.01455,0.00909,0.15584,0.05018,0.09092,-0.01842,0.03653,-0.04143,0.06936,-0.04101,-0.12412,-0.04492,-0.00829,0.0472,0.03108,0.00654,-0.05167,0.0426,0.07006,-0.05094,0.03696,-0.07497,0.01582,-0.02532,-0.03195,-0.0686,0.03897,-0.03117,0.19625,0.01167,0.01842,-0.0475,0.03375,-0.1319,-0.03765,-0.04834,-0.01101,-0.03298,-0.04343,-0.03373,0.09152,-0.03609,-0.01694,0.04631,0.14737,-0.01534,0.02231,0.09124,-0.0953,0.0724]},{"domain":"classical_physics","key":"wave_speed","name":"Speed of a periodic wave","package":"classical-physics-ai999x","example":"A water wave moves at a wave speed of 40 m/s. Its frequency is 96.5 Hz. Find the wavelength.","v":[0.02424,0.0516,-0.03239,0.05568,0.0398,0.07871,-0.0083,0.06284,0.01247,-0.00216,-0.06802,-0.02639,0.17213,-0.06083,-0.04307,0.03596,-0.1049,-0.00829,0.04118,-0.06473,-0.12286,-0.01825,0.05562,0.056,-0.09598,-0.08524,0.08611,-0.0077,0.02838,-0.02923,0.03675,-0.05323,-0.02574,0.01321,-0.05234,-0.02112,0.12912,-0.00589,-0.00298,0.05507,-0.05755,-0.04391,0.03843,0.01968,-0.05872,0.03618,-0.04103,0.07719,0.06737,-0.09912,-0.00348,0.01723,-0.08058,-0.06738,0.04907,-0.06399,-0.06865,-0.06809,-0.06509,0.04222,0.10644,-0.14507,0.0529,0.02317,0.0348,0.00575,0.0081,0.00818,0.008,-0.02024,0.08191,0.08123,0.02716,-0.0583,0.07049,-0.00055,0.09196,-0.12987,0.11738,-0.07476,0.0378,-0.019,0.00571,-0.06602,0.0577,-0.07295,-0.03191,-0.06729,0.03144,0.11432,-0.11997,-0.00116,-0.04807,-0.03279,-0.02318,-0.03884,-0.01601,0.06503,0.0879,0.02218,-0.04972,0.15007,-0.02639,-0.07356,-0.05732,0.05136,0.03763,-0.00149,0.0747,0.02079,0.02631,-0.17354,0.04774,-0.01738,-0.03105,0.11918,-0.02407,0.06586,0.03965,-0.0155,0.04804,-0.02184,-0.01429,0.03386,0.04941,0.02955,0.00468,-0.07201,-0.0685,-0.07195,0.00809,0.06843,0.10171,0.00374,-0.00448,0.0332,0.00256,0.03106,0.03348,-0.08783,-0.07361,0.13637,-0.04327,-0.02782,0.04491,0.03487,-0.02245,0.01308,-0.11019,0.00622,0.02318,-0.01262,-0.12716,-0.0185,0.11436,0.0217,0.02553,-0.05338,-0.05702,-0.12681,-0.16899,0.00842,-0.01993,-0.07425,-0.01454,6e-05,-0.00627,-0.06057,0.06266,-0.00894,0.03136,0.02413,0.09507,0.05132,-0.01188,0.00322,0.08456,-0.14354,0.1271,-0.02108,0.04339,0.01205,-0.00998,0.02735,-0.00102,-0.07077,-0.02384,-0.03678,-0.04072,0.07832,-0.04377,-0.04455,-0.0047,-0.03935,0.07696,0.06701,0.00862,0.03354,-0.0147,0.01308,0.02023,-0.01281,0.03151,0.06013,-0.1225,-0.0157,-0.00915,0.07939,-0.0245,-0.01075,-0.00556,-0.00728,-0.08172,-0.05843,0.03971,0.03534,-0.04744,0.00039,0.06775,0.04116,-0.14087,-0.0134,0.03072,0.07898,0.05093,0.08383,-0.00321,0.16494,0.08313,-0.10182,-0.06011,0.08403,0.01233,0.0432,-0.0165,0.02751,-0.05601,-0.11742,-0.09133,0.00179,0.00576,0.00194,0.01657,-0.07103,0.02265,-0.01478,0.09245,0.06601,0.07601,0.08272,-0.00225,0.02482,-0.11357,-0.06819,-0.08649,0.03727]},{"domain":"classical_physics","key":"heat","name":"Heat for a temperature change","package":"classical-physics-ai999x","example":"A spoon weighs 0.272 kg. Its specific heat capacity is 2230 J/(kg*K). It warms up by 5.02 K. How much heat energy did it gain?","v":[0.11001,0.07895,-0.04448,0.00271,-0.00222,0.00764,0.03642,-0.12649,-0.01532,0.00477,-0.03164,-0.00526,0.06455,0.06938,0.01529,-0.07081,-0.06367,0.00679,0.04851,-0.00372,0.10416,0.03576,-0.0758,-0.07157,-0.07142,0.0207,0.02908,-0.00577,-0.04597,0.03647,-0.03041,0.05084,-0.08337,0.03245,-0.01598,0.09647,-0.09697,-0.07794,-0.02212,-0.0654,0.0044,0.02694,0.05384,0.09437,-0.03798,0.03658,-0.01957,0.03422,0.09333,0.00442,-0.07327,0.00747,0.10765,0.0667,0.0744,-0.01362,0.15121,0.01702,0.01282,0.04899,-0.04923,-0.15901,0.01713,0.07942,-0.00689,0.04133,-0.12141,0.05827,0.0045,0.06904,0.10745,-0.00938,-0.0929,0.00892,0.05882,-0.00409,0.06723,-0.04302,0.01486,0.02431,-0.09865,-0.10568,0.03954,0.00195,0.00328,-0.06447,-0.04558,-0.07027,-0.04793,0.04503,0.01439,-0.08909,0.07579,0.02919,-0.0654,-0.02397,-0.11716,0.03548,0.05099,-0.10263,0.09542,0.00914,-0.13561,-0.00459,-0.17575,0.07877,0.10073,0.06506,-0.0082,0.06036,0.01922,0.11266,-0.04258,-0.04556,0.05704,0.01037,0.15852,0.04786,-0.00301,0.0302,-0.10663,0.03214,0.05938,-0.02278,-0.00047,0.06013,-0.02586,-0.09843,-0.00653,0.00149,0.02662,-0.021,0.04519,-0.00217,0.06233,-0.07103,0.0768,-0.04364,-0.02694,-0.09553,0.01948,-0.00225,0.03389,-0.03707,0.03831,0.06604,-0.02836,-0.02837,-0.05745,0.01948,0.09823,-0.0161,-0.09217,-0.08842,-0.06294,0.01506,-0.05034,-0.13254,0.0263,-0.05514,0.01352,0.07649,0.02962,0.08778,-0.03024,0.0737,-0.01976,-0.06111,-0.04303,-0.0092,-0.02275,-0.05461,-0.05902,0.04191,-0.13926,-0.00893,-0.0798,-0.09225,-0.07354,0.08767,0.09209,0.10748,-0.01697,-0.05732,-0.04634,-0.11017,-0.02143,-0.06856,-0.01247,-0.07078,-0.0407,0.09709,-0.02658,0.08311,0.04813,0.04577,0.00146,0.0859,0.02858,-0.00737,0.0494,-0.07149,0.11752,-0.02511,0.02572,-0.06984,0.04004,7e-05,-0.06066,-0.06917,-0.04167,-0.06282,-0.01505,0.00679,0.0951,0.02585,0.02306,-0.1039,0.07019,0.13259,-0.01567,0.04765,0.00225,0.0247,-0.04974,0.03203,-0.01612,0.01671,-0.00308,0.08333,-0.0146,0.05394,0.03187,-0.04138,0.04737,0.01769,0.08055,-0.06914,-0.03582,0.05057,-0.08225,-0.08411,-0.05125,0.08783,-0.05991,-0.0386,0.06581,-0.0449,0.05511,0.00623,-0.09856,0.06162,0.00415,0.05641,-0.00084,0.09533]},{"domain":"classical_physics","key":"max_height_vertical_throw","name":"Maximum height of a vertical throw","package":"classical-physics-ai999x","example":"A toy rocket shoots upward at 8.42 m/s. It goes up 165 cm before stopping. Find the gravitational acceleration.","v":[-0.08175,0.07062,0.05212,-0.03418,-0.07578,0.02587,0.00393,-0.02615,0.03972,-0.00481,-0.07205,0.02246,-0.00873,0.00159,0.02239,0.01682,-0.00423,-0.0173,0.06114,-0.0782,0.03669,-0.03438,0.02626,-0.08397,-0.04722,0.00137,0.02163,0.09796,-0.05585,0.03686,-0.0254,0.10885,-0.01451,0.03563,-0.03276,-0.09562,0.06486,-0.07539,0.02468,-0.04571,0.03355,-0.06443,0.07587,0.03132,-0.01793,0.06781,-0.0096,-0.04101,-0.09555,-0.00782,0.05626,0.00778,0.02533,-0.01143,-0.0266,0.05649,-0.02374,0.0552,-0.08936,0.10139,0.00041,-0.06937,0.07134,-0.09539,-0.07383,-0.02675,0.05969,0.00786,-0.02574,0.01861,0.04104,0.05554,0.06318,-0.06866,0.01946,0.10807,-0.08605,0.06245,-0.0271,-0.0314,0.01577,0.04431,-0.11306,0.08169,-0.16744,0.04242,0.05368,-0.14302,-0.03334,0.10051,0.01528,0.12917,-0.0464,0.12578,0.0234,0.02641,0.05375,-0.04537,0.0169,0.0476,-0.07729,-0.03988,0.01032,0.05668,-0.02536,-0.05488,0.07087,0.0796,-0.11612,-0.0003,-0.05511,0.07968,0.0124,0.02828,0.05858,0.06117,0.0152,-0.02949,0.01574,-0.07173,0.09825,-0.01567,0.09184,-0.09065,-0.07826,-0.05553,-0.0366,-0.0673,0.07591,0.10629,0.08262,0.04705,-0.01926,0.03155,0.07357,-0.04368,0.10868,0.04472,0.00856,0.00901,0.03802,0.10904,0.03197,0.01183,0.08652,0.03982,0.02285,0.06072,0.10212,0.02561,-0.05319,-0.04194,-0.07849,-0.01452,-0.09526,0.00258,-0.11091,-0.05565,-0.12824,-0.07223,-0.00396,-0.03147,0.04509,-0.03014,-0.02785,0.06271,-0.01563,0.09584,0.02715,0.04768,0.04823,0.04003,0.04903,-0.08565,-0.05971,0.01316,-0.05095,-0.0067,-0.00545,-0.04531,-0.0359,-0.09447,0.0305,0.09025,0.05315,-0.01962,-0.00676,0.01017,-0.09222,-0.03564,-0.00501,-0.01815,0.02471,-0.01241,-0.01,-0.05179,-0.07959,-0.02575,-0.0742,-0.07244,-0.01509,0.1057,0.04097,0.03566,0.04854,0.02595,-0.04142,0.02944,0.09851,-0.13948,-0.02864,0.06676,0.03986,-0.05808,-0.03827,0.01809,0.04293,0.04686,-0.03263,0.0345,-0.09751,-0.05722,0.07236,0.04217,-0.08625,0.00183,-0.04452,0.12772,-0.05793,-0.14003,-0.03306,0.12993,-0.0825,-0.15409,0.00055,0.02586,0.04413,0.03241,-0.01793,-0.04581,-0.01822,0.14993,-0.01834,0.05027,-0.03938,-0.14505,0.00741,0.01027,0.05292,-0.19487,-0.0258,0.01784,0.0482,-0.07721,0.03369,0.04762]},{"domain":"classical_physics","key":"time_to_top_vertical_throw","name":"Time to the top of a vertical throw","package":"classical-physics-ai999x","example":"An object floats up for 2.66 s in a region with gravitational acceleration of 19 m/s^2. What was the launch speed?","v":[-0.05682,0.06565,0.03347,0.03043,-0.09037,0.00578,0.03952,-0.02636,0.08619,0.00296,-0.08494,0.04596,-0.00701,0.0136,0.02112,0.04265,-0.02811,0.00433,0.05551,-0.09017,0.02212,-0.07209,0.0072,-0.09876,0.01662,-0.00142,0.01337,0.09591,-0.04279,0.05897,0.01616,0.10627,-0.01968,0.01707,-0.00912,-0.10569,0.04339,-0.09738,0.01409,-0.05062,0.06227,-0.04496,0.05255,0.04078,-0.05311,0.06595,-0.00967,-0.01405,-0.06515,0.0084,0.01595,-0.02079,-0.03885,-0.03345,-0.03845,0.05147,0.01484,0.08091,-0.09091,0.09838,-0.01823,-0.00338,0.0647,-0.05561,-0.06195,-0.0767,0.08319,-0.01518,0.00317,0.02007,0.02051,0.00508,0.08101,-0.11509,0.03537,0.09956,-0.08077,0.08187,-0.00028,0.00339,0.0066,0.03939,-0.09635,0.11483,-0.17755,0.06147,0.04009,-0.15972,-0.00318,0.08118,-0.03143,0.10561,-0.0681,0.09886,0.07502,-0.00571,0.08732,-0.04615,-0.03762,0.09102,-0.06647,-0.05417,0.00328,0.03758,-0.03354,-0.09874,0.07745,0.07874,-0.00794,-0.02167,-0.0413,0.06079,-0.02353,0.0167,0.05422,0.07922,-0.00736,-0.00345,0.00519,0.00893,0.04595,0.00446,0.08248,-0.08027,-0.06231,-0.03189,-0.00195,-0.06816,0.06449,0.15751,0.0851,0.00156,-0.05939,0.01731,0.08191,-0.07104,0.09193,0.0495,0.02007,-0.00325,0.01137,0.1023,0.02861,-0.02831,-0.0,0.02447,0.00724,0.10261,0.11201,0.09662,0.00033,-0.09197,-0.06428,-0.02309,-0.13082,0.01554,-0.09401,-0.07864,-0.11425,-0.05667,0.01762,-0.02177,0.04988,0.02947,-0.03741,0.08726,0.02584,0.16047,0.02742,0.05627,0.09586,0.05132,0.03646,-0.05985,-0.06163,0.02215,-0.04463,0.0172,-0.02105,-0.0413,-0.05826,-0.12119,0.05411,0.04265,0.04341,0.00234,0.00834,0.0129,-0.09235,-0.00686,-0.02166,-0.06393,0.01652,-0.03309,-0.00059,-0.04194,-0.03111,-0.06156,-0.01398,0.00781,-0.04941,0.12301,0.02087,0.00803,0.01672,0.06463,-0.01875,-0.0237,0.06528,-0.13459,0.00128,0.0381,0.04141,-0.06769,-0.02748,-0.002,0.01783,-0.00328,-0.00909,0.00949,-0.10947,-0.03031,0.0659,-0.01053,-0.0713,-0.04004,-0.02863,0.09412,-0.04302,-0.10699,-0.0187,0.08096,-0.0949,-0.19156,-0.00832,0.02811,0.03517,-0.00253,0.00787,-0.03755,-0.01009,0.13566,-0.01077,0.0611,-9e-05,-0.16316,0.00959,-0.05361,0.06007,-0.17416,-0.00385,0.02881,0.03245,-0.08069,0.02419,0.02959]},{"domain":"classical_physics","key":"normal_force_incline","name":"Normal force on an incline","package":"classical-physics-ai999x","example":"Calculate the normal force on a 13 kg rock resting on a hillside inclined at 69.5 deg, subject to a gravitational acceleration of 5.26 m/s^2.","v":[-0.0835,0.01521,-0.01518,-0.082,-0.01114,0.07383,0.01414,-0.00021,0.07009,-0.01008,-0.00886,0.0343,0.03266,-0.05525,0.03679,-0.04533,-0.03259,0.14727,-0.00607,0.0967,-0.09962,-0.00711,-0.00472,0.0387,-0.0294,-0.04594,-0.02533,0.18792,-0.08326,-0.15673,-0.05788,0.01818,0.13155,0.0597,-0.02689,0.03625,-0.0317,-0.00119,0.06539,0.01015,0.10821,-0.05123,-0.03935,0.04376,0.04026,0.0788,0.01347,0.00309,0.02833,0.04688,-0.02176,0.02076,0.02195,0.02695,-0.02699,0.01073,-0.12054,0.03898,0.04893,-0.01937,-0.01763,0.06401,-0.05556,-0.06824,0.21062,0.05497,0.10931,-0.01348,0.05144,-0.00111,-0.08787,-0.03829,0.14986,-0.06274,-0.02395,0.02905,-0.00811,-0.06028,0.01192,-0.00877,-0.07025,0.019,-0.04374,-0.06321,0.05072,0.01008,-0.05127,-0.03331,0.02047,0.04733,0.0216,0.01198,0.07676,-0.01591,0.00441,-0.00692,0.10203,0.04851,0.06916,-0.06494,-0.0098,-0.00747,-0.08951,-0.00117,0.01977,-0.04789,0.11221,-0.04775,0.06157,-0.08265,-0.11095,0.07283,-0.02335,0.00336,0.04253,-0.06916,0.10254,-0.08441,-0.0132,0.05643,-0.00885,0.04777,0.04747,-0.14882,0.01986,-0.02974,-0.02092,-0.01282,0.04588,-0.03243,-0.00931,0.028,-0.06195,-0.04125,0.01065,0.10248,-0.06335,0.04105,-0.1269,-0.05371,-0.0735,-0.00481,-0.07621,-0.0276,0.04808,-0.11028,0.07276,0.04024,-0.05203,-0.01544,-0.01468,0.07048,-0.1234,0.11782,-0.086,0.05566,-0.01559,-0.08584,0.04011,-0.06198,-0.04791,-0.01081,-0.04375,0.0387,0.01604,-0.02227,-0.02646,0.03546,-0.03208,-0.0652,0.0267,0.03878,-0.01411,0.0544,0.00139,0.08534,0.01047,-0.02845,-0.16612,-0.07033,-0.03787,-0.00839,-0.03242,-0.05132,0.12815,-0.00507,-0.07923,-0.02239,-0.07092,-0.01238,0.20034,0.01327,0.00726,-0.06544,0.01261,0.04733,-0.04804,0.00911,-0.05535,0.07426,0.03504,-0.04509,-0.0224,0.03187,0.00867,-0.00978,0.08875,0.13543,0.07282,0.07884,-0.05914,0.02335,-0.10539,-0.08902,-0.03253,-0.0278,0.02672,0.06679,0.01281,-0.0341,-0.07855,-0.08162,0.01215,0.08115,-0.04167,-0.02104,-0.03398,0.04807,-0.07468,-0.01092,-0.11274,0.12787,-0.02102,0.0251,-0.00352,-0.02956,0.07735,0.01339,-0.06405,0.04881,-0.05749,0.03248,0.02643,-0.01464,0.06215,-0.06574,0.03693,0.02103,0.01935,-0.01386,-0.03057,0.11539,0.01913,0.12268,-0.03366,0.09444]},{"domain":"classical_physics","key":"weight_component_along_incline","name":"Component of the weight along an incline","package":"classical-physics-ai999x","example":"Find the gravitational acceleration when a mass of 18.6 kg has a component of the weight along the incline of 118 N and the angle of the incline to the horizontal is 63.6 deg.","v":[-0.12704,0.09307,-0.01411,-0.05015,-0.06096,0.09823,0.09431,-0.14208,-0.01731,-0.07786,-0.03526,0.04141,0.02097,-0.04623,-0.00635,-0.04106,-0.1442,0.15777,0.02774,0.06309,-0.03261,0.0127,0.0285,0.08355,-0.0378,0.02674,-0.04203,0.03173,-0.09184,-0.0265,-0.08935,0.01434,-0.01151,-0.02017,0.0608,0.06266,-0.15526,0.07056,-0.01157,0.12728,0.02165,0.00426,-0.03927,0.06949,-0.06381,0.15771,0.10724,-0.03409,0.11358,-0.02625,-0.01794,0.03781,0.08645,0.02734,0.01029,0.08011,-0.12003,-0.04008,0.01886,0.09657,-0.05712,0.08104,-0.05971,-0.00744,0.16399,0.06509,0.05476,0.02063,0.04684,-0.09884,-0.05098,0.02315,0.17448,-0.12618,-0.02383,0.05282,0.01709,-0.08554,-0.02465,-0.05734,-0.0055,-0.00013,0.03874,-0.05409,-0.0073,0.01628,-0.06117,-0.09134,-0.01062,0.07085,-0.00401,-0.02199,0.01538,0.01163,-0.04072,-0.06493,0.02623,0.06681,0.0609,-0.06145,-0.02548,-0.03416,-0.09941,0.03525,0.041,0.00597,0.13996,-0.03128,-0.0423,0.03572,-0.03794,0.07436,-0.04202,-0.01609,0.0309,-0.07633,0.01919,-0.0719,0.02709,-0.0159,-0.01085,0.05766,0.00359,-0.08102,0.03463,0.02991,-0.01911,-0.08232,0.03056,-0.04637,-0.00114,0.09413,0.0132,-0.04813,-0.01579,0.06423,-0.00053,0.00373,-0.05812,-0.11746,-0.09546,-0.12991,-0.09489,0.03485,0.03868,-0.16402,0.03385,0.05006,0.01223,0.09177,-0.076,-0.02417,-0.11558,0.00616,-0.0204,0.10497,-0.02921,-0.05532,0.03422,0.00023,-0.00067,-0.03845,-0.09327,0.01266,-0.00068,0.06268,0.00234,0.043,0.00132,-0.00074,0.13961,0.05888,-0.03177,0.03332,0.03292,0.11539,0.05795,-0.03268,-0.07652,-0.04858,-0.02988,0.02668,-0.02921,-0.02503,0.09229,0.02436,-0.05874,-0.00227,-0.03873,-0.04991,0.03765,0.07639,-0.01113,-0.06236,0.04845,0.07524,-0.07738,0.00742,-0.06177,0.06721,-0.02349,-0.05839,-0.08183,0.00845,-0.0454,-0.04224,0.02786,0.05389,0.05336,0.0505,-0.03185,0.03736,-0.08578,0.00144,-0.01399,-0.07642,0.03768,0.05453,0.04318,0.01729,-0.11148,-0.09218,0.01432,0.09056,-0.00325,0.00541,-0.02891,0.06301,-0.00651,-0.01006,-0.05577,0.0599,-0.0905,-0.01529,-0.0038,-0.02755,0.07325,0.06361,-0.00425,-0.00688,0.04237,0.02842,0.0535,0.02621,0.04927,-0.02223,0.01958,0.0188,0.054,-0.03864,-0.07665,0.06688,0.04614,0.07381,-0.04843,0.14318]},{"domain":"classical_physics","key":"acceleration_frictionless_incline","name":"Acceleration down a frictionless incline","package":"classical-physics-ai999x","example":"Calculate the acceleration down the incline for a block on a frictionless slope of 26 deg, assuming a gravitational acceleration of 8.16 m/s^2.","v":[-0.03587,0.03798,-0.0726,-0.04432,-0.06866,0.04041,0.10904,-0.0826,0.0007,-0.00642,-0.02262,-0.01163,0.06243,-0.16771,-0.04041,-0.03832,-0.05168,0.09223,0.02028,0.06762,-0.0833,-0.0279,0.00218,-0.0107,-0.07773,-0.13373,-0.00649,0.01674,-0.07714,-0.04776,-0.08579,0.05807,0.05047,-0.04875,0.01672,0.02861,0.04368,-0.02403,-0.01944,0.08338,0.02532,-0.07926,-0.09931,0.04593,-0.01805,0.11729,0.07365,0.00384,0.07415,0.02351,0.04568,0.01243,7e-05,-0.00062,-0.07887,0.04726,-0.06288,-0.02416,0.0405,-0.01969,0.03906,0.0801,-0.05206,0.04964,0.13069,0.05343,0.01886,0.01139,0.00753,-0.08851,-0.04982,0.04547,0.13607,-0.06143,0.01151,0.10355,0.06256,-0.03206,-0.12834,0.01554,0.00311,0.01509,0.03261,-0.01797,0.06667,0.06554,-0.03841,-0.09013,0.00901,0.08087,0.04114,-0.00945,0.04156,0.0524,-0.06197,0.06975,0.06127,0.00136,0.16036,-0.05865,-0.00088,0.01638,-0.04639,-0.00191,0.00027,0.00439,0.13844,-0.02557,0.00798,0.09867,-0.01308,0.06532,-0.00459,0.01114,0.11012,-0.03613,-0.02383,-0.06025,-0.05051,0.01926,0.01044,0.05462,0.08179,-0.04387,0.04738,-0.0003,-0.08713,-0.00757,-0.0308,-0.02972,0.0347,0.0352,0.01548,-0.05502,-0.0264,0.09532,0.01814,0.04256,-0.058,-0.0674,-0.1185,-0.0431,-0.08564,0.01625,0.06795,-0.05184,0.08271,0.00383,-0.01989,0.00753,-0.04544,-0.00341,-0.12637,-0.03184,-0.01377,0.11243,-0.04866,-0.05331,0.00827,-0.02353,-0.02127,-0.06115,-0.01113,0.0856,-0.04188,-0.01921,0.02314,0.03495,0.07238,-0.05258,0.11889,0.07307,0.0348,0.05515,-0.01293,0.04981,0.07634,-0.04452,-0.02216,-0.12421,-0.10285,0.00661,0.00853,0.06871,0.09781,0.04613,-0.07438,-0.00661,0.05195,0.02992,0.11059,-0.05931,-0.00482,-0.06834,0.0016,-0.02047,-0.01826,-0.01761,-0.01466,0.01697,0.0044,-0.01649,-0.08128,-0.01992,0.06536,-0.0296,0.01529,0.08331,0.15695,0.00774,-0.00266,0.00504,-0.1637,-0.02934,-0.07982,-0.02875,-0.00576,0.07983,-0.02636,-0.05162,-0.16893,-0.08332,0.10161,0.13478,-0.01213,-0.0591,-0.0971,0.03034,-0.00343,0.01463,-0.0859,0.05114,-0.11452,-0.04353,0.00905,-0.0548,0.05288,0.10693,-0.05754,0.07356,0.00745,0.06887,0.05688,0.00234,0.11406,-0.06013,0.0161,-0.10318,0.03494,-0.13075,-0.10388,0.04326,0.01548,0.04424,0.00194,0.09111]},{"domain":"classical_physics","key":"spring_launch_speed","name":"Speed of a body launched by a spring","package":"classical-physics-ai999x","example":"A 2.49 kg mass reaches a speed of 3.9 m/s when a spring compressed by 0.41 m returns to its natural length. What is the spring constant?","v":[-0.01497,-0.03186,0.0102,-0.2139,0.07453,0.05764,-0.02178,0.02057,-0.03215,0.01529,-0.11286,0.03404,0.04656,-0.1191,0.07572,-0.04179,-0.06987,-0.03155,-0.01272,-0.00099,-0.08404,0.06789,0.1526,0.0341,-0.0912,0.03244,0.06207,0.06006,0.03382,-0.07264,0.01729,-0.0314,-0.00925,0.02652,0.04698,-0.00385,0.0982,-0.06867,-0.01858,-0.03098,-0.03724,-0.10461,-0.07134,0.08715,0.00345,0.07452,-0.01631,0.07446,0.04459,0.0004,-0.01136,-0.06508,0.00292,-0.1537,0.00164,-0.01929,-0.05351,0.06219,0.07548,0.05806,0.01582,-0.07709,-0.05372,-0.08261,-0.12212,-0.01064,-0.0357,0.01059,-0.02858,0.05633,-0.01634,-0.01604,-0.0079,-0.07539,-0.10825,0.1173,-0.02172,-0.02912,0.01893,0.08513,0.01894,0.02025,-0.06481,0.08542,-0.00859,-0.01662,0.04609,-0.04965,-0.02331,0.097,0.03858,0.08881,0.0823,-0.00466,0.00631,0.09803,-0.03534,0.01236,0.08907,0.02023,0.00864,0.07839,-0.0048,-0.02417,-0.14385,-0.06068,0.1195,0.05499,-0.06726,-0.00256,-0.01236,0.03346,0.03885,-0.03454,-0.07012,0.03428,0.03853,-0.00059,0.05884,-0.04796,0.03272,0.02126,0.04139,-0.02033,-0.00955,-0.06607,0.04811,0.00444,-0.04333,-0.04351,-0.01537,0.08099,0.08301,0.01554,0.00136,0.10202,0.08402,0.10284,0.00825,-0.02744,-0.12417,0.05417,-0.03233,-0.08991,-0.01269,0.10132,0.03982,0.0402,-0.04581,-0.07516,0.03601,0.08186,-0.01715,-0.09154,-0.08023,0.02798,0.04135,-0.08257,-0.06949,-0.07179,0.00162,0.00102,-0.01184,0.05529,-0.01944,0.00121,0.07938,-0.04848,-0.04406,0.15648,-0.0511,0.01596,0.0919,0.04235,-0.01297,-0.05303,-0.03091,0.00597,0.04475,-0.09568,0.04884,-0.07184,0.01523,0.02227,0.02637,0.07525,0.02171,-0.01692,-0.04455,-0.00731,0.05051,-0.11692,-0.03305,-0.07375,0.02336,-0.06106,-0.00513,-0.03714,-0.11365,0.02283,0.15265,0.11212,-0.04046,-0.01915,0.03359,-0.03404,0.01403,0.11875,0.0714,-0.02593,-0.01775,-0.03468,0.03008,-0.06236,0.04307,-0.06744,0.00373,0.10351,0.00401,0.05395,-0.12351,-0.07305,0.03054,0.07597,0.02274,0.09176,-0.01217,0.09217,-0.01976,-0.07235,-0.04604,0.14466,-0.06391,-0.01183,-0.06848,-0.10194,0.00424,0.08934,-0.11956,-0.03444,-0.04932,-0.0256,0.04342,0.07881,0.00222,-0.08579,0.03834,-0.07688,0.01686,0.0402,-0.00845,0.09406,-0.00949,-0.0773,-0.0667,0.03886]},{"domain":"classical_physics","key":"net_work_kinetic_energy","name":"Work-energy theorem","package":"classical-physics-ai999x","example":"A vehicle of mass 1.47 kg changes velocity from 11.4 km/h to 4.8 m/s. Find the net work done on the vehicle.","v":[0.13911,-0.02641,0.04542,-0.05113,0.04153,0.09249,-0.02584,-0.09777,-0.06776,0.00316,-0.01935,-0.00169,-0.04828,-0.11919,0.0327,-0.0806,-0.03525,-0.00579,-0.00083,0.0123,0.01219,0.11742,0.05886,0.08393,-0.19211,0.04492,0.09002,0.02901,-0.10076,-0.01381,-0.05197,-0.03788,-0.0757,0.07132,-0.01767,0.05845,-0.06734,-0.04909,0.02629,-0.16256,-0.03864,-0.05069,-0.04747,-0.01092,-0.02147,0.03593,-0.00495,0.02821,0.0377,-0.02539,0.0442,-0.06491,0.02648,0.03174,0.14784,-0.00433,-0.03442,0.13391,0.03191,2e-05,0.03683,-0.03239,-0.00784,-0.03381,0.03459,0.0643,0.02579,-0.1123,-0.06734,0.08222,0.0271,-0.02472,-0.01226,-0.12485,0.01227,0.05662,0.07558,-0.01166,-0.01621,-0.00394,-0.13108,0.01034,-0.03239,-0.01929,-0.09226,-0.02489,0.06777,-0.07334,-0.06025,0.00527,0.01584,0.04032,0.00131,-0.07201,-0.0737,0.0336,0.02262,0.06234,0.0259,0.02038,0.03463,0.01415,-0.04247,-0.03084,-0.15994,0.00143,0.04323,-0.02828,0.04095,0.06123,0.01615,0.06233,0.00626,0.00419,-0.09395,0.00103,0.06362,-0.11479,0.13857,0.05619,-0.00396,-0.05829,0.03165,0.06874,0.013,0.00799,0.08185,-0.02801,0.00533,0.05396,-0.0152,0.02511,-0.00299,0.02587,-0.12612,-0.09046,0.05511,0.10725,-0.0045,-0.00878,-0.03964,0.00306,-0.02302,0.03942,-0.04836,0.0303,-0.08144,0.03265,0.06116,-0.09419,0.06071,0.06389,-0.10402,-0.03396,-0.08607,0.04472,-0.00295,-0.10503,0.0056,-0.0755,0.03922,-0.07243,-0.00793,0.02652,-0.06497,0.014,0.01068,-0.04428,-0.01003,0.03301,0.04393,0.01707,0.04314,0.05358,-0.02674,-0.02715,0.06523,-0.00023,0.00841,-0.13061,0.09996,-0.07774,0.02937,-0.10753,0.01157,0.05001,-0.04063,-0.04877,0.07614,-0.02504,-0.08261,0.02853,0.01765,0.11852,0.05298,-0.00571,-0.06673,0.00461,0.01662,-0.08029,-0.03662,0.09215,0.02767,-0.06164,0.00997,0.01961,0.00083,-0.07858,0.03457,-0.0557,-0.0009,-0.05522,-0.06295,0.01874,0.06294,-0.10604,0.05511,-0.01857,0.03537,-0.05516,0.05662,-0.03261,0.00743,0.13465,0.00639,0.05298,-0.0218,0.1502,-0.00683,0.01616,-0.05826,0.13669,0.0415,0.03433,0.04267,-0.14284,0.01167,-0.04403,-0.01497,-0.05085,0.11808,-0.04638,0.03295,0.20371,0.05262,-0.10464,0.01999,0.00405,0.11058,0.05769,-0.01886,0.0387,0.00136,-0.05581,-0.01204,0.10566]},{"domain":"classical_physics","key":"tension_hanging_at_rest","name":"Tension in a rope holding a hanging body","package":"classical-physics-ai999x","example":"A weight of 1060 g is suspended from a cord. The tension in the cord reads 5.41 N. What is the gravitational acceleration here?","v":[-0.12383,0.01684,-0.00473,0.02415,-0.01883,0.06296,0.07456,-0.01381,0.10341,-0.02696,-0.04597,0.10876,-0.02174,-0.07585,0.05426,-0.08023,-0.08435,-0.01131,0.08057,-0.08211,0.06582,0.04701,-0.00461,-0.1356,-0.09396,0.12067,-0.06909,0.05618,-0.07107,-0.17381,-0.04817,0.01761,0.0571,-0.01349,-0.19106,0.07088,0.0015,0.04197,0.16891,-0.00499,0.05659,0.02045,-0.21464,0.07383,-0.06693,0.06403,0.02591,-0.04633,0.01811,-0.0187,-0.0886,0.01009,0.0761,-0.06509,0.05864,-0.08651,-0.17458,-0.03303,0.00819,0.08471,-0.04243,-0.00279,-0.02352,-0.00524,0.01272,-0.00524,0.01876,-0.01141,0.09405,-0.00213,0.00313,-0.04182,0.05364,-0.13226,-0.02857,0.03235,-0.06279,-0.02835,-0.02777,0.00963,-0.07406,-0.03548,-0.01099,-0.11022,0.08025,0.13126,-0.01923,-0.02826,-0.04225,0.06756,-0.12416,-0.04633,-0.01045,0.01823,0.01282,0.0268,0.08074,0.057,-0.02242,0.02839,-0.02954,-0.0982,-0.12145,0.0678,0.07169,-0.03801,0.07888,-0.02268,-0.033,0.00538,-0.12675,-0.02475,0.04722,0.02762,0.00588,0.04215,0.02811,-0.02642,0.06685,-0.0545,0.03575,-0.02608,-0.01109,0.08547,0.1065,-0.01765,0.01307,-0.01491,-0.05118,-0.02578,0.06668,-0.0531,-0.01147,-0.0103,0.06018,-0.00292,0.05011,-0.09545,-0.04963,-0.12528,0.00757,-0.01842,0.11803,0.05403,0.10451,-0.01243,0.09861,0.07194,0.03029,-0.08858,0.0001,-0.10034,-0.02191,0.00035,-0.00676,-0.04643,0.01507,-0.03037,-0.06291,-0.1204,-0.00652,-0.00641,-0.0065,0.04617,-0.00752,0.0205,-0.01519,-0.04151,-0.03142,0.03603,0.04497,-0.07064,0.00509,0.02677,0.05451,0.07897,-0.06221,-0.05338,-0.0334,0.13005,0.05659,0.02109,0.05556,0.0263,0.07588,-0.04191,0.03244,-0.06538,-0.00339,-0.07084,0.07779,0.08285,0.04746,-0.03692,0.08458,0.05084,0.00487,0.0723,-0.01996,0.03017,0.0244,-0.04926,-0.11073,-0.05953,-0.0374,0.04224,0.01533,0.05545,-0.03531,-0.01863,-0.01585,0.03956,-0.07816,-0.06619,0.06044,-0.01707,-0.00208,0.09662,-0.06775,0.0303,-0.08194,0.09752,0.08794,0.03535,-0.00454,0.01318,0.08563,0.06373,-0.01797,0.00371,0.05465,-0.00521,-0.08378,-0.07063,-0.00736,0.0691,-0.01926,-0.05795,0.00468,0.01949,0.07098,0.0941,0.01148,0.04855,-0.01735,0.00482,0.06833,0.05541,0.01718,0.04277,-0.05195,0.06025,0.04752,0.00904,0.01362,0.01291]},{"domain":"classical_physics","key":"average_force_from_momentum_change","name":"Average net force from a change of momentum","package":"classical-physics-ai999x","example":"An object slows down such that its momentum decreases from 6.9 kg*m/s to 3.5 kg*m/s in 0.61 s. Find the average net force.","v":[0.00309,0.00098,0.00316,-0.02764,0.03642,0.02306,0.06483,-0.04813,-0.0374,0.10169,0.01112,0.00427,0.02452,-0.03273,-0.01462,-0.0233,0.00106,0.03721,-0.00243,0.04204,0.02457,-0.05673,-0.02488,0.06003,-0.04422,0.02605,0.0341,0.02624,-0.01631,-0.05906,0.00598,0.03793,0.01052,0.05069,-0.14104,0.10555,-0.00731,-0.1155,0.0384,0.02514,-0.03941,-0.0545,0.02878,0.06111,-0.00751,0.05289,0.03311,0.00886,0.0383,0.01307,-0.06719,-0.00673,-0.06574,0.09486,0.15109,-0.01159,-0.04916,0.04143,0.07851,-0.111,-0.04258,0.08194,-0.04519,0.01731,0.02805,0.01777,-0.00581,-0.00184,0.01445,0.02469,0.04913,-0.04559,-0.06949,-0.09205,0.02923,0.07223,0.04426,-0.01771,-0.04302,-0.07211,-0.19823,-0.08862,0.02036,-0.04934,0.03854,-0.03781,0.04379,-0.05371,-0.09004,-0.01082,-0.02622,0.02827,-0.05662,-0.09123,-0.03895,-0.01294,0.12019,0.01131,0.0361,0.0425,-0.01703,0.0429,-0.00826,-0.03875,-0.0534,0.08769,0.02289,-0.08587,0.12505,0.11629,0.00147,0.02088,0.0011,-0.00274,-0.08109,-0.0155,0.01416,0.07391,0.05271,0.02419,-0.0372,0.0202,0.0647,0.14756,-0.05553,-0.06952,-0.00231,-0.01135,0.12626,0.02316,-0.0758,-0.02824,0.01542,-0.00945,-0.14048,-0.16502,0.06888,0.1029,0.05289,0.0106,0.00448,0.0456,0.04979,-0.09024,-0.05432,0.0441,-0.0216,0.02077,0.03103,0.02509,0.02858,-0.09335,-0.10373,-0.08372,0.02812,0.04566,0.0081,-0.0245,-0.02596,0.01738,0.01192,-0.03343,0.09085,0.02709,-0.0811,0.0267,0.06034,-0.09051,0.00347,-0.02678,-0.03694,-0.02267,0.0362,0.03405,0.03679,0.03309,0.04184,0.02145,-0.05893,0.01023,0.0341,-0.068,0.0851,-0.06912,-0.03578,0.05922,-0.07283,-0.03041,0.03675,-0.11538,-0.03664,0.12107,-0.01028,-0.02499,0.0086,0.08041,-0.06775,-0.10029,0.03259,-0.01979,-0.06529,0.03538,0.05205,-0.00113,-0.0161,0.06077,0.05976,0.00264,0.07751,0.0874,-0.03336,-0.0047,-0.05753,-0.10288,-0.03115,-0.17663,-0.01848,0.12565,-0.02174,-0.0847,0.10459,0.05375,0.04146,0.12506,-0.00486,-0.06301,-0.0121,0.04533,0.05543,0.0037,-0.10746,0.01493,0.00329,0.03225,-0.04472,-0.07731,0.00611,-0.1095,0.08496,0.07885,0.04839,0.00168,-0.12205,0.16003,0.15593,-0.14159,0.09757,0.01726,-0.01071,0.04335,-0.07496,0.06768,-0.03352,-0.02545,-0.12761,-0.00671]},{"domain":"classical_physics","key":"speed_after_fall_from_rest","name":"Speed after falling from rest","package":"classical-physics-ai999x","example":"A toy rocket falls from rest for a height of 3.11 m. The gravitational acceleration is 6.99 m/s^2. What speed does it reach?","v":[-0.05925,0.03697,0.06362,-0.07345,-0.01955,0.10103,0.01414,-0.0315,-0.07743,-0.04805,-0.04767,-0.01692,-0.00733,-0.1026,-0.05193,-0.12237,-0.03797,-0.02872,0.0397,-0.02603,-0.05516,-0.0124,0.1061,0.09796,-0.00885,0.0131,0.03091,0.01892,-0.07007,-0.07267,-0.09437,0.10252,0.00012,-0.01456,-0.02215,0.02876,0.12311,-0.05916,-0.04187,-0.03238,0.03962,-0.05953,-0.05983,-0.03112,-0.05178,0.11026,-0.00624,0.01293,-0.00722,0.11136,0.0168,-0.04662,0.03393,-0.11814,-0.04673,0.04904,0.04646,0.02474,-0.01172,0.00081,-0.04277,-0.01728,0.03776,-0.05161,-0.11794,0.02502,0.0858,0.05371,0.00822,0.05346,0.10568,0.07828,0.01811,-0.05728,-0.11627,0.02962,-0.03893,-0.01371,-0.1085,-0.00376,0.02833,0.06356,0.03585,0.06222,-0.06955,0.08167,-0.0146,-0.08607,-0.00836,0.13807,0.05331,0.09798,-0.04105,0.10979,-0.00799,0.10591,0.08391,-0.07098,-0.00969,-0.01075,-0.01471,-0.0461,0.02565,-0.07004,-0.05919,0.00997,0.1136,-0.00259,-0.07897,0.03155,-0.05641,0.07088,0.03281,0.02491,-0.01644,0.05251,-0.02147,-0.05483,0.03175,-0.01624,-0.05794,-0.0381,0.02317,-0.02539,0.04014,0.08043,-0.03457,0.0956,-0.04521,0.03143,0.08613,0.02774,0.00444,-0.01472,0.00939,0.003,0.06591,0.14353,0.08346,-0.01316,-0.08072,0.16157,0.03137,-0.03236,-0.09498,-0.01517,0.10319,0.02372,0.01607,0.01268,0.08344,-0.0368,0.00522,-0.06689,-0.04399,0.07146,-0.02581,-0.06695,-0.09834,-0.028,0.06407,0.07904,0.04146,-0.01452,-0.14151,-0.11004,0.03557,0.05052,0.02243,0.05834,0.0307,0.05991,0.045,0.05235,-0.01092,-0.05779,-0.06731,0.11149,-0.01191,-0.06862,-0.07966,0.01433,-0.02966,0.06446,0.11299,-0.00572,-0.05326,-0.06179,0.07062,0.03873,-0.05022,-0.04661,0.05386,-0.08377,-0.0139,-0.05199,-0.07315,-0.07181,-0.07058,0.05021,-0.02456,0.07894,-0.0813,-0.10968,0.03756,0.01253,-0.1157,-0.00525,0.04682,-0.09847,0.0222,0.04474,-0.01053,-0.02915,-0.06403,-0.00037,0.11913,0.15646,0.01295,-0.01107,-0.05648,-0.0771,0.08537,0.02432,-0.0218,0.05418,-0.008,0.10272,0.01689,-0.04358,-0.02382,0.05963,-0.13523,-0.03133,-0.00783,-0.09474,-0.05285,-0.00163,-0.05249,0.06101,0.01299,0.01822,-0.04875,0.07683,0.05128,-0.00375,0.02637,-0.01589,0.087,0.02892,-0.06904,-0.05752,-0.04801,-0.08445,0.16998,0.00414]},{"domain":"classical_physics","key":"electric_force_in_field","name":"Force on a charge in an electric field","package":"classical-physics-ai999x","example":"A charge of 2 uC is placed in an electric field of 30000 N/C. What is the electric force on it?","v":[0.04769,-0.01238,-0.00851,-0.10082,0.00608,0.01002,-0.03243,-0.02962,-0.08658,-0.13666,0.00516,-0.04083,0.02537,0.04144,0.04315,-0.05664,-0.13744,0.095,0.09101,0.03249,0.00433,0.05272,0.04668,-0.01234,-0.02064,0.04816,-0.06442,0.05774,-0.05651,-0.09567,0.00346,0.05635,0.15769,0.00694,-0.14765,0.09609,0.03941,-0.03147,0.0379,-0.01471,0.14639,0.06805,0.05565,0.01884,-0.00133,0.04344,0.0246,0.00324,-0.00647,-0.00639,-0.04648,-0.07964,-0.07733,0.05009,-0.0531,0.03471,-0.12605,0.04578,0.01212,-0.01224,0.01054,0.03283,-0.07062,-0.11582,-0.04804,0.01676,0.08206,0.08608,-0.01064,0.03283,0.09672,0.0351,-0.06524,-0.04738,-0.06779,-0.01081,0.00275,-0.00824,0.01866,0.02307,-0.03626,-0.12794,-0.01512,-0.04684,-0.12047,0.02908,0.04673,-0.09825,0.02451,-0.0639,0.05493,-0.02868,0.07243,0.03378,-0.02689,-0.06225,-0.08394,-0.05055,0.13437,-0.08159,0.03995,-0.06487,0.05068,-0.02083,-0.03247,0.04595,0.05786,-0.00394,0.08713,-0.14164,-0.02626,0.00642,0.10503,0.04772,0.11059,0.05677,0.05701,0.102,-0.00245,-0.05473,-0.11186,0.02276,-0.01039,-0.00399,-0.08509,-0.06186,0.06563,0.0101,0.06331,-0.02616,-0.00214,0.01353,-0.03054,-0.08707,-0.06499,-0.06969,0.05968,0.01801,-0.04081,-0.17474,0.06455,0.00371,-0.03438,0.01797,0.03097,-0.0684,0.12247,0.01225,0.02552,0.05891,0.0848,-0.00199,-0.00829,-0.02781,-0.02509,0.01048,0.07604,0.01775,-0.06842,0.03928,-0.0118,0.04668,0.05083,-0.0038,-0.06349,0.10772,0.01686,-0.01326,-0.10744,-0.06412,-0.04097,-0.08755,0.02063,0.15047,0.07501,0.10873,-0.02256,0.06571,-0.07179,0.06001,-0.00996,-0.02533,0.05082,-0.03601,0.02371,0.02747,-0.02027,-0.01623,-0.05357,0.0327,0.07853,-0.01692,-0.0338,0.01662,-0.09458,-0.00953,-0.07177,-0.07313,-0.05278,0.02491,-0.028,0.02259,0.09958,0.00772,-0.02573,0.10212,-0.10757,0.02226,0.12726,0.06078,-0.03802,0.06699,0.06366,-0.01097,0.04718,-0.09283,-0.07159,-0.00265,-0.00211,0.00764,-0.16911,0.0043,0.04469,0.01321,0.06167,0.02826,0.06924,-0.1067,0.11865,0.02108,-0.02094,-0.00802,-0.02819,0.07785,0.02138,-0.03803,0.08911,-0.04512,0.04051,-0.02681,-0.12994,-0.02072,0.01066,-0.00211,0.01676,-0.01987,0.06423,-0.00128,0.00456,0.02564,0.0495,0.05096,0.03458,0.07934,0.00486,0.1256]},{"domain":"classical_physics","key":"point_charge_field","name":"Electric field of a point charge","package":"classical-physics-ai999x","example":"What is the electric field 0.3 m from a point charge of 2 uC?","v":[0.04637,-0.02634,0.03452,-0.1011,0.05546,-0.05197,-0.05208,0.01831,-0.02843,-0.15738,-0.02462,-0.0476,0.03624,0.06441,0.02799,-0.03509,-0.07393,0.07561,0.04421,0.02688,-0.05476,-0.02711,-0.02598,-0.03098,-0.01484,0.04714,-0.08095,0.0332,-0.00183,-0.07059,0.03661,0.03397,0.0827,-0.0407,-0.11093,0.12626,0.06143,0.03308,0.04356,-0.07393,0.08108,0.0732,-0.01201,0.03947,-0.13831,0.07679,0.01592,-0.01041,-0.05075,-0.04846,0.05388,-0.02675,-0.05415,0.00857,-0.09708,0.00394,-0.0964,0.10454,-0.01005,-0.03981,0.01799,-0.00768,-0.03741,-0.1612,-0.06764,0.01663,0.03143,0.05322,-0.05772,0.07792,0.04624,0.05528,-0.11666,-0.02906,-0.01554,-0.00609,0.01021,-0.01086,-0.07641,0.0714,0.03098,-0.03887,-0.03382,-0.01002,-0.05947,0.06651,0.0536,-0.0777,0.03519,-0.065,0.10169,0.01422,0.06488,0.08635,-0.0326,-0.03371,-0.09608,-0.01463,0.04932,-0.06594,0.03256,-0.10719,0.02314,0.01227,-0.09988,0.00349,0.01491,0.01248,0.03806,-0.07681,0.02775,-0.03036,0.03765,0.13516,0.15045,0.0496,0.07204,0.07867,-0.05832,-0.0785,-0.03847,-0.01914,0.03102,-0.01204,-0.1045,-0.07987,0.07236,0.01467,0.10107,-0.03483,0.04793,0.02991,-0.02972,-0.03377,-0.03718,-0.04465,0.05994,0.03631,-0.10153,-0.12592,0.0194,0.01338,-0.04773,-0.02704,0.03376,-0.03713,0.11957,0.01208,0.03423,0.08533,0.03296,-0.03645,0.08869,-0.0625,0.02172,0.09191,0.09348,0.03201,-0.03033,0.02132,-0.11948,-0.02557,0.00378,-0.02462,-0.00494,0.06136,-0.04091,-0.05237,-0.01963,-0.04099,-0.00961,-0.12997,0.01095,0.05994,0.0896,0.00429,-0.1167,0.0656,-0.07759,0.08075,0.02718,-0.02621,0.07348,-0.03901,0.06735,0.07061,-0.0336,-0.01417,0.01712,-0.04724,0.04024,-0.08193,0.06034,0.12765,-0.04236,-0.00837,-0.04966,-0.09843,0.00078,-0.07636,-0.02782,-0.00747,0.15439,-0.0336,0.01286,0.04416,-0.08492,-0.02364,0.16704,0.04672,-0.03474,0.03407,0.08957,-0.07734,0.05149,-0.06639,-0.12003,-0.07065,0.01011,0.03806,-0.10325,-0.02263,0.08155,0.09463,-0.00547,0.0328,0.08929,-0.09625,0.1174,-0.00155,0.04555,-0.01455,0.03092,0.04219,-0.0529,-0.00937,0.05055,-0.03193,0.02774,-0.07873,0.003,-0.06062,0.03077,-0.01539,-0.06851,0.00938,0.05159,0.01671,0.02902,0.09202,0.10292,0.07489,0.05388,0.01325,-0.01406,0.08689]},{"domain":"classical_physics","key":"point_charge_potential","name":"Electric potential of a point charge","package":"classical-physics-ai999x","example":"What is the electric potential 0.5 m from a point charge of 3 nC?","v":[0.05752,-0.04842,0.04027,-0.05324,0.04393,-0.03915,-0.05673,0.04086,-0.07294,-0.10659,-0.0561,-0.0335,-0.01955,-0.0335,0.02616,-0.01641,-0.10942,0.07049,-0.0311,0.04392,-0.02576,0.00359,-0.03737,-0.00038,-0.01798,-0.00282,-0.04184,0.05545,0.06258,0.01163,-0.02257,0.0416,0.06621,-0.01197,-0.11989,0.11394,0.0701,0.0063,0.03942,-0.04346,0.03503,0.08403,0.00901,0.04525,-0.1026,0.09807,-0.0744,-0.03757,-0.01584,0.02717,0.08914,-0.0275,-0.0705,0.00623,-0.09266,-0.06277,-0.04679,0.08801,-0.05143,0.00696,0.0348,0.02926,-0.02592,-0.13529,-0.05265,0.07195,0.02492,0.00557,-0.03952,0.08467,0.0807,0.06944,-0.07815,-0.03253,0.01021,0.08824,-0.09658,-0.05603,-0.07546,0.05781,-0.01679,-0.02106,-0.06282,-0.07514,-0.03984,0.03096,0.05654,-0.03099,0.02753,-0.07746,0.15386,0.12402,0.01209,0.04636,-0.07632,0.03765,-0.04254,-0.03089,0.0376,-0.00386,0.05957,-0.07749,0.0727,0.03432,-0.14374,0.01109,0.025,0.03049,0.03121,-0.09095,0.04218,-0.07227,0.00962,0.12036,0.126,-0.01914,0.02539,0.02278,-0.04789,-0.06687,0.03688,-0.07535,0.02687,0.00945,-0.07918,-0.01052,0.01571,0.04438,0.08589,0.03764,0.07755,0.04686,0.04492,-0.03557,-0.00357,-0.0222,0.04219,0.03721,-0.02625,-0.12882,-0.00851,-0.00623,-0.00651,-0.10493,0.06192,-0.08427,0.07925,-0.03385,0.06655,0.10443,-0.02689,0.00469,0.11062,-0.01756,-0.04493,0.10999,0.07753,-0.02411,0.01166,-0.02277,-0.19502,-0.05721,0.05815,-0.03261,0.03855,0.0105,0.00498,-0.05192,0.01631,-0.09811,-0.06434,-0.06313,0.00021,0.02138,0.08569,-0.00094,-0.16264,0.02497,0.00419,0.02291,0.02819,-0.06469,0.0978,-0.00747,0.03272,0.01322,-0.0996,-0.07378,0.02169,-0.07223,0.00544,-0.04572,0.10913,0.14526,-0.00191,-0.0463,-0.04649,-0.04484,0.0793,-0.07382,-0.04166,-0.0323,0.11566,-0.0229,-0.01834,-0.03353,-0.08557,-0.08753,0.12877,0.06904,-0.00954,-0.00535,0.07091,-0.07398,0.08217,-0.00018,-0.06081,-0.08079,-0.01174,-0.02045,-0.08618,-0.03483,0.04293,0.14128,0.0255,0.0243,0.0254,-0.06935,0.10578,-0.04522,0.00191,0.00471,-0.01162,0.04688,-0.08262,-0.01901,-0.01359,0.05945,0.06105,-0.05636,0.0118,0.01191,0.08025,-0.04656,-0.00542,-0.06763,0.01675,0.02512,0.03234,0.11494,0.09756,0.05456,0.07271,-0.03843,0.05198,0.12795]},{"domain":"classical_physics","key":"uniform_field_potential","name":"Potential difference in a uniform field","package":"classical-physics-ai999x","example":"Parallel plates are 5 mm apart with a uniform electric field of 2000 V/m between the plates. What is the potential difference?","v":[0.01437,-0.09173,0.14172,0.01092,0.01652,-0.06378,0.03435,0.01753,0.00875,-0.02814,0.04626,-0.01567,0.05146,0.0001,0.12135,-0.0828,-0.08752,0.03766,-0.03787,0.06469,0.02426,0.04127,0.05025,-0.05558,0.06818,0.0288,-0.01737,-0.025,-0.01411,-0.0376,0.01337,0.09823,-0.00189,-0.0297,-0.10003,0.12972,0.08562,-0.04882,0.07256,0.03434,0.00781,0.03705,0.12661,-0.08824,-0.04376,-0.05254,-0.07923,0.02387,-0.05925,0.10103,-0.05717,0.02261,-0.12231,-0.04288,-0.01336,0.00832,0.06634,0.06812,0.01112,-0.00951,0.00675,0.0594,0.0179,-0.14294,0.00061,0.12054,-0.00366,0.06,-0.0178,0.06582,0.14867,0.16901,-0.02159,0.00991,-0.08976,0.07159,-0.07053,-0.02388,-0.0099,-0.00545,-0.02256,-0.07532,-0.00042,-0.04033,-0.13251,-0.00089,0.14237,0.04575,0.0744,-0.01915,-0.00767,-0.00562,-0.01959,0.02934,-0.06708,0.05516,0.00567,-0.06249,0.02664,0.04707,0.00433,0.0151,0.02248,0.05206,-0.0892,0.01654,0.10617,-0.0428,0.02755,-0.08604,-0.03075,-0.04731,-0.03679,0.02706,0.03633,-0.02981,-0.00737,0.01789,-0.111,0.03282,-0.04358,0.00849,-0.10022,0.09825,-0.05535,-0.0576,0.07032,0.07421,-0.03074,-0.05058,0.0742,0.07852,0.06824,-0.01859,-0.18626,-0.01571,0.02095,-0.00571,0.10027,-0.00158,0.05481,-0.05788,0.03453,0.00469,0.08956,-0.04171,-0.02664,0.03952,0.08029,0.13298,0.07609,-0.01345,0.08958,0.02745,0.04362,-0.10101,0.04382,-0.08193,-0.00538,0.00857,-0.00907,0.01531,0.13684,-0.03971,0.02945,0.02841,-0.07118,-0.05234,-0.02417,-0.09851,-0.10815,-0.06821,0.0155,0.01952,0.05178,0.05464,-0.08554,0.04583,-0.02152,-0.07222,0.01347,-0.01145,0.04739,0.0133,0.06369,0.06024,-0.01302,-0.10088,0.04213,-0.04659,-0.00288,0.06904,-0.00614,0.04207,-0.0286,-0.11596,-0.03035,-0.06441,0.00993,0.01983,0.00568,0.02375,-0.0062,-0.12358,-0.05249,-0.01322,-0.0792,-0.0586,0.02914,0.03205,-0.08914,0.05585,-0.0683,-0.07162,0.05296,-0.00147,0.07936,0.00894,-0.07923,-0.0513,-0.1419,-0.08026,0.08889,-0.04833,0.02685,-0.01613,-0.03616,0.02259,0.11083,0.01101,-0.05262,-0.09526,-0.02499,0.06946,0.07268,-0.00992,-0.03375,0.00769,-0.01009,-0.0473,-0.14333,0.01199,0.08225,-0.0484,0.08624,-0.05271,-0.02043,-0.0913,0.02399,0.03977,0.08156,-0.0115,-0.07822,0.02592,0.05725,0.06396]},{"domain":"classical_physics","key":"capacitance_definition","name":"Charge on a capacitor","package":"classical-physics-ai999x","example":"A 10 uF capacitor is charged to 12 V. How much charge does it hold?","v":[-0.00655,0.07468,-0.01533,-0.04398,-0.05837,-0.08941,0.06086,-0.00807,-0.08259,-0.03311,-0.02481,0.01307,0.02625,0.0689,0.10076,-0.01362,-0.14584,0.03046,0.09187,0.01042,0.10212,0.07105,0.01004,-0.02406,-0.20503,-0.02715,0.0334,0.03538,-0.03322,-0.0873,-0.0332,0.1359,0.03735,-0.01567,-0.09896,0.07602,0.03756,-0.09712,0.04584,0.00958,0.0618,0.04591,0.03454,-0.00766,-0.0211,-0.03389,-0.06726,0.06749,0.06288,-0.00727,0.00151,-0.08068,-0.01507,0.01426,-0.01352,0.02742,-0.04606,-0.00817,-0.10108,0.05402,-0.00076,-0.09926,-0.14312,-0.02726,-0.04057,0.00389,-0.01402,-0.00882,-0.0529,0.02558,0.02688,0.08568,0.01719,0.06643,-0.0013,0.01717,-0.02487,-0.07292,-0.00361,0.00108,0.00597,-0.13643,-0.04035,-0.03801,-0.00623,0.00808,0.03124,-0.02312,0.01452,-0.01365,0.11317,0.01667,0.10061,0.01694,-0.00676,-0.03983,-0.05021,-0.04964,0.04124,-0.11375,-0.03666,-0.01556,0.04431,-0.01193,-0.05618,-0.01737,0.11627,0.01091,0.08888,-0.00372,0.0314,-0.06354,0.01204,0.04644,0.09761,0.06186,0.09043,0.11286,-0.04622,0.05966,-0.07436,-0.01153,0.08765,0.12045,-0.09712,0.03378,0.06372,-0.06058,-0.02728,0.04247,0.00588,0.05352,-0.01889,-0.04064,0.05092,-0.11402,0.09605,0.0174,-0.05387,-0.07498,0.07613,-0.02754,0.00817,-0.0802,0.03623,-0.05126,0.06154,0.11108,0.04886,0.10182,0.01425,0.01043,0.05155,-0.06044,-0.06856,0.05138,-0.04701,-0.06164,-0.07521,0.06194,-0.07888,-0.00277,0.14302,0.0419,0.04201,0.11528,0.00444,0.05417,-0.0383,-0.13575,-0.08102,0.01474,0.02731,-0.03491,-0.06085,0.02502,-0.07331,-0.05384,0.06769,0.01232,0.03615,0.12155,0.11257,0.02895,-0.04149,-0.08471,-0.13869,-0.09192,-0.05596,0.04987,0.05342,-0.10194,-0.0465,-0.04084,-0.0177,-0.02639,-0.02675,0.05493,0.04994,0.00761,-0.04645,0.02943,0.11751,-0.08996,0.00921,0.01654,-0.10928,-0.08302,0.09885,0.03297,-0.01073,-0.09684,0.02189,-0.01732,0.024,-0.11502,0.01625,0.01043,-0.05585,0.04646,-0.10326,0.03272,0.10089,-0.00875,0.02348,0.04372,0.02086,-0.0319,0.13642,0.0197,0.00844,-0.00126,-0.01803,0.04279,0.04417,0.06038,0.05648,0.01936,0.0352,-0.09967,-0.12271,-0.03137,0.0724,0.00749,0.04987,-0.07444,0.02854,-0.04167,0.03969,-0.0081,0.02568,0.03352,-0.05242,0.06258,-0.01911,0.10589]},{"domain":"classical_physics","key":"capacitor_energy","name":"Energy stored in a capacitor","package":"classical-physics-ai999x","example":"A 100 uF capacitor is charged to 20 V. What is the energy stored in the capacitor?","v":[0.04432,0.00696,-0.00948,-0.04968,-0.05821,0.00334,0.05405,-0.03139,-0.07896,0.02007,-0.00604,0.00871,-0.01451,0.09323,0.05451,-0.0263,-0.05422,0.00866,0.00253,-0.02697,0.04276,0.09125,-0.00762,0.03399,-0.20879,0.01502,0.12626,0.03332,-0.10762,-0.03816,-0.04923,0.06284,-0.01485,0.02622,-0.08027,0.11744,0.01593,-0.07752,0.01246,-0.06899,-0.03348,0.00391,0.00854,0.02581,-0.01451,0.02139,-0.08353,0.01636,0.06302,0.06743,0.05767,-0.07009,-0.04509,0.10023,-0.00475,0.02564,-0.03935,0.00778,-0.17781,0.06479,-0.00245,-0.08412,-0.10478,-0.04616,-0.0561,0.00954,-0.08296,-0.07048,-0.04874,-0.01308,0.0381,0.07432,-0.02371,0.06915,-0.03676,0.04944,0.02383,-0.08485,-0.0315,-0.0357,-0.02503,0.00976,-0.06011,-0.09021,0.0039,-0.13287,0.00682,0.00604,-0.03042,-0.01549,0.06878,0.08847,0.10069,0.02194,-0.07371,0.00922,-0.01895,-0.09648,0.0415,-0.0547,-0.03987,0.0805,0.01672,0.01843,-0.17629,-0.13507,0.07353,-0.01477,-0.0349,-0.00337,0.09129,-0.01215,0.04125,0.01578,0.04246,-0.02081,0.08477,-0.01611,0.01967,0.11154,-0.05719,-0.0061,0.09931,0.0756,-0.14067,0.03443,0.01169,0.00404,-0.02953,0.08026,0.00914,-0.00759,0.04673,0.02996,0.15703,-0.00535,0.0848,0.00077,0.00698,-0.05484,0.05293,-0.07146,0.03649,0.01884,0.06304,0.00056,0.00082,0.08084,0.04974,0.03015,0.00474,0.03166,0.13373,-0.11603,-0.03782,0.03715,-0.01811,-0.06893,-0.01634,0.01123,-0.02899,0.01325,0.13308,0.11601,0.02629,0.0361,-0.00772,0.08726,-0.06682,-0.02762,-0.05897,0.00325,0.05635,-0.05132,-0.06795,-0.06882,-0.0309,-0.02261,0.10743,-0.01741,0.05753,0.03771,0.01263,0.01972,-0.05892,-0.05527,-0.09605,-0.06703,0.00671,0.01857,0.05233,-0.1434,0.02408,0.00306,-0.0055,-0.0116,-0.04296,0.03564,0.03099,-0.04848,0.0415,0.01159,0.12677,-0.0601,0.05287,-0.10966,-0.09792,-0.1321,0.02482,-0.04349,0.01792,-0.08797,0.01473,0.03101,-0.02641,-0.10597,0.02459,-0.11865,-0.00553,-0.01325,-0.02828,0.0193,0.08232,0.08183,-0.03799,0.03446,0.0692,-0.00399,0.09385,0.01994,0.01521,-0.00063,-0.00496,0.17079,-0.02959,0.04039,0.03458,0.0395,0.0065,-0.05637,-0.12222,0.00917,0.11767,0.05893,0.0349,-0.05335,-0.0003,-0.01691,0.08193,-0.00312,-0.02881,-0.01671,-0.10168,0.06878,-0.02191,0.10873]},{"domain":"classical_physics","key":"parallel_plate_capacitor","name":"Capacitance of parallel plates","package":"classical-physics-ai999x","example":"A capacitor has parallel plates of area 0.01 m^2 with a plate separation of 1 mm. What is its capacitance?","v":[-0.02503,-0.09061,0.08941,0.0016,-0.02072,-0.08809,0.01095,0.00363,0.00766,0.09792,-0.00066,0.06771,0.09415,0.07601,0.0549,-0.05925,-0.02878,0.04843,0.11805,0.11759,0.08856,0.03299,0.14487,-0.07154,-0.13552,-0.03079,0.00947,0.0762,-0.00894,-0.03952,-0.03613,0.08532,-0.01949,-0.05104,-0.07675,0.15274,-0.01708,-0.08945,-0.01058,0.01964,0.07751,0.05128,0.0552,-0.04949,-0.05407,-0.06898,-0.00546,0.01583,-0.03913,0.08494,-0.00264,-0.05022,0.06008,0.08591,-0.05443,0.07592,0.02086,0.15962,-0.01178,0.00254,0.02815,-0.09393,-0.12919,-0.03534,-0.1041,0.01541,-0.05068,0.0296,0.00199,0.03321,0.13611,0.07108,-0.04691,0.0323,-0.02859,-0.02547,-0.02601,-0.14816,-0.05014,-0.04489,0.01296,-0.04199,0.02133,-0.02463,-0.01241,-0.03167,0.00475,0.0083,0.03176,-0.02868,-0.03658,0.02602,0.01146,0.05958,-0.04104,-0.05402,-0.03476,-0.04905,-0.02157,-0.09107,-0.02911,0.07465,-0.01483,0.08163,-0.09565,-0.03124,0.07823,-0.13203,0.02944,0.01739,0.08391,-0.04636,-0.01448,-0.0024,0.05646,-0.06582,0.03101,0.06178,-0.10151,0.11202,-0.02788,0.06638,0.08489,0.13519,-0.12954,-0.03388,-0.01945,0.01869,-0.04761,-0.03874,0.02054,0.09305,0.01737,-0.02583,-0.08684,-0.05107,0.08244,0.0531,-0.01494,0.05816,0.04802,-0.07236,-0.00036,-0.00582,0.06696,-0.01095,-0.04905,0.0443,-0.00089,0.0474,0.08661,0.07836,-0.03813,0.07827,0.02105,0.01977,-0.00061,-0.09133,-0.00295,0.03339,0.01635,0.04419,0.093,-0.01396,-0.0103,0.07553,-0.0104,0.09125,-0.03255,-0.11765,-0.09713,-0.08192,0.08757,0.03885,0.05918,-0.06119,-0.03567,0.08732,0.02019,0.00214,0.07735,-0.013,0.02515,0.02641,0.01136,0.06466,-0.09984,-0.09062,-0.0159,-0.07046,0.08546,-0.04863,-0.05509,-0.10164,-0.04827,-0.02435,0.02352,0.01686,0.02389,-0.08217,0.08766,0.00654,0.04711,-0.0365,0.06525,0.00256,-0.08903,-0.10183,-0.00018,0.02289,-0.09876,-0.06259,0.01764,-0.08393,-0.03297,-0.02307,0.00565,0.00027,-0.06178,0.04779,-0.04979,-0.10436,0.09187,-0.11312,0.01851,0.03898,-0.00153,-0.0414,0.15319,0.01411,0.00178,-0.02218,0.03698,0.02071,6e-05,0.0851,-0.01285,-0.04669,0.00399,-0.11366,-0.10743,0.03293,0.03509,0.01125,0.07717,-0.04417,-0.03309,-0.10242,0.03834,-0.04916,0.03569,0.07469,-0.08051,0.0125,0.03548,0.08769]},{"domain":"classical_physics","key":"ohm_power_current","name":"Power from current and resistance","package":"classical-physics-ai999x","example":"A current of 2 A flows through a 5 ohm resistor. What power does it dissipate?","v":[0.14505,-0.0774,-0.07415,-0.05423,0.00357,0.04569,0.13185,-0.17084,-0.0497,0.02447,-0.09093,-0.1481,0.0221,-0.0233,-0.02837,0.05526,-0.09115,-0.0854,-0.01238,0.00079,0.03682,-0.01864,-0.02404,-0.00015,-0.08257,0.04821,-0.00507,0.02631,0.07189,0.08912,0.02947,0.00382,-0.11719,0.07333,0.03289,0.06454,-0.02897,-0.0875,0.01544,-0.05844,-0.04432,-0.03156,-0.07783,-0.00115,-0.09019,-0.01443,-0.04629,0.04549,0.12443,-0.05356,0.04426,0.06324,0.02444,-0.02653,0.09573,-0.03761,0.02498,0.01672,-0.08003,-0.03537,0.09642,-0.10952,0.00737,-0.11787,0.06466,-0.01625,0.01856,0.02675,-0.03308,-0.03045,0.01778,-0.02831,-0.06487,-0.0698,-0.05933,0.02545,0.09665,0.00314,-0.0716,-0.05608,-0.09867,-0.02156,-0.05076,0.05653,0.05271,-0.00435,0.06477,-0.13667,-0.00324,-0.07544,0.04674,-0.06999,-0.01345,-0.04113,0.04549,0.01256,0.04335,0.08232,-0.04994,0.02334,0.04882,0.00165,0.0271,-0.05204,-0.06669,0.04416,0.10156,0.0416,-0.02887,0.03638,0.07597,0.02814,-0.04359,-0.0102,-0.02199,0.0496,0.03895,-0.09236,0.02107,-0.06571,0.0485,0.05757,0.07527,-0.03673,-0.02748,-0.034,-0.10198,-0.06298,-0.0372,0.10653,-0.03112,-0.05935,0.02093,-0.0257,0.01382,0.07159,0.03878,-0.03764,-0.03022,0.00574,-0.11136,-0.03053,-0.00334,0.00833,0.05343,0.07439,0.00213,-0.0921,0.01414,-0.08943,-0.04089,0.11342,-0.13205,0.05252,0.11612,0.04622,-0.0771,0.00131,0.10371,0.00748,0.00157,-0.00866,0.06697,-0.00072,-0.2263,-0.02142,-0.03676,-0.03772,-0.06527,-0.11447,0.01233,0.01559,-0.01144,0.07422,-0.14912,0.01599,0.01622,-0.07446,0.08954,-0.03412,0.06122,0.04886,-0.02786,0.0576,-0.00288,-0.08075,-0.04803,0.06263,-0.12196,0.01143,0.01905,0.01491,0.02388,0.01333,0.08235,0.03088,-0.04819,0.0175,0.02278,0.04169,0.07391,0.13832,0.10698,-0.06473,0.02463,0.05781,-0.10502,0.00055,0.05176,-0.05458,0.0025,0.10204,0.02931,0.03127,0.0555,0.01072,-0.03592,-0.0165,0.02905,0.01487,0.10377,0.01224,-0.02137,0.062,-0.00916,-0.01057,-0.0,0.05978,0.10746,0.04941,-0.01293,0.05233,0.0898,0.0453,-0.01431,-0.0241,-0.06696,-0.0465,-0.02783,0.00341,-0.00039,0.03179,-0.00088,0.0287,-0.02499,0.04575,0.02477,0.00141,0.04716,0.04465,0.09587,-0.05518,0.15999,0.13019,-0.04966,0.03954]},{"domain":"classical_physics","key":"ohm_power_voltage","name":"Power from voltage and resistance","package":"classical-physics-ai999x","example":"A 6 ohm resistor is connected across 12 V. What power does it dissipate?","v":[0.11894,-0.12662,-0.02081,-0.06402,-0.00934,0.01776,0.09325,-0.10719,-0.01439,-0.02757,-0.01132,-0.16274,-0.00618,-0.05795,0.02366,0.01261,-0.09777,-0.05325,-0.04718,0.044,-0.01905,0.03033,-0.00361,0.04588,-0.07735,0.05293,0.05226,-0.02706,0.01359,0.11928,-0.03257,0.03682,-0.13311,0.0905,0.01611,0.01569,0.03777,-0.11948,0.04192,-0.04067,0.00675,-0.01232,-0.07755,-0.07358,-0.04429,-0.02656,-0.04554,-0.02385,0.03683,0.01098,0.09261,0.06193,-0.07176,-0.02248,0.10842,-0.04165,0.03869,-0.05316,-0.08839,1e-05,0.10995,-0.04514,-0.0373,-0.03388,0.08518,0.00094,0.05378,-0.02714,0.01103,0.02446,0.04649,0.00134,-0.05669,-0.01574,-0.01985,0.08176,-0.03167,-0.01858,0.02626,-0.06414,-0.07862,-0.01673,-0.08927,-0.03133,0.00902,0.00587,0.08839,-0.12592,-0.00993,-0.03631,0.098,-0.04485,-0.01318,-0.06624,0.01154,0.03752,0.09617,0.08011,0.00243,0.0757,-0.00254,0.05738,0.1145,-0.06912,-0.07342,0.01079,0.10529,0.03457,-0.06191,-0.01658,0.03225,-0.0417,-0.08896,-0.00633,-0.10562,0.06195,-0.0267,-0.10854,0.05902,-0.07987,0.04688,0.04036,0.00463,-0.06165,0.0006,0.03604,-0.04495,-0.07597,-0.07806,0.10355,0.01291,-0.02254,0.03138,-0.01238,-0.00331,0.05262,0.05507,-0.05092,0.01723,0.0107,-0.08769,0.0561,0.04122,-0.00493,0.04919,-0.00647,-0.01746,-0.1137,0.03219,0.00284,-0.04837,0.12068,-0.0812,0.03222,0.1204,0.0218,-0.08995,0.0255,0.07755,0.04142,-0.04872,0.0543,0.04126,-0.01516,-0.13545,0.03189,-0.05853,0.00035,-0.03449,-0.17689,-0.00415,0.04592,-0.06857,0.07139,-0.10304,0.0003,0.01785,-0.07407,0.10191,-0.12264,0.02148,0.09742,0.00625,0.03323,0.02786,-0.121,-0.02521,-0.01351,-0.1111,0.11907,-0.02319,-0.01334,-0.04188,0.02842,0.11945,-0.01552,-0.05729,0.0216,0.06495,0.08256,0.00024,0.05452,0.10054,-0.07048,-0.03197,0.09712,-0.14324,-0.0621,0.0527,-0.05157,-0.02268,0.04761,-0.01305,-0.0224,0.05706,-0.02858,0.01759,0.00914,-0.01991,-0.01518,0.01432,0.06968,0.01891,0.04856,0.02442,0.01703,-0.00727,0.14249,0.13241,0.07303,-0.04521,0.09185,0.00924,0.05137,-0.07183,-0.03385,-0.09557,0.03847,-0.05007,0.01019,0.01798,0.0362,0.01264,-0.00332,0.0542,0.00155,-0.01445,0.00189,0.10874,0.04651,0.078,-0.09073,0.09559,0.10274,0.00502,0.04106]},{"domain":"classical_physics","key":"resistivity","name":"Resistance of a uniform wire","package":"classical-physics-ai999x","example":"A copper wire of resistivity 1.68e-8 ohm*m has a wire length of 10 m and a cross-sectional area of 1e-6 m^2. What is its resistance?","v":[0.10103,-0.09376,0.01262,0.01701,0.09886,0.03565,0.06233,-0.12792,0.02271,0.0683,-0.05028,0.05434,0.09479,-0.00792,0.02212,0.0118,-0.05501,-0.03301,-0.01647,-0.01368,-0.00148,-0.03522,-0.06038,0.02118,0.04374,0.09117,-0.0463,-0.07526,0.02391,0.067,-0.05966,0.06205,-0.07735,0.08337,0.0581,-0.00501,0.02378,0.02854,0.04763,0.07533,0.04093,0.00849,-0.02757,0.01775,-0.13523,-0.05434,0.02046,0.06991,-0.024,-0.01602,-0.06801,0.03701,0.04013,-0.11294,0.07908,-0.02552,0.10612,0.01707,-0.02213,0.0248,0.08962,-0.05638,-0.06411,0.02074,-0.01331,0.0128,0.13199,0.00926,-0.09907,-0.02839,-0.13207,0.00071,-0.18343,-0.00919,0.0192,0.01958,-0.02519,0.0163,-0.02751,-0.02216,0.02924,-0.02001,-0.01075,-0.01755,0.115,0.08092,0.04524,0.03814,0.03997,0.01526,-0.0346,-0.06283,-0.0665,0.03863,-0.05947,0.01821,-0.0582,0.08621,0.00217,0.03802,0.03809,-0.04986,-0.00482,0.02436,0.04561,-0.05658,0.02275,0.01367,0.08122,0.04461,0.00562,0.01634,-0.10817,-0.04296,-0.09124,0.03235,0.0297,-0.05438,-0.00206,-0.09489,0.07097,0.1043,0.0036,0.0299,0.01788,-0.02828,-0.06591,-0.09512,-0.05339,0.03095,0.05579,0.06919,0.03025,-0.03694,-0.05577,0.01811,0.01145,-0.08686,-0.04533,-0.00308,-0.02075,-0.05353,-0.03286,0.00796,-0.02123,-0.0682,0.07381,-0.02779,-0.04398,-0.07463,0.08879,0.06053,-0.06086,-0.08178,0.07236,0.07314,-0.05831,-0.01006,0.12113,-0.04609,-0.05838,-0.00243,0.16226,0.01924,0.05225,-0.0674,0.05519,-0.01945,-0.09259,-0.12516,0.01068,-0.10022,0.01171,0.17967,-0.04813,-0.06407,-0.02689,-0.09711,0.09616,-0.10861,0.11069,0.01376,0.07093,-0.00701,-0.03199,0.01045,-0.02213,0.04458,-0.08128,0.01649,0.00409,-0.04132,0.00463,-0.10029,0.05319,-0.09775,0.00492,0.0061,-0.00754,0.02439,-0.03088,0.00254,0.03945,-0.04932,-0.105,-0.02396,0.00888,0.03297,0.01065,0.0697,-0.00585,0.09847,-0.00733,0.01096,-0.03263,-0.06348,0.01768,-0.03935,-0.01495,0.0633,-0.11231,-0.02126,0.01732,-0.02151,0.11468,-0.04406,0.02041,0.10191,0.1034,-0.08701,-0.11139,0.07988,0.0789,0.0136,-0.02792,-0.05331,-0.09829,-0.01172,-0.06852,-0.03576,-0.04783,0.11288,-0.01136,-0.14749,0.01812,0.07594,0.08329,0.10358,-0.04631,0.15534,0.0752,-0.01622,0.06329,0.0296,0.0174,0.09008]},{"domain":"classical_physics","key":"magnetic_force_charge","name":"Magnetic force on a moving charge","package":"classical-physics-ai999x","example":"A proton with charge 1.6e-19 C moves at 2e6 m/s perpendicular to the field of a 0.5 T magnetic field. What is the magnetic force on it?","v":[0.01911,0.04207,-0.00407,-0.00263,0.00593,0.05629,0.07532,-0.04483,0.00093,-0.02405,-0.07408,-0.02812,0.09754,-0.01167,0.07951,-0.01424,-0.16069,0.03392,0.08887,0.09393,-0.06352,0.15222,0.01885,0.00408,-0.00494,0.01005,0.01214,0.01464,-0.01816,-0.03669,0.03046,0.03882,0.06559,0.06086,-0.18716,0.04399,0.03196,-0.06633,-0.00498,0.03746,0.05004,0.05725,0.18578,-0.02557,0.06066,0.00214,0.10188,0.07977,0.10356,-6e-05,-0.04313,-0.08132,-0.00898,0.05789,0.0444,0.08509,-0.08416,-0.01464,0.06811,-0.012,0.04084,-0.0308,-0.13116,-0.16577,-0.06285,-0.02214,0.09237,0.1048,-0.0614,0.05228,0.04658,0.05562,-0.04995,-0.08598,-0.02089,-0.05634,0.07018,0.04221,0.03217,-0.01154,-0.00459,-0.08547,0.00525,-0.01827,-0.08434,0.01779,0.05346,-0.13141,0.04207,0.00688,0.05344,-0.06653,0.0586,0.00684,0.0275,-0.01827,0.02454,0.02556,0.1512,-0.00534,0.05327,-0.1039,0.00559,-0.01678,-0.03371,-0.04632,-0.00363,0.01101,0.09397,-0.02646,-0.09637,0.00341,0.17021,-0.00724,0.00092,0.03158,0.02383,0.05377,-0.08306,-0.0073,-0.06162,0.03979,0.00547,-0.01297,-0.00419,0.01453,0.04064,-0.02552,0.0541,-0.01075,-0.04227,0.0086,0.02989,-0.07949,-0.01871,-0.05996,-0.00918,-0.00825,-0.0741,-0.10798,-0.0233,-0.01912,-0.0338,-0.03383,-0.00565,-0.09607,0.08886,0.03962,-0.00727,0.02055,0.05094,-0.02339,-0.08289,-0.06708,-0.05211,0.00524,0.02519,0.04999,-0.09562,-0.05124,0.10146,-0.01732,0.03425,-0.09476,-0.12696,-0.0376,0.01547,-0.10152,-0.12536,-0.04853,-0.05214,-0.02362,0.01369,0.04372,0.06542,0.08041,0.06211,0.03035,-0.05787,0.01827,0.05237,0.04715,0.02469,-0.01972,0.05835,-0.00711,-0.02764,-0.05176,-0.03009,-0.00364,-0.04401,0.00615,-0.06975,-0.02321,-0.01702,-0.04447,-0.06894,0.01165,-0.07283,0.08726,-0.066,-0.03111,0.00082,0.03788,-0.02837,0.09486,-0.0478,0.11128,0.09316,0.02441,-0.09167,0.07199,-5e-05,0.03874,0.03631,-0.11203,-0.09892,0.03609,0.07369,0.03115,-0.15079,-0.06886,-0.00241,0.03377,0.00661,0.07148,0.02475,-0.00824,0.18536,0.10304,-0.1009,0.00968,0.0518,0.0899,0.02104,-0.05694,0.04361,0.01853,0.03365,-0.04183,-0.09406,0.03993,-0.04466,0.05166,-0.01028,-0.08953,0.07737,0.03682,-0.02715,-0.03383,0.02586,0.04701,0.04985,0.08921,-0.0751,0.0219]},{"domain":"classical_physics","key":"magnetic_force_wire","name":"Magnetic force on a current-carrying wire","package":"classical-physics-ai999x","example":"A wire carrying 5 A has a wire length of 0.2 m perpendicular to the field of a 0.4 T magnetic field. What is the magnetic force on the wire?","v":[0.05481,-0.01381,-0.03829,-0.0413,0.00562,0.1332,0.05214,-0.11564,0.01406,0.0678,-0.10813,-0.01212,0.10528,-0.01822,0.02755,-0.03548,-0.18765,0.00691,0.08647,0.01859,-0.08477,0.08648,-0.02832,0.02045,0.04194,0.01382,0.03037,0.05158,-0.00325,0.02024,0.01344,0.01439,-0.00319,0.09017,-0.01433,-0.01708,0.00974,-0.00195,-0.01226,0.03518,-0.01146,-0.02293,0.18264,0.07679,0.01449,-0.02976,0.05269,0.12585,0.08676,-0.01593,-0.08692,-0.04335,-0.03217,-0.04126,0.03763,0.02513,-0.06696,-0.03227,0.0099,-0.0127,0.1087,0.06286,-0.12152,-0.16044,-0.07076,0.05125,0.09868,0.08058,-0.09563,-0.05148,-0.00491,-0.0007,-0.08078,-0.07037,-0.05599,-0.06673,0.01272,0.00154,-0.03731,-0.05505,0.0195,-0.02806,0.03127,-0.07657,-0.00174,-0.00361,0.02566,-0.06327,0.01817,-0.01469,-0.03829,-0.08766,-0.01522,0.0085,0.04755,0.01102,-0.00569,0.03833,0.01939,0.01715,0.05874,-0.0627,-0.10388,0.0395,0.02886,-0.0449,-0.04095,-0.03792,0.11035,-0.01245,-0.0967,0.00559,0.15433,0.011,0.02147,-0.01439,0.06475,0.02318,-0.08212,0.01091,-0.0226,0.12585,-0.01526,-0.14014,-0.03073,0.01717,0.01187,-0.00022,0.06441,-0.04122,0.01202,0.04468,0.04965,0.00708,-0.04865,0.02349,-0.0064,-0.06394,-0.02868,-0.10648,-0.01811,-0.08583,-0.09965,-0.04464,0.01123,-0.06234,0.09964,0.0527,0.04683,-0.12982,0.04212,0.0049,-0.05491,-0.03898,-0.01197,0.0311,0.00823,0.02676,0.0263,-0.10035,0.12234,-0.05779,0.01159,-0.05364,-0.082,-0.09333,0.09787,-0.07951,-0.14799,-0.05539,-0.01957,-0.01615,0.00878,0.11264,0.03515,-0.00533,-0.00499,-0.06884,0.03774,0.00404,0.07871,-0.0457,-0.00239,-0.02072,-0.00635,0.04717,0.02028,0.04104,-0.03949,-0.06666,-0.00144,0.04574,-0.03839,-0.04233,-0.04052,-0.00397,-0.06776,-0.01555,-0.10544,0.0789,0.02088,-0.01027,-0.06273,-0.02635,-0.01472,0.04438,-0.005,0.14192,0.0324,0.00316,-0.10258,0.16104,-0.00757,0.10924,0.08158,-0.06529,-0.01374,-0.03446,0.05136,0.00498,-0.11739,-0.04615,0.01402,0.05693,0.03068,0.02015,0.11822,-0.00761,0.16423,0.04481,-0.11713,-0.02213,0.02931,0.08549,-0.00372,-0.00098,0.07873,-0.01516,0.00233,-0.01965,-0.05865,0.05527,0.00856,-0.01541,-0.02381,0.00611,0.05018,0.11338,-0.00733,-0.00415,0.06691,-0.03208,0.10008,0.12485,-0.10437,0.04665]},{"domain":"classical_physics","key":"long_wire_field","name":"Magnetic field of a long straight wire","package":"classical-physics-ai999x","example":"What is the magnetic field 5 cm from a long straight wire carrying 10 A?","v":[0.06031,-0.00932,-0.05985,-0.04278,0.04723,0.04045,0.00808,-0.06561,0.03648,0.0978,-0.14276,-0.04405,0.14262,0.01627,-0.04762,-0.02039,-0.13519,-0.04226,0.07378,-0.04003,-0.10247,-0.0362,-0.0312,-0.08295,0.08806,-0.03352,-0.014,-0.06485,0.01826,0.02331,0.06576,0.04464,-0.03233,0.09063,0.03613,0.0102,0.04862,0.05922,0.03304,-0.02819,-0.07712,-0.00709,0.11763,0.13148,-0.09137,0.02027,0.0744,0.09439,0.01246,-0.05306,-0.06314,-0.00841,0.01098,-0.05825,0.01751,0.0197,0.00994,0.00875,0.01081,-0.0579,0.07215,-0.02915,-0.0485,-0.18237,-0.13748,0.06167,0.11617,0.10575,-0.10238,-0.02037,0.06097,-0.00044,-0.1501,-0.03245,-0.04147,-0.0948,0.02852,-0.05879,-0.05768,0.00939,0.06553,0.03761,0.04705,-0.0531,0.01286,0.03402,0.03919,-0.04678,0.04471,-0.0342,0.00467,-0.03976,-0.0647,0.06392,0.07543,0.05362,-0.03611,-0.0348,-0.04317,0.03052,0.04984,-0.08591,-0.08823,0.08171,-0.0244,-0.10208,-0.04571,-0.0442,0.10093,0.03498,-0.06247,-0.03134,0.081,0.10522,0.0669,-0.0018,0.07318,0.05036,-0.16175,-0.01579,0.02094,0.09264,0.00564,-0.06754,-0.05729,-0.00546,0.01553,0.04916,0.03082,-0.01224,0.00514,0.04913,0.09369,0.01144,-0.02137,0.04503,0.00788,-0.05684,-0.07341,-0.05352,0.01827,-0.03825,-0.05761,-0.03616,0.02909,0.03426,0.06705,0.04759,0.03656,-0.10586,0.02604,0.00253,0.03914,-0.00072,0.08861,0.0027,0.0309,0.00104,0.03775,-0.11366,0.03756,-0.0165,0.04021,-0.09418,-0.0515,-0.10024,0.02917,-0.13289,-0.11435,-0.0142,0.00789,-0.06144,0.04013,0.06131,-0.01839,-0.08041,-0.0348,-0.05557,0.05887,0.06315,0.11889,-0.04216,0.01007,0.02728,0.00197,0.07858,0.02599,0.03704,0.00708,-0.09927,-0.01343,-0.06018,0.02313,-0.00188,-0.0109,-0.0675,-0.00865,-0.03931,-0.05636,0.00695,0.02777,0.00564,-0.01662,-0.07245,0.00849,-0.0561,0.07917,0.03122,0.00843,-0.00965,-0.10366,0.12799,0.01285,0.02469,0.08286,-0.02388,-0.09517,-0.08562,0.05281,0.06668,-0.09553,-0.04111,0.07119,0.09718,0.00773,0.03459,0.10932,0.02339,0.11392,-0.05549,-0.02357,-0.03764,0.09303,0.04057,-0.02211,0.04593,0.02645,0.00413,-0.00951,-0.03663,0.00195,0.0859,0.01047,-0.06642,-0.05334,-0.00425,0.0263,0.03741,-0.11745,0.01505,0.11627,-0.02223,0.08203,0.11625,-0.11668,0.07498]},{"domain":"classical_physics","key":"solenoid_field","name":"Magnetic field inside a long solenoid","package":"classical-physics-ai999x","example":"A solenoid has 1000 turns per meter and carries 2 A. What is the magnetic field inside it?","v":[0.0134,-0.00572,-0.09154,-0.0319,0.08929,0.04974,0.09,0.04789,0.07009,0.08167,-0.07524,-0.13206,0.15939,-0.00321,-0.0094,-0.01893,-0.15712,-0.0034,0.07965,0.03094,-0.05782,-0.00157,-0.08129,-0.05467,0.11537,-0.00902,0.043,-0.00463,0.08227,0.00017,0.04505,0.02239,-0.01439,-0.01377,-0.01474,-0.04517,0.02637,-0.03765,0.07669,0.0685,-0.06583,0.04599,0.07684,0.1137,0.02274,0.04317,0.01862,0.08361,0.12143,0.03522,-0.03483,-0.02191,0.02262,-0.02537,-0.04416,0.06257,-0.04334,0.00663,0.0059,-0.04889,-0.03119,0.03784,0.02215,-0.12521,-0.04533,0.09325,0.05588,0.08902,-0.05676,0.01998,0.06638,0.0003,-0.09281,0.00185,-0.09001,-0.03952,0.08872,-0.0667,-0.08988,0.03167,-0.00035,0.12771,-0.02088,-0.03473,0.0051,0.01625,0.01924,-0.07271,0.04621,-0.06433,0.06473,-0.04097,-0.05495,-0.02677,0.02004,0.08421,-0.00492,-0.06479,0.0456,0.07183,0.08515,-0.05809,0.00432,-0.01138,-0.02099,-0.0903,-0.0152,-0.07365,0.11528,0.00271,-0.09607,-0.00484,0.04507,0.03205,0.02286,-0.01002,0.11654,0.0555,-0.18035,-0.03342,-0.03907,0.03531,0.03514,0.03042,-0.0155,0.00411,0.05975,0.05838,-0.03537,-0.04419,-0.03783,0.03095,0.03864,0.02576,0.07061,0.04863,-0.06008,0.00117,-0.07265,-0.00049,0.00365,-0.09331,0.00517,-0.0218,-0.01586,-0.0187,-0.00921,-0.01431,-0.00908,-0.09564,0.05052,-0.05856,0.03706,-0.02847,0.05136,-0.0705,-0.02419,0.06732,-0.02164,-0.10968,0.12038,-0.13995,-0.02249,-0.04491,-0.12013,-0.15503,0.08785,-0.16726,-0.09879,-0.0023,-0.03514,-0.0303,0.02862,0.03126,-0.04372,-0.00313,0.00988,-0.07935,0.00765,0.05513,0.06277,-0.01394,-0.03438,0.0898,0.03729,0.03005,0.03183,0.09954,0.00105,-0.04891,0.0292,0.01652,0.06438,-0.07617,-0.04133,-0.02732,0.03797,-0.052,-0.20477,0.07464,0.02253,-0.00528,-0.04226,0.04098,0.1356,-0.05733,0.04931,0.03709,-0.06354,0.01617,-0.07593,0.03688,0.03869,0.01804,0.01938,0.04971,-0.05331,-0.07255,0.04696,-0.03142,-0.11523,-0.03457,0.08024,0.08628,0.02255,-0.00528,0.03755,0.01131,-0.00157,-0.07525,-0.00288,-0.11494,0.0114,0.02466,-0.0547,0.02396,-0.04965,0.00533,0.01192,0.04468,-0.09723,0.05897,0.04714,-0.03516,0.04852,-0.03232,0.11369,0.01447,-0.11745,-0.01696,0.07538,-0.00119,0.07684,0.09802,-0.08947,-0.03842]},{"domain":"classical_physics","key":"surface_gravity","name":"Gravitational acceleration at a distance from a mass","package":"classical-physics-ai999x","example":"A planet has a mass of 5.97e24 kg and a radius of 6.37e6 m. What is the acceleration due to gravity at its surface?","v":[-0.0512,-0.06179,0.04316,-0.04173,0.12013,0.03735,0.06283,-0.08497,0.05581,0.00929,-0.02189,-0.03133,0.09811,-0.01269,-0.11884,-0.04216,-0.01783,0.07227,0.04672,0.05144,0.07437,-0.09135,0.03369,-0.00957,-0.03755,0.04257,0.06775,0.01544,-0.09014,-0.12005,-0.08146,0.05016,-0.04654,-0.00121,-0.01229,0.03114,-0.0542,0.12683,0.00556,-0.07516,-0.00545,0.04728,-0.16486,-0.00455,-0.07388,0.12694,-0.02075,0.03065,0.06065,0.07168,-0.07586,0.08388,0.09987,0.02395,-0.11461,0.05943,-0.05715,-0.03419,-0.039,0.09115,-0.0028,-0.13765,-0.05742,0.01405,0.07926,0.04992,0.08231,0.08975,0.01633,0.05344,0.08088,-0.09511,-0.0161,-0.10287,-0.02572,0.11866,-0.00887,-0.03935,-0.15706,-0.00087,-0.05448,0.10586,-0.00634,-0.00953,0.02681,0.08587,0.08725,-0.06866,0.00627,-0.02427,0.00456,-0.00704,0.04811,0.03039,-0.03431,0.0742,0.02187,0.01262,0.00844,-0.02507,0.09078,-0.10041,0.02881,-0.03692,-0.03974,-0.068,0.09834,-0.04017,-0.05581,0.02321,0.00464,0.0453,-0.08174,0.00743,0.08917,0.00021,0.05276,0.02029,-0.03752,0.03831,0.04456,0.02278,0.03066,-0.07887,0.03924,-0.05129,-0.03904,-0.00931,-0.03809,-0.03042,-0.02653,0.07103,0.02138,-0.01588,-0.05042,0.07587,0.0492,0.05904,0.03456,-0.09035,-0.01562,0.02405,-0.00879,-0.05666,0.02842,-0.03373,0.13626,-0.08908,0.02095,-0.02791,0.02845,-0.041,-0.03722,-0.10454,-0.03507,0.13093,0.09682,-0.02986,-0.06005,-0.05184,-0.12129,0.07249,0.064,-0.03799,-0.09648,0.01505,0.01351,0.02715,0.02663,0.06346,-0.05141,-0.01118,0.0132,-0.04511,-0.00384,-0.00389,-0.06251,-0.03817,-0.05749,0.07027,0.07569,0.00152,0.06881,0.01832,0.11249,-0.0391,0.00203,0.01023,-0.11206,-0.21093,0.03496,0.11752,-0.02847,-0.01097,-0.03422,0.01331,0.01074,0.02113,-0.11851,-0.05981,-0.06557,0.03897,-0.12305,0.00865,-0.01225,-0.03548,-0.01226,-0.06258,0.02918,-0.02868,-0.10135,0.06299,0.03734,-0.14918,0.04784,-0.03094,0.01071,-0.03902,0.09918,0.09302,0.00834,0.03591,0.0812,0.03415,-0.00869,-0.04181,-0.01092,-0.03541,0.06942,-0.0261,0.11359,0.05308,0.02467,-0.06807,0.03229,0.04748,-0.02027,-0.0458,-0.05096,0.05941,-0.02627,-0.03387,0.00666,-0.01986,0.02125,0.12443,0.10227,-0.01334,0.0199,0.00357,-0.06114,0.05006,-0.02788,0.06429,-0.03994,0.07504]},{"domain":"classical_physics","key":"orbital_speed","name":"Speed in a circular orbit","package":"classical-physics-ai999x","example":"A satellite is in a circular orbit of radius 6.77e6 m around a planet of mass 5.97e24 kg. What is its orbital speed?","v":[0.01361,-0.07336,-0.02993,-0.00476,0.08259,-0.07083,-0.0334,-0.02194,0.09742,0.06185,0.04565,-0.0288,0.10685,-0.1331,-0.03433,-0.01213,-0.08438,-0.04655,0.02468,0.01706,-0.00112,-0.03404,0.04214,-0.05815,-0.04365,-0.02769,0.11322,-0.04025,-0.06326,-0.08872,-0.01051,-0.00738,0.02924,0.0377,-0.03393,-0.0344,0.00833,0.02925,0.00498,0.02127,0.09049,0.06712,-0.12105,-0.00296,-0.00217,0.08578,-0.01201,0.06536,0.04191,-0.05257,-0.1315,-0.03642,0.02679,0.01247,0.03083,0.00847,-0.04678,0.01866,-0.00574,0.10125,-0.02605,-0.07757,-0.03324,-0.04317,-0.03694,0.01387,0.11537,-0.01642,0.0729,0.09926,0.01215,-0.05703,-0.01329,-0.10777,-0.08484,0.04529,-0.08888,0.00928,-0.00782,0.04793,-0.01869,0.07953,0.00724,0.04072,0.05717,0.00314,0.09206,0.02395,-0.00655,-0.04269,0.04031,0.00143,0.02031,-0.01024,-0.1065,0.07546,-0.02427,0.08433,0.02719,-0.06925,0.00479,-0.03588,0.12205,-0.10468,-0.09731,-0.1083,0.02783,-0.03262,-0.02834,-0.01438,-0.07235,-0.02147,0.02129,0.02124,-0.04237,0.0704,-0.01053,0.01692,0.0091,-0.00365,0.0515,-0.03203,-0.08224,0.00904,0.02497,-0.02495,0.02647,0.02347,-0.15776,0.01015,-0.02604,0.04673,-0.00269,0.07515,-0.03098,0.05941,-0.00454,0.11081,0.08587,-0.03693,-0.08281,0.09543,0.04749,0.01538,0.00268,-0.00199,0.0022,-0.08545,-0.12328,0.07589,0.04345,0.08124,-0.10205,-0.11455,-0.09103,0.02836,0.0846,-0.02258,0.00795,-0.06325,-0.00217,0.15677,0.00517,-0.14504,-0.04381,0.02066,0.03035,-0.03546,0.02125,0.09234,-0.05051,-0.07437,0.02667,0.00126,-0.05095,0.01608,-0.00718,0.15186,0.01469,-0.00153,0.09465,0.0541,0.11673,0.02183,0.09626,-0.07814,-0.03086,-0.04756,-0.10198,-0.19954,-0.01615,0.04811,-0.01488,-0.06966,0.00778,-0.0388,-0.0382,0.11609,-0.00463,0.04037,0.04928,-0.00498,-0.03109,0.06268,-0.07991,-0.03617,0.00319,0.09565,0.02546,-0.02108,0.01037,-0.0678,0.13861,-0.12008,0.01077,0.00036,-0.07525,-0.02579,0.07987,0.11098,-0.14337,-0.02408,-0.04025,0.03636,0.03616,0.0823,-0.02337,0.09415,0.08046,0.03364,0.00394,0.09726,-0.01709,-0.07557,-0.01409,-0.09779,-0.04123,-0.04873,-0.06827,0.00139,-0.05731,-0.00437,0.03132,-0.05679,0.01913,0.03724,0.04046,-0.08524,-0.01584,0.06159,-0.06729,0.10881,-0.01335,0.02245,-0.0391,0.10426]},{"domain":"classical_physics","key":"orbital_period","name":"Period of a circular orbit","package":"classical-physics-ai999x","example":"A satellite orbits a planet of mass 5.97e24 kg at an orbital radius of 4.22e7 m. What is its orbital period?","v":[-0.00901,-0.03165,-0.05864,0.08484,0.05189,-0.04389,0.05991,-0.04756,0.12102,0.13048,0.05145,0.00751,0.11264,-0.05101,-0.04602,0.00076,-0.02093,-0.01064,0.1093,-0.05368,0.04428,-0.05951,-0.04155,-0.07434,-0.01476,-0.03875,0.04909,-0.0126,-0.02966,-0.02288,-0.01848,0.02741,0.01566,0.047,-0.00182,-0.02267,-0.05067,0.09739,0.02627,0.00386,0.09186,0.04198,-0.15127,0.00318,-0.06699,0.08498,-0.03725,0.14509,0.07332,-0.00908,-0.18524,0.08135,0.00134,0.03969,0.04962,0.0019,-0.07152,-0.0218,-0.00638,0.0785,-0.0643,-0.03849,-0.09693,0.06125,0.09196,0.00299,0.09665,-0.05963,0.07406,0.00104,0.0285,-0.09816,-0.01132,-0.15761,-0.06709,0.05989,-0.10096,0.02253,-0.05306,0.02584,-0.00235,0.02933,0.04113,-0.02395,0.12294,0.02539,0.0418,-0.01573,-0.01958,-0.07993,-0.02353,-0.06662,-0.0438,-0.03012,-0.0624,0.04115,0.01228,0.05434,-0.0926,-0.00062,0.01343,-0.01506,0.07457,0.00143,-0.10014,-0.078,0.0256,-0.02378,-0.02237,-0.02571,-0.04624,-0.03117,-0.06118,-0.00919,0.00482,0.01832,0.01281,0.03885,-0.03491,0.11386,-0.0182,-0.00649,-0.08023,0.02789,0.0076,-0.0002,0.06203,-0.02925,-0.10502,0.10091,-0.03008,0.02349,-0.03418,0.04388,0.00675,0.08312,0.01682,0.07878,0.14647,-0.01109,-0.06812,0.00133,0.02247,-0.00155,-0.00696,0.03288,-0.02255,-0.10592,-0.08828,0.06226,0.03479,-0.02868,-0.06949,-0.13459,-0.05765,0.08841,0.10552,0.0041,0.01807,-0.02825,-0.03035,0.11835,-0.00047,0.00022,-0.10718,0.03754,0.0456,0.0735,0.03249,0.07627,-0.02459,-0.04513,-0.00173,0.08155,-0.04799,0.0205,-0.04956,0.0957,-0.02838,0.04762,-0.00178,0.0608,0.11016,-0.01757,0.06671,-0.04831,0.04343,-0.01556,-0.0932,-0.24014,0.00537,0.09882,0.01269,-0.07825,0.02683,0.0041,0.01507,0.09454,0.0012,0.03745,0.07193,7e-05,-0.05999,0.07149,-0.09342,0.01347,0.05028,0.0012,-0.05214,-0.06463,0.02893,-0.08981,0.07574,-0.13335,0.02439,-0.00173,-0.11623,-0.05492,0.12854,0.00522,-0.14586,0.00712,-0.04945,-7e-05,0.02198,0.01146,-0.02179,0.00843,0.04653,0.03765,0.01403,0.0128,-0.0417,-0.02047,-0.02533,-0.01448,-0.01377,-0.08016,-0.01571,0.04274,-0.02072,-0.0517,0.06563,-0.03754,0.02695,0.05394,0.04591,-0.14658,-0.03692,-0.02113,-0.03738,0.08916,0.06005,0.00502,-0.09533,0.06757]},{"domain":"classical_physics","key":"ideal_gas_moles","name":"Ideal gas law","package":"classical-physics-ai999x","example":"2 moles of an ideal gas are held at 300 K in a volume of 0.05 m^3. What is the pressure?","v":[-0.00455,-0.02831,-0.09924,-0.0175,0.04995,0.12467,0.03602,-0.02408,0.07631,0.06511,-0.03182,0.02064,0.00166,0.04946,-0.01256,0.01513,0.08431,-0.00143,0.09048,0.13951,0.06454,-0.06148,-0.02583,0.02924,-0.03441,0.04994,0.09915,0.05732,0.06268,0.0363,0.02905,-0.02058,0.09183,0.06185,-0.10221,0.06758,-0.06419,0.08386,0.0407,0.03311,-0.0137,-0.02477,-0.02799,0.09043,0.00994,-0.01897,-0.00351,-0.06644,0.14224,-0.02513,0.09429,-0.11559,-0.00347,0.12098,-0.03034,-0.16894,-0.03116,0.00401,0.12753,0.03206,-0.0606,-0.07072,-0.09903,-0.04194,0.05646,-0.19532,0.01525,-0.05631,-0.05078,0.08927,-0.0587,0.0296,0.05012,-0.11493,0.05067,0.03557,0.05433,-0.05088,0.07154,0.03036,0.06336,0.00446,-0.00582,0.05431,0.08334,0.10331,0.06363,-0.0233,-0.05683,0.02078,0.04312,-0.02467,-0.06884,0.02933,-0.03846,-0.01024,-0.00801,0.02329,0.04484,0.01639,-0.00435,-0.07295,-0.03107,-0.06548,-0.08379,-0.03015,-0.05264,-0.03044,0.09353,0.00938,-0.01541,-0.11983,0.03447,-0.00168,-0.10558,-0.03882,-0.03575,0.0071,-0.00715,0.02678,0.06528,-0.08081,0.01483,-0.12827,0.10362,-0.07173,0.03701,-0.01708,0.07265,0.00559,-0.11544,-0.05677,-0.04209,-0.00822,-0.08153,-0.05852,-0.09278,0.00866,0.08576,0.04449,-0.02695,-0.02269,0.0268,0.0236,0.06317,0.03288,0.03076,-0.12459,-0.02947,-0.09931,-0.04692,0.1281,-0.04878,-0.00699,-0.00337,0.10552,-0.02752,0.07115,0.11521,-0.11126,-0.06112,-0.01564,0.00393,-0.09765,-0.15472,0.00518,0.0776,-0.05796,0.00971,-0.02665,-0.04767,-0.07511,-0.02579,0.01136,0.06295,-0.03634,-0.01175,-0.06631,0.11174,0.03582,0.12196,0.0507,-0.03423,0.02133,0.00094,-0.00545,0.05383,-0.02646,-0.10221,-0.0931,-0.02085,0.06318,-0.02149,0.0087,0.00216,0.03528,-0.00213,0.09184,-0.1146,0.07175,0.07754,-0.01353,0.04241,0.07753,0.0072,0.03819,0.04762,0.0104,0.05902,0.017,-0.01744,-0.0926,0.02224,0.00719,0.04551,-0.03875,-0.02662,-0.11472,-0.04972,-0.02268,-0.0104,0.02867,0.0027,-0.09756,-0.14003,-0.02559,0.03201,-0.01687,-0.05966,-0.08092,0.10688,-0.02196,0.0731,0.01338,0.02052,0.06236,-0.07273,0.03303,-0.04703,-0.08926,-0.00957,0.07262,0.04059,0.07195,0.07267,0.00553,0.04327,0.00438,-0.05746,0.00017,0.01696,0.02726,0.01654,-0.02048,-0.00979,-0.03826]},{"domain":"classical_physics","key":"latent_heat_fusion","name":"Heat to melt or freeze","package":"classical-physics-ai999x","example":"How much heat is needed to melt 2 kg of ice at 0 C? 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The coefficient of linear expansion is 12e-6 1/K. 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nm?","v":[-0.0007,-0.02942,-0.00065,-0.01486,0.04734,0.03587,0.08644,-0.11946,-0.11153,-0.02167,0.06571,0.01753,0.06275,-0.01771,-0.05578,-0.02746,0.03383,0.0479,0.10238,0.01127,-0.06049,0.07952,-0.01012,0.06699,-0.00639,-0.00279,-0.0043,-0.00635,-0.04488,0.0223,0.04861,-0.00072,-0.0914,0.05688,-0.06639,-0.00926,0.14261,-0.00499,-0.00512,-0.08681,-0.03266,-0.07445,-0.0468,0.04942,-0.02582,0.04587,-0.0655,-0.05006,-0.00537,0.04631,0.09098,-0.03642,-0.02391,0.08269,-0.0527,-0.06285,0.01487,0.09328,-0.07129,0.01492,0.02421,-0.03819,0.05006,0.04852,-0.04897,0.01153,-0.03296,-0.04495,0.02057,-0.04139,0.09511,0.04155,0.05485,0.0136,0.12184,0.00713,0.03284,-0.08102,-0.01063,-0.02754,0.09685,0.04386,0.05502,0.02573,-0.01883,-0.04622,0.03244,-0.10398,0.01596,-0.0354,0.00715,0.00853,0.05471,-0.11847,-0.05394,-0.06767,0.07343,0.04456,0.12014,-0.02726,-0.01227,0.08229,0.03037,-0.08692,-0.12701,-0.05315,-0.04293,-0.1047,-0.02872,0.00359,-0.05183,-0.09732,0.01113,-0.08988,-0.0156,0.08199,-0.06238,-0.01553,-0.01487,0.00375,-0.09141,0.09584,-0.01867,0.03539,0.004,0.0085,0.07619,-0.00602,-0.13181,0.01609,-0.06749,0.05284,0.13298,-0.00975,0.09308,-0.01871,-0.00341,0.0707,0.09587,-0.0328,-0.01187,0.10441,0.04621,-0.03179,0.04586,0.04034,0.06107,-0.12436,-0.08365,0.00317,0.10311,0.08657,-0.02368,0.04649,0.05797,0.1114,0.0447,0.0106,0.08163,-0.02609,-0.03752,0.02925,0.01408,-0.01192,-0.15573,-0.09075,-0.01319,0.0355,-0.1146,-0.02425,0.05552,-0.02566,0.02098,0.00291,0.00716,0.02165,0.02322,-0.01104,0.07459,-0.06185,0.11085,0.03839,-0.04179,0.09532,-0.07764,-0.13544,-0.10296,-0.149,-0.07459,-0.00804,0.00714,-0.10353,0.10835,-0.03373,-0.03257,-0.02186,0.01368,0.00627,-0.04039,-0.04417,0.03405,0.00134,0.07286,-0.02636,0.07317,-0.07787,-0.01484,0.03802,0.00699,0.0684,-0.12437,0.08924,0.04556,-0.02785,0.09998,0.00662,-0.06707,-0.03221,0.08196,0.00314,-0.08178,-0.15007,0.08393,0.00834,0.00082,-0.01253,0.06146,0.03344,0.08373,-0.09275,0.06575,0.14076,0.07941,0.08732,0.02616,-0.00258,-0.00991,-0.04201,-0.03311,-0.08514,-0.11403,0.01111,-0.0216,0.02593,0.00229,-0.00575,0.01887,-0.05276,-0.00949,0.10535,-0.08173,-0.01488,-0.05442,0.04374,-0.06812,0.10655]},{"domain":"classical_physics","key":"photon_momentum","name":"Momentum of a photon","package":"classical-physics-ai999x","example":"What is the momentum of a photon with a wavelength of 500 nm?","v":[-0.11052,-0.01457,-0.0181,-0.03238,0.15854,-0.04445,0.10867,-0.01183,-0.07352,0.02978,-0.03199,-0.00105,0.12416,0.01164,-0.06198,-0.01633,-0.04084,0.04996,0.04108,0.00319,0.04466,0.00025,-0.14185,0.03356,0.02954,-0.02924,-0.0272,0.0186,0.01089,0.0381,0.06244,0.01853,-0.09215,0.00992,-0.07287,0.02478,0.0292,0.04085,0.00832,0.01624,-0.03677,-0.06698,0.03281,0.09204,0.03913,0.08741,-0.0427,0.03556,0.04781,0.06081,0.02723,0.04093,-0.0553,0.04718,0.04339,0.04985,-0.04766,-0.03651,-0.00068,-0.0247,-0.03246,-0.03386,8e-05,0.06775,-0.04916,-0.0333,0.01933,-0.00704,0.00437,-0.0068,-0.00804,0.02084,0.00472,-0.03632,0.14379,0.05769,0.08384,-0.09037,0.01615,-0.12123,-0.09262,0.03403,0.00472,0.04837,0.11913,-0.05336,0.01832,-0.03153,-0.0247,-0.02165,-0.00657,-0.08683,-0.07456,-0.10602,-0.05423,-0.06275,0.09229,0.08192,0.04176,-0.00019,-0.01055,0.11916,-0.01433,-0.01935,-0.09341,0.0262,-0.01356,-0.07586,-0.00377,0.03626,-0.01341,-0.11058,0.01502,-0.07328,-0.06623,0.03447,-0.01912,0.05355,0.01078,-0.01562,-0.05252,0.07406,-0.01762,0.07394,0.03437,-0.11802,0.04719,-0.03513,-0.02871,0.0165,-0.02544,0.03197,0.20522,-0.01316,0.05839,0.02963,0.01239,0.05086,0.12589,0.00416,0.03893,0.00203,0.07669,-0.13184,-0.00366,0.03305,0.00915,-0.08037,-0.04413,-0.04091,0.04298,0.02474,-0.14126,0.04053,0.06054,0.1356,0.02615,0.09815,0.01648,0.00602,-0.05709,0.04689,0.05415,-0.0357,-0.10007,-0.02558,0.00348,-0.04995,-0.1092,-0.02555,-0.00361,-0.00859,0.01193,0.00998,-0.04866,0.00105,0.06061,-0.04704,0.06335,-0.01316,0.13323,0.0132,0.04557,0.0646,-0.08677,-0.1502,-0.07348,-0.06886,-0.04167,-0.08555,-0.02398,-0.03614,-0.01065,-0.06824,-0.03703,0.04645,-0.06729,0.01397,0.02078,-0.05381,0.05106,-0.00975,0.10553,0.01363,0.0603,-0.01201,0.03786,0.09023,-0.01369,0.09475,-0.09442,0.04898,0.01956,-0.12765,0.09831,-0.02502,-0.08173,0.10188,0.08798,-0.05708,-0.00604,-0.11442,0.03947,0.0807,0.01758,0.0349,0.01413,0.03293,0.1123,-0.14091,-0.06509,0.15369,0.09592,0.00315,-0.03118,-0.00789,-0.04944,-0.0402,-0.03384,-0.07529,-0.04773,0.03554,-0.06973,0.03032,0.00746,-0.07446,0.08682,0.04377,-0.07972,0.12628,-0.03145,0.01365,-0.01689,-0.07557,-0.12011,-0.00343]},{"domain":"classical_physics","key":"de_broglie","name":"De Broglie wavelength","package":"classical-physics-ai999x","example":"An electron has a momentum of 1e-24 kg*m/s. What is its de Broglie wavelength?","v":[-0.08702,-0.02107,0.04713,-0.00258,0.13707,0.02409,0.06669,-0.03859,-0.07992,0.05988,-0.01099,0.0348,0.10466,-0.01022,-0.01814,-0.0029,-0.02279,-0.00773,0.01582,0.05303,-0.01122,0.00308,-0.0302,0.0599,-0.0194,-0.05074,-0.03385,-0.06902,0.087,0.01729,-0.02277,-0.06611,-0.02097,-0.05474,-0.0571,-0.00614,-0.01653,-0.06989,-0.00339,-0.07814,0.05653,-0.0287,0.03687,0.06606,-0.00118,0.07248,0.0346,0.0634,0.04222,0.05256,-0.02263,-0.08128,-0.06264,0.01874,0.08335,0.00416,-0.01513,-0.03257,-0.00656,-0.00786,-0.01602,0.02348,-0.03058,-0.00352,-0.03203,0.04588,0.01256,-0.1157,-0.00777,0.03528,0.05187,-0.0901,0.00535,-0.12305,0.07579,0.077,0.11235,-0.09452,0.03663,-0.08355,-0.09028,-0.03538,0.02414,-0.06259,0.02726,-0.05308,0.11488,0.00825,0.07139,0.05776,-0.01334,-0.03551,-0.03544,-0.01663,0.00375,-0.01799,0.05595,0.01999,0.07184,-0.04571,-0.04461,0.11231,0.09196,-0.01529,-0.09651,-0.00633,0.03371,-0.01902,-0.02067,-0.01627,0.06598,-0.06142,-0.03257,-0.01454,-0.0277,-0.04201,-0.02849,0.08104,0.0368,-0.04735,-0.04085,0.07229,0.00418,0.10473,0.04548,-0.16115,0.05962,-0.06205,0.04069,0.02232,0.01676,0.00851,0.22766,0.00218,-0.01219,-0.00897,0.01028,0.03687,0.06282,-0.04049,-0.04406,-0.05481,0.03695,-0.04354,-0.01592,0.02125,0.03394,-0.06102,-0.05545,-0.02582,0.06982,0.05652,-0.10765,0.03324,0.07152,0.07232,0.14962,0.0478,0.01333,-0.01699,-0.00813,0.04284,0.0481,-0.01914,-0.14644,-0.04477,0.0665,-0.11486,-0.10676,-0.02359,0.00123,0.06557,-0.01964,0.014,0.06937,-0.02179,0.04352,-0.08507,-0.03156,-0.00737,0.11815,0.03818,0.06792,-0.00865,-0.02334,-0.10598,0.01777,-0.0936,0.03712,-0.03452,-0.0326,0.01764,-0.1144,-0.03629,0.00014,0.05124,-0.08084,0.10325,0.04784,-0.02877,-0.03685,-0.0403,-0.01136,-0.00426,-0.09628,-0.00512,0.10736,0.02417,0.01353,-0.0004,0.04007,-0.04009,-0.00981,-0.12685,0.09455,-0.05362,-0.17909,0.0655,0.11408,0.03671,-0.1278,-0.06614,-0.01631,0.0689,0.06508,0.05603,0.00672,0.0262,0.14436,-0.07275,-0.05866,0.16174,0.14208,-0.04895,0.01694,-0.07543,-0.1147,-0.0038,-0.08481,-0.10484,-0.04981,-0.04001,-0.04333,0.04605,-0.01804,-0.01057,0.0878,0.05106,-0.02347,0.12394,-0.07459,-0.01706,0.03439,0.01239,-0.04419,0.04629]},{"domain":"classical_physics","key":"rest_energy","name":"Rest energy","package":"classical-physics-ai999x","example":"What is the rest energy of a 1 g mass?","v":[-0.05689,0.03477,0.10437,-0.04603,0.10482,0.04431,0.03824,-0.03395,-0.02861,0.09847,-0.03251,0.11962,-0.02408,-0.00296,-0.05246,-0.11134,-0.02653,0.07002,-0.01382,-0.1045,-0.01308,0.06395,0.02153,0.03144,-0.06347,0.07377,0.02905,0.01285,-0.05978,-0.02428,-0.06971,-0.0886,-0.01167,-0.01056,-0.00291,0.05599,-0.03516,-0.01925,0.03496,-0.15225,0.02654,0.02615,-0.02358,-0.01251,0.08291,0.06706,-0.08654,-0.0222,0.00414,0.08451,-0.01721,-0.02302,-0.03503,-0.03468,-0.02809,-0.04505,0.10801,0.02557,-0.00141,-0.01186,0.03199,-0.11914,0.08516,0.03137,0.05392,0.07615,-0.12878,0.02186,0.01985,0.10178,-0.00207,-0.07003,-0.01206,-0.02608,-0.00576,0.06765,0.09147,-0.0389,0.04398,0.0635,0.07717,-0.02445,0.05004,-0.00994,-0.05114,-0.09238,-0.05639,-0.00217,-0.01024,-0.08664,0.06808,0.03213,0.08462,0.0485,0.0012,0.07192,0.06079,0.00089,0.00958,0.03089,0.09175,-0.11451,-0.10869,-0.06802,-0.14083,-0.13748,0.12653,-0.03018,-0.17615,-0.06294,-0.0353,0.09025,0.02435,-0.046,0.02445,0.04116,0.1487,-0.10653,0.099,0.03603,-0.11841,-0.00343,-0.02164,-0.06119,0.06415,0.07682,0.02792,0.11335,0.01852,0.05372,-0.04068,0.05068,-0.07033,-0.06798,0.06372,0.01823,-0.00403,-0.02635,-0.08387,0.04427,-0.02706,0.05217,0.05801,-0.03488,-0.03508,0.07326,0.12554,-0.029,0.03368,-0.04662,0.07486,0.03641,0.04803,-0.07262,-0.08149,0.05429,0.00078,-0.04963,0.06329,-0.02964,0.09619,0.11304,0.02983,0.05705,-0.08268,-0.03397,-0.02801,0.0762,-0.06612,-0.00105,-0.05059,0.00983,0.0628,0.05096,-0.03069,0.00811,0.00982,0.00549,-0.03502,-0.03053,0.01082,0.07475,-0.1138,-0.00254,0.00781,-0.00473,-0.08011,-0.06632,0.02625,-0.02172,-0.0688,-0.07482,0.13287,0.05064,0.00754,-0.0188,-0.06918,-0.01475,-0.04932,-0.02083,-0.01525,0.01552,0.01506,-0.06972,-0.0549,-0.11957,0.05422,-0.00061,-0.0686,-0.04995,0.0664,-0.05455,0.01522,-0.02005,0.04983,0.02322,-0.07524,-0.08284,0.03491,0.0097,0.01592,-0.03964,-0.01101,0.07071,0.03934,0.10345,-0.0285,0.03878,0.02605,0.07094,0.08953,0.11148,-0.00808,0.12404,-0.0064,-0.07691,0.00513,-0.07151,-0.05964,-0.03434,-0.09687,-0.0921,0.00094,0.02231,-0.00918,-0.00817,0.0165,0.01775,0.03439,0.11872,-0.04503,0.01324,-0.06455,0.14389,0.03455,0.05868]},{"domain":"classical_physics","key":"pendulum_period","name":"Period of a simple pendulum","package":"classical-physics-ai999x","example":"What is the period of a pendulum with a pendulum length of 1 m?","v":[-0.14694,-0.0416,-0.01269,0.05273,0.00715,0.03386,0.09234,0.02297,0.04852,0.11995,-0.04466,0.02516,0.15237,0.0006,-0.06182,0.02928,-0.04847,0.04134,0.11124,-0.10671,-0.02822,-0.03381,-0.0706,-0.03546,-0.00079,-0.03331,-0.05642,0.00741,0.05992,0.09739,-0.04493,0.1006,-0.02906,0.03056,-0.05903,-0.06946,0.00039,0.0139,-0.02976,0.03888,0.04738,-0.11228,-0.08898,0.13045,0.03149,0.03959,0.02953,0.11035,0.05344,0.02346,-0.09768,0.13568,-0.02246,0.04524,-0.04978,-0.0368,-0.09369,-0.00625,-0.04032,-0.02294,-0.05033,0.02198,-0.08201,0.06435,0.02524,0.03823,-0.00984,-0.07035,0.00054,-0.00414,0.08765,0.00956,-0.0341,-0.16915,0.01486,0.02371,0.11364,-0.02464,-0.05729,-0.00938,-0.04145,0.10502,0.05898,0.02005,0.13464,0.03663,0.05103,-0.09665,0.04847,-0.06361,-0.03307,-0.15531,-0.09462,0.0298,0.01438,0.04989,0.06183,-0.01147,-0.03113,-0.00088,-0.02547,0.12015,-0.00972,0.03017,-0.06073,-0.02861,0.03692,-0.07644,0.01388,-0.02137,-0.01478,-0.06501,0.02442,0.01501,0.0122,-0.01228,-0.06474,0.04834,-0.08879,0.0405,-0.01043,-0.00351,-0.06925,-0.00176,-0.03626,0.02565,0.04212,0.00263,0.02515,0.07243,0.07704,0.00683,0.09229,-0.07382,0.02801,0.10849,0.03368,0.1188,-0.04434,0.0233,0.08435,0.02384,0.05526,-0.01162,0.0329,0.01127,0.0221,0.0107,-0.10106,0.06494,0.00587,-0.02964,-0.05078,-0.09974,0.10584,0.10935,0.08752,-0.04623,-0.06132,-0.09601,0.01103,0.00653,-0.05727,0.08856,-0.09736,0.0177,0.08712,0.078,-0.03462,-0.07827,-0.03219,0.10378,0.07785,0.1271,0.01085,0.00945,-0.00309,-0.07401,0.09768,0.05432,-0.03323,-0.00269,0.04188,-0.00471,0.02201,0.06126,0.02323,-0.07252,-0.06634,-0.07445,0.04455,-0.04907,0.02589,-0.09957,0.02583,0.01552,0.08548,-0.04897,0.03698,0.11188,0.03829,-0.07332,-0.07252,0.0374,0.00768,0.02022,-0.01504,-0.10849,0.01807,0.02662,-0.00739,-0.07519,-0.07639,-0.04667,0.08202,0.05268,-0.07253,0.05227,0.02879,-0.16905,-0.09879,-0.04974,0.04517,-0.0205,0.02941,-0.0508,-0.00191,0.00401,-0.02128,0.01651,-0.04195,-0.01016,-0.09088,-0.02632,-0.0537,0.06604,-0.06126,0.00743,0.05248,0.05085,0.0635,0.09779,-0.0224,-0.01336,0.0675,-0.07064,0.06577,-0.08385,-0.02484,-0.13369,0.06931,0.02189,-0.0033,-0.09898,-9e-05,-0.00367]},{"domain":"classical_physics","key":"spring_oscillation_period","name":"Period of a mass on a spring","package":"classical-physics-ai999x","example":"A 0.5 kg mass oscillates on a spring with a spring constant of 200 N/m. What is the period?","v":[-0.02074,0.00779,-0.0567,-0.04169,0.02806,-0.02493,0.04464,0.01931,0.0772,0.08976,0.0212,0.04778,0.11629,-0.01604,0.10795,-0.00425,-0.04617,0.0065,0.09186,-0.02745,0.03158,-0.03983,-0.00559,-0.03043,-0.04372,0.00138,-0.00713,-0.04408,0.09838,-0.05894,0.05555,0.00277,-0.04776,0.02628,-0.0016,-0.05309,0.02205,0.07881,0.00145,-0.08788,-0.02012,-0.02428,-0.11951,0.12235,-0.05963,0.10457,-0.06064,0.11874,0.08771,0.01825,-0.08854,0.07404,-0.02714,-0.071,0.06103,-0.08632,-0.06409,-0.02144,0.0157,0.08278,-0.04215,-0.08585,-0.04342,0.07281,0.10527,0.03431,0.00691,-0.0224,0.06189,0.00965,0.09521,-0.14878,-0.0383,-0.07225,-0.09061,0.06613,-0.03315,-0.07861,-0.02949,0.05844,0.00256,0.02448,0.05917,0.01878,0.0628,-0.01791,0.04519,-0.05295,0.0501,-0.0113,-0.04565,-0.08566,0.02471,-0.0092,0.01252,0.01509,-0.02973,0.00516,-0.0065,0.08138,-0.0014,0.04179,-0.07111,-0.0265,-0.13207,0.01214,0.18538,-0.02225,-0.07741,-0.06278,0.0083,-0.05626,-0.06896,-0.05118,-0.07052,0.00354,0.04478,0.03693,-0.036,0.08296,-0.04551,-0.00491,-0.02656,-0.00917,-0.06991,-0.11891,0.00244,-0.1224,-0.06773,0.05405,0.01921,0.06844,0.06585,0.04724,0.0669,0.07639,-0.06007,0.11503,0.07313,0.03406,-0.07704,0.03719,0.01052,-0.05781,-0.05641,0.0524,-0.00955,0.0081,-0.03844,0.03326,0.00251,-0.06177,-0.00394,-0.13507,-0.02368,0.04182,0.12484,-0.06051,-0.02911,-0.08197,-0.06316,0.08829,0.01308,0.12579,-0.08532,-0.01781,0.07614,-0.04717,-0.03688,0.07728,-0.06721,0.01856,0.06267,0.18388,0.04766,0.00545,-0.05661,-0.03948,-0.00448,-0.0369,0.00597,0.09119,0.0707,-0.00745,-0.00556,-0.00328,-0.04572,-0.05977,-0.07908,-0.076,-0.05785,0.00572,-0.00276,-0.09102,0.02531,-0.00396,0.11167,0.07051,-0.06275,0.11941,0.1206,0.0038,-0.14811,0.03967,-0.03731,0.0425,0.03722,0.01694,-0.04422,-0.02108,0.03173,-0.09469,-0.03177,0.01325,0.08648,0.02602,-0.13068,0.02407,0.00434,-0.06819,-0.1006,0.05831,-0.01592,0.05938,0.01444,0.03061,-0.0134,-0.01527,-0.00778,-0.02913,-0.01284,0.02148,-0.04793,0.02859,-0.07995,0.0398,0.00293,0.04545,-0.04417,0.00235,-0.05779,-0.0738,0.0225,0.0383,0.09488,-0.108,0.11884,-0.10693,-0.00356,0.06192,0.05675,0.08479,0.03805,-0.08493,-0.10384,0.00434]},{"domain":"classical_physics","key":"torque_lever","name":"Torque of a force","package":"classical-physics-ai999x","example":"A wrench applies an applied force of 50 N at a lever arm of 0.3 m, at an angle of 90 degrees. What is the torque?","v":[0.03572,-0.00576,0.01508,-0.06437,-0.05267,0.11434,-0.01186,-0.06334,0.0663,0.02657,-0.01378,0.03484,7e-05,0.02101,0.03372,-0.06904,-0.0785,0.07527,0.02831,-0.0092,-0.11897,-0.03899,-0.04976,-0.06569,0.03711,0.0468,0.02586,0.04194,-0.01154,-0.0003,0.07836,0.06445,-0.01107,-0.05066,-0.08247,0.1268,0.04387,-0.03609,-0.07793,0.02108,0.08511,-0.06566,0.0845,0.04443,-0.03224,-0.02952,0.00565,-0.06783,0.08068,0.05162,-0.03,-0.00877,-0.06517,0.04292,-0.04146,0.02607,-0.11277,0.00829,-0.01008,-0.0465,0.04702,0.04406,-0.16978,-0.06211,0.00788,-0.03437,0.01443,-0.02532,-0.1725,-0.03037,0.0417,-0.06128,-0.08692,-0.06374,0.0379,0.04285,-0.04115,0.01383,-0.08595,-0.00338,-0.11012,-0.00815,0.04406,-0.0985,0.05451,-0.0021,-0.04481,-0.02366,-0.08647,-0.06962,-0.09175,0.01771,0.0995,-0.09493,-0.08884,0.00172,0.05648,0.08015,0.02911,-0.03873,-0.00718,-0.046,0.04454,0.01748,0.04938,0.00595,-0.06107,-0.10618,0.02733,-0.12105,0.08486,-0.04557,0.08813,0.01121,0.04482,0.04037,0.02374,-0.07525,0.00124,-0.01217,-0.01886,-0.00727,-0.05585,-0.03223,-0.01267,0.03879,-0.04685,-0.03503,0.09392,-0.01727,-0.09568,0.03788,-0.00278,0.0259,-0.02263,0.01396,0.08246,-0.02752,0.03546,-0.06003,0.05036,-0.05212,-0.03248,-0.08484,0.04297,-0.02601,0.02988,0.04038,0.02755,-0.07644,-0.01175,0.02616,-0.12011,-0.03908,0.04292,0.09576,0.02287,0.00543,0.09644,-0.08985,-0.03322,-0.14998,-0.11542,0.08813,-0.02892,-0.0711,-0.01409,-0.08057,-0.02895,0.01739,-0.06452,-0.00582,0.05004,0.16941,0.04293,-0.00403,0.04,0.01651,0.0235,0.10332,0.05524,-0.05989,0.05033,-0.04414,0.04,-0.05097,0.01076,-0.0172,-0.04932,-0.07594,0.15599,0.01788,-0.09669,-0.06318,0.08169,0.11161,-0.03355,0.07937,-0.04853,0.04737,-0.01015,-0.04695,-0.06956,0.03264,0.02446,0.07206,0.05461,0.0587,0.03824,0.01755,-0.05023,0.07108,-0.03173,0.00155,0.05636,-0.11993,-0.03841,-0.01749,0.07687,-0.10614,0.07162,-0.04494,0.11124,-0.00551,0.01249,0.01981,0.15348,0.03217,0.08297,0.10295,0.10248,0.05002,-0.02398,0.02613,-0.13842,0.0734,0.01844,-0.04671,0.00983,-0.03372,-0.04656,-0.02162,0.0541,0.01038,0.01584,0.0878,0.07966,0.15521,0.07289,-0.01492,0.03264,0.06022,0.05834,-0.05339,-0.06207,0.09132]},{"domain":"classical_physics","key":"rotational_kinetic_energy","name":"Rotational kinetic energy","package":"classical-physics-ai999x","example":"A flywheel with a moment of inertia of 2 kg*m^2 rotates at 10 rad/s. What is its rotational kinetic energy?","v":[0.17131,-0.0646,-0.01217,0.03011,0.00649,0.03587,0.02527,-0.05468,-0.0031,0.04209,-0.03461,0.04468,-0.01365,0.03723,-0.03944,-0.15185,-0.1165,-0.04066,-0.04245,0.00073,0.04144,0.0865,-0.10475,0.03511,-0.07629,0.08375,0.15644,0.03194,0.05046,0.03824,-0.04327,-0.00434,-0.05533,-0.01635,-0.04671,0.07522,-0.08212,0.08979,0.01721,-0.11409,-0.03044,-0.10038,-0.04718,0.09757,-0.05591,0.02582,0.07313,-0.09593,0.10934,0.02049,0.00734,0.03184,-0.01404,0.04682,-0.04623,0.00054,0.0364,0.01238,-0.14684,-0.01223,0.02465,0.01157,-0.09833,-0.05755,0.00422,-0.04779,-0.05663,-0.06537,-0.05858,0.08274,-0.03733,-0.03158,-0.09429,-0.02627,0.06887,-0.00113,0.09209,0.13936,-0.0898,-0.02762,-0.04394,0.07024,-0.02003,-0.02394,0.0181,-0.01931,0.00955,-0.04896,-0.08211,-0.03652,-0.02164,-0.04538,0.06455,-0.06152,-0.11165,-0.00645,-0.02846,0.0057,0.00615,-0.03463,-0.0183,0.023,0.00749,0.02809,-0.12569,-0.0786,0.07023,-0.00028,-0.04269,0.00299,0.07358,0.01465,0.01778,-0.06706,-0.00916,0.01654,0.08669,-0.11162,0.04279,0.06784,0.03499,-0.03697,-0.01131,0.03829,-0.00909,0.047,-0.00262,-0.05937,0.00693,0.04139,-0.03547,-0.01576,0.02686,0.02054,0.10663,0.03432,0.01144,-0.00845,0.0557,0.09638,-0.0443,-0.01545,-0.0392,0.02311,-0.11302,0.02375,-0.11646,-0.01142,0.06963,-0.08886,0.02284,0.06549,-0.11001,-0.11879,0.00188,0.0378,-0.00064,0.00482,0.05135,-0.11674,0.00494,-0.02607,0.00986,0.08288,-0.01687,0.04092,-0.03409,-0.02022,0.02064,0.14479,-0.01728,-0.03575,-0.04495,0.04045,-0.10065,-0.02972,-0.02201,0.03808,-0.00095,-0.13573,0.10046,-0.07032,-0.08193,-0.03282,0.06643,0.00394,-0.05913,0.00231,0.09304,-0.01822,0.003,0.05335,0.00893,-0.00397,-0.00802,-0.04227,-0.05496,0.11413,0.02434,0.0503,-0.02887,0.04625,0.03691,0.00725,0.03308,-0.01678,0.04986,-0.04006,0.0002,0.00412,0.12944,0.07616,-0.09372,0.07888,-0.07557,-0.03402,-0.02547,-0.1004,0.16424,-0.05749,-0.0192,-0.0624,0.10242,0.17651,-0.02412,0.02699,0.03201,-0.04872,0.04912,0.01167,0.05959,0.10254,0.04722,0.11545,-0.03108,-0.0345,-0.06888,-0.0326,-0.01237,-0.06243,0.00817,-0.00289,0.15005,0.06427,-0.03568,0.05386,0.05237,0.05684,0.07608,0.05888,-0.095,0.08358,0.00662,-0.01861,-0.08263,0.0365]},{"domain":"classical_physics","key":"angular_momentum","name":"Angular momentum of a rotating body","package":"classical-physics-ai999x","example":"A turntable with a moment of inertia of 0.5 kg*m^2 rotates at 8 rad/s. What is its angular momentum?","v":[0.06134,-0.01438,-0.05856,-0.0137,0.06202,0.03169,0.00159,-0.0604,0.02519,0.08173,-0.03223,0.03394,0.06877,0.04722,-0.04909,-0.11085,-0.1277,-0.01332,-0.02591,0.02542,0.04785,0.01117,-0.14514,-0.00592,-0.0219,0.01563,0.13195,0.09556,0.04697,0.08345,-0.0309,0.02051,-0.01478,-0.03812,-0.07405,0.06497,-0.10912,0.06676,0.00452,-0.04154,0.00437,-0.16035,-0.05016,0.11692,-0.02961,-0.03252,0.07467,-0.05501,0.08149,-0.0492,-0.02195,-0.02283,0.01521,0.0287,-0.06869,0.05964,0.00344,-0.03442,-0.10204,0.00351,-0.00467,0.06018,-0.13415,-0.05143,-0.01545,-0.06127,0.06234,-0.05161,-0.0243,0.0436,-0.05211,-0.02442,-0.07821,-0.01461,0.11858,-0.03326,0.0953,0.1164,-0.12642,-0.00631,-0.09414,0.03489,0.05877,-0.01214,0.09486,-0.01196,-0.0198,-0.04839,-0.09927,0.00432,-0.00654,-0.0554,-0.02287,-0.08576,-0.09169,-0.02462,-0.01208,0.04724,0.0214,-0.1043,-0.01864,0.02712,0.03264,-0.06693,0.03895,-0.04727,-0.00882,-0.01227,-0.03031,0.02907,0.06794,0.00895,0.00912,0.01212,-0.00133,0.0283,0.08203,0.00937,0.02252,0.01136,0.05393,-0.00119,-0.02,0.11681,0.00183,-0.02824,-0.00127,-0.06522,0.08689,0.00971,-0.03,0.01518,0.06914,0.0273,0.0576,0.00233,-0.01739,-0.03534,0.03716,0.01391,0.0003,-0.01937,0.01083,-0.07511,-0.11556,-0.01996,-0.05952,0.01106,0.04389,-0.0329,0.05225,0.09941,-0.18755,-0.10166,0.01331,0.08513,-0.01131,0.04169,0.05641,-0.02526,-0.0211,-0.05677,0.00641,0.04476,-0.02501,0.0018,0.02859,-0.05946,-0.02406,0.09136,-0.02888,-0.00296,-0.07846,0.00321,-0.06458,0.06828,-0.05543,-0.01486,-0.02084,-0.06652,0.14567,-0.05333,-0.01818,-0.01299,0.05107,-0.02905,-0.0432,-0.00409,0.0022,-0.12519,-0.01652,0.1662,-0.07231,-0.1081,-0.02211,0.00689,-0.09585,0.07258,0.01995,0.05257,-0.06748,-0.02914,-0.05409,0.0652,0.03755,0.10551,0.09525,0.02189,-0.00515,0.06161,0.09372,0.08712,-0.04954,-0.00048,-0.04819,-0.07936,-0.02336,-0.02698,0.13106,-0.0383,-0.01905,-0.03052,0.07791,0.15775,-0.00607,0.06253,0.05465,-0.02258,0.04472,-0.00669,0.06332,0.09498,0.0362,-0.00238,-0.00542,0.01557,-0.12405,-0.05855,-0.02188,-0.10871,-0.02304,0.01818,0.1123,0.07713,-0.00127,0.0347,0.09762,0.10434,0.05986,0.05846,-0.08518,0.02272,0.12417,-0.04134,-0.16013,0.02363]},{"domain":"classical_physics","key":"tangential_acceleration","name":"Tangential acceleration of a point on a rotating body","package":"classical-physics-ai999x","example":"A point on a rotating wheel is at a radius of 0.5 m. The wheel has an angular acceleration of 4 rad/s^2. What is the tangential acceleration of the point?","v":[-0.02545,-0.0386,-0.00104,0.00441,-0.06794,0.05149,-0.11499,-0.01335,0.09897,0.01415,0.02228,0.04522,0.01995,-0.03739,-0.08361,-0.07313,-0.00945,0.01255,0.08358,-0.00253,0.0163,-0.08195,-0.1707,-0.09225,-0.0258,-0.01144,0.08842,0.06421,0.01508,-0.00345,0.06935,0.07473,0.04152,-0.08638,0.00364,0.00282,0.02406,0.10678,0.004,0.0604,0.00949,-0.05863,-0.05136,0.03602,-0.16851,0.01941,0.10321,-0.04537,-0.00445,-0.02676,0.03808,-0.00593,0.02998,0.02808,-0.14504,-0.00198,0.01611,-0.0385,-0.09518,-0.03851,0.06295,0.04729,-0.07519,0.02706,-0.01451,-0.05414,0.00884,-0.00046,-0.06085,0.03913,-0.12844,-0.05242,-0.01605,-0.00396,0.03362,-0.05169,0.11829,0.06223,-0.15902,0.11114,-0.01073,0.0322,0.04076,-0.00145,0.02141,0.05664,0.00439,-0.0656,-0.03537,-0.0954,-0.04606,-0.08564,0.0615,-0.02454,-0.19462,-0.01688,-0.04166,0.06473,0.06022,-0.03047,-0.07396,-0.08141,0.09686,-0.0239,0.03241,0.02799,-0.01625,-0.04052,0.01527,0.08252,0.01115,0.00381,-0.07408,0.03933,0.11122,0.04767,0.06972,-0.01045,0.04997,0.05853,0.05917,-0.0372,-0.03649,0.06333,0.01118,0.02382,-0.02669,-0.06473,0.04881,-0.04296,-0.11186,-0.02212,-0.03001,-0.02181,-0.0422,0.05941,-0.02878,-0.09049,-0.04983,0.01465,-0.05353,-0.04774,-0.05408,-0.00101,0.06649,0.01386,0.07524,0.07551,-0.07829,0.03193,-0.01095,0.06436,-0.08973,-0.08395,0.01589,0.12805,0.00919,0.04508,-0.03351,-0.09042,-0.09555,-0.13682,-0.06634,0.14785,-0.02466,-0.03576,-0.03067,-0.05391,0.13971,0.04263,-0.015,0.01718,-0.02801,0.06733,-0.00063,0.05691,-0.02493,-0.02827,-0.05264,0.09676,0.04108,-0.03935,0.01329,0.00805,0.05813,-0.00451,-0.04537,-0.03096,-0.04402,-0.16369,0.08814,0.07079,-0.10561,0.00376,0.04781,0.02351,-0.03538,0.0618,0.06859,0.0556,-0.0014,-0.03327,-0.05381,0.05334,0.08556,0.08019,0.07001,-0.01748,0.11206,0.04394,0.03909,0.05306,-0.0935,-0.01501,-0.03358,-0.08275,-0.04316,-0.06867,0.01649,-0.01801,0.04251,-0.05416,0.1398,0.14486,0.03854,-0.06963,0.07172,0.05531,0.05517,0.02716,0.0258,0.03837,0.02792,0.0527,-0.06755,0.1162,-0.03573,0.00204,0.06519,0.00782,0.0522,0.07762,0.03217,0.00265,-0.06713,0.05795,-0.02198,0.0397,0.05923,-0.04715,-0.03476,0.10135,0.01295,-0.06222,-0.01882,-0.00246]},{"domain":"classical_physics","key":"centripetal_acceleration_omega","name":"Centripetal acceleration from angular velocity","package":"classical-physics-ai999x","example":"A centrifuge rotates at an angular velocity of 3 rad/s. What is the centripetal acceleration at a radius of 2 m?","v":[0.05398,0.00037,-0.00553,0.11126,-0.08012,0.04498,-0.05507,-0.07232,0.06144,0.03249,0.01326,0.02406,0.07103,-0.00396,-0.10139,-0.08491,-0.09124,0.03296,-0.00809,0.03709,0.0704,-0.03571,-0.15653,-0.03443,-0.09935,0.00513,0.13353,0.01936,-0.0098,0.03954,0.03482,0.04803,-0.00387,-0.06068,-0.06154,-0.05194,-0.02666,0.09894,0.0264,0.08552,0.01309,-0.11293,-0.04565,0.10921,-0.03595,0.03871,0.14285,-0.01938,0.01873,-0.00175,0.02263,-0.03951,0.01263,0.08684,-0.07298,-0.00726,0.00137,-0.04666,-0.1296,0.0208,0.10471,0.06369,-0.05998,0.04844,0.05468,-0.08047,0.00403,-0.08866,-0.01493,0.01496,-0.04653,0.05942,0.02465,-0.00228,0.05989,-0.03654,-0.0102,0.11545,-0.14699,0.09095,0.01113,0.08582,0.04923,-0.04572,-0.02994,0.0356,-0.00601,-0.05567,-0.0576,-0.07866,0.02597,-0.08359,0.04531,-0.01321,-0.13857,-0.00719,-0.01415,0.07188,0.01101,-0.06393,-0.09283,-0.0401,0.18461,-0.00955,0.11616,-0.01377,0.0325,-0.04648,0.08857,0.07496,-0.03312,0.0086,-0.04603,-0.0757,0.01458,0.0793,0.10501,-0.02167,0.01474,0.07997,0.03642,-0.09186,-0.03549,0.04366,-0.03464,0.04644,0.04712,-0.04321,0.03653,-0.09862,-0.03256,-0.12253,-0.0569,-0.01248,-0.03032,0.0757,-0.04204,-0.04457,0.03474,0.02581,-0.05912,0.03401,-0.01117,-0.01093,0.05674,-0.0204,0.03529,-0.01543,-0.09024,0.07025,0.10011,0.13777,-0.0741,-0.08259,0.00686,0.05212,-0.01204,0.02297,-0.01569,-0.03518,-0.0426,-0.04853,0.01091,0.02856,-0.06934,-0.06119,-0.00213,-0.0192,0.11243,0.01851,0.01245,0.01431,-0.10265,0.02288,-0.06247,0.10627,-0.09914,-0.042,0.02295,-0.00723,0.05112,-0.00811,-0.05118,-0.04564,0.06388,0.0658,-0.06155,0.01711,-0.02247,-0.1449,-0.00122,0.11272,-0.09069,-0.0753,-0.06541,-0.06361,-0.0331,0.08468,0.04506,0.08986,-0.08297,-0.00584,0.00041,0.09387,0.00235,0.11371,0.02946,-0.0147,0.03995,0.03202,0.05526,-0.02053,-0.04061,0.01669,-0.0625,-0.05044,-0.00761,-0.06759,0.04707,0.07949,-0.06178,-0.03796,0.09861,0.13034,0.04548,-0.05251,-0.01544,0.06029,0.04817,0.08485,-0.03239,0.05772,-0.00414,0.13282,-0.05344,0.02881,-0.05693,0.00085,0.04812,-0.02587,-0.0314,0.06649,-0.00246,-0.03508,-0.02898,-0.0161,-0.09351,0.04386,0.02683,0.01593,-0.13254,0.08966,0.03866,-0.00308,-0.05195,-0.02747]},{"domain":"classical_physics","key":"angular_momentum_point_mass","name":"Angular momentum of a point mass on a circle","package":"classical-physics-ai999x","example":"A 2 kg satellite moves at 3 m/s in a circular orbit of radius 4 m. What is its angular momentum?","v":[-0.03264,-0.00159,-0.07919,-0.06782,0.05495,-0.05936,-0.01963,-0.08195,0.04602,0.09084,0.01486,-0.04829,0.14456,-0.02801,0.00031,-0.04173,-0.06163,-0.04569,0.01924,-0.00917,-0.0091,0.01063,-0.08895,-0.0829,-0.05996,-0.00797,0.1108,0.03663,-0.00412,0.01243,-0.00079,-0.00447,-0.02448,0.01027,-0.05835,-0.00958,-0.10913,0.04544,0.00042,-0.0017,0.04074,-0.05017,-0.0509,0.0732,-0.02776,0.03625,-0.03216,0.08593,0.02382,-0.06808,-0.0886,-0.02936,-0.02294,0.06031,0.04229,0.07083,-0.04269,-0.04925,-0.03047,0.04693,0.00851,0.05115,-0.11661,-0.01151,0.00116,-0.03063,0.0714,-0.03969,0.05107,0.08524,-0.07762,-0.0293,-0.04406,-0.05211,0.04697,0.01955,-0.03077,0.08269,-0.06074,0.00127,-0.09135,0.01463,0.03855,-0.01519,0.14279,-0.07758,0.05341,-0.02236,-0.08221,-0.02599,0.03545,-0.0457,-0.04996,-0.09309,-0.1231,0.02713,0.01618,0.08745,0.03797,-0.12168,-0.03353,0.001,0.05368,-0.15528,-0.00958,-0.05671,-0.03804,0.01325,-0.09909,0.02124,0.00353,6e-05,0.03167,0.0325,-0.03809,0.04774,0.05013,0.06072,-0.00249,0.06832,0.00289,-0.03269,-0.07189,0.12263,0.01932,-0.03465,0.07359,-0.06667,-0.01331,0.06263,-0.03197,0.00633,0.0661,0.05926,0.03142,0.02492,-0.01367,0.07962,0.09024,-0.06353,-0.05104,0.0128,0.06375,-0.03343,-0.01539,0.00347,-0.01901,-0.0098,-0.07843,0.06115,0.02894,0.07812,-0.11952,-0.13373,-0.02507,0.10081,0.0291,0.07705,0.0361,-0.01772,0.04158,0.03515,-0.02312,-0.07175,-0.01487,-0.03701,0.00032,-0.11053,-0.00266,0.058,-0.06244,-0.03597,-0.01116,-0.02186,-0.02276,0.047,-0.08433,0.0504,-0.01653,0.01063,0.14861,0.06502,0.04658,0.01716,0.03372,-0.04547,-0.07332,-0.02542,-0.04038,-0.20483,-0.0502,0.11242,-0.05785,-0.1167,-0.00825,0.03757,-0.08637,0.07531,0.08543,0.06378,-0.01795,-0.09407,-0.04484,0.08188,-0.00399,0.09204,0.07958,0.08058,-0.00675,-0.01186,0.06557,0.01531,0.06103,-0.07129,-0.02097,-0.07552,-0.02871,0.01893,0.09419,-0.00035,-0.08305,-0.06924,0.02507,0.15561,0.00918,0.07932,0.03224,0.09116,0.10064,0.05042,0.03219,0.11448,0.00224,-0.0096,-0.02132,-0.07049,-0.08921,-0.09859,-0.06573,-0.05292,0.01798,0.0028,0.14234,-0.00665,-0.01175,0.0292,0.12,0.04488,0.04764,0.05811,-0.13402,0.05091,0.11816,-0.05109,-0.12729,0.04855]},{"domain":"classical_physics","key":"absolute_pressure_depth","name":"Absolute pressure at a depth in a fluid","package":"classical-physics-ai999x","example":"The atmospheric pressure is 101325 Pa. What is the absolute pressure 10 m below the surface of water of density 1000 kg/m^3?","v":[0.05472,0.00751,-0.11451,-0.06027,0.11769,0.17251,0.08812,-0.01174,0.00405,0.02179,0.02171,0.08348,-0.00809,0.03411,-0.0178,-0.01506,0.10521,0.04825,0.10027,0.00684,0.04695,-0.14938,-0.03158,0.05538,-0.01749,0.06606,0.01003,0.12811,-0.01243,0.03075,0.06539,0.03845,0.00885,-0.06826,-0.03945,0.09949,0.00256,0.10662,-0.00297,0.03433,-0.07347,-0.03077,-0.06689,-0.00057,-0.03563,0.03349,-0.07348,-0.09373,0.082,-0.02354,0.06709,-0.13307,0.03741,0.09976,-0.11954,-0.14988,-0.02546,0.02949,0.05295,0.06933,0.03928,-0.05425,0.01491,0.01687,0.01371,-0.08156,0.00045,-0.05824,0.01651,0.01869,-0.05577,-0.03358,0.09673,-0.03865,0.03278,-0.01448,0.12177,-0.06311,-0.08299,0.03774,0.03724,0.0548,-0.01685,-0.0514,0.06276,-0.02198,0.05104,-0.0776,-0.04153,0.03443,0.00707,0.02406,-0.08822,0.05295,-0.07956,-0.06708,0.06726,0.04455,0.04702,0.03175,-0.04422,-0.08926,-0.04593,-0.01092,0.00153,-0.03159,0.00439,0.03836,0.04531,0.02336,-0.02487,-0.0037,-0.02563,0.00818,-0.07022,-0.09644,0.0281,0.03111,0.00733,-0.00921,0.0324,-0.01993,-0.04115,-0.01555,0.01898,-0.04617,-0.10752,0.00436,0.13819,-0.06993,-0.01399,0.01046,0.08645,-0.01433,-0.03171,-0.03641,-0.05916,-0.0521,0.06975,-0.10582,-0.10602,-0.0014,-0.02557,0.05134,0.02556,-0.06646,0.05414,-0.0484,0.00823,-0.09191,-0.02667,0.07948,-0.09048,0.0356,-0.0161,0.13126,-0.04219,0.00064,-0.04939,-0.09541,-0.075,0.03264,0.05475,-0.0397,-0.13711,-0.04142,0.05886,-0.05537,0.11311,-0.06467,-0.04889,-0.07245,0.03449,-0.01759,0.07353,0.0306,0.02681,-0.08084,0.066,0.1596,0.09272,0.03567,-0.08857,-0.01158,0.06324,0.04335,-0.04169,-0.00167,-0.11214,-0.16823,0.01436,0.08868,-0.01642,-0.07346,-0.05907,0.03125,0.03082,0.09833,-0.04087,-0.03353,-0.03206,0.0473,-0.05213,0.06238,0.03846,-0.01649,-0.07926,-0.04987,-0.07335,0.11723,-0.03048,-0.0222,0.00309,-0.02607,0.01545,-0.03667,-0.05407,-0.11843,-0.01697,0.01522,0.14832,-0.06557,-0.04315,-0.02377,-0.06673,0.02281,-0.05612,-0.06464,0.04987,0.02226,0.0518,0.01751,0.10464,0.04586,-0.02448,0.09733,-0.0311,0.02675,0.05645,-0.03658,-0.01258,0.00812,0.056,0.05787,0.095,-0.00118,0.03625,0.03519,-0.02452,-0.05035,0.00176,0.03038,0.14031,0.06579,0.0494,-0.02337]},{"domain":"classical_physics","key":"flow_rate_volume_time","name":"Flow rate as volume per time","package":"classical-physics-ai999x","example":"A hose fills a 2 L bucket in 10 s with water. What is the flow rate?","v":[-0.03714,-0.03635,-0.10821,-0.04292,0.0286,-0.01244,0.03939,-0.04353,0.00974,0.02543,0.0001,-0.07422,0.12059,-0.03907,0.04363,0.04978,-0.03771,0.13876,-0.09643,0.01361,-0.00978,0.04132,-0.10913,-0.07888,-0.12601,-0.05332,0.03343,0.09893,-0.04838,0.05077,0.08239,-0.02657,-0.02009,0.05049,-0.03488,-0.02618,0.04083,-0.08819,0.04568,0.12489,0.04286,-0.0109,-0.12457,-0.04676,-0.01825,0.02159,-0.02625,-0.05594,0.06661,-0.02641,-0.00892,-0.03674,-0.1265,-0.17329,0.00533,0.00506,0.06403,-0.03514,-0.12293,-0.03895,0.07567,0.01612,-0.07522,0.08434,-0.02107,0.00994,0.11014,-0.0429,-0.02273,0.06322,0.02941,-0.08135,-0.01067,-0.07271,0.0927,0.05026,0.1049,-7e-05,0.04973,-0.06922,-0.02803,-0.05222,-0.0056,0.02561,-0.03241,0.04937,-0.06165,-0.03131,-0.02809,0.00868,-0.00014,-0.11914,-0.03981,0.06054,-0.06267,0.0415,0.04533,-0.05193,0.08845,0.02309,0.02161,-0.0153,0.05872,-0.0774,0.00334,-0.10527,0.08881,0.00561,0.02075,0.04161,0.03086,-0.12419,9e-05,0.04096,-0.00883,0.02078,0.01733,0.08925,-5e-05,-0.01957,-0.02216,0.0696,0.0573,0.03037,-0.00929,-0.07289,-0.01745,-0.0028,0.0086,0.0355,-0.07133,-0.00269,0.0308,-0.00979,0.08514,-0.04379,-0.07178,0.09124,-0.07408,-0.05212,-0.09091,0.06706,-0.09085,-0.14459,-0.03037,0.01468,-0.01251,0.0643,-0.06017,-0.00025,-0.00434,-0.03089,0.0259,-0.0578,-0.04243,0.05946,-0.02594,-0.01522,0.06151,-0.06473,0.13271,-0.11675,0.04708,0.02597,0.02809,0.04357,0.0153,-0.01532,-0.05231,-0.08545,0.00725,0.05319,-0.03888,-0.00211,-0.05924,0.03873,-0.01113,-0.00804,0.04407,0.11002,0.02505,0.11593,0.06539,0.00926,0.11558,0.06495,0.02648,-0.0081,-0.05197,0.00059,-0.04104,-0.04484,-0.0555,0.08336,0.01639,0.14381,0.10259,0.06626,0.10366,0.07056,0.07843,-0.00165,-0.01871,-0.00532,-0.05764,0.01928,-0.11894,-0.07423,0.0639,0.0283,0.05279,0.0136,0.03574,0.01528,-0.0032,-0.06409,-0.06034,-0.01236,0.08148,-0.01826,0.14581,-0.03876,-0.07919,-0.04629,0.061,-0.03324,-0.00206,0.09055,0.07708,0.0018,-0.14042,-0.01809,0.03653,0.06123,0.03889,0.11017,-0.00541,-0.03508,-0.0882,-0.04475,-0.03496,-0.06291,-0.0095,-0.13784,0.04932,-0.06182,0.09014,0.00879,0.12463,0.06936,0.07404,-0.03194,-0.00613,-0.0608,-0.0743,0.10524]},{"domain":"classical_physics","key":"flow_rate_area_speed","name":"Flow rate through a cross section","package":"classical-physics-ai999x","example":"Water flows through a pipe with a cross-sectional area of 3e-4 m^2 at a speed of 2 m/s. What is the flow rate?","v":[-0.01653,-0.0878,-0.00832,-0.0143,0.03355,-0.02259,-0.0481,-0.02966,-0.06236,-0.00508,0.00143,-0.02886,0.15923,-0.09197,0.067,0.0717,0.00141,0.08287,-0.07069,0.08867,0.00509,0.05155,0.08238,-0.05297,-0.13888,0.00828,0.02764,0.12585,-0.04642,0.07426,-0.01357,-0.0298,-0.00587,0.05556,-0.11247,-0.00787,0.1076,-0.13223,0.03316,0.16048,0.07328,0.01786,-0.08118,-0.05418,0.0194,-0.00588,0.01903,-0.0448,0.03858,-0.00636,0.00827,-0.10007,0.02718,-0.09335,0.0264,0.00896,0.05234,0.01205,-0.06034,0.0019,0.10848,-0.05338,-0.16013,0.04854,-0.05212,-0.0505,0.04107,0.08594,0.01476,0.0454,-0.02455,-0.03302,-0.04612,-0.09296,0.00162,0.04672,0.10134,-0.02567,0.0559,-0.02463,-0.02618,-0.08152,0.01468,0.00863,-0.0474,0.03213,-0.0338,-0.00571,-0.02332,0.02447,-0.04302,-0.08439,-0.01016,0.0515,-0.09215,0.03764,0.06648,-0.04992,0.16777,-0.03038,0.00092,-0.01915,0.01569,-0.08133,0.05385,-0.12981,0.08847,-0.00924,0.01793,0.03191,0.02437,-0.06157,0.05273,0.0534,-0.09385,-0.01004,-0.01216,0.00911,-0.052,-0.12354,0.01005,0.0595,0.04425,0.0533,-0.01522,-0.11651,-0.0455,-0.02793,-0.02646,0.02539,-0.10836,0.01601,0.07254,-0.01068,0.05209,-0.05245,-0.0618,0.06571,-0.03197,0.01499,-0.10086,0.05794,-0.08727,-0.07733,-0.0359,-0.02655,-0.00738,0.04705,-0.06392,-0.00597,0.01486,0.03992,-0.05513,-0.01106,0.03234,0.04704,-0.07441,-0.043,0.06282,-0.05167,0.13539,-0.05015,0.1015,-0.06968,0.05547,0.00593,-0.10838,-0.00284,-0.08902,-0.07957,-0.0461,0.0215,0.05882,-0.02966,0.01183,-0.03366,0.00185,0.0684,0.03067,0.04631,0.06649,0.07528,-0.0297,0.00852,0.05345,0.058,-0.01772,0.01345,-0.09236,-0.00719,-0.05104,0.02127,-0.07249,0.02482,0.01331,0.07961,0.08049,0.04252,0.05999,0.05086,0.08726,-0.05109,-0.01937,0.01429,-0.05506,0.02377,-0.10919,-0.04346,0.03702,0.07241,0.09123,0.03469,0.05125,-0.00106,-0.03902,-0.05646,-0.04353,-0.00123,0.08516,0.04354,0.06072,-0.07192,-0.10376,-0.03431,0.08354,-0.01553,-0.06869,0.11862,0.11158,-0.02458,-0.16639,0.07329,0.12273,0.10552,0.07957,0.08317,0.00827,-0.0662,-0.02931,-0.09785,-0.04331,0.06811,0.00121,-0.09487,0.00969,0.00332,0.07665,-0.04448,0.0821,0.02843,0.05114,0.0332,-0.06284,-0.05389,-0.01652,0.07454]},{"domain":"classical_physics","key":"volume_expansion","name":"Thermal expansion of volume","package":"classical-physics-ai999x","example":"Water with an original volume of 1 L and a coefficient of volume expansion of 2.1e-4 1/K is heated by 50 K. What is the change in volume as it expands?","v":[0.05,-0.03673,-0.02453,0.05812,0.00202,0.07796,-0.02776,0.07023,0.02673,0.06011,0.01599,-0.00993,-0.06329,0.01545,0.02538,-0.11385,0.03755,0.09691,0.05356,0.03118,0.05994,0.11214,-0.15629,-0.03049,0.00849,-0.12364,0.04639,0.04401,-0.05299,-0.04457,-0.06892,0.02409,-0.02614,-0.00685,-0.03516,-0.13654,-0.02561,-0.09816,0.02245,-0.01058,0.02689,0.13365,-0.01414,-0.04733,0.04366,-0.05811,0.04252,-0.0049,-0.06937,-0.0772,0.03858,0.06408,0.05515,-0.07801,-0.0362,0.04434,0.05083,0.06869,0.00542,-0.047,0.05917,0.07857,-0.02498,0.08926,-0.01381,0.01631,0.13693,-0.09492,0.05287,0.19081,0.12983,-0.10724,-0.08481,0.00783,-0.04502,-0.01454,0.00183,-0.07327,0.00504,0.05944,-0.04071,-0.00784,-0.08218,-0.09861,0.0278,0.13704,-0.0304,-0.00193,-0.02307,-0.05647,0.02709,-0.07802,0.05196,0.03842,-0.10315,0.01212,-0.07821,-0.02452,0.09415,-0.04772,-0.01046,0.01686,-0.06715,-0.00567,-0.09492,-0.08572,0.03843,0.0584,0.05384,0.04966,0.1046,0.01615,-0.0028,-0.03136,-0.02786,0.00122,0.06661,0.02842,0.07863,-0.10492,0.04138,0.0056,0.03455,0.01723,-0.01275,0.06644,-0.01985,-0.12318,0.03641,0.00635,-0.06048,-0.03348,0.03737,-0.00893,-0.03388,-0.03406,0.04738,0.01877,-0.03795,-0.13759,0.06592,0.01212,-0.07027,0.05438,-0.03356,0.01429,0.05913,0.04915,-0.05163,0.0671,0.05467,-0.00132,0.05607,-0.09334,-0.05797,-0.02683,-0.06093,-0.05773,-0.00168,-0.10472,-0.05442,-0.08173,-0.01153,0.05207,0.0439,0.06942,0.04651,-0.07334,-0.00595,-0.08399,-0.04946,0.09743,-0.08124,0.11066,0.03973,-0.0749,-0.08327,-0.04509,0.01976,-0.04055,-0.01603,-0.01867,-0.04584,-0.10682,0.04087,-0.05169,0.0156,-0.00105,-0.06131,0.02499,-0.02073,-0.02123,0.08166,-0.0571,0.05079,0.05217,0.07566,-0.04269,-0.03648,-0.00687,0.01241,-0.00492,0.16749,0.05732,0.10336,0.05425,-0.03376,-0.02839,0.04405,-0.00722,0.03384,-0.10466,-0.0212,0.00672,0.1047,0.10533,-0.03325,-0.03668,0.04569,0.04198,-0.06756,-0.04948,0.09535,-0.03557,0.03008,0.0474,0.06615,0.12699,0.06404,0.02884,-0.12311,-0.00638,0.01433,-0.14428,0.01234,0.12454,-0.07205,-0.01989,0.03397,-0.04051,0.11961,-0.02086,0.02208,-0.02093,0.08782,-0.02313,-0.01209,0.02399,0.03652,-0.04929,-0.05014,-0.033,-0.08933,-0.04608,0.04315,0.03862]},{"domain":"classical_physics","key":"engine_efficiency","name":"Efficiency of a heat engine","package":"classical-physics-ai999x","example":"A heat engine takes in a heat input of 1000 J and produces a work output of 300 J. What is its efficiency?","v":[0.12482,0.09417,-0.13111,-0.08716,0.10267,-0.02999,-0.02352,-0.03171,-0.01958,0.04568,-0.05394,-0.10088,0.0422,0.02363,0.00676,0.03423,-0.02103,0.03468,0.03649,-0.07771,-0.02956,0.08653,-0.07101,-0.06595,-0.06833,0.00334,-0.06502,0.00309,-0.01445,0.13881,0.01506,0.0326,0.06018,0.09047,-0.01588,0.02255,-0.01632,-0.07768,0.00488,-0.06269,0.04891,0.00708,-0.0941,0.02879,-0.00143,0.0049,0.01201,-0.01594,-0.0607,0.03143,0.04079,-0.03747,-0.05002,-0.0384,0.03369,0.12895,0.05551,0.02214,-0.06543,-0.10911,0.00516,-0.17733,-0.02583,0.11614,0.07808,0.01565,-0.03617,-0.06647,-0.11441,0.12009,-0.04923,0.12053,-0.03842,-0.11531,0.07081,0.04417,0.07853,0.13345,0.01284,-0.02221,-0.04868,-0.0213,-0.04055,0.01588,-0.1002,-0.11125,0.06796,-0.10034,0.0148,0.00544,-0.03023,0.05375,0.07968,0.03728,-0.04277,0.03088,0.08784,0.03838,0.04332,0.02067,0.00258,0.04514,0.01705,-0.08224,-0.05427,-0.01983,0.09254,-0.05481,-0.01489,0.03273,-0.00156,-0.04806,0.02111,-0.00293,-0.01999,0.11055,-0.02128,-0.06752,0.08318,0.07683,-0.10177,-0.02707,0.00057,-0.05645,-0.05168,0.00785,-0.00504,0.00027,-0.04184,0.05685,0.01082,0.01414,-0.01727,0.00813,0.00651,-0.0212,0.00051,0.05175,-0.06599,0.0399,0.01628,-0.031,-0.08547,0.04528,0.12742,0.04942,-0.03445,-0.06741,0.08327,-0.01693,0.0102,-0.02096,-0.10763,-0.04574,0.05638,0.09279,-0.06243,-0.07155,0.00741,-0.08703,-0.04382,-0.04434,-0.07812,-0.0439,0.03913,-0.05567,-0.05378,0.10042,0.03277,-0.01626,-0.05369,-0.00513,-0.10263,0.03141,-0.07975,-0.04865,0.06157,-0.01634,0.10026,0.05382,0.03861,-0.09858,0.05082,-0.13674,-0.05012,0.01017,-0.04042,-0.01146,-0.09896,0.01255,-0.04732,0.01355,-9e-05,0.07298,0.02925,0.0436,-0.03882,0.07783,0.0813,-0.00698,-0.03477,0.01939,0.10974,0.07503,0.04064,-0.10186,0.02609,0.01708,-0.03287,-0.07043,-0.03598,-0.15496,-0.06961,0.13285,0.08683,0.02498,0.03981,-0.01559,0.14762,-0.033,-0.02914,0.03383,-0.00853,0.00032,0.0652,0.08973,0.08849,0.04919,0.03307,0.02831,-0.07368,0.07345,0.01196,0.08846,0.09029,-0.05552,0.03653,-0.00278,0.00394,-0.05005,0.03595,-0.02973,0.07984,-0.01555,-0.03074,-0.00261,-0.01767,-0.02062,0.06244,-0.09415,0.05607,-0.02703,0.0636,0.07377,-0.15274,-0.0639]},{"domain":"classical_physics","key":"carnot_efficiency","name":"Carnot (maximum) efficiency","package":"classical-physics-ai999x","example":"A heat engine works between a hot reservoir temperature of 600 K and a cold reservoir temperature of 300 K. What is its maximum efficiency?","v":[0.01133,-0.00021,-0.05808,0.02347,0.04823,0.05872,-0.01094,0.02184,0.0689,0.07657,-0.04115,0.02973,0.02283,0.04584,0.00473,0.03456,0.00922,0.04349,0.12217,-0.10706,0.00586,-0.00822,-0.08321,-0.1389,-0.01188,0.00349,-0.08339,0.08181,0.02581,0.08201,-0.00749,0.00132,0.11611,0.03512,-0.07519,0.03804,-0.07103,-0.03661,0.01556,-0.09714,0.05875,-0.0181,-0.04145,0.04369,-0.04108,-0.04013,0.07842,-0.02628,-0.01682,0.00159,0.06158,0.00082,-0.0094,-0.01681,-0.00316,-0.01789,0.01928,0.01725,0.03073,-0.03654,-0.05848,-0.14834,0.03289,0.06211,0.03962,-0.07351,-0.02391,0.01754,-0.05428,0.13324,-0.0823,0.15834,0.0012,-0.11376,-0.017,0.05488,-0.04465,0.01468,0.00377,0.0538,0.07773,0.00445,-0.10516,-0.03295,-0.0096,-0.02386,0.08288,0.00998,-0.02371,-0.10363,0.0372,0.20973,0.05684,0.06868,0.00768,-0.04092,0.08,-0.04602,-0.04177,-0.00081,-0.01455,-0.02003,-0.01254,-0.064,-0.04144,-0.02827,0.01421,-0.04177,-0.0894,0.009,-0.06831,0.02349,0.0653,0.03631,-0.00649,0.0371,-0.00736,-0.03794,0.04907,0.05051,-0.00658,-0.01922,0.01205,-0.07135,-0.04314,-0.01912,0.05981,-0.05147,0.03953,-0.02511,-0.02688,0.02569,-0.15221,-0.02172,-0.04009,-0.02265,0.0268,0.00095,-0.00943,0.06271,0.04262,0.0182,-0.02423,0.11537,0.07433,0.02745,-0.02219,-0.12525,0.02802,-0.02358,-0.00524,0.05002,-0.16806,-0.05669,-0.01253,0.13454,-0.09998,0.01265,-0.10117,-0.05384,-0.05353,0.04077,-0.10281,-0.08514,-0.02782,-0.0299,-0.02273,0.08013,0.07957,0.00496,-0.03165,-0.07949,-0.07127,0.00776,-0.03272,0.01074,0.02634,0.01102,0.08319,0.04551,0.06885,-0.08887,-0.00105,-0.06125,-0.08453,0.0335,-0.0967,0.01769,-0.13352,0.01925,0.01819,0.05161,0.02127,0.03612,0.05798,0.02707,-0.00259,0.04164,0.07376,0.04276,0.00983,0.02618,0.1499,0.16937,0.03898,-0.05554,0.01638,0.06062,-0.05908,-0.09965,-0.04754,-0.12677,-0.06594,0.08943,0.04966,0.10873,-0.01916,0.05832,0.05722,-0.05663,-0.11264,0.03901,0.02583,-0.13415,-0.02675,0.15336,0.01195,-0.01597,-0.05053,0.00761,0.03938,0.03758,0.01482,-0.01336,0.09747,0.06669,0.04621,0.01266,-0.01487,-0.02442,0.02419,0.05161,0.02718,0.06375,-0.05193,0.00536,-0.04196,-0.05167,-0.0664,-0.05968,0.02607,0.09196,0.13801,0.07918,-0.12153,-0.07788]},{"domain":"classical_physics","key":"shm_max_speed","name":"Maximum speed of a mass on a spring","package":"classical-physics-ai999x","example":"A 1 kg mass oscillates in simple harmonic motion on a spring with a spring constant of 100 N/m and an amplitude of 0.1 m. What is its maximum speed?","v":[-0.09774,0.02035,0.04151,-0.05489,0.0129,-0.01255,0.00973,0.02416,0.02924,0.03493,-0.06002,0.06847,0.03731,-0.02668,0.05805,-0.01176,-0.0825,-0.04742,0.05807,-0.03116,0.00396,0.0654,0.06886,-0.00293,-0.0694,0.05236,-0.0109,-0.01181,0.05385,-0.0619,0.00447,0.00052,0.03593,0.04037,-0.05738,-0.04985,-0.02278,-0.0346,-0.04303,-0.09088,-0.0847,-0.00528,-0.03918,0.07677,-0.0067,0.07424,-0.03551,0.03929,0.05204,0.01931,0.00487,-0.00644,0.01246,-0.09855,0.04082,-0.05347,-0.04674,-0.01329,0.0415,0.07533,0.03351,-0.1291,0.02994,0.01135,0.01572,-0.02623,-0.00206,-0.04077,0.08613,0.10404,0.0701,-0.04944,-0.01361,-0.05275,-0.10815,0.10123,-0.03578,-0.07528,0.00733,0.09133,0.01128,0.03512,-0.08288,0.0114,0.03682,-0.00186,0.03339,-0.00859,0.0107,-0.01529,0.03807,-0.0056,0.09248,0.00669,-0.01079,0.05639,0.0189,0.02241,0.09405,0.03999,-0.02217,0.06809,-0.04345,-0.1297,-0.10607,-0.04908,0.09774,0.03614,-0.17682,-0.08979,-0.07287,0.03416,0.08445,-0.00158,-0.05729,0.02236,0.04003,-0.00752,-0.03759,0.02172,0.0866,0.01619,0.00515,-0.00542,-0.10956,-0.0795,0.01919,-0.08526,-0.06605,-0.03675,-0.01235,0.1466,0.08223,0.03607,0.02733,0.09927,-0.05335,0.14902,0.03244,0.03467,-0.0316,0.08558,0.00819,-0.03304,-0.0038,0.07739,0.00679,0.03925,-0.08228,0.0554,-0.04308,0.06459,-0.04105,-0.09856,-0.05645,0.07847,0.05561,-0.03198,-0.14237,-0.06298,0.01015,0.08607,-0.0172,-0.01832,-0.05651,-0.02572,0.06148,-0.11514,0.01446,0.12616,-0.104,-0.03614,0.05397,0.02329,0.04812,-0.0416,0.02546,-0.06367,-0.01116,-0.04801,0.085,0.05851,0.03415,0.07083,-0.02745,0.01922,-0.0914,-0.03636,-0.05256,-0.04154,-0.07619,-0.00507,-0.0001,-0.08772,0.02327,-0.06378,0.06164,0.0464,-0.12587,0.07111,0.11154,-0.03415,-0.08983,0.10482,0.00975,0.02839,-0.09574,0.11924,-0.03277,-0.04578,-0.03707,-0.09128,-0.041,-0.04389,0.03541,0.06546,-0.11132,0.09824,-0.03342,0.03203,-0.06327,-0.03387,0.00207,0.04812,0.02282,0.09168,-0.07776,0.11679,0.01822,-0.05673,0.01801,0.12098,-0.03809,0.05452,-0.00245,-0.01487,-0.09057,0.08595,-0.10097,-0.07314,-0.06801,-0.00112,-0.01655,0.01278,0.08343,-0.14082,0.11293,-0.0161,-0.04422,0.08213,0.02073,0.13078,0.05285,-0.07963,-0.07714,0.10383]},{"domain":"classical_physics","key":"intensity_power_area","name":"Intensity as power per area","package":"classical-physics-ai999x","example":"A power of 100 W falls uniformly on an area of 2 m^2. What is the intensity?","v":[0.02668,-0.12477,0.02827,0.0207,0.04603,0.04598,-0.02196,0.02133,-0.05753,0.01681,0.03134,-0.08134,0.08192,-0.02485,-0.03784,0.00641,0.00363,-0.00946,0.07048,0.0627,0.05353,-0.01877,0.1097,-0.02907,-0.07677,0.09228,-0.00588,0.11652,-0.05117,0.00598,0.06606,0.05431,-0.09066,0.06488,-0.05567,0.11747,-0.02455,-0.01714,-0.02181,-0.00831,0.08128,0.06675,-0.0368,-0.0521,0.04888,0.0749,-0.02914,-0.00626,0.03345,0.05989,-0.03697,0.06121,-0.02521,-0.05719,-0.05936,-0.0797,0.06981,-0.08242,-0.02529,0.0758,0.08568,0.06481,-0.06412,-0.01734,0.00666,-0.01686,-0.08618,0.07093,0.09527,-0.00212,0.08864,0.02805,-0.06574,0.03416,-0.06988,-0.00514,0.04768,-0.01908,-0.07102,-0.01593,-0.00716,-0.06408,0.07642,-0.0657,-0.03927,-0.02574,0.03014,-0.05269,-0.00286,-0.02379,-0.01809,-0.02718,-0.06539,-0.07737,-0.069,0.00763,0.14175,0.07206,0.10923,0.10267,-0.00706,0.05181,-0.02226,0.00636,-0.01454,-0.06048,0.05206,-0.07609,0.05484,0.0306,0.02612,-0.02812,0.04194,-0.01916,-0.01818,0.03822,-0.04099,-0.112,-0.01697,-0.00212,-0.09387,-0.053,0.03388,-0.00415,-0.03626,-0.10308,-0.06042,0.0358,-0.10702,0.063,-0.03496,0.03371,0.09268,-0.05745,-0.05155,-0.02147,0.05878,0.01502,0.02012,0.13483,0.03985,0.08916,-0.0011,0.00645,0.04617,-0.03357,0.00492,-0.05831,0.06317,-0.06484,0.00828,0.06601,-0.00867,0.02412,0.03615,-0.00202,-0.14078,-0.12928,0.10273,0.07131,0.02013,0.09232,0.08018,-0.03842,-0.00856,0.05776,-0.06589,0.03065,-0.11755,-0.09271,-0.01547,0.07526,0.00355,-0.00255,0.02252,-0.04268,0.06993,0.06221,-0.0057,-0.10798,0.02532,0.06626,-0.08263,-0.06805,-0.01899,-0.03315,-0.06141,0.08613,-0.11933,-0.0357,-0.11035,-0.03246,0.03005,0.01328,0.03503,0.04994,-0.05957,-0.09625,-0.0502,0.00281,0.10041,-0.00535,0.03745,-0.0691,0.05371,0.01643,-0.11914,-0.10844,-0.00553,0.02116,0.05137,-0.04663,0.06558,-0.05345,0.06228,0.08638,0.07,-0.05384,0.05147,-0.05094,-0.00102,-0.11337,-0.09993,0.02689,0.05246,-0.04999,-0.01254,-0.02374,0.12157,-0.0153,-0.07962,0.07695,-0.01096,0.02302,0.13944,0.10747,0.05403,-0.26076,-0.00676,0.02892,-0.02994,0.01838,-0.00791,0.09193,-0.08186,-0.03282,0.10257,-0.02841,0.02289,0.02322,-0.00395,-0.00673,0.02953,0.09997,0.00274,0.05579]},{"domain":"classical_physics","key":"wavelength_in_medium","name":"Wavelength of light in a medium","package":"classical-physics-ai999x","example":"Light with a wavelength in vacuum of 600 nm enters glass with an index of refraction of 1.5. What is the wavelength in the medium?","v":[0.05454,0.02975,0.00022,-0.0281,0.03725,0.13428,0.08233,-0.0359,-0.00493,-0.10085,0.08688,-0.01167,0.09196,-0.05264,-0.0651,-0.0198,0.01377,0.00092,0.116,0.04325,-0.11821,0.03503,-0.01026,0.11474,-0.03244,-0.02599,0.01747,-0.00074,-0.01558,-0.05952,0.05404,-0.06415,-0.07026,0.02595,0.07564,-0.01062,0.15248,-0.08178,-0.01484,-0.09564,-0.04184,0.02777,0.01071,-0.02314,-0.10475,0.02683,-0.05134,-0.09362,0.07153,-0.07897,-0.02889,0.0562,0.01335,0.04893,-0.08859,-0.05537,-0.00911,0.00587,-0.07553,-0.02831,0.10094,0.05023,0.10856,-0.05309,-0.00151,0.12209,0.03478,0.00105,-0.00528,0.08547,0.04297,-0.02219,0.09053,0.03328,0.02511,-0.01682,-0.00557,-0.02313,0.12286,0.01449,0.08334,-0.01119,0.05035,0.03522,-0.0151,-0.00994,-0.00262,-0.19458,0.08406,0.08599,-0.06017,0.07581,-0.00535,-0.04536,0.06572,-0.0881,0.03196,0.03841,0.05773,-0.09276,-0.00687,0.08532,0.02625,-0.06357,0.05775,-0.02847,-0.05408,-0.08009,0.09858,-0.03479,-0.04244,-0.11416,0.01284,-0.09107,-0.08135,-0.00736,0.02539,-0.01076,-0.02743,0.01525,0.01269,0.09479,-0.01624,0.07679,0.05555,-0.03588,0.07466,-0.05363,-0.19516,0.02455,-0.02336,0.02031,0.07603,0.00142,0.05209,0.04887,0.03177,0.07285,-0.05299,-0.05424,-0.08043,0.13206,0.04447,0.0069,0.02974,-0.06599,0.07796,-0.10688,-0.09201,-0.04664,0.07671,0.11041,-0.01497,-0.04524,0.03802,0.00976,0.01798,-0.08462,-0.02995,-0.00497,-0.11254,-0.01572,-0.01632,-0.1083,0.09957,-0.07043,0.03344,-0.08685,0.0834,-0.01576,-0.02977,-0.03577,-0.00454,-0.01589,0.06599,0.03791,-0.01542,-0.10811,0.10024,-0.08112,0.10855,0.04673,-0.08577,0.03712,-0.01918,-0.00567,-0.02474,-0.08001,-0.1014,0.08524,0.03625,0.02006,0.02783,-0.13706,0.00093,0.03488,0.04165,-0.03622,-0.10096,0.00371,-0.07455,0.09058,0.04993,0.01471,-0.01673,-0.03443,0.11872,0.06625,-0.11515,0.09207,-0.05172,0.07719,0.00994,0.01294,-0.01761,-0.04804,-0.05855,-0.02784,0.04626,-0.03812,0.03618,-0.11855,0.07318,0.02244,-0.01061,-0.00798,-0.04404,0.03305,0.0276,-0.07769,0.01872,-0.01454,0.0043,0.07047,0.07011,-0.09072,0.06265,-0.01104,-0.00928,0.03004,-0.00392,-0.01417,-0.01574,-0.00319,0.07778,0.02706,0.02237,-0.03571,-0.0598,0.02198,-0.08347,0.00478,-0.00784,-0.00186,-0.0847,-0.00721]},{"domain":"classical_physics","key":"index_of_refraction","name":"Index of refraction","package":"classical-physics-ai999x","example":"The speed of light in the medium is 2e8 m/s for a certain glass. What is the index of refraction of the glass?","v":[0.06963,0.0849,0.0379,-0.05729,0.04499,0.05758,0.03506,0.02152,-0.00766,-0.09423,-0.00657,-0.03698,0.09551,-0.06553,-0.08635,-8e-05,-0.06796,-0.02992,0.05048,-0.00714,-0.05534,0.04604,-0.01087,0.03808,-0.07203,0.01494,0.0549,0.02055,-0.0419,-0.09094,0.07548,-0.03519,-0.04153,-0.00408,0.05512,0.03996,0.12759,-0.12679,-0.0055,-0.07366,-0.06333,0.03022,0.00914,-0.05425,-0.05777,0.02388,-0.06994,-0.08878,0.04817,-0.07983,-0.00373,0.04268,-0.02515,0.00833,-0.07365,0.01673,0.00675,-0.02849,-0.06598,-0.04201,0.1413,-0.0109,0.0399,-0.12251,-0.05065,0.06946,0.0483,0.04828,-0.0243,0.19175,-0.03153,-0.05053,0.02899,-0.02137,0.00625,-0.03887,0.03701,0.00917,0.17657,0.07679,0.03645,-0.02837,0.00267,0.08998,-0.05642,-0.02629,-0.06515,-0.17036,0.07464,0.09811,-0.03305,0.09274,-0.00774,0.03187,0.0555,-0.04548,-0.00633,0.02015,0.06875,-0.11198,0.0033,0.05177,0.03099,-0.03217,0.02745,-0.01569,0.03079,-0.01197,0.11874,-0.05435,0.00713,-0.07143,0.05387,-0.06622,-0.07548,0.01626,0.07297,-0.02327,-0.06383,-0.0305,0.05596,0.04775,-0.02365,0.06164,0.09557,-0.06393,-0.00076,0.00315,-0.19277,0.05388,0.05061,-0.00144,0.0179,-0.00642,0.06049,0.12076,0.01848,0.10877,-0.12872,-0.02655,-0.05829,0.1408,0.03923,0.05344,0.01818,-0.06717,0.07529,-0.06738,-0.08483,-0.01541,0.06816,0.0565,-0.02813,-0.09132,-0.00786,-0.05284,-0.00197,-0.09846,-0.07969,-0.02771,-0.05159,0.10733,0.03507,-0.12857,0.16563,-0.04421,-0.00893,-0.10705,0.07681,0.01119,-0.06796,-0.0617,0.04187,0.00567,0.00927,-0.02521,-0.02308,-0.02902,0.10678,-0.02938,0.07494,-0.01667,-0.07019,0.01335,0.03598,0.00515,-0.02853,0.00031,-0.11411,0.13169,0.01688,-0.0034,-0.05059,-0.10798,0.03335,0.0419,0.04342,0.02513,-0.04708,0.01671,-0.05905,0.11376,0.07858,0.04997,-0.04489,-0.00806,0.08942,0.0903,-0.08408,0.08766,0.00028,-0.00248,0.00372,-0.00338,-0.04968,-0.08764,-0.04817,0.00525,0.03708,-0.03884,0.06053,-0.09294,0.03579,0.00736,-0.03227,0.05914,-0.05084,0.05672,0.02463,-0.02628,-0.05777,-0.04159,0.00768,0.06696,0.07593,-0.11746,0.08728,-0.00534,0.00496,0.05993,0.01557,0.02539,-0.03391,-0.03462,0.01146,-0.01812,0.0166,-0.04428,-0.06536,0.02512,-0.01937,0.06705,-0.06544,-0.00871,-0.041,-0.02282]},{"domain":"classical_physics","key":"mirror_focal_length","name":"Focal length of a spherical mirror","package":"classical-physics-ai999x","example":"A concave mirror has a radius of curvature of 0.4 m. What is its focal length?","v":[0.06004,-0.07249,-0.0062,-0.06346,0.11506,-0.02192,0.0183,-0.02887,0.06104,-0.05352,-0.01802,-0.12431,0.01027,-0.03403,-0.02514,0.02334,-0.03804,0.11287,0.17717,-0.03168,-0.10231,0.03814,-0.03446,-0.03546,-0.0112,0.00398,0.00525,-0.10782,0.13849,-0.10257,0.04202,0.02383,0.01357,-0.00464,0.03765,-0.09401,0.06316,0.02798,0.01102,0.02178,-0.03509,0.00829,-0.02363,-0.03338,0.0689,0.0672,-0.00968,0.05836,-0.00062,-0.0341,0.04459,0.03683,-0.07507,0.00484,-0.12679,0.0543,-0.0592,-0.04937,-0.04261,-0.02873,0.09769,0.01817,-0.0259,0.03435,-0.01321,0.10775,-0.08229,-0.09064,-0.05767,-0.08325,0.14744,0.02563,-0.1193,0.04471,0.06114,-0.0255,0.03811,0.01227,-0.00931,-0.01785,0.01653,-0.0208,0.04244,0.00469,0.18557,-0.02118,0.02374,-0.05386,0.01633,-0.02745,0.09399,-0.10013,0.00532,0.02857,-0.00189,-0.03045,-0.02973,0.0182,-0.01377,-0.05072,0.02014,0.01908,0.00686,0.03155,-0.12034,-0.06016,0.04863,0.0467,0.08921,-0.00792,-0.02075,-0.08012,0.10618,-0.06493,-0.0115,0.01893,0.09872,0.01098,-0.00864,-0.00444,-0.00727,0.05075,-0.06518,-0.01235,0.04491,-0.03983,0.0038,-0.02802,-0.00259,0.07191,-0.04761,0.00521,0.01574,0.03509,0.07886,0.00408,-0.10135,0.14983,-0.05217,0.01053,0.16882,0.00162,0.02327,-0.08782,0.03994,0.0252,0.13014,-0.00961,0.00501,0.12497,0.06297,0.04335,-0.08211,-0.0987,0.05501,-0.04958,-0.02945,-0.00184,-0.05084,0.00821,-0.01543,0.00723,-0.04246,-0.05188,-0.04903,0.06466,0.00783,0.01612,0.05784,0.01498,-0.14247,0.15434,0.03962,0.10173,-0.09281,-0.12889,-0.03722,-0.04636,0.09957,-0.04326,0.07331,0.00855,0.06844,-0.00042,0.01481,-0.01476,-0.01474,-0.01405,-0.0671,0.01595,0.08499,0.00921,-0.11359,-0.11781,0.05332,0.06075,0.02756,-0.05972,0.04536,-0.01282,-0.08051,-0.02565,0.04769,-0.02534,0.01188,-0.06393,-0.01034,0.00384,-0.06766,-0.04091,-0.02318,-0.04969,0.04673,-0.04216,-0.09006,-0.02416,-0.10521,-0.01814,0.10087,0.02939,0.02395,-0.06919,-0.05567,0.09054,-0.01594,-0.04754,-0.00192,0.15543,-0.00988,-0.07036,0.01628,0.03212,0.01234,-0.03122,-0.11448,-0.01499,-0.06317,-0.14017,-0.10346,0.0996,0.00391,-0.00253,-0.06625,0.03249,0.08339,0.03295,-0.03511,0.0282,-0.05963,-0.03079,0.05892,0.04928,0.07597,0.06447,-0.05663,0.0394]},{"domain":"classical_physics","key":"rms_voltage","name":"Rms voltage of a sinusoidal supply","package":"classical-physics-ai999x","example":"An AC supply has a peak voltage of 170 V. What is the rms voltage?","v":[0.02393,-0.00807,0.0092,0.00698,-0.07194,-0.0931,-0.0505,0.01462,-0.03371,0.01409,0.02044,-0.04671,0.02362,0.01701,0.10111,-0.00397,0.00601,0.03181,0.00146,0.03994,0.03464,-0.05329,0.02326,0.04534,0.0428,0.08694,0.08697,0.05098,-0.02663,-0.04536,-0.18022,0.05071,0.04616,0.00525,-0.07945,-0.11356,0.07118,-0.03167,0.08043,-0.00338,0.02205,-0.03282,0.11242,0.01136,0.0255,0.00731,-0.01149,-0.07567,-0.12301,-0.00379,0.0684,0.06146,-0.03826,0.0516,0.03165,-0.09806,0.06608,-0.02071,-0.04345,0.02648,0.05094,0.00771,0.02743,0.03352,0.06105,0.01693,0.02006,0.10745,-0.03433,-0.01726,0.07242,0.05166,0.05335,-0.0158,-0.0443,0.00655,-0.04272,-0.08656,-0.05358,0.06509,0.00608,0.11122,-0.02652,-0.19602,0.06839,-0.02413,-0.03052,-0.02655,-0.06053,-0.11589,0.10587,0.03766,0.00991,-0.02571,0.00513,0.02456,0.09877,-0.07339,0.07044,0.08234,-0.09103,0.01399,0.09527,-0.09691,-0.07398,-0.10496,0.0381,0.08095,-0.10946,-0.02414,-0.14381,-0.06933,-0.01161,0.08533,-0.08644,0.07477,-0.02344,-0.03331,-0.10997,-0.09665,0.12353,0.03446,-0.04232,-0.07601,-0.15372,-0.00378,0.01911,-0.02764,0.08127,0.04341,-0.08,-0.00563,-0.0482,0.04999,-0.064,0.02775,-0.07353,-0.02722,0.04086,0.01378,0.01188,0.08216,0.06221,0.00114,0.05671,-0.01977,0.07036,0.10866,0.00788,0.12736,-0.027,0.02193,-0.02369,0.05129,-0.03463,0.0333,-0.04692,0.08928,-0.0582,-0.02264,0.02318,0.04018,0.09636,-0.02577,-0.0697,0.01869,-0.0979,-0.0399,0.00375,-0.05366,-0.08607,0.05946,-0.11489,0.00205,-0.00775,-0.05625,0.03674,-0.07302,-0.04043,-0.02801,-0.05455,0.03734,-0.02277,0.14248,0.06039,-0.01379,-0.11476,-0.03139,0.01099,0.052,-0.11628,-0.06973,0.01246,0.02659,0.07557,-0.00511,0.01202,0.07533,0.02741,0.13395,0.04126,-0.07562,-0.0566,0.04258,0.00898,-0.05673,-0.1339,-0.0094,0.07066,-0.02654,-0.03591,-0.04343,-0.03307,0.01482,0.00041,0.08308,-0.08146,0.01693,-0.0327,-0.06428,-0.0739,-0.00812,0.06015,0.02035,0.08065,0.09739,-0.10479,0.01477,0.02724,-0.08422,-0.01079,0.05415,0.00237,0.0325,-0.01487,0.00384,-0.11692,-0.02939,0.10971,0.03743,0.09466,0.03077,-0.09622,0.03582,0.05309,-0.02399,0.01994,0.01396,0.024,0.10592,-0.00564,0.06448,-0.07072,-0.00691,-0.02903,-0.01964]},{"domain":"classical_physics","key":"rms_current","name":"Rms current of a sinusoidal supply","package":"classical-physics-ai999x","example":"An AC circuit has a peak current of 10 A. What is the rms current?","v":[0.04149,0.03359,-0.04653,-0.03189,-0.03868,-0.07155,-0.01726,-0.04436,-0.05521,0.06865,-0.054,-0.03431,0.0813,0.03319,0.04938,0.04027,0.00933,-0.03625,0.05186,0.00221,0.0861,-0.06418,-0.00269,0.00902,0.03171,0.08451,0.0296,0.11313,0.05731,-0.0835,-0.12094,0.01571,0.02845,0.0028,-0.0564,-0.05114,0.0215,-0.01665,0.06958,-0.08017,-0.04892,-0.04748,0.0911,0.10639,0.01143,0.01393,0.003,-0.01016,-0.044,-0.09314,0.00532,0.0392,0.07095,0.01663,-0.01028,-0.11625,0.021,0.03255,-0.07492,-0.02476,0.06604,-0.03124,0.04705,-0.05279,0.02323,-0.00579,-0.03966,0.14267,-0.09262,-0.05734,0.01796,0.02012,0.02462,-0.08875,-0.09278,-0.04699,0.076,-0.08969,-0.17362,0.05929,-0.02064,0.09573,0.01894,-0.04454,0.12837,-0.05363,-0.03343,-0.06931,-0.07261,-0.14983,0.05617,0.03169,-0.01721,0.01033,0.06417,0.03457,0.04315,-0.06326,0.00333,-0.00424,-0.03121,-0.02535,-0.00857,-0.07454,-0.05434,-0.05567,0.01599,0.07576,-0.0367,0.03622,-0.11166,-0.01203,0.03812,0.08401,0.00305,0.05769,0.03586,0.00365,-0.1478,-0.07984,0.09967,0.06332,0.02054,-0.04592,-0.16238,-0.0453,-0.03974,-0.03943,0.08058,0.05299,-0.09651,-0.04191,-0.02994,0.0424,-0.01886,0.06547,-0.09422,0.01549,-0.04512,0.04574,0.00236,-0.00186,0.01852,0.02225,0.07513,0.04317,0.10457,0.11348,-0.00955,0.05334,-0.00552,0.04467,-0.07678,0.03327,-0.0014,0.08079,-0.04732,0.0482,-0.01129,-0.04472,0.066,-0.00531,0.13794,-0.01787,-0.1261,-0.05163,-0.03908,-0.08873,-0.0089,0.01156,-0.064,0.04138,-0.06321,0.03179,-0.06696,-0.03416,0.03319,-0.0677,-0.05907,0.04134,-0.00648,0.03263,-0.0432,0.15755,0.06211,0.02319,-0.15229,0.04268,-0.00614,-0.05625,-0.06853,-0.02696,0.05542,-0.00633,0.00848,0.0278,0.02718,0.06274,0.02097,0.11518,0.09281,0.02231,-0.07138,0.03831,0.04591,-0.08526,-0.10122,0.0315,0.08344,-0.03368,0.00291,0.03239,-0.00905,0.05535,-0.00081,0.12929,-0.13916,0.00506,-0.01563,-0.03034,0.02753,-0.05497,-0.0035,0.0573,0.07615,0.06218,-0.11486,-0.07611,0.01948,-0.07986,0.02983,0.00186,0.08565,0.01665,0.07038,-0.00156,-0.08207,-0.09824,0.10442,0.03384,0.0625,0.04609,-0.08823,0.05856,-0.02893,0.0315,0.04291,-0.00654,-0.03114,0.08318,0.02534,0.11892,-0.01836,0.05485,-0.12495,-0.03472]},{"domain":"classical_physics","key":"loop_center_field","name":"Magnetic field at the centre of a circular loop","package":"classical-physics-ai999x","example":"A circular loop of wire with a radius of 0.1 m carries a current of 5 A. What is the magnetic field at its centre?","v":[0.05758,-0.02943,-0.10845,-0.03982,-0.02738,0.07008,0.02337,0.04887,0.04068,0.08853,-0.06428,-0.08235,0.16458,-0.01701,-0.06108,-0.01444,-0.11361,-0.06156,0.07249,-0.00662,0.00083,-0.04147,-0.0488,-0.06808,0.00887,-0.02084,0.02293,-0.05571,0.08253,0.00076,0.08814,0.00436,0.00303,0.01415,-0.05191,-0.07364,0.03807,0.00261,0.08662,-0.01341,-0.01001,0.02907,0.03837,0.17267,0.02968,0.10978,0.07907,0.11126,0.06214,-0.01503,-0.00452,-0.09353,0.05086,0.04041,-0.03116,0.00097,-0.0358,-0.06698,-0.00484,-0.00841,0.02599,0.0431,0.00777,-0.09028,-0.06531,-0.03326,0.08011,0.09468,-0.05313,0.06145,0.05689,-0.01356,-0.03505,-0.09172,-0.10965,-0.07026,-0.109,0.00497,-0.12519,0.01342,-0.00562,0.08783,0.0359,-0.02904,0.00212,0.04461,0.10394,-0.08943,0.00701,-0.05546,0.02142,0.01733,-0.03477,0.08835,0.04191,0.10024,-0.03679,0.0132,-0.01095,-0.02846,0.00277,-0.09381,-0.06251,0.01038,0.00999,-0.02365,-0.00865,-0.05752,0.06008,0.02789,-0.06509,-0.01766,0.10394,0.08187,0.02079,0.00941,0.1355,-0.03791,-0.08107,-0.07541,-0.06011,-0.06996,-0.02086,0.01173,-0.07774,-0.05219,0.05756,0.06175,-0.00427,-0.0005,-0.02049,0.00978,0.09396,-0.00395,0.03422,0.02424,-0.0259,-0.02092,-0.03803,-0.01387,-0.02578,-0.08035,0.01188,0.003,0.08657,0.04179,0.11336,-0.06064,0.04059,-0.06195,-0.00162,0.07333,0.10989,0.00117,0.07365,-0.02668,0.00355,0.08478,-0.00615,-0.10437,0.06543,-0.04312,-0.00945,-0.15269,-0.08466,-0.12619,0.04435,-0.18351,-0.03904,0.00885,0.06126,-0.04199,0.02174,-0.01979,-0.00401,-0.04835,-0.1009,0.01752,0.00733,0.02716,0.0642,0.02886,-0.02373,-0.00707,0.01227,-0.02556,-0.01882,0.09596,-0.02711,-0.12494,0.01957,0.06035,-0.03734,-0.05045,-0.01408,-0.04979,0.01339,0.06515,-0.06373,0.07644,0.01136,0.03941,-0.04069,-0.02839,0.01477,-0.12653,0.12722,0.05407,-0.04414,-0.03095,-0.02573,0.10533,0.09771,0.10596,-0.01576,-0.01778,-0.11372,-0.09205,0.07286,0.04903,-0.10817,0.02753,0.0116,0.07493,-0.00536,0.09865,0.07543,0.02845,0.10585,0.01428,-0.04438,-0.0545,0.05579,0.06951,-0.06763,-0.01672,-0.02613,-0.02164,0.025,-0.01049,0.03146,0.03757,0.01094,-0.08249,-0.04255,-0.03911,0.00346,0.0161,-0.12462,0.03212,-0.00056,0.00211,0.08477,0.15905,-0.13771,0.02472]},{"domain":"classical_physics","key":"rl_time_constant","name":"Time constant of an RL circuit","package":"classical-physics-ai999x","example":"An inductor of inductance 0.5 H is connected in series with a 100 ohm resistor. What is the time constant?","v":[-0.01027,0.08915,-0.10488,-0.03173,-0.11337,0.07285,0.16169,-0.00164,0.14465,0.0745,0.0422,0.05996,0.05021,0.10969,0.05185,-0.01356,-0.08974,-0.05201,-0.03508,-0.01789,-0.05865,-0.05372,-0.05422,-0.01349,0.18727,-0.04865,0.02042,-0.02424,0.12109,-0.03677,0.00528,0.05999,-0.02157,-0.04614,0.00517,0.07219,0.03967,0.0409,-0.01907,0.00387,-0.02921,-0.0443,-0.09594,0.04073,-0.01834,-0.01001,0.07806,-0.00423,0.10021,-0.05127,-0.03967,-0.03352,-0.04337,-0.05711,-0.07137,-0.04894,0.04954,0.08052,-0.08204,0.10349,-0.06693,0.09861,-0.0512,-0.05591,0.03402,-0.05717,0.00706,0.06506,0.02045,-0.07172,-0.08173,-0.05548,-0.06326,-0.04711,-0.0525,-0.07246,-0.03901,-0.00689,-0.10843,-0.08148,0.04265,0.04271,-0.02141,0.03287,0.03003,0.04483,0.03292,-0.05957,-0.07318,-0.07682,-0.02299,0.03956,-0.04373,-0.09941,0.09976,0.01123,-0.01495,-0.01807,-0.06539,0.00381,-0.01323,-0.03212,-0.06636,-0.03993,-0.02227,0.03039,-0.06804,-0.04748,0.00917,-0.03934,-0.01824,-0.09003,-0.0008,0.01861,-0.0168,-0.00032,0.09129,0.0039,-0.03268,0.02667,-0.03428,-0.01544,0.09174,0.00206,-0.08389,0.03064,0.02598,-0.01468,-0.05076,0.07573,-0.04489,0.01261,0.02205,0.08353,0.119,-0.05967,-0.0831,-0.02885,-0.00503,0.00043,-0.04851,0.00254,0.12947,0.01627,-0.10926,-0.09163,0.05546,-0.02781,0.06886,0.03377,0.00134,-0.04303,0.02073,-0.08361,0.02776,-0.03593,-0.01064,0.06098,-0.04422,-0.12112,-0.00246,0.06373,0.05458,0.12722,-0.11292,-0.12308,0.08291,-0.09475,-0.01973,0.01322,0.04215,-0.03812,-0.03007,0.02787,-0.05122,-0.05555,0.0785,0.10952,0.08465,0.00034,-0.06726,0.00834,0.04435,-0.00543,0.01698,-0.07586,-0.02987,0.01642,-0.15446,0.02169,0.01762,0.00081,0.08151,-0.02488,-0.04183,-0.00919,-0.06225,0.03523,-0.02606,0.08651,0.07378,0.09778,-0.05031,-0.00486,-0.00209,-0.04244,0.10911,0.05646,-0.08309,-0.03367,0.05504,0.03493,0.03096,0.03094,0.03181,0.00162,-0.01698,-0.01629,-0.01161,-0.00374,-0.05409,-0.01784,-0.03826,-0.0221,0.0401,0.07559,0.04123,0.03912,0.1139,-0.21317,0.02138,-0.16282,-0.05495,-0.05223,-0.0515,-0.06034,-0.03761,-0.02373,0.03051,0.00572,-0.01343,0.08403,-0.00444,0.01072,0.06597,0.07163,0.12258,0.00757,0.08842,0.12694,0.03155,0.06111,0.00558,0.10313,-0.0568,0.06704]},{"domain":"classical_physics","key":"inductive_reactance","name":"Reactance of an inductor","package":"classical-physics-ai999x","example":"An inductor of inductance 0.03 H is in an AC circuit at a frequency of 60 Hz. What is its reactance?","v":[-0.05828,0.08158,-0.1266,0.00452,-0.03139,0.06004,-0.01519,0.04752,0.12392,0.06649,-0.02578,-0.03031,0.05905,0.06904,0.03573,-0.0533,-0.09336,-0.05937,0.0506,0.0199,-0.09709,0.06461,-0.01,0.05373,0.02197,-0.09131,0.06549,-0.08738,0.00884,-0.04925,-0.1362,0.08228,0.00533,-0.07833,0.00588,0.09408,0.01671,0.01244,-0.02525,0.05651,-0.09191,-0.07832,-0.00885,0.07513,0.04273,0.00649,0.01794,0.05073,0.00743,-0.09064,0.03181,-0.0068,0.01525,-0.01388,-0.15032,0.04492,0.03933,0.00195,-0.09029,0.05843,-0.04615,0.00053,-0.0555,-0.00099,-0.02078,-0.03019,0.03794,0.10322,0.00297,-0.03088,-0.04462,-0.0417,-0.10017,-0.06009,-0.07107,-0.02399,0.02362,-0.04898,-0.0354,-0.20362,0.03097,0.05087,-0.00651,-0.00796,0.01344,-0.04359,0.02712,-0.08939,-0.06626,0.00287,0.00901,-0.01603,-0.03017,-0.03373,0.05274,0.00462,-0.06825,-0.04584,0.04468,-0.02722,-0.03558,0.03683,-0.07634,-0.08598,0.0232,0.07223,-0.06171,0.01571,-0.01862,-0.04891,-0.04832,-0.04171,0.03248,-0.02598,0.01779,-0.04513,0.14829,0.01142,-0.03819,-0.07787,-0.00043,-0.03273,0.09148,-0.00845,-0.03198,0.04279,0.00859,-0.0445,0.06287,0.0307,-0.0469,0.05532,0.09228,0.10245,0.02703,0.04057,-0.12805,0.00813,-0.06047,-0.02007,-0.04531,0.02023,0.07285,0.01289,-0.04941,-0.07537,0.10889,-0.03946,0.07095,-0.01304,0.11444,0.01005,-0.00207,-0.0106,0.05767,-0.05813,-0.02095,0.07403,0.01053,-0.06649,0.01328,-0.01607,0.08357,0.00626,-0.11256,-0.14329,0.05137,-0.18801,-0.02573,0.02247,0.02072,-0.07125,0.03194,0.03663,-0.00356,-0.02324,0.14062,-0.01777,0.05559,0.05264,-0.039,0.02016,-0.07646,0.0583,0.00757,-0.1154,-0.07143,6e-05,-0.03971,0.02253,0.07502,0.01086,-0.00041,-0.0618,-0.1048,0.01217,-0.04515,0.08374,-0.13372,0.09025,0.05001,0.03378,-0.01293,0.01458,-0.10177,0.00622,0.01645,0.09003,-0.10615,0.01995,0.048,-0.04088,0.08989,0.07539,-0.02965,0.01589,0.07648,0.13647,0.08675,-0.01978,-0.03213,-0.02847,-0.03628,0.07659,-0.00688,0.07775,-0.05572,0.06889,0.09618,-0.15482,0.01634,-0.08159,-0.05263,0.06895,-0.0057,-0.0595,-0.02704,0.02493,-0.01244,0.01793,-0.01251,0.11786,0.00291,0.01494,0.03861,0.01451,0.04843,0.04468,0.13196,0.05823,-0.10673,0.01257,0.01804,0.03344,-0.04931,0.14567]},{"domain":"classical_physics","key":"capacitive_reactance","name":"Reactance of a capacitor","package":"classical-physics-ai999x","example":"A capacitor with a capacitance of 1 uF is in an AC circuit at a frequency of 60 Hz. What is its reactance?","v":[0.01654,0.05293,-0.03613,0.07301,-0.02265,0.01745,-0.03927,-0.0422,0.05232,0.06217,-0.01297,0.0096,0.09208,0.0619,0.09696,-0.06436,-0.07225,0.02035,0.13797,0.00537,-0.03895,-0.00286,0.03993,-0.01316,-0.16572,-0.1054,0.0689,-0.0947,-0.02852,-0.04083,-0.08531,0.18056,-0.04149,-0.04654,-0.0348,0.12429,0.00997,-0.03579,-0.06705,0.09208,-0.03259,-0.04307,-0.00065,0.07435,-0.03019,-0.0425,-0.0273,0.07652,0.01807,0.04386,0.05576,-0.02389,0.00704,0.05834,-0.02921,0.06911,0.01467,-0.01294,-0.15741,0.04332,-0.07418,-0.14997,-0.08518,0.06446,-0.01359,-0.07992,-0.01052,-0.01083,-0.10903,-0.0214,0.0171,0.04328,-0.02385,-0.01988,-0.03412,0.04367,-0.041,-0.16787,0.07426,-0.07883,0.03574,-0.00878,-0.04599,-0.03157,0.05156,-0.03156,-0.00885,-0.06781,0.01877,-0.01964,0.03317,-0.0198,0.03578,-0.02073,0.00769,-0.04031,-0.07724,-0.08519,0.00317,-0.05048,-0.05167,0.11526,-0.01237,-0.07399,0.00035,0.06424,0.03031,-0.04102,0.01238,0.05483,-0.00127,-0.00539,0.03146,-0.0376,0.06044,-0.00838,0.08075,0.04719,-0.03343,0.01303,-0.06556,-0.03656,0.10171,0.09478,-0.0773,0.04286,0.00486,-0.07723,0.02726,-0.03364,-0.05504,0.02574,0.04153,0.01179,-0.01823,-0.01074,-0.0097,-0.05953,-0.00294,0.04372,-0.02739,0.03811,0.00166,-0.08793,-0.04027,-0.0895,0.06591,0.01919,0.02386,0.02265,0.10939,0.03804,0.01116,0.05777,0.03336,-0.02221,0.00212,0.06435,0.00892,0.01593,-0.03236,0.00898,0.14394,0.00515,-0.06547,-0.0248,0.07398,-0.06312,0.05262,-0.03363,-0.01113,-0.06581,0.1268,0.04704,-0.04599,-0.02245,-0.00112,0.01718,0.0593,0.04879,-0.01211,0.06111,-0.01828,0.03503,-0.04272,-0.11428,-0.1249,-0.06148,-0.01209,-0.01145,0.20645,-0.07738,-0.07042,-0.15255,-0.10771,0.03084,0.03125,0.10187,-0.08629,0.05701,-0.02864,0.03189,0.08436,-0.01815,-0.09672,0.02135,-0.02008,-0.00348,-0.0585,0.02574,-0.03546,-0.07935,0.03695,0.03818,-0.04825,-0.03544,0.12189,0.1255,0.02475,0.04832,-0.05119,0.02428,0.05847,-0.02098,0.05551,0.05898,-0.03405,0.01076,0.13836,-0.01806,0.05698,-0.05139,-0.01129,0.12696,-0.04908,0.06781,0.01607,0.03314,-0.04814,0.00764,-0.17446,0.04025,-0.02421,-0.01765,0.10123,0.03469,-0.03674,-0.07848,0.08006,0.04751,-0.11154,0.08193,-0.02548,0.03106,0.00071,0.06735]},{"domain":"classical_physics","key":"lc_resonance","name":"Resonant frequency of an LC circuit","package":"classical-physics-ai999x","example":"A resonant circuit has an inductance of 0.01 H and a capacitance of 1 uF. What is the resonant frequency?","v":[-0.01798,0.08146,-0.07216,-0.06497,-0.05968,-0.01731,-0.00551,0.07185,0.09116,0.13746,0.01889,0.01055,0.03791,0.17397,-0.03397,-0.0263,-0.03049,0.0605,0.0307,-0.00471,-0.03567,-0.00765,0.03933,-0.00454,-0.02136,-0.11157,-0.10747,-0.02598,0.07027,-0.02301,-0.05206,0.07217,0.00632,0.03461,0.01705,0.09846,0.05527,-0.06737,-0.02321,0.11194,-0.00175,-0.0815,0.02066,-0.00071,-0.03697,0.03901,-0.01167,0.14304,-0.04165,-0.04731,0.00428,-0.0619,0.01341,0.01724,-0.12949,0.045,-0.00479,0.03109,-0.18783,0.06998,0.00379,-0.05093,0.00516,0.03071,0.01119,0.00525,0.0428,-0.06642,-0.07595,-0.0666,-0.02253,0.07831,-0.08352,-0.06288,-0.05927,-0.01397,-0.01172,-0.08716,-0.11171,-0.05085,0.0624,0.05978,-0.08802,-0.00918,-0.01436,-0.08828,0.03459,-0.03811,-0.05921,-0.03119,0.05636,0.12744,0.01874,-0.01985,0.09561,0.01176,-0.10814,0.04696,0.01541,-0.09351,-0.05673,0.07806,-0.00899,-0.07377,0.0093,-0.04649,0.05223,-0.05383,0.04124,0.08943,0.02446,-0.13202,0.03092,-0.09701,0.03799,0.03304,0.12443,0.03046,0.02441,-0.01212,0.05069,-0.05376,0.08193,0.09942,-0.16206,-0.00074,-0.00051,-0.11258,-0.02902,-0.05111,-0.04367,0.0264,-0.01748,-0.03856,0.09138,0.01475,-0.07307,0.05736,-0.08045,-0.02695,0.11407,0.0745,0.10782,-0.05327,0.04523,-0.06404,0.04005,-0.05824,0.04586,-0.01073,0.08195,0.04999,0.02095,0.01881,0.06507,0.01005,0.00815,0.03015,-0.00827,0.00226,-0.01521,-0.07125,0.10893,0.08841,-0.08189,0.02164,0.06673,0.1087,-0.01157,-0.07124,-0.01175,0.02961,0.09002,0.06909,0.00871,-0.03113,0.05701,0.05772,0.1275,-0.09636,0.03098,-0.01398,0.07409,0.01127,-0.01379,-0.06828,-0.14441,0.01691,-0.07729,0.03748,0.12718,-0.00339,0.02983,-0.03515,0.0074,-0.05527,-0.05272,0.00707,-0.06831,-0.08471,0.05856,0.09541,-0.01277,0.02151,-0.00224,-0.0677,0.09,0.0853,-0.03284,-0.04956,0.04919,-0.03661,0.10648,0.04563,-0.06179,-0.01273,0.03072,0.03713,0.0716,-0.09355,-0.10786,-0.021,0.02359,-0.02112,-0.107,0.11833,0.01962,-0.01077,0.01621,-0.01778,0.0464,-0.08145,0.04428,-0.01992,-0.03064,-0.00349,0.00609,-0.12085,-0.00098,0.0008,-0.01759,-0.03961,0.00074,-0.0605,-0.02506,-0.01313,0.01751,-0.06218,0.08791,0.02021,-0.0199,-0.00774,0.04673,0.02683,-0.01003,0.11724]},{"domain":"classical_physics","key":"angular_velocity_time","name":"Angular velocity under constant angular acceleration","package":"classical-physics-ai999x","example":"A flywheel rotating at an initial angular velocity of 2 rad/s has an angular acceleration of 3 rad/s^2 for 4 s. What is its final angular velocity?","v":[0.12405,0.00832,-0.01727,0.05042,-0.05078,0.08223,-0.01805,-0.07503,0.05814,0.00698,0.01938,0.1025,0.05155,0.03534,-0.05118,-0.07118,-0.10414,-0.01579,0.02239,0.04702,0.07472,-0.04101,-0.20138,0.07772,-0.01228,-0.00506,0.11684,0.05296,0.00777,0.08768,0.05989,0.02229,-0.02345,-0.05284,-0.0415,0.00147,-0.0477,0.0821,0.00156,-0.00907,-0.04551,-0.14756,-0.10011,-0.00409,-0.06985,-0.05408,0.08698,-0.03868,0.06161,-0.02714,-0.00673,-0.01453,0.01744,0.03322,-0.0192,0.04704,0.03764,0.03152,-0.14001,0.01354,0.0401,0.10861,-0.06708,0.04657,0.0671,-0.06255,0.07887,-0.06089,-0.03476,-0.05854,-0.04533,0.01824,-0.04125,0.0025,0.06986,-0.0452,0.05029,0.13195,-0.11369,0.06769,0.03744,0.02988,0.09325,-0.00068,-0.01983,0.0559,-0.01579,-0.03882,-0.02981,-0.01231,0.01054,-0.13641,0.01081,-0.07768,-0.2116,-0.06124,-0.00114,0.02122,0.01312,-0.03538,-0.04077,0.00414,0.09592,-0.0514,0.09011,-0.01426,-0.02695,-0.04612,0.07553,0.05882,0.0401,0.01953,-0.12392,-0.02905,0.01224,0.04004,0.05549,-0.07095,-0.01304,0.07185,-0.00339,-0.03297,-0.03349,0.04326,0.00279,0.04713,0.01354,-0.07782,0.04198,-0.05197,0.00986,-0.0173,-0.08481,0.02438,-0.0116,-0.05349,0.00512,-0.03334,0.13061,0.00784,-0.0338,0.05516,-0.07634,-0.02786,-0.05409,-0.04365,-0.05988,0.04693,0.00293,0.00252,0.10165,0.00429,-0.14914,-0.14527,-0.05617,0.07904,-0.04215,0.02406,-0.00525,-0.07277,-0.04803,-0.07796,0.0319,0.17726,-0.02365,-0.0717,0.05415,0.01756,0.09478,0.03387,0.10695,0.04011,-0.10532,0.07483,-0.07693,0.09764,-0.0911,-0.07618,0.02006,-0.09176,0.01784,-0.04924,-0.03644,-0.05085,0.03255,0.02377,-0.08983,0.01328,0.00504,-0.14048,-0.02726,0.06542,-0.07556,-0.05073,-0.00456,-0.03411,0.01381,0.00629,0.026,0.0295,-0.10151,0.00316,-0.02434,0.0557,0.05161,0.11156,0.04753,-0.01105,0.07781,0.00566,0.11717,0.00616,-0.08657,0.02947,-0.05212,-0.05139,0.1046,-0.10912,-0.05584,-0.00303,-0.02618,-0.02863,0.06864,0.08469,0.09242,-0.08983,-0.00286,-0.01247,0.0641,0.01942,0.00984,-0.00674,8e-05,0.07913,0.01911,0.05874,-0.03051,0.00677,0.07443,-0.00645,0.01847,0.05741,0.02391,0.07799,-0.01467,0.00429,-0.01547,0.01403,0.10894,-0.02041,-0.07071,0.03427,0.03,-0.03487,0.05278,0.03343]},{"domain":"classical_physics","key":"angular_velocity_angle","name":"Angular velocity and angle turned under constant angular acceleration","package":"classical-physics-ai999x","example":"A flywheel starts from rest and spins up with an angular acceleration of 2 rad/s^2 through an angular displacement of 25 rad. What is its final angular velocity?","v":[0.08831,-0.00922,0.01673,-0.01863,0.00847,0.17044,-0.07405,-0.12578,0.03579,0.00226,0.02743,0.06837,0.02043,0.01345,-0.02062,-0.04191,-0.09967,-0.05817,0.03277,0.03544,-0.00491,-0.00504,-0.08074,0.0849,-0.0419,-0.05536,0.11767,0.09847,-0.00609,0.05408,-0.01982,0.00493,-0.03936,-0.05534,-0.02741,0.01904,-0.01681,0.06964,-0.02205,0.05037,-0.06916,-0.09677,-0.02039,0.00382,0.00862,-0.08146,0.09835,0.01238,0.04841,0.0056,0.01363,-0.02818,0.04445,0.05175,-0.06302,0.03871,0.0462,0.05129,-0.10596,0.0594,0.09077,0.10073,-0.08417,-0.08545,0.00705,0.01385,0.03739,-0.0684,-0.02659,-0.04731,-0.0536,-0.03569,-0.03762,0.07234,0.06011,-0.02572,0.05488,0.13315,-0.08692,0.15034,-0.00615,0.01913,0.10365,0.07184,0.03237,-0.01156,0.01424,0.03539,0.00509,0.05935,-0.01836,-0.10008,0.09571,-0.10587,-0.21438,-0.04944,0.007,0.0223,0.06688,-0.06024,-0.01048,0.02683,0.0775,-0.09455,0.01802,0.00441,-0.06833,0.00662,0.033,0.03603,0.03302,0.08067,-0.00464,-0.03003,0.01485,0.03287,0.10935,-0.10784,0.02168,-0.01568,0.0066,-0.0044,-0.04597,0.02636,-0.01543,0.04429,-0.0387,-0.06074,0.02899,-0.0673,-0.05363,-0.05313,-0.04385,-0.02275,-0.05817,-0.02672,-0.0221,0.01813,0.05952,-0.06305,-0.09577,0.02237,-0.09171,-0.017,-0.01438,-0.02161,-0.0292,0.07516,-0.02172,-0.01255,0.07761,0.08193,-0.17763,-0.10988,0.01108,0.05364,-0.08428,-0.00388,0.00206,-0.06868,-0.0522,-0.07771,-0.00042,0.14257,-0.03504,-0.14045,0.07416,-0.05437,0.01929,0.07306,0.04623,0.05299,-6e-05,0.00225,-0.00134,0.15193,-0.12534,-0.03258,-0.02857,-0.0978,0.02383,-0.01224,-0.02591,0.02741,0.05759,0.01759,-0.08777,-0.02717,0.01078,-0.1446,0.01742,0.10225,-0.05354,-0.07743,-0.02069,-0.00746,-0.07094,-0.02039,-0.07118,-0.0334,-0.04587,0.00061,-0.03626,0.0789,0.08921,0.08138,0.04969,0.02929,0.07906,0.02372,0.07948,0.00805,-0.08385,0.05137,-0.04067,-0.03669,0.05097,-0.10659,-0.04453,0.01402,-0.02268,-0.0518,0.05414,0.09629,0.09956,-0.06378,0.02255,0.09633,0.07954,0.05119,-0.00639,0.03846,0.05218,0.02599,-0.06534,0.06709,-0.00784,-0.02781,0.05563,-0.0292,-0.03678,0.06232,0.05539,0.10364,-0.07438,0.07326,-0.0118,0.07894,0.01069,-0.00329,-0.11908,0.09849,-0.00045,-0.019,0.00497,0.00066]},{"domain":"classical_physics","key":"engine_energy_balance","name":"Energy balance of a cyclic heat engine","package":"classical-physics-ai999x","example":"A heat engine takes in a heat input of 1000 J and has 700 J of heat rejected per cycle. What is its work output?","v":[0.05853,0.0561,-0.12105,-0.04793,0.03921,-0.00064,-0.03605,-0.02104,-0.01171,0.13756,0.01657,-0.0475,-0.0153,0.04885,0.0291,-0.03343,0.02674,0.05654,0.01098,-0.10783,-0.07773,-0.01699,-0.09527,-0.04671,-0.12098,-0.00292,-0.04181,0.00652,-0.03532,0.08033,0.01999,0.03243,0.05159,0.10751,-0.0043,0.06955,-0.04341,-0.08327,0.02413,-0.04921,0.08526,-0.0457,-0.08564,0.02818,0.00922,-0.0317,-0.00396,-0.04642,-0.06229,0.02372,-0.04738,-0.00944,0.01112,0.03364,0.07461,-0.01624,0.01,0.06428,0.05507,-0.08634,-0.01474,-0.09096,-0.00475,0.11092,0.12028,-0.03399,-0.11995,-0.06361,-0.12387,0.0381,-0.01718,0.11867,-0.04542,-0.07491,0.05975,-0.0071,0.04375,0.13118,0.07316,0.01418,-0.07454,-0.08269,-0.0677,-0.01072,-0.10266,-0.04052,0.02484,-0.04053,-0.03399,-0.00525,-0.03776,-0.01087,0.09668,0.10232,-0.04118,0.02702,0.10457,0.00838,0.01767,0.02632,0.02243,-0.02782,0.02629,-0.08152,-0.09319,-0.00269,0.05205,-0.09706,-0.02725,0.0479,-0.03768,-0.08003,-0.02349,-0.01833,0.03127,0.09166,0.03642,-0.09952,0.09754,0.15537,-0.11091,-0.07312,0.01319,-0.06533,-0.02354,-0.0346,0.07029,-0.01882,-0.02533,0.03168,-0.05628,-0.03359,-0.02849,0.02387,0.00586,-0.06887,-0.0514,0.02877,-0.07239,0.02513,0.00948,-0.02262,-0.08578,0.01545,0.09857,0.06804,-0.04621,-0.04617,0.03818,-0.05295,0.09488,-0.03785,-0.08939,0.01304,-0.02636,0.14017,-0.0719,-0.08249,0.03083,-0.0271,-0.05661,0.00043,-0.04708,-0.01005,-0.05062,-0.02224,-0.07417,0.10414,0.0457,0.00658,0.01292,0.01875,-0.11466,-0.01344,-0.05411,-0.0665,0.02353,0.01657,0.0506,0.02591,0.05092,-0.08867,0.0867,-0.10395,0.01894,0.00708,0.0038,-0.04367,-0.01115,-0.04795,-0.02274,0.08493,0.06991,0.12486,0.0671,0.01762,-0.13629,0.14633,0.04741,-0.02687,0.00447,0.01976,0.07415,-0.01623,0.01857,-0.06519,-0.02408,-0.0521,0.00897,-0.08821,0.02754,-0.12389,-0.02159,0.10687,0.11966,0.01871,0.02655,-0.02711,0.12367,-0.07491,0.05684,0.05491,-0.06944,0.02903,0.05096,0.11646,0.03612,0.02243,-0.01762,0.11535,-0.08799,0.00919,0.05917,0.11097,0.07905,-0.07079,0.04261,0.00913,0.00533,-0.08329,0.04571,-0.05774,0.03079,0.02435,-0.0235,-0.03726,0.03129,-0.01036,0.03147,0.00617,0.05802,-0.01541,0.10579,0.11867,-0.1086,0.00586]},{"domain":"classical_physics","key":"cop_refrigerator","name":"Coefficient of performance of a refrigerator","package":"classical-physics-ai999x","example":"A refrigerator has 1200 J of heat removed using a work input of 400 J. What is its coefficient of performance?","v":[0.18142,-0.0756,-0.13716,-0.01703,-0.07475,0.01103,-0.10904,-0.0113,-0.0705,0.0016,-0.0735,-0.07024,-0.0013,-0.1047,0.05954,-0.10735,-0.01932,-0.05741,-0.06763,0.0442,-0.08822,0.13689,-0.01394,-0.0118,-0.04639,-0.00843,-0.00193,-0.07124,0.02204,0.0034,0.10767,0.10605,-0.04919,0.0042,-0.08224,0.05247,-0.07996,-0.08879,-0.06171,0.02006,-0.07113,0.0031,-0.08422,0.04727,0.10326,-0.06869,0.05823,-0.0388,-0.07485,-0.02194,0.03666,0.06755,0.06128,0.00196,-0.08939,0.00578,-0.00265,0.0618,-0.00755,-0.09417,0.05126,-0.08731,-0.03458,-0.02246,0.06658,0.03462,0.01021,-0.06066,-0.09277,0.03784,0.05016,0.05379,-0.06479,0.06041,0.04742,-0.01854,0.06393,-0.03711,0.10947,0.03361,-0.0556,0.06482,0.0336,0.03651,-0.09471,-0.03883,0.01966,-0.07387,0.10871,0.00969,0.03186,-0.03681,0.06755,0.01495,-0.05098,0.04911,0.04952,0.06805,0.00231,-0.05651,-0.0005,0.02591,-0.04942,0.03659,-0.02811,-0.03559,0.10313,0.0258,0.0459,-0.1309,0.01925,0.04095,0.03855,0.025,0.10125,0.06306,0.02991,-0.05334,0.02339,0.11087,0.01683,-0.0738,0.01951,0.07532,-0.05607,0.03371,-0.0389,-0.00479,-0.1023,0.10828,-0.01827,-0.07917,0.06018,0.02189,0.09438,-0.0632,0.1076,0.01114,-0.13387,-0.07057,0.10679,-0.15748,-0.06456,0.0425,0.05777,-0.03763,0.07726,0.03476,0.04989,-0.10452,0.03198,-0.04998,-0.03762,0.04229,0.00813,0.12104,0.0285,-0.04579,-0.0135,-0.01681,0.06102,-0.01742,-0.00286,0.01811,0.04845,-0.09733,0.0509,0.02044,0.0213,0.07249,0.09069,-0.00981,-0.11996,0.10183,-0.08668,-0.07271,0.0008,0.05719,0.14142,-0.01775,0.01334,0.0479,-0.02135,-0.04817,-0.01401,0.06505,-0.07104,-0.06576,-0.00833,0.10058,-0.02401,-4e-05,0.08301,0.00295,-0.03777,0.01427,-0.06181,0.08079,-0.01809,0.00455,0.0349,0.12112,0.06963,-0.15037,0.04726,-0.00943,-0.1388,-0.02569,-0.02004,-0.10363,0.03972,-0.12452,-0.05011,0.01764,0.07879,-0.0279,-0.00244,0.00088,0.08754,-0.03404,-0.02204,0.02398,0.0046,0.03593,0.03975,0.08691,0.06341,0.0803,-0.04906,0.01241,-0.02683,0.02148,-0.00662,0.02522,0.00017,-0.00348,0.02994,-0.02963,-0.07724,0.00436,-0.013,-0.01642,0.06014,-0.02895,0.01463,0.09462,0.02089,0.00184,-0.00548,-0.02078,-0.05848,-0.00736,-0.0411,0.0359,-0.09377,-0.07078]},{"domain":"classical_physics","key":"cop_heat_pump","name":"Coefficient of performance of a heat pump","package":"classical-physics-ai999x","example":"A heat pump delivers 1500 J of heat delivered for a work input of 500 J. What is its coefficient of performance?","v":[0.14717,-0.05135,-0.186,-0.03262,-0.06506,-0.04986,-0.05672,-0.06436,-0.06708,-0.03355,-0.08237,-0.11403,0.00313,0.02021,0.03798,0.0148,-0.01043,0.04985,0.00401,0.09637,-0.05152,0.11805,-0.05217,0.01881,-0.02713,-0.00144,0.0183,-0.01037,-0.02127,0.09997,0.05671,0.04918,-0.00966,0.03611,-0.03814,0.00695,-0.10891,-0.02251,-0.04408,0.00894,-0.03598,0.07034,-0.05288,0.09024,0.03465,-0.09551,0.04612,-0.05689,0.01279,-0.03551,0.06015,0.04348,0.07816,0.07991,-0.02773,0.0823,0.01502,0.07151,-0.0738,-0.06455,0.01286,-0.10392,-0.00456,0.05131,0.04866,0.00382,-0.02979,-0.02251,-0.08532,0.02761,-0.00447,0.02573,-0.04006,0.00647,0.07692,0.02733,0.01704,-6e-05,0.14574,-0.0489,-0.06461,0.04118,-0.00767,0.04717,-0.13315,-0.05506,-0.00884,-0.14592,0.07975,-0.00679,-0.00824,-0.095,0.04883,-0.00847,-0.13706,0.02227,0.03302,0.07472,0.08374,-0.02156,-0.01774,0.01824,-0.01484,-0.00615,-0.01526,-0.0584,0.05153,0.0377,0.06403,-0.02358,0.0452,0.02775,-0.01087,0.0255,0.06288,0.08292,0.01812,-0.03155,-0.02538,0.08748,-0.02098,-0.03165,0.02454,-0.00611,-0.10385,0.0456,-0.03578,-0.04257,-0.01993,0.05787,-0.05334,-0.07828,0.08135,0.0574,0.05082,-0.05637,0.0881,-0.00122,-0.07473,-0.05247,0.09272,-0.21194,-0.02042,0.00955,0.13965,-0.04767,-0.04113,-0.05045,0.0109,-0.07387,0.01287,-0.00907,-0.02983,0.02946,-0.05591,0.14206,0.01326,-0.10033,-0.00855,-0.01889,0.03659,-0.06327,0.01788,0.08677,0.02053,-0.0884,0.08726,-0.02712,-0.00427,0.0608,0.08669,-0.00823,-0.1557,-0.00776,-0.12481,-0.02661,0.0355,0.10466,0.13488,0.05597,0.10197,0.01915,-0.0522,-0.04603,-0.0549,0.05208,-0.08947,-0.09221,-0.0932,0.07037,-0.04627,0.00333,0.02463,0.05838,-0.10338,0.00445,-0.06555,0.09241,-0.01344,-0.039,0.00362,0.06224,0.13352,-0.03691,0.03357,-0.00923,-0.10688,-0.04638,-0.02836,-0.03977,-0.0475,-0.09833,-0.05034,0.02542,0.11879,0.0095,-0.00157,-0.04274,0.11389,0.06158,0.0388,-0.03331,-0.00153,-0.00587,0.01479,-0.00433,0.10435,0.05934,0.01859,-0.03285,-0.05013,0.10317,0.05423,0.02757,0.00406,0.04325,-0.0834,0.02247,0.04139,-0.0243,-0.04087,0.02216,-0.01792,0.00868,-0.01993,0.03383,0.0434,0.00759,0.04435,-0.10376,0.00202,-0.03513,0.00897,-0.06159,-0.09237,0.10108]},{"domain":"classical_physics","key":"cyclotron_radius","name":"Radius of a charged particle's circle in a magnetic field","package":"classical-physics-ai999x","example":"A proton of mass 1.67e-27 kg and charge 1.6e-19 C moves at 1e6 m/s perpendicular to a magnetic field of 0.5 T. What is the radius of the circular path?","v":[-0.03291,-0.00512,-0.00479,0.02134,-0.01123,-0.00768,0.01241,0.03938,0.08564,0.01888,-0.02617,-0.03675,0.11951,-0.05839,0.06686,0.00797,-0.14331,-0.00458,0.04912,0.05699,0.00422,0.06952,0.01812,-0.05165,-0.04495,0.00535,0.01921,-0.02396,0.073,-0.10745,0.02306,0.00065,0.09828,0.02539,-0.05983,-0.02969,-0.00132,-0.00031,-0.00112,0.01757,0.05644,0.1199,0.1212,-0.01749,0.03761,0.07665,0.1177,0.09949,0.04804,-0.06203,-0.03619,-0.02917,-0.03232,0.05308,0.00187,0.08364,-0.0281,-0.0138,0.07045,0.0326,0.05951,0.01746,-0.01715,-0.09608,-0.02979,-0.01733,0.00714,0.06585,-0.10729,0.07572,0.02734,0.04701,0.02364,-0.08174,-0.01449,-0.05621,0.00439,0.10259,0.03072,0.12323,0.01108,-0.10895,0.02774,0.01819,-0.08095,0.01546,0.09286,-0.02538,0.06883,-0.03771,0.10137,-0.10519,0.08062,0.01366,0.023,-0.01954,0.00915,0.03363,0.04416,-0.03409,0.02385,-0.13459,0.0231,0.03779,-0.0343,-0.04976,0.02178,0.01491,0.02272,-0.04726,-0.08354,0.05835,0.02687,0.02006,-0.01905,-0.01667,0.11094,-0.02648,-0.13295,-0.05935,-0.10564,-0.06976,-0.04834,0.09485,-0.09583,-0.00241,0.06385,-0.02136,0.00188,0.00798,-0.06402,-0.04396,0.06009,-0.05974,-0.03898,-0.01274,-0.01623,-0.0298,-0.06981,-0.07876,0.00556,-0.06137,0.0311,-0.004,0.06725,-0.08422,0.20067,0.11746,-0.02794,0.03613,0.09131,0.03857,0.01193,-0.06063,-0.01934,-0.02761,0.03066,0.00799,-0.09836,-0.04667,0.0718,0.00165,0.01897,-0.06904,-0.09585,-0.0213,-0.00057,-0.10419,-0.07382,-0.0286,-0.04725,-0.00165,0.03384,0.00268,0.0631,0.09064,-0.01075,0.1019,-0.08764,0.00567,0.0132,0.13955,0.13328,-0.02798,0.08826,-0.06248,-0.04051,-0.06733,-0.02549,-0.03904,-0.07452,-0.01251,-0.01735,0.01365,0.01961,-0.06856,-0.10892,0.00574,0.06474,0.00806,-0.05691,-0.06552,-0.06032,-0.00614,-0.02664,0.02098,0.03448,0.0981,0.03666,-0.0231,-0.04669,0.05028,0.10284,0.00881,-0.0234,-0.09087,-0.12876,-0.04959,0.09733,0.10698,-0.18646,-0.11302,0.03011,0.04713,-0.00514,0.0873,-0.00082,0.02178,0.12003,0.10536,-0.08941,0.04417,0.06541,0.01926,-0.06442,-0.10917,-0.00809,-0.00627,-0.00651,-0.05282,-0.07929,0.05398,0.06579,0.01531,-0.11141,-0.02787,0.02068,0.00335,-0.07982,0.02978,-0.01432,0.09013,0.0408,0.04153,-0.07759,0.0414]},{"domain":"classical_physics","key":"rc_time_constant","name":"Time constant of an RC circuit","package":"classical-physics-ai999x","example":"An RC circuit has a resistor of 1000 ohm and a capacitor of 8 uF. What is the time constant?","v":[0.04983,0.09759,-0.05017,0.03386,-0.1094,0.06332,0.13401,-0.07999,0.03291,0.05926,0.06787,0.13257,0.05247,0.12761,0.11572,-0.01222,-0.07836,-0.00014,0.01672,-0.06555,0.05972,-0.11234,-0.00807,-0.03924,-0.01605,-0.02936,-0.02023,-0.01179,0.06191,-0.07659,0.06992,0.0858,0.00097,-0.05212,-0.08248,0.13266,0.02797,0.013,-0.05137,0.02377,-0.0009,0.01347,-0.07026,-0.00934,-0.14804,-0.03111,0.04473,0.00829,0.10547,0.0793,-0.05152,-0.03307,-0.0017,0.00928,0.06546,0.01615,0.00483,0.07188,-0.13324,0.07488,-0.06853,-0.06694,-0.04027,-0.04306,0.06366,-0.08405,-0.00318,0.02116,-0.11923,-0.05556,-0.01684,0.05832,-0.00123,-0.02701,-0.00132,-0.01044,-0.03832,-0.03921,-0.04737,0.03406,0.0805,-0.05904,-0.03783,0.04333,0.03143,0.08606,0.03472,0.00386,0.00253,-0.09025,0.00989,0.03519,0.02514,-0.07242,0.02398,-0.07266,-0.01064,-0.02984,-0.10112,-0.01328,-0.00858,-0.0269,-0.01303,-0.02033,-0.05703,0.01164,0.02061,-0.01095,0.06901,0.00101,0.0161,-0.04916,-0.05367,0.01942,0.04382,0.09597,0.06081,0.02248,-0.00765,0.10878,-0.06466,-0.05161,0.08289,0.07689,-0.1119,-0.00207,-0.0572,-0.10678,-0.14198,0.088,-0.03896,-0.01764,-0.04054,-0.02623,0.06481,-0.09133,0.07766,-0.08888,0.00289,0.00365,-0.02056,-0.02688,0.06371,-0.0776,-0.13472,-0.07376,0.04228,0.05862,0.02588,0.0606,0.00846,-0.08132,0.02184,-0.08298,-0.01298,-0.01212,0.01017,0.00798,-0.05486,-0.02932,-0.04365,0.03029,0.09782,0.16194,-0.04266,0.04436,0.03277,0.02239,-0.00871,-0.0091,0.01485,-0.02395,0.07649,0.03256,-0.10777,-0.0276,-0.05669,0.06771,0.04941,0.0148,-0.03408,0.08562,0.12656,-0.01619,-0.03108,-0.08926,-0.06133,-0.0586,-0.14491,0.02579,0.11368,-0.10623,0.03881,-0.06152,0.03172,0.04148,0.03376,0.05383,0.00496,0.00181,0.00606,0.12984,0.08479,0.04572,0.03932,-0.01734,-0.02578,-0.00086,0.03118,-0.00708,0.00737,-0.02363,-0.00232,-0.00549,-0.00114,-0.10179,-0.00809,-0.08178,-0.06315,0.07852,0.00674,0.04858,0.07429,-0.08518,0.02548,0.04792,0.03558,-0.02356,0.10457,-0.07145,-0.01457,-0.09758,-0.01047,0.00659,-0.10158,0.04278,0.01154,-0.00685,0.03734,-0.03979,-0.13184,0.02609,-0.02064,-0.02882,0.12379,0.08632,0.0499,-0.08782,0.00403,0.12339,0.06756,0.12142,-0.06294,0.11238,-0.03604,0.01681]},{"domain":"classical_physics","key":"rc_discharging","name":"Voltage of a discharging capacitor","package":"classical-physics-ai999x","example":"A capacitor of 8 uF with an initial voltage of 12 V discharges through a 1000 ohm resistor. What is the voltage across the capacitor after 8 ms?","v":[0.0649,0.03037,-0.00346,0.01107,-0.08015,0.02746,0.05171,-0.04473,-0.00877,0.03294,-0.04445,0.07029,-0.06454,0.0467,0.16744,0.00534,-0.16283,0.01179,-0.00222,-0.10191,0.09063,-0.02539,0.06019,0.00513,-0.11642,-0.04842,0.04311,0.02517,0.01391,-0.06894,0.01085,0.08557,0.05722,-0.03883,-0.10086,0.09181,0.02031,-0.06475,-0.00993,0.0231,-0.02272,0.02043,-0.02935,-0.02105,-0.13678,-0.04132,-0.01274,0.02184,0.01645,0.02083,-0.01637,-0.0169,0.02773,-0.01636,0.09983,0.0371,0.02527,0.04875,-0.1018,0.03374,0.04958,-0.0654,-0.05868,-0.07279,-0.01019,-0.04348,0.04589,0.01858,-0.13813,0.02989,0.10674,0.01853,0.0861,0.03022,-0.02928,0.05169,-0.04308,-0.041,0.04289,0.00345,0.04414,-0.03199,-0.02895,-0.04377,-0.00135,0.04951,0.02179,-0.0067,-0.0088,-0.05738,0.04398,0.02711,0.08117,-0.02979,0.04435,-0.03405,0.03043,-0.04113,-0.00166,0.0002,0.0224,-0.04777,0.07075,-0.06053,-0.12286,-0.05873,0.02061,0.02456,0.04683,-0.06221,0.06531,-0.01073,-0.04978,0.02254,-0.02728,0.1961,-0.04143,-0.00918,0.06601,0.06741,0.00208,-0.05685,0.09954,0.09289,-0.11027,0.01919,-0.03652,-0.07887,-0.09784,0.10727,-0.01062,0.01205,-0.03777,-0.11303,0.02638,-0.12344,0.11494,-0.04487,0.00832,-0.08895,-0.02414,-0.00244,0.01203,-0.1155,-0.03131,-0.03315,0.07172,0.09025,-0.0208,0.05804,0.00656,-0.06291,-0.01225,-0.02898,0.02074,-0.03468,-0.03446,0.00807,-0.0458,0.04807,-0.06763,-0.00435,0.09428,0.07139,-0.0743,0.10169,0.03523,0.06655,-0.0345,-0.06556,-0.01541,0.05098,0.03642,-0.03123,0.00358,-0.01263,-0.10785,-0.02358,0.06268,-0.05326,0.04107,0.1028,0.02485,0.0212,-0.05918,-0.10261,-0.06256,-0.08014,-0.07363,0.05441,0.16644,-0.15992,0.03659,-0.05998,0.12715,0.0392,0.04805,-0.0047,0.01344,-0.01179,-0.03371,0.08195,0.08489,-0.01608,0.06401,0.02881,-0.12488,-0.07292,0.05215,-0.05368,0.02472,-0.07814,0.05315,0.02263,0.02943,-0.18854,0.06727,-0.03897,-0.10037,0.02054,0.03653,-0.00203,0.17045,-0.00976,-0.01386,0.04517,-0.04705,0.05523,0.13419,0.08567,-0.03395,-0.02864,-0.02722,0.03915,-0.05678,0.04525,0.06177,0.03542,0.05972,-0.01978,0.01103,0.04934,0.04044,0.00742,0.08075,-0.05646,0.01095,-0.05676,0.06456,0.05058,0.08091,-0.04084,-0.01522,0.05634,0.055,0.04394]},{"domain":"classical_physics","key":"rc_charging","name":"Voltage of a charging capacitor","package":"classical-physics-ai999x","example":"An uncharged 8 uF capacitor starts charging through a 1000 ohm resistor from a 9 V emf. What is the voltage across the capacitor after 8 ms?","v":[0.04256,0.10437,0.0429,0.00868,-0.08306,0.04878,0.08197,-0.02209,0.02131,-0.01655,-0.04275,0.03852,-0.00132,0.13056,0.11842,-0.00871,-0.12327,0.05955,0.0955,-0.0215,0.09063,0.02051,-0.02095,0.0264,-0.08403,-0.00342,0.04672,0.04658,-0.02848,0.00714,-0.01953,0.05733,0.09213,-0.0605,-0.10052,0.09253,0.04747,-0.13515,0.00884,0.05912,0.00324,0.05772,-0.0282,-0.04622,-0.16276,-0.05574,-0.00347,-0.00457,0.01582,0.04954,0.02379,-0.06423,0.00552,0.04572,0.00166,0.06007,-0.01215,0.02392,-0.08508,0.00645,0.01725,-0.02107,-0.06961,-0.02821,-0.0254,-0.03947,0.09457,0.01061,-0.01401,0.0637,0.00447,0.09442,0.03889,0.02243,0.02307,0.04705,-0.05229,-0.02976,-0.06828,0.0428,0.10234,-0.0207,-0.06215,-0.03,-0.05521,0.07092,0.00591,-0.03684,-0.04928,-0.08048,0.05663,0.1083,0.04903,-0.03168,0.00102,-0.05252,-0.01644,-0.09153,0.01488,0.00602,-0.04005,-0.02054,0.05558,-0.04305,-0.06987,-0.09878,0.05049,0.03348,0.07164,-0.05609,-0.00617,-0.00978,-0.01146,0.0754,-0.00099,0.11929,-0.00748,0.03532,-0.01174,0.08489,-0.00238,-0.06597,0.06277,0.02668,-0.13066,0.05222,0.03223,-0.13539,-0.12758,0.11315,0.04001,0.02458,-0.05099,-0.08621,0.01268,-0.08876,0.11583,-0.05662,0.00612,-0.02445,0.01736,0.01414,0.0159,-0.11985,-0.0607,-0.10072,0.02619,0.06404,0.01653,0.12991,-0.02848,-0.08403,-0.00081,-0.10711,-0.02528,0.06153,-0.01465,0.04785,-0.05936,0.05374,-0.08448,-0.05736,0.05921,0.10468,-0.04135,0.06381,-0.01896,0.11764,-0.06524,-0.06268,-0.01788,0.06918,-0.01877,0.01274,-0.01713,-0.05619,-0.09,-0.04081,0.02887,0.04232,-0.02885,0.01171,0.08281,-0.01418,-0.08116,0.00686,-0.07742,-0.06469,-0.10993,0.03994,0.10172,-0.13234,0.05148,-0.02497,0.06853,0.03419,-0.02111,-0.0549,0.09497,0.02709,-0.08954,0.02572,0.10854,0.09386,0.03703,0.0291,-0.09058,-0.05708,0.05344,0.00185,-0.02898,-0.06875,0.01008,0.02501,0.00308,-0.16511,0.00262,-0.06921,-0.06757,0.00977,-0.02209,0.05535,0.17637,-0.00789,-0.02486,-0.05094,-0.04826,0.02961,0.15089,0.0166,-0.00249,-0.04174,-0.03949,0.03366,-0.03442,0.01572,0.06684,0.06931,0.1068,-0.05771,-0.01977,-0.00501,-0.00769,0.03422,0.08154,-0.10151,-0.01346,-0.09211,0.08968,0.07695,0.04497,0.05095,0.02017,0.05799,0.01434,0.0354]},{"domain":"classical_physics","key":"area_expansion","name":"Thermal expansion of an area","package":"classical-physics-ai999x","example":"A steel plate with an original area of 2.0 m^2 and a coefficient of linear expansion of 12e-6 1/K is heated by 50 K. What is the change in area?","v":[0.1021,-0.00761,0.0618,0.07679,-0.02182,0.04059,-0.09758,0.01477,-0.02352,0.05337,0.00926,-0.0646,-0.00815,0.05206,-0.01052,-0.0463,0.16641,-0.02194,0.10252,0.08396,0.09528,0.06932,0.00769,-0.03783,-0.04803,0.01582,0.03612,0.02307,0.01013,-0.03086,-0.09356,0.10097,0.00548,-0.00732,-0.07522,-0.02206,0.0333,-0.05403,-0.03042,-0.11105,0.05842,0.07571,-0.04661,-0.01274,0.00791,-0.03735,0.05702,0.0148,-0.06349,0.00529,0.00146,0.07631,0.14138,-0.00598,-0.00087,0.03969,0.07316,0.07472,0.04353,-0.04619,0.03595,-0.01543,-0.09743,0.04357,-0.04563,0.01301,-0.00393,0.08238,0.06472,0.13881,0.0554,-0.1014,-0.12456,-0.00782,-0.06551,-0.10661,0.03775,-0.05453,-0.09841,0.03404,-0.03087,-0.04919,0.02626,-0.08017,-0.02948,0.06211,0.01371,0.03039,-0.07042,-0.01927,-0.05467,-0.09595,0.03314,-0.02466,-0.1566,-0.10418,-0.01097,-0.0113,0.11478,-0.08727,-0.03996,0.06811,-0.11798,0.04685,-0.00823,0.02918,0.08162,-0.01147,0.01802,0.05701,0.04579,0.04454,-0.04693,-0.01144,-0.01948,-0.04683,0.04512,0.00727,0.05102,-0.0618,-0.0059,0.02451,0.06497,0.04068,-0.00884,0.04153,-0.089,-0.06896,0.01043,0.05171,-0.08166,0.04237,0.0078,0.0157,-0.16306,-0.04773,0.05896,-0.01164,0.01027,-0.08985,0.039,-0.11707,-0.03687,0.09104,-0.01742,-0.01218,0.06629,0.07023,-0.02653,0.04916,0.05586,0.02716,-0.02057,-0.03787,-0.03011,-0.04869,-0.14105,-0.04691,0.00525,-0.05612,0.00281,-0.01531,0.03036,0.1156,0.05942,0.01685,-0.06216,-0.01623,-0.03522,-0.07575,-0.04665,-0.0055,0.0675,0.12634,0.10223,-0.07761,-0.09481,0.0176,-0.01886,-0.0709,0.02481,-0.00807,-0.11876,-0.06998,-0.02041,-0.0202,-0.04861,-0.0619,-0.1057,-0.03938,-0.04797,0.03837,0.04132,-0.0604,0.00646,0.05008,0.06305,-0.04519,0.04325,0.00868,0.12361,-0.03943,0.11516,-0.05517,0.1191,0.05773,-0.02685,0.00818,0.03953,0.05634,0.13227,-0.06836,-0.01349,0.03405,0.06187,0.06564,0.00112,-0.04584,-0.01467,0.03168,-0.11824,-0.07815,0.02519,-0.02899,0.02494,0.02697,0.05548,0.02176,0.12407,0.01312,-0.02669,0.0506,0.05164,-0.08388,-0.01089,0.13431,-0.01114,-0.04081,0.00492,-0.0414,0.09615,0.01025,-0.00906,0.01921,-0.02645,-0.01,0.02413,-0.08556,0.00985,-0.0616,-0.12034,0.05529,-0.15661,0.00263,0.08287,0.09056]},{"domain":"classical_physics","key":"motional_emf","name":"Emf of a rod moving through a magnetic field","package":"classical-physics-ai999x","example":"A rod of length 0.2 m slides along rails at 3 m/s through a magnetic field of 0.5 T. What is the motional emf?","v":[-0.03289,0.05483,0.04898,0.0089,0.05149,0.01307,0.02879,0.02338,0.02862,0.08547,-0.04048,-0.06205,0.09958,0.06232,0.04371,0.03195,-0.06076,-0.02579,0.01893,-0.01399,-0.04098,0.06417,-0.07437,-0.00082,0.03558,0.0714,0.02912,-0.0525,-0.00871,0.057,0.07629,-0.00607,-0.02116,-0.01647,-0.04888,0.06178,0.1541,-0.10586,0.03265,-0.01089,-0.02405,0.02089,0.13577,-0.06521,0.00984,-0.073,0.10444,0.00839,-0.05825,-0.0043,-0.0462,-0.0872,-0.03376,0.01471,-0.00914,0.01703,-0.00283,-0.01363,0.04969,-0.10828,0.04139,-0.02742,-0.05801,-0.13185,-0.07783,0.04943,0.08739,0.12386,0.01976,0.09589,0.02888,0.12805,-0.10151,-0.03416,-0.02074,-0.00952,0.0986,-0.00413,-0.05834,0.02044,0.12608,0.08082,-0.0114,-0.05248,-0.0866,-0.00044,0.02488,-0.05104,-0.00493,0.00185,-0.05075,0.02391,-0.0257,0.03142,-0.008,0.12227,0.01231,-0.04225,0.08511,0.07448,0.05349,-0.08285,-0.02597,0.0036,-0.0924,-0.05622,-0.05135,-0.03927,0.08102,-0.00224,-0.1554,-0.02761,0.11293,0.08509,-0.07943,0.04672,0.01207,0.02683,-0.1356,-0.01182,-0.00842,0.00672,-0.1229,-0.0404,-0.01298,0.08248,0.10251,0.06657,0.00313,-0.01468,0.07848,0.04214,-0.04737,0.00575,-0.02917,0.03811,0.01396,-0.02238,-0.09512,-0.00437,-0.06844,0.00565,0.00411,-0.01824,-0.04053,-0.09906,-0.01278,0.01612,-0.03956,0.02309,0.0348,-0.07962,-0.04246,-0.18659,0.08239,-0.0094,0.01783,0.05965,-0.04482,-0.10602,0.06463,-0.02893,0.01486,-0.04726,-0.0074,-0.07132,-0.05224,-0.09731,-0.12206,-0.05576,-0.11384,0.00191,0.06294,0.04517,0.05435,-0.0759,0.00383,-0.04082,-0.00968,0.07177,0.06066,-0.12129,0.0681,0.05914,0.02616,0.02853,-0.02171,-0.00617,0.01736,-0.00099,-0.05504,-0.07416,0.02842,-0.04733,-0.00933,-0.02387,-0.00247,-0.02081,-0.00278,0.10482,0.06647,-0.04008,0.00813,0.03973,-0.0091,0.04175,-0.07058,0.11637,-0.01231,-0.06566,-0.05606,0.09348,-0.14678,0.11764,0.06883,-0.06336,-0.06726,0.01038,-0.00267,-0.04474,-0.13965,-0.05795,0.03031,0.10183,0.04853,0.01704,0.03884,0.10007,0.13186,-0.0471,-0.08964,-0.01754,0.01594,0.0531,0.03863,-0.09983,-0.03722,-0.01449,0.01529,-0.0001,-0.07038,0.04601,0.00097,-0.05215,0.10937,-0.02725,0.1055,0.01846,-0.01693,0.11828,0.05514,-0.03224,0.04499,0.07023,0.00067,-0.04808]},{"domain":"classical_physics","key":"rl_current_decay","name":"Current dying away in an RL circuit","package":"classical-physics-ai999x","example":"In an RL circuit with an inductor and a time constant of 2.5 ms, an initial current of 10 A is switched off. What is the current after 2.5 ms?","v":[0.04379,0.02447,-0.09657,-0.01303,-0.07429,0.05529,0.044,-0.0045,0.01127,0.13868,-0.09224,0.10872,0.0077,0.02402,0.01888,-0.0521,-0.13241,-0.12145,-0.02206,-0.04762,-0.03383,-0.03198,-0.01456,-0.00722,0.12042,-0.03817,0.02031,0.06911,0.10347,-0.08117,0.02251,0.06934,0.01193,-0.10993,0.03047,0.07412,0.00753,-0.00025,0.05179,-0.0456,-0.01178,-0.03131,0.0334,0.09023,-0.02818,0.01409,0.0501,0.06931,0.06176,-0.07895,-0.05352,-0.10108,0.06134,-0.14877,-0.0437,-0.05753,0.00585,0.08799,-0.08849,0.03129,0.01511,0.09059,0.02938,-0.14236,-0.04794,-0.04243,-0.07926,0.1134,-0.03006,-0.03566,0.00293,-0.0778,-0.01291,-0.06889,-0.08816,-0.17532,0.02452,-0.0325,-0.1452,-0.03059,0.07272,0.05203,0.03522,0.07133,-0.00671,0.02398,0.04423,-0.04751,-0.03064,-0.08841,0.00118,0.01738,-0.00025,0.00873,0.06506,0.04752,0.00221,-0.09696,-0.02743,-0.06189,0.04357,-0.10105,-0.05762,-0.04291,-0.07854,0.02423,0.0183,-0.07005,0.06579,-0.03247,0.05762,0.01502,-0.00936,0.09858,-0.00589,0.08877,0.04583,0.01326,-0.02752,-0.01232,-0.00529,-0.01007,0.05431,0.07005,-0.08592,0.02874,-0.08352,-0.00339,-0.08435,0.08406,-0.04306,-0.0145,-0.0164,-0.02485,0.12624,0.00855,-0.06537,-0.01381,-0.03271,-0.0533,-0.00388,-0.05434,0.03932,-0.02124,-0.0169,0.08729,0.10056,0.03192,0.07566,-0.02232,0.0266,-0.11378,0.01479,-0.01018,0.03254,-0.06276,0.01298,0.02095,-0.03949,-0.06179,0.07867,0.01331,0.06891,0.03331,-0.16091,-0.12617,0.09363,-0.05647,-0.02431,0.08285,0.05594,0.04497,0.02655,-0.03007,-0.01533,-0.09499,-0.04654,0.00679,0.04574,-0.02265,-0.00946,0.03202,0.02455,0.00715,0.01008,-0.04544,0.00154,0.02871,-0.02577,-0.04995,0.10486,-0.05613,0.07859,-0.13276,0.05262,0.00906,0.01062,0.00143,0.01653,0.03551,-0.00419,0.09642,-0.0087,-0.09092,0.07453,-0.07067,0.05483,0.04607,-0.00142,-0.04254,0.02193,0.05525,0.10713,0.01725,0.11634,-0.0536,-0.08788,0.00072,-0.0825,0.03395,0.04795,-0.06051,0.04107,0.00198,0.02609,0.10282,0.03775,-0.03481,0.03305,-0.10553,0.05142,-0.14008,-0.01152,0.01665,0.00582,-0.05566,0.02738,-0.10108,0.06578,0.00372,0.09288,0.1483,0.01864,0.05055,0.01818,0.07874,0.09104,-0.03974,0.0404,0.08544,0.05422,0.03523,0.04884,0.12709,-0.00993,0.01493]},{"domain":"classical_physics","key":"damped_angular_frequency","name":"Angular frequency of a damped oscillator","package":"classical-physics-ai999x","example":"A 2 kg mass on a spring with a spring constant of 50 N/m has a damping coefficient of 4 kg/s. What is the damped angular frequency?","v":[0.15136,-0.00616,-0.05775,-0.06556,0.00624,0.00226,-0.0424,-0.01615,0.02687,-0.06836,0.0629,0.00364,0.01606,-0.06166,0.04063,-0.13769,-0.05846,-0.05809,0.02999,0.0071,-0.05342,-0.00227,-0.00793,0.10323,-0.01658,-0.08893,0.15074,0.00494,0.06369,0.01239,0.08873,0.0246,-0.11843,0.06173,-0.00094,-0.01691,-0.00893,0.03645,0.02811,-0.01929,-0.13816,-0.06947,-0.07282,0.06906,-0.07817,-0.06585,-0.0464,0.07918,0.06343,-0.02444,0.02217,0.04716,0.05282,-0.00907,0.04508,0.00048,-0.07631,0.00963,-0.05451,0.07064,0.10026,0.00302,-0.03065,0.0086,0.10674,-0.00819,-0.05603,0.00633,0.00102,0.0009,0.06408,-0.04524,-0.00379,0.06094,0.0814,-0.02901,0.00803,-0.06732,-0.0759,-0.03669,0.01311,-0.00543,0.04455,-0.01555,0.08534,-0.03516,0.04506,-0.07546,0.06464,0.08178,-0.02468,-0.11964,0.06659,-0.17487,-0.04115,-0.05555,-0.03262,-0.03098,0.02185,-0.02293,-0.05101,0.01433,-0.08755,-0.09144,0.05069,0.01858,0.09318,0.00195,-0.08477,0.00896,0.09357,-0.01086,-0.07048,-0.0508,-0.14859,-0.01226,0.05975,-0.06655,-0.03623,0.03982,-0.08842,-0.02019,0.01622,-0.04891,-0.00675,-0.13059,-0.11075,-0.08278,-0.0551,-0.02802,0.02851,0.04769,0.03558,-0.00204,-0.01791,0.01456,-0.08034,0.04073,0.06445,0.1086,-0.06643,-0.0121,0.0494,-0.07691,-0.03321,0.01593,-0.0036,0.01795,-0.05005,-0.06391,0.04727,0.01992,-0.03142,-0.10928,-0.03295,0.11015,0.02888,-0.01777,0.008,-0.05755,-0.01819,0.02674,-0.03782,0.05722,-0.0436,-0.11227,0.13365,-0.10755,-0.05336,-0.00783,0.03043,0.01998,0.01122,0.09814,-0.00678,0.0285,-0.04306,-0.04278,0.10137,-0.08749,0.10399,0.06741,-0.02824,-0.00647,0.0075,0.03567,-0.13333,0.06558,0.00031,-0.01729,-0.0814,0.02708,-0.03951,-0.18235,-0.07173,-0.02454,0.04224,0.04735,-0.00097,0.01182,-0.01275,0.04856,-0.06256,0.06313,0.03881,0.03234,0.02554,0.05404,0.04944,-0.10796,0.03047,0.01237,-0.05885,0.08985,0.02431,-0.03202,0.03954,0.08628,0.0035,-0.0558,-0.02226,-0.00626,0.11801,0.11399,-0.04204,-0.00297,0.03986,0.01857,0.04082,0.07184,0.06384,0.06511,0.06814,0.02585,0.01029,0.08115,-0.07452,0.048,-0.01092,-0.03586,-0.03521,0.05196,0.1169,0.0498,0.1171,-0.01957,0.06126,-0.03926,0.2148,0.02193,0.03755,0.00642,0.11312,-0.04175,0.01103,0.00873]},{"domain":"classical_physics","key":"damping_ratio","name":"Damping ratio","package":"classical-physics-ai999x","example":"A damped oscillator has a 2 kg mass, a spring constant of 50 N/m and a damping coefficient of 4 kg/s. What is the damping ratio?","v":[0.12641,-0.03324,-0.04616,-0.01079,0.00365,-0.02402,-0.01719,0.08494,0.01348,-0.03402,0.06375,-0.0258,-0.02861,0.01272,0.07199,-0.02621,-0.08291,-0.00499,0.00858,0.06807,0.02546,-0.0659,0.0363,0.02445,0.00278,-0.09066,0.03317,-0.01742,0.13799,-0.04821,0.09231,0.06159,-0.09306,0.08539,0.02756,-0.00216,0.04809,0.06816,0.05202,-0.01201,-0.04201,0.01984,-0.07518,0.02908,-0.09527,0.01032,-0.0135,-0.03349,-0.00541,0.01165,0.04883,0.05166,0.05073,-0.0005,0.11493,0.03513,-0.04912,0.01066,-0.03437,0.03947,0.01893,-0.12053,0.08234,0.01153,0.04419,-0.00141,-0.00964,0.05316,0.02361,0.03656,0.16359,-0.05222,0.00669,0.01476,0.02928,-0.0478,0.00379,-0.10706,-0.0317,-0.04547,-0.02182,0.06431,-0.08028,-0.02949,0.11791,0.0437,0.03079,-0.03001,0.03236,-0.01692,-0.05361,-0.06841,0.10176,-0.1874,0.08132,0.00083,-0.06188,-0.07395,-0.00237,-0.02468,-0.03717,0.01962,-0.08645,-0.04604,-0.09461,0.03136,0.14258,-0.00037,-0.08561,-0.02155,0.0512,-0.0488,-0.05509,-0.07503,-0.1886,-0.03501,0.05778,-0.05542,-0.05379,0.0139,-0.09415,-0.06938,0.09199,-0.02385,-0.03355,-0.05493,-0.10093,-0.03336,-0.03408,-0.04756,-1e-05,0.02247,0.06806,-0.00778,-0.03544,-0.03359,-0.02798,0.06988,0.01538,0.09043,-0.00147,0.02956,0.13526,-0.02828,-0.0371,0.0104,-0.01497,-0.00411,-0.0388,-0.02784,-0.05427,-0.02558,-0.03894,-0.11923,0.00601,-0.02708,0.07322,-0.01301,-0.0371,-0.10593,0.00412,0.01507,-0.00346,-0.03576,-0.00794,-0.03883,0.12807,-0.13502,0.0033,-0.02029,-0.04107,-0.03947,-0.01772,0.004,0.07574,-0.03693,0.04349,0.02755,0.10641,0.00898,0.07061,0.03784,0.05955,-0.01685,0.02673,-0.05461,-0.15356,0.1254,-0.01412,0.02762,-0.03156,-0.06781,0.04742,-0.21091,-0.07467,-0.01407,0.0415,0.04382,-0.04001,0.04558,0.03156,0.02456,0.0029,0.04569,0.05065,-0.06138,-0.00355,-0.02937,-0.00594,-0.05464,-0.12609,0.00599,-0.03935,0.09187,0.06816,0.00442,-0.03845,0.12512,-0.07877,0.00105,0.01277,-0.01292,0.10818,0.0777,-0.03463,0.05832,-0.00487,-0.01181,0.03804,0.0446,0.00218,0.03215,0.04685,-0.15723,-0.02139,-0.00363,-0.07425,0.08651,0.04411,-0.00691,-0.03432,0.07399,0.06665,0.05712,0.14976,-0.01181,0.11232,-0.07632,0.14568,0.03749,0.01931,0.07165,0.09111,-0.0297,0.00452,-0.02435]},{"domain":"classical_physics","key":"quality_factor","name":"Quality factor of a damped oscillator","package":"classical-physics-ai999x","example":"What is the quality factor of a damped oscillator with mass 2 kg, spring constant 50 N/m and damping coefficient 4 kg/s?","v":[0.15711,0.02364,-0.0679,-0.07743,0.00336,-0.13808,-0.02049,0.06602,-0.05467,-0.09042,0.05137,-0.03533,-0.02967,0.02648,0.08283,-0.0784,-0.02963,-0.03891,0.00408,0.05234,0.00812,-0.00256,0.04413,0.0387,-0.02365,-0.04261,0.03325,-0.06616,0.14116,-0.04048,0.09427,0.08701,-0.10002,0.05847,-0.08105,0.03587,-0.0062,0.022,0.01818,0.0084,-0.10649,0.02372,-0.09081,0.07717,-0.03136,0.04314,-0.02224,0.04296,0.03681,-0.00755,0.00909,0.06914,0.04442,-0.05184,0.12642,0.02515,-0.05926,0.11177,0.02437,0.08922,-0.01031,-0.13504,-0.02776,-0.02705,0.08463,0.02127,-0.02493,-0.01686,-0.03804,0.03886,0.16416,-0.03031,-0.02349,0.05073,0.05283,-0.05378,0.03732,-0.04121,-0.0269,-0.04175,0.01592,0.00715,-0.0518,0.00163,0.09819,-0.00874,0.04928,-0.07566,0.09937,0.04228,-0.08888,-0.10313,0.09009,-0.18692,0.03101,0.01179,0.01708,0.02006,0.00912,-0.02327,-0.01664,-0.0067,-0.11593,-0.04027,-0.05314,0.03141,0.12899,-0.03767,0.01975,-0.08393,0.02312,-0.00575,-0.00552,-0.06746,-0.13355,-0.02801,0.0175,0.01878,-0.02598,0.0059,-0.10389,0.03053,0.02278,-0.00834,-0.09611,-0.09472,-0.17116,-0.02904,-0.04853,0.0535,-0.03128,-0.0217,0.02425,-0.00509,0.07855,-0.00441,-0.02466,0.08143,-0.01973,0.05658,-0.00795,-0.03088,0.13477,-0.02622,-0.01482,0.00454,0.09292,-0.00253,0.01978,0.02201,0.01356,-0.00835,-0.02179,-0.11181,0.06717,0.00596,0.07139,-0.05069,-0.10198,-0.0624,-0.05199,-0.03337,0.01303,-0.03784,0.0012,-0.0501,0.16116,-0.08278,-0.05313,-0.05579,-0.08744,0.02107,-0.0544,0.06842,0.04007,0.05573,-0.01554,-0.01443,0.08964,0.03347,0.09962,0.11026,0.04971,0.00485,-0.02274,-0.06301,-0.16889,0.04434,-0.02818,0.03065,-0.05031,-0.08363,0.0151,-0.14293,-0.01507,-0.03199,0.06353,0.01138,0.00129,0.01898,0.02448,0.04081,0.05738,0.01036,0.03582,-0.02591,-0.03092,0.01195,0.0661,-0.11843,-0.02426,-0.06502,0.00209,0.09944,0.03942,-0.02324,-0.09124,0.08688,-0.04501,0.0164,-0.04685,0.00431,0.07577,0.04934,-0.03181,0.00288,0.01644,0.03941,0.00838,0.0203,0.03206,0.03295,0.09606,-0.07332,0.01118,0.06307,-0.02072,-0.00949,0.00614,-0.00294,-0.04456,0.02916,0.06557,-0.04475,0.11587,-0.04763,0.09378,-0.02028,0.15243,0.03717,0.04449,0.03283,0.11681,-0.00856,-0.0461,-0.0869]},{"domain":"classical_physics","key":"driven_amplitude","name":"Steady-state amplitude of a driven damped oscillator","package":"classical-physics-ai999x","example":"A 2 kg mass on a spring with spring constant 50 N/m and damping coefficient 4 kg/s is driven by a periodic force of amplitude 10 N at a driving frequency of 3 rad/s. What is the steady-state amplitude?","v":[-0.03267,0.00255,-0.0699,-0.0606,0.06276,0.02172,-0.06851,-0.02182,0.0392,0.03412,0.09367,-0.06678,-0.0006,-0.03402,-0.02791,-0.11007,-0.04287,-0.02126,-0.02855,-0.05713,-0.03155,0.01654,0.04148,0.06367,-0.00861,-0.07094,0.10805,0.04617,0.01576,-0.03803,0.10181,-0.0468,-0.07739,0.08221,-0.03739,0.12488,-0.05635,0.02956,-0.01199,0.07263,-0.03316,-0.04674,-0.10592,0.07044,-0.09323,-0.04343,-0.00012,0.04551,0.11048,-0.04188,-0.02805,0.04391,0.0027,0.0555,-0.0219,0.02037,-0.12233,0.06495,0.05269,0.03973,0.10058,-0.04414,0.02662,-0.03319,0.07995,0.01613,-0.00436,0.01985,0.08547,-0.11264,0.06369,-0.00065,-0.00164,-0.00557,0.03496,-0.02741,-0.02914,-0.06645,0.0251,-0.04537,-0.04168,-0.00619,-0.01217,-0.06227,0.13313,-0.0573,0.06692,-0.00763,-0.07976,0.00841,-0.08599,-0.04094,0.06658,-0.03173,-0.06186,-0.08425,-0.00565,0.01044,0.06732,-0.14417,-0.06546,-0.04507,0.04336,-0.11846,0.09145,0.055,0.08748,-0.05243,0.03333,-0.01616,0.11415,-0.01796,0.00448,-0.01507,-0.0699,-0.03897,0.06847,-0.03558,-0.09817,-0.01993,-0.023,-0.0646,-0.06748,-0.00921,-0.04452,-0.07501,-0.10638,-0.02734,-0.05515,-0.07007,-0.01796,0.01759,0.04359,0.03083,-0.15809,0.0542,-0.04845,-0.04868,-0.01584,0.03183,-0.01877,0.04838,-0.02004,-0.00625,0.03494,0.03069,-0.01069,-0.10785,-0.05182,-0.0185,0.07105,0.10841,-0.05054,-0.0443,-0.0855,0.12531,0.02994,0.00551,0.08385,-0.03953,0.00425,-0.0302,-0.01988,0.03497,-0.09917,-0.10281,0.09481,-0.14505,-0.03243,-0.00496,-0.03253,0.02908,-0.07948,-0.00153,0.0805,0.10069,-0.00144,0.02535,0.08558,-0.00264,0.12797,0.08177,0.03129,-0.04511,0.00714,0.02085,-0.13666,-0.0065,-0.0305,-0.05178,-0.08677,0.10907,-0.06166,-0.09609,-0.08749,0.11876,-0.02908,0.07757,-0.0773,-0.08741,0.01279,0.01435,-0.14063,0.09401,-0.0415,0.07573,-0.01118,0.10346,0.08661,-0.00872,0.05208,-0.00521,0.00051,0.06416,0.03409,0.0602,-0.01008,0.03304,-0.01892,-0.02842,0.0406,0.00161,-0.00451,0.11374,-0.09488,-0.02783,0.04723,0.01098,0.04379,0.07798,0.02368,-0.0132,0.05991,0.08614,-0.03702,0.05279,-0.02022,0.0791,-0.08184,-0.03286,-0.05797,0.07319,0.04828,0.03212,0.09697,-0.00075,0.07217,0.02934,0.10272,0.12809,0.0674,-0.06199,0.07158,-0.03299,-0.00456,0.04374]},{"domain":"classical_physics","key":"amplitude_resonance_frequency","name":"Amplitude-resonance frequency of a driven damped oscillator","package":"classical-physics-ai999x","example":"A driven oscillator has mass 2 kg, spring constant 50 N/m and damping coefficient 4 kg/s. What is its amplitude resonance frequency?","v":[-0.0211,0.04891,-0.02646,-0.04492,-0.01279,-0.01013,-0.03918,0.01123,0.08877,0.08343,0.08287,0.00504,-0.01622,0.02811,0.04135,-0.11757,-0.03461,0.04086,0.07507,-0.01729,0.02028,-0.05199,0.0297,0.03377,0.05082,-0.06024,-0.04681,0.03319,0.07692,-0.03383,0.16122,-0.02709,-0.05013,0.12213,-0.07023,0.09025,-0.06338,0.00325,-0.07324,0.03114,-0.06795,-0.02211,-0.03507,0.00718,-0.08304,0.04012,0.04799,0.05274,0.07449,-0.06664,0.00282,0.04168,-0.01705,0.02387,-0.05565,0.00618,-0.13676,0.08391,0.04217,0.01517,0.12317,-0.05349,0.05377,-0.0169,0.09138,-0.05933,0.03863,-0.02693,0.03374,-0.05565,0.11783,-0.02993,-0.03878,-0.04876,-0.03156,0.02645,-0.03504,-0.08829,-0.00743,-0.05512,0.03139,0.04823,-0.11051,-0.09839,0.10627,0.01985,0.04008,-0.04493,-0.03427,-0.14249,-0.09097,0.02246,0.10639,-0.02676,-0.04327,-0.07399,0.03974,0.03099,0.04126,-0.10414,-0.03933,-0.06093,-0.02398,-0.1046,0.00083,0.05006,0.01482,-0.01033,-0.04942,-0.02143,0.0305,0.0048,0.03177,-0.03145,-0.05898,-0.02841,0.07163,-0.05699,-0.06794,-0.04885,0.00076,-0.0044,-0.02651,0.01574,-0.13099,-0.11379,-0.13103,-0.07502,-0.05186,-0.06172,-0.0319,0.06933,0.02361,0.01918,-0.13814,0.0771,-0.01285,-0.00967,0.01281,0.07009,0.02041,0.1095,0.08475,0.0303,0.05882,0.0183,0.02082,-0.13441,-0.02181,0.01111,0.00851,0.04765,-0.07334,-0.05506,-0.03518,0.13681,0.02933,0.00741,0.02576,-0.00097,0.03949,-0.0371,-0.02287,0.01764,-0.06335,-0.05059,0.13939,-0.05107,0.01386,-0.03848,-0.10406,0.00116,-0.01223,0.06451,0.11104,0.03119,0.04315,0.02603,0.09471,0.01562,0.10698,0.05824,0.03298,-0.01403,-0.02211,-0.01648,-0.16158,0.00021,-0.0207,-0.01559,-0.03269,0.0131,-0.05474,-0.1258,-0.04589,0.04313,-0.00636,0.02516,-0.10646,-0.07563,0.06083,0.03178,-0.04831,0.16383,0.00583,0.00327,-0.04654,0.14416,0.01928,-0.0761,0.00889,-0.06805,0.00199,0.05068,0.04878,0.09572,-0.06249,0.13475,0.00933,-0.05891,-0.01389,-0.00961,0.01709,-0.00266,-0.14014,-0.01162,-0.05009,0.00539,-0.00091,0.00792,0.0982,0.018,0.00992,0.07387,-0.02503,0.10376,-0.07838,0.02079,-0.02851,-0.01308,-0.06079,0.06258,0.01137,0.05803,0.09877,-0.0768,0.00719,-0.06272,0.05863,0.05005,0.05635,0.00012,0.16283,0.02192,0.00413,0.07512]},{"domain":"classical_physics","key":"coupled_fast_mode","name":"Higher normal-mode frequency of two coupled oscillators","package":"classical-physics-ai999x","example":"Two identical masses of 2 kg are each attached to a wall by a spring of spring constant 40 N/m and joined by a coupling spring of 10 N/m. What is the higher normal mode frequency?","v":[-0.08917,-0.0699,-0.01546,-0.05537,-0.08056,-0.03271,-0.10301,0.05558,0.11132,0.03255,0.07476,0.13303,0.01832,0.04135,0.0218,-0.12569,-0.01778,-0.03784,0.09384,0.02286,0.01205,0.09359,0.05623,-0.01422,-0.00875,-0.04761,-0.01174,0.11305,-0.13113,-0.04053,0.07963,-0.05227,-0.02486,0.05706,-0.05186,0.00279,-0.06108,0.03909,0.02713,-0.09645,-0.0948,-0.02387,-0.03222,0.09517,-0.13232,-0.02574,-0.07242,0.12631,-0.03965,-0.03124,-0.10037,0.07303,0.00119,0.06114,-0.05631,0.03339,-0.04696,0.08939,-0.03421,0.01066,-0.02711,0.01168,0.05239,-0.07523,0.07657,-0.02559,0.16962,0.04908,0.05971,0.04101,0.04851,-0.06555,-0.02698,0.06857,-0.06761,-0.02604,-0.15629,-0.03043,0.01641,0.0738,0.00447,-0.04959,-0.06994,0.05146,-0.05739,-0.07878,0.02566,0.03541,0.00355,0.08456,0.00364,0.06289,0.03529,0.04886,-0.00283,-0.08087,-0.0103,-0.01427,-0.06058,-0.02395,0.02004,-0.00479,-0.06118,0.05312,0.06727,-0.06404,0.04308,0.01577,-0.10586,-0.00576,0.04196,-0.06183,-0.03724,0.02653,-0.04834,-0.01554,0.14247,-0.00229,0.00449,-0.05031,-0.07259,-0.00192,0.05189,0.03401,-0.05794,0.00645,-0.01855,-0.11282,-0.03722,0.034,0.02886,0.0032,-0.1567,-0.01276,0.01764,0.02137,-0.09987,0.07829,0.07769,0.01716,-0.04808,0.03626,0.01135,-0.05417,0.07163,0.09045,-0.02119,0.08708,-0.04623,0.00922,-0.03498,0.02623,-0.03289,0.03574,-0.01645,-0.04398,0.06096,-0.0579,-0.02263,-0.00914,0.08234,0.03817,0.03185,0.03301,0.03112,0.03194,-0.02338,-0.00183,0.0101,0.0433,0.03796,0.05166,0.05524,-0.02295,-0.05161,0.00535,-0.01981,0.0389,-0.11768,-0.10247,-0.01642,0.06788,-0.12569,-0.03573,-0.06216,0.05649,-0.11738,0.00333,-0.03861,0.00895,0.01171,0.12254,-0.00344,-0.02795,-0.02985,-0.07942,0.02285,-0.05817,-0.00095,-0.02556,0.13418,0.02075,-0.00415,0.16537,-0.0356,0.05632,-0.03561,0.15041,0.01045,0.04407,-0.00734,-0.08867,-0.07218,-0.04845,-0.06228,0.08777,0.02669,0.094,0.02155,-0.01274,0.04492,-0.06382,0.06039,0.10709,-0.0528,0.02553,0.0417,-0.11332,-0.07148,-0.0488,0.0411,0.1157,0.02271,0.00206,0.0733,0.03827,0.042,-0.02229,-0.01102,-0.03797,0.05747,0.00072,0.0878,0.03522,-0.08571,-0.11952,-0.07657,-0.06179,0.05172,0.04344,-0.05402,0.12428,0.08745,-0.06168,0.00521,0.05905]},{"domain":"classical_physics","key":"physical_pendulum_period","name":"Period of a physical pendulum","package":"classical-physics-ai999x","example":"A physical pendulum of mass 2 kg has a moment of inertia of 0.5 kg*m^2 about its pivot, and the distance from the pivot to the center of mass is 0.3 m. What is its period?","v":[-0.07585,-0.02089,0.00407,0.0535,-0.00951,0.00521,0.08527,0.04266,0.05284,0.06383,-0.05271,0.08439,0.08248,-0.04378,-0.09459,0.00896,0.00448,0.03892,0.10571,-0.06848,0.04381,-0.05618,-0.06198,-0.08713,-0.07236,-0.0237,0.0097,0.0094,0.03193,0.05752,-0.0393,0.04063,-0.00773,-0.0014,-0.00863,-0.01246,-0.00263,0.05668,-0.00038,-0.09167,0.0345,-0.13744,-0.10885,0.13369,-0.07435,0.04393,0.01825,0.07847,0.09702,0.01766,-0.0839,0.09078,0.05591,0.04063,-0.0461,-0.03912,-0.12167,0.01603,0.00372,-0.0563,-0.1051,-0.02239,-0.11399,0.08703,0.07728,-0.01734,0.02014,-0.07827,0.00525,0.02821,0.08938,-0.07818,-0.04052,-0.199,-0.01276,0.02493,0.11985,-0.03439,-0.09755,0.04812,-0.04893,0.08155,0.08776,-0.01129,0.13247,0.04072,-0.00386,-0.10993,-0.01519,-0.0463,-0.08723,-0.06759,-0.04429,0.03758,0.00619,0.02462,0.03841,0.03022,-0.06734,0.0156,0.00128,0.0441,-0.02818,0.0175,-0.08575,-0.02713,0.04932,-0.07694,-0.0671,0.00815,0.00462,-0.02708,0.06817,0.08415,-0.00792,-0.03213,-0.01173,0.03265,-0.06689,0.07268,0.05687,-0.03341,-0.06672,0.05574,-0.04586,-0.00521,0.0087,-0.04252,0.0718,0.06841,-0.00246,0.02655,0.05188,-0.03559,0.08051,0.08578,-0.0061,0.08515,-0.03024,-0.03246,0.05898,-0.03391,0.10094,-0.03758,0.04532,0.0637,0.0062,-0.01574,-0.0283,0.04245,-0.03011,0.01733,-0.09187,-0.08984,0.1582,0.09411,0.08087,-0.06205,0.02181,-0.02775,-0.04995,-0.01461,-0.06213,0.12515,-0.07569,0.07225,0.02391,0.02712,-0.04795,-0.02987,-0.10905,0.07676,0.06741,0.07351,0.03848,0.03392,-0.00722,-0.05417,0.03672,0.06615,0.08979,0.01283,0.06004,-0.0083,0.02755,0.01502,-0.0094,-0.04753,-0.03893,-0.14766,0.09296,-0.04462,-0.07784,-0.12531,0.0617,-0.01367,0.07375,0.0015,0.03188,0.05963,0.02476,-0.08481,-0.09649,0.07019,-0.0615,0.00656,0.04727,-0.09194,0.02792,-0.00564,-0.0346,-0.05315,0.01342,-0.09929,0.07278,0.00508,-0.10919,0.02178,0.12451,-0.11188,-0.01859,-0.0173,0.02577,-0.00437,-0.08826,0.00549,-0.01446,0.02331,-0.05942,0.0917,0.12514,0.05675,-0.03501,-0.02345,-0.04499,0.03858,-0.07182,0.01115,0.06597,-0.01415,0.07829,-0.00354,0.01149,0.06253,0.07861,0.01084,0.08756,-0.09634,-0.03672,-0.06525,0.00368,0.02384,0.08497,-0.09097,-0.09135,0.02289]},{"domain":"classical_physics","key":"double_pendulum_slow_mode","name":"Lower normal mode of a double pendulum","package":"classical-physics-ai999x","example":"A double pendulum has equal masses and a length of each arm of 1 m. What is the lower normal mode frequency?","v":[-0.11214,-0.09244,0.04125,-0.08803,0.0132,-0.01018,-0.00213,0.06529,0.06761,0.07047,-0.02619,0.04184,0.12602,-0.03704,-0.05929,-0.08382,0.00246,0.05509,-0.00968,0.00168,-0.118,0.05677,-0.06275,0.00459,0.05001,-0.04446,0.03124,0.12128,-0.10712,0.05095,-0.02355,0.03197,-0.03224,0.05993,0.01561,-0.06932,-0.04247,-0.06253,-0.02684,-0.02662,-0.01328,-0.09522,-0.1189,0.08052,0.00031,-0.06578,-0.05759,0.20159,-0.04045,0.00817,-0.08077,0.05855,-0.07625,-0.00376,-0.06225,0.04847,-0.00906,0.03844,-0.04425,-0.03658,-0.01476,0.04945,-0.03764,0.00895,0.07772,0.07294,0.00277,0.02807,0.04429,0.08591,-0.04688,0.01829,0.05174,-0.08478,0.07323,-0.03139,-0.08672,0.01797,-0.03332,-0.06291,-0.09678,0.08365,0.06224,0.03358,0.02769,-0.08623,-0.00452,-0.02966,0.07551,0.08889,0.00201,-0.04516,-0.0514,0.06839,0.0703,0.05004,0.01577,0.05913,-0.03205,-0.03111,-0.07285,0.11163,-0.04991,0.01622,0.02487,-0.11299,0.05438,-0.06538,0.01616,-0.04594,0.05711,-0.11221,-0.00557,0.00476,-0.07854,-0.09501,0.012,-0.05405,-0.03461,0.04393,-0.01808,-0.01781,0.00571,-0.01498,-0.03651,0.08633,-0.0087,0.02605,0.00664,0.0105,0.18407,-0.00599,0.03195,0.01628,-0.00723,0.09121,-0.04906,0.11665,-0.00739,0.04001,0.01749,0.0697,0.0611,-0.08145,-0.00742,0.06524,0.09852,0.06883,-0.13435,-0.00055,0.07033,0.08669,-0.04983,0.00265,0.05262,0.0455,0.12741,-0.05932,-0.04457,-0.02875,0.03797,0.04722,-0.06353,0.03298,0.06157,-0.02589,-0.01198,0.07456,-0.09709,-0.05952,-0.03272,0.14184,0.10355,0.05786,-0.09305,-0.0596,-0.00318,-0.05239,-0.0535,-0.12505,-0.06925,0.01561,-0.1126,-0.05497,0.01031,0.11794,-0.1322,-0.00555,0.00039,-0.00382,0.09194,0.02678,-0.02127,-0.0118,0.00958,-0.0957,0.0473,-0.07687,0.10682,0.1013,0.00781,-0.08385,-0.06837,0.02211,-0.07004,-0.0,0.03544,0.0567,-0.01439,-0.04055,-0.05361,0.01248,-0.07422,-0.06954,0.03869,0.03488,0.01105,0.14281,0.0964,-0.14694,-0.03595,-0.02308,-0.00828,0.06197,-0.0161,0.03548,0.02091,-0.05729,-0.05142,0.04318,0.05604,0.06831,0.03373,-0.00715,0.01483,0.00868,-0.095,0.04335,-0.0175,-0.01854,0.03783,0.01538,0.08793,-0.06334,-0.03724,-0.01579,-0.0057,-0.02231,0.02514,-0.06472,-0.067,0.01604,0.02413,-0.06685,0.1033,0.01825]},{"domain":"classical_physics","key":"double_pendulum_fast_mode","name":"Higher normal mode of a double pendulum","package":"classical-physics-ai999x","example":"A double pendulum has equal masses and a length of each arm of 1 m. What is the higher normal mode frequency?","v":[-0.10404,-0.0523,0.0279,0.00237,-0.02289,-0.00575,-0.0746,0.07345,0.11435,0.04215,-0.00309,0.14365,0.03969,0.07,-0.0168,-0.05608,0.01948,0.06095,0.07547,0.00749,-0.04355,0.04789,-0.00749,-0.01721,0.02327,-0.05415,0.01206,0.12649,-0.13467,0.06431,0.02147,-0.01221,0.00258,0.0826,-0.02905,-0.02442,-0.06098,-0.03027,-0.00242,-0.05008,-0.0404,0.00272,0.00675,0.11489,-0.12354,-0.05859,-0.00706,0.09348,-0.044,-0.01314,-0.0913,0.08063,-0.00284,0.10783,-0.08102,0.10668,-0.04403,0.08171,-0.08764,-0.07757,-0.05447,0.05732,0.02197,-0.11191,0.04243,-0.01929,0.09476,0.02051,0.05325,0.0451,-0.01778,0.02997,-0.04259,-0.03208,0.07704,-0.03716,-0.06051,-0.00794,-0.00982,-0.02869,-0.11059,0.00757,-0.07543,-0.01725,-0.00752,-0.02567,-0.02533,-0.01704,0.01163,0.06803,-0.04628,0.04001,0.00442,0.09538,0.04135,-0.02773,0.04986,0.04131,-0.03972,-0.05046,-0.0151,0.05437,-0.0916,0.09325,0.05658,-0.1065,-0.0045,-0.02124,-0.05574,0.00255,0.00107,-0.04714,-0.04317,0.06202,-0.0453,-0.0729,0.05616,-0.05434,-0.01868,-0.01892,0.01865,0.02997,-0.02609,-0.0094,-0.03137,0.0921,-0.02371,-0.03575,0.02021,0.04754,0.08441,-0.01167,-0.10268,-0.05356,-0.00429,0.12256,0.01679,0.03817,0.00617,0.03356,0.05534,0.07074,0.06276,-0.02637,0.08265,0.08485,0.0459,0.09896,-0.05987,0.0453,-0.03922,0.05666,-0.06844,0.0507,-0.01478,0.03935,0.00271,-0.07227,-0.04345,-0.09413,0.06787,0.0343,-0.00167,0.00983,0.09378,0.01536,-0.08827,0.07826,-0.0486,-0.05203,0.00525,0.09935,0.08772,-0.0286,-0.05479,-0.0176,-0.01638,-0.00502,-0.08934,0.01351,-0.03117,-0.00373,-0.08744,-0.05444,-0.05393,0.12244,-0.13498,-0.02054,-0.02101,-0.0333,0.03431,0.058,-0.03818,-0.03139,0.04182,-0.09899,-0.00579,-0.16458,0.11153,-0.00484,0.04416,-0.066,0.05849,0.16048,-0.03277,0.05108,0.07608,0.10291,0.05025,0.01174,-0.09669,-0.00113,-0.10268,-0.10484,-0.06604,-0.00173,-0.02015,0.11751,0.04848,-0.07185,0.02554,-0.09768,0.06481,0.10216,-0.00787,-0.02669,-0.01611,-0.08417,-0.07063,-0.04623,0.05793,0.08194,0.01398,-0.02025,0.08512,0.09393,-0.04697,0.00949,0.07927,-0.07036,0.04322,0.08565,0.08349,0.00164,-0.11423,-0.09678,-0.09295,-0.00648,0.03855,-0.09311,-0.04635,0.07216,0.09189,-0.0761,0.09616,0.01881]},{"domain":"classical_physics","key":"vis_viva","name":"Orbital speed on an elliptical orbit (vis-viva)","package":"classical-physics-ai999x","example":"A satellite on an elliptical orbit around a planet of mass 5.972e24 kg has a semi-major axis of 8.0e6 m. What is its orbital speed at a distance from the center of 7.0e6 m?","v":[0.06311,-0.09112,0.05853,-0.11378,0.11307,-0.11095,-0.03444,-0.03544,0.08351,0.01792,0.05677,-0.03314,0.06372,-0.08086,-0.06022,-0.0051,-0.03125,-0.01049,0.01021,0.01209,-0.02288,-0.02103,0.05721,0.02349,-0.00916,0.00274,0.12242,0.02291,-0.02589,-0.07795,-0.00329,0.01351,0.0169,0.013,-0.01732,0.04228,-0.00838,0.07459,5e-05,0.00853,0.02853,0.05075,-0.08674,-0.06789,-0.07384,0.04329,0.0202,-0.05412,0.0109,-0.07183,-0.07674,-0.01272,0.00367,0.01079,-0.02791,0.00869,-0.07348,0.07485,0.04538,-0.01463,-0.01349,-0.10237,-0.00684,-0.04507,-0.04834,0.00972,0.12906,0.00554,0.08215,0.08187,0.02217,-0.05009,0.03885,-0.03913,-0.03686,0.02746,-0.04503,-0.03817,-0.10559,0.01569,-0.00497,0.08322,-0.05266,0.06383,0.05515,0.02922,0.06734,0.00401,-0.04194,-0.06963,0.05201,0.01324,0.08259,-0.052,-0.16284,0.08681,0.01637,0.0686,0.01659,-0.03998,0.04535,-0.01277,0.13359,-0.12823,-0.0561,-0.18705,-0.0295,-0.03069,-0.05614,-0.02556,-0.02495,0.03726,-0.00885,0.06568,-0.02331,0.08578,0.0372,0.02042,0.00917,-0.01852,0.1059,-0.00206,-0.02172,0.07435,0.02112,-0.06575,0.01226,0.05146,-0.13804,-0.03104,-0.03792,0.05209,0.00189,-0.00587,-0.07844,0.06379,0.05422,0.14468,-0.0038,-0.05654,-0.03474,0.06701,0.06176,-0.0109,-0.02672,-0.03577,-0.03769,-0.08682,-0.11197,0.13765,0.02304,0.03505,-0.02431,-0.13405,-0.0741,0.02876,0.10087,-0.06502,0.04964,-0.09042,-0.04542,0.06417,-0.00301,-0.15602,-0.05192,0.01314,-0.01874,-0.02342,0.0524,0.08899,-0.07336,-0.07448,0.04539,-0.05468,0.02264,-0.00458,-0.01191,0.12021,-0.05406,0.03122,0.14819,-0.02649,0.0526,0.05827,0.10241,-0.02381,-0.08064,-0.0638,-0.06039,-0.20309,0.00413,-0.02412,-0.00625,-0.0332,0.0276,-0.07133,-0.02403,0.02749,-0.03237,-0.08444,0.02183,-0.01526,-0.00497,0.06213,0.0062,0.00459,0.00281,0.04079,0.03175,-0.03227,-0.08338,-0.035,0.14174,-0.06582,0.07527,-0.00146,-0.02467,-0.04332,0.07394,0.14775,-0.06212,-0.08642,0.03638,0.10912,0.01299,-0.02368,0.02447,0.11674,0.07539,-0.02004,0.11918,0.04934,0.04251,-0.05091,0.01008,-0.06101,-0.0673,-0.02549,-0.02731,-0.02151,0.0078,-0.04466,0.05487,0.01735,0.05952,0.02474,0.065,-0.03779,0.08908,0.05796,-0.01905,0.0627,-0.01124,-0.01864,0.0088,0.1221]},{"domain":"classical_physics","key":"escape_speed","name":"Escape speed","package":"classical-physics-ai999x","example":"What is the escape speed from a planet of mass 5.972e24 kg and radius 6.371e6 m?","v":[0.00871,-0.04221,0.088,0.02697,0.08419,0.00937,-0.00052,-0.0603,0.05749,-0.05776,-0.02219,-0.07262,0.06273,-0.04091,-0.0353,-0.03859,-0.07442,0.04744,-0.03706,0.04105,-0.00629,-0.01392,0.1083,-0.03906,-0.05032,-0.01458,0.13402,0.00474,-0.06974,-0.02058,-0.01066,0.01689,-0.05436,-0.03971,-0.04377,0.00957,0.00153,0.04001,-0.04471,-0.10459,0.00849,0.11215,-0.15299,-0.01642,-0.03301,0.094,-0.03477,0.01448,-0.0194,0.01321,0.01768,-0.03243,0.0186,-0.04407,0.00339,0.002,-0.01932,0.03928,-0.04692,0.05408,0.02486,-0.1278,-0.01092,-0.10908,-0.00726,0.03809,0.07932,0.1004,0.01015,0.05911,0.06686,-0.00873,-0.00803,-0.07396,-0.02448,0.05661,-0.03826,-0.04759,-0.11,0.05919,0.0183,0.02449,-0.0553,0.02952,-0.09666,0.02574,0.0448,-0.00978,-0.01956,-0.01514,0.0877,0.11527,0.11676,-0.00337,-0.00406,0.01849,-0.02766,0.02044,0.05143,-0.07717,0.07406,-0.14189,0.00625,-0.05536,-0.14226,-0.00451,0.06926,-0.02904,-0.0593,-0.01092,-0.01865,0.05695,-0.05681,0.00883,0.0979,0.02813,0.07022,-0.07033,0.00877,-0.01591,0.09309,-0.01773,-0.08205,-0.04888,0.02662,0.08979,0.01567,0.05178,-0.02957,0.01055,-0.0296,0.03814,-0.01183,0.05623,-0.11205,0.01714,0.10894,0.10576,-0.0299,-0.11255,-0.05679,0.13111,0.03209,-0.04879,0.05004,0.00284,0.13536,0.01271,-0.08711,0.07611,0.07384,-0.03664,-0.03285,-0.10318,-0.04546,0.10138,0.03664,0.01328,0.01511,-0.09733,-0.10298,0.02871,0.04854,-0.12258,-0.12196,0.00462,-0.0495,-0.00147,0.01935,0.09446,-0.04934,0.01912,0.01605,-0.06927,0.01948,-0.06726,-0.04861,0.00287,-0.05155,0.08655,0.06979,-0.0706,0.02812,0.04001,0.09797,0.01031,-0.00362,-0.05951,0.02135,-0.10937,-0.05327,0.00023,-0.00318,-0.0409,0.0312,0.00897,-0.01154,-0.0057,-0.0175,-0.04691,0.03962,0.00844,-0.00684,0.04807,-0.0465,-0.05553,0.04246,0.03113,0.13509,-0.02575,-0.12384,0.0577,0.13092,-0.18796,-0.01874,-0.07938,-0.03075,-0.00491,0.12066,0.13228,-0.13685,0.00712,0.02484,-0.02288,0.00464,0.08755,-0.01505,0.02069,0.01909,-0.02087,0.14071,0.06778,-0.00786,-0.03624,-0.06509,-0.0009,-0.04848,-0.06435,-0.12279,-0.04732,-0.08386,-0.00851,0.0624,-0.01098,-0.00214,0.08385,0.00188,-0.02408,0.06417,0.01326,-0.05473,0.11501,-0.00267,0.09621,0.06625,0.07077]},{"domain":"classical_physics","key":"kepler_period_semi_major","name":"Orbital period from the semi-major axis (Kepler's third law)","package":"classical-physics-ai999x","example":"A planet orbits a star of mass 1.989e30 kg on an elliptical orbit with a semi-major axis of 1.496e11 m. What is its orbital period?","v":[0.04393,-0.03047,-0.04236,0.03098,0.09391,-0.04373,0.03924,-0.08091,0.09031,0.09064,0.06183,0.00083,0.10814,-0.03463,-0.0362,0.04261,0.00693,0.03439,0.13248,-0.01803,0.04415,-0.00582,0.00259,0.01413,0.00356,-0.0613,0.04553,0.06299,-0.03787,0.03199,-0.05516,0.027,0.01594,0.08972,-0.01455,-0.0237,-0.10649,0.13008,0.00707,-0.00202,0.05837,0.03917,-0.15542,-0.03266,-0.11403,0.05253,-0.02047,0.10001,0.10966,-0.02206,-0.14349,0.07306,-0.00145,0.0438,0.03029,0.00406,-0.0901,-0.00135,0.05002,0.02816,-0.06231,-0.05724,-0.12385,0.09451,0.07431,-0.01897,0.11173,-0.04987,0.09263,-0.01167,0.04963,-0.0975,0.00164,-0.13018,-0.09573,0.05867,-0.07411,0.00316,-0.0769,-0.04302,-0.01705,0.03439,-0.01651,-0.01259,0.1195,0.04145,-0.03117,-0.04364,-0.02979,-0.06596,-0.03159,-0.05684,-0.00501,-0.06452,-0.08467,0.01481,0.01774,0.02654,-0.05101,0.00652,0.06243,0.04264,0.10959,0.01299,-0.05232,-0.10563,-0.02837,-0.01526,-0.02845,-0.03669,0.01056,-0.00214,-0.03527,-0.00696,-0.00523,-0.00492,0.02151,0.04621,-0.04816,0.10765,-0.0161,0.0437,-0.01462,0.08231,-0.01508,0.00819,0.08829,-0.02882,-0.09048,0.06376,-0.05322,-0.01109,-0.06521,0.00819,0.00476,0.04331,0.03418,0.14367,0.12748,-0.0372,-0.0628,-0.01601,-0.00707,0.01622,-0.0541,0.00659,-0.0851,-0.09766,-0.10482,0.0805,0.01226,-0.0627,-0.09003,-0.14124,-0.06771,0.08474,0.13081,0.0077,0.01757,-0.08647,-0.01709,0.09813,-0.01052,0.01887,-0.13554,0.05192,0.0294,0.08305,0.01664,0.09653,-0.03249,-0.04708,0.01796,0.02634,-0.0137,-0.00586,-0.04977,0.0845,-0.06721,0.0782,0.0037,0.00155,0.04935,0.00063,0.04005,-0.04416,-0.00712,-0.02993,-0.09392,-0.20673,0.00603,0.06239,-0.01379,-0.11701,0.05528,0.02731,0.00813,0.06413,-0.03167,0.01852,0.0935,-0.01378,-0.02426,0.13683,-0.0101,0.04393,0.0284,-0.02429,-0.06331,-0.0788,-0.00638,-0.07904,0.05418,-0.09635,0.06623,0.06276,-0.08723,-0.02689,0.09613,0.03792,-0.12843,-0.05681,-0.05132,0.00138,0.01098,-0.03665,-0.01153,-0.01742,0.08741,-0.05021,0.0477,-0.00808,-0.03378,-0.00783,0.01786,0.02771,-0.00781,-0.06105,0.02638,0.05075,-0.00693,-0.01523,0.07493,0.01797,0.02804,0.05388,0.04428,-0.13626,0.02681,-0.05178,-0.04281,0.0918,0.07409,-0.01538,-0.03958,0.08586]},{"domain":"classical_physics","key":"inertia_solid_sphere","name":"Moment of inertia of a solid sphere","package":"classical-physics-ai999x","example":"A uniform solid sphere has a mass of 2 kg and a radius of 0.5 m. What is its moment of inertia about its center?","v":[0.04601,-0.07059,-0.04695,0.00135,0.17553,0.06599,0.06811,0.01414,0.06357,-0.00156,0.00086,-0.0126,0.07725,-0.08043,-0.05016,-0.01784,-0.02356,-0.08311,0.023,-0.04861,0.14133,-0.0871,-0.00122,-0.02399,-0.02509,-0.02278,0.06324,0.02004,0.06989,-0.02786,-0.02341,-0.02866,0.01899,-0.00641,-0.01121,-0.00261,-0.03329,0.05786,0.03067,-0.09421,-0.06903,0.00019,-0.10983,0.12637,-0.01852,0.03973,0.05019,6e-05,0.05327,-0.03434,-0.03603,0.02984,0.00978,-0.02691,-0.0555,0.01982,0.01799,0.02636,-0.04711,0.05541,-0.02652,-0.03894,-0.06869,0.00194,0.06174,0.00605,0.02506,-0.03046,-0.05438,0.06524,0.08033,-0.08885,-0.0819,0.03392,-0.01168,0.0653,-0.05197,0.04662,-0.07735,-0.01913,-0.04393,-0.01358,0.0549,0.02528,0.10686,0.04415,0.01723,0.0045,-0.01285,-0.08869,-0.00334,0.02665,-0.01895,-0.08932,-0.00402,-0.01034,-0.04883,0.03918,0.03594,-0.05577,0.00548,-0.04235,-0.02669,0.01176,-0.13434,0.02127,0.07648,0.02006,-0.01276,0.07312,0.04812,0.09636,0.01511,0.02079,-0.00405,-0.08443,0.1371,0.01031,-0.14092,0.0693,0.02843,-0.07543,-0.039,0.01536,0.04434,-0.07986,0.02028,-0.06146,-0.00828,0.01769,0.02903,0.04594,0.03085,0.03579,-0.01126,-0.0117,-0.04343,-0.01251,-0.01161,0.02881,-0.07991,-0.02362,0.09178,0.02385,-0.08099,0.06979,0.06445,-0.0032,0.01184,0.01449,0.01189,0.05608,-0.04353,-0.11446,0.03746,0.08887,-0.09607,-0.00639,0.04907,0.01105,-0.02978,-0.0381,0.05078,0.04934,0.01494,0.08398,0.02551,-0.07079,0.08074,0.07637,-0.08448,-0.01209,0.02381,-0.07481,-0.0984,0.00316,-0.05762,-0.03269,-0.04681,-0.0702,0.14971,0.13912,0.10623,0.07753,0.04885,-0.02992,-0.03406,0.02237,-0.00721,-0.0573,-0.02025,0.11135,-0.04983,-0.01947,0.00464,-0.01971,0.03931,-0.0369,-0.05403,-0.02823,-0.08665,0.00263,-0.06573,0.01696,0.01408,0.02699,-0.06525,-0.04904,-0.01991,0.04491,0.0185,0.09497,-0.00071,-0.11114,-0.06797,-0.00469,-0.09261,-0.03418,0.12419,0.02254,-0.02958,-0.0052,0.08643,-0.00713,0.01774,0.02766,-0.07651,0.01247,-0.03343,-0.07943,0.07283,0.07366,-0.05407,-0.03742,0.00562,-0.01428,-0.13504,-0.12992,-0.13844,0.03445,-0.07364,-0.05972,0.11,0.10193,0.11218,0.04275,0.1189,0.04292,-0.07736,0.15376,0.01127,0.0031,0.09764,-0.02362,-0.2893,0.03903]},{"domain":"classical_physics","key":"inertia_hollow_sphere","name":"Moment of inertia of a thin spherical shell","package":"classical-physics-ai999x","example":"A uniform hollow sphere has a mass of 2 kg and a radius of 0.5 m. What is its moment of inertia about its center?","v":[0.0579,-0.09324,-0.08663,0.01373,0.09807,0.07994,0.12499,-0.03677,0.05034,0.02756,0.00489,-0.00025,0.01422,-0.05173,-0.04331,-0.01053,-0.01447,-0.01083,0.05917,-0.04387,0.09852,-0.15306,-0.02484,0.02778,-0.05281,-0.04551,0.04244,0.00105,0.07189,-0.08218,0.01215,-0.01109,0.04789,-0.01032,-0.05103,-0.0052,-0.07699,0.06337,-0.0142,-0.05492,-0.088,-0.03778,-0.13474,0.18643,-0.04156,0.06726,0.07452,-0.04762,0.04696,-0.01865,0.05215,-0.02634,-0.00499,0.03258,-0.03806,-0.0147,0.04949,0.03679,-0.01559,0.0655,-0.03188,0.01264,-0.03694,0.06369,0.07819,0.02955,0.01485,-0.10356,-0.05699,-0.05847,0.07843,-0.14041,-0.04336,0.07738,-0.00855,-0.02957,0.01916,-0.00397,-0.20363,0.02165,-0.01755,-0.04885,0.0864,-0.01502,0.0381,-0.01294,0.01857,0.01983,-0.01419,-0.04165,-0.02249,0.0402,-0.05754,-0.04166,0.0308,0.09205,-0.06307,0.05267,-0.00844,-0.02704,0.02871,-0.07179,-0.01128,-0.01909,-0.09111,-0.00902,0.10548,0.03445,-0.04435,0.13164,0.00438,0.05503,0.03482,-0.00296,-0.01079,-0.06333,0.05481,0.09213,-0.06748,-0.03809,0.03739,0.04357,0.024,0.10064,-0.02097,0.02191,0.00662,-0.01479,-0.02224,-0.04153,-0.11629,0.00776,0.16193,0.00891,0.04895,-0.11242,-0.09782,-0.00936,-0.01702,-0.07184,-0.09164,-0.03788,0.06725,-0.00749,0.03069,0.02847,0.12004,-0.02517,0.00882,0.01075,-0.02222,0.0923,0.01538,-0.04038,-0.00149,0.02407,-0.01382,0.01235,0.0344,0.02698,-0.05289,-0.04531,0.03816,0.00731,0.04373,0.04225,0.00684,-0.07997,0.02567,0.03435,-0.04461,-0.01369,0.00048,-0.07407,-0.08386,0.01385,-0.07404,-0.10156,-0.02429,-0.06033,0.14921,0.11254,0.10031,0.05265,0.06209,-0.00835,-0.03201,-0.04522,0.02974,-0.10837,0.00117,0.11913,-0.05031,-0.02707,0.0543,0.02649,0.0701,0.00835,-0.01025,-0.07802,-0.07598,0.0002,-0.14222,-0.00291,0.02596,0.0574,0.00293,-0.00262,-0.0202,0.03245,0.03637,0.06043,0.11722,-0.07481,-0.07825,-0.04998,-0.12411,-0.04358,0.12498,0.01811,0.03319,0.03512,0.04705,0.02653,0.00526,-0.03587,-0.04373,-0.0078,-0.02205,-0.06163,0.03093,0.02274,0.00174,-0.00817,0.00175,-0.04217,-0.07146,-0.02262,-0.12283,-0.0037,-0.03692,-0.00669,0.07675,0.16063,0.0901,0.03119,0.06273,0.0586,-0.01683,0.13568,-0.05154,0.03515,0.07553,0.01346,-0.22608,0.00917]},{"domain":"classical_physics","key":"inertia_solid_disk","name":"Moment of inertia of a solid disk about its axis","package":"classical-physics-ai999x","example":"A uniform solid disk has a mass of 2 kg and a radius of 0.5 m. What is its moment of inertia about its center?","v":[0.08468,-0.0175,-0.03959,-0.03637,0.12522,0.04025,0.08405,0.01059,-0.03644,0.05432,0.07516,0.02559,0.01777,0.00142,-0.02506,0.02327,-0.04377,-0.14004,-0.04831,-0.08609,0.05142,-0.07461,-0.06618,-0.05785,-0.02041,0.00574,-0.02084,-0.01758,0.04246,-0.09718,0.01941,-0.01924,0.00736,-0.06693,-0.00211,0.06535,-0.00202,0.0571,0.0221,-0.10027,-0.08341,-0.08325,0.01319,0.04985,-0.06678,0.0207,0.04421,-0.13396,0.07758,-0.00464,-0.07194,0.12184,0.01612,0.02479,-0.07181,0.05751,0.09003,0.02671,-0.0454,0.03876,0.00957,-0.06962,-0.03723,-0.02608,0.02535,0.04587,0.03988,0.07754,-0.14808,0.07827,0.04771,-0.09461,-0.0527,0.13582,0.06729,0.04273,0.009,0.04703,-0.09622,-0.0037,-0.02105,-0.00039,0.10955,-0.00912,0.05103,0.05186,0.06038,0.05491,0.01355,-0.05339,-0.10247,0.0042,0.00551,-0.07273,-0.04766,-0.00039,-0.07719,0.05045,0.07384,0.03566,0.01349,-0.0478,-0.06765,-0.03596,-0.10226,0.10894,0.09224,-0.06247,-0.05018,-0.009,-0.00072,0.08784,-0.01741,0.0737,-0.00491,0.00561,0.10263,-0.06786,-0.10544,0.08919,0.07997,-0.04701,-0.04076,0.06364,-0.04991,-0.04752,-0.05634,0.00111,-0.01136,0.00942,-0.05688,0.07407,-0.00795,-0.03522,-0.00977,0.04407,-0.1056,-0.06029,0.04487,0.04873,-0.05181,-0.04129,0.0837,-0.04043,-0.07704,0.12759,-0.0105,-0.0509,0.00922,-0.01522,-0.00942,0.04907,-0.07553,-0.02609,0.10013,0.04453,-0.04671,0.02802,0.03572,-0.00478,-0.04266,-0.00339,0.02105,0.08327,0.07631,0.07466,-0.02145,-0.07484,0.10437,0.11286,-0.09165,-0.04849,0.01649,-0.06163,-0.09989,0.06416,-0.03704,0.04996,-0.00319,-0.10555,0.14918,0.13711,0.05668,0.12943,-0.02404,-0.05563,-0.01356,-0.03153,0.01377,-0.09838,0.02433,0.11736,-0.03665,-0.05809,0.02731,-0.10422,-0.0061,0.02355,-0.10103,-0.05874,0.00169,0.01421,-0.04827,0.01481,0.02272,0.02562,-0.0204,-0.02178,-0.03985,-0.01989,0.06342,0.09492,0.03515,-0.07811,0.00454,-0.01133,0.01794,-0.0609,0.04275,-0.06432,-0.01812,0.01012,0.05615,0.04206,0.04197,0.05212,-0.05633,0.09379,-0.06521,-0.05365,0.04212,0.06466,0.0159,0.02624,0.02576,-0.00787,-0.05536,-0.04929,-0.04236,0.07444,-0.09434,-0.02104,0.10247,-0.03847,0.13831,-0.02445,0.10016,0.03299,-0.10193,0.04541,0.01402,-0.01405,0.08961,-0.00167,-0.19761,0.01117]},{"domain":"classical_physics","key":"inertia_rod_center","name":"Moment of inertia of a thin rod about its center","package":"classical-physics-ai999x","example":"A uniform rod of mass 3 kg and length 2 m rotates about its center. What is its moment of inertia?","v":[-0.00078,0.01484,0.03458,-0.08009,0.12467,-0.01848,0.08894,0.08039,-0.01868,0.09873,0.00173,-0.01115,0.07313,0.00941,-0.06576,0.01797,0.01138,-0.04389,-0.06289,-0.10339,0.06063,-0.05726,-0.1144,-0.06605,0.00374,0.01957,-0.02687,0.02562,0.03629,0.00692,-0.01615,0.03915,-0.05146,-0.06936,0.00763,0.00978,0.04813,0.02103,-0.01587,-0.05074,-0.04069,-0.02519,-0.0067,0.12468,-0.04229,0.04368,-0.00171,-0.07615,0.03087,-0.05296,-0.0643,0.04389,0.00691,0.04176,-0.04992,-0.01238,0.00331,0.01252,-0.01715,0.03656,-0.03784,-0.07524,-0.09779,-0.02834,0.08101,0.05055,0.00452,0.04493,-0.06429,0.10234,-0.00794,-0.04627,-0.12752,0.03101,-0.01027,0.04997,0.04036,0.03722,-0.13835,-0.0045,-0.01169,0.00345,0.05887,-0.01987,0.10561,-0.03239,0.04707,-0.02004,-0.0608,-0.01378,-0.06232,0.01844,-0.02242,0.03474,-0.0107,0.10253,0.03402,0.11896,-0.03765,-0.00692,-0.01979,-0.00941,-0.02317,0.01265,-0.07322,-0.04472,0.04397,-0.02331,-0.01819,-0.03862,-0.02494,0.03885,0.09915,-0.0331,-0.10035,-0.03679,0.10888,0.01375,-0.08879,0.05231,0.08492,-0.03438,0.0173,0.05007,-0.0478,0.04485,0.07084,-0.04023,-0.02586,-0.00751,0.05761,0.04672,0.06674,0.02242,0.04766,0.0336,-0.05656,0.01538,-0.04625,-0.07366,0.01742,-0.03276,0.1754,-0.05241,-0.11933,0.12396,-0.02573,0.02048,0.01782,-0.04809,-0.03442,0.10378,-0.02021,-0.08411,0.13843,0.04442,-0.04927,0.0202,0.05408,0.02654,-0.04425,-0.04428,0.04089,-0.03017,0.09592,0.05323,-0.00364,-0.08991,0.01148,0.01077,-0.19575,-0.02917,0.04808,0.02213,-0.07104,-0.10527,-0.056,-0.06993,-0.07691,-0.07023,0.12695,0.10396,0.12369,-0.01975,0.00096,-0.06683,-0.01211,0.00571,0.05303,-0.10298,0.00472,0.03669,-0.13706,-0.08951,0.02375,-0.09965,0.06839,0.02246,0.0002,-0.04415,-0.02991,-0.03363,-0.0636,0.00537,-0.09721,0.03384,0.04734,0.00112,-0.03467,0.0118,0.00688,0.14538,-0.00843,-0.05112,0.00056,-0.0136,-0.10271,0.05671,0.05765,-0.03812,-0.0198,0.02934,0.05175,0.08346,-0.00082,-7e-05,0.05689,0.13766,-0.05692,-0.04726,-0.00956,0.04102,-0.01218,0.04626,-0.02076,-0.01456,-0.12022,-0.00259,-0.08954,0.06882,-0.03273,0.00921,0.08843,-0.05112,0.09896,-0.02966,0.19062,0.03588,-0.09996,0.15182,0.03955,0.01053,0.07465,-0.02378,-0.16607,-0.02294]},{"domain":"classical_physics","key":"inertia_rod_end","name":"Moment of inertia of a thin rod about one end","package":"classical-physics-ai999x","example":"A uniform rod of mass 3 kg and length 2 m rotates about one end. What is its moment of inertia?","v":[-0.02594,0.01511,0.00955,-0.04016,0.07047,-0.03871,0.07132,0.07183,-0.00439,0.04884,-0.03829,0.00935,0.10677,0.02051,-0.06113,0.02493,0.00783,-0.05065,-0.0397,-0.08359,-0.00954,-0.00927,-0.1129,-0.02642,0.07664,0.04327,-0.04389,0.05051,0.02064,0.04241,-0.06758,0.02365,-0.11709,0.01058,0.04867,0.05545,0.03345,0.06717,0.02623,-0.05109,0.04889,-0.05598,-0.07504,0.0535,-0.03738,0.029,-0.00402,-0.10083,0.02595,-0.0433,-0.10237,0.07341,-0.03219,-0.00416,-0.07753,0.00799,0.02635,0.0103,0.04406,-0.00706,-0.04987,-0.05712,-0.13567,-0.04029,0.0317,0.10892,0.02014,0.01589,-0.05062,0.01232,-0.02042,0.05486,-0.15471,0.01927,-0.01086,0.0075,0.10298,0.02325,-0.09579,-0.02242,0.0109,-0.04239,0.06969,-0.01677,0.10348,0.0061,-0.03895,0.02682,-0.01029,0.00836,-0.09974,-0.06118,-0.03264,-0.00254,-0.00606,0.0159,0.08254,0.05764,-0.06947,0.06507,0.0313,-0.03585,-0.07013,0.03202,-0.02755,-0.0836,0.00484,-0.03394,-0.00793,0.00429,-0.02242,0.01277,0.07381,-0.0103,-0.11089,-0.00668,0.05122,-0.05497,-0.04753,0.08275,0.00544,0.00372,-0.03122,0.07214,-0.01582,0.17273,0.02945,-0.02714,0.07379,0.05037,0.09814,0.09924,0.00067,0.00074,0.05967,-0.04507,-0.07106,0.01162,-0.09144,-0.01124,-0.02246,-0.01186,0.09115,-0.06006,-0.1422,0.11128,0.0314,0.03971,0.0323,-0.04495,-0.02231,0.04349,-0.08937,-0.15973,0.1069,0.08954,-0.06775,-0.02201,0.08952,-0.04338,-0.10772,0.00843,0.06123,0.09724,0.12039,0.04732,-0.06479,-0.05324,-0.04973,0.07377,-0.17282,0.03145,0.06651,0.00252,-0.05706,-0.01599,-0.05849,-0.09004,-0.03223,-0.08299,0.02076,-0.00496,0.07746,0.01314,-0.07802,-0.03797,-0.01517,-0.02947,0.11315,-0.07973,-0.02072,0.04956,-0.08914,-0.07471,0.07858,-0.03931,-0.00478,-0.0869,0.07033,-0.10633,0.05708,-0.04904,-0.00866,-0.0306,-0.02744,0.10964,-0.03191,-0.00568,-0.05401,-0.00046,0.04879,0.07796,-0.08296,-0.00638,0.01686,-0.02131,-0.04022,0.03751,0.00118,-0.09756,-0.03031,0.0528,0.08356,0.04158,0.03156,-0.0019,0.06806,0.06252,-0.06283,-0.08204,0.03794,-0.00683,-0.00891,-0.00534,0.05678,0.01587,-0.04593,-0.02939,-0.11787,0.07228,-0.0635,0.05687,0.11588,-0.04485,0.12572,-0.00081,0.19152,0.0683,0.00389,0.16206,0.06785,0.0048,0.07596,-0.05526,-0.05422,0.01135]},{"domain":"classical_physics","key":"rolling_incline_acceleration","name":"Acceleration of a body rolling without slipping down an incline","package":"classical-physics-ai999x","example":"A cylinder of mass 2 kg and radius 0.2 m with a moment of inertia of 0.04 kg*m^2 rolls without slipping down an incline. The angle of the incline is 30 degrees. What is its acceleration?","v":[-0.01466,0.03256,-0.03463,-0.01262,0.01725,0.02651,0.09943,0.01263,-0.01713,0.01565,-0.02002,0.00696,0.04297,-0.15342,-0.11995,0.00232,0.01143,0.09873,0.04356,0.00229,0.10921,-0.02902,-0.0054,0.00635,-0.04706,-0.02459,0.05805,0.05493,-0.06598,-0.05338,-0.0572,-0.00765,0.05039,-0.06748,0.07945,0.0289,-0.05263,0.08067,0.00836,-0.00572,-0.04163,-0.04388,-0.11712,0.03202,-0.05992,0.1377,0.13221,-0.0067,0.09864,-0.05973,0.07578,0.01015,0.08198,-0.00523,-0.09597,0.03482,-0.01315,0.0422,0.06843,0.01105,0.01287,0.04781,-0.0431,0.0035,0.1578,0.0335,0.0484,-0.02689,0.0255,-0.01925,-0.13885,-0.0243,0.0532,-0.06077,0.01183,0.05262,0.04337,0.01108,-0.10544,0.02675,-0.00704,-0.00773,0.02551,-0.05787,0.08053,0.06027,-0.03378,-0.11204,-0.09471,-0.01321,0.02249,0.09003,0.01063,0.07597,-0.03533,0.02611,0.04501,0.08642,0.088,0.00763,-0.03304,0.0103,-0.00879,-0.04267,-0.06884,0.02789,0.07341,8e-05,-0.12163,0.08398,-0.00586,0.12433,-0.01591,0.02172,0.02527,-0.07962,0.03657,-0.04645,-0.08389,0.07174,0.08423,-0.02302,0.05904,0.01762,-0.0275,-0.01866,-0.0097,-0.06896,-0.0702,-0.02599,0.03303,0.0546,-0.04846,-0.06047,-0.00947,0.105,-0.0672,-0.00043,-0.07164,-0.06288,-0.10595,-0.06222,0.03593,-0.0135,-0.00937,0.01439,-0.01232,0.02112,-0.03018,-0.00542,-0.13299,0.08078,-0.14007,-0.05871,0.05815,0.0823,-0.13912,-0.03032,0.02486,-0.03073,-0.04627,-0.11755,0.02576,0.11421,0.00969,0.03575,0.01084,0.01796,0.12369,0.0303,-0.02351,0.07016,-0.00813,-0.0741,-0.01598,0.03997,0.05171,-0.00752,-0.11134,-0.08475,0.0131,0.0452,0.08032,0.05177,0.09446,0.00931,-0.1211,0.02764,-0.00636,-0.02721,0.13469,0.05143,-0.07117,-0.01825,0.02715,-0.08326,-0.08012,-0.05323,-0.01735,-0.04707,-0.02129,-0.06224,-0.115,0.02306,0.00706,-0.03002,0.00438,0.07068,0.08847,0.03547,0.00424,0.04156,-0.10963,-0.0969,-0.07623,-0.01969,-0.06008,0.05299,0.04597,-0.02698,-0.03746,-0.06366,0.03774,0.16924,-0.01451,-0.03503,-0.03642,0.14351,-0.06399,-0.02839,0.00343,0.09606,-0.08852,-0.01023,-0.02135,-0.04484,-0.04063,0.06826,0.03089,0.06844,0.03643,0.00868,0.08299,0.00527,0.0725,-0.0238,0.07909,-0.05711,-0.02776,0.03571,-0.09051,0.07601,0.0848,0.05133,-0.11025,0.06033]},{"domain":"classical_physics","key":"atwood_massive_pulley","name":"Acceleration of an Atwood machine with a massive pulley","package":"classical-physics-ai999x","example":"In an Atwood machine the heavier mass is 3 kg and the lighter mass is 2 kg. They hang over a pulley with a moment of inertia of 0.02 kg*m^2 and a radius of 0.1 m. What is the acceleration of the masses?","v":[-0.08237,-0.02712,-0.04096,-0.00799,0.07214,0.0075,0.04564,-0.04626,0.01485,0.10703,0.01289,0.09429,0.05453,-0.03858,-0.10327,-0.04968,0.0093,0.02107,0.13184,-0.01063,0.15742,-0.07546,-0.00196,-0.01335,-0.07956,0.06556,-0.04808,0.06438,-0.06168,-0.08056,0.01053,-0.06728,-0.04991,-0.0593,0.01576,0.0064,-0.05327,0.06576,0.0393,-0.09208,-0.01341,-0.05313,-0.13974,0.07393,-0.09579,0.10145,0.07411,-0.03516,0.13573,0.00515,-0.04638,0.04411,0.0365,0.02496,-0.11679,-0.0354,0.00707,0.00449,0.01974,0.00483,-0.03033,0.01068,0.01875,0.05574,0.01907,0.03988,0.04156,0.04883,-0.008,-0.02527,-0.01059,-0.06432,0.0561,-0.08083,-0.03384,-0.01267,0.02529,-0.04716,-0.10154,0.12665,-0.07514,-0.03039,0.04917,0.02017,0.00788,0.03699,0.10407,-0.06484,-0.04975,-0.08307,0.00483,-0.0427,0.02018,0.09999,-0.0699,-0.03955,0.02104,0.05721,0.0312,-0.06549,0.03734,0.00294,-0.02265,-0.0352,-0.02112,-0.03767,-0.05241,-0.06634,-0.13549,0.09082,0.04898,0.05065,-0.01788,0.0526,-0.01029,-0.07182,0.02142,0.04729,-0.0079,0.02455,0.06418,-0.00273,0.0291,0.06302,-0.02159,0.00727,-0.06284,-0.03186,0.03276,-0.00178,0.03145,0.00751,-0.10984,-0.02707,-0.08165,0.07704,-0.12079,-0.0475,0.05893,0.02013,0.02769,-0.06234,0.11558,0.02036,0.10246,0.05361,0.0558,0.01017,0.02542,-0.01755,-0.03233,0.05136,-0.13478,-0.02615,0.01217,0.09126,-0.05972,-0.02247,-0.05769,-0.06576,-0.01219,-0.08308,0.08296,0.04489,-0.05395,-0.00952,0.04015,0.07807,0.07349,-0.00767,-0.05383,0.00572,-0.0198,0.06114,0.03049,0.13419,0.02976,-0.04855,-0.05451,0.02948,0.0964,0.07919,0.01378,0.07919,-0.01273,0.01313,-0.10674,0.0181,-0.06294,-0.16276,0.07956,0.21822,-0.03416,-0.00611,-0.01322,-0.05674,-0.05854,-0.02006,-0.02986,0.0328,0.0543,-0.04642,-0.14075,0.12477,0.02867,0.008,0.01362,0.00593,0.00575,0.07621,-0.03002,0.03815,-0.09902,-0.15955,-0.02244,-0.02369,0.00487,-0.00143,0.01422,0.01817,0.09929,-0.02503,-0.01131,0.07058,-0.08312,-0.06188,-0.0318,0.01766,-0.06522,-0.02535,0.00437,0.05427,-0.01497,-0.02698,0.07289,-0.0526,-0.10381,-0.01594,0.01183,-0.03586,0.02299,0.02002,-0.00789,0.06868,0.05889,-0.05446,0.06355,-0.06253,-0.01716,0.04534,-0.02547,0.14813,0.17885,0.01188,-0.05611,0.10568]},{"domain":"classical_physics","key":"torque_free_precession","name":"Body-frame precession rate of a torque-free symmetric body","package":"classical-physics-ai999x","example":"A torque-free symmetric body spins with a spin angular velocity of 10 rad/s. Its transverse moment of inertia is 2 kg*m^2 and its moment of inertia about the symmetry axis is 3 kg*m^2. What is the precession rate?","v":[0.13816,0.02489,-0.0525,0.00125,0.08412,0.13742,0.00085,-0.04498,0.1119,0.02478,-0.04916,0.05471,-0.05417,-0.05817,-0.03139,-0.06082,-0.016,0.00211,0.03941,-0.01822,0.00432,0.03546,-0.11489,-0.01347,0.00064,-0.07356,0.0608,0.02956,0.05816,0.14147,0.04076,-0.00655,0.02326,0.02901,0.017,0.06743,-0.00439,-0.06025,0.04753,-0.03782,0.01216,-0.16877,-0.08838,0.08725,-0.06378,-0.12599,0.02256,-0.04438,0.10317,-0.04732,0.00748,-0.0791,0.04269,0.01585,-0.02311,-0.00217,-0.05186,0.0064,-0.07421,-0.08637,-0.02681,0.03499,-0.0957,-0.00732,0.03085,-0.0732,0.04909,-0.02322,-0.10531,-0.05698,-0.00275,-0.01006,0.06466,-0.01785,-0.03886,-0.06743,0.03287,0.07433,-0.0359,-0.06312,0.01063,-0.00187,-0.00216,-0.03731,0.04474,0.0242,-0.09824,-0.10753,0.01098,-0.05723,0.04072,0.01611,-0.03283,-0.03774,-0.06653,0.08177,0.01165,0.07255,-0.01889,-0.08835,-0.02873,-0.04246,0.04132,0.04749,0.12794,-0.12971,0.09477,-0.00072,0.01117,0.01524,0.02507,0.08648,-0.00856,0.06142,0.01342,0.00601,0.01823,0.01036,-0.01513,-0.06717,0.04326,0.00111,-0.07843,0.0972,0.05335,0.08715,-0.02534,-0.02958,-0.02126,-0.06666,-0.03878,-0.00436,-0.00837,-0.02924,0.01071,-0.05522,0.03327,-0.02454,-0.04511,0.03949,-0.02774,0.03963,-0.08075,-0.08638,-0.07251,0.04142,-0.05057,-0.02948,-0.06393,0.00755,0.04437,-0.00201,-0.00286,-0.0915,-0.05636,0.14013,0.0184,0.04025,0.08292,-0.11949,0.04239,-0.07268,0.09537,0.15766,-0.09932,0.01184,0.01533,0.05875,-0.09397,0.12487,0.09461,0.00718,0.01688,-0.05792,-0.09014,0.13413,-0.0175,-0.00746,-0.07276,-0.05253,0.06069,-0.06259,-0.02314,-0.0225,0.08376,-0.00301,-0.05314,0.00567,0.00749,-0.0384,0.10435,0.10676,-0.08637,-0.14872,0.01387,-0.02678,0.04155,0.12123,-0.09157,0.03167,-0.00098,0.05978,-0.06259,0.09888,0.05703,0.09541,0.05183,0.08673,-0.06351,0.01932,0.02267,0.07298,-0.07157,-0.00291,-0.01959,-0.11988,-0.03773,-0.03915,0.10148,-0.03862,-0.02694,-0.1177,0.06673,0.05324,0.00608,0.08582,-0.02124,-0.11843,0.03585,-0.01909,0.09682,0.00474,-0.07784,-0.01876,0.03118,0.11503,-0.06383,0.03599,-0.00236,-0.00392,0.04062,-0.00185,0.09233,0.05709,0.04241,0.11891,0.05808,-0.03117,0.04866,0.0153,-0.04133,0.0088,0.07917,-0.01163,-0.01623,-0.03701]},{"domain":"classical_physics","key":"foucault_precession_period","name":"Precession period of a Foucault pendulum","package":"classical-physics-ai999x","example":"A Foucault pendulum swings in Paris at a latitude of 48.85 degrees. What is its precession period?","v":[-0.00229,0.04075,-0.06431,0.14456,0.0029,0.14868,-0.01812,-0.07125,0.1345,0.06109,0.00336,0.03552,0.03377,0.02006,-0.01573,0.00273,-0.02619,-0.00043,0.15476,-0.01474,-0.06087,0.0153,-0.03663,-0.04965,0.08511,-0.10977,-0.02715,-0.09619,0.05952,0.10969,0.00991,0.03711,-0.02149,0.00127,0.05026,-0.00617,-0.00076,-0.02439,-0.01175,0.04437,0.02748,-0.13054,-0.06016,0.0745,0.00882,-0.03149,0.01934,0.10966,0.0735,0.01975,-0.06896,0.02463,-0.07231,0.00396,-0.0516,-0.03558,-0.09308,-0.03565,-0.01422,-0.05741,-0.01855,0.09957,-0.15248,0.05613,0.01787,0.02441,-0.00023,-0.10726,-0.01696,-0.05638,0.04374,-0.01098,0.01517,-0.06966,0.01209,-0.03473,0.05977,-0.00064,-0.01895,0.03964,0.02293,0.01178,0.06327,-0.00559,0.06135,-0.0444,-0.00591,-0.01873,0.14128,-0.04864,-0.02489,-0.11728,-0.09355,-0.05468,-0.14359,-0.02047,0.08716,-0.01455,-0.1201,-0.01127,-0.08105,0.01169,-0.00256,0.01654,0.02553,0.0128,0.00516,0.0052,0.0496,-0.02011,0.085,0.03757,0.11605,0.03242,0.08226,-0.0027,0.04368,0.0031,0.00886,0.03021,-0.15467,-0.05515,-0.09543,-0.00088,-0.01275,0.13719,-0.02156,0.01451,0.01939,0.07552,0.00955,-0.0893,0.04524,-0.06043,-0.04142,0.06667,0.06041,0.06857,0.06724,0.09072,0.05527,0.07387,0.02782,-0.09165,-0.04458,-0.01268,0.02328,-0.08454,-0.05052,0.12446,0.09497,-0.06563,0.00855,-0.05711,0.04387,0.07026,0.05533,-0.02597,-0.09336,-0.09652,0.06003,0.07867,-0.01603,0.09077,-0.04736,-0.01302,0.03718,0.10927,-0.12733,-0.001,0.0463,0.10514,0.08458,0.01352,-0.05223,0.09331,-0.00182,-0.01334,0.03366,-0.07822,-0.08342,-0.04156,0.00757,-0.05911,0.0384,0.00996,-0.05745,-0.01677,-0.00544,-0.01041,0.03368,0.05753,-0.0212,-0.1592,0.01004,0.01278,0.12533,0.01262,-0.08219,0.0676,0.0583,-0.01632,-0.06651,0.05622,0.01351,0.05001,0.02435,0.01989,0.01134,0.00686,0.01852,-0.06544,-0.06783,0.06194,-0.00898,0.00248,-0.08735,0.00738,0.0737,-0.0435,-0.18246,-0.04376,0.06016,-0.03486,0.04278,-0.06443,0.01148,-0.09369,0.03229,0.0438,0.01357,-0.0136,-0.1472,-0.00487,-0.04796,0.08321,-0.04761,-0.04809,0.08483,-0.0252,0.04548,-0.07872,-0.01059,0.04723,0.04317,-0.00231,-0.00491,-0.13428,-0.00936,-0.0248,0.00329,0.00425,0.09316,0.00105,-0.00939,0.07659]},{"domain":"classical_physics","key":"bead_hoop_equilibrium","name":"Off-axis equilibrium of a bead on a rotating hoop","package":"classical-physics-ai999x","example":"A bead slides without friction on a rotating hoop of radius 0.2 m. The hoop rotates at 10 rad/s about its vertical diameter. What is the equilibrium angle of the bead?","v":[-0.07743,-0.03956,-0.11053,0.08259,-0.05232,0.07186,0.05701,-0.02094,0.00582,0.01549,0.00952,-0.04419,-0.04688,0.05378,-0.14295,0.0,-0.02483,-0.09025,0.06317,-0.03422,-0.03696,-0.01197,-0.05408,-0.01628,-0.01379,-0.0873,-0.0275,0.09445,-0.01333,-0.0354,0.05891,0.11213,-0.01925,-0.07832,-0.07951,-0.00289,-0.02058,0.03725,0.01998,0.00635,0.04579,-0.1058,-0.07597,0.06617,-0.00287,0.02185,0.08338,-0.04167,0.04098,-0.00712,0.08251,-0.02486,0.108,0.08693,-0.08557,0.02377,-0.04114,-0.07043,-0.04649,0.04048,0.04856,0.09475,-0.037,0.02637,0.06895,-0.00215,-0.1014,-0.21204,0.00024,-0.12965,-0.05523,0.02326,0.09159,-0.03012,0.01691,0.02447,-0.11221,0.12375,-0.00158,0.12694,0.00882,-0.01236,-0.00604,0.00433,-0.02698,-0.00386,0.03384,-0.04634,0.00205,0.12853,0.04487,-0.03179,-0.02429,0.05285,0.0062,0.04451,0.04971,0.00965,-0.05454,-0.01024,-0.05267,-0.04217,0.13494,0.00635,0.12294,-0.04442,0.04485,0.02478,-0.06238,-0.00113,0.07397,0.04533,0.06613,0.05961,0.07564,0.06249,0.0755,-0.03879,-0.00867,-0.012,-0.01415,-0.01478,-0.07809,-0.00945,-0.00566,0.04673,-0.01023,-0.06915,0.04431,-0.0463,0.03586,-0.06394,0.01805,-0.05772,-0.00948,0.00608,-0.09171,0.04742,-0.02619,-0.0116,-0.06549,-0.00192,-0.02953,-0.07325,0.10776,0.0623,0.10503,0.0191,-0.02574,0.00627,0.08763,0.21953,0.03898,-0.06937,0.01872,0.03872,-0.01645,0.04563,-0.05711,-0.04185,0.05145,-0.07003,0.02218,0.06315,-0.11335,-0.07992,-0.00846,-0.06901,-0.01118,0.02652,0.06102,0.08646,-0.10005,-0.08021,-0.0514,0.10779,-0.04656,0.04526,-0.00309,-0.08449,0.01116,0.01836,-0.0356,0.0049,-0.00483,-0.03031,-0.06995,0.03366,0.04918,-0.05851,-0.0405,0.17539,-0.03986,-0.0658,-0.0355,-0.03237,-0.07998,-0.00587,0.00993,0.03701,-0.03739,-0.01912,-0.09816,-0.03532,0.0463,0.08744,0.00887,0.08762,0.05017,-0.0528,-0.00264,-0.00843,-0.06227,0.13586,-0.06179,0.01452,-0.06877,-0.07908,-0.00567,0.00943,-0.07238,-0.01089,-0.01839,0.09118,0.03011,0.04638,0.03567,0.07288,0.02993,0.1098,-0.05445,0.04814,0.01031,-0.00383,-0.09839,-0.03182,-0.13615,0.03875,-0.01533,-0.0399,0.00605,0.0831,0.04408,0.07037,0.07199,-0.09235,0.02399,-0.01265,-0.00547,0.0188,-0.08526,0.04691,0.13749,-0.05898,0.06688,0.10123]},{"domain":"classical_physics","key":"elastic_collision_first_final","name":"Final velocity of the first body in a one-dimensional elastic collision","package":"classical-physics-ai999x","example":"In an elastic collision the first mass is 2 kg with a velocity of the first of 3 m/s, and the second mass is 1 kg with a velocity of the second of 0 m/s. What is the final velocity of the first?","v":[0.09151,-0.00487,0.03882,-0.04285,0.03831,3e-05,0.01861,0.03935,0.03372,-0.03847,0.00228,0.05562,-0.05303,-0.10328,0.06794,-0.05135,-0.0279,-0.01748,0.10713,0.00086,0.15091,0.14599,0.05783,0.1135,-0.10072,0.03935,0.01525,0.0701,-0.16005,0.01348,-0.02585,0.00374,-0.03497,0.0414,-0.07305,0.07665,-0.05225,0.05757,0.14866,-0.08918,-0.00739,0.00125,-0.0502,-0.0441,-0.04879,0.01119,-0.00381,0.15722,-0.03574,-0.00973,-0.07568,0.08547,-0.00416,-0.03696,0.07665,0.19671,-0.01692,0.04175,0.03496,0.01153,-0.10266,-0.05294,0.03009,-0.05899,0.04195,-0.02481,0.10375,-0.03071,0.1204,-0.01453,0.02927,-0.09298,0.02022,-0.09046,0.00325,0.02214,0.0999,-0.06959,-0.01007,0.01649,0.03785,-0.0472,-0.01196,0.00516,0.04296,0.04636,-0.03512,0.00688,-0.07771,0.09638,0.06632,-0.06618,0.00926,-0.13568,0.03274,0.0059,-0.01009,0.03722,-0.10013,-0.02187,0.07177,0.05196,-0.03399,0.02759,-0.02076,-0.06267,0.05331,0.03622,0.01272,-0.01844,-0.01941,0.03969,-0.00428,-0.03855,-0.07764,0.03225,0.02373,-0.05835,0.10184,-0.01304,-0.08143,-0.04445,0.02924,0.2,0.03774,-0.02652,-0.03418,-0.02488,0.12374,0.0107,0.01261,0.05321,-0.08281,-0.09243,0.04055,-0.05287,0.0397,0.04904,-0.02151,0.0003,0.01781,0.01073,0.08075,-0.00591,0.07832,0.00691,-0.01547,0.02435,-0.0105,-0.03702,-0.00213,0.03534,-0.08455,-0.08365,-0.02985,0.02135,-0.09331,-0.00769,0.00475,0.01242,-0.03952,-0.07104,0.00082,-0.01916,-0.01449,0.07643,-0.09934,-0.01862,0.05033,0.0489,-0.04649,0.10473,0.01718,-0.07106,0.08628,-0.00216,-0.07297,-0.057,-0.10557,-0.16101,0.13116,-0.04775,0.04901,-0.0246,-0.08268,0.06682,-0.01874,-0.06434,0.04052,-0.03563,-0.04699,0.09286,-0.00518,0.07278,0.07813,-0.04604,-0.01682,-0.08343,0.06585,-0.07746,-0.08562,-0.03033,0.01591,-0.02235,0.04241,0.08203,0.01033,-0.01404,-0.00601,-0.04811,-0.05426,-0.11191,-0.00722,-0.02624,-0.09253,-0.08979,-0.00284,0.04875,-0.03802,0.02517,-0.03659,-0.06285,0.06104,0.01071,-0.01837,0.06238,-0.00445,0.047,0.06049,0.04173,0.01368,0.05864,-0.00042,-0.048,0.07096,-0.08149,0.05457,-0.03485,0.01614,-0.00352,0.09031,-0.11777,0.01122,0.1157,0.0959,-0.09449,0.04831,0.04353,0.01746,0.04097,-0.13662,0.04252,0.04028,-0.06029,0.00228,0.03596]},{"domain":"classical_physics","key":"elastic_collision_second_final","name":"Final velocity of the second body in a one-dimensional elastic collision","package":"classical-physics-ai999x","example":"In an elastic collision the first mass is 2 kg with a velocity of the first of 3 m/s, and the second mass is 1 kg with a velocity of the second of 0 m/s. What is the final velocity of the second?","v":[0.07465,-0.01277,0.04933,-0.06814,0.04644,0.02122,0.00864,0.02309,0.03125,-0.04384,0.01807,0.03394,-0.03046,-0.09405,0.0587,-0.04232,-0.03893,0.0076,0.09331,0.00508,0.1342,0.14353,0.08834,0.10145,-0.08297,0.02638,0.03475,0.09944,-0.164,0.03837,-0.02396,-0.01494,-0.06101,0.04591,-0.04637,0.08363,-0.07781,0.07382,0.1515,-0.10798,-0.00472,-0.0065,-0.043,-0.04109,-0.08115,0.0019,0.01752,0.14177,-0.02879,-0.01696,-0.05674,0.09367,-0.01282,-0.01428,0.06226,0.21098,-0.02651,0.06602,0.02033,0.03159,-0.09731,-0.06059,0.03965,-0.04447,0.01296,-0.02349,0.11665,-0.03152,0.11554,-0.03131,0.03693,-0.12295,0.02539,-0.08777,0.00879,-0.00562,0.06225,-0.07151,-0.00313,0.00996,0.02586,-0.03655,-0.03001,0.05158,0.03014,0.03628,-0.0121,-0.01421,-0.0947,0.09655,0.03793,-0.02357,0.00821,-0.09182,0.03793,-0.0203,-0.01529,0.02602,-0.12496,-0.04511,0.08358,0.07575,-0.00828,0.04168,-0.02616,-0.08715,0.01586,0.04988,-0.01708,-0.02723,0.00809,0.02568,0.02095,-0.04554,-0.07883,-0.02319,0.06173,-0.06746,0.07973,-0.01014,-0.09823,-0.02053,0.02822,0.18481,0.02126,-0.00959,-0.02442,-0.00979,0.13144,0.01586,0.01377,0.02082,-0.113,-0.07227,0.00623,-0.02771,0.03776,0.06267,-0.01149,0.01145,0.00479,0.01253,0.09996,0.01224,0.08224,0.01287,-0.02562,0.02078,-0.01821,-0.01432,0.00251,0.07689,-0.08525,-0.07568,-0.02954,0.04205,-0.06843,-0.0174,-0.00538,0.02963,-0.02869,-0.07834,0.00468,-0.03206,-0.02197,0.07485,-0.10516,0.00291,0.04064,0.04036,-0.05019,0.1094,0.02176,-0.07296,0.06252,-0.03104,-0.04921,-0.02258,-0.10126,-0.15533,0.12657,-0.03691,-0.00468,-0.03489,-0.06335,0.07902,-0.02336,-0.04937,0.04354,-0.02219,-0.03727,0.08786,-0.01921,0.05589,0.07235,-0.08023,-0.04923,-0.11817,0.08364,-0.08736,-0.05264,-0.0135,0.03749,-0.03499,0.00558,0.08576,0.01465,0.01792,-0.005,-0.08009,-0.05414,-0.1337,0.0349,-0.03073,-0.07741,-0.05962,-0.02989,0.06495,-0.02246,0.01992,-0.00176,-0.09353,0.04685,0.00908,-0.00364,0.06471,-0.00721,0.01685,0.03688,0.0367,0.01546,0.05841,0.01491,-0.05007,0.06269,-0.08729,0.02643,0.00445,0.04632,-0.03017,0.10595,-0.10303,0.01969,0.13354,0.07821,-0.07758,0.01417,0.02359,0.01987,0.00953,-0.14695,0.04161,0.04224,-0.07855,-0.00228,0.04289]},{"domain":"classical_physics","key":"rocket_delta_v","name":"Velocity change of a rocket (Tsiolkovsky)","package":"classical-physics-ai999x","example":"A rocket with an exhaust velocity of 3000 m/s has an initial mass of 1000 kg and a final mass of 400 kg after the burn. What is its change in velocity?","v":[0.03491,0.08156,0.07738,0.05966,0.07574,-0.0476,-0.04003,0.0237,0.02256,0.05686,0.02047,0.0459,-0.04382,-0.08634,0.11194,-0.07389,-0.06945,0.00431,0.14768,0.01864,0.10725,0.03536,-0.00496,-0.03279,-0.10555,-0.00885,-0.02105,-0.02269,-0.04574,0.03742,-0.04549,-0.01704,-0.01964,-0.09047,-0.04458,-0.00017,0.00264,-0.01066,0.03409,-0.01488,0.09217,-0.01884,0.05224,-0.07401,0.05939,0.03146,-0.01472,0.00341,-0.05773,-0.09012,-0.03869,0.07879,-0.05158,0.01948,0.09867,0.05928,-0.00648,-0.01883,-0.00974,-0.07448,-0.08397,-0.03938,0.08248,-0.0109,0.06558,0.01417,0.04342,0.10409,-0.01916,0.12095,-0.03857,0.03668,-0.00782,0.03182,-0.0058,0.09824,0.09076,-0.06993,-0.12877,-0.13451,0.00725,-0.09869,-0.03891,-0.03566,-0.04537,-0.00119,0.01088,-0.08113,-0.11309,0.00385,0.04364,-0.04742,-0.04505,-0.03471,-0.02381,0.00353,0.04638,0.04498,0.06406,-0.05522,0.027,0.04383,-0.05072,-0.06563,-0.01014,-0.02638,0.11093,-0.04745,-0.0313,0.09516,0.03244,0.116,-0.04411,0.02389,-0.08958,0.0658,0.00113,-0.01401,0.05049,-0.01896,0.01303,0.00339,-0.06079,0.15244,-0.00052,0.02366,0.00939,-0.05911,0.01499,-0.02297,-0.03185,0.11666,-0.10277,-0.02245,0.04175,-0.17914,0.07153,0.07127,0.10293,-0.02623,-0.02487,0.10438,-0.04383,0.00827,0.02783,0.02884,-0.01113,0.04248,-0.03004,0.01967,0.07061,-0.11351,-0.14824,-0.17073,-0.11663,-0.02217,-0.114,0.01139,0.01399,-0.06052,0.00227,-0.06121,0.03204,-0.05762,-0.06085,0.02717,0.03908,-0.05891,-0.02826,0.10961,-0.07828,0.0503,0.01017,0.01966,0.08139,-0.01482,0.00667,-0.13845,-0.07057,0.01568,0.01538,-0.03796,-0.00766,0.01028,0.02686,0.00699,-0.06448,-0.09597,0.13909,-0.07208,-0.04975,0.05296,-0.05558,-0.02705,0.0979,0.00527,-0.06094,-0.01594,-0.0725,-0.00063,-0.14116,0.01134,0.08383,0.00563,-0.03802,0.0474,0.02708,0.07621,0.09248,0.01594,-0.07489,0.05073,0.05761,-0.01879,0.05842,-0.16001,0.01136,0.05017,-0.0249,-0.00546,0.00127,-0.01932,0.00317,-0.0022,-0.00313,0.01152,-0.06283,0.07394,-0.039,-0.00679,0.09705,-0.01583,0.00794,0.00973,0.06,-0.03735,0.07801,-0.06033,0.04517,0.06364,0.06388,0.04491,0.07126,0.05373,0.08038,-0.01807,-0.00362,0.00359,0.15296,-0.04454,-0.0616,0.10008,-0.0081,-0.01921,0.10291,0.01877]},{"domain":"classical_physics","key":"two_resistors_series_parallel","name":"Two resistors in series and in parallel","package":"classical-physics-ai999x","example":"What are the series and parallel equivalents of 6 ohm and 3 ohm resistors?","v":[0.01155,-0.06336,-0.01321,0.04703,-0.05645,-0.04587,0.10123,0.0067,0.06116,0.0398,0.0104,0.01817,-0.07664,0.01946,0.01719,-0.10565,-0.05862,0.02865,-0.0421,0.0602,0.02406,-0.00801,0.0752,0.00398,-0.0344,0.03752,-0.08392,-0.02948,-0.04526,-0.05246,-0.05244,-0.00393,-0.08577,-0.00175,0.07159,0.04953,0.05422,-0.00018,-0.01846,0.0246,0.06102,0.11568,-0.03276,-0.09872,-0.11914,-0.07848,-0.03251,0.07868,-0.03721,0.00825,-0.12371,0.16006,-0.04233,0.03577,0.03995,-0.03518,-0.0396,0.01205,-0.01294,0.04887,-0.05281,-0.02402,-0.02058,-0.09305,-0.01484,0.03131,0.04213,-0.08118,0.1097,-0.00996,0.10009,0.0373,-0.01423,-0.09541,-0.03455,0.00979,-0.03874,0.01617,0.03173,-0.06438,0.07764,-0.04643,-0.022,0.09012,0.04753,0.01127,0.04208,0.04832,-0.03123,0.00809,-0.07151,0.13517,-0.01123,0.03745,0.061,-0.09375,0.00478,0.09429,-0.13281,0.02794,0.02032,-0.02111,-0.01325,0.10079,-0.00069,-0.05618,0.02486,-0.02054,-0.13095,0.02931,-0.01575,-0.09061,-0.04281,0.0032,-0.02813,0.02567,0.03088,0.01123,0.07073,-0.01904,-0.06161,0.01838,0.05608,0.03939,-0.05132,0.05945,0.03103,-0.02403,0.02043,0.00028,0.00575,-0.05059,-0.12756,0.04341,-0.04132,-0.11365,-0.06234,0.08876,-0.12397,0.02303,-0.17628,-0.03164,-0.04481,0.08289,0.18287,-0.01122,0.00181,-0.00208,0.01285,0.05328,-0.14682,0.13613,-0.06538,-0.02525,0.15961,-0.03924,-0.11027,-0.04985,0.02617,-0.00318,0.05657,0.08484,0.00734,-0.07192,0.02554,0.03311,-0.14284,0.06552,-0.05527,-0.08675,0.00552,0.00463,0.02659,0.10144,-0.03967,0.02082,0.031,0.04338,0.01608,-0.08914,-0.05128,0.00527,0.01409,0.02674,-0.00131,0.08375,-0.00192,0.00224,-0.07366,0.06044,0.00784,0.10785,0.01141,0.10575,0.04313,-0.11882,-0.07255,-0.02614,0.06676,-0.10172,0.01026,0.03704,0.01503,0.05276,-0.03739,0.09004,-0.05103,0.05107,-0.02686,-0.0197,0.00636,0.01664,-0.10863,-0.01737,-0.12342,-0.01351,0.04814,0.01696,-0.13987,0.09307,0.03788,-0.00944,0.04347,-0.03199,0.0715,0.08685,0.02323,0.05398,0.13034,0.03467,-0.03034,-0.02765,0.01581,-0.02034,-0.03074,-0.07961,-0.02379,-0.01438,-0.02155,-0.08253,0.04167,-0.0166,0.00852,-0.05865,0.01557,0.00666,-0.02649,-0.04574,0.02138,0.10661,0.07445,0.14184,-0.01603,-0.01002,-0.05826,0.05882]},{"domain":"classical_physics","key":"uniform_acceleration_state","name":"Velocity and displacement after constant acceleration","package":"classical-physics-ai999x","example":"A body moving at 4 m/s accelerates uniformly at 2 m/s^2 for 5 s. What are its final velocity and displacement?","v":[0.06326,-0.02738,0.01962,0.05148,-0.00119,0.05085,0.11009,-0.01438,0.02034,-0.04055,0.07737,0.04728,0.00567,-0.09232,0.07048,0.02239,-0.03642,-0.03351,0.07204,0.04207,0.10605,-0.00411,-0.1343,0.06503,0.02225,0.00169,0.0532,-0.04254,0.00636,-0.07239,0.1027,0.05968,0.00755,-0.02522,-0.06371,-0.03835,0.04783,0.0258,-0.00853,0.03866,-0.03611,-0.13974,-0.03586,-0.20246,-0.05899,0.01012,0.01769,0.00819,0.03552,-0.01024,0.04149,-0.04105,-0.05406,-0.00268,0.08363,0.00293,0.06432,0.01285,-0.05124,-0.03098,-0.02052,0.02799,0.03376,0.07279,0.03833,0.01449,0.09801,0.05959,-0.02271,-0.02771,0.01993,0.06805,0.00636,-0.01862,-0.01806,0.00482,0.08691,0.03473,-0.05777,0.00992,0.03391,0.00931,0.04511,-0.0032,-0.05845,0.11564,0.04557,-0.05499,0.04304,-0.02932,0.0409,-0.0584,-0.05944,-0.00375,-0.07844,0.06713,0.00226,-0.00536,0.10341,-0.02622,0.04729,0.02475,0.09789,-0.04341,-0.00396,0.02616,0.04717,-0.02903,0.00814,0.10662,-0.05475,0.04882,-0.15174,-0.01816,0.02201,0.05941,-0.08631,-0.04886,-0.03564,0.04083,-0.01158,-0.03057,0.01523,0.05671,0.01127,0.06973,0.06088,0.01251,0.03885,-0.03498,0.07669,0.01575,-0.03053,-0.06162,-0.07818,-0.17282,0.04421,0.02199,0.11132,-0.01476,0.02056,0.12498,0.03648,0.05236,0.03955,-0.01905,-0.04236,0.05968,0.00666,0.02573,-0.04674,-0.05824,-0.05176,-0.13303,-0.03173,0.01224,-0.05327,-0.01131,-0.06297,-0.0601,-0.05628,-0.05987,0.15607,0.19927,-0.01015,-0.03947,0.03306,-0.08238,0.12363,-0.02642,0.02394,0.02745,-0.02355,-0.04634,-0.06087,0.05972,-0.04627,-0.10716,0.05787,-0.08474,0.06312,-0.01979,0.02707,0.01039,-0.009,-0.06478,-0.0475,-0.0258,0.0326,-0.09971,-0.08622,0.01894,-0.08964,-0.03042,0.02271,-0.06837,0.0224,-0.01704,-0.03678,0.04651,-0.09199,0.04291,-0.00043,-0.11583,-0.00238,0.06304,-0.05051,0.03093,0.12759,-0.01809,0.04067,-0.04314,-0.00437,-0.06382,0.06175,-0.01213,0.15667,0.03585,-0.19739,-0.01154,-0.024,0.00016,0.00941,0.067,0.0815,-0.02277,-0.11362,0.03419,-0.03529,-0.03847,-0.06279,-0.04743,0.03864,0.0238,0.05039,0.03778,-0.03148,0.00332,0.07599,0.05449,0.01026,0.08017,-0.10505,0.06722,0.13899,-0.09656,0.01755,-0.06082,0.06752,-0.08752,-0.02025,0.01593,-0.11976,-0.09134,0.12625,-0.05404]},{"domain":"earth_science","key":"airy_isostasy","name":"Mountain root by Airy isostasy","package":"earth-science-ai999x","example":"Airy isostasy with elevation = 3 km, crustal density = 2800 kg/m^3 and mantle density = 3300 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flux emitted by a black or grey body (Stefan-Boltzmann)","package":"earth-science-ai999x","example":"Stefan boltzmann with temperature = 288 K and emissivity = 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speed and direction from components","package":"earth-science-ai999x","example":"Wind speed and direction with u component = 5 m/s and v component = -3 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allowed reflections of a cubic crystal","package":"materials-science-ai999x","example":"Allowed reflections: structure = FCC, count = 6","v":[0.02505,-0.11712,0.02374,-0.01757,0.13299,0.0837,-0.03459,-0.04884,0.06822,-0.1588,0.03173,-0.038,-0.12035,0.07251,-0.0076,0.03339,0.07896,-0.10888,0.06763,-0.02114,0.11631,-0.00754,0.11728,0.03996,-0.03246,-0.09755,-0.01597,0.07574,-0.00263,0.01668,-0.05693,0.04003,-0.01812,-0.00481,0.00077,-0.01228,0.08192,0.03958,0.02786,-0.09714,-0.02505,0.05136,0.00204,-0.03177,0.02047,-0.09566,-0.11119,0.02906,-0.05323,-0.03594,0.01364,0.14724,-0.03654,0.07779,0.0125,0.03131,-0.01324,0.0475,0.07264,0.04531,-0.05296,0.07549,-0.05154,-0.08074,-0.07326,-0.00955,-0.0503,-0.06831,-0.03744,-0.02681,-0.04965,0.00148,-0.02504,0.10866,0.0516,-0.06701,-0.06964,0.02514,0.03771,0.05134,0.05915,-0.04928,-0.0028,-0.04524,0.10955,-0.01437,-0.12302,-0.02483,0.00616,-0.03115,0.10315,-0.05785,0.08031,-0.03349,-0.07148,-0.0592,-0.10409,0.09604,0.01493,-0.02721,0.03171,0.05518,-0.15894,-0.05338,0.06458,0.07784,0.07002,2e-05,0.09446,-0.03121,-0.00354,-0.01294,0.06097,0.07291,0.01085,-0.11338,0.03885,-0.09797,0.01334,0.06177,0.02352,-0.03745,0.02322,0.01703,-0.04435,-0.15173,-0.0822,0.05402,-0.01864,-0.00723,-0.04943,0.05481,0.10491,0.0038,0.05645,0.001,-0.02967,-0.04837,0.0482,-0.00271,0.06382,-0.04151,0.03674,-0.04001,-0.06003,-0.10099,-0.06523,0.11067,0.0738,-0.0028,-0.04656,0.05323,-0.04323,-0.00218,0.00305,-0.00374,-0.06104,-0.13896,-0.03115,-0.02577,0.08239,-0.03042,0.06177,-0.07568,-0.0256,-0.03522,0.03326,-0.027,0.09558,0.0862,-0.00428,0.0027,-0.00817,0.03589,-0.01475,0.02191,0.01411,0.09409,-0.12166,-0.05038,0.08267,0.0913,0.00799,0.10478,-0.03895,-0.07658,0.02154,-0.03493,-0.071,0.18782,-0.02534,-0.03309,0.0002,-0.07029,0.03806,0.04364,0.07301,-0.08021,-0.04143,-0.15252,-0.03559,0.06973,-0.01743,0.03543,0.01478,0.05121,-0.03085,-0.00586,0.03515,0.12083,0.03498,-0.00249,-0.0309,-0.05077,-0.07177,0.08637,-0.06438,-0.02139,-0.01567,-0.04806,-0.06181,-0.01172,0.00535,-0.00303,0.09375,0.00329,0.0856,0.05112,-0.09537,0.0171,0.02792,0.07271,-0.02307,-0.05648,0.04692,0.0413,0.07299,0.02955,-0.01948,0.03154,0.03653,-0.02424,-0.07992,-0.02733,-0.03043,-0.00922,-0.0769,0.06372,0.07461,0.07227,-0.1142,0.03243,0.06289,0.07105,-0.03501,-0.06783]},{"domain":"materials_science","key":"angle_between_directions","name":"Angle between two lattice directions in any crystal","package":"materials-science-ai999x","example":"Angle between lattice directions: a = 0.3 nm, b = 0.3 nm, c = 0.5 nm, alpha = 90, beta = 90, gamma = 120, u1 = 1, v1 = 0, w1 = 0, u2 = 0, v2 = 1, w2 = 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between two directions in a cubic crystal","package":"materials-science-ai999x","example":"Angle between cubic directions: u1 = 1, v1 = 0, w1 = 0, u2 = 1, v2 = 1, w2 = 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between two lattice planes in any crystal","package":"materials-science-ai999x","example":"Angle between planes: a = 0.4 nm, b = 0.4 nm, c = 0.4 nm, alpha = 90, beta = 90, gamma = 90, h1 = 1, k1 = 1, l1 = 1, h2 = 1, k2 = 1, l2 = 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90","v":[0.07608,0.03864,-0.01998,0.02122,-0.01578,0.06368,-0.04538,-0.08387,-0.06666,0.01384,-0.07052,-0.0083,0.01068,0.04694,-0.1351,0.00658,-0.04141,0.00101,-0.05921,-0.04285,0.08005,-0.10528,-0.00643,0.10538,-0.03673,-0.01515,-0.02361,-0.05339,0.05527,0.05192,0.07068,0.04839,-0.02249,0.0764,0.07161,-0.02707,-0.00589,-0.07533,0.08641,-0.09185,0.00233,0.01088,-0.10582,0.07881,-0.0268,0.01544,-0.04355,-0.08732,-0.0805,0.0655,-0.06883,0.03617,0.14183,0.07571,-0.00224,0.01485,0.02545,0.0111,-0.05664,0.0339,-0.11412,-0.02585,-0.02275,-0.06224,0.0057,0.05509,0.05755,-0.02334,-0.0665,-0.07644,0.03804,-0.07245,0.19567,-0.21587,-0.03045,-0.0393,-0.01714,0.00389,0.02929,0.11101,-0.00947,0.03112,0.08007,-0.04595,-0.03543,0.08854,0.04237,0.00589,-0.03548,-0.00072,0.05971,-0.00974,0.01548,0.08291,0.04134,-0.05618,-0.10517,-0.01658,-0.04688,-0.00289,0.02456,-0.07315,0.06415,-0.08326,0.05527,-0.09928,-0.05602,0.02933,0.01891,0.03653,0.00193,-0.00627,0.04368,-0.0415,-0.02754,-0.0439,-0.0395,0.03378,0.0547,-0.08475,-0.0262,-0.12539,-0.02388,-0.1038,-0.0255,0.13825,-0.0446,0.03435,0.06559,-0.05456,0.06214,0.076,-0.07602,0.01721,-0.03387,0.01395,-0.08603,-0.04664,0.03551,-0.02604,0.10508,-0.04474,-0.01227,0.02531,-0.06072,-0.05666,0.05976,-0.02537,-0.03923,0.11516,-0.01944,0.10356,0.04468,-0.01922,0.06094,-0.02005,0.12371,-0.02097,0.11526,-0.09359,0.04643,-0.11276,-0.00772,-0.07109,0.00452,0.03813,0.1423,0.07751,0.02777,-0.05963,0.05688,-0.05607,-0.02389,0.01332,0.07009,0.07084,0.06747,-0.14239,0.02677,-0.05884,0.08391,0.09287,-0.10449,-0.00518,-0.05949,-0.00978,0.02259,0.05673,-0.06975,-0.06144,-0.08335,0.02833,-0.03067,0.00285,-0.06452,0.05631,0.01908,-0.0424,0.05099,-0.03869,-0.01885,-0.05263,-0.06435,-0.02269,-0.03855,-0.10751,0.03212,-0.05556,-0.05323,0.01159,-0.00468,0.00113,0.03985,0.07294,0.10408,0.01141,0.05342,0.00605,-0.02633,0.04563,0.06272,-0.09544,-0.04538,-0.00721,0.11552,0.10009,0.05958,0.00512,0.03644,0.04037,0.03278,0.04591,0.00221,0.00706,-0.09005,-0.07016,0.01662,0.07309,0.04029,-0.14332,0.10481,0.05231,-0.07601,-0.01416,-0.02673,0.00866,-0.03422,0.06395,0.12729,0.05521,-0.01997,0.06417,-0.03231,-0.00168,0.00396,0.01209]},{"domain":"materials_science","key":"avrami_kinetics","name":"Avrami 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0.4","v":[-0.08091,-0.0032,0.03862,0.00777,-0.07776,-0.04504,-0.03477,0.06606,-0.0426,0.02031,0.00362,-0.00149,0.06515,0.09069,-0.04098,0.05731,-0.038,0.00345,0.05914,0.0189,-0.02122,0.12857,-0.05349,0.04336,-0.00495,-0.02617,-0.08537,-0.0085,-0.01808,-0.02252,0.14079,-0.06921,-0.00443,0.06903,0.02354,-0.06264,0.01608,-0.10689,0.02297,0.14362,0.06372,0.04696,0.0225,-0.02396,-0.03335,-0.04592,-0.08053,-0.04328,-0.06094,-0.11448,-0.02575,0.03117,-0.04883,-0.03097,-0.07127,0.12028,-0.06719,-0.09835,0.01542,0.01172,0.09438,0.02482,0.04483,0.02724,-0.06548,-0.01511,0.08794,0.01493,0.06145,-0.07845,-0.03852,0.04309,0.04685,-0.01048,0.03412,-0.02555,0.01527,0.01396,0.06125,-0.04361,0.16657,0.04184,-0.08532,0.02911,0.12767,-0.03129,0.02425,-0.09956,0.01871,0.08438,-0.15587,0.02483,-0.05389,0.07549,-0.01125,-0.0149,-0.06826,-0.06257,0.00403,0.07404,0.01643,0.02858,0.08432,-0.01167,-0.02954,-0.02583,0.02766,0.0817,-0.07442,0.0316,0.0377,0.05765,0.01923,-0.00094,-0.06205,-0.07166,0.02251,-0.06465,0.04048,-0.04807,-0.18447,0.00582,-0.01806,0.08713,0.01177,0.06756,-0.00563,-0.017,-0.13938,0.03837,0.00697,0.04169,-0.01091,-0.03528,-0.03589,-0.02749,-0.05721,0.00376,-0.03019,-0.03465,0.05169,-0.02315,0.0273,-0.08731,-0.01992,0.10016,-0.01256,-0.00192,-0.12404,0.0902,0.06511,-0.03336,0.03923,-0.09002,-0.05174,-0.05493,0.04811,0.0489,0.04479,-0.05764,-0.04788,-0.09836,0.0583,-0.04396,0.05765,0.0543,-0.11894,0.04905,-0.0816,0.04611,-0.00881,-0.06804,0.0186,0.11727,-0.01689,0.01805,0.04609,0.0083,-0.03081,-0.10049,0.00529,-0.09871,-0.04743,0.00798,0.00121,0.01906,0.04945,0.04932,0.03949,-0.01505,0.12193,-0.00763,0.03867,0.01158,-0.10463,0.03159,0.05784,-0.04632,-0.04715,0.2136,-0.02577,-0.02473,0.10418,-0.04154,-0.07813,-0.14137,0.04033,0.00956,0.05593,-0.03552,0.03968,0.01292,0.00323,0.06673,0.05813,-0.05953,0.09142,0.0053,-0.02552,-0.12671,0.01986,-0.06782,0.02193,-0.00474,0.08971,0.02905,0.16727,0.07871,-0.02647,-0.07993,0.01342,-0.01731,-0.0821,0.00448,0.1073,-0.03377,-0.07311,-0.07778,-0.03156,0.12425,-0.01677,-0.03631,0.05308,-0.03834,0.1008,0.00403,0.00733,0.03681,-0.0462,0.05983,0.05591,-0.09078,0.01477,-0.05453,0.00461,0.05128]},{"domain":"materials_science","key":"copolymer_degree_of_polymerization","name":"Average repeat-unit weight and degree of polymerization of a copolymer","package":"materials-science-ai999x","example":"Copolymer degree of polymerization: formula1 = C4H6, formula2 = C8H8, f1 = 0.75, Mn = 350000 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2.5e-6]","v":[-0.1686,-0.10323,-0.00354,-0.0181,-0.03141,-0.05242,-0.1427,-0.01777,-0.07348,-0.06499,-0.14541,-0.02407,0.03922,-0.04476,-0.00551,-0.04485,0.01222,0.01959,-0.06489,-0.08555,-0.03212,0.10738,0.03623,0.04836,-0.05006,0.04634,0.00495,-0.04222,-0.08302,0.05066,-0.02723,-0.03845,-0.02678,0.05623,0.01276,0.03837,-0.01122,-0.01391,0.00139,-0.03808,0.07204,0.03021,-0.13425,0.00607,-0.042,0.06773,-0.04378,0.02618,0.0409,-0.04879,0.04364,0.06083,0.02019,0.11151,-0.01349,0.08271,0.01359,0.05597,0.0607,0.00897,0.04515,0.00966,-0.00768,0.08662,-0.05122,0.05434,0.02532,0.04913,-0.08288,-0.02053,-0.03833,0.00324,-0.05777,-0.11855,-0.01199,-0.03938,-0.05693,0.03154,0.02118,-0.03657,-0.03845,-0.07687,-0.04729,-0.0838,-0.02111,-0.05402,-0.05259,0.04072,-0.01475,-0.00241,0.04837,0.0917,0.08737,-0.01749,0.02548,-0.05009,-0.05561,0.06867,0.11275,-0.02694,0.03269,0.19549,0.08218,0.04299,0.11219,0.02507,0.11456,-0.02368,0.05292,0.02535,0.06196,0.0159,-0.02349,0.0258,0.00604,-0.08822,-0.02866,0.05238,-0.04827,-0.04214,-0.00244,0.0389,-0.05004,-0.02779,0.01879,0.01328,-0.04928,0.05478,-0.09316,-0.04415,-0.00451,-0.16374,-0.09094,0.02687,-0.00209,0.04646,-0.0454,0.00205,0.01088,-0.05479,-0.0163,0.0649,0.02418,0.0431,-0.03843,-0.00951,-0.04189,0.05067,-0.02688,0.06666,-0.01078,0.00198,-0.10789,0.05355,-0.09655,-0.04516,-0.07378,0.03174,0.03522,0.11149,-0.02144,-0.06521,0.04056,0.07011,-0.11336,0.02453,-0.10362,-0.00518,-0.02943,-0.00087,0.02321,0.08024,-0.05866,-0.05353,-0.01477,0.02169,0.01239,0.17386,0.00761,-0.00491,-0.09603,0.09587,-0.10802,-0.05645,0.04519,0.09638,-0.11735,0.00098,-0.12284,0.1446,-0.02065,-0.001,0.00528,-0.00059,-0.03355,0.10352,-0.00807,0.04328,0.00148,0.02268,0.01826,0.02448,0.04222,-0.13771,-0.11642,0.03813,-0.04058,-0.02046,0.04394,0.03479,0.04346,-0.04323,-0.0249,-0.05914,0.11393,0.05627,-0.0315,-0.09944,0.01565,0.15324,-0.0136,-0.07356,0.08049,0.07264,0.00658,0.00727,0.09499,0.08451,-0.00227,0.07607,-0.02668,-0.07795,0.08121,0.09123,-0.067,0.05391,0.09104,0.11931,-0.03272,0.06561,-0.04349,-0.03811,0.00942,-0.02437,-0.07253,0.10836,0.02514,-0.00952,0.00299,0.08697,-0.06461,-0.03856,-0.02296,0.06737,-0.01413,-0.03315]},{"domain":"materials_science","key":"critical_crack_length","name":"Critical 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fibre length","package":"materials-science-ai999x","example":"Critical fiber length: sigma_f = 3.5 GPa, d = 10 um, tau_c = 20 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parameter from the atomic radius","package":"materials-science-ai999x","example":"Lattice parameter from atomic radius: structure = FCC, R = 0.1278 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angle of a cubic (h k l) reflection","package":"materials-science-ai999x","example":"Cubic reflection angle: a = 0.3615 nm, h = 1, k = 1, l = 1, lambda = 0.1542 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1","v":[0.04434,0.03576,0.00409,0.02085,0.06381,0.02403,0.02949,-0.06695,0.01959,0.02243,0.01139,-0.1051,0.0078,0.14574,-0.06132,0.05868,0.11403,0.01061,-0.04127,0.04257,0.11503,0.06737,-0.01561,-0.08425,0.07637,-0.02209,-0.00962,-0.03935,-0.05826,0.03548,-0.09202,0.13266,-0.00713,0.01638,0.01862,0.03659,-0.01512,0.04767,-0.04843,0.00085,0.02428,-0.07974,-0.04826,-0.10583,-0.07127,-0.04756,-0.08524,-0.07379,-0.15622,-0.09504,0.1,-0.02919,-0.07921,0.03838,-0.10853,0.04945,0.07838,-0.00467,-0.03746,-0.01983,0.04435,-0.00926,-0.03974,0.0288,-0.10344,-0.04829,-0.04591,-0.03169,-0.05049,-0.04931,-0.07873,-0.00143,-0.02833,-0.12415,-0.00767,-0.02276,-0.0808,0.04809,-0.04669,-0.01622,0.07922,0.00279,-0.03153,0.01402,-0.00164,0.03062,-0.11355,0.01359,0.03559,-0.0508,-0.00907,0.05853,-0.01503,-0.00272,0.05763,-0.08686,-0.04712,0.02862,0.05898,-0.05703,-0.07935,-0.00923,0.05624,0.02014,0.0492,0.08939,0.06473,-0.04156,-0.05298,0.03426,0.10319,-0.06655,-0.02311,0.12829,0.0307,0.07848,-0.02294,0.05353,-0.04967,0.0834,-0.05451,0.05218,0.08153,0.00772,-0.09306,0.05237,-0.06655,0.07979,-0.03224,-0.05913,-0.05343,0.0663,0.06577,-0.08447,0.00348,0.01523,-0.02933,0.03386,0.03537,0.09221,0.07585,-0.07031,0.09266,-0.03949,0.07649,-0.07735,-0.08805,0.04413,0.06001,0.01464,-0.04316,-0.11076,0.07609,0.06449,0.01249,-0.07613,0.03277,-0.02609,0.04361,-0.1058,0.07218,0.12135,0.12591,0.00554,0.00239,-0.09172,-0.03537,-0.0635,-0.01756,0.0708,0.02869,-0.13189,-0.00727,-0.04688,-0.08598,-0.0178,0.06169,0.14193,-0.02839,-0.01214,0.03473,-0.04763,-0.12886,0.13411,0.0833,-0.05875,0.11708,-0.0189,0.01769,0.08988,0.02045,-0.04437,-0.02078,-0.0451,0.07043,-0.01723,4e-05,0.10561,-0.02225,-0.0299,0.06215,0.03869,-0.00401,-0.13523,0.01049,0.00828,0.04283,0.04693,0.01546,-0.00115,-0.02746,-0.11072,0.0314,-0.0733,0.05698,0.06222,0.04963,0.02063,0.01291,0.03054,-0.03014,-0.0264,-0.0299,0.05864,0.02314,-0.05098,0.09432,-0.00098,-0.06839,-0.10106,0.08938,0.03067,-0.05042,3e-05,0.17983,0.09178,-0.01529,0.02495,-0.00073,-0.00203,0.06037,0.00817,-0.0011,0.03025,-0.04033,-0.04099,-0.05816,-0.05709,-0.01519,0.00691,-0.0663,0.08563,0.05968,0.03014,-0.01696,0.11655]},{"domain":"materials_science","key":"d_spacing_orthorhombic","name":"Interplanar spacing in an orthorhombic crystal","package":"materials-science-ai999x","example":"Orthorhombic interplanar spacing: a = 0.4 nm, b = 0.5 nm, c = 0.6 nm, h = 1, k = 1, l = 0","v":[0.02409,-0.09673,0.01212,-0.03678,0.11514,-0.01326,0.03257,0.01938,0.09549,0.10873,0.04345,-0.06084,-0.05519,0.14171,-0.02207,0.05318,0.06533,0.04038,-0.01253,-0.06353,0.07284,-0.11206,-0.00334,-0.07011,-0.00552,-0.021,0.072,0.0317,-0.02294,-0.0042,0.02017,0.09656,0.11302,-0.03209,-0.06519,0.07063,0.0995,0.04449,-0.04457,0.01944,0.03984,-0.08289,0.00664,-0.05386,-0.05426,-0.08918,-0.09089,-0.07247,-0.06906,-0.04786,-0.01476,-0.00546,-0.01798,0.0521,-0.01666,-0.0715,0.08952,0.03334,0.09419,0.06109,0.03644,-0.06839,0.03219,-0.04954,-0.06646,-0.03332,-0.03608,-0.06615,-0.04922,-0.05968,0.02571,-0.04251,0.00435,-0.10888,-0.03332,0.01857,0.1386,0.01069,0.08317,0.02603,0.05435,-0.0585,-0.08535,0.00028,0.04818,0.02978,-0.01436,-0.02788,-0.01146,0.0106,0.01212,0.0525,-0.03232,0.05116,-0.05561,0.00547,0.03518,0.06292,0.07174,-0.01937,-7e-05,0.04879,0.02595,-0.08228,-0.08716,-0.0317,-0.08887,0.00967,-0.01689,0.00811,0.04739,-0.0228,0.0484,0.10169,0.03248,0.01464,-0.05063,0.10839,-0.01366,0.03842,0.06761,0.12924,0.03669,0.07504,-0.04346,-0.09017,-0.07174,-0.01931,-0.05522,0.03658,-0.00594,0.10619,0.14091,-0.13162,0.01641,-0.02373,-0.06143,-0.03224,0.01567,0.05349,0.07359,-0.08349,0.12225,0.04735,-0.00336,-0.03397,-0.11909,-0.02626,0.11424,-0.02633,-0.04437,-0.05604,-0.00752,0.00541,0.01135,-0.00194,0.02754,-0.02806,0.08678,-0.04028,0.06009,0.06549,0.08673,-0.00076,-0.02391,-0.01716,0.07284,-0.08551,-0.00047,-0.01579,-0.04041,-0.10153,-0.02629,0.03658,-0.0325,-0.01583,0.01768,0.05359,-0.00171,-0.09846,0.15026,0.04861,0.00488,0.12884,0.07112,-0.11654,0.03465,0.03606,-0.04693,-0.00919,0.11978,-0.03958,0.0418,-0.0961,0.02556,0.00989,-0.03178,0.14589,-0.0319,-0.0593,0.04759,-0.00961,-0.05403,-0.03493,-0.08877,-0.0074,0.06472,0.03264,-0.04613,-0.01117,-0.10653,-0.16519,0.02295,-0.07043,0.06176,0.06568,-0.08189,0.06731,-0.08405,-0.0228,0.09231,-0.03358,0.06422,0.1038,0.00653,-0.02452,-0.04096,0.01374,-0.04058,0.00731,-0.08098,0.08374,-0.02154,-0.0601,0.05239,0.09874,0.01042,-0.02014,-0.06489,0.04511,0.02983,-0.0247,0.00196,-0.03978,-0.02417,-0.11282,0.00642,-0.10213,0.02394,0.08246,0.02019,0.06106,0.16464,0.05049,-0.08617,-0.03547]},{"domain":"materials_science","key":"d_spacing_tetragonal","name":"Interplanar spacing in a tetragonal crystal","package":"materials-science-ai999x","example":"Tetragonal interplanar spacing: a = 0.3 nm, c = 0.5 nm, h = 1, k = 0, l = 1","v":[-0.02878,-0.0889,0.10684,0.01727,0.03914,0.05686,0.01693,-0.00805,0.13232,0.03943,0.08071,-0.06874,0.01953,0.05054,-0.0234,-0.02543,0.07203,-0.03224,-0.00103,-0.04929,0.10399,-0.01415,-0.02683,-0.14369,-0.00395,-0.01151,0.05687,0.04626,0.00297,-0.00645,-0.03582,0.09621,0.06145,-0.08739,0.00401,0.09252,-0.00635,-0.00962,-0.02891,0.06726,-0.00372,-0.06213,0.02226,-0.02709,-0.1096,-0.07964,-0.14512,0.01659,-0.14563,-0.04855,-0.0233,0.05947,-0.044,0.0185,-0.01039,0.03941,0.045,0.03751,0.00477,0.05151,0.0401,-0.0799,0.00566,-0.06474,-0.09,-0.03394,-0.01437,-0.05049,-0.03709,-0.0526,0.00527,0.04217,-0.005,-0.07591,-0.04571,-0.06838,-0.03703,0.01601,-0.01765,0.05053,0.0182,-0.15073,0.02198,-0.0376,-0.05518,0.0303,-0.16643,-0.0489,-0.00376,-0.02009,0.03337,0.11779,-0.08812,0.00179,0.01329,-0.08241,-0.03867,0.01472,0.02108,-0.06871,-0.03203,-0.03541,0.01639,0.07363,0.01401,0.11017,0.07053,-0.05201,0.06227,0.06214,0.12684,-0.10793,-0.07573,0.0476,0.06332,0.04601,-0.03401,0.03472,-0.0155,0.10626,-0.04696,0.13597,0.08552,0.02783,0.04985,0.00324,-0.05857,-0.01516,-0.02482,-0.04655,-0.02798,0.09522,0.04811,-0.01508,-0.00882,0.00306,0.08433,-0.02698,-0.00267,0.0897,-0.01785,-0.07853,0.06651,0.0207,0.02807,0.00288,-0.09645,0.12151,0.12537,-0.05347,-0.03409,0.05003,0.03564,0.11538,-0.02407,-0.03721,0.00691,-0.06976,-0.03445,-0.06601,0.03346,0.08476,0.05088,0.06405,-0.04465,-0.02103,-0.03185,-0.08842,-0.0072,0.02194,-0.00387,-0.08016,-0.02571,-0.07649,-0.06427,-0.01832,-0.01448,0.01958,-0.04085,0.05173,0.088,-0.03281,-0.01435,0.05047,0.04973,-0.00706,0.14596,0.0022,0.03881,0.02697,0.01017,0.03349,-0.08879,0.02648,0.03238,0.05556,-0.02009,0.14799,0.0304,-0.0288,0.04486,0.03336,-0.03865,-0.20855,-0.01791,0.06988,0.01053,-0.00481,0.01453,-0.02093,-0.01249,-0.09095,-0.02128,-0.11773,0.08475,-0.02191,-0.04456,0.06454,0.06076,-0.06044,-0.01783,-0.04984,0.06215,0.06691,0.0395,-0.07023,-0.02075,-0.07971,-0.08282,0.04539,0.03634,-0.10225,-0.08883,-0.01107,0.11703,0.15162,0.03526,-0.10449,0.06816,0.04095,0.04999,0.04383,0.08687,-0.00934,-0.11865,-0.00794,-0.06285,-0.07235,0.0514,0.03526,0.02797,0.06949,8e-05,0.05366,-0.09843,0.0104]},{"domain":"materials_science","key":"d_spacing_triclinic","name":"Interplanar spacing in a general (triclinic) lattice","package":"materials-science-ai999x","example":"Triclinic interplanar spacing: a = 0.5 nm, b = 0.5 nm, c = 0.7 nm, alpha = 90, beta = 90, gamma = 120, h = 1, k = 0, l = 0","v":[0.02138,-0.04929,0.0864,0.06774,-0.03982,0.10202,0.01648,-0.01531,0.09958,0.06539,0.05544,-0.03317,0.03339,0.14864,-0.03251,0.03143,0.08188,0.03843,-0.00363,-0.00361,0.15559,0.04567,0.0271,-0.04794,0.04947,-0.05882,0.02367,0.06737,-0.01803,0.00386,-0.05851,0.08213,-0.01057,-0.00803,-0.00074,0.06975,0.03161,0.03755,-0.06924,0.14786,0.03024,-0.04125,0.0257,-0.03068,-0.03088,-0.07614,-0.06143,-0.04734,-0.15756,-0.00858,0.07901,0.02057,-0.08772,0.01912,-0.0614,0.07104,0.09689,0.03357,-0.0321,0.0207,0.02929,0.00036,-0.01833,-0.06703,0.05132,-0.03452,-0.00714,-0.035,-0.15975,-0.12015,-0.02742,0.03832,0.1256,-0.12432,-0.07521,0.03741,0.08191,0.00866,-0.00466,0.07005,0.10639,-0.05755,-0.02288,0.04457,-0.03076,0.00136,-0.05568,0.05901,-0.03164,0.01367,-0.01044,-0.00167,-0.01519,-0.00897,0.04982,-0.05154,-0.06061,0.02884,0.0251,-0.05879,-0.02912,-0.00326,0.04739,-0.03227,0.02064,0.03915,0.03056,-0.05197,-0.03555,-0.02916,0.08666,-0.04143,-0.15592,-0.00312,0.1004,0.02787,-0.08103,0.09143,-0.02755,0.07765,-0.02679,0.08428,0.10298,0.07403,-0.10108,0.06912,-0.14238,0.04017,-0.02787,-0.10035,-0.10335,0.02012,0.13571,-0.09173,-0.09389,-0.0466,0.00124,-0.00681,0.06372,-0.03216,0.06808,-0.06632,-0.0379,-0.03248,0.01123,-0.08191,-0.06567,0.04965,0.05561,0.03862,0.06431,-0.04382,0.0217,0.01217,0.04412,-0.01113,0.06876,-0.08345,0.15662,-0.03731,0.04336,0.06905,0.02443,0.11727,0.04298,-0.06305,0.00312,-0.03919,-0.08984,0.0378,0.03875,-0.09227,0.01953,-0.02062,-0.00079,0.02071,0.00314,-0.0106,-0.06598,-0.04841,-0.0072,-0.03184,0.00394,0.11921,0.10079,0.01507,0.09234,-0.10694,0.04063,-0.04352,-0.01812,0.00828,0.01034,0.00327,0.06027,0.08706,-0.06152,0.10754,0.05343,-0.07069,0.03664,0.03364,-0.02886,-0.14684,-0.02195,-0.0281,0.06438,0.06216,0.02133,-0.03532,0.01676,-0.12066,-0.11145,0.01893,0.00122,0.08185,0.02737,-0.0573,0.00759,0.01298,-0.02594,-0.12302,-0.00907,0.09489,-0.0012,-0.06641,0.03435,0.02616,0.07923,0.03323,-0.0109,0.016,-0.08433,-0.09841,-0.01633,0.07264,0.03599,-0.01667,-0.00051,-0.02956,0.07475,-0.02016,0.03996,-0.02302,-0.08999,-0.02893,-0.10093,-0.07202,-0.00059,0.00524,-0.03432,-0.00518,0.0412,0.06342,-0.13441,0.00588]},{"domain":"materials_science","key":"debye_heat_capacity","name":"Molar heat capacity of a solid (Debye model)","package":"materials-science-ai999x","example":"Debye heat capacity: theta_D = 343 K, T = 1000000 K","v":[-0.1401,0.01452,-0.02555,-0.00133,0.00739,-0.03069,0.00907,-0.00524,0.04987,0.01791,0.05748,-0.02381,0.04305,-0.00133,-0.04523,0.0464,0.05334,-0.12541,-0.0842,0.0213,0.10152,-0.04487,-0.09589,0.06179,0.00781,-0.08309,0.05427,0.04312,0.07146,-0.03377,-0.00541,0.03248,-0.00027,-0.00193,-0.01743,0.00578,0.01605,-0.08346,-0.00919,-0.09522,0.02609,-0.05579,0.11591,-0.04239,-0.07534,-0.06721,-0.03025,0.01787,0.08592,0.03239,-0.05822,-0.00939,0.02637,-0.00896,0.02758,0.01109,0.00971,-0.01488,0.03038,0.03106,-0.03194,-0.03861,0.02725,0.04607,0.04207,-0.10045,-0.04658,-0.04241,-0.1445,0.0464,0.08497,0.05309,0.02888,0.05416,0.14571,0.01882,-0.10808,-0.06332,0.01224,0.00772,-0.06479,0.03965,-0.04548,-0.03132,0.09832,0.04421,-0.02851,-0.00472,0.05238,-0.01749,0.09278,-0.03901,0.02561,0.06787,-0.06814,-0.05076,-0.12415,-0.00345,0.13904,-0.08602,0.03223,-0.00424,0.10207,-0.00361,-0.13416,0.0743,0.06946,0.13933,0.01023,0.23272,0.02916,-0.01191,-0.06074,0.04626,-0.03205,0.05941,-0.03531,-0.07105,-0.00706,0.02154,0.05818,-0.09278,0.05839,-0.07182,0.066,-0.09997,-0.01563,-0.02355,-0.06178,-0.04401,0.04471,0.06022,0.02548,0.00477,0.02069,-0.01048,-0.0314,-0.09755,-0.01627,0.02939,0.00794,-0.05019,0.05235,-0.06725,-0.03265,0.02939,0.00579,-0.05483,-0.10802,-0.0536,-0.00507,-0.04434,0.04495,-0.06581,-0.11671,0.01636,-0.00612,-0.02878,0.02657,-0.06388,0.00943,-0.16225,-0.01552,-0.00733,-0.0497,0.04774,-0.05552,-0.1624,0.0994,-0.06867,0.08043,-0.02296,-0.0477,-0.08361,-0.10804,-0.04136,-0.02353,-0.02632,0.01865,0.01564,0.16503,0.09422,-0.01095,0.07028,-0.0318,-0.12229,-0.00097,0.01215,-0.00321,-0.04743,0.03289,0.03403,-0.04578,0.10087,-0.02309,0.01531,-0.00334,0.14658,0.02188,-0.0254,-0.04015,-0.10715,0.04114,0.01419,0.0027,0.00664,0.01119,0.01881,0.04703,-0.08104,-0.02054,0.01437,-0.00744,-0.00259,0.14871,0.03543,0.00398,-0.05111,-0.00788,0.07317,-0.0809,0.07412,0.05999,-0.03973,0.06057,-0.00756,0.13022,-0.02139,-0.06264,0.05939,0.00526,-0.02594,0.08835,0.00997,-0.01106,0.05383,-0.01313,0.08889,-0.06612,0.04232,-0.03559,0.06029,-0.02329,-0.00454,0.14343,0.03858,0.0501,0.12451,0.01668,0.03849,0.02112,-0.02258,0.02166,0.03236,-0.00517,-0.128]},{"domain":"materials_science","key":"degree_of_polymerization","name":"Repeat-unit molecular weight and degree of polymerization","package":"materials-science-ai999x","example":"Degree of polymerization: formula = C2H3Cl, Mn = 106000 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diffusion flux (Fick's first law)","package":"materials-science-ai999x","example":"Fick's first law: D = 3e-11 m^2/s, C1 = 1.2 kg/m^3, C2 = 0.8 kg/m^3, x1 = 5 mm, x2 = 10 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in a semi-infinite solid (Fick's second law)","package":"materials-science-ai999x","example":"Fick's second law: C0 = 0.25 wt%, Cs = 1.2 wt%, x = 0.5 mm, D = 1.6e-11 m^2/s, t = 7 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25","v":[-0.0309,-0.05254,0.11053,0.01882,0.01621,0.01815,-0.06776,-0.01697,-0.00421,-0.04605,-0.06666,0.03945,-0.00625,0.0366,-0.0707,-0.04464,0.01313,-0.03336,-0.09215,0.04515,0.07062,0.04992,0.07169,0.09744,-0.00652,0.02789,-0.00961,-0.02013,0.03129,0.10859,-0.06553,-0.01798,0.00374,0.00884,-0.06047,-0.06096,-0.03624,-0.02253,0.02689,-0.10897,0.08383,0.15911,-0.05675,-0.01379,0.08669,-0.02832,0.00192,-0.02181,0.04188,0.0347,-0.03082,0.04793,0.03999,0.11172,-0.09593,0.05788,-0.03867,0.05861,0.01356,0.09761,-0.02863,0.07144,-0.07312,-0.02524,-0.02278,-0.0053,-0.14289,-0.0321,0.05913,-0.00892,0.1108,-0.09299,0.02697,-0.04149,0.02376,-0.00339,-0.06811,0.07579,-0.08715,-0.01004,0.03557,0.0275,-0.06441,-0.00042,-0.01576,0.12776,0.08493,0.10376,-0.02073,0.04838,-0.04915,0.06759,0.03356,0.1551,0.06683,-0.08396,0.03813,0.13685,-0.00567,-0.00818,0.05047,0.07843,0.02769,0.13899,-0.03957,0.04652,0.09276,0.03338,-0.02152,0.09147,-0.05537,0.01363,-0.07584,0.05101,0.01427,-0.02876,0.00436,0.00582,0.09494,-0.06749,0.02128,0.00901,0.01783,-0.03562,0.00439,-0.15722,-0.10422,0.04716,0.01361,-0.08951,-0.06588,0.03189,-0.03984,-0.08597,-0.0168,0.0187,0.0327,-0.01971,-0.00402,0.02363,0.01749,-0.07058,0.03792,0.08252,0.01466,-0.10827,0.0249,0.06502,0.12369,0.0471,0.07716,0.0134,-0.06845,0.13604,-0.03806,-0.04349,0.07078,-0.03834,-0.02556,-0.00763,-0.07596,0.04869,-0.01466,-0.02483,-0.06195,-0.03398,-0.03524,0.04649,-0.111,-0.00093,-0.01477,-0.10937,-0.0485,-0.10989,0.06881,-0.05694,0.04859,0.00733,0.05934,-0.1324,-0.00145,0.03901,0.0206,0.05453,0.03644,-0.00776,0.0681,0.00326,-0.06783,-0.03835,-0.00376,-0.0615,0.0229,0.01834,0.01448,-0.00074,-0.08136,0.01608,-0.02844,-0.10482,0.01797,0.06446,-0.06614,-0.12914,0.02523,-0.11975,-0.00873,-0.04901,0.00536,-0.03789,0.06643,-0.01248,0.06793,-0.03082,-0.09126,-0.00168,-0.09514,-0.02269,-0.00994,0.06282,-0.14548,-7e-05,0.03379,-0.07532,0.04306,0.04631,0.06934,0.03808,-0.00691,0.14785,-0.08241,0.05246,0.0612,-0.10732,0.01414,0.04505,0.10739,0.04113,0.01222,0.04564,0.01044,0.00211,-0.13003,0.0585,-0.07626,0.10503,-0.06029,0.00074,-0.03339,0.12879,-0.08149,-0.04972,-0.00914,-0.01173,0.02962,0.04202]},{"domain":"materials_science","key":"hcp_cell_density","name":"Volume 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modulus, bulk modulus and Lame constant from E and Poisson's ratio","package":"materials-science-ai999x","example":"Elastic constants: E = 200 GPa, nu = 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strain of a Kelvin-Voigt viscoelastic solid","package":"materials-science-ai999x","example":"Kelvin-Voigt creep: sigma0 = 5 MPa, E = 500 MPa, eta = 1e11 Pa*s, t = 200 s","v":[0.05083,-0.04764,0.00919,-0.03199,-0.10638,-0.05886,0.02556,-0.00194,-0.00914,-0.0074,-0.03136,0.02391,0.04483,0.01616,0.06362,-0.05398,-0.03769,-0.05548,-0.10623,0.05907,0.02198,0.08066,-0.03299,0.10551,0.01668,0.01166,-0.01729,0.01823,0.1276,-0.05545,0.0733,-0.02348,-0.06914,0.0399,0.01531,-0.08162,0.01715,-0.03043,-0.04762,-0.01164,0.05929,0.05271,-0.12212,-0.08775,-0.05187,0.05845,0.04575,0.02058,-0.04492,-0.01983,-0.05587,-0.00071,0.01055,-0.00625,-0.02803,0.09139,-0.12888,0.03,0.0769,-0.01928,0.05042,0.03778,0.01567,0.06505,-0.05793,0.00505,0.00075,-0.02762,-0.09322,-0.0371,0.03876,-0.04817,0.01378,-0.0539,0.13314,-0.05131,-0.05184,-0.01853,-0.06414,-0.11475,0.00765,0.07736,-0.03733,-0.05463,0.01679,0.02709,-0.03823,0.04956,0.08634,0.05178,-0.06503,0.06327,0.07411,-0.01013,0.03718,-0.05965,-0.00246,-0.01537,-0.00883,-0.01743,0.03061,0.07493,0.05526,0.10826,0.0406,0.12944,0.12467,-0.08579,-0.02542,-0.03047,0.10932,0.02458,-0.09736,0.03759,-0.02855,-0.05122,-0.00571,-0.0134,-0.02788,-0.00646,-0.05706,-0.03539,-0.002,0.01018,-0.01807,-0.0693,-0.03967,0.05578,-0.13277,-0.01442,0.11988,-0.05004,-0.02627,-0.0157,-0.06677,-0.02326,0.04754,0.02427,0.03073,0.02805,0.02498,0.02452,0.05508,-0.06916,-0.00806,-0.03526,-0.05602,0.07081,-0.1187,0.15622,0.01393,-0.04352,0.01419,-0.02955,-0.13397,-0.03456,0.00574,-0.05625,0.01362,-0.1447,-0.12392,-0.09274,0.06827,0.09862,-0.13169,0.00817,-0.08803,0.0101,-0.04647,-0.00188,0.02187,0.00021,-0.05409,0.02251,0.07272,-0.0007,-0.03154,0.09691,0.10321,-0.08249,0.01864,-0.02719,-0.02651,-0.03389,0.07229,0.03753,-0.02314,-0.00631,-0.03964,0.07832,0.03053,-0.13355,-0.00825,0.02252,-0.03363,0.05216,0.06089,0.0034,0.01625,0.16218,-0.04617,0.01199,0.06446,-0.0701,-0.02244,-0.10495,0.0193,-0.11089,0.09303,-0.02407,0.09073,-0.00618,0.01943,0.00622,0.08565,-0.02333,0.00171,0.00206,-0.06216,0.04128,-0.02145,-0.02733,0.11975,-0.00238,0.08411,-0.05394,0.17295,-0.05889,0.05091,0.07906,-0.02864,-0.13202,0.12726,0.0183,-0.01899,0.01047,-0.04448,0.06332,0.00122,0.08823,0.05083,-0.04551,0.06742,0.00063,0.11815,-0.02435,0.03335,-0.01233,0.09483,0.13794,0.06874,-0.1216,-0.02983,-0.07007,-0.05153,-0.02121]},{"domain":"materials_science","key":"larson_miller_parameter","name":"Larson-Miller parameter (creep rupture)","package":"materials-science-ai999x","example":"Larson-Miller parameter: T = 1073 K, t_r = 1000 h","v":[-0.05567,-0.03704,-0.00557,0.00598,-0.09393,-0.03457,0.03965,0.00034,0.01426,0.00907,-0.06358,-0.0483,0.04722,0.12129,-0.04777,0.05537,-0.00254,0.03632,-0.08485,-0.06678,-0.0061,-0.03137,-0.1192,0.05322,0.04922,0.03956,0.00382,-0.06268,0.09259,0.01895,0.00065,0.00985,-0.0106,0.00424,-0.04639,0.02753,0.00053,0.05286,-0.05594,-0.04435,0.01105,-0.08141,0.04539,0.02254,-0.00357,-0.06103,0.02115,-0.00933,-0.02746,-0.14562,-0.12672,-0.0234,-0.03802,0.04445,-0.00222,0.01005,-0.04324,0.02503,0.01837,0.04512,0.06154,0.07972,0.01098,-0.00771,-0.04974,-0.05953,-0.15577,0.06715,0.00864,-0.00182,-0.05529,0.00923,-0.04529,-0.19783,0.0225,-0.09083,0.01391,0.00023,-0.07091,0.0145,-0.0043,-0.02363,0.00728,0.01316,0.08441,0.04335,-0.02188,-0.02676,-0.04062,0.02208,-0.00811,0.13851,-0.07067,0.02264,0.033,-0.05695,0.0037,0.0185,-0.03216,-0.00174,0.03616,0.04031,-0.12557,-0.02488,-0.08036,0.00863,-0.11442,0.08866,-0.01117,-0.04221,0.00348,-0.04626,-0.00493,-0.00243,0.01277,0.00336,0.03523,0.10373,-0.05529,0.086,-0.05679,-0.04557,0.0637,-0.02235,-0.01624,0.00869,0.07675,0.06896,0.0087,0.0495,0.06393,0.00607,-0.01104,-0.03409,0.00161,-0.08757,0.00861,-0.04827,0.05604,0.07766,0.06699,-0.02053,0.2713,-0.0023,-0.18122,-0.02421,-0.05236,0.05179,-0.00265,0.10531,0.07706,-0.16208,0.0084,0.02757,-0.10957,0.01232,-0.03042,0.04177,-0.02067,-0.06709,-0.11019,0.03754,0.03357,0.06131,-0.05854,0.00796,0.05856,-0.04913,0.03688,0.05886,0.03999,-0.01952,-0.0479,-0.03084,-0.04183,-0.04081,0.08362,0.0709,0.06566,0.03876,-0.0092,0.06092,0.05216,0.0587,0.09416,0.04585,-0.05457,0.17532,-0.11662,0.12539,-0.0494,-0.07267,0.0518,0.0141,-0.00643,-0.02397,-0.01615,0.05025,0.04019,0.14906,0.04226,0.03629,0.01017,-0.00327,0.03861,-0.08552,0.04013,0.05812,-0.02745,-0.04351,0.00137,-0.04868,0.04608,-0.06743,0.05112,0.01076,0.0152,-0.00269,-0.06848,0.05362,0.07141,-0.04466,0.00893,-0.05426,-0.08915,-0.03583,0.20149,-0.02702,-0.01226,-0.06282,0.03418,-0.10585,0.09152,-0.11459,0.03827,0.04165,-0.00718,0.07765,-0.04072,0.07276,-0.01734,-0.01517,-0.01431,0.02284,0.056,0.03069,-0.03904,-0.00643,-0.01964,0.07045,0.00407,0.07515,0.12616,0.0694,-0.08254,-0.06953]},{"domain":"materials_science","key":"lattice_parameter_from_density","name":"Lattice parameter and atomic radius from the density","package":"materials-science-ai999x","example":"Lattice parameter from density: structure = FCC, rho = 8.96 g/cm^3, A = 63.55 g/mol","v":[-0.06596,-0.1471,-0.0121,0.00668,0.12216,0.00806,0.02684,-0.02717,0.12381,0.02578,0.0086,-0.06792,0.07409,0.10949,-0.07248,0.05965,0.0983,-0.00825,0.00758,0.04997,0.19111,-0.04026,0.00256,0.11304,0.05237,-0.0866,0.04187,0.00393,-0.01029,-0.04435,-0.00188,0.0277,-0.03734,-0.08453,0.08467,-0.03264,0.17182,-0.00162,0.02717,-0.06254,0.05315,0.0326,0.00015,-0.04937,0.05349,0.06108,-0.14697,0.00123,-0.0979,-0.09287,-0.01738,0.04019,0.02154,0.06773,-0.08803,0.00592,0.06059,-0.01446,0.0606,0.09972,0.01543,-0.00255,0.049,0.0083,0.0655,-0.02114,-0.00396,-0.01915,-0.11716,-0.0669,-0.07717,0.01314,-0.06694,-0.13122,0.03226,0.02092,0.03922,-0.05825,-0.07751,0.11908,0.00636,0.00685,0.02288,-0.01476,0.04047,-0.01658,0.00186,0.03835,0.00803,-0.07678,0.05911,0.03156,-0.02064,0.04995,-0.03129,-0.05422,-0.21173,0.08054,0.04516,-0.01146,0.0607,-0.05483,-0.00066,0.00103,0.00799,0.07365,0.0073,0.0499,0.02088,-0.00571,-0.02121,-0.06183,-0.06957,0.04845,-0.04899,-0.02214,0.02784,0.10699,0.00415,0.02042,0.01961,-0.06974,0.0234,0.0034,-0.10709,-0.08244,-0.08829,0.03347,0.00774,-0.06465,-0.01463,0.13513,0.10366,-0.01679,-0.01466,0.07655,-0.04949,-0.0917,-0.02569,-0.02351,0.07938,-0.01909,0.17096,-0.02546,-0.0222,-0.00858,0.06391,0.05148,0.01665,0.00784,0.06806,0.0004,0.04615,-0.05315,-0.0092,-0.01234,0.0162,-0.03424,0.02359,0.01782,0.04324,-0.04587,0.07084,-0.03658,0.0467,-0.00643,0.12402,0.00104,-0.05513,-0.05906,-0.02671,-0.08293,-0.08117,-0.05998,-0.09922,0.09688,0.04606,0.02804,0.00137,0.02397,0.12151,0.16268,0.0093,0.10941,0.02565,-0.06204,-0.0106,0.0088,-0.05214,-0.04329,-0.06349,0.03021,0.01516,-0.03119,0.0632,0.03455,0.05464,0.04078,0.01901,-0.08752,-0.05072,0.03392,-0.07831,-0.04266,-0.01344,-0.09999,0.05205,0.02377,-0.01064,-0.0052,-0.02345,-0.10345,0.04949,-0.05699,-0.05091,0.02665,-0.07309,-0.0093,0.02974,0.00684,0.03837,0.00465,-0.02829,0.05974,0.10529,-0.05046,0.07862,-0.02471,-0.1303,0.03474,0.00525,0.10732,-0.00582,-0.07926,-0.11644,-0.10994,-0.07216,-0.05197,-0.0666,-0.00632,0.07744,-0.0152,-0.04354,-0.03804,-0.04441,-0.05602,-0.0174,0.04191,-0.00129,0.04846,-0.05514,0.06726,0.06854,0.00747,-0.10987,-0.01774]},{"domain":"materials_science","key":"lever_rule","name":"Phase fractions by the lever rule","package":"materials-science-ai999x","example":"Lever rule: C0 = 35 wt%, C1 = 31.5 wt%, C2 = 42.5 wt%","v":[-0.0544,0.16166,0.09847,0.00599,0.01448,0.05756,-0.03537,-0.04807,0.04893,-0.02128,-0.10431,0.04472,-0.00864,-0.07299,-0.0673,-0.06777,-0.04862,-0.01106,-0.01877,0.01873,0.00285,0.04086,0.00511,0.0227,0.05556,0.05245,-0.00823,-0.01179,-0.06492,0.0494,-0.06816,-0.06501,-0.07103,0.03482,0.11021,-0.00855,-0.05723,-0.04105,0.02958,-0.06492,-0.02371,0.09026,-0.07108,-0.00415,-0.04583,0.03015,-0.10485,0.05003,-0.12235,0.01777,-0.11267,0.09866,-0.02123,-0.00051,0.00829,0.1091,0.04864,0.02617,0.01606,0.01885,-0.06387,0.06834,-0.02772,-0.08592,0.06837,0.06429,0.06913,-0.07919,0.01881,-0.13512,-0.05045,-0.06107,0.00433,-0.11224,0.00306,-0.02941,-0.09744,-0.00092,0.1691,0.07389,0.00875,-0.06643,0.11029,-0.1193,0.00741,0.0634,0.02715,0.10695,0.01481,0.0861,-0.09428,0.02155,-0.03576,-0.01294,-0.02599,-0.0571,-0.09034,0.10101,-0.12837,-0.00146,0.01034,0.00627,-0.00421,-0.01261,0.0181,-0.01658,0.02901,0.04194,-0.05758,0.13816,0.06559,-0.01334,0.02219,-0.04683,-0.03519,-0.10177,0.07743,-0.02854,-0.00265,0.07085,-0.14866,0.03179,-0.06227,0.01099,0.021,0.17202,0.03813,0.03653,0.00408,0.02147,0.02733,0.05616,-0.11907,-0.06419,-0.02264,-0.0415,-0.07885,0.08772,0.02251,-0.08941,0.03481,-0.08211,-0.04842,0.02138,0.01878,0.01619,0.04869,0.11141,0.01117,0.05062,-0.03603,0.01722,-0.04118,0.0184,0.05293,0.08225,0.01536,-0.02625,0.06967,0.06899,0.01251,-0.10538,-0.02827,0.01921,0.07363,0.04376,0.01085,0.05799,0.10258,-0.00456,0.035,0.03774,-0.07806,-0.15329,0.06029,0.08601,0.06492,-0.07763,-0.01921,-0.05516,-0.01733,0.11104,-0.05367,-0.04603,-0.14397,0.04783,0.03033,0.03232,-0.01844,-0.06804,-0.04468,0.06922,0.0246,0.02628,0.0357,-0.01343,0.04105,-0.1193,0.00126,-0.07744,-0.02181,-0.03951,-0.01943,-0.04238,-0.10364,-0.09014,0.01942,-0.00086,-0.06322,0.05578,-0.01439,0.06474,0.02364,0.00742,0.17322,-0.00963,0.0043,0.00646,0.02913,0.04245,-0.04255,-0.06033,-0.03063,-0.03725,0.06115,0.04046,0.02009,0.07837,0.04662,0.10443,-0.02667,-0.00631,-0.06567,-0.03078,0.00924,0.006,0.08518,-0.01942,0.05075,-0.04206,0.00466,-0.07803,0.10322,0.04216,-0.0005,0.02269,-0.02107,-0.04931,0.09376,0.00447,-0.10942,-0.02061,0.08735,0.02478,0.06215,0.02439]},{"domain":"materials_science","key":"linear_density","name":"Linear density along a crystal direction","package":"materials-science-ai999x","example":"Linear density: structure = FCC, u = 1, v = 1, w = 0, a = 0.3615 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and weight-average molecular weight and dispersity","package":"materials-science-ai999x","example":"Molecular weight averages: M = [10000, 20000, 30000], fraction = [0.2, 0.5, 0.3], basis = number","v":[-0.05581,-0.02754,0.04111,-0.04225,-0.03091,0.01544,-0.03397,-0.05539,-0.03806,-0.12195,0.03085,0.12303,0.02886,0.05923,0.01591,-0.07177,-0.07299,-0.16327,-0.15432,0.05171,-0.02062,-0.08646,-0.12259,0.00844,0.01398,0.02264,-0.01303,-0.12025,0.01168,-0.01356,0.02352,-0.00924,-0.04407,0.01347,-0.05321,-0.08407,0.0273,0.01389,0.09413,-0.02379,-0.15124,0.05385,0.08322,-0.00343,-0.00307,0.03379,0.01698,-0.00386,0.07134,-0.03304,-0.07948,0.09223,0.0955,0.0108,0.07145,0.07939,-0.09704,-0.04779,-0.05359,0.01075,0.00215,0.03883,0.00587,-0.12622,-0.00091,-0.01554,0.01235,-0.00495,-0.01957,-0.06743,-0.11103,-0.00868,-0.03877,0.05405,0.04909,0.00261,-0.1574,0.04254,-0.02467,0.00687,-0.05414,0.01178,0.03542,-0.00687,0.13552,0.04935,0.02749,-0.00658,-0.01359,0.04838,-0.1181,0.04762,-0.00565,0.06705,0.03468,-0.01684,-0.02071,0.00811,-0.11315,-0.00894,0.04117,0.02835,-0.02452,0.00315,0.05401,-0.01681,0.01133,0.07454,0.08985,0.13122,-0.00695,-0.05038,-0.01055,-0.03519,-0.16476,-0.0386,-0.00159,-0.04145,0.08387,0.05082,0.09296,-0.02708,-0.10493,-0.02524,-0.06322,-0.00259,-0.01181,-0.07485,-0.09543,0.07359,0.00604,0.12723,0.03286,-0.00912,0.04525,0.00713,0.03341,-0.00906,-0.04491,0.07361,0.07131,-0.04086,0.07149,0.04062,-0.03608,-0.00286,-0.01126,-0.00044,-0.04942,-0.03675,0.02199,0.00017,0.00892,0.01528,0.04909,-0.03973,0.09253,-0.07648,0.04579,-0.01434,0.03698,-0.0369,0.05678,-0.0205,0.08332,0.09995,-0.01104,0.05521,0.01913,-0.01884,0.12359,-0.05153,-0.03246,0.00482,-0.03065,-0.00849,0.08537,-0.0307,-0.04268,-0.02566,0.13678,-0.01213,-0.06832,0.01638,0.03551,0.07663,-0.03043,0.13571,-0.01311,-0.07343,-0.06375,-0.067,0.03084,0.04742,-0.06002,-0.04964,-0.02595,-0.11821,-0.05652,0.049,-0.12334,-0.00148,0.00739,-0.00869,0.06585,-0.00784,0.06654,-0.02863,-0.06717,-0.0583,0.052,0.07582,0.017,-0.05433,0.03541,0.00535,0.18132,0.0268,-0.00831,0.03303,0.03222,0.08375,0.01149,0.04429,0.06527,-0.14054,0.06835,-0.05818,0.02104,-0.08019,0.05696,0.08917,-0.05763,0.06507,0.16449,-0.00192,0.02087,0.03446,-0.01537,-0.00953,0.13113,-0.00118,0.00171,0.0195,-0.03574,0.08611,-0.02087,0.09429,0.02867,0.01718,0.08641,-0.12541,-0.0345,-0.04771,-0.08965,-0.07379]},{"domain":"materials_science","key":"offset_yield_strength","name":"0.2 % offset yield strength from a stress-strain curve","package":"materials-science-ai999x","example":"Offset yield strength: strain = [0, 0.002, 0.004, 0.006, 0.008], stress = [0, 400, 520, 560, 580], E = 200 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density of a crystal plane","package":"materials-science-ai999x","example":"Planar density: structure = FCC, h = 1, k = 1, l = 1, a = 0.4 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potential of a p-n junction","package":"materials-science-ai999x","example":"Built-in potential: Na = 1e23 m^-3, Nd = 1e22 m^-3, ni = 1e16 m^-3, T = 300 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energy of a free-electron gas","package":"quantum-physics-ai999x","example":"Fermi energy: n = 8.47e28 m^-3","v":[0.05386,-0.08731,0.02106,-0.06679,0.00799,0.09491,-0.04635,-0.03522,-0.01407,-0.03278,-0.01627,-0.07156,-0.08181,0.01582,-0.03137,0.05528,-0.01915,-0.01236,0.07713,0.01597,-0.11512,0.10884,0.06123,0.02154,-0.00741,-0.01868,-0.04911,-0.08733,-0.06996,0.0297,-0.0793,-0.0301,0.02049,0.11183,0.09173,0.09561,0.02345,-0.06146,-0.0263,-0.05542,0.03509,-0.04082,0.02036,-0.03186,0.01568,0.01345,-0.15699,-0.01692,-0.15864,-0.01142,0.0221,-0.02141,-0.01005,0.02947,-0.12185,-0.07385,0.00665,0.06784,0.05578,-0.045,0.02714,0.04259,-0.01,-0.03984,-0.03129,0.0815,0.05732,-0.11522,-0.1024,-0.04054,0.01124,0.07385,-0.12411,-0.03312,0.16363,0.05506,0.07906,-0.0379,0.04886,-0.0395,0.15607,-0.0328,-0.06664,-0.00407,-0.0513,-0.06041,-0.05264,0.04014,0.06947,0.02993,0.04615,0.03005,-0.01067,-0.03491,-0.12131,-0.02564,-0.09182,-0.01204,0.10791,-0.06913,0.02516,0.1613,0.00826,0.00667,-0.03182,-0.02574,0.10483,0.02355,-0.00134,-0.0141,0.02544,0.01275,-0.05962,0.03113,0.048,-0.01898,0.03848,-0.03538,0.05228,0.04212,-0.04144,0.10694,0.02381,-0.02219,-0.0407,0.00259,0.01615,-0.00337,-0.00661,0.00043,-0.01267,-0.05505,-0.13044,-0.00815,-0.0215,0.03954,0.07483,-0.0418,-0.01648,-0.04071,-0.03628,0.12144,-0.01678,0.09266,-0.06344,0.01725,0.01762,0.06113,-0.08384,0.07236,0.06403,0.06976,-0.04571,0.06242,0.01097,-0.00739,0.10325,0.00842,0.02913,-0.00241,0.01812,-0.08105,0.03158,0.03905,-0.01191,0.03175,-0.03021,0.11865,-0.1419,0.05795,0.03861,0.0162,0.0855,0.06201,0.03128,-0.00358,-0.05774,0.08379,-0.04975,0.13898,0.07829,-0.11735,-0.04836,0.04753,-0.07792,0.10558,0.02448,-0.06688,0.02566,0.11354,0.00083,-0.0056,-0.02522,-0.08894,-0.00174,0.04642,-0.02499,-0.07449,0.02773,-0.01698,-0.09631,-0.10221,0.09717,-0.09888,-0.04093,-0.02599,-0.02029,0.01711,-0.00819,-0.07074,0.14466,0.09834,-0.00197,0.04637,-0.09507,-0.05715,-0.11003,-0.03119,0.06775,-0.06964,-0.17822,0.03188,0.0374,-0.02873,0.0135,0.03514,0.06531,-0.0259,-0.01572,0.03917,0.06024,0.04574,0.04124,0.05235,-0.09007,0.00156,0.0088,-0.03238,0.10879,0.03793,-0.01966,0.0156,0.00547,-0.00685,-0.0192,0.01606,-0.05299,0.02392,0.0568,-0.01516,0.02187,-0.00983,-0.13643,0.06962,0.04904,-0.02077]},{"domain":"quantum_physics","key":"fermi_energy_metal","name":"Fermi energy of a metal from its density","package":"quantum-physics-ai999x","example":"Fermi energy of a metal: rho = 8960 kg/m^3, M = 63.546 g/mol, z = 1","v":[0.01857,-0.0471,-0.03576,-0.0162,0.04478,0.07894,0.03882,0.00951,0.04489,0.02475,-0.02953,-0.08866,-0.00905,0.01841,-0.05135,0.12295,0.03791,-0.06467,0.02522,0.01773,0.05288,0.07343,0.0132,0.0668,0.0546,0.08573,0.03513,-0.04805,-0.12322,-0.00805,-0.0663,-0.03869,-0.08536,0.05297,0.12979,0.02627,0.00478,-0.01314,0.06686,-0.08914,-0.01778,0.02475,0.00252,-0.01192,0.05296,0.04995,-0.1554,-0.00094,-0.09321,-0.03613,-0.05881,0.04481,-0.00072,0.04252,-0.09396,0.01091,0.01983,0.01094,0.07164,0.02972,-0.0045,0.0119,0.0247,0.05676,0.03818,0.10191,0.04167,-0.07869,-0.03797,-0.01103,0.01937,0.06534,-0.05932,-0.07415,0.1871,0.05123,0.18014,-0.08674,0.07542,-0.03811,0.0554,0.01188,-0.03991,-0.09919,0.02737,-0.02978,0.05828,0.13507,0.01573,0.0253,0.00331,-0.03808,-0.09629,-0.06091,-0.07098,-0.00272,-0.20399,-0.00113,0.0117,0.04731,0.12506,-0.04463,-0.07921,-0.02976,-0.04641,0.05391,0.1169,0.11088,0.01153,0.04605,-0.02737,0.04363,-0.10422,0.03084,-0.01175,-0.04313,0.0387,-0.0218,0.02421,0.08793,0.03196,-0.07071,0.01148,0.01087,-0.0352,0.00351,-0.06391,-0.05987,0.01097,0.00643,-0.04721,0.09032,-0.04347,-0.00931,-0.00515,0.01937,-0.01289,-0.04901,-0.00763,-0.02627,0.07925,-0.02834,0.05879,0.10287,-0.01898,-0.032,0.01853,-0.0437,0.04347,0.0503,0.05009,0.11856,-0.0585,-0.0622,-0.0058,-0.00177,0.0438,-0.02477,-0.00237,-0.03154,-0.04555,-0.11044,0.02498,-0.08416,-0.01522,0.04114,-0.02331,0.09351,-0.06175,-0.05505,-0.00757,-0.04641,0.02264,0.02823,8e-05,0.02892,0.02094,-0.00126,-0.1005,0.12354,0.23888,0.03627,-0.06113,-0.02023,-0.05644,0.05281,-0.02039,-0.07317,0.02766,-0.02436,-0.0454,-0.01631,-0.03615,-0.05778,0.02214,0.01181,-0.03265,0.03243,0.04005,-0.08247,-0.14927,-0.11709,0.03317,-0.07233,-0.06806,-0.08281,0.03673,0.02663,-0.0488,-0.04749,0.07016,0.12379,0.0187,-0.00326,-0.08235,-0.02579,-0.1203,-0.02373,0.0805,-0.03137,-0.08175,0.03787,0.05484,-0.03388,-0.0542,-0.03607,0.03557,-0.00586,-0.08272,0.077,0.05057,0.10485,0.05242,-0.03748,-0.1136,-0.09361,-0.04491,0.0272,-0.05703,0.07744,-0.02211,0.03509,0.01291,0.01505,0.03045,-0.04193,0.01119,0.07949,0.00707,0.13645,-0.0665,-0.01213,0.0444,0.05491,0.00721,-0.05689]},{"domain":"quantum_physics","key":"fermi_gas_chemical_potential","name":"Chemical potential of an ideal Fermi gas","package":"quantum-physics-ai999x","example":"Fermi gas chemical potential: n = 1e28 m^-3, T = 1 K, m = 9.1093837139e-31 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states of a finite square well","package":"quantum-physics-ai999x","example":"Finite square well: V0 = 10 eV, a = 0.5 nm, m = 9.1093837139e-31 kg","v":[-0.15034,-0.10064,0.07696,-0.0426,0.02067,-0.06949,0.08162,-0.11948,-0.09715,-0.02872,0.09716,0.10977,-0.06668,-0.11788,0.05044,-0.02503,0.02667,-0.01633,0.00427,0.03991,0.0583,0.0771,0.05323,0.02867,0.01461,0.04079,-0.01391,0.025,-0.01724,0.01438,-0.04303,-0.07393,-0.03811,-0.04438,0.00622,-0.00632,0.03335,-0.0118,0.05913,-0.13092,0.02069,0.0109,0.04156,0.01629,0.02555,-0.04321,-0.09765,0.02557,-0.07796,0.01519,0.01675,-0.00471,-0.01692,0.02344,-0.02899,0.04888,0.02388,0.07807,0.09492,0.05258,-0.04149,0.05437,0.00953,0.0251,0.07699,0.08364,0.00725,-0.09843,-0.01345,0.00835,0.0215,-0.07835,0.01736,0.10708,0.00524,-0.0008,-0.21236,0.05203,-0.0675,0.08178,0.03663,-0.08563,-0.05048,-0.04658,-0.07197,-0.10258,-0.02708,0.07016,0.06893,-0.0733,0.09471,0.07025,0.02573,0.04176,-0.06205,-0.03224,0.14988,-0.02229,0.02784,0.05697,0.00822,0.04546,-0.04553,0.03841,-0.03211,-0.03955,0.05285,-0.00523,-0.06251,-0.04311,-0.09925,0.00227,-0.10879,-0.01093,-0.03391,-0.07719,0.05982,-0.09664,0.03575,0.04496,0.00402,0.00094,-0.06387,0.05826,0.02861,0.08341,0.0081,0.05017,0.10154,0.06125,0.09335,0.10877,0.03715,0.00062,0.09458,-0.07281,0.10028,-0.02162,0.06901,-0.04395,-0.04897,0.02478,0.02897,0.03269,-0.02388,-0.10006,0.01295,0.05589,-0.02579,-0.06031,0.0331,0.05577,-0.05642,-0.06771,-0.10388,0.06341,0.01477,-0.06099,-0.01652,0.11455,0.05122,-0.05379,-0.014,-0.02387,-0.14663,-0.03907,0.06942,0.01777,0.0521,-0.04894,0.02365,0.14641,-0.06829,-0.01533,0.05169,0.00989,-0.0723,0.00991,-0.10588,0.00263,0.10232,0.02898,-0.02565,-0.05239,0.0092,0.01109,-0.02002,-0.04675,0.06691,-0.09049,-0.12452,0.01341,0.04386,0.0433,-0.05594,-0.06353,-0.08097,-0.01428,0.0806,0.03283,-0.02406,-0.0515,-0.10045,-0.01749,0.00645,-0.01726,-0.13927,0.00388,-0.08023,-0.01,-0.00409,0.03721,0.10229,0.01742,-0.0082,-0.04371,-0.05855,-0.03459,0.09376,-0.01571,-0.06731,0.08555,-0.06729,0.00117,0.02023,0.07669,-0.083,-0.06729,0.00198,0.08455,0.0503,-0.05049,-0.00553,0.07108,0.04672,-0.07025,-0.00455,0.1163,0.11811,0.01766,0.0245,0.02204,-0.00019,0.05345,-0.1141,0.03045,0.02094,0.06121,0.0665,0.08249,0.04326,-0.14652,-0.01164,0.05422,0.00029,0.01431]},{"domain":"quantum_physics","key":"fixed_target_cm_energy","name":"Centre-of-mass energy of a fixed-target collision","package":"quantum-physics-ai999x","example":"Centre-of-mass energy: m1 = 1, E1 = 7, m2 = 1","v":[0.00016,-0.01897,0.12503,-0.05165,0.04427,0.05227,0.02035,0.05705,-0.00745,-0.00451,0.15928,0.12089,-0.0686,-0.06508,0.04587,-0.02623,0.05287,0.03504,0.01128,0.05064,0.05645,0.16155,0.01531,-0.00661,-0.0661,0.05619,-0.06181,0.03654,0.01201,0.0108,-0.06156,-0.10196,-0.08385,0.02868,-0.07532,0.0007,-0.08776,0.01312,0.00882,-0.1897,0.0131,0.05951,0.0052,-0.01353,-0.03244,0.04353,-0.06415,0.10294,0.05577,-0.02694,-0.04282,0.01013,-0.00649,-0.00052,-0.01613,0.09299,-0.0543,-0.00072,-0.01457,0.07384,-0.03734,0.00875,0.03046,-0.05431,0.06564,0.0637,-0.08458,-0.07149,0.01674,0.07349,-0.02446,-0.08137,0.02569,-0.00989,0.00019,0.0271,-0.03935,-0.03264,-0.05814,0.13336,0.18858,-0.0228,0.01933,0.09078,-0.03326,-0.07557,-0.02534,0.00147,0.02912,-0.07303,0.05219,-0.03197,0.08625,0.01477,0.03973,0.0058,0.03636,0.05925,-0.01747,-0.06676,0.05692,-0.05868,-0.14197,0.00933,-0.07699,-0.1505,0.05159,-0.02045,-0.12462,-0.02331,0.00514,0.11691,0.00508,-0.01497,-0.06067,-0.02799,0.18755,-0.12102,-0.05832,0.01132,-0.15151,-0.0014,0.00481,0.10833,0.01109,-0.0134,0.03807,0.01465,0.0963,0.04369,-0.00227,-0.02029,-0.09081,-0.04077,0.10709,0.03012,0.03285,-0.0543,-0.00036,-0.01709,-0.01346,-0.00156,0.14732,-0.0185,-0.02126,0.00664,0.05489,0.05888,-0.07162,0.00944,0.01739,0.07023,0.09122,-0.01228,-0.04906,0.01149,-0.01935,-0.06569,0.02691,0.00908,0.02598,-0.00278,0.08005,0.02319,-0.11837,0.00821,-0.06095,0.0084,0.01357,-0.00669,0.00112,0.09856,0.01935,-0.05737,0.02499,-0.05415,-0.0313,0.12872,-0.14883,0.03623,0.0639,0.08425,0.01525,-0.02284,-0.00826,0.03368,-0.00471,-0.05595,-0.01129,-0.04394,-0.12027,-0.00505,0.03995,0.09704,0.01388,-0.06552,-0.04574,-0.05851,-0.00153,0.02408,-0.10839,-0.12128,-0.04934,-0.00308,-0.06878,-0.05736,0.06424,0.01398,-0.03943,-0.00032,0.02333,0.02043,0.03824,-0.09069,-0.05525,-0.0276,-0.05576,-0.01716,0.06649,0.0467,0.01004,-0.09033,-0.07058,0.01021,-0.00822,0.01119,-0.03295,0.03924,0.00608,0.08085,0.11987,0.05149,-0.0077,0.00492,0.12767,-0.08674,0.01877,-0.06065,0.03295,-0.03406,0.01165,-0.04049,0.04182,0.12518,-0.05872,-0.01509,0.08027,0.04521,0.03539,0.07632,-0.07629,-0.0644,0.05399,0.05473,-0.02722,-0.0497]},{"domain":"quantum_physics","key":"gate_rotation_axis","name":"Bloch-sphere rotation of a single-qubit gate sequence","package":"quantum-physics-ai999x","example":"Gate rotation: gates = H","v":[-0.0596,0.00064,-0.0213,0.10915,0.15423,0.0133,0.0272,-0.04292,0.05139,-0.06158,0.04238,-0.05202,-0.04719,0.00503,0.05968,0.00822,-0.03932,-0.08861,0.0261,0.03613,0.00465,-0.06593,-0.05877,-0.03827,-0.07586,-0.06925,0.02972,0.0318,0.03465,0.03274,-0.03919,0.04768,-0.01243,-0.04911,-0.06891,0.09202,-0.01335,0.04991,-0.03885,0.01483,0.08122,-0.05928,0.07805,0.00155,0.06408,-0.09057,0.04333,0.03695,-0.01681,-0.055,-0.03534,0.08655,-0.01854,-0.12676,0.01758,-0.00216,0.00106,0.15367,0.07664,-0.00114,0.04822,-0.0294,-0.0616,-0.08409,0.0613,-0.00352,-0.03566,-0.02249,-0.15661,0.04394,0.06709,-0.0074,-0.00249,0.16558,0.1469,0.00754,-0.03398,0.21069,-0.00198,0.04266,-0.04499,0.01962,0.10413,0.06484,-0.02294,0.0424,-0.09084,0.02423,0.12128,-0.00574,-0.02541,-0.10783,0.08148,-0.11361,-0.03894,-0.0602,0.10151,0.03275,0.07114,-0.02895,-0.01126,-0.08533,0.05633,0.07481,0.0173,-0.03548,-0.0896,-0.0728,-0.08377,-0.13743,-0.03293,0.03617,0.0996,0.03264,0.03492,-0.03436,-0.01236,-0.12826,0.05169,-0.12068,-0.00032,-0.01962,-0.04725,-0.08427,-0.07989,-0.10649,-0.03284,-0.08641,0.06982,0.04441,0.00916,-0.12814,-0.0765,0.01604,0.10945,-0.06986,-0.00228,0.02506,-0.04502,-0.12242,-0.01679,-0.09482,-0.06662,0.03545,0.04155,-0.0084,0.04513,-0.0123,0.05135,-0.01063,0.04102,-0.0817,-0.10593,0.04221,0.01688,0.05721,-0.07702,0.01812,0.04026,-0.0125,0.04795,-0.04052,0.06859,-0.03153,-0.04587,-0.03144,0.03384,0.03887,-0.03086,0.03896,-0.0031,-0.08647,-0.01666,0.01333,-0.00173,0.02023,-0.05867,0.0668,-0.06401,-0.02919,-0.04711,0.10346,0.02309,-0.05705,0.10407,-0.08066,-0.01625,0.02049,0.00424,0.03106,0.11507,-0.00993,0.07978,-0.05965,-0.02562,0.00921,0.01853,0.02917,-0.02409,0.00797,-0.06356,-0.04352,-0.04074,-0.01278,-0.00511,0.03154,0.01862,0.01082,0.05522,0.05918,0.0981,0.03741,-0.05107,0.00069,-0.01534,-0.13419,-0.09273,0.01466,0.07681,-0.02602,-0.04448,0.01185,0.06659,-0.00961,0.07407,-0.05854,0.10391,-0.02009,0.06677,-0.0371,0.0964,0.07525,-0.02983,-0.05499,-0.02654,0.08806,0.09347,-0.02033,0.08586,-0.0856,0.04492,-0.01237,-0.03832,0.06874,-0.08133,-0.0306,0.04722,0.03528,0.02655,-0.00856,0.06237,0.0359,0.02462,-0.09981,0.04589,0.00129]},{"domain":"quantum_physics","key":"grover_search","name":"Success probability of Grover's search","package":"quantum-physics-ai999x","example":"Grover search: n_qubits = 2, M = 1, k = 1","v":[-0.0596,0.0243,-0.07686,0.02478,0.08534,-0.0598,0.0778,-0.06051,0.00592,-0.0181,0.06096,-0.10324,0.02891,0.02037,-0.02939,-0.04136,0.00323,-0.0157,0.01732,0.04676,0.01315,-0.00591,0.03532,-0.03232,-0.01304,0.05887,-0.02098,-0.021,0.03939,-0.0095,0.00646,0.07033,-0.03669,-0.03765,-0.07813,0.05375,-0.05409,0.01172,-0.01382,0.02732,0.05255,-0.05836,0.06858,-0.03411,-0.0423,0.01391,0.03085,0.06003,0.04794,0.01036,-0.03429,0.04477,0.06212,-0.13074,-0.09284,0.03992,-0.0068,0.12304,0.09867,-0.04685,-0.02645,-0.15767,-0.00311,-0.00242,-0.00878,-0.00828,0.04863,-0.04512,-0.04451,0.00068,0.13105,-0.05453,0.00926,0.16181,-0.02576,0.13475,-0.07362,0.18569,-0.06146,0.15203,0.02005,0.00901,0.09099,0.00564,-0.08929,-0.00993,0.08431,-0.05297,0.10911,-0.03641,-0.01485,0.03457,0.03718,-0.01261,-0.07366,-0.03416,0.07944,0.1477,0.13116,-0.07875,-0.01467,0.02601,0.01035,0.02744,0.0129,0.03382,-0.13245,-0.05051,-0.0193,-0.10324,-0.03424,0.04378,-0.05637,0.00717,0.07946,0.00134,-0.00357,-0.06986,0.03528,-0.05365,-0.00041,0.06724,0.01952,0.00752,-0.04701,-0.16322,0.03727,-0.04741,0.03266,0.0068,0.09568,-0.06985,-0.1329,0.03814,0.07593,-0.02771,-0.04412,0.02311,-0.03068,-0.07833,-0.10762,-0.00286,-0.09983,0.02111,0.02469,-0.08766,0.09875,-0.03394,0.031,-0.00683,0.02928,-0.03143,-0.09001,0.03558,0.01657,0.06418,-0.12412,-0.04442,0.00435,0.01404,-0.06663,0.06588,0.0085,-0.05861,-0.07338,-0.04332,0.1544,-0.01659,-0.03088,-0.03143,-0.00011,-0.08525,-0.16251,-0.01774,0.05401,0.0774,-0.0057,-0.01523,-0.061,-0.03829,-0.01555,0.09526,0.01213,-0.06019,0.01718,-0.09046,-0.09159,0.07522,-0.05161,-0.02399,0.05001,0.10252,-0.01662,-0.05946,-0.07067,0.09221,0.01285,0.03827,-0.02942,-0.02608,0.00884,0.04878,-0.04004,-0.00247,0.03381,-0.05256,0.02386,0.04005,0.01296,0.0057,-0.00466,-0.05399,0.06591,0.02785,-0.06975,-0.02033,-0.03736,0.09491,0.08306,0.01157,-0.00902,0.06189,0.03942,-0.0217,0.0107,-0.05008,0.02137,-0.12108,-0.12086,-0.05772,-0.05242,0.06958,-0.05362,-0.03221,-0.0113,0.03386,0.0618,0.06275,-0.01707,-0.02481,0.05458,-0.11381,-0.05872,0.07358,-0.02407,0.03793,0.05347,0.05099,0.01811,0.08984,0.11326,-0.11376,-0.00112,-0.0118,0.10387,0.05919]},{"domain":"quantum_physics","key":"harmonic_oscillator_forbidden_probability","name":"Probability beyond the classical turning points (harmonic oscillator)","package":"quantum-physics-ai999x","example":"Forbidden region probability: n = 0","v":[-0.06769,-0.12154,0.01998,0.01994,0.07203,-0.00639,0.01988,-0.13232,-0.04204,-0.02211,0.02204,0.02794,-0.12015,-0.00547,0.08178,0.00417,0.07375,-0.05272,-0.01626,-0.01204,-0.04892,0.04384,-0.03485,-0.06102,0.02921,-0.01859,-0.05124,-0.01278,0.10263,0.02306,0.04358,0.08076,-0.00047,0.04346,-0.10846,0.04659,-0.06638,-0.05699,-0.04563,0.01356,0.02032,-0.0813,0.08718,0.14489,0.00178,0.00852,-0.14858,0.06904,-0.05696,-0.07314,-0.0091,-0.0705,0.01085,-0.05118,-0.025,-0.03566,-0.02189,0.02212,0.07125,-0.04499,0.00795,0.05652,0.04104,-0.06385,0.06576,-0.05386,-0.03113,-0.09393,0.02863,-0.06269,0.01737,-0.03109,-0.00491,0.0785,0.02798,0.01096,-0.11529,0.09001,0.07347,0.14699,0.00413,0.03429,-0.01275,-0.01038,-0.04218,-0.1076,-0.03937,0.05557,0.06498,0.00768,0.00146,0.11316,0.06706,0.00212,-0.0264,0.13743,0.09398,0.0105,0.02498,0.03863,0.04122,-0.003,0.05509,-0.0755,-0.00857,-0.00539,-0.15046,0.04963,0.03028,-0.05628,-0.07238,0.0255,0.06411,-0.02599,0.05669,-0.0677,-0.00876,-0.04718,-0.00872,-0.04632,-0.03644,0.02085,-0.10797,0.00941,-0.08621,0.01463,-0.07547,-0.07464,0.05356,0.08967,-0.04117,-0.10704,0.12251,-0.13786,0.10387,-0.03732,-0.00119,0.01962,0.05071,-0.0353,-0.02275,-0.01788,0.01889,-0.07457,0.01275,-0.06469,0.03406,-0.10273,-0.07012,-0.01005,-0.04383,0.01427,-0.05724,-0.01639,0.04222,0.12089,0.08067,0.01699,0.05314,-0.00503,-0.01135,-0.0063,0.01002,-0.04782,-0.04792,-0.05885,0.17141,-0.05905,-0.00409,0.01741,-0.01796,0.09582,0.00509,-0.0205,0.03794,0.103,-0.04205,0.04613,-0.09326,-0.07274,0.06805,0.07222,0.00777,0.01595,-0.07768,-0.1075,0.02047,0.09789,0.01282,-0.04828,-0.01867,0.0172,0.01962,-0.06191,-0.09019,-0.06208,0.01638,-0.03484,-0.01255,0.06019,0.08834,0.01844,-0.06661,0.09674,0.14163,0.04976,0.00583,0.11005,-0.05675,0.07844,-0.01906,0.06194,0.09944,-0.00864,-0.0001,0.02094,-0.00853,0.15606,0.05499,-0.01084,0.03262,0.10581,-0.00396,-0.02503,-0.05578,0.02043,0.04254,-0.01382,0.0278,-0.05686,0.02491,-0.04376,0.04474,-0.12416,-0.04637,0.11257,-0.05693,0.16656,-0.0045,0.0551,0.00163,0.00454,-0.00971,0.06868,-0.04977,-0.0495,-0.01371,0.02177,0.01445,0.04261,0.03019,0.04741,0.10031,-0.00588,0.10428,-0.08896]},{"domain":"quantum_physics","key":"harmonic_oscillator_levels","name":"Quantum harmonic oscillator levels","package":"quantum-physics-ai999x","example":"Harmonic oscillator: m = 1.67262192595e-27 kg, omega = 1e14 rad/s, n = 0","v":[-0.05212,-0.0397,0.04556,-0.15273,-0.00428,-0.01516,-0.02698,-0.11821,-0.05002,-0.08429,0.06654,0.0176,-0.07925,0.00907,0.03334,-0.02743,0.10072,0.0545,0.0009,-0.05836,-0.02787,0.00365,-0.09987,-0.00759,-0.01479,0.03779,0.05031,-0.05585,-0.06204,0.02126,-0.05505,0.06219,-0.023,-0.0307,-0.05936,0.02879,-0.04468,0.06306,0.05477,-0.15226,-0.06384,-0.07672,-0.05733,0.0818,-0.02361,0.01181,-0.12544,0.01143,-0.12497,-0.10304,-0.02532,-0.05183,-0.04837,0.01932,-0.06184,-0.05289,-0.00995,0.07737,0.00763,-0.0627,0.00506,0.10687,-0.00199,0.04958,0.1066,-0.03003,-0.0789,-0.10916,0.0008,0.00784,0.0324,0.03637,0.09611,0.09581,0.03023,0.06203,-0.10882,0.06858,-0.02185,0.03721,0.0338,0.05718,0.00604,-0.0277,-0.07565,-0.1457,-0.00729,0.05873,0.01198,-0.06328,-0.01439,-0.00486,0.05086,-0.08214,-0.1365,0.03378,0.08573,-0.03184,0.07302,0.01852,-0.02997,0.00883,-0.04322,-0.09767,-0.03892,-0.02821,0.03304,0.00161,-0.06866,-0.02028,0.03449,-0.00623,-0.10854,0.00966,0.04301,0.03448,0.05244,-0.05647,0.07699,0.0078,-0.03426,0.0233,-0.01719,0.00968,-0.01714,0.00177,-0.00062,-0.08943,0.00779,0.02738,-0.04368,0.07607,0.0811,0.01756,0.13377,0.01511,-0.00017,0.09119,0.13232,0.04205,-0.07935,0.03757,-0.03261,0.02405,0.02516,0.01599,0.00514,0.05243,-0.02183,-0.01487,0.01118,0.00852,-0.01086,-0.01983,-0.00481,0.15479,0.1303,0.05469,0.11388,0.03578,0.02422,-0.00665,0.04098,0.08156,-0.03808,-0.03874,0.02353,0.06694,-0.06223,0.00312,0.11115,-0.02663,0.02196,0.01256,0.01702,0.02008,-0.10042,0.07876,-0.12113,-0.06627,0.08993,-0.00207,-0.09509,0.01154,-0.05388,-0.02369,-0.08393,0.02226,0.08208,-0.0825,-0.05112,-0.05282,0.0653,0.05146,-0.04105,-0.1123,-0.05454,-0.03971,0.00704,-0.00511,-0.00679,-0.0811,-0.09352,-0.0251,0.10619,0.01404,0.04751,0.04364,-0.01062,0.00655,0.02423,0.05397,-0.00609,0.0159,-0.04686,-0.08561,0.01145,-0.09236,0.09149,-0.08671,-0.09705,0.02833,0.09205,0.11007,-0.07706,-0.0584,0.10687,-0.01087,-0.01951,0.00979,0.18445,0.0373,0.05559,0.02327,0.07701,0.09844,-0.03311,0.05213,0.00236,-0.06848,0.00474,-0.01115,0.08488,0.06043,-0.10485,-0.04627,0.04043,0.00735,0.13112,0.12644,-0.00672,-0.01995,0.03182,-0.04209,0.07058,0.05486]},{"domain":"quantum_physics","key":"heisenberg_minimum_uncertainty","name":"Minimum momentum uncertainty (Heisenberg)","package":"quantum-physics-ai999x","example":"Minimum uncertainty: dx = 0.1 nm, m = 9.1093837139e-31 kg","v":[-0.07175,0.11259,-0.0136,0.13711,0.00059,0.00158,0.15581,0.03127,-0.04604,-0.07571,0.01121,0.01619,-0.00649,0.00079,0.02805,-0.0453,0.05875,-0.02993,-0.02081,0.03405,0.04294,0.09071,-0.02381,-0.02776,0.0321,0.08967,0.04811,-0.08278,-0.00071,0.07894,-0.01315,0.09764,0.01642,-0.02195,-0.04779,-0.05593,-0.04557,0.0229,0.01657,-0.00668,0.05637,-0.05592,0.06405,0.03146,0.04129,0.00832,0.01007,0.00964,0.07526,-0.05029,0.06856,-0.02393,-0.12346,0.08509,0.01724,0.05757,0.08894,0.06129,0.01927,-0.00988,-0.13103,0.07505,-0.02254,0.13103,-0.07234,0.06029,-0.03118,-0.02478,-0.02172,0.04815,-0.07878,-0.01404,0.12263,-0.00854,0.07142,0.05719,-0.06106,-0.04327,0.00802,-0.00194,0.01097,0.01537,-0.06637,-0.06564,-0.03641,0.00561,-0.07804,0.10076,-0.03682,-0.02288,-0.01108,-0.0703,0.03883,-0.01496,0.0075,-0.02497,0.0725,0.06944,0.02145,0.08685,-0.03408,0.11715,-0.0345,-0.01382,0.00606,0.02049,0.00415,-0.00397,-0.06671,0.10161,0.05066,0.00227,0.05921,0.00186,-0.10319,-0.00936,-0.0458,-0.04316,0.02053,0.0128,0.03053,-0.01248,0.0142,0.21156,-0.07395,-0.13521,-0.01512,-0.07545,0.12148,0.00905,-0.11662,-0.03791,0.12133,-0.0594,0.02191,-0.03458,-0.00763,0.08674,0.15193,0.00641,0.06768,-0.02938,0.05656,-0.033,-0.00357,0.01826,0.01663,-0.09706,-0.03214,0.04219,-0.0357,-0.10338,-0.07356,-0.0332,0.10176,0.00226,0.10896,-0.00247,0.00834,0.09496,0.0338,0.08366,-0.02122,-0.00276,0.00676,-0.00684,0.06265,-0.05122,-0.07218,-0.11553,-0.03314,0.0076,0.03305,-0.07356,0.00345,0.02266,-0.00328,0.08546,0.04289,0.01407,0.09299,-0.07477,0.03813,0.06073,-0.07772,-0.11588,-0.00523,-0.03112,0.06202,-0.03178,-0.03904,-0.13348,-0.06151,-0.09678,0.04232,-0.10603,-0.04929,0.02651,0.06931,-0.07141,-0.09577,-0.09336,-0.02495,-0.10418,-0.06224,0.05678,0.007,0.04867,-0.0072,0.01437,-0.0421,0.12422,0.07744,-0.12785,0.02982,-0.06109,-0.06532,0.0183,0.02501,-0.03844,-0.09045,-0.01532,-0.00044,0.01059,-0.01426,-0.03698,0.01895,0.03476,0.04155,-0.03933,0.01603,0.07524,0.01648,-0.03024,0.07952,0.0544,-0.11112,0.04123,-0.04259,-0.00462,-0.01013,0.10998,-0.07675,0.08663,-0.00789,-0.06859,-0.05276,-0.01368,-0.08767,0.02204,-0.03781,-0.04108,0.09592,-0.17222,-0.00107,0.03082]},{"domain":"quantum_physics","key":"hydrogen_radial_expectations","name":"Radial expectation values of a hydrogen-like state","package":"quantum-physics-ai999x","example":"Radial expectation values: n = 2, l = 1, Z = 1","v":[-0.0678,-0.16283,-0.02965,-0.04471,0.07821,-0.03488,-0.03657,-0.08765,-0.03492,0.02818,0.10339,-0.08917,-0.01395,0.01598,0.05989,0.0507,0.01417,0.05558,-0.00827,0.00399,0.05325,-0.12849,-0.05614,-0.01642,0.01982,-0.01481,0.00626,-0.06645,0.12621,-0.02691,-0.00258,0.07528,0.0646,-0.06291,0.01963,0.01323,0.07367,0.0682,-0.01729,0.02056,0.03833,-0.01296,-0.05709,0.01621,-0.07427,0.00794,-0.02757,-0.13191,-0.15805,-0.14085,-0.01695,-0.02263,0.04898,0.06039,-0.11719,-0.11331,0.06681,0.08019,0.00056,-0.01629,-0.04336,0.11974,-0.01958,-0.03934,0.08756,0.06047,0.01925,-0.00657,-0.04835,-0.02997,0.0225,-0.00428,-0.07553,0.06481,0.03721,-0.01879,-0.11383,0.06289,-0.06479,0.1358,-0.03139,0.05631,-0.02252,-0.01394,-0.03506,-0.04654,-0.06164,0.0269,0.01199,-0.13527,0.02244,0.04661,0.08345,-0.07605,-0.01828,0.03952,-0.05654,-0.05057,-0.04119,-0.0556,0.04072,-0.06755,0.17994,0.00037,0.01628,-0.00826,-0.02382,-0.03798,0.10923,-0.08118,0.04288,-0.10695,-0.04597,-0.0166,-0.01517,0.02813,0.02852,-0.01599,0.04111,-0.12555,0.01927,-0.05016,0.02602,0.1212,-0.06286,-0.00764,0.03063,0.0466,0.08097,0.01998,-0.05118,-0.04496,0.1051,0.0329,-0.04339,0.042,0.03588,0.04606,-0.08346,-0.10002,-0.02236,0.04416,0.01221,0.07043,0.01357,0.05326,0.08454,0.03332,-0.00176,0.05472,-0.05334,0.09487,0.04648,-0.07259,-0.02746,-0.04939,0.16829,-0.0067,0.05526,-0.06528,-0.0353,-0.02529,-0.02137,-0.04113,-0.12171,0.00968,0.10788,0.01159,-0.01093,0.03584,-0.02144,-0.01906,-0.06003,0.03273,0.00465,0.03914,0.00464,0.06922,-0.1454,0.04791,0.02229,0.11768,0.02585,-0.07546,0.06797,-0.08849,-0.07292,0.07051,0.04924,-0.1029,-0.0426,-0.0179,0.0696,-0.05425,0.0185,-0.04331,-0.00194,0.0671,0.02262,-0.05431,0.01129,0.03459,-0.01312,-0.02881,0.08966,-0.01151,0.02697,0.10093,-0.0445,-0.00933,0.06425,0.06487,0.06972,0.01901,-0.0558,-0.11236,-0.03312,-0.01386,0.11198,0.03795,0.08466,0.03589,0.10238,0.03512,-0.05633,-0.02514,0.11282,-0.01905,0.06733,-0.10092,-0.02587,-0.04027,0.0484,-0.08399,-0.05912,0.01828,-0.04566,0.06935,-0.06364,-0.01689,0.05775,0.03388,-0.01658,-0.02098,-0.12615,-0.03997,0.00188,0.07152,0.01698,0.10874,-8e-05,0.06778,-0.02708,-0.0277,-0.05262,0.00235]},{"domain":"quantum_physics","key":"hydrogen_radial_probability","name":"Probability of finding the electron within a radius","package":"quantum-physics-ai999x","example":"Radial probability: n = 1, l = 0, Z = 1, R = 52.9177210544 pm","v":[-0.08372,-0.11512,-0.00817,-0.06035,0.12755,-0.0387,0.02043,-0.06002,-0.03341,-0.00732,0.05147,-0.10447,0.00349,0.04027,0.0356,0.0602,0.06492,0.04447,0.02419,0.03668,0.01496,-0.05995,0.02721,-0.00619,0.02631,-0.00378,-0.00406,-0.04279,0.10677,-0.0594,0.02854,0.0568,0.02131,-0.03189,-0.01193,0.01595,0.07563,-0.07042,-0.10308,0.07884,0.08699,-0.08778,-0.02361,0.05855,-0.12747,0.02605,-0.04496,-0.08036,-0.10891,-0.11831,0.01998,-0.04837,0.05547,0.03136,-0.14334,-0.10549,0.08596,0.05775,-0.00348,-0.01779,-0.03398,0.00612,0.00047,-0.00648,0.04271,0.05287,0.0741,-0.0062,-0.02335,-0.05303,0.02798,-0.08492,-0.03806,0.02219,-0.00094,0.03596,0.02311,0.04403,-0.01437,0.13636,0.00964,-0.01904,0.10031,-0.00798,-0.0628,-0.06615,0.07828,0.03559,0.03616,-0.12581,0.03402,0.07399,-0.02539,-0.06196,0.01608,0.06531,-0.0058,-0.06717,0.06367,-0.07154,0.03326,-0.05398,0.15733,-0.12472,-0.03339,-0.03847,-0.17728,-0.02518,0.11611,-0.07136,-0.03215,-0.04605,0.04396,0.01781,0.02772,-0.07916,0.01416,0.01176,-0.00327,-0.13947,-0.02231,-0.00037,-0.04379,0.10699,-0.0302,-0.02667,-0.00209,0.03884,0.11502,-0.01788,-0.05311,-0.05444,0.10495,0.04191,-0.07182,0.06334,0.02252,0.03658,-0.02744,-0.09822,-0.02049,0.04321,0.074,-0.02438,0.02343,-0.01206,0.1482,-0.02943,-0.06842,0.06587,-0.06584,0.10911,0.01677,-0.02263,0.03822,-0.00113,0.11142,-0.00522,0.09523,-0.06135,-0.04662,-0.01738,-0.05765,-0.05349,-0.02766,-0.05815,0.15323,-0.07457,-0.058,-0.03802,-0.10331,-0.00644,-0.1087,0.00719,0.01555,0.06859,-0.00915,-0.00157,-0.05012,0.01954,0.09398,0.11091,0.09969,0.0508,-0.00368,-0.07386,-0.02575,-0.01892,-0.03328,-0.11704,0.02359,0.0928,0.01231,0.0059,-0.06487,-0.0602,0.0077,0.03125,0.04237,-0.03921,-0.00187,-0.02776,-0.07735,0.07173,0.02107,-0.05483,0.03701,0.10366,0.02417,0.01758,-0.00785,-0.01101,0.14596,0.00761,-0.08571,-0.04986,-0.03019,0.07732,0.04498,0.02676,0.09153,0.07161,0.0324,-0.02001,-0.05553,0.02942,0.07652,-0.00289,0.04372,-0.0354,-0.01511,0.03921,0.07663,-0.11092,-0.13181,-0.08646,-0.03684,0.0508,-0.10393,-0.00193,0.0117,-0.04888,-0.04204,0.03116,-0.06371,-0.02048,-0.00815,0.02602,0.02922,0.10132,-0.00537,0.05155,0.08325,0.04996,0.00091,-0.00766]},{"domain":"quantum_physics","key":"hydrogen_transition","name":"Photon from a hydrogen-like transition (Rydberg formula)","package":"quantum-physics-ai999x","example":"Hydrogen transition: Z = 1, n_upper = 3, n_lower = 2","v":[-0.02956,-0.05618,0.02541,-0.05814,0.02391,0.01694,0.03605,-0.12996,-0.07425,0.00763,0.08513,-0.0076,-0.03688,0.01596,0.02146,-0.00685,0.07461,0.06273,0.05895,-0.07568,-0.0177,-0.0239,-0.09132,-0.00328,0.00045,-0.05839,-0.02312,-0.10091,-0.15031,-0.03356,0.00532,-0.03512,-0.0433,0.06152,0.04814,0.00181,0.13671,-0.02939,-0.07239,-0.04876,-0.00716,0.00464,-0.05168,0.02473,-0.07824,0.05009,-0.13405,0.00608,-0.13526,0.01689,0.03573,-0.00656,-0.04687,0.05181,-0.07427,-0.10581,-0.00889,0.01502,-0.01646,0.04975,-0.02093,0.11471,0.14976,0.0021,0.03567,0.01903,0.05185,0.04344,0.11301,-0.0544,0.10051,0.09716,0.06698,0.03167,0.05766,0.00967,-0.17011,0.0355,0.01689,0.03203,0.11773,-0.04439,0.03533,0.01723,-0.05061,-0.11141,0.00813,-0.07068,0.0152,-0.0617,0.02809,0.08136,-0.02777,-0.07351,0.0644,-0.05186,-0.01267,-0.1155,0.0074,0.01026,0.04705,-0.00506,0.05639,-0.07809,-0.05199,-0.04875,-0.10078,-0.05244,0.02485,-0.03854,-0.06128,-0.11587,-0.02488,-0.04301,-0.05716,0.06585,-0.03255,0.00553,0.0347,-0.08023,-0.15567,-0.01436,0.0203,0.05399,0.00071,0.1665,0.02865,0.01169,0.0243,-0.0208,-0.05772,-0.01374,0.02405,0.03231,-0.01425,-0.00548,0.00749,-0.00843,0.16335,-0.01071,-0.14124,0.18523,0.09342,-0.09075,0.04952,0.00472,0.03578,-0.04441,-0.06076,0.02793,-0.00703,0.04062,0.06202,-0.00301,0.0312,-0.00312,0.08462,0.01249,0.1288,-0.00384,-0.01409,-0.02051,-0.01684,0.00754,-0.06923,-0.08132,0.04316,0.03793,-0.05318,-0.02239,0.09724,0.03792,-0.004,0.02174,0.07376,0.10189,-0.02682,0.01272,-0.0093,-0.05192,0.00302,0.05877,-0.00508,0.03874,-0.08309,0.02144,-0.0314,-0.0414,0.01923,-0.03345,-0.03645,0.07811,0.03006,0.015,-0.07491,-0.14751,-0.01239,-0.02588,0.03624,-0.02647,0.05514,0.01994,0.01622,-0.03825,0.02861,0.00444,0.0184,0.12977,-0.12023,-0.02756,-0.03739,0.08565,-0.01664,0.0492,-0.01964,-0.0097,0.02237,0.09794,0.01543,-0.03939,0.01652,0.01063,0.14658,-0.01147,-0.06216,0.07659,0.05835,-0.00759,0.00229,-0.11433,0.15715,-0.01541,-0.06526,-0.05198,0.04076,-0.05633,-0.01147,0.04037,-0.01533,-0.05152,-0.03585,0.00048,0.00194,-0.01264,-0.03322,-0.01554,-0.04117,-0.0392,0.15421,0.11607,-0.07444,0.07182,-0.03352,0.0601,0.04287,-0.02991]},{"domain":"quantum_physics","key":"hydrogen_transition_reduced_mass","name":"Hydrogen-like transition with the reduced-mass correction","package":"quantum-physics-ai999x","example":"Reduced-mass transition: Z = 1, n_upper = 3, n_lower = 2, M_u = 1.00727646688","v":[-0.02389,-0.01558,0.05092,-0.05555,0.06171,0.01014,0.05654,-0.14003,-0.01108,0.02289,0.11545,0.0045,0.00488,0.04885,0.01509,0.00496,0.1097,0.06995,0.12938,-0.04182,0.0718,0.02058,-0.07145,0.00927,-0.01012,-0.02771,-0.03363,-0.08639,-0.10135,-0.01352,-0.02324,-0.04236,-0.03325,0.00015,0.06217,0.03557,0.03648,-0.01651,-0.03354,-0.05711,0.02652,0.03492,-0.09221,-0.01972,-0.07149,0.04933,-0.09195,-0.04015,-0.06768,-0.01545,0.01047,0.01298,0.01631,0.03989,-0.04647,-0.0595,0.02569,0.02871,0.00969,0.03613,-0.01698,0.05124,0.15894,0.05073,0.11364,0.06293,0.11857,0.06103,0.07637,-0.05012,0.05064,-0.02711,0.11258,0.04883,-0.00491,0.05554,-0.1061,0.0431,0.01868,0.12175,0.09711,-0.10235,0.03754,-0.01683,-0.05727,-0.11398,0.0317,-0.0421,0.05958,-0.13237,0.05718,0.04641,0.00541,-0.02989,0.05753,-0.00854,-0.04127,-0.10758,0.00752,0.02134,0.08839,-0.09823,0.00172,-0.11558,-0.07712,-0.08435,-0.04227,-0.01896,-0.01685,-0.06293,-0.04751,-0.03307,-0.03524,-0.08708,-0.09154,0.01012,-0.00754,0.02713,0.02764,-0.08274,-0.13013,-0.04367,0.0587,0.14661,0.04363,0.11905,0.0548,0.01376,0.05073,-0.04644,-0.04574,-0.00781,0.00721,-0.02209,-0.05594,0.00495,0.03637,0.01638,0.14453,-0.05739,-0.06056,0.07821,0.08372,-0.06701,0.03332,0.03965,0.05107,-0.02404,-0.02877,0.00147,-0.05139,0.04592,0.05205,-0.02833,-0.04047,-0.03182,0.1057,-0.0482,0.0657,-0.0235,-0.01616,-0.05636,-0.01013,0.02237,-0.07995,-0.03624,0.06414,-0.02157,0.01099,-0.03638,0.02765,0.04738,0.01539,-0.02065,0.00723,0.18722,0.01608,-0.06437,-0.04259,0.01034,0.07547,0.12751,0.02075,-0.02533,-0.09703,-0.01739,-0.06245,-0.01486,0.02438,-0.08262,-0.02477,0.10824,0.04611,-0.04092,-0.04935,-0.16245,-0.04067,0.00926,0.03204,-0.05597,0.00743,0.03482,-0.1111,-0.02748,0.0154,-0.00939,0.06213,0.09753,-0.13121,-0.05773,-0.06978,0.05715,0.00567,0.0405,-0.02144,-0.00707,-0.04582,0.0445,0.00019,0.01849,0.04224,0.00959,0.08737,-0.03696,-0.08047,0.04308,0.0203,0.01284,-0.00445,-0.08457,0.15266,0.02666,-0.02471,-0.09987,0.05032,-0.1036,-0.00829,0.06249,-0.02523,-0.01457,-0.06635,-0.05059,-0.05533,-0.01071,-0.03559,-0.01,0.03162,0.0248,0.10118,0.1358,-0.12856,0.09495,0.01644,0.10042,0.0349,-0.02917]},{"domain":"quantum_physics","key":"infinite_well_levels","name":"Energy levels of a particle in a box","package":"quantum-physics-ai999x","example":"Particle in a box: m = 9.1093837139e-31 kg, L = 1 nm, n = 1","v":[-0.18564,-0.09793,0.09701,-0.11682,0.0607,-0.06836,0.07606,-0.14276,-0.12617,0.01392,0.04768,0.06886,0.00707,-0.02476,0.05086,-0.02435,0.06993,0.04633,-0.02235,-0.00303,0.02516,0.06495,-0.07126,0.07258,-0.00647,0.04699,-0.03603,-0.0496,-0.00926,-0.0064,-0.03183,-0.01112,0.03942,-0.05952,0.02556,0.00204,0.00167,-0.01216,0.03363,-0.13452,-0.01662,-0.08671,0.03093,0.05219,-0.003,0.05138,-0.01365,0.01342,-0.03194,0.00561,0.01724,-0.04254,-0.11486,0.00723,0.02033,-0.01704,0.0615,0.05573,0.0762,-0.03938,-0.04691,0.07352,-0.00416,0.04472,0.04984,0.08287,-0.00441,-0.13877,0.00379,0.02979,-0.01707,-0.06051,0.06494,0.04106,0.07248,0.04099,-0.01579,-0.03719,-0.01493,0.04137,0.02334,-0.05867,0.00509,-0.02675,-0.05746,-0.0833,0.03036,0.0657,0.0916,-0.06681,-0.02664,-0.00163,0.01715,-0.02512,-0.00734,0.04369,0.13514,-0.03637,0.08446,-0.01213,-0.03755,0.09735,0.02834,-0.02173,-0.0795,-0.01457,0.0211,-0.05201,-0.04235,-0.07608,0.01609,-0.06377,-0.11921,-0.03981,0.03161,-0.10394,0.13317,-0.00519,0.00245,-0.03419,-0.10331,0.07908,0.03814,0.09615,0.0284,-0.03874,0.07457,0.00821,-0.00954,0.04337,0.04164,0.03858,0.17413,0.03028,0.05445,0.0143,0.00564,0.07863,0.04964,-0.02256,-0.11465,-0.02582,0.01129,-0.02931,-0.0261,-0.05451,0.08124,0.10611,-0.05507,-0.10326,0.00207,0.03415,-0.04088,-0.02265,0.01672,0.05657,0.11076,0.03599,0.05974,0.06513,0.05656,-0.03614,0.08601,0.03048,-0.06054,-0.03065,0.05985,-0.01725,-0.14421,-0.05623,-0.0097,0.03134,-0.04668,0.00363,0.0134,-0.00907,-0.03547,-0.01829,-0.10134,-0.01983,0.17773,0.06174,0.05906,0.03212,-0.07901,-0.10806,-0.02148,-0.08835,0.0587,-0.05986,-0.08026,-0.0144,0.02797,0.06123,-0.0878,-0.04185,-0.08794,0.0026,0.02096,-0.05943,-0.00139,-0.08779,-0.12806,-0.06109,0.01815,0.00981,0.06753,0.02131,0.01021,0.00114,0.02801,0.03001,0.06703,-0.06222,0.02071,-0.07497,-0.08698,0.00536,0.12135,-0.01159,-0.162,0.00659,-0.02293,0.05777,0.01596,0.01169,0.06069,-0.04346,0.0124,-0.00151,0.09283,0.05728,0.06815,0.03196,0.05308,-0.03374,0.01568,0.02199,-0.04361,-0.11027,-0.08525,-0.05023,-0.0153,0.01721,-0.11242,-0.03914,0.10437,0.08633,0.02184,0.20533,0.00876,-0.06293,-0.0102,0.04064,-0.00475,0.04654]},{"domain":"quantum_physics","key":"infinite_well_probability","name":"Probability of finding a particle in part of a box","package":"quantum-physics-ai999x","example":"Particle in a box probability: n = 1, L = 1 nm, x1 = 0.25 nm, x2 = 0.75 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from a particle-in-a-box transition","package":"quantum-physics-ai999x","example":"Particle in a box transition: m = 9.1093837139e-31 kg, L = 1 nm, n_upper = 2, n_lower = 1","v":[-0.1191,-0.07353,0.09128,-0.03634,-0.01997,0.00396,0.03245,-0.16984,-0.05785,0.0348,0.07486,0.07338,-0.03173,-0.0224,0.05421,-0.05669,0.08904,0.0638,0.03752,-0.06693,0.01863,0.06702,-0.13931,0.02726,0.01878,0.01261,-0.04361,-0.0687,-0.08338,-0.01927,0.02199,-0.02553,-0.007,-0.00046,0.04756,0.01001,0.07148,0.0048,-0.03224,-0.02117,-0.10677,-0.04382,0.07679,0.02258,-0.02192,0.03812,-0.07708,0.07025,-0.06916,0.05945,0.01979,0.02197,-0.11933,0.00688,0.02729,0.00906,0.03577,-0.00218,0.08789,0.02454,-0.04217,0.07409,0.11818,0.06176,0.09155,0.01385,0.04149,-0.03591,0.07987,-0.02826,-0.01414,0.05422,0.10443,0.04733,0.01757,0.02811,-0.16239,-0.0076,-0.0401,0.03437,0.15156,-0.07955,0.01396,0.05823,-0.07322,-0.11877,-0.00331,0.04974,0.04669,-0.04765,0.02604,0.04056,-0.01562,0.01069,0.04182,0.00356,0.07885,-0.05726,0.02081,0.05372,-0.01094,0.05142,0.00374,-0.00181,-0.05787,0.01948,-0.02171,-0.08107,-0.03914,-0.08015,-0.03715,-0.07907,-0.13915,-0.07311,-0.02836,-0.03187,0.12714,-0.03491,0.01811,-0.03054,-0.17385,0.02289,0.00456,0.0753,0.04885,0.12613,0.034,0.00797,-0.06789,0.00779,0.05334,-0.00072,0.05673,0.03018,-0.01214,0.03726,0.04545,0.04576,0.16351,-0.0019,-0.18067,0.06514,0.02951,-0.12182,-0.03488,-0.08309,0.06847,0.06712,-0.06871,-0.11519,0.02438,-0.03125,0.03855,-0.02252,-0.03175,0.01771,0.05595,-0.00564,0.06597,0.04976,-0.02184,-0.0289,0.04255,0.07897,-0.03942,-0.06122,0.03996,0.04554,-0.09552,-0.04365,0.06778,0.09119,0.01188,-0.01115,-0.01152,0.0529,-0.05504,-0.06705,-0.06982,-0.07802,0.03365,0.06055,0.05307,0.02204,-0.08049,-0.03338,-0.02087,-0.05164,0.07519,-0.08417,-0.11033,0.03285,0.04598,0.06631,-0.09995,-0.08919,-0.01373,-0.02565,0.03002,-0.04914,0.08987,-0.0197,-0.07335,-0.07409,0.02925,-0.00517,-0.01142,0.10908,-0.10675,-0.0543,-0.02569,0.05165,0.00716,0.0317,0.00075,0.00501,0.00312,0.10784,0.09547,-0.03351,-0.10245,0.03092,0.03624,-0.02566,-0.03003,0.04066,0.03367,-0.03234,0.01752,-0.0715,0.1397,-0.03,-0.06947,0.04421,0.07222,-0.03533,0.02682,0.00673,-0.0279,-0.04671,-0.03625,-0.05015,-0.03214,-0.01845,-0.10273,-0.01312,0.0041,0.0181,0.08939,0.17918,-0.05246,-0.008,-0.03843,0.06833,0.03426,-0.03879]},{"domain":"quantum_physics","key":"infinite_well_uncertainty","name":"Position 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mass of two particles","package":"quantum-physics-ai999x","example":"Invariant mass: E1 = 50; p1 = 30, 0, 40; E2 = 50; p2 = -30, 0, 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g factor and anomalous Zeeman shift","package":"quantum-physics-ai999x","example":"Landé g factor: L = 1, S = 0.5, J = 1.5, mJ = 0.5, B = 1 T","v":[0.03184,0.02177,-0.07685,-0.00339,0.05766,0.03052,0.04719,-0.16773,-0.01215,0.05157,-0.00198,-0.15683,0.06496,0.03189,-0.07305,-0.0316,-0.02065,0.03979,-0.02793,0.07925,0.01845,0.04775,-0.0721,0.00043,0.06201,-0.04531,0.10723,-0.06888,-0.00763,0.06172,-0.02597,0.00986,-0.01752,0.02937,-0.05422,0.02117,-0.04146,0.03426,0.01875,-0.08683,-0.00524,-0.07439,0.06539,0.04362,0.07488,-0.00651,-0.03574,0.08337,0.01968,-0.07197,-0.03958,-0.03249,0.06352,0.03659,0.03677,0.06384,-0.07357,0.00905,-0.01723,0.00157,-0.04573,0.04192,-0.03079,-0.065,-0.03612,-0.03818,-0.00989,-0.01649,-0.07054,-0.01271,0.05797,-0.00389,-0.00896,0.06573,0.03804,-0.12018,0.01169,0.11285,0.02715,0.00722,0.06367,0.08965,0.03037,0.01142,-0.03791,-0.0906,-0.01413,-0.14164,0.10475,-0.02369,-0.0329,-0.05344,-0.03268,-0.05716,-0.07736,0.03491,0.02715,-0.09793,0.01666,-0.06598,0.03015,-0.01332,-0.01546,-0.06136,0.05056,-0.03172,-0.08678,-0.04552,0.00459,0.05231,-0.0065,-0.00114,0.04572,-0.01684,0.01688,-0.06355,0.0184,0.00897,-0.00245,0.0077,-0.00443,0.04749,0.02815,-0.02999,-0.01278,-0.0773,0.02911,-0.00388,0.12012,0.05826,0.04369,-0.03112,0.09731,0.02409,0.14662,-0.06651,-0.01412,-0.04344,-0.00304,-0.04806,0.03008,-0.08867,-0.03385,0.01817,-0.03321,-0.02515,0.04099,0.00425,0.07521,-0.04292,0.01129,-0.00038,-0.02417,-0.04456,0.00404,0.01457,0.13262,0.07792,-0.01114,-0.12318,0.09697,-0.0813,-0.00379,0.00155,-0.11738,-0.05329,0.18402,0.04238,-0.11931,0.09155,0.01995,0.00959,-0.08323,-0.02613,0.00366,0.09651,-0.04564,0.04812,-0.09903,-0.00797,0.12168,0.00698,-0.06274,-0.08963,-0.01911,-0.0344,0.013,0.04246,0.02869,-0.05266,-0.03735,0.09845,0.05249,-0.01072,-0.07991,-0.10471,-0.05152,-0.00883,-0.04543,0.06801,-0.05315,-0.03851,-0.04568,0.02254,0.17618,0.00456,0.06616,0.07803,-0.06345,0.02877,-0.0341,0.18001,-0.04445,0.01661,-0.02921,-0.06333,0.0045,-0.06938,0.09923,-0.03436,-0.09578,0.05048,0.06471,0.05609,-0.15522,0.03986,0.14606,-0.06288,0.04708,-0.03088,-0.00132,-0.02503,0.13409,-0.0667,0.02281,0.07761,0.04456,0.084,-0.0073,-0.02365,-0.05899,-0.01536,0.05615,0.079,-0.14553,-0.04225,0.11343,0.0594,0.02082,-0.03021,0.00035,-0.08242,0.08906,0.10277,-0.05122,-0.07295]},{"domain":"quantum_physics","key":"larmor_precession","name":"Larmor precession of a spin-1/2","package":"quantum-physics-ai999x","example":"Larmor precession: particle = proton, B = 1 T, t = 0 s","v":[0.02706,0.02117,-0.14467,0.05194,0.08637,0.16334,-0.0069,-0.00607,0.11612,0.10556,0.02875,-0.02288,0.01423,0.08424,-0.00296,-0.0274,-0.14852,0.09237,0.04267,-0.0235,-0.05667,0.00636,-0.14643,-0.04034,0.11397,-0.10729,-0.00077,-0.06744,0.06891,0.07915,0.00856,0.0231,0.05345,0.01612,-0.02453,0.08412,0.01167,-0.01568,-0.05902,0.02789,0.01956,-0.08187,0.13309,-0.01119,-0.02288,-0.09968,0.05161,-0.01792,0.0291,-0.06671,-0.04358,-0.01959,-0.03379,0.05699,-0.06506,0.04884,0.00908,0.02684,-0.01146,0.04653,0.00773,0.01819,0.02144,-0.04316,-0.07126,-0.0076,-0.06427,0.023,-0.05287,-0.06784,0.0004,-0.01,-0.04081,-0.05155,-0.01913,-0.05257,0.06378,0.06351,0.0664,0.05205,0.11876,0.05239,0.00753,-0.00729,-0.08957,-0.01487,-0.06811,-0.08546,0.1436,-0.08946,0.05293,-0.11605,-0.05306,-0.06362,-0.0812,0.00842,0.06637,-0.03102,0.04527,0.00013,-0.01313,-0.03375,-0.02864,-0.03507,0.06047,-0.11968,-0.07653,-0.04178,-0.01786,3e-05,0.0582,0.03746,0.0136,0.07181,0.00059,-0.07718,0.05534,0.02222,-0.02511,-0.03139,-0.03283,-0.02644,-0.02691,0.04409,-0.07804,0.02902,0.02519,-0.02114,0.06676,-0.01837,0.02923,0.04879,0.03204,-0.02939,0.01071,-0.04994,0.02167,-0.04189,-0.00987,-0.04763,-0.05473,-0.00622,-0.057,-0.07532,-0.13945,-0.04593,0.01322,0.01976,0.06994,0.00734,0.0773,-0.05075,0.07818,0.00485,-0.04348,-0.02282,0.09757,0.0769,0.00278,-0.13636,0.06753,-0.0519,0.01248,0.11738,-0.08065,-0.05714,0.11157,0.1415,-0.13609,0.04927,0.1267,-0.04918,-0.01221,0.00278,-0.01348,0.05779,0.06435,0.07088,-0.07911,0.01511,-0.02765,-0.02381,-0.0331,-0.0902,0.02134,0.04804,0.02775,0.07262,0.00209,-0.00637,-0.00053,0.01653,0.01021,-0.12985,0.01631,-0.11217,0.02638,-0.08506,-0.07067,0.0642,0.00179,0.03352,-0.10327,0.06423,0.11374,0.03903,0.11022,0.11367,-0.04663,0.05029,0.05022,0.12558,-0.04995,0.02578,-0.05835,-0.0361,0.0174,-0.07699,0.06619,-0.00982,-0.13874,-0.01365,0.03526,0.00078,-0.00355,0.01421,0.08016,-0.1118,0.10096,-0.05396,0.02896,-0.10981,0.012,-0.04707,-0.00037,0.06005,-0.01311,0.0644,0.00855,-0.01489,-0.02109,0.00173,-0.00253,0.11154,-0.0401,-0.1001,0.02414,-0.03138,0.01547,0.00218,0.06734,-0.03362,0.1242,0.07612,-0.01315,-0.00587]},{"domain":"quantum_physics","key":"length_contraction","name":"Length contraction","package":"quantum-physics-ai999x","example":"Length contraction: L0 = 100 m, v = 0.6 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factor","package":"quantum-physics-ai999x","example":"Lorentz factor: v = 0.6 c","v":[0.05537,0.05049,0.02117,0.07498,0.00972,-0.02623,-0.05683,0.07219,0.04849,0.02552,0.0171,-0.08644,-0.00689,-0.00526,0.01747,-0.01806,-0.17409,-0.01503,-0.1125,0.04344,0.04023,0.12767,0.00751,-0.04065,0.09576,0.02492,-0.02899,-0.02172,-0.01514,0.06892,-0.02231,-0.01556,0.01103,-0.03037,-0.06402,0.03559,0.00256,-0.08353,-0.10606,0.02741,0.0443,-0.02334,0.07306,-0.09008,0.06129,-0.0604,0.00746,-0.0506,-0.04647,-0.03018,0.02932,-0.06554,-0.10009,0.00427,0.00989,0.09349,0.00466,0.05143,-0.04916,0.01875,0.08966,-0.08283,0.14639,-0.02919,-0.06253,0.09379,0.0642,0.04695,-0.12746,0.09722,-0.05662,0.10681,0.05473,-0.11924,-0.0443,0.0019,0.03488,-0.04517,0.16962,0.05493,0.14995,0.1202,-0.08165,0.01653,-0.10857,-0.04508,-0.07237,-0.00503,0.05742,0.00826,0.06994,0.05539,-0.01888,-0.06801,0.06405,0.06431,0.02979,-0.07382,0.07918,-0.05726,-0.06065,-0.01344,-0.04077,-0.06587,0.01946,-0.11603,-0.03567,-0.05534,0.08742,0.03519,-0.00704,0.03477,0.06438,-0.01857,-0.03895,0.02778,0.00297,0.00162,-0.03327,-0.04024,-0.06105,0.00607,-0.02331,0.04494,-0.01694,0.06949,-0.0208,0.08348,-0.04043,0.02268,0.03407,0.03466,-0.03247,-0.05493,-0.05273,-0.0332,-0.06992,-0.03123,-0.00337,0.03975,0.05767,0.1526,0.093,0.04821,-0.0706,-0.0447,0.02551,-0.00718,-0.03117,0.12361,0.115,-0.00658,0.07879,-0.08271,-0.03702,-0.16087,0.05742,-0.07533,-0.04348,-0.06893,0.07592,0.0158,0.01517,-0.05651,0.06101,0.00777,0.06688,0.04635,0.01112,-0.06138,-0.07937,0.06067,-0.00076,0.05331,0.0016,0.02856,-0.00429,0.12749,0.12726,-0.03279,-0.03325,-0.07339,0.05159,-0.0091,0.10074,-0.02969,-0.00966,-0.01173,-0.06661,0.0863,-0.09348,-0.09845,0.00511,-0.02991,0.01793,-0.09676,-0.02127,-0.06822,0.02525,0.03086,-0.01215,-0.07964,0.01402,-0.00106,-0.00874,0.02627,-0.02622,0.07662,0.033,-0.00132,0.01725,0.0818,-0.00669,-0.00979,0.02984,0.0272,-0.02245,0.01094,-0.09331,0.07865,-0.10123,-0.06266,-0.01861,0.06054,-0.00756,-0.00855,0.04678,0.06826,0.10892,-0.01443,-0.03555,0.05497,-0.04224,-0.09421,0.02195,-0.06373,-0.01033,0.02122,0.01571,-0.12344,0.06625,0.13402,0.02109,-0.08143,0.02081,-0.07398,-0.05523,-0.02417,-0.04061,0.00331,0.10385,0.03101,-0.12644,0.09469,-0.04866,0.00378]},{"domain":"quantum_physics","key":"moseley_k_alpha","name":"K-alpha X-ray line (Moseley's law)","package":"quantum-physics-ai999x","example":"Moseley's law: Z = 29","v":[0.01269,-0.00966,0.00205,0.04316,-0.04314,0.03963,-0.07291,-0.01047,0.02975,0.01704,0.04039,-0.03627,-0.02207,0.01011,-0.07091,0.09741,0.08135,0.04581,-0.01028,-0.09737,-0.02833,0.04049,-0.10698,0.12837,-0.04138,-0.05633,-0.03078,-0.0092,-0.04123,-0.03636,-0.04633,-0.07037,-0.01532,0.07372,0.02663,-0.01674,0.08308,0.01518,-0.01524,-0.02177,-0.08272,-0.00524,-0.07162,0.03086,-0.06503,0.06909,-0.15498,0.06491,0.04268,0.05188,0.01349,0.09105,0.02542,0.03936,-0.07027,-0.03837,0.00052,0.01451,-0.03053,0.07255,-0.1027,0.03974,0.09551,0.13581,0.00574,0.02491,-0.00283,0.04392,-0.04323,-0.03509,-0.00804,0.0834,0.13274,-0.09181,0.022,0.11811,0.07195,0.0524,0.12208,0.09625,0.02411,0.05493,0.05501,-0.02777,-0.01294,-0.07812,-0.01288,0.10232,0.01391,-0.04964,0.05011,-0.00075,0.01784,-0.09794,0.02964,-0.18439,-0.10084,-0.16587,0.05366,-0.03177,0.03198,-0.01068,-0.05471,-0.05711,-0.0089,0.05588,-0.0816,-0.02292,0.02208,0.04548,-0.02641,-0.09525,-0.00345,-0.0648,-0.10418,-0.01838,-0.05639,-0.05124,0.07563,0.01254,-0.02708,-0.08042,0.06281,0.03179,-0.03423,0.07175,0.03757,0.03787,0.02954,-0.05473,-0.06691,0.05013,-0.03042,0.05401,-0.05049,-0.03537,-0.04818,0.01211,0.09739,-0.02253,-0.01283,0.04744,-0.02605,-0.04921,-0.06229,-0.06354,0.05345,0.01049,-0.0361,-0.03412,-0.0005,0.12383,-0.00739,0.05857,0.07997,-0.05052,0.07087,0.02771,0.02756,-0.12277,-0.09811,-0.10332,-0.06575,0.0937,-0.11269,-0.01715,-0.00367,0.00503,-0.07244,0.01494,0.08509,-0.04825,0.10845,0.03016,0.05259,0.0058,0.0244,-0.09296,0.00765,-0.02468,0.00092,0.07128,-0.01723,0.0229,-0.06601,-0.02264,-0.03067,-0.01915,0.00209,0.05116,-0.06565,-0.03712,0.0242,0.03081,-0.03233,-0.02494,0.03585,-0.05843,0.06426,-0.05821,0.04467,-0.05589,-0.00239,0.02317,-0.01497,-0.11193,0.07921,0.09204,-0.04404,-0.03494,-0.07217,0.13598,-0.03831,0.03434,-0.00515,0.07931,-0.05532,0.04358,0.02193,0.05062,-0.06778,-0.02463,0.05468,0.06957,-0.00268,0.05523,0.06869,0.01727,0.0676,0.01532,0.0262,0.08126,-0.00898,-0.05318,-0.07708,-0.16124,0.02741,-0.02877,-0.15957,-0.01367,-0.05121,0.01166,-0.01095,-0.00591,-0.04135,0.06297,-0.03556,0.03879,0.15674,0.11321,-0.17292,0.10012,-0.02002,0.04754,0.07448,-0.04556]},{"domain":"quantum_physics","key":"nuclear_reaction_threshold","name":"Q value and threshold energy of a nuclear reaction","package":"quantum-physics-ai999x","example":"Reaction threshold: m_a = 4.002603254, m_X = 14.003074004, m_Y = 16.999131757, m_b = 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0","v":[0.02719,-0.12792,-0.02662,0.10252,0.019,-0.09064,0.02581,0.01753,-0.02101,-0.09571,0.06327,-0.02107,0.0059,0.0132,-0.02106,-0.04032,0.0135,-0.1151,0.07759,-0.03382,0.0475,0.04384,0.06954,0.03364,0.01659,-0.0989,-0.02792,-0.0556,-0.0205,-0.02872,0.03136,0.10488,-0.05535,-0.05205,-0.05653,0.07428,0.05227,0.07382,0.02881,0.07463,0.09717,-0.02778,0.08404,-0.02823,-0.0765,-0.12243,0.01787,0.02464,-0.0792,-0.09009,-0.02601,0.11361,-0.07552,-0.12163,-0.07207,-0.01309,0.00859,0.159,0.07701,-0.01915,0.0481,-0.09073,-0.02735,0.04436,0.01542,0.03993,0.07303,-0.02866,-0.13006,0.0195,0.07679,-0.01897,-0.05625,0.13177,0.1407,0.02989,0.01697,0.04489,-0.13189,-0.02526,0.02771,-0.05227,0.03089,0.00883,0.03538,-0.03598,-0.05438,0.01966,0.03891,0.00752,-0.07506,-0.09679,-0.00078,-0.04089,-0.11111,-0.06844,0.05488,0.05687,-0.00686,-0.08018,-0.04289,-0.02129,0.02151,0.07652,-0.01019,-0.07548,0.01086,-0.07331,-0.00539,-0.1113,-0.04727,-0.02139,0.05293,0.1326,-0.00342,-0.07084,-0.01846,-0.06231,0.04374,-0.02146,0.05738,0.0492,-0.03116,0.02689,-0.10859,-0.1015,-0.07674,-0.06329,0.06672,0.06493,0.0022,-0.07274,-0.08897,0.02992,0.07122,-0.03456,0.02843,0.06704,-0.01179,-0.18733,0.07369,-0.0232,-0.04179,0.04652,0.05067,0.02118,0.11593,0.03913,0.0825,0.05505,-0.00157,-0.0404,-0.09123,-0.03899,0.03884,-0.07297,0.03159,-0.06684,-0.0264,-0.00188,0.04527,-0.04365,0.03573,-0.07879,-0.04635,0.00759,0.00261,0.09307,0.05217,-0.05753,-0.02116,0.03942,-0.084,0.03984,-0.00329,0.02659,0.06324,0.00798,-0.0598,-0.02075,0.05896,0.03957,0.02423,0.03025,0.00935,-0.02952,0.00891,0.03719,0.05286,0.06486,-0.03251,-0.00053,0.03316,-0.00268,-0.01213,-0.01836,0.04366,-0.02943,-0.03762,-0.04236,0.05365,0.0633,0.05982,-0.0465,-0.03229,-0.03717,-0.09219,-0.01902,0.08755,0.13305,0.06998,0.02151,0.02636,0.07827,-0.1143,-0.06119,-0.11033,0.06169,0.05976,0.06001,-0.03768,-0.01695,0.05048,0.00636,0.01201,0.00126,0.02088,-0.05765,0.0394,0.02305,0.00013,0.05675,-0.04477,0.01517,0.00291,0.10654,0.07072,-0.0628,0.00404,-0.00968,0.17048,-0.0934,-0.04818,0.06084,-0.10523,-0.03848,-0.02548,0.07137,0.03595,-0.00103,0.15643,-0.07535,-0.04005,-0.10426,-0.05372,0.10823]},{"domain":"quantum_physics","key":"qubit_state_bloch","name":"Qubit state on the Bloch sphere","package":"quantum-physics-ai999x","example":"Qubit state: a_re = 0.6, a_im = 0, b_re = 0, b_im = 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oscillation of a driven two-level system","package":"quantum-physics-ai999x","example":"Rabi oscillation: Omega = 1e6 rad/s, Delta = 0 rad/s, t = 1.5707963267948966 us","v":[-0.02878,-0.04188,-0.08157,0.07917,0.01762,-0.05187,0.01002,-0.11645,0.08249,0.10102,0.04808,-0.01416,-0.04884,0.06457,-0.02747,-0.04178,0.01859,-0.03307,-0.02971,-0.0753,0.03521,-0.06521,-0.0898,0.02375,0.02558,-0.04946,0.0047,-0.03809,0.03055,-0.00803,0.10472,0.05156,-0.03477,0.03379,-0.05583,0.17445,-0.03194,0.03876,-0.12334,-0.04548,0.00999,-0.08163,0.0567,0.01488,-0.08288,-0.09678,0.0237,0.08982,-0.06186,-0.20258,-0.12025,0.09669,-0.04337,-0.05009,-0.00404,-0.002,-0.05992,0.09696,0.0391,0.02743,0.01211,0.01566,0.07348,-0.03388,0.07916,-0.11718,-0.01933,-0.0176,-0.01601,-0.11834,0.01111,0.01186,0.02603,0.10641,0.08846,-0.05361,-0.05334,0.06225,-0.05781,0.072,0.00154,0.02254,0.02995,-0.00939,-0.04022,-0.09703,0.04534,-0.03841,0.04831,-0.01813,-0.09774,-0.03515,0.04753,0.0123,-0.10785,-0.03485,0.16876,-0.02388,0.08568,-0.08363,-0.07611,-0.08268,0.08353,-0.02317,0.00512,-0.00362,-0.16719,0.05807,0.10495,0.02215,0.03592,-0.01305,-0.06737,0.00476,0.02966,-0.05323,-0.06789,-0.07671,0.05987,-0.05709,-0.06066,-0.0475,-0.12432,0.04364,-0.02445,-0.10822,-0.07837,-0.10685,-0.05733,-0.01768,-0.01731,-0.05677,-0.02922,0.05483,0.0196,0.02016,-0.0291,-0.03138,0.07134,-0.03616,-0.10142,0.0775,-0.07653,-0.03923,-0.04363,0.00793,-0.02111,0.00527,0.05045,-0.01982,0.03598,-0.03751,-0.0122,0.04797,-0.04363,0.10018,0.08655,0.02138,0.11946,-0.01369,0.06393,-0.06155,0.05503,0.02679,0.00574,-0.03538,0.09598,0.06772,0.00857,-0.03851,0.05524,0.05268,-0.06525,0.04784,0.06464,0.09171,-0.05258,0.0809,-0.04892,-0.08628,0.05182,0.10893,0.00285,-0.06331,-0.05849,-0.02699,-0.01668,0.05013,0.07207,0.0124,-0.05325,0.0458,-0.00727,-0.04396,-0.00737,-0.01788,0.03199,-0.0115,-8e-05,-0.00769,-0.01724,-0.01273,0.00988,0.04506,0.01436,0.01747,-0.01685,0.06368,-0.00863,0.05447,0.06822,-0.03441,0.03173,-0.00809,-0.02269,-0.10197,-0.10872,-0.0141,0.02823,-0.0668,0.07303,0.04398,-0.0317,0.03596,-0.01078,-0.05647,0.1153,-0.09685,0.08781,0.03602,0.05334,-0.09713,0.01387,0.10632,0.00202,0.0841,0.06979,0.08578,0.04443,0.00268,0.1466,-0.0203,0.04582,0.05576,-0.08897,-0.03544,0.01875,0.01724,0.05872,0.07226,0.10593,-0.08742,0.0747,-0.02052,0.03372,-0.01511]},{"domain":"quantum_physics","key":"radioactive_dating_age","name":"Age from the remaining fraction (radioactive dating)","package":"quantum-physics-ai999x","example":"Radioactive dating: fraction = 0.25, T_half = 5730 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decay law","package":"quantum-physics-ai999x","example":"Decay law: T_half = 5730 yr, N0 = 1e20, t = 11460 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aberration of light","package":"quantum-physics-ai999x","example":"Aberration of light: theta = 90 deg, v = 0.6 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Doppler shift","package":"quantum-physics-ai999x","example":"Relativistic Doppler shift: f = 1e14 Hz, v = 0.6 c, motion = 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energy from momentum","package":"quantum-physics-ai999x","example":"Relativistic energy from momentum: m = 1 kg, p = 224844343.5 kg*m/s","v":[-0.08669,-0.01763,0.04241,-0.04384,0.07476,-0.04785,0.11741,0.049,-0.01437,0.02318,0.07224,0.05681,0.00473,-0.0513,0.01442,-0.07119,0.00678,0.01621,-0.00723,-0.02078,0.0452,0.05343,-0.00453,0.05789,-0.0368,0.07093,0.0662,-0.01531,0.04431,0.04699,-0.03499,-0.12828,-0.04678,0.0099,-0.02391,-0.01557,-0.08854,-0.00338,0.01075,-0.13066,-0.03209,-0.06378,0.01119,0.01988,-0.04277,0.09502,-0.07247,0.00357,0.03782,0.03035,-0.02393,-0.02404,-0.07807,0.10823,0.04791,0.06671,-0.01621,-0.03428,0.0348,0.00493,-0.02726,-0.00171,0.02229,-0.08117,-0.01405,0.04053,-0.04886,-0.11407,-0.04986,0.08129,-0.10094,0.00811,0.0089,-0.07481,0.07287,0.04844,0.12184,-0.04549,0.07057,0.0464,0.04885,-0.04388,-0.0461,0.01586,0.00211,-0.10994,-0.02916,0.11553,-0.02949,-0.0415,0.03229,0.02022,-0.07396,-0.02619,-0.04036,-0.03324,0.08501,0.01003,0.00245,-0.01738,-0.00369,0.02457,-0.11201,-0.01111,-0.11072,-0.08084,0.00411,-0.05377,-0.12794,0.14244,0.04759,0.08212,-0.00949,-0.02212,-0.06669,-0.0621,0.10832,-0.01298,0.00648,0.0171,-0.0766,0.10932,-0.03019,0.11041,0.04069,-0.0443,0.06257,-0.05018,0.08431,0.08243,0.02246,-0.02691,-0.00132,-0.00194,0.03683,-0.04639,0.03476,-0.06976,-0.00129,0.05423,-0.02758,-0.00574,0.10717,0.03966,-0.05017,-0.00821,-0.01349,0.09167,-0.06538,-0.00856,-0.05884,0.11737,0.01946,-0.08098,-0.01353,0.0383,0.01167,-0.03251,0.02597,-0.06215,0.03582,-0.0579,0.02215,0.05562,-0.07051,0.02565,-0.06995,0.0007,-0.06151,-0.00093,-0.02334,0.01654,0.05313,-0.05124,0.01357,0.06158,0.02609,0.06537,-0.07165,0.09372,0.15394,-0.06746,0.04723,0.04969,-0.0579,0.02953,-0.03959,-0.15363,-0.02083,-0.05692,-0.09629,0.02301,-0.04053,0.11657,-0.05193,-0.06634,-0.13789,-0.02216,0.11496,-0.07542,-0.03237,-0.13898,0.04771,0.08417,-0.04169,0.00583,0.07135,0.02901,-0.00896,-0.00965,0.01204,0.09235,0.03804,-0.07178,0.02955,-0.03849,-0.14285,-0.03077,0.02455,-0.00525,0.02608,-0.12667,-0.01296,0.16097,-0.06162,-0.00196,-0.02,0.04273,0.07283,0.06694,0.0393,0.14345,0.09478,0.00174,0.0117,-0.07727,0.03656,-0.05507,0.05713,-0.08307,0.0081,0.02377,0.08705,0.18058,-0.01062,-0.00335,0.07324,0.03173,0.01846,0.11814,-0.04519,-0.02317,-0.04871,-0.02799,-0.11817,-0.03128]},{"domain":"quantum_physics","key":"relativistic_momentum_energy","name":"Relativistic momentum and energy","package":"quantum-physics-ai999x","example":"Relativistic momentum and energy: m = 1 kg, v = 0.8 c","v":[-0.07669,0.02318,0.07398,-0.03068,0.07977,-0.05857,0.08326,0.07,0.01467,0.01973,0.03876,0.09208,-0.05567,-0.01935,-0.00374,-0.09583,-0.04476,0.0306,-0.09936,-0.06357,0.01823,0.09787,-0.02962,0.05596,-0.01441,0.07862,0.04147,-0.05136,-0.02059,0.08316,-0.00355,-0.10573,-0.0619,-0.03111,-0.03778,-0.00942,-0.05407,-0.02315,0.0119,-0.15666,0.0363,-0.05411,0.05454,-0.02354,-0.01445,0.07279,-0.09159,-0.05708,0.02798,0.03823,0.00561,-0.01179,-0.0713,0.10643,0.00271,0.05562,0.03706,-0.01015,0.01017,-0.01907,-0.006,-0.09302,0.11187,-0.01709,0.00174,0.11389,-0.0849,-0.03532,-0.06606,0.15275,-0.08682,0.01619,0.01437,-0.06348,0.05258,0.10011,0.14986,-0.0864,0.09076,0.02088,0.07345,0.04136,-0.04966,0.00026,-0.06606,-0.08577,-0.05503,0.02261,-0.00168,-0.05311,0.04561,0.04642,-0.03781,0.00341,-0.01415,0.03647,0.0878,0.00896,0.04449,-0.01316,0.00468,-0.03742,-0.11896,-0.00754,-0.11708,-0.13665,0.0427,-0.03529,-0.1548,0.14976,0.02277,0.05046,0.05083,-0.01198,-0.09118,-0.02074,0.05059,-0.0701,0.06023,0.04607,-0.0753,0.03751,-0.00694,0.02752,0.05976,-0.00156,0.10143,0.03777,0.04647,0.05044,-0.00579,0.0292,-0.06187,-0.00788,0.05311,-0.02257,0.01171,-0.05995,-0.0144,0.10013,0.00089,0.0803,0.07027,-0.01979,-0.0391,0.03775,-0.03947,0.04586,-0.0226,-0.00864,-0.02887,0.08518,0.05663,-0.11065,-0.06106,-0.03804,0.01886,-0.05471,0.0614,-0.11014,0.07429,0.03362,0.02205,0.02341,-0.01089,0.03656,-0.10483,0.05434,-0.02206,0.01476,-0.03509,-0.03041,0.06384,0.01303,-0.01541,-0.01375,0.01536,0.09593,0.04401,0.04399,0.11619,-0.06279,-0.02481,0.01137,-0.03572,0.02442,-0.07503,-0.1053,0.03594,-0.00859,-0.13921,-0.04613,0.02385,0.08401,0.0114,-0.09945,-0.0954,-0.03945,0.09001,-0.03902,-0.04612,-0.06931,0.07292,0.01083,-0.11829,-0.04842,0.08847,0.05165,-0.00259,-0.05434,0.03741,0.09219,0.02417,-0.09667,0.07533,-0.04093,-0.11577,-0.04221,-0.01685,-0.03927,0.00982,-0.07604,-0.06193,0.15752,-0.05963,0.02467,-0.01575,0.05464,0.06784,0.03783,0.02826,0.14776,0.09083,0.068,0.00991,-0.10603,0.05139,-0.03489,0.00972,-0.13583,0.0156,0.06138,0.03648,0.06591,0.03532,-0.01374,0.01058,-0.00886,0.01126,0.07513,-0.01987,-0.00617,-0.07478,0.05273,-0.0606,-0.05834]},{"domain":"quantum_physics","key":"relativistic_speed_from_kinetic_energy","name":"Speed from relativistic kinetic energy","package":"quantum-physics-ai999x","example":"Speed from kinetic energy: m = 1 kg, K = 22468879468420441 J","v":[-0.03877,-0.01668,0.06769,-0.02276,0.07134,-0.08538,0.05642,0.08828,0.01477,0.02896,0.03128,-0.00609,-0.0261,-0.0598,0.05053,-0.06701,-0.09995,-0.03507,-0.11563,0.00907,0.07204,0.15295,0.03314,0.03521,-0.01498,0.04051,0.10747,-0.0548,0.03719,0.01133,-0.03088,-0.10191,-0.04733,0.01863,-0.04439,-0.04832,-0.09796,-0.02385,-0.0511,-0.12631,0.01371,-0.05401,0.06919,-0.01308,-0.03119,0.05595,-0.02025,0.05722,0.03093,-0.01543,0.02221,0.00172,-0.11389,0.05939,0.05768,0.10785,-0.00628,-0.00705,0.04605,-0.0067,-0.01192,-0.09497,0.06025,-0.05049,-0.0452,0.10441,-0.03533,-0.03704,-0.09948,0.18467,-0.08294,0.02978,0.01951,-0.12401,0.06651,0.06475,0.08445,-0.09354,0.15949,-0.00256,0.03706,0.03481,-0.10979,0.06277,-0.04828,-0.08396,-0.02208,0.04491,0.02073,-0.03313,0.06004,0.03408,-0.02662,-0.04351,0.046,0.01912,0.10163,-0.03737,0.04271,-0.02454,-0.02204,0.04168,-0.10532,0.01268,-0.09991,-0.0881,0.02228,-0.02649,-0.07606,0.08989,0.06146,0.07083,0.04124,-0.05344,-0.10008,-0.01959,0.07621,-0.01489,-0.0196,-0.0154,-0.07195,0.02172,-0.02117,0.11651,0.00421,-0.01485,0.04708,-0.01388,0.04562,0.05145,0.0098,-0.0236,0.00413,-0.00231,2e-05,-0.07609,0.00586,-0.00389,0.03661,0.02469,-0.02069,0.08333,0.10928,0.00855,-0.11272,-0.04339,-0.03886,0.09987,-0.0898,0.01278,0.00104,0.03753,0.03894,-0.07664,-0.03165,-0.05488,0.05383,-0.04709,-0.04823,-0.12597,0.07373,-0.03723,0.02676,-0.00964,-0.05628,0.06532,-0.03626,-0.04971,-0.05129,-0.01178,-0.05085,0.01718,0.05647,-0.00422,0.01831,0.05535,0.02304,0.12679,-0.0176,0.00904,0.13285,-0.06602,0.07166,0.05582,0.03041,-0.01909,-0.06859,-0.11067,-0.00868,0.05685,-0.08098,-0.05074,-0.03208,0.03173,-0.02289,-0.07569,-0.06403,0.00056,0.11119,-0.01109,-0.03737,-0.11372,0.07226,0.00791,-0.02913,0.01909,0.027,0.05927,0.012,-0.00105,0.01842,0.07054,0.05427,-0.08713,0.06067,-0.01088,-0.09169,0.0511,0.00435,0.01181,-0.03732,-0.15794,-0.0061,0.1336,-0.06199,0.02672,-0.02212,0.04704,0.11825,0.02793,-0.04299,0.14079,0.06295,-0.02399,0.01469,-0.16331,-0.00036,0.00465,0.06709,-0.10034,0.04618,0.0745,0.05593,0.09876,-0.0001,0.00327,0.02121,-0.0041,-0.00959,0.0967,-0.05398,0.06043,-0.09905,-0.03678,-0.07536,-0.02218]},{"domain":"quantum_physics","key":"relativistic_velocity_addition","name":"Relativistic velocity addition","package":"quantum-physics-ai999x","example":"Velocity addition: u_prime = 0.5 c, v = 0.5 c","v":[0.07213,0.02458,0.01966,0.057,-0.02008,0.00413,-0.01266,0.069,0.07108,-0.06995,0.03797,0.04154,-0.10184,-0.03359,-0.0164,-0.09974,-0.09523,-0.10711,0.01167,-0.03373,0.08056,0.08204,-0.016,0.01511,-0.01397,0.04724,0.03124,-0.09121,0.02376,0.0889,0.0958,0.02315,-0.03455,-0.03491,-0.08777,-0.0337,-0.00529,-0.0805,-0.0515,-0.01353,0.04651,-0.05557,0.12492,-0.11892,-0.02651,-0.03581,0.04638,0.03146,-0.03116,-0.05156,0.02908,0.03666,-0.09578,0.07471,0.0575,0.0435,-0.03535,-0.00711,0.01381,-0.06729,-0.00805,-0.01853,0.14912,-0.05356,0.05749,0.05981,0.069,-0.02852,-0.06072,0.06284,-0.04603,0.04115,0.05624,-0.03077,-0.02464,-0.04496,0.08436,-0.06227,0.13894,0.08826,0.17794,0.027,-0.04243,-0.01454,-0.04578,0.07129,-0.02078,-0.00527,-0.07048,0.0089,0.01451,0.04721,0.00593,0.08106,0.02939,0.08074,0.05097,0.00775,0.00943,-0.08363,-0.01428,-0.10864,0.03926,0.06211,0.09926,-0.09655,0.04016,-0.01494,-0.02401,0.1735,-0.01434,-0.00949,0.03283,0.00897,0.01152,0.00679,-0.04492,-0.02489,-0.0284,0.02679,-0.00562,-0.07461,-0.09549,0.11778,0.13983,0.03043,0.09678,0.0462,0.07348,0.02426,0.03952,0.0041,-0.11956,-0.07853,-0.11083,-0.06191,0.01687,-0.00074,0.00536,-0.00733,0.05538,0.05895,-0.00336,-0.06272,0.03555,-0.02012,-0.07042,-0.0019,-0.02244,0.06589,-0.04904,-0.0161,0.10686,-0.10923,-0.11962,-0.01486,-0.01745,-0.11125,-0.06434,-0.09564,0.09899,-0.06072,0.05498,-0.01607,0.11064,0.03245,-0.03059,-0.01586,0.08503,-0.07516,-0.01752,0.0272,0.05933,-0.0045,-0.03701,0.06982,-0.0181,-0.04783,0.11525,-0.01072,0.04189,-0.08062,0.03028,-0.02956,0.00968,-0.07452,0.01292,-0.05044,-0.00947,-0.01719,-0.08083,-0.06092,-0.05544,0.00922,0.0742,-0.13473,0.03306,-0.03703,0.05958,0.05373,-0.09179,0.02608,0.00062,-0.04902,-0.08639,0.10429,0.00035,0.09296,0.04508,0.01462,0.08196,0.08578,0.01417,0.02783,0.11209,0.01288,-0.02797,-0.01979,-0.10759,-0.00907,0.01092,-0.08032,-0.02997,0.03699,-0.06984,-0.05381,-0.06402,0.05219,0.12775,-0.05512,0.01366,-0.01514,0.038,0.04356,0.08733,-0.03266,-0.01074,0.04012,0.03264,-0.07648,0.08828,0.06521,-0.02532,0.04618,0.13374,-0.0658,-0.11105,-0.06015,0.03385,0.03535,-0.07914,0.00613,-0.04472,-0.09717,0.00525,-0.04909]},{"domain":"quantum_physics","key":"rest_energy","name":"Rest energy (mass-energy equivalence)","package":"quantum-physics-ai999x","example":"Rest energy: m = 9.1093837139e-31 kg","v":[-0.0296,0.00997,0.06624,0.01447,0.0509,0.03952,0.04233,-0.0155,0.00832,0.04997,-0.00405,0.13689,-0.04998,0.00446,-0.02787,-0.08522,0.03483,0.07744,-0.05988,-0.06396,-0.03852,0.05948,-0.0411,0.09607,-0.02657,0.07664,0.05055,-0.03399,-0.02087,-0.02112,-0.12697,-0.08344,-0.01535,-0.05163,0.02686,-0.0378,-0.0313,0.08002,0.06218,-0.2025,0.02246,0.0401,-0.02922,0.02882,0.04523,0.06678,-0.11757,-0.07898,0.005,0.07298,0.01314,-0.00563,0.01513,0.0678,-0.07045,-0.05566,0.02887,0.01516,-0.01922,-0.00727,0.01087,-0.11428,0.01332,0.06606,0.05753,0.14184,-0.18262,-0.03049,-0.04316,0.10977,-0.02449,-0.04986,-0.03183,0.0173,0.07487,0.05611,0.1238,-0.05571,-0.06635,0.05115,0.03618,0.05168,0.0487,-0.01914,-0.07425,-0.04731,-0.07825,0.00285,0.03592,-0.05378,0.04531,0.00729,0.09427,0.10913,-0.00634,0.04569,0.02245,0.00638,-0.03383,0.03747,0.0751,-0.08888,-0.1079,0.02595,-0.07409,-0.14266,0.08672,-0.03404,-0.15093,-0.02855,-0.00089,0.05176,-0.01009,-0.01343,-0.00324,0.00366,0.11553,-0.09672,0.08503,0.00867,-0.06814,0.00914,-0.01812,-0.09251,-0.01384,0.01899,0.03461,0.09451,0.0257,0.01459,-0.05684,0.08938,-0.0763,-0.01176,0.11668,0.02007,0.00622,-0.04987,-0.06381,0.05919,-0.03804,0.01464,0.00313,-0.01297,-0.01608,0.02976,0.08713,0.00451,0.10187,-0.0586,0.02393,0.02261,0.08536,-0.06255,-0.10859,0.02249,0.03101,-0.07007,0.10363,-0.03466,0.02516,0.09422,0.03753,0.08299,-0.05516,0.01074,-0.08894,0.10763,-0.08508,0.01844,0.01278,-0.02219,0.03704,0.07932,-0.03135,-0.03754,-0.006,0.00402,-0.02627,-0.02142,0.01279,0.03069,-0.09843,0.00115,0.01082,0.03246,-0.043,-0.06819,0.08463,-0.01009,-0.10553,-0.0664,0.10118,0.06979,-0.01203,0.00851,-0.08466,0.04328,-0.00055,-0.05828,-0.06579,0.00415,0.02113,-0.10919,-0.09521,-0.10085,0.07136,-0.03554,-0.06431,-0.1264,0.08532,0.01902,0.03307,-0.03436,0.03681,-0.02714,-0.13495,-0.10544,0.03985,-0.02028,0.01423,0.00292,-0.04822,0.11547,0.03631,0.0441,-0.00073,0.02192,0.01291,0.06222,0.0704,0.07958,0.04727,0.1209,0.01298,-0.00315,0.03102,-0.04443,-0.00732,-0.06665,-0.03568,-0.08673,-0.0346,0.02197,-0.04651,0.05033,0.02013,0.04422,0.06158,0.09102,0.0183,-0.00687,-0.1026,0.13182,-0.00114,-0.02408]},{"domain":"quantum_physics","key":"semi_empirical_mass_formula","name":"Semi-empirical mass formula (liquid-drop binding energy)","package":"quantum-physics-ai999x","example":"Semi-empirical mass formula: Z = 26, A = 56","v":[-0.03924,-0.03456,-0.01474,-0.11975,0.03593,0.08336,0.09974,0.01436,-0.03401,0.06538,0.16297,0.00191,-0.0741,0.04341,-0.03764,0.0539,-0.01295,0.09325,0.0641,-0.01325,0.10611,-0.01027,-0.00155,0.03191,0.0594,-0.06844,0.05618,-0.01265,-0.00928,0.10827,-0.0797,-0.04765,-0.01828,0.03157,-0.01917,0.07409,-0.00607,-0.05824,0.01763,-0.05775,-0.03292,0.08814,0.00186,-0.00898,0.00458,-0.00812,-0.08419,-0.10558,0.00588,0.01164,-0.00518,-0.034,0.01354,0.12642,-0.009,-0.04121,-0.04047,0.0585,-0.02787,0.06998,-0.00128,0.03587,0.05174,0.02787,0.05903,0.11479,-0.0326,0.02502,0.04005,0.0056,0.01873,-0.03553,0.00555,0.03162,-0.06566,0.08636,-0.0436,-0.04182,0.0938,-0.00145,-0.01342,-0.06771,-0.06085,-0.11022,-0.05293,-0.06376,-0.00611,-0.00323,0.05066,-0.09498,-0.00675,0.00236,0.0925,-0.0684,0.03445,-0.01059,-0.06203,-0.14849,0.06967,0.06628,0.0701,-0.04421,-0.09947,-0.10632,-0.03391,-0.11258,0.05642,-0.04859,-0.10709,-0.06557,-0.04009,0.05154,0.1133,-0.07074,-0.08054,0.01048,0.06994,0.01005,-0.02728,0.05894,-0.06688,-0.01143,0.03071,0.10599,-0.05684,0.16544,0.03637,0.13695,0.02884,-0.02957,-0.01983,0.05478,0.05834,-0.15378,0.02671,0.00559,0.09161,-0.03748,-0.05685,-0.05002,-0.00204,0.09508,0.16224,0.03636,-0.08017,0.02643,0.05135,-0.03241,0.00674,0.00295,0.03412,0.02849,-0.00495,-0.13028,0.00939,-0.01668,0.01717,-0.00089,0.00807,-0.03046,0.07275,0.00958,0.00893,0.00273,-0.13647,-0.02068,0.06378,0.01324,0.03574,-0.08586,-0.05991,0.04354,0.04476,-0.02944,0.0731,0.00177,0.07897,0.02986,-0.07897,0.13636,0.01807,0.04417,-0.0341,-0.04584,0.04584,0.0561,-0.04851,-0.01186,0.07128,-0.07774,-0.08595,0.04572,0.11389,-0.05108,-0.10923,-0.11899,-0.02838,-0.00689,-0.08673,-0.00612,0.00986,-0.01825,-0.03107,0.10137,0.06273,-0.09946,0.01063,0.04862,-0.09217,-0.03748,-0.06162,-0.01156,-0.04484,0.03737,-0.00832,0.10464,0.01728,0.01572,0.09058,0.05379,0.02629,0.02548,0.03048,-0.02719,0.02708,0.03836,-0.01227,0.07551,0.02145,0.03976,0.04041,-0.04141,-0.12484,-0.01362,0.01425,-0.07454,-0.00516,0.03354,0.00895,0.01626,-0.15521,0.13441,0.00279,0.001,-0.06599,-0.10568,0.02621,0.04828,0.06583,0.05334,-0.06248,-0.02394,0.05899,0.10476,0.06887,0.0008]},{"domain":"quantum_physics","key":"single_qubit_circuit","name":"State of a qubit after a sequence of gates","package":"quantum-physics-ai999x","example":"Single-qubit circuit: start = 0; gates = 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de Broglie wavelength","package":"quantum-physics-ai999x","example":"Thermal de Broglie wavelength: m = 9.1093837139e-31 kg, T = 300 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dilation","package":"quantum-physics-ai999x","example":"Time dilation: t0 = 1 s, v = 0.6 c","v":[-0.02051,0.06016,-0.0042,0.06173,-0.00371,-0.01167,0.0699,0.08423,0.1667,-0.02452,0.08034,0.04478,0.0045,0.1084,-0.02157,-0.01979,-0.06235,0.01285,-0.0883,-0.04005,-0.00464,0.0252,-0.05476,-0.09355,0.11232,-0.011,-0.0227,-0.07201,0.09142,0.10471,0.10964,0.02751,-0.06102,-0.09597,-0.07578,0.00994,-0.01933,-0.00416,-0.06822,-0.05842,0.02501,-0.06333,0.08239,0.01253,-0.06926,-0.05249,0.03812,-0.04932,0.02478,0.00333,-0.02117,-0.00458,-0.10528,0.10928,-0.00558,0.0556,-0.01255,0.04502,-0.0272,-0.00585,0.00436,0.00116,0.09724,0.01826,-0.01602,0.03813,0.01883,-0.03019,-0.02087,0.18845,-0.10504,-0.05632,-0.03361,-0.04557,0.03953,-0.08027,0.00864,-0.03607,0.04561,0.06569,0.09739,0.10578,-0.03973,0.06335,-0.0238,-0.02075,-0.08621,-0.09543,0.08621,0.006,-0.05437,0.01835,-0.07908,0.02422,0.04589,0.06669,0.11188,-0.02471,-0.01335,-0.03925,-0.00782,-0.02705,-0.13108,-0.05596,-0.05217,-0.12409,-0.03536,-0.02693,0.08215,0.0282,-0.01605,0.00289,-0.03115,0.00707,-0.04158,0.05464,-0.01513,0.08806,0.0437,0.06781,0.01054,0.06763,-0.10405,0.0561,0.06929,-0.02281,0.00568,0.03821,-0.01344,0.06062,-0.01216,-0.07068,-0.09406,-0.06172,0.02682,0.03358,0.03942,-0.0379,0.03157,0.01649,0.00265,0.09462,0.01696,-0.03752,-0.09785,0.03838,-0.0705,0.00255,-0.05026,0.11294,0.06492,-0.13415,0.10223,-0.0406,-0.07263,-0.02612,0.11685,-0.08656,-0.00331,-0.12297,0.07928,0.00104,0.01076,0.05492,-0.03728,-0.07718,0.03415,0.12544,0.01138,-0.025,0.06226,-0.00877,0.05325,0.18114,-0.02555,0.04621,-0.04839,0.0839,0.08169,0.04644,0.03998,-0.08254,0.05689,-0.09798,0.01448,0.00711,0.03473,-0.00849,-0.0333,-0.00751,0.01,-0.10362,0.01373,-0.07578,0.0768,-0.07855,0.10877,-0.10597,0.02001,0.09186,0.04741,0.01114,0.01426,-0.02752,0.01454,0.04923,0.07228,0.00332,-0.03513,-0.0133,0.1169,0.02799,-0.00712,-0.05035,0.11037,0.00925,-0.08747,-0.07012,-0.04777,-0.07396,-0.01899,-0.03765,-0.03628,-0.07189,-0.00882,-0.11725,0.06055,0.01014,0.11189,-0.06085,-0.03584,-0.01065,0.01258,-0.09007,0.08905,0.01942,0.00941,0.04362,0.04293,-0.04223,0.07531,0.04263,-0.0342,-0.02393,0.08955,-0.06205,-0.10479,-0.12139,-0.04971,-0.0267,0.07317,-0.0044,-0.01272,0.00482,-0.03006,-0.06233]},{"domain":"quantum_physics","key":"two_body_decay","name":"Kinematics of a two-body decay","package":"quantum-physics-ai999x","example":"Two-body decay: M = 139.57039, m1 = 105.6583755, m2 = 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of a two-level system","package":"quantum-physics-ai999x","example":"Two-level system: dE = 0.025 eV, T = 300 K, g0 = 1, g1 = 1","v":[-0.14195,-0.11941,0.02832,-0.05489,-0.03352,-0.02097,-0.00018,-0.15146,-0.03892,0.10528,-0.01405,-0.06014,-0.0627,-0.03414,0.05086,-0.06664,-0.05111,-0.0485,-0.0389,-0.03093,0.0044,0.00641,0.00084,0.00171,-0.04159,-0.036,0.01271,0.01802,-0.04822,0.043,-0.06154,0.0278,-0.05909,-0.00659,0.04759,0.17877,-0.06548,-0.06807,-0.02278,-0.13156,0.04173,0.02615,0.03445,0.07639,-0.00133,0.01051,0.00865,0.11258,-0.09196,0.02913,-0.08529,0.00338,0.04731,-0.04856,0.07805,0.0842,0.08095,0.02985,0.0234,0.03815,-0.06592,0.07324,0.05874,-0.08093,0.01261,-0.11285,-0.01049,-0.02208,-0.04113,0.01593,0.10005,0.01886,-0.01114,0.04422,0.04499,0.02536,-0.18745,0.05546,0.10181,-0.03864,0.05464,-0.00503,-0.05075,0.02316,-0.02381,-0.0746,0.03261,0.00986,0.04695,0.05452,-0.07393,0.01679,0.05227,-0.11025,0.00099,-0.00602,0.02609,-0.0644,0.00724,-0.08676,0.01674,0.06446,0.13469,0.00867,-0.07263,-0.13684,0.10268,0.0482,-0.00379,0.03943,0.04226,0.01043,-0.0161,-0.05238,0.05159,-0.00856,-0.00508,-0.05646,0.06722,-0.03166,-0.04372,0.05683,0.08991,0.04651,0.01577,0.00861,-0.08056,-0.03068,0.00563,0.059,0.05655,-0.06626,0.02675,-0.07592,0.05043,-0.025,0.01553,0.00312,0.00538,-0.00896,-0.0594,-0.01352,-0.03902,0.09864,0.0577,0.05792,-0.01872,0.06565,0.00389,0.04043,-0.01213,-0.05704,-0.00432,0.03769,0.09491,-0.0873,0.11977,0.00877,0.07269,-0.02063,0.16035,-0.07004,-0.00615,-0.01887,-0.11981,0.06602,0.00695,0.04322,-0.02391,0.02067,0.14082,0.00308,-0.0594,-0.09113,-0.03226,-0.02217,-0.07257,0.10656,-0.06185,0.00357,0.10791,-0.02106,-0.07445,-0.00759,-0.02832,-0.05835,0.05838,0.05354,0.01644,0.01025,0.01511,0.07311,0.04824,0.04427,-0.03056,-0.05656,-0.04639,0.04573,0.02273,-0.00745,-0.02275,-0.13027,0.04449,-0.11812,0.17623,0.05575,0.00719,-0.05782,-0.08851,0.007,0.00891,0.04465,0.01703,0.00208,0.07902,-0.06829,-0.0015,0.04477,0.0476,0.05399,-0.07649,0.02192,0.06593,-0.0477,-0.10299,-0.01077,0.08604,-0.1232,-0.0092,0.08025,0.03483,-0.03825,-0.02427,-0.10465,0.08066,0.04746,0.04297,0.02944,-0.02816,0.04424,0.13903,-0.00441,0.0994,0.01717,0.03788,-0.02394,0.0114,0.02016,0.06486,-0.14997,-0.07484,-0.02035,-0.04738,0.06427,0.09859,0.00038]},{"domain":"quantum_physics","key":"two_qubit_circuit","name":"Two-qubit circuit: probabilities and entanglement","package":"quantum-physics-ai999x","example":"Two-qubit circuit: start = 00; gates = H0 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of blackbody radiation (Wien's displacement law)","package":"quantum-physics-ai999x","example":"Wien's displacement law: T = 5778 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3j symbol","package":"quantum-physics-ai999x","example":"Wigner 3j symbol: j1 = 1, m1 = 1, j2 = 1, m2 = -1, j3 = 0, m3 = 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tunnelling through a triangular barrier (field emission)","package":"quantum-physics-ai999x","example":"Field emission: W = 4.5 eV, F = 5e9 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ceiling of a jet aircraft","package":"aerospace-engineering-ai999x","example":"Absolute ceiling: W = 100 kN, S = 30 m^2, T0 = 1 kN, CD0 = 0.02, AR = 7, e = 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propeller in axial flight (momentum theory)","package":"aerospace-engineering-ai999x","example":"Ideal propeller: T = 25.132741228718345 N, V = 3 m/s, D = 2 m, rho = 1 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range of a propeller aircraft","package":"aerospace-engineering-ai999x","example":"Propeller range: eta = 0.8, c = 0.0000001 kg/J, LD = 15, W0 = 27.18281828459045 kN, W1 = 10 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airspeed from true airspeed","package":"aerospace-engineering-ai999x","example":"Calibrated airspeed: V = 150 kt, hp = 0 ft","v":[0.08478,0.02209,0.0351,0.00058,0.00429,-0.03486,-0.01648,-0.00948,-0.08566,-0.07924,-0.02639,0.04057,-0.03082,0.13211,-0.03224,-0.00454,0.03473,0.0208,0.02302,-0.01906,-0.03677,-0.01027,0.08108,0.00641,-0.08743,-0.04511,0.07146,-0.04314,0.07193,-0.05902,-0.03259,0.09116,0.0449,-0.01365,-0.03531,-0.03138,0.05302,-0.00556,-0.07075,0.01634,-0.08051,-0.06586,-0.00548,0.05062,-0.09317,-0.05607,0.01024,-0.05527,-0.06872,-0.0005,-0.01539,-0.06347,0.03772,0.10137,0.11788,-0.13245,0.05113,-0.05723,-0.01051,0.03696,-0.07047,-0.02375,-0.03828,-0.15319,-0.13117,-0.01901,0.02175,-0.12693,-0.06459,-0.00828,-0.03552,0.05255,0.15019,-0.0072,0.02211,-0.0091,0.17659,0.00313,0.01369,0.14765,-0.0745,0.01824,-0.00711,0.02426,-0.08636,-0.07915,0.10865,0.00585,0.03524,-0.03759,0.06054,-0.03038,-0.04471,0.05161,-0.00687,0.00324,-0.05834,-0.0121,-0.00927,-0.0767,-0.00306,0.01069,-0.0043,0.00627,0.03338,-0.03976,-0.06321,0.04128,-0.05449,0.03081,0.02719,0.00056,-0.0281,0.09864,-0.00553,0.02282,-0.06529,0.02669,-0.08655,-0.05529,-0.05339,0.06831,-0.01719,-0.04511,0.00405,0.14736,0.01598,0.07473,0.02749,-0.07596,-0.08375,-0.10062,-0.02252,0.04442,0.01556,-0.1686,-0.04507,-0.01219,-0.03482,0.04938,0.06564,0.12405,-0.02587,-0.05292,-0.00285,0.06914,0.02327,0.05049,-0.04332,0.08081,0.09997,0.06015,-0.03125,0.13269,-0.06353,-0.02113,-0.10221,-0.01267,0.01695,-0.05006,-0.02275,-0.15249,0.00421,-0.01737,-0.14306,0.05267,-0.00433,-0.01511,0.0835,-0.05708,-0.05621,-0.02154,0.04018,0.06495,0.00677,-0.02854,0.00489,-0.00258,0.14386,0.07791,0.19162,0.04393,0.05892,0.01414,-0.01105,0.031,0.01219,-0.10623,-0.02315,0.07484,0.08456,-0.04661,0.04326,-0.0495,-0.00925,-0.03471,0.06125,0.05395,0.06201,0.08771,-0.02351,-0.01437,-0.04867,-0.07973,-0.022,0.02441,-0.1052,0.0244,0.02262,-0.06739,-0.02298,0.06666,0.08545,0.12532,0.01231,-0.07735,-0.01045,0.06342,-0.01285,-0.03575,0.02783,-0.01131,0.05347,0.0545,-0.06685,-0.07084,0.01346,0.04084,0.00379,0.06344,-0.03561,0.03679,-0.00425,-0.01717,-0.05282,0.04109,0.02535,0.09019,-0.05361,0.07785,0.06353,-0.08251,0.09434,3e-05,0.04866,0.01223,-0.03725,-0.12121,-0.03452,0.01724,0.00634,0.09684,-0.08305,0.03627,-0.13057,-0.01977]},{"domain":"aerospace_engineering","key":"aero_characteristic_velocity","name":"Characteristic velocity c* of a rocket propellant","package":"aerospace-engineering-ai999x","example":"Characteristic velocity: Tc = 3000 K, Mw = 20 g/mol, gamma = 1.2","v":[0.00338,0.02836,-0.02694,0.02888,-0.06706,-0.01072,0.05193,0.13059,0.04372,0.02399,-0.02615,0.06562,0.05766,-0.01568,0.00047,0.08917,-0.03821,-0.06223,-0.01319,0.00222,0.08167,-0.03922,-0.05624,0.02186,0.02941,3e-05,-0.01491,-0.0053,-0.09788,0.00203,0.01713,0.02177,0.06866,0.03148,0.07353,-0.0892,0.07005,0.06498,-0.04529,0.00536,0.04788,0.00133,0.12747,-0.0013,-0.00143,-0.10063,-0.02909,-0.07384,0.0172,-0.00667,-0.00962,0.04609,0.03297,0.06933,0.03353,0.07227,-0.07654,0.01021,0.0375,0.04116,-0.01104,-0.11741,0.09992,0.00648,-0.03988,-0.03619,-0.07276,0.02996,-0.10856,0.0415,-0.15145,0.1227,-0.05138,0.03621,0.11207,0.09447,0.01643,-0.05097,0.05502,-0.10625,-0.00189,0.03756,-0.06828,-0.05783,0.00011,-0.03578,-0.04972,-0.04838,-0.04164,0.07529,0.03343,0.06605,-0.01325,0.09797,0.00774,0.06018,-0.0088,0.0316,-0.0489,0.0284,-0.03211,0.03998,-0.02594,-0.02976,0.04253,-0.086,0.03176,0.02933,-0.03635,0.14451,0.03389,-0.04305,-0.03282,0.04861,-0.05747,0.07749,-0.05799,-0.05891,-0.04377,0.0414,0.05398,-0.06065,0.05219,0.02487,-0.00811,0.08619,0.04596,-0.13056,-0.13217,0.01095,-0.03001,0.08757,-0.02978,-0.08704,0.05223,-0.07443,-0.06572,0.01372,-0.06578,0.05219,0.05758,0.06534,0.06512,-0.05702,-0.02015,0.03849,-0.07385,0.01818,-0.02656,-0.01066,0.04236,-0.09702,-0.00345,-0.11239,-0.07813,-0.06415,-0.04707,-0.06773,0.01974,-0.02791,-0.05909,-0.1651,0.0531,-0.09781,-0.05916,0.12713,0.03761,0.01281,-0.0024,0.06204,0.04494,0.07282,-0.05837,0.01288,-0.03995,0.04852,0.06973,-0.05153,0.14767,0.00024,0.01784,-0.07847,-0.02497,0.00359,-0.01082,0.03626,-0.01004,-0.00789,0.00262,0.11641,0.01001,-0.09105,0.0022,-0.00584,-0.00326,-0.0499,-0.06876,0.04986,-0.00362,-0.04721,-0.06781,-0.09568,0.05812,0.00748,-0.16892,-0.00465,0.02208,0.09475,0.07359,-0.05712,-0.05474,0.07997,0.09379,-0.04089,0.10027,-0.052,-0.07068,0.03512,0.06107,0.11395,-0.06674,-0.03934,-0.0439,0.0928,-0.05676,-0.13304,0.09723,0.02033,-0.03131,-0.00505,0.08114,0.02755,0.09028,-0.03889,0.07253,-0.0917,0.02857,0.10217,0.01499,0.02521,0.13956,0.11226,0.0937,-0.0148,0.02419,0.06924,-0.01465,-0.00307,0.04077,0.00215,-0.03013,-0.0035,-0.13995,0.01182,-0.04026,-0.08059]},{"domain":"aerospace_engineering","key":"aero_choked_mass_flow","name":"Choked mass flow through a nozzle throat","package":"aerospace-engineering-ai999x","example":"Choked mass flow: p0 = 100 kPa, T0 = 300 K, A = 10 cm^2","v":[-0.05417,-0.00771,0.08019,0.03981,-0.04226,0.08124,0.0776,-0.0284,0.11988,0.05064,-0.03251,0.10403,0.05684,0.00952,0.03275,0.08767,-0.01166,0.0273,0.10085,0.06437,0.06246,-0.0574,0.03116,-0.06628,-0.0319,0.03638,-0.07132,0.07965,0.11885,-0.04401,-0.02405,-0.06182,0.07995,-0.0736,-0.12691,-0.00291,-0.07129,-0.03731,-0.02979,-0.0499,0.07572,0.01136,-0.11621,-0.01439,0.05896,0.00531,0.04031,-0.07293,0.03807,0.15604,0.01079,-0.01715,0.0618,-0.04977,0.10694,0.02321,0.03674,0.00563,0.09427,0.01423,0.00611,-0.07508,-0.06233,-0.03566,0.04475,-0.04303,0.0515,0.06839,-0.01713,0.00576,0.02289,0.03527,-0.03672,0.00865,-0.07794,0.02909,0.01766,-0.01145,-0.09648,0.11963,0.09523,-0.06625,-0.0245,0.01757,-0.02849,-0.04632,-0.08095,0.07025,-0.09224,-0.10587,0.01759,0.03813,-0.00212,0.11193,-0.0277,-0.04722,0.05619,0.04714,-0.01571,-0.02439,0.08142,-0.04305,-0.01986,0.05962,-0.00774,-0.00911,0.01874,-0.00115,-0.19845,0.01988,-0.12959,0.12277,0.05629,-0.09169,-0.06275,-0.08628,0.06038,-0.04773,-0.02294,-0.05858,0.0567,0.02668,0.09259,0.00354,-0.05695,-0.05633,0.00346,-0.03874,0.03177,0.00619,-0.05726,0.0948,-0.06421,-0.02296,0.04709,-0.01408,0.04979,-0.00371,-0.04453,-0.00278,-0.08578,0.01321,0.00918,0.04281,0.09652,-0.04322,0.04834,-0.10313,-0.03838,-0.00531,0.00525,-0.06163,0.00355,0.0342,-0.11255,-0.01317,-0.10948,0.04712,-0.05732,-0.04382,-0.00465,0.04791,0.01727,-0.10244,-0.12914,0.1578,0.08596,-0.03599,0.02617,-0.00152,-0.04199,-0.059,0.03073,0.0258,0.11199,-0.00802,-0.09449,-0.0462,0.04735,0.03031,-0.02391,0.1221,0.04912,-0.04238,-0.03635,0.03865,-0.068,0.0153,0.00091,-0.03161,-0.07768,0.00344,-0.06169,0.06515,0.03003,0.04519,-0.02571,0.0553,-0.01294,-0.04732,0.08501,-0.06275,-0.13736,0.02478,0.02413,-0.02796,-0.05553,0.03803,-0.04952,-0.05709,0.03886,0.08744,0.09458,-0.05465,0.00393,0.1058,-0.08944,0.02618,0.02588,0.02656,-0.07753,-0.04117,-0.04251,-0.10274,-0.03649,-0.10015,-0.08287,0.0663,0.00879,0.11068,0.04782,-0.01697,-0.01029,-0.09036,0.08248,0.02107,0.00316,-0.00113,0.01493,-0.032,0.11852,0.06455,-0.0185,0.0942,-0.05956,0.0592,-0.01108,-0.04362,0.03883,-0.03465,-0.10334,0.14705,-0.02719,0.05703,0.01448,0.023]},{"domain":"aerospace_engineering","key":"aero_circular_orbit","name":"Circular orbit at an altitude above the Earth","package":"aerospace-engineering-ai999x","example":"Circular orbit: h = 19134.409799999998 km","v":[-0.00476,-0.03826,-0.06544,0.18438,-0.06369,-0.13036,-0.08807,0.04828,0.12599,0.07455,-0.05564,-0.04936,0.03225,-0.02881,-0.07518,-0.06508,0.0534,-0.07617,0.00456,-0.12066,-0.10615,-0.0452,-0.04113,-0.12603,0.03908,-0.0005,0.00263,-0.02278,-0.05384,-0.02859,0.03027,0.09688,0.01571,0.00617,-0.00935,-0.0867,0.10492,-0.02613,0.00142,0.0548,0.10316,0.09761,-0.02886,0.02527,-0.06702,-0.02766,-0.05202,-0.01071,-0.04385,0.02858,-0.09925,0.00951,-0.00713,0.10305,-0.01447,0.02614,-0.04023,0.05478,-0.05272,-0.0288,-0.07781,-0.02974,-0.05276,0.00684,-0.06937,0.05309,0.09428,-0.08645,-0.0234,0.03246,0.05964,0.00386,0.02336,-0.11504,0.02587,0.02911,-0.10013,0.11262,0.10121,0.06511,-0.00078,0.03502,-0.0696,0.02126,-0.10756,-0.00924,0.05492,0.02984,0.06779,0.01856,0.09061,-0.04074,-0.0818,0.02131,-0.05814,0.03702,0.04485,0.03446,-0.05519,0.08219,-0.05313,-0.00872,0.04343,-0.00958,-0.04081,-0.07002,-0.0676,0.05446,0.07856,-0.00921,0.03346,-0.02543,-0.08692,0.04414,0.01233,0.09991,-0.07602,-0.03967,-0.00841,0.0179,0.08093,-0.00122,-0.10052,-0.10755,0.05897,0.03216,0.00253,0.06134,-0.04689,0.09018,-0.0167,-0.00219,-0.03826,0.05734,0.03735,0.00677,0.02502,0.03399,0.08216,0.09969,0.02852,0.14226,-0.05705,-0.05641,-0.02282,0.02006,-0.00042,0.02885,-0.01135,0.12083,0.04616,-0.03215,-0.01875,-0.05766,-0.08514,-0.06485,-0.03537,-0.02463,-0.02135,-0.08847,0.07671,0.07469,-0.0075,-0.04083,-0.02779,0.05953,-0.09596,0.02862,0.02383,0.07673,0.06228,-0.03551,0.05936,-0.01295,-0.12582,-0.02771,0.00427,0.18451,0.09723,0.02437,-0.01281,-0.01104,0.07081,0.10535,-0.00734,-0.03176,0.06828,0.00999,0.00061,-0.06844,-0.09578,-0.01821,0.10806,-0.01222,-0.01192,-0.04646,0.00491,0.05531,0.08611,0.00278,0.04917,-0.02998,-0.02102,-0.02137,-0.08763,-0.00712,0.05965,-0.01057,0.00604,-0.07463,0.09457,-0.07826,0.08038,-0.02028,-0.06733,-0.04768,-0.04781,0.00379,0.02739,0.04281,-0.19022,0.01375,0.00208,0.03378,0.08717,0.04872,-0.08707,-0.00938,0.04172,0.03435,-0.04486,0.01622,-0.07897,-0.02748,0.02454,-0.01344,0.03677,-0.06172,0.02655,-0.09574,-0.01585,0.05408,0.04748,-0.11438,-0.03182,-0.01653,-0.01467,-0.16177,-0.00333,-0.07287,0.06367,0.15357,-0.01257,0.0338,-0.0079,0.02335]},{"domain":"aerospace_engineering","key":"aero_critical_mach","name":"Critical Mach number of an airfoil","package":"aerospace-engineering-ai999x","example":"Critical Mach: Cp0 = -0.43, rule = prandtl-glauert","v":[0.07904,0.02615,-0.00676,0.11596,-0.05747,0.08126,0.05563,0.00181,0.07699,-0.1102,-0.09876,0.05012,0.04293,0.01114,0.00018,0.00983,0.08436,0.02406,0.14681,0.08909,-0.06067,0.05916,0.07789,0.06461,0.04207,0.01993,0.07662,0.02471,0.02594,0.09839,0.00884,0.02487,-0.02755,0.07589,0.00293,-0.04121,-0.01573,-0.05382,-0.04262,0.02332,-0.07545,-0.04358,-0.08914,-0.01537,0.0583,0.0436,-0.03503,-0.04374,0.04614,-0.02926,0.06992,-0.11118,0.05296,-0.02665,-0.04868,-0.04149,-0.04362,-0.04822,0.00584,-0.00567,-0.02597,-0.01178,-0.06423,0.01497,0.01422,0.02455,-0.0526,0.00135,-0.09547,0.00192,-0.05607,0.06682,0.01673,-0.00401,0.02664,0.04216,0.13895,0.02904,0.02992,0.1039,0.19408,0.08311,-0.01826,-0.02243,-0.0517,-0.03145,-0.13023,0.04401,0.00534,-0.10319,-0.03921,-4e-05,-0.09356,-0.03114,-0.05707,-0.05082,0.0176,-0.01473,-0.02249,0.02903,0.02086,0.03816,0.01081,-0.00588,0.13085,-0.01127,-0.05792,-0.00189,-0.07044,0.00153,0.03971,-0.03544,0.00603,-0.04819,-0.11146,-0.10934,-0.07395,-0.05974,-0.04288,0.07862,-0.01678,-0.02842,0.0945,0.08448,-0.01747,-0.04688,-0.00506,0.01581,0.03832,-0.0769,-0.05484,-0.0227,-0.0147,-0.01379,0.02413,-0.03982,0.01056,0.11851,-0.01843,0.02895,-0.04234,-0.02399,-0.03349,0.01684,-0.02706,0.03807,0.1216,-0.10157,-0.01261,0.01516,0.00104,0.05113,-0.08938,0.04227,-0.09,-0.01362,0.02246,-0.0075,0.0217,0.05187,-0.0538,-0.03032,-0.13093,0.06448,-0.01761,0.07836,0.07041,-0.01898,0.01495,0.07391,-0.04659,-0.02966,0.07957,0.02299,0.01489,-0.03567,-0.03898,-0.0158,0.10353,-0.00011,-0.06383,-0.03102,0.06808,0.00873,-0.0169,0.06913,-0.05039,-0.0289,0.00292,0.05369,0.02878,-0.16053,-0.0715,-0.0381,0.04408,-0.02508,-0.05002,-0.01411,0.02641,-0.00321,-0.02075,-0.0063,-0.11887,0.02259,-0.01,0.01449,0.00734,-0.09198,-0.13338,-0.04663,-0.07872,0.14543,0.03774,0.05105,-0.03328,0.00338,-0.0442,0.03433,0.05905,0.0823,-0.05643,-0.0447,-0.02449,-0.11162,-0.09532,-0.02288,-0.05977,0.14399,0.0693,0.08763,0.03344,0.04972,-0.01461,0.04698,0.02028,0.06794,-0.04205,0.10114,-0.05843,0.02625,0.06126,-0.16896,0.09664,-0.00205,0.06226,0.13419,-0.00954,-0.01895,-0.17598,-0.02229,-0.15131,0.0812,0.05102,0.12886,-0.02883,-0.00458]},{"domain":"aerospace_engineering","key":"aero_delta_v_gravity_loss","name":"Gravity 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expansion fan","package":"aerospace-engineering-ai999x","example":"Expansion fan: M1 = 1, theta = 26.379760813416457 deg","v":[0.07282,-0.03228,0.03434,0.01029,0.00312,0.14826,-0.00483,-0.00976,0.01935,-0.05789,-0.03535,-0.02947,-0.02331,0.10708,0.07007,-0.01225,-0.05731,-0.02675,0.06557,0.06366,-0.02343,-0.01504,0.04039,-0.09123,-0.06256,-0.13901,-0.07107,0.05044,-0.08044,0.01548,0.10665,0.04012,-0.06447,-0.1218,-0.0509,-0.01673,-0.05949,-0.03119,-0.09054,0.09376,-0.02571,0.05867,0.09259,-0.00105,0.13059,-0.00275,0.05858,-0.00632,-0.02961,0.02441,-0.07724,0.04642,0.00379,-0.00948,0.02757,0.03554,0.01906,-0.14267,-0.06998,-0.09081,-0.03111,0.02663,0.06079,-0.13556,0.06898,0.04148,0.03312,-0.08387,-0.09835,-0.01348,-0.00448,0.03073,-0.04821,0.12901,0.03774,-0.02724,0.05978,0.00083,0.03949,0.00592,-0.08016,-0.10456,-0.0202,0.04739,-0.03016,-0.14169,0.04065,-0.01759,-0.03431,-0.07872,0.0259,0.01343,0.05734,0.02737,-0.0281,0.0824,0.06384,0.0159,-0.01756,-0.00905,0.15221,0.03613,-0.02868,0.01991,0.0763,0.00352,0.04472,0.01219,-0.0141,0.02706,0.10289,-0.00382,-0.09213,0.00221,0.11046,-0.02114,0.04417,0.04053,-0.00661,-0.1291,0.01452,-0.00595,0.08765,0.09805,-0.03273,0.0328,-0.00042,-0.05616,0.01925,-0.00275,-0.04903,-0.00475,-0.00634,-0.04086,0.06332,0.07598,-0.00222,-0.01079,-0.02979,-0.09154,-0.0299,-0.0241,-0.02957,-0.06597,0.0704,0.1971,-0.01965,0.04153,-0.01544,0.08813,0.00707,0.04519,-0.03177,0.05174,-0.00124,-0.04011,-0.09344,-0.01686,0.13457,-0.02667,-0.02816,-0.20092,-0.01853,0.00126,0.00034,-0.09688,0.0666,-0.0524,0.02406,0.0716,0.03054,0.0573,-0.00998,0.04342,0.0608,0.09428,-0.09311,-0.07262,0.00767,-0.00822,-0.07003,0.02718,-0.02724,-0.03782,0.08066,0.11887,-0.0096,0.05036,0.05023,-0.07382,-0.0214,0.00026,0.02204,-0.08622,0.05111,-0.01145,-0.05884,-0.0145,-0.07135,-0.02527,-0.0075,-0.07104,0.03993,0.00415,0.08507,-0.02595,-0.01446,0.00909,-0.01073,0.00502,-0.12457,0.0416,-0.01262,0.00401,-0.05097,-0.07379,-0.01182,0.04284,0.08888,-0.00041,-0.00807,-0.08961,0.05534,0.11161,-0.04508,-0.10799,-0.01306,0.03682,0.07518,0.07363,-0.06307,-0.05848,-0.00264,0.03519,-0.0361,0.04426,0.02762,-0.03677,0.02817,0.07341,0.12111,-0.01113,0.14616,0.00311,-0.00382,0.00698,-0.01152,0.06588,0.04668,-0.06985,-0.1103,0.04352,-0.07854,0.12257,-0.02205,-0.13905]},{"domain":"aerospace_engineering","key":"aero_fanno_flow","name":"Fanno flow (adiabatic duct flow with friction)","package":"aerospace-engineering-ai999x","example":"Fanno flow: M = 2","v":[-0.0616,0.01454,0.00034,-0.00711,0.00841,-0.09159,0.05095,0.00258,-0.08476,0.02233,-0.01151,-0.01244,0.02422,0.0519,-0.03493,0.0417,-0.05076,-0.04087,-0.0013,0.06307,-0.04538,-0.00217,0.05598,-0.02863,-0.00035,-0.04851,-0.16015,-0.07406,-0.02205,0.01283,0.12369,-0.04492,0.06663,-0.12796,0.10136,0.0339,0.11683,-0.08568,-0.05329,0.12436,0.08359,-0.02024,0.02943,-0.05277,0.01188,0.00523,0.08462,-0.08676,0.04864,0.00788,-0.06545,0.01812,-0.00036,-0.02617,-0.02506,-0.03358,0.05281,-0.02691,-0.02097,-0.03212,0.01886,-0.03665,0.02191,-0.00581,-0.02454,0.0916,0.01656,0.12886,-0.06,0.0768,-0.01613,0.05646,-0.09639,0.08513,0.07539,-0.06372,0.0553,-0.01329,-0.00278,-0.00706,0.04341,-0.03589,-0.00417,0.06966,0.07119,-0.07307,0.05679,0.01812,-0.07698,-8e-05,0.00989,-0.09166,0.04041,0.00336,-0.03285,0.06845,0.01208,-0.04675,0.02877,-0.08935,0.13293,0.01172,-0.04333,-0.05969,0.02669,-0.00019,0.00998,0.07475,0.01574,0.0402,-0.02178,-0.01264,0.02985,-0.05791,-0.0119,-0.04972,-0.00171,0.01603,-0.02921,-0.0761,-0.01639,0.03772,0.05092,-0.00464,-0.03745,-0.02624,-0.15311,0.02692,0.0151,0.11676,-0.10972,0.0391,-0.01287,-0.08634,0.0473,0.15316,-0.02082,-0.02744,-0.01251,0.0094,-0.01582,-0.04809,0.04354,-0.07647,0.10935,0.09,0.04216,-0.08634,-0.06588,-0.02686,-0.00886,-0.0782,-0.01632,0.01588,-0.02001,-0.12779,0.01085,-0.05304,0.04063,-0.05405,-0.03319,0.03065,0.05789,-0.03603,0.04327,0.03694,0.19945,-0.06579,0.08959,0.06178,-0.01975,0.07807,0.04368,0.11994,-0.0214,0.05842,-0.04787,-0.0145,0.09969,-0.09631,-0.02668,0.05566,0.03217,0.1378,-0.05883,-0.00125,0.07941,0.14394,0.00305,-0.00365,0.04527,-0.02216,-0.01515,-0.01558,-0.01876,-0.01231,0.02464,-0.01425,0.00666,-0.15501,0.08482,-0.03473,-0.02911,-0.03399,0.1063,-0.11503,0.01814,0.024,0.0183,-0.00624,-0.05945,0.00368,0.02301,-0.00661,-0.05822,0.0671,-0.05099,0.06825,-0.08829,0.04384,-0.02519,0.00281,0.06145,0.04552,-0.01169,-0.13725,-0.00276,0.11648,0.00446,-0.0366,-0.15449,-0.02657,-0.02789,-0.06064,0.04926,-0.07518,0.15583,0.03306,-0.01001,0.05913,0.11448,-0.01409,0.01775,-0.0552,0.09586,0.03042,0.00541,-0.0939,-0.01759,-0.08003,-0.06215,0.09795,-0.03214,0.01476,0.10803,-0.12592]},{"domain":"aerospace_engineering","key":"aero_flight_condition","name":"Mach number, dynamic pressure, equivalent airspeed and Reynolds number at an altitude","package":"aerospace-engineering-ai999x","example":"Flight condition: V = 100 m/s, h = 0 m","v":[-0.06681,0.01848,0.07988,-0.01453,-0.00633,-0.14758,-0.00785,0.07904,-0.03789,-0.03475,-0.00773,0.01415,0.00436,0.03823,-0.07773,-0.067,0.14196,0.02332,-0.01411,0.00576,-0.1532,0.08184,4e-05,-0.00197,-0.02054,0.01891,0.02227,-0.06369,-0.09881,0.01879,-0.01492,-0.02344,0.03162,-0.00271,0.02086,-0.08245,0.05766,-0.01595,0.01964,-0.00234,-0.03292,0.05714,0.00464,0.02349,-0.06118,-0.02306,0.05385,-0.06437,-0.0521,-0.05624,-0.07891,-0.06877,0.04101,0.02968,0.00345,-0.0494,-0.05829,-0.03817,-0.06588,-0.12396,-0.06953,-0.04094,0.09992,-0.07364,-0.04492,0.10976,0.0802,-0.05939,-0.01672,0.07529,-0.03156,0.11484,0.0272,-0.00707,0.12671,-0.06525,0.14094,0.04818,0.01199,0.07895,0.02815,0.02797,-0.12613,0.12599,-0.03189,-0.04928,0.08033,-0.03528,0.04985,-0.08046,-0.00354,-0.13936,-0.09391,0.11886,0.03165,0.01313,0.0069,0.07427,-0.07407,-0.02858,-0.00351,0.02153,0.02588,-0.01669,0.169,0.05469,-0.0484,0.07711,-0.0277,-0.00222,0.0032,-0.03147,-0.11266,0.05541,-0.08849,0.04715,-0.03181,0.01057,-0.07813,0.00772,0.09787,-0.03958,0.02337,-0.04039,0.04134,0.0424,0.00465,0.05849,0.03012,-0.05486,-0.06328,0.04605,-0.12526,0.06745,0.08849,0.06438,-0.04022,0.02752,-0.09016,0.07172,0.07622,0.09765,0.0296,-0.09143,-0.04154,0.02362,0.1232,0.0143,-0.09596,0.02941,0.08975,0.04354,-0.06207,0.0759,-0.10547,-0.03746,-0.0236,0.05497,0.02423,-0.08305,-0.02067,-0.1666,0.02578,-0.00657,0.03652,0.06335,-0.0654,-0.08684,0.04626,0.00342,0.02055,-0.04414,0.01404,0.08245,-0.03455,-0.04146,-0.05132,-0.00232,0.09429,0.00519,0.12696,0.01988,0.07072,0.10369,-0.03399,0.01851,0.02566,-0.09305,0.00767,0.01427,0.0068,-0.05183,0.06405,0.02995,-0.00045,-0.05255,0.00766,-0.00158,0.04099,0.06087,-0.03243,-0.07503,0.00251,-0.015,-0.02723,-0.02989,0.03716,-0.05186,-0.02133,-0.00399,-0.04623,0.05442,-0.02885,0.06398,-0.02604,-0.0291,-0.05344,0.12083,-0.04915,-0.03334,-0.00959,-0.0306,0.06212,-0.0039,-0.04847,-0.14742,-0.05046,0.0984,-0.04956,-0.09171,-0.06549,0.03453,-0.05677,0.08425,0.02696,-0.03759,0.05964,0.11304,0.05698,-0.10032,0.0906,-0.02576,0.05398,-0.04852,0.00948,0.02883,0.04916,-0.00949,-0.05362,0.04771,0.05984,0.06436,-0.09051,0.00817,-0.10559,-0.05002]},{"domain":"aerospace_engineering","key":"aero_geopotential_altitude","name":"Geopotential 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15","v":[-0.00727,-0.07171,0.13966,0.07272,-0.0663,-0.11015,0.061,-0.02274,0.0534,-0.03573,0.08936,0.01801,0.02179,0.06798,0.06683,-0.0002,-0.0351,-0.00172,-0.09404,-0.04288,-0.09807,0.02915,0.04419,-0.09824,0.0135,-0.01178,0.02511,-0.01804,-0.09134,0.04395,0.00738,0.05783,-0.10169,-0.00444,-0.00467,0.03373,0.0422,-0.01505,0.05038,-0.03409,-0.07782,-0.00558,0.06523,-0.00521,-0.05408,0.04768,-0.00915,-0.01577,-0.04608,-0.08598,0.0185,0.01204,0.06915,0.01735,0.06916,-0.00581,0.01952,-0.03048,-0.06899,-0.08494,-0.04637,0.02621,-0.02906,-0.13703,-0.01394,0.02649,0.0827,-0.01614,-0.1373,0.04403,0.12344,0.05932,0.03756,-0.04276,0.11041,-0.02613,-0.04791,0.14772,0.0675,-0.06499,0.02554,0.04285,-0.09875,0.04326,-0.02519,-0.01496,0.04259,0.03393,0.0418,0.07074,-0.05537,-0.0153,-0.06694,-0.02021,0.07641,0.01441,0.08298,-0.00155,-0.13568,0.02725,-0.02986,0.08431,0.0298,0.04523,0.01603,-0.02904,0.0039,0.12357,0.02355,-0.0217,0.06053,-0.00854,-0.01738,0.04502,-0.09628,-0.00431,-0.02179,-0.05189,-0.1092,0.00756,-0.01988,-0.00265,0.02052,0.00287,0.01545,-0.07774,-0.08184,0.04534,-0.07888,-0.0273,0.05952,-0.04618,-0.01789,-0.04748,-0.05582,-0.01287,0.11441,0.06797,-0.03502,-0.00396,-0.10893,0.11673,-0.01357,-0.05714,-0.07741,0.05903,0.04723,0.05299,0.04738,0.03679,0.03813,-0.09411,-0.09672,-0.07224,-0.0313,-0.0454,0.03531,0.02283,0.10662,-0.04961,0.07787,-0.1052,0.07272,0.02609,-0.06722,0.03908,-0.04271,-0.04703,0.03102,-0.04645,0.04686,0.07515,0.06853,-0.01242,-0.03748,-0.09112,0.0041,-0.08687,0.09915,0.0289,-0.04444,0.00317,0.04452,-0.02903,0.09682,0.08885,0.00011,0.00867,0.12138,0.0028,-0.06335,-0.05338,0.13199,-0.03047,0.02963,0.01045,0.01841,0.0319,0.05008,0.07281,0.075,-0.05065,-0.00671,-0.13605,-0.02337,0.01685,-0.0233,-0.04938,-0.03798,-0.06908,-0.0345,0.04503,-0.01127,0.18673,-0.01581,-0.08008,0.11053,0.17364,0.00252,-0.02593,0.04077,-0.0868,0.0663,0.031,-0.03145,-0.01703,-0.01192,0.05169,0.00722,-0.02837,-0.04929,0.03305,-0.18203,0.03358,0.05314,-0.0495,0.01825,-0.01079,-0.1327,-0.02921,0.06643,0.00855,0.16502,-0.07411,-0.08931,0.06271,0.08538,0.05341,-0.01951,-0.09006,0.0055,-0.00811,-0.00947,-0.03943,0.01681,-0.01216]},{"domain":"aerospace_engineering","key":"aero_ideal_exhaust_velocity","name":"Ideal rocket exhaust velocity","package":"aerospace-engineering-ai999x","example":"Exhaust velocity: Tc = 3000 K, Mw = 20 g/mol, gamma = 1.4, pc = 1 MPa, pe = 127.80452546295093 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fraction of a rocket with identical stages","package":"aerospace-engineering-ai999x","example":"Identical stages: n = 1, dv = 4078.4710789429123 m/s, Isp = 300 s, eps = 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drag in level flight","package":"aerospace-engineering-ai999x","example":"Induced drag: W = 10 kN, S = 16 m^2, V = 50 m/s, h = 0 m, AR = 8, e = 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2","v":[0.04913,-0.13095,-0.04715,0.09209,-0.08342,0.0303,0.01052,0.09159,0.03422,0.01256,-0.03252,0.00771,0.03645,0.05618,-0.09334,0.17041,0.06778,-0.11274,0.00862,0.095,0.03283,-0.09938,0.05295,-0.09841,-0.01447,-0.01025,-0.01758,0.00491,0.03276,0.0033,0.08229,0.01851,0.061,-0.04868,-0.00627,0.06361,0.03371,0.0532,0.03467,-0.00107,0.06177,0.05577,0.02416,-0.00474,-0.01967,-0.00465,0.09583,-0.09824,0.03428,0.18532,0.02221,0.01526,0.17564,0.04737,0.07878,0.00927,-0.04104,-0.09143,0.05329,-0.03807,-0.04352,-0.15269,0.08278,0.03388,-0.02105,-0.00588,0.06613,0.05285,-0.05297,0.04194,-0.03122,0.11183,-0.04925,-0.02897,-0.00035,-0.0469,0.07151,-0.02334,0.03222,-0.004,0.03006,-0.06392,-0.04054,0.06878,0.0506,-0.06259,-0.04389,0.00063,-0.10187,-0.10639,-0.03478,0.03757,-0.02494,-0.01133,-0.05488,-0.02293,-0.04704,-0.01624,-0.02434,0.06399,0.02683,-0.01681,0.03895,0.01595,0.02029,-0.06346,0.16037,-0.00968,-0.10592,0.10128,0.01485,-0.0684,-0.04426,-0.02441,-0.10773,-0.11976,-0.01424,0.03372,-0.0445,0.00242,0.07117,-0.10742,0.14909,-0.0098,-0.02281,-0.02851,-0.00742,0.06369,-0.00325,0.06327,-0.03974,0.1084,-0.09487,-0.0139,0.03317,0.03464,-0.04484,0.00865,-0.07852,0.08174,0.01257,0.02478,-0.0143,0.06435,0.0419,0.05761,-0.06826,-0.10955,-0.03538,-0.01732,-0.06071,-0.08434,0.00682,-0.00765,-0.01347,-0.11875,-0.06831,0.01482,0.05922,-0.13849,0.02467,-0.04885,-0.03586,-0.11623,-0.05035,0.05578,-0.0043,-0.04678,0.07297,0.06231,0.04494,-0.02155,0.01259,0.02934,0.10606,0.0385,0.00165,0.13848,0.13897,0.06189,-0.02917,0.03294,0.01427,-0.07844,0.02948,0.0665,-0.12066,0.04506,-0.0079,-0.05712,-0.05542,-0.03372,0.08738,0.00856,-0.03493,0.08308,-0.01555,0.02791,-0.04576,-0.04512,0.07006,-0.10293,-0.01488,-0.00857,0.01133,-0.06453,-0.05383,-0.02815,-0.06897,0.0129,0.00215,0.06397,-0.04316,-0.00914,0.00922,0.07066,-0.08502,-0.01763,-0.05136,-0.02217,-0.02274,0.00711,-0.03475,0.06102,0.01441,-0.14361,-0.0284,0.02363,0.06132,-0.04012,-0.00231,-0.0684,-0.0167,-0.0242,0.03275,-0.03005,0.05585,0.00791,0.01296,0.04196,0.13228,0.0107,0.07029,0.03006,0.03217,0.06506,0.07486,-0.06465,-0.06762,0.00099,-0.02444,0.05523,-0.17074,0.01327,0.00309,-0.08005]},{"domain":"aerospace_engineering","key":"aero_j2_apsidal_rotation","name":"Rotation of the line of apsides from J2","package":"aerospace-engineering-ai999x","example":"Apsidal rotation: hp = 500 km, ha = 500 km, i = 63.4 deg","v":[0.119,-0.00936,-0.05414,0.08119,0.02742,-0.01859,-0.06899,-0.09373,0.10069,0.07649,-0.02809,-0.0237,0.00413,-0.04013,-0.00893,0.01399,0.06736,0.00459,-0.00188,-0.0422,-0.07226,-0.01469,-0.08154,0.0336,0.01694,-0.06095,0.03582,0.05793,0.07171,0.05013,-0.10643,0.04026,0.0225,0.04562,0.00574,0.07951,0.01345,0.00453,0.0517,0.02491,0.12134,-0.0277,-0.03413,-0.0082,-0.03104,-0.08474,0.00963,-0.12006,0.06073,-0.01764,-0.04251,0.02532,0.09137,0.07998,0.00672,-0.01376,-0.07885,0.15161,-0.01876,-0.0802,-0.01733,0.02714,-0.06574,0.04174,0.04639,0.01597,0.02151,-0.09713,-0.13773,-0.03699,0.04048,-0.00582,0.17642,-0.08874,0.02571,0.02233,0.0374,0.08783,0.02421,-0.02389,-0.06822,0.05131,-0.00427,-0.03619,-0.066,0.00979,-0.08509,-0.11303,-0.08935,-0.04392,-0.00539,-0.02641,-0.08954,0.02349,-0.08245,0.0823,-0.02624,0.00837,0.04383,0.00234,-0.03165,0.08123,0.10239,-0.02822,0.02175,-0.07935,0.03967,0.04832,-0.00142,-0.03149,0.06398,0.05788,0.02067,-0.06271,0.01521,0.05696,-0.00032,-0.00434,0.04948,-0.04813,0.09346,-0.05107,-0.00828,-0.05953,0.03064,0.02894,-0.00381,-0.05975,-0.05684,0.01609,-0.00516,-0.09614,0.01789,-0.04156,0.08777,-0.02524,0.03272,0.05477,0.05206,0.05863,0.02316,0.0284,-0.03639,0.07786,0.07664,-0.00476,-0.03491,-0.19381,-0.05302,0.05996,-0.12636,0.04618,-0.02319,-0.05009,0.0076,0.02169,0.06899,0.01789,-0.00864,-0.06485,0.06256,0.0082,0.02754,-0.02042,-0.10821,0.03292,0.03018,0.02012,-0.00743,0.12558,0.10158,-0.05468,0.08217,-0.1629,0.01793,0.05248,-0.01393,0.03444,0.01541,-0.05053,-0.0666,-0.06024,0.01296,-0.05878,0.02663,0.0109,-0.04857,0.02987,0.03161,-0.08645,0.06853,0.05534,0.05789,-0.05884,-0.05697,-0.01596,-0.08736,0.08274,0.07513,-0.04346,0.02246,-0.00028,-0.04953,0.04794,-0.04973,0.0466,0.10071,-0.00689,-0.10176,-0.0235,0.00267,-0.01694,0.00483,0.07336,-0.06539,0.00347,-0.02878,-0.08814,0.01702,-0.00773,-0.12746,-0.05228,0.11364,0.05912,0.09403,0.02412,-0.11533,-0.10692,-0.04159,0.0978,0.10384,-0.02713,-0.00138,-0.12453,-0.03253,0.06047,0.02742,0.02174,0.08958,-0.0487,-0.03205,0.1016,0.07474,0.05687,0.02432,0.06135,0.04638,-0.15989,0.07253,-0.13818,-0.02719,0.13588,-0.01647,-0.06035,0.04087,-0.0032]},{"domain":"aerospace_engineering","key":"aero_j2_nodal_regression","name":"Nodal regression from the Earth's oblateness (J2)","package":"aerospace-engineering-ai999x","example":"Nodal regression: hp = 19134.409799999998 km, i = 60 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a jet needs for a cruise range","package":"aerospace-engineering-ai999x","example":"Fuel for range: R = 10800 km, V = 200 m/s, c = 1 1/h, LD = 15, W0 = 271.8281828459045 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range at constant altitude and lift coefficient","package":"aerospace-engineering-ai999x","example":"Jet range at constant altitude: W0 = 400 kN, W1 = 100 kN, S = 100 m^2, h = 0 m, CL = 0.5, CD = 0.05, c = 0.00001 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problem (orbit through two positions in a given time)","package":"aerospace-engineering-ai999x","example":"Lambert problem: r1 = [7000, 0, 0], r2 = [0, 7000, 0], tof = 1457.1291594215038 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ground roll","package":"aerospace-engineering-ai999x","example":"Landing roll: W = 10 kN, S = 10 m^2, h = 0 m, VTD = 30 m/s, mu = 0.4, CL = 0.25, CD = 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coefficient in level flight","package":"aerospace-engineering-ai999x","example":"Lift coefficient in level flight: W = 10 kN, S = 16 m^2, V = 50 m/s, h = 0 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coordinated turn at a bank angle","package":"aerospace-engineering-ai999x","example":"Level turn at bank angle: V = 100 m/s, phi = 45 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turn at a load factor","package":"aerospace-engineering-ai999x","example":"Level turn at load factor: V = 100 m/s, n = 2","v":[-0.01538,-0.00337,0.03581,0.05835,0.0116,0.05945,0.00098,-0.07027,0.07158,-0.10423,0.02793,-0.05191,0.00656,0.02031,0.04173,0.06877,-0.00236,0.00207,0.00656,0.07058,-0.021,0.03668,-0.00689,-0.02621,0.01132,-0.10075,0.11821,-0.02365,-0.01769,-0.05262,-0.05989,-0.00898,0.04046,0.04532,0.07206,-0.0544,0.03667,0.08295,-0.03383,0.09786,-0.00535,-0.00708,-0.02127,0.09741,0.09993,0.06303,0.12635,0.05206,0.04183,-0.06651,-0.02124,-0.10447,0.00235,0.01109,-0.0843,-0.11797,-0.08642,-0.10285,-0.04266,0.04889,0.01834,0.08412,-0.03915,-0.00686,0.02844,0.03947,-0.03094,-0.07305,-0.03593,0.04755,-0.08493,-0.04592,0.09966,0.05376,0.02398,-0.01125,-0.00159,0.11054,-0.08116,0.06644,-0.02255,0.06463,0.00928,0.03913,-0.05083,-0.06238,0.06927,0.04356,0.03988,-0.02387,-0.03102,-0.07286,-0.0288,-0.12413,-0.02606,0.03498,0.00646,0.04983,-0.01364,-0.01558,-0.00573,-0.02463,0.00745,-0.10156,0.04723,-0.02973,-0.04789,0.03214,0.06179,-0.0789,-0.014,0.04018,0.08294,-0.03722,-0.00511,0.00767,0.03118,-0.08013,0.01602,-0.15451,-0.07915,0.0462,-0.06034,-0.08622,-0.03262,-0.02312,-0.11692,0.06965,0.04032,-0.04582,-0.07482,-0.0401,-0.01183,-0.01013,0.10331,-0.0597,-0.08372,0.06768,0.01311,0.03967,-0.03621,0.06436,0.03469,-0.01978,-0.04047,0.01639,0.10481,0.01171,0.00884,0.07387,0.11761,0.14646,0.0096,0.03073,-0.06333,0.0133,-0.04722,0.03146,0.07731,-0.02277,-0.00538,-0.09552,-0.01535,0.032,-0.11563,-0.11509,0.09179,0.00094,-0.01882,-0.03507,0.01712,0.01403,-0.04449,0.02339,0.11118,0.16411,-0.1045,-0.03534,-0.03878,-0.00933,0.06689,0.02635,0.08212,-0.07394,0.12234,0.03566,-0.03628,-0.09221,-0.07163,-0.05275,0.07478,0.1184,-0.02147,-0.05031,-0.04183,0.01579,-0.0543,0.09519,0.00263,0.1262,-0.02039,-0.04902,-0.08963,0.02276,0.08923,-0.02072,0.02344,0.02453,0.02275,0.00048,0.03411,0.06989,0.02746,0.08759,-0.09145,-0.06873,-0.11826,-0.06437,0.01698,0.02116,-0.0495,-0.00798,0.02849,0.02969,0.02255,-0.09589,0.05512,0.14996,0.03536,0.11625,-0.09287,0.1149,-0.0673,-0.04163,-0.15161,0.00042,0.03329,-0.0484,-0.03116,-0.03796,0.00102,0.0314,0.05884,-0.02501,0.0352,0.0153,0.06126,0.02995,-0.10535,0.02212,-0.06138,0.01201,-0.08284,0.04815,-0.15781,0.01264]},{"domain":"aerospace_engineering","key":"aero_mach_from_area_ratio","name":"Mach number from the area ratio A/A*","package":"aerospace-engineering-ai999x","example":"Mach from area ratio: ar = 1.6875, regime = supersonic","v":[0.03794,-0.1024,-0.046,0.01502,-0.02281,0.0027,-0.01212,0.0528,-0.03545,-0.04379,-0.02237,0.03433,-0.02658,0.09061,-0.02584,0.07418,0.07051,-0.08207,0.04093,0.11768,-0.01864,-0.05526,0.14163,-0.05903,-0.02948,-0.01732,-0.00273,0.01214,0.01233,0.05179,0.03122,0.02915,0.00182,0.02109,-0.01807,-0.02615,0.00537,-0.00064,-0.04537,-0.01681,0.03453,0.07476,0.03778,-0.04391,-0.01826,-0.00611,0.10276,-0.05662,-0.09552,0.11687,0.04664,0.04029,0.13656,-0.03045,0.06105,0.12859,-0.0373,-0.13217,0.01622,0.01727,0.02963,-0.05006,0.07371,-0.02408,0.0213,0.03836,0.09996,0.0951,-0.09792,0.0298,-0.02827,0.08561,-0.09217,0.03535,-0.01515,-0.0809,0.02294,-0.05342,-0.00695,-0.00356,-0.02701,-0.04904,-0.0513,0.02109,0.00181,-0.03543,-0.04041,-0.03862,-0.09511,-0.11271,-0.0549,-0.00643,0.00958,-0.01179,-0.08899,-0.03558,-0.00892,0.00934,0.06204,-0.03103,0.01731,0.0861,0.03027,0.02021,0.08549,-0.07088,0.11727,0.05586,-0.10386,0.08014,0.052,-0.03803,-0.17516,-0.01316,-0.0494,-0.05592,-0.06539,-0.02972,-0.06786,0.02609,0.00986,-0.02887,0.18585,0.04435,-0.04405,-0.05075,-0.11925,0.03437,-0.00112,0.04033,-0.06093,0.14943,-0.01938,-0.06942,-0.0004,0.04488,0.00447,-0.04122,-0.0369,0.04234,0.03042,0.04471,0.04217,0.02821,-0.02283,0.02356,-0.0417,0.02355,-0.08168,0.03902,0.02871,-0.02228,-0.09217,0.02522,-0.05613,-0.09212,-0.11541,0.00248,0.1323,-0.10335,0.04769,-0.01806,0.06132,-0.02721,0.02968,0.10252,-0.03991,0.06768,0.12151,0.01417,0.06605,0.02068,0.10564,0.07182,0.06811,-0.03684,0.01693,0.12928,0.09218,0.09146,0.04711,0.05099,0.01656,-0.05415,-0.00406,0.07655,-0.12478,0.03192,-0.04074,-0.03336,-0.08709,-0.01449,0.03983,-0.03193,-0.00543,0.00793,-0.02197,-0.03935,-0.04345,0.04214,0.08074,-0.14595,0.00288,0.0032,0.08902,-0.03365,-0.13146,-0.0718,-0.11273,0.07191,-0.04612,0.04407,-0.03608,0.02814,-0.03638,-0.01714,-0.07406,-0.04449,-0.06587,0.01934,0.03149,-0.09002,-0.05125,0.0093,0.06934,-0.06903,-0.01649,-0.01454,0.12709,-0.07623,0.00601,-0.0148,0.01604,-0.00286,0.05987,0.03216,0.07048,-0.01974,0.10724,-0.02287,0.11631,0.00026,0.04751,0.02178,-0.03764,0.0584,0.09416,-0.04703,-0.01333,-0.05281,-0.05404,0.05345,-0.14853,0.08724,0.00131,-0.03361]},{"domain":"aerospace_engineering","key":"aero_mach_from_pitot","name":"Mach number from pitot and static pressures","package":"aerospace-engineering-ai999x","example":"Mach from pitot: p = 10 kPa, pt = 18.92929158737854 kPa","v":[-0.04792,0.02244,-0.08706,0.02296,0.02765,0.02625,0.08112,0.09205,-0.00525,-0.04004,-0.01276,0.03622,0.0116,0.11982,-0.11696,-0.00109,0.05423,0.01267,-0.0208,-0.00984,-0.01814,-0.09473,0.00439,0.01441,-0.04407,-0.02981,-0.04922,-0.04429,0.08158,-0.02673,0.13881,0.04634,0.01102,-0.04262,0.05818,-0.01318,0.03661,0.06145,-0.02223,0.00587,0.00411,-0.05467,-0.01083,-0.07459,-0.04493,0.04156,0.00205,-0.06107,-0.0639,0.07388,-0.08299,-0.02518,0.05212,0.1248,0.00555,-0.05527,0.01946,-0.14655,-0.06639,0.01399,-0.0483,0.02878,0.06486,-0.1182,-0.03084,0.03969,0.00678,-0.03037,-0.05614,0.08002,-0.07905,0.03305,0.00124,0.00119,0.00437,-0.03398,0.16328,0.0204,0.05639,0.1132,0.0011,-0.00256,-0.00704,0.08518,0.07287,-0.14069,-0.01095,0.05616,0.00964,-0.12782,0.01162,-0.02198,-0.08549,0.02035,-0.01753,-0.07538,-0.01129,0.02741,-0.07897,-0.09407,0.0305,0.0121,0.10621,0.02871,0.07503,-0.01761,-0.00381,0.0755,-0.1343,0.1047,0.04497,-0.06413,-0.11657,0.07342,-0.04376,-0.08528,0.02279,0.04168,-0.03896,0.03616,-0.04952,0.01458,0.10046,-0.10011,0.06758,-0.02878,-0.01832,0.11523,0.13001,-0.00575,-0.02977,0.00139,-0.11945,0.03338,-0.00771,-0.01849,-0.06618,-0.00423,-0.06038,0.14729,-0.09954,0.12374,-0.02559,-0.04335,0.03559,0.04496,-0.03667,0.05517,-0.05712,0.01224,-0.03914,0.08261,-0.02216,0.09137,-0.10028,-0.07588,-0.05447,-0.07448,0.08453,-0.12781,-0.09473,-0.05188,0.00629,-0.03705,0.06091,0.03285,-0.03617,-0.038,-0.00346,-0.00972,-0.00264,-0.06249,0.03954,0.12114,0.01454,0.00194,0.0293,-0.01979,0.06892,0.10273,0.00574,0.04766,0.06828,-0.02805,-0.00951,0.07479,0.01892,-0.12247,-0.03153,0.03475,-0.05766,-0.00919,0.00547,0.14411,0.01865,-0.06243,-0.0284,-0.02467,-0.01395,-6e-05,0.06706,-0.0314,0.00565,0.11072,-0.02504,-0.11562,0.00272,-0.00589,-0.02014,-0.0234,0.01075,0.12028,0.02332,-0.02764,-0.06169,0.03128,-9e-05,0.00201,-0.0284,0.03232,0.06079,0.00188,-0.10383,0.15299,-0.07206,-0.08416,-0.06221,0.02649,0.04378,-0.0341,-0.05957,0.07253,0.02555,-0.02035,0.01569,0.03868,0.0662,0.04387,0.01892,-0.01564,0.04609,-0.13544,0.0602,0.05009,-0.01735,-0.02431,0.02873,-0.02825,-0.07487,-0.05281,0.017,0.06206,-0.08184,0.14532,-0.08506,-0.04805]},{"domain":"aerospace_engineering","key":"aero_mach_from_prandtl_meyer","name":"Mach number from the Prandtl-Meyer angle","package":"aerospace-engineering-ai999x","example":"Mach from Prandtl-Meyer angle: nu = 26.379760813416457 deg","v":[-0.02427,0.02107,0.04848,0.09687,-0.04254,0.11031,0.05359,-0.05693,0.0174,-0.05158,-0.05669,0.08074,0.03255,0.07237,0.04865,0.02523,-0.01168,-0.04344,0.09073,0.14648,-0.04578,0.04879,0.08008,-0.04461,0.00476,-0.08394,-0.02748,0.10987,0.05463,0.05719,0.02191,0.05385,-0.06181,0.00561,-0.08548,-0.10468,-0.08421,-0.05866,-0.08407,-0.0733,-0.03386,-0.0376,0.07341,-0.04107,0.07568,-0.08159,0.03535,-0.07448,-0.00633,0.02509,-0.00985,-0.0291,0.02322,0.04663,-0.10961,-0.04971,0.00775,-0.02537,-0.04725,-0.0845,-0.02993,0.00821,0.04099,-0.02805,0.01528,0.05399,-5e-05,-0.11393,-0.1774,0.01205,-0.08677,0.07086,-0.00533,0.08898,0.04085,-0.05137,0.10285,0.04735,0.05027,0.03715,0.02396,0.00169,0.00764,0.00336,0.00365,-0.03991,0.00909,0.02457,0.0407,-0.08744,0.06776,0.11213,0.06519,-0.02857,0.01711,-0.04961,0.07096,-0.07982,-0.04195,-0.00415,0.08409,0.01009,-0.01019,-0.05561,0.10669,0.01025,-0.11927,0.06751,-0.16228,-0.00697,-0.0249,0.03641,-0.03574,0.03638,0.00494,-0.04805,-0.02465,-0.07241,-0.07652,-0.07591,0.07754,0.0359,0.08013,0.05852,-0.05232,0.03951,0.03185,-0.02994,0.01742,-0.00458,-0.0612,0.06712,-0.1243,0.05537,0.06302,-0.00276,0.02991,0.0439,-0.00357,0.04124,0.04742,0.09806,0.02626,0.02742,0.05453,0.07613,0.07787,-0.08336,-0.04133,0.07798,0.01262,0.10841,-0.1035,0.04616,-0.08242,-0.03479,-0.04538,-0.01211,0.09607,-0.00877,-0.02313,-0.1504,-0.0552,-0.04399,-0.02213,-0.05554,0.03573,-0.07983,-0.03509,0.05663,-0.04481,-0.0254,0.01754,0.03823,0.06557,0.04957,-0.02608,0.01107,0.0431,-0.04189,-0.04323,-0.00486,-0.0046,0.01187,0.06425,0.1155,-0.0909,-0.1013,0.04666,-0.01143,-0.10611,-0.03979,0.00804,-0.08312,0.01389,-0.04741,-0.07723,-0.03949,-0.11566,0.01728,-0.03075,-0.07936,0.04086,0.09896,0.05557,-0.08543,0.0653,0.04461,-0.0309,-0.02828,-0.1042,0.17007,0.0124,-0.00065,-0.05167,-0.01072,-0.0811,0.05009,0.02105,0.03096,-0.04808,-0.17823,0.00925,-0.00478,-0.0966,-0.11691,-0.02267,0.03953,0.05271,0.01919,0.02727,0.03288,0.03505,-0.00639,0.00979,0.03116,0.02062,0.06313,-0.03137,-0.07458,0.11142,0.04188,0.07372,0.0991,0.02668,0.0176,-0.0217,0.00083,-0.05251,-0.11068,-0.05438,0.0937,0.03926,0.13116,-0.00051,-0.01424]},{"domain":"aerospace_engineering","key":"aero_mach_from_pressure_ratio","name":"Mach number from the stagnation-to-static pressure ratio","package":"aerospace-engineering-ai999x","example":"Mach from pressure ratio: p0/p = 7.824449066867265","v":[0.0304,0.01973,-0.06125,-0.00132,-0.08893,0.04495,-0.00019,0.05471,-0.00234,-0.0858,-0.10955,0.01681,-0.04486,0.05155,-0.0539,0.15028,0.10395,-0.06828,0.0081,0.01217,0.03871,-0.06903,0.0232,-0.05799,-0.00682,-0.01235,0.07666,-0.02276,0.01374,0.02317,0.06503,0.04336,0.02642,-0.02855,-0.02878,0.03114,-0.01451,0.11402,0.03313,0.01895,-0.01001,0.03238,0.00094,0.03957,-0.08912,0.00903,0.02819,-0.09245,-0.01636,0.1228,0.0624,-0.02918,0.13756,0.04983,0.08267,0.02575,-0.07222,-0.15129,-0.02763,0.00612,-0.04758,-0.11264,0.05525,0.00151,-0.04288,0.06321,0.05149,0.0381,-0.03066,0.0443,-0.06666,0.10744,-0.01866,-0.00325,0.01347,-0.0219,0.14777,0.01386,0.00886,0.00229,0.04416,-0.0609,-0.06408,0.06562,0.09832,-0.1023,-0.02037,-0.04416,-0.11586,-0.10159,0.00427,0.1018,-0.07357,-0.0364,0.01805,-0.00903,-0.04436,0.01618,-0.03245,0.01381,0.03384,-0.02869,0.03439,0.04373,0.05677,-0.01417,0.10466,-0.01149,-0.10308,0.11967,0.00326,-0.0279,-0.03191,-0.08751,-0.09282,-0.09185,0.02553,0.03591,-0.05328,-0.00368,0.0908,-0.0573,0.10707,0.03075,0.00209,0.01279,-0.05902,0.02961,0.00945,-0.05126,-0.0546,0.12062,-0.12614,-0.01769,0.04298,0.03448,-0.05973,-0.02142,-0.05793,0.00168,-0.00889,0.05416,0.00319,0.00957,0.01614,0.03784,-0.07387,-0.0888,-0.04697,0.03706,-0.05904,-0.1296,-0.00842,-0.00616,-0.00757,-0.09498,-0.0348,0.09383,0.04954,-0.13804,-0.00906,0.01864,-0.01761,-0.06776,-0.07966,0.05897,-0.02083,-0.05499,0.07562,0.01316,0.04977,-0.06408,0.03653,0.01216,0.07194,0.11647,-0.01799,0.05323,0.11568,0.08483,0.05057,0.05785,0.07568,-0.05353,0.0586,0.00371,-0.14623,0.02308,0.00297,0.00926,-0.06071,-0.06313,0.03041,0.03913,-0.0236,0.05263,-0.03706,0.05592,-0.10736,-0.04224,0.03206,-0.09195,-0.01358,0.03385,0.01449,0.00717,-0.0454,-0.01488,-0.08824,-0.00528,-0.05139,0.17422,-0.05789,0.00907,-0.02491,-0.01888,-0.13192,0.0419,-0.08794,0.01732,0.10975,-0.00803,0.01987,0.09744,-0.05341,-0.11415,-0.01451,0.01728,0.06861,-0.01156,0.01708,-0.07299,-0.02702,-0.04557,0.04814,0.02557,0.08877,0.09538,0.01781,0.04573,0.11159,-0.04662,0.12173,0.07478,0.01657,0.08164,0.07408,-0.05246,-0.00083,-0.05296,-0.02799,0.05536,-0.11257,0.05226,-0.02193,-0.11393]},{"domain":"aerospace_engineering","key":"aero_max_climb_angle_jet","name":"Steepest climb angle of a jet","package":"aerospace-engineering-ai999x","example":"Maximum climb angle: W = 100 kN, S = 30 m^2, h = 0 m, T = 30 kN, CD0 = 0.02, AR = 7, e = 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deflection angle of an attached oblique shock","package":"aerospace-engineering-ai999x","example":"Maximum deflection angle: M1 = 2","v":[0.07655,-0.01734,0.12641,0.01909,-0.05255,0.03569,0.01668,-0.08773,0.08265,-0.03078,-0.03309,0.06365,0.00656,0.06851,0.08321,0.06243,0.00379,-0.05686,0.0116,0.02679,-0.00428,-0.01039,-0.00714,-0.02533,-0.02195,-0.0378,-0.06836,0.03428,-0.05054,0.00084,0.12462,0.03463,0.06424,-0.06808,-0.08129,-0.06271,-0.00164,0.00965,-0.06803,0.03133,-0.01477,0.01798,0.15728,0.02068,0.0763,-0.02035,0.00223,-0.0825,0.03811,0.10009,0.04058,0.01461,0.00727,0.00358,0.13961,0.03387,-0.05926,-0.11137,-0.0518,-0.0431,-0.02015,0.02623,0.06345,-0.06281,0.08916,-0.07423,-0.01697,-0.04458,-0.0003,-0.01797,-0.02423,0.06896,-0.05508,0.07848,0.06215,-0.01616,0.03833,0.03467,0.02512,0.05144,-0.04506,-0.08466,-0.11092,0.03882,-0.01656,-0.0826,0.018,-0.10329,0.06558,-0.04239,0.07796,0.16285,0.06412,0.06659,-0.08444,0.06292,-0.00528,-0.09016,-0.02327,0.01076,0.08927,0.02958,-0.03776,-0.03638,0.01773,0.06489,-0.07311,0.08704,-0.14184,-0.04092,-0.06379,0.00705,0.0367,0.1084,0.01957,0.00637,-0.05435,0.00161,-0.01623,-0.02565,0.07408,0.07994,0.02731,-0.00681,-0.06643,-0.02,-0.02758,-0.03378,0.11501,0.04686,-0.00998,0.0575,0.01526,-0.03457,0.06321,0.04387,0.01689,-0.05119,-0.03369,0.08039,0.01293,-0.03862,0.02798,0.01282,0.02527,0.05442,-0.0322,-0.02878,-0.02123,0.02412,-0.02636,-0.09303,-0.0987,-0.0188,-0.11702,0.01745,-0.12918,0.01093,-0.00775,0.00732,-0.02107,0.0775,0.01461,-0.00493,-0.14567,-0.01395,0.10139,-0.10965,0.08745,0.04591,0.00143,0.03175,-0.05925,0.00064,0.0152,-0.0004,-0.01403,-0.06388,0.07241,-0.07777,-0.07008,0.08287,0.04984,0.01376,0.02029,-0.0459,-0.04297,0.03338,0.10352,-0.03017,-0.17789,-0.03098,0.10659,-0.13544,-0.07374,0.06054,-0.11494,0.04372,-0.02027,0.0217,0.05671,-0.0639,0.05727,0.12236,0.00116,0.05121,-0.02499,-0.00289,-0.09401,-0.02454,-0.09601,-0.04958,-0.12072,0.0173,-0.07837,0.04629,-0.11165,0.12541,-0.03785,-0.02456,-0.06619,0.02289,-0.02864,0.08275,-0.06546,0.03934,-0.0183,0.04173,0.11991,-0.02811,-0.07263,-0.0053,0.00602,-0.08582,0.0649,0.07097,-0.06308,0.06766,0.01676,-0.01991,-0.05231,0.10792,0.06604,0.02616,0.00644,-0.06878,0.05924,0.04091,-0.08908,-0.09836,-0.04234,0.08198,0.01125,0.12339,-0.00889,0.01964]},{"domain":"aerospace_engineering","key":"aero_max_rate_of_climb_jet","name":"Maximum rate of climb of a jet","package":"aerospace-engineering-ai999x","example":"Maximum rate of climb of a jet: W = 100 kN, S = 30 m^2, h = 0 m, T = 1 kN, CD0 = 0.02, AR = 7, e = 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rate of climb of a propeller aircraft","package":"aerospace-engineering-ai999x","example":"Maximum rate of climb of a propeller aircraft: W = 11 kN, S = 16 m^2, h = 0 m, P = 1 kW, eta = 0.8, CD0 = 0.03, AR = 7.5, e = 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for minimum drag, minimum power and best jet range","package":"aerospace-engineering-ai999x","example":"Speeds for minimum drag: W = 10 kN, S = 20 m^2, h = 0 m, CD0 = 0.02, AR = 10, e = 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of a multistage rocket","package":"aerospace-engineering-ai999x","example":"Multistage rocket: Isp = [300, 300], m0 = [2718.2818284590453, 500], mf = [1000, 183.93972058572118]","v":[-0.04262,0.08648,0.05108,-0.00923,0.06747,-0.07712,0.02731,0.00464,0.05146,-0.02747,0.07355,0.04351,-0.08534,-0.10765,0.04076,0.04049,-0.03328,-0.02144,0.02542,0.07428,0.04539,-0.0491,-0.07252,0.02508,-0.06375,0.0699,-0.0634,-0.00886,-0.0302,0.00825,-0.08501,-0.07626,-0.04588,-0.06439,0.12365,-0.03644,0.01597,0.04208,0.05329,-0.06091,0.09754,0.1035,0.01043,-0.05243,0.01464,-0.03851,-0.0855,-0.05257,-0.02078,0.03879,-0.10556,0.06079,-0.07374,0.13048,-0.00484,0.03313,-0.03008,-0.02118,0.07467,-0.04752,-0.13734,0.03425,0.0542,-0.01485,0.02648,0.06218,0.07562,0.01561,0.04393,0.07301,-0.04319,0.03249,-0.05,0.02696,0.0368,0.10281,-0.07107,-0.00772,-0.10512,-0.09762,-0.09042,-0.07658,0.02732,-0.02667,-0.02829,-0.01618,-0.07851,-0.03959,-0.07128,0.06477,-0.01109,-0.01346,-0.06684,-0.07381,-0.04948,-0.02862,0.02422,0.10939,-0.05707,0.00695,-0.02785,0.02759,-0.07443,-0.08432,0.03722,0.04685,0.08305,0.01924,-0.03114,0.13993,0.02439,0.03393,-0.03242,-0.01167,-0.12069,0.03268,-0.00109,-0.00869,0.05659,0.05123,-0.00159,0.06733,-0.04559,0.05635,0.04406,0.00211,-0.03371,-0.01056,0.0105,-0.00198,-0.07217,0.12539,-0.08615,0.0048,0.13766,-0.05248,-0.02133,0.12122,0.01439,0.06768,-0.00355,0.05004,-0.07794,0.01338,0.11031,0.02648,-0.05689,0.04597,0.0558,-0.01061,-0.13157,-0.03275,-0.05504,-0.08921,-0.03561,-0.01034,-0.09061,-0.01212,0.01577,-0.01911,-0.06182,-0.08326,0.02188,-0.03019,-0.02534,0.01047,0.01186,0.05841,0.01472,0.14047,-0.02923,0.00662,-0.04907,-0.14818,0.12483,0.0579,0.00632,-0.05283,-0.00551,0.03781,-0.01198,0.01965,-0.02531,-0.07087,-0.06334,0.10269,0.02552,-0.06013,0.19223,-0.068,-0.00597,0.06384,0.02892,0.08778,0.0051,-0.0155,-0.08354,-0.02663,-0.00846,1e-05,-0.09248,-0.05484,0.04449,0.10243,-0.16409,0.09452,0.05584,-0.00069,-0.01693,0.00597,-0.06043,0.07986,-0.04904,-0.10299,0.04307,-0.06583,-0.01951,-0.04144,-0.03343,0.00419,-0.03471,0.06746,-0.06754,0.0741,-0.00999,-0.10674,-0.03506,0.10539,-0.09621,0.05062,0.11749,-0.08134,0.00581,-0.02656,0.0687,0.05793,0.04253,0.03855,0.0257,-0.03993,0.04949,0.05894,0.09918,0.00222,0.10418,0.06294,0.04568,-0.01937,0.1221,-0.01521,-0.01911,0.00068,-0.03267,-0.09027,0.00845,0.00886]},{"domain":"aerospace_engineering","key":"aero_naca4_thin_airfoil","name":"Thin-airfoil theory for a NACA 4-digit airfoil","package":"aerospace-engineering-ai999x","example":"NACA 0012 thin airfoil: alpha = 0.1 rad","v":[0.02903,0.05875,0.18061,0.05865,-0.03954,-0.04487,0.00533,0.00176,0.09109,-0.03078,0.00856,0.0935,-0.01211,-0.04427,0.02427,0.06311,0.08251,-0.01152,0.03227,-0.10816,-0.07985,-0.01303,0.02006,-0.04286,-0.03502,-0.06775,0.04861,0.05042,-0.09,0.01982,0.01851,0.08247,0.03281,0.04623,0.00775,-0.08713,0.04025,-0.06833,-0.05497,-0.03065,-0.06025,0.04153,0.09405,-0.0386,-0.08915,-0.01231,-0.05004,-0.05724,-0.03458,-0.02106,-0.01349,-0.04352,0.03943,-0.04628,0.06991,0.02062,-0.03476,0.11203,-0.01751,-0.01875,-0.0143,0.03382,0.01717,-0.10497,0.04577,-0.02379,0.05927,-0.01593,-0.04623,0.01077,0.09537,0.00708,-0.02728,-0.00348,0.04713,0.02847,0.08205,0.09448,0.01422,-0.01122,0.00433,-0.08261,-0.02794,0.01347,0.00837,-0.06021,-0.03169,0.04343,0.03075,-0.06879,-0.03466,-0.03917,-0.05003,-0.01672,-0.02935,-0.10099,0.03755,-0.06412,-0.04248,-0.07353,-0.0452,0.09172,0.09516,-0.03222,0.13132,0.04266,-0.06891,0.05715,-0.06852,-0.01704,0.04571,0.01622,0.07286,-0.10735,-0.10567,0.02204,0.02815,-0.05233,-0.00906,0.02119,-0.04308,0.07044,0.09005,0.00975,-0.08754,0.05569,0.03958,-0.0004,0.07173,0.00938,-0.00262,0.03173,-0.03932,-0.02416,-0.01716,-0.09117,-0.00417,-0.02312,-0.02079,-0.04352,0.11633,-0.02815,0.1127,-0.04377,-0.06145,0.09502,0.14422,0.0876,-0.02208,0.01746,-0.00651,0.01527,-0.01321,0.07746,-0.0344,-0.03719,0.0167,0.02291,-0.01301,0.1076,-0.05916,-0.09359,-0.14288,0.02405,0.07174,0.01042,0.0169,-0.06454,-0.08013,0.02234,-0.01245,-0.03574,0.05886,-0.0243,0.07332,-0.0597,-0.1003,-0.11157,0.11768,0.02105,-0.0471,0.04911,0.02683,-0.0676,-0.01705,0.01062,-0.05027,-0.11937,0.06836,-0.05183,0.13123,-0.00197,-0.08346,0.08675,-0.00411,0.0051,-0.04742,0.01652,0.17148,-0.06582,0.0418,-0.08537,-0.10855,-0.01235,0.00915,0.11396,-0.01946,-0.08124,-0.08245,-0.10094,-0.00987,0.03317,-0.03392,0.14545,0.01748,-0.01259,0.00979,0.12394,0.02403,-0.03376,0.04474,0.05314,-0.01498,-0.04607,-0.04598,-0.05224,-0.00083,0.22791,0.07811,-0.01627,-0.00281,0.08731,-0.07213,0.00125,-0.01694,0.04033,-0.01149,-0.02681,0.09931,-0.07271,0.06323,0.01305,0.05095,0.04882,-0.00737,0.03149,-0.03198,-0.04896,-0.14447,-0.01175,-0.08705,0.11545,0.04108,0.03253,-0.07602,-0.0619]},{"domain":"aerospace_engineering","key":"aero_neutral_point","name":"Neutral point and static margin (wing and tail)","package":"aerospace-engineering-ai999x","example":"Neutral point: h_ac = 0.25, a_w = 5, a_t = 5, St_S = 0.2, lt_c = 4, deps = 0.5, h_cg = 0.3","v":[0.06226,0.06649,0.08442,-0.02632,-0.02194,0.00138,-0.013,0.03393,0.04459,-0.04748,-0.05925,0.04603,-0.0787,-0.04762,-0.06139,0.05087,0.04006,0.00442,0.07266,-0.10377,-0.00652,0.00282,-0.10329,-0.07076,0.00757,-0.0462,0.0906,-0.07656,-0.09322,0.03669,-0.002,2e-05,0.03677,0.0201,0.19277,0.00592,-0.0236,0.00444,0.01932,0.02042,-0.09641,0.06321,0.00971,0.07145,-0.03423,0.08504,0.03836,-0.09819,-0.02712,-0.00192,-0.03036,-0.06949,0.06227,0.0756,0.08686,0.02012,-0.2216,-0.02992,-0.06361,-0.04351,-0.11469,0.03731,-0.00375,-0.09806,0.00804,0.02823,0.04485,-0.03527,0.02031,-0.00216,0.04813,0.10561,0.04601,-0.10508,0.06035,-0.04038,0.03872,0.07435,0.07198,-0.02589,-0.06795,-0.00343,-0.07294,-0.00871,0.02586,-0.04453,-0.07563,0.07608,-0.13257,-0.03608,-0.05352,0.00059,0.01969,0.07053,0.01494,-0.09808,0.00466,-0.02068,-0.09591,-0.01887,-0.09088,0.01619,0.08443,0.06716,0.11829,0.05265,0.02063,0.03198,-0.02529,0.04863,0.05367,-0.0811,-0.01726,-0.0089,0.01876,0.05766,0.109,-0.05777,-0.01782,0.12831,0.01197,-0.04814,0.07145,0.03001,-0.0603,0.09058,-0.01262,-0.10372,-0.0017,-0.00741,-0.10262,0.04561,-0.04746,-0.06101,0.02333,-0.00974,0.01356,0.03256,-0.1002,-0.08323,0.0541,-0.02633,0.03872,-0.04599,-0.06774,0.03995,-0.01513,0.00535,-0.04137,0.04815,0.02815,0.01153,-0.00134,0.06606,-0.02347,0.04323,0.07209,0.01476,0.08832,0.04161,0.00144,-0.14642,-0.09163,0.08067,0.023,0.04236,-0.05354,-0.04261,0.03919,0.04095,0.09291,-0.0004,0.08583,-0.01626,0.04926,0.0402,0.02184,-0.08441,0.03655,0.01904,-0.03507,-0.02864,0.03936,-0.05037,0.12673,0.04938,0.08274,-0.0003,0.05612,-0.04078,0.10912,-0.03409,-0.0457,0.08282,0.03567,0.05486,-0.02096,0.02447,0.18718,-0.03085,0.0144,-0.02342,-0.09802,-0.04944,0.07224,0.01351,0.13844,-0.05333,-0.08089,-0.01412,-0.08409,0.09761,-0.01392,0.04237,0.00657,-0.02911,-0.07233,0.05393,-0.06492,0.01422,0.05142,0.03717,0.04618,0.05826,0.01389,-0.03373,-0.07668,0.05946,0.02823,-0.02032,0.0432,3e-05,-0.08058,-0.0551,-0.11151,-0.08646,-0.06747,0.01656,0.00196,0.02918,0.10513,-0.0231,0.12056,0.04831,-0.06527,0.02533,0.06314,0.03697,-0.08739,0.00657,-0.13778,-0.02837,-0.10872,-0.06393,-0.05542,-0.01878]},{"domain":"aerospace_engineering","key":"aero_normal_shock","name":"Normal shock relations","package":"aerospace-engineering-ai999x","example":"Normal shock: M1 = 2","v":[0.05806,-0.09443,-0.01668,-0.00462,0.00561,0.04129,-0.0222,0.08427,0.04958,-0.01945,-0.03155,0.0421,-0.01083,0.14955,-0.02525,0.05824,0.02375,-0.03345,0.01457,0.02124,0.03642,-0.18152,0.01985,-0.01542,-0.03552,-0.03734,-0.05547,0.0319,-0.07824,-0.05058,0.16219,0.0152,0.0417,-0.01899,0.00579,0.0589,0.05665,0.11558,0.05056,0.03195,0.03312,0.02807,0.1052,-0.0334,-0.01543,-0.00319,-0.00124,-0.01283,-0.08161,0.12679,-0.06008,0.09926,0.0521,0.07352,0.16318,0.02548,0.02508,-0.10505,-0.09219,-0.03798,-0.08904,-0.11844,0.1159,-0.10439,0.03598,-0.01648,0.06182,0.03399,-0.01816,0.04726,-0.0313,0.01731,0.00749,-0.01763,0.01349,-0.04757,0.04035,-0.00387,0.06031,0.06593,-0.0003,-0.05549,-0.0688,0.06486,0.02176,-0.14034,0.00537,-0.04787,-0.02749,-0.08522,0.0988,0.06739,-0.01331,-0.01284,-0.02118,0.04061,0.02057,-0.0225,-0.05911,-0.01811,0.07073,0.02936,-0.04334,0.04798,-0.08554,-0.11012,0.04655,0.06082,-0.01172,0.0548,-0.00086,-0.10326,-0.10582,-0.02059,-0.06196,-0.10565,0.04507,0.08542,-0.01932,-0.021,-0.04438,-0.03214,0.14553,-0.0173,-0.00531,-0.04418,-0.02183,0.02617,0.05023,0.01946,0.03005,0.05606,-0.04853,-0.0856,0.04078,0.06062,-0.07577,0.01695,-0.05156,0.05102,-0.02858,0.07139,0.0759,-0.07124,0.05962,0.14457,-0.08235,-0.01238,-0.03024,0.00952,0.00614,-0.07932,-0.01877,0.07567,-0.02394,-0.15862,-0.05114,-0.07512,0.08542,-0.10448,-0.02013,-0.05857,0.05956,-0.09474,0.07934,0.02454,0.00244,0.00017,0.07819,-0.02675,-0.02066,-0.00046,-0.07782,0.06111,-0.02371,0.08898,0.04745,-0.00645,0.07713,0.03004,-0.01047,0.04611,0.05934,-0.04525,0.0147,0.01971,-0.06111,0.13275,-0.02271,0.02089,0.00207,-0.0109,0.1,-0.01155,0.0198,-0.08018,-0.02634,-0.02484,-0.03595,0.01435,0.08209,-0.10002,0.06475,0.03525,0.03405,-0.04298,-0.04336,0.00828,-0.05061,0.07666,-0.10343,0.04455,-0.09229,-0.05772,-0.0413,0.00296,0.00973,0.08275,-0.03055,-0.01294,0.08247,-0.02159,-0.00816,0.10574,-0.11549,-0.05826,-0.01984,-0.03558,0.06682,-0.02918,-0.11722,-0.02587,-0.00707,-0.09163,0.07543,-0.02175,0.04245,0.08159,0.03722,0.05851,0.08115,0.01949,0.11439,0.06051,-0.01719,-0.04069,0.03315,-0.03541,-0.04207,-0.03257,-0.0387,0.06378,-0.1405,0.12703,-0.01132,-0.06551]},{"domain":"aerospace_engineering","key":"aero_normal_shock_from_pressure_ratio","name":"Normal shock from its pressure ratio","package":"aerospace-engineering-ai999x","example":"Normal shock from pressure ratio: p2/p1 = 4.5","v":[0.06745,-0.09746,-0.01816,-0.05615,0.014,0.03879,-0.02312,0.0787,0.03569,-0.02859,-0.0305,0.03605,-0.01504,0.16096,0.00605,0.05952,0.00102,-0.0254,-0.01867,0.01823,0.02452,-0.1772,0.04471,-0.00441,-0.01549,-0.03338,-0.02838,0.05432,-0.10442,-0.07931,0.17383,0.00236,0.05369,-0.02448,-0.03404,0.07816,0.02229,0.09593,0.0703,0.02125,0.05293,0.04317,0.12278,0.00131,0.02006,0.00168,-0.02273,0.01093,-0.07487,0.13548,-0.05397,0.0738,0.03903,0.08665,0.17371,0.03308,-0.02843,-0.10752,-0.07435,-0.01089,-0.09754,-0.10195,0.104,-0.1181,0.03044,-0.03492,0.02083,0.05602,0.04984,0.01812,-0.06056,0.03565,-0.03205,-0.00426,0.02495,-0.07263,0.00455,0.00549,0.04026,0.07059,-0.00091,-0.06676,-0.06886,0.05229,0.00459,-0.12987,0.00291,-0.07031,-0.00276,-0.05541,0.07186,0.05747,-0.01532,-0.0209,0.01194,0.06476,-0.00182,-0.02902,-0.06313,-0.01962,0.07764,0.01911,-0.05294,0.05371,-0.05744,-0.11541,0.06504,0.04933,0.0144,0.04098,-0.00924,-0.0826,-0.12804,-0.01566,-0.03486,-0.07931,0.06685,0.09425,-0.03114,-0.02681,-0.0581,-0.01979,0.14278,-0.06076,-0.01837,-0.02841,-0.02559,0.02037,0.06996,-0.01139,0.02847,0.06708,-0.02187,-0.0869,0.08726,0.05812,-0.05214,0.02979,-0.04349,0.03637,-0.04695,0.07207,0.06656,-0.04604,0.07048,0.11737,-0.08732,-0.02292,-0.04083,-0.00557,0.01374,-0.0686,0.02298,0.08147,-0.01027,-0.14432,-0.03242,-0.04006,0.04969,-0.0936,-0.02418,-0.00906,0.09676,-0.09687,0.03261,0.01584,-0.00846,-0.02805,0.05381,-0.01668,0.02011,0.01162,-0.08922,0.04678,-0.03482,0.08252,0.02173,-0.03286,0.05716,0.02469,-0.01698,0.05359,0.05791,-0.08192,0.0141,0.02128,-0.03859,0.12225,-0.00126,0.02095,-0.01974,-0.00188,0.10752,-0.06059,0.00694,-0.06438,-0.06311,-0.00643,-0.062,0.02408,0.09046,-0.07502,0.07678,0.02006,0.07094,-0.02921,-0.05403,-0.00489,-0.08802,0.07667,-0.10042,0.06354,-0.10638,-0.07849,-0.06274,0.00691,0.00764,0.0731,-0.00139,0.00108,0.06816,-0.01209,-0.00943,0.10311,-0.10941,-0.03499,-0.01025,-0.04636,0.07398,-0.02061,-0.11801,-0.07356,-0.03209,-0.07944,0.09033,-0.01865,0.06163,0.04674,0.00222,0.07306,0.02069,0.03122,0.11685,0.06424,-0.00897,-0.04561,0.05907,-0.01034,0.00816,-0.01545,-0.02839,0.04228,-0.1556,0.14126,0.01089,-0.04035]},{"domain":"aerospace_engineering","key":"aero_nozzle_normal_shock","name":"Normal shock position in a converging-diverging nozzle","package":"aerospace-engineering-ai999x","example":"Normal shock in a nozzle: pc = 1 MPa, pb = 682.5585882398435 kPa, eps = 3","v":[0.08337,-0.03356,0.03829,-0.0849,0.01706,0.01603,-0.0491,0.05053,0.01723,0.02974,-0.10027,0.03127,0.00966,0.04046,0.03126,0.04692,0.04292,0.01423,-0.02391,0.04133,0.00462,-0.1217,0.02817,-0.01705,0.01239,0.00107,-0.02692,0.15238,0.11236,-0.06983,0.14195,0.01013,0.10868,-0.08281,-0.04828,-0.00279,0.01893,-0.04434,-0.00689,0.0615,0.08199,0.07741,-0.06646,0.01225,0.1812,-0.00798,-0.01712,-0.03318,-0.11963,0.12819,0.04934,-0.09667,0.09396,0.0029,0.02535,0.02469,-0.01019,-0.11764,-0.07405,-0.00647,-0.0027,-0.06637,-0.03528,-0.03931,0.03862,-0.08504,0.03971,0.05159,0.00268,-0.01115,-0.07451,0.01952,-0.0122,-0.01657,-0.09673,-0.09598,0.04363,0.04854,-0.00369,0.0763,0.01937,-0.0174,-0.04289,0.05038,-0.01753,-0.11969,0.04686,-0.05669,-0.02339,-0.10386,0.06249,-0.01184,0.02664,0.03895,0.02771,0.05069,0.06832,-0.01228,-0.01285,-0.07165,0.16633,-0.00581,0.04033,0.07416,-0.04412,-0.03133,0.02867,0.00768,-0.05821,0.04626,0.00622,0.03523,-0.08731,-0.14393,-0.02835,-0.0345,-0.03741,-0.02165,-0.01022,-0.05483,-0.04051,0.00936,0.03466,-0.02643,-0.00738,-0.04168,-0.03939,0.02758,0.10491,0.00304,-0.01463,0.06271,0.05034,-0.1294,0.13218,-0.01106,-0.07941,0.07807,-0.04666,0.00441,-0.14975,-0.00211,-0.0715,-0.01613,0.12789,0.00199,0.02692,3e-05,-0.04728,-0.00413,0.06287,0.03758,0.04362,0.0495,0.02436,0.02249,-0.07757,0.02003,0.07156,-0.04487,-0.02667,0.05621,0.09529,-0.01292,-0.08054,0.10725,0.02091,0.0389,-0.00978,0.00027,-0.01362,-0.00555,-0.01602,0.0673,0.07949,-0.04882,-0.06887,-0.1112,0.00282,-0.06253,-0.02828,0.03457,-0.0728,-0.06681,0.02875,0.03508,-0.00436,0.07575,0.03083,0.00805,-0.09998,0.00448,0.00895,-0.06248,0.00033,0.04372,-0.05542,0.03251,0.08794,0.06158,0.07258,-0.05692,0.00983,-0.05447,0.21481,0.00447,-0.05294,-0.00469,-0.053,0.03051,-0.10948,0.01698,0.02798,-0.02331,-0.09209,-0.0444,-0.04086,0.07913,0.00779,-0.03827,0.01494,-0.05986,-0.02094,0.06229,-0.11272,0.02885,-0.00971,-0.03968,0.07097,0.02692,-0.0719,-0.0708,0.04354,0.01932,0.03092,0.00765,-0.04189,0.02334,0.00856,-0.01413,0.16376,0.1213,0.06535,0.04095,0.07624,-0.10042,-0.04397,-0.02769,0.08952,-0.06032,-0.00758,0.06065,-0.1044,0.10026,0.14803,-0.04787]},{"domain":"aerospace_engineering","key":"aero_oblique_shock","name":"Oblique shock from the deflection angle","package":"aerospace-engineering-ai999x","example":"Oblique shock: M1 = 2, theta = 10.62290962494955 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shock from the wave angle","package":"aerospace-engineering-ai999x","example":"Oblique shock from wave angle: M1 = 2, beta = 90 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2","v":[-0.04271,0.01648,0.06717,0.04736,-0.00571,0.0795,0.08034,-0.03198,0.02075,-0.08465,-0.08943,-0.01125,0.08821,0.05728,0.03099,0.06058,0.02437,-0.01629,0.08003,0.13269,-0.06585,0.05186,0.00536,-0.0134,-0.05581,-0.01319,0.00585,0.08762,0.01442,0.0403,-0.01226,0.01482,-0.0834,0.04509,-0.00319,-0.07365,0.01024,-0.05504,-0.05967,0.0139,-0.04355,-0.06147,0.03194,-0.03746,0.08768,-0.02803,-0.03244,-0.00134,0.07789,0.07322,-0.0643,-0.05438,-0.00408,-0.01514,-0.06719,-0.04119,0.01717,-0.10572,-0.03921,-0.12446,-0.02754,-0.0229,-0.03037,0.04158,0.04474,0.02463,0.02584,-0.03247,-0.13199,0.06668,-0.13106,0.12108,0.01278,0.01924,-0.01291,-0.00082,0.17696,0.08965,0.11068,-0.00496,-0.03891,-0.04327,0.04809,0.04286,0.01772,-0.05887,-0.00207,0.06877,0.01778,-0.00857,0.04618,0.02928,-0.01234,-0.05263,-0.07657,-0.06909,0.04386,-0.09362,-0.04604,0.0742,0.12334,-0.01683,0.0463,-0.06386,0.07779,0.04383,-0.0913,0.07135,-0.14054,0.04891,0.01639,-0.0298,-0.02639,-0.04519,-0.05674,-0.04525,-0.01045,-0.06629,-0.10257,-0.00065,0.05342,0.04077,0.08254,0.00361,0.0283,-0.00655,0.05807,0.00247,0.0433,-0.02011,-0.00532,0.05572,-0.12144,0.05894,0.0004,0.03261,-0.05021,0.10825,-0.01552,0.11685,-0.05627,0.07589,0.02073,-0.01346,0.00068,0.00176,0.05991,-0.04746,-0.08906,-0.0062,-0.0132,0.11485,-0.13953,0.02099,-0.01694,0.00114,-0.05387,0.03084,0.08205,-0.04316,-0.0122,-0.10015,-0.14686,0.02452,-0.03215,-0.08937,-0.01575,-0.0908,-0.07971,0.10199,-0.06346,-0.00921,0.0672,0.01789,0.06271,0.01463,-0.02937,-0.08466,0.03622,-0.04418,0.00655,-0.00254,0.03487,0.05323,0.07375,0.13854,-0.04884,-0.05712,0.0265,-0.0002,-0.06374,-0.00144,-0.01012,-0.00726,-0.02634,0.01232,-0.09728,-0.02052,-0.16666,0.02798,0.00947,-0.0953,0.04623,0.14578,-0.01095,-0.04704,0.08309,0.03307,-0.00148,-0.0014,-0.10606,0.10934,-0.0531,0.05213,-0.03788,-0.07908,-0.06185,0.06469,0.06507,0.09413,-0.01109,-0.124,0.0068,-0.01034,-0.10615,-0.08372,0.0335,0.02102,0.0588,0.08174,-0.0199,0.11726,0.04332,0.05416,-0.02918,-0.04696,0.05891,0.01392,-0.10201,-0.08452,0.0624,-0.09399,0.05275,0.05898,0.02678,0.04097,0.00758,0.01014,-0.05144,-0.03542,-0.1068,0.10964,0.00525,0.06251,-0.00973,-0.06003]},{"domain":"aerospace_engineering","key":"aero_pressure_altitude","name":"Pressure 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2","v":[0.01024,-0.0116,-0.02962,0.05691,-0.12685,-0.04206,0.03716,0.03434,0.04201,0.00406,0.05433,0.01948,0.01432,0.025,-0.04499,0.03859,-0.04075,-0.07311,0.02921,0.08114,0.02285,-0.07363,-0.03067,-0.0806,0.04903,-0.03811,-0.12162,0.00257,0.03555,-0.00865,0.04426,0.04756,0.05874,-0.09272,0.06425,-0.01026,0.09814,0.01016,-0.03162,0.04157,0.15554,0.01978,-0.00196,-0.11853,0.00945,-0.04595,0.11895,-0.07372,-0.01225,0.10635,-0.06906,0.00025,0.10734,-0.01915,0.07419,-0.01068,0.05021,-0.05626,0.00067,0.00263,-0.03671,-0.06103,0.08113,0.07189,0.0344,0.08593,0.01227,0.11606,-0.0389,0.04553,-0.00648,0.14941,-0.0522,0.02764,-0.0291,-0.01474,0.03686,0.01511,-0.10227,0.01298,0.04701,-0.04138,-0.00918,0.02528,0.03223,-0.03546,-0.06958,0.05072,-0.04107,-0.07388,-0.09169,-0.05646,0.04594,0.03134,-0.13937,-0.03528,-0.05928,-0.00613,0.01292,-0.04517,0.05091,-0.0073,-0.00627,0.07851,0.0603,0.05926,0.1382,0.07092,-0.11716,0.08198,-0.05331,-0.07874,-0.00237,-0.04158,-0.03977,-0.05013,0.04029,-0.03583,-0.04692,-0.00635,-0.06492,-0.09204,0.16971,-0.06612,-0.03462,-0.04242,-0.08334,0.02632,0.00838,0.06895,-0.09006,0.06309,-0.03315,-0.0287,0.03639,0.00444,0.01435,-0.01285,-0.06541,0.03468,-0.03912,0.01913,-0.03706,0.03196,0.10012,0.05137,0.02157,-0.07637,-0.055,-0.03671,-0.03928,-0.11013,0.01916,0.01193,-0.04924,-0.16582,-0.07357,-0.00208,-0.01687,-0.15119,-0.05836,0.0828,0.00554,-0.01923,0.01986,0.10297,0.01803,-0.05271,0.10425,0.03298,0.00752,0.00494,0.03422,0.02311,0.00094,0.00505,-0.04488,0.04999,0.02086,-0.03965,-0.0626,0.01978,-0.01812,-0.01053,0.02168,-0.09429,-0.00983,0.0719,-0.03027,-0.00105,-0.13295,-0.08608,0.02181,0.08151,0.05437,0.02246,0.01173,0.05089,-0.00995,-0.09121,0.08948,-0.11212,0.0042,-0.01147,0.08497,-0.05975,-0.01809,0.10113,0.00672,-0.02417,0.05112,0.09781,-0.02031,0.07021,0.05291,0.13321,0.01243,-0.0262,-0.08217,0.07683,-0.07462,-0.00681,0.0044,0.01111,-0.01299,-0.1447,0.00114,0.06107,0.05408,-0.01071,-0.05382,-0.07904,0.04653,-0.0809,0.05442,0.02881,0.07222,0.01538,-0.00856,0.01887,0.174,-0.02742,0.00676,0.0132,0.06406,0.07595,0.02966,-0.09947,0.00745,-0.06379,-0.08482,0.09644,-0.10866,0.06448,0.14277,-0.03064]},{"domain":"aerospace_engineering","key":"aero_rocket_delta_v","name":"Rocket 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rocket engine performance","package":"aerospace-engineering-ai999x","example":"Rocket engine performance: pc = 1 MPa, Tc = 3000 K, Mw = 20 g/mol, gamma = 1.4, At = 0.01 m^2, eps = 1.6875, pa = 0 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to climb with a linearly decreasing rate of climb","package":"aerospace-engineering-ai999x","example":"Time to climb: RC0 = 10 m/s, Hc = 10 km, h1 = 0 m, h2 = 6321.205588285577 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(stagnation) air temperature in flight","package":"aerospace-engineering-ai999x","example":"Total temperature: V = 316.96778261595074 m/s, T = 250 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airspeed from calibrated airspeed","package":"aerospace-engineering-ai999x","example":"True airspeed: CAS = 120 kt, hp = 0 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height and apogee of a vertical rocket","package":"aerospace-engineering-ai999x","example":"Vertical rocket: Isp = 300 s, m0 = 2718.2818284590453 kg, mf = 1000 kg, tb = 100 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loading","package":"aerospace-engineering-ai999x","example":"Wing loading: W = 600 kN, S = 120 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absorber: number of transfer units and height (Colburn)","package":"chemical-engineering-ai999x","example":"Absorber transfer units: y1 = 0.02, y2 = 0.001, x2 = 0.0, m = 1.2, A = 1.5, HOG = 0.6 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flame temperature (complete combustion, NASA polynomials)","package":"chemical-engineering-ai999x","example":"Adiabatic flame temperature: fuel = CH4, excess_air = 0.0, T_in = 300.0 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reactor outlet temperature","package":"chemical-engineering-ai999x","example":"Adiabatic reactor temperature: n0 = [1.0, 2.0, 0.0], nu = [-1.0, -1.0, 1.0], cp = [[30.0, 0.01], [29.0, 0.004], [45.0, 0.02]], dH = -60000.0 J/mol, T_ref = 298.15 K, T_in = 400.0 K, key = 1, X = 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(saturation) temperature from the Antoine equation","package":"chemical-engineering-ai999x","example":"Antoine boiling temperature: A = 8.07131, B = 1730.63, C = 233.426, units = mmHg_degC, base = log10, P = 101325.0 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pressure from the Antoine equation","package":"chemical-engineering-ai999x","example":"Antoine vapour pressure: A = 8.07131, B = 1730.63, C = 233.426, units = mmHg_degC, base = log10, T = 373.15 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reactor conversion after a time (second order)","package":"chemical-engineering-ai999x","example":"Second-order batch reactor conversion: k = 0.0001 m^3/(mol*s), CA0 = 1000.0 mol/m^3, t = 40.0 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heating of a stirred tank: temperature after a time","package":"chemical-engineering-ai999x","example":"Batch heating temperature: m = 1000.0 kg, cp = 4180.0 J/(kg*K), UA = 2000.0 W/K, T_s = 393.15 K, T0 = 293.15 K, t = 3600.0 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heating of a stirred tank: time to reach a temperature","package":"chemical-engineering-ai999x","example":"Batch heating time: m = 1000.0 kg, cp = 4180.0 J/(kg*K), UA = 2000.0 W/K, T_s = 393.15 K, T0 = 293.15 K, T = 353.15 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reflux ratio of a binary column (Underwood)","package":"chemical-engineering-ai999x","example":"Minimum reflux ratio: alpha = 2.5, zF = 0.5, xD = 0.95, q = 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separator balance (binary distillation column)","package":"chemical-engineering-ai999x","example":"Two-product separator balance: F = 100.0 mol/s, zF = 0.4, xD = 0.95, xB = 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feed flows that make a product of given composition","package":"chemical-engineering-ai999x","example":"Blending feed flows: W = [[0.9, 0.1], [0.2, 0.8]], p = [0.5, 0.5], P = 100.0 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cake filtration: filtrate volume after a time","package":"chemical-engineering-ai999x","example":"Cake filtration volume: A = 1.0 m^2, dP = 100000.0 Pa, mu = 0.001 Pa*s, alpha = 100000000000.0 m/kg, c = 20.0 kg/m^3, Rm = 10000000000.0 1/m, t = 600.0 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pressure drop (Carman correlation)","package":"chemical-engineering-ai999x","example":"Carman pressure drop: dp = 0.0008 m, eps = 0.4, vs = 0.05 m/s, rho = 1000.0 kg/m^3, mu = 0.001 Pa*s, L = 1.0 m","v":[0.02385,-0.03355,-0.02585,-0.02026,-0.04067,-0.00964,0.08347,-0.01048,-0.11589,0.04931,0.10695,0.00364,-0.00346,0.10109,-0.07936,0.08477,0.07627,-0.17781,0.09518,0.05625,0.0564,0.0528,0.04882,0.05431,-0.05952,0.04771,-0.032,-0.10458,-0.08321,-0.06911,-0.08337,0.03179,-0.00302,-0.05374,-0.18044,0.10396,0.08491,-0.01783,-0.06274,0.01945,0.07435,0.0498,0.03052,-0.06199,-0.06454,0.03989,0.0553,-0.00141,-0.02781,-0.08161,0.06951,-0.02219,-0.05683,0.03778,0.04024,0.03104,0.02559,0.03461,-0.00754,-0.00505,0.03685,-0.05305,0.00414,-0.09795,-0.08525,0.03919,-0.05949,-0.02605,0.02185,-0.06297,-0.0411,0.06735,0.08413,-0.01344,0.04528,0.00381,-0.07326,-0.03962,-0.08783,-0.04691,0.09572,0.02285,-0.05789,0.07808,0.11962,-0.115,-0.00444,-0.05729,0.07732,0.01601,-0.04461,0.01907,-0.08358,0.0243,0.09869,0.00464,0.13046,-0.06179,0.01312,-0.03035,0.01332,0.00494,-0.02679,-0.00952,0.04379,0.1009,0.14248,0.06729,0.00537,-0.03459,-0.04838,0.02627,-0.10832,-0.02348,0.00287,-0.06242,0.09659,0.05873,0.0309,-0.1481,-0.03117,0.00645,-0.0741,0.08943,0.00458,-0.00532,-0.0925,0.0845,0.05502,0.00951,-0.05484,-0.01831,0.15872,-0.00895,-0.00494,0.01702,0.02435,-0.06531,0.05601,0.08186,-0.14521,0.00013,0.02653,0.05417,0.0039,-0.03321,0.00671,-0.07319,-0.13655,0.08369,0.03171,0.01513,0.13048,0.04483,0.03905,0.0675,-0.02142,0.037,-0.03583,0.07007,0.00226,0.02147,0.08245,-0.07267,-0.04243,-0.01496,0.02069,-0.02996,-0.08048,-0.04432,-0.04312,0.0635,-0.02925,-0.02475,0.15174,0.09416,0.01745,0.05226,-0.05088,-0.01726,-0.05886,0.02454,0.00611,0.05966,0.0328,0.04806,0.02713,-0.04104,-0.05362,-0.03153,-0.06418,0.12556,-0.00783,-0.01456,-0.1051,0.01055,-0.07342,0.00277,-0.0395,-0.03974,-0.12282,-0.03558,-0.00221,-0.08143,0.00654,0.00979,-0.09683,-0.07584,0.07218,-0.02944,-0.02559,-0.01689,-0.02206,0.03215,-0.06047,-0.00346,-0.00823,0.0452,0.00151,0.01357,0.04218,-0.05698,0.04041,-0.00809,-0.05336,-0.00375,-0.00354,0.08207,0.04736,0.03487,-0.01227,0.10482,-0.08575,0.02981,0.08149,-0.07813,-0.11384,0.08866,0.09895,0.09734,-0.0595,0.00676,0.03906,-0.01399,0.08711,0.00122,-0.03477,-0.04521,0.02132,0.0685,0.00279,-0.12204,0.01896,-0.07079,0.00794,-0.02173]},{"domain":"chemical_engineering","key":"chemeng_closed_loop_stability","name":"Closed-loop stability of a P-controlled process (closed-loop poles)","package":"chemical-engineering-ai999x","example":"Closed-loop stability: num = [1.0], den = [1.0, 3.0, 3.0, 1.0], Kc = 10.0","v":[-0.01194,-0.11959,-0.01575,0.00673,-0.00251,-0.04099,-0.01457,0.03346,-0.0456,-0.05824,-0.05307,0.08448,0.10079,0.15101,-0.03349,0.10284,-0.06258,0.00345,0.0628,0.00292,0.01284,-0.03756,0.0043,-0.0797,0.16932,-0.05173,-0.05549,0.02226,-0.00084,0.12018,-0.01215,0.01751,-0.07856,0.06491,-0.05894,0.0112,-0.02091,0.0327,0.06964,-0.02285,0.07209,0.07068,0.09256,0.07405,0.10298,0.04928,0.11148,0.04524,0.05119,0.0646,0.0442,-0.10645,0.02941,0.08043,0.02182,0.03843,-0.07129,0.07502,0.08669,-0.03732,-0.04441,-0.01626,-0.02348,-0.07507,-0.05098,-0.11817,0.02254,-0.04353,0.1394,-0.0317,-0.00618,0.0208,-0.17051,0.02653,0.00717,-0.013,-0.12437,0.04889,0.07361,0.04979,-0.02862,-0.12009,-0.03357,0.05364,-0.02522,0.03289,0.06519,-0.04472,0.00634,-0.04189,-0.04765,-0.0184,0.04776,-0.02832,0.04819,0.05523,0.01377,-0.01165,-0.03379,0.06881,-0.01461,0.01287,-0.04431,0.04014,0.04745,-0.02962,0.06156,-0.12834,-0.04126,0.05317,-0.00473,0.0795,0.07674,0.0641,-0.05542,0.04673,0.06434,0.01529,0.02111,0.01246,0.05788,0.02482,0.06026,0.05668,-0.08111,-0.00718,0.04417,-0.00144,-0.10315,-0.05586,-0.04715,-0.06559,0.01013,-0.1252,0.04789,0.13472,0.07134,-0.05111,-0.02687,0.00723,0.03259,0.02281,0.04486,-0.01761,0.00831,-0.00203,-0.04,-0.00171,0.05901,0.05217,0.04356,-0.06257,0.009,0.08284,-0.0106,-0.02374,0.04739,0.04459,-0.11698,-0.06949,0.02447,0.10487,-0.03121,-0.06588,0.0255,0.00818,0.01498,0.00528,0.06403,0.04001,0.06799,0.00481,-0.04411,0.00346,0.02046,-0.02095,-0.01608,0.0201,-0.06728,0.10813,-0.10692,-0.05129,-0.00399,0.00813,0.06677,-0.0146,5e-05,0.00896,-0.018,0.04416,-0.0572,0.0432,0.08001,-0.06136,-0.06216,-0.02828,-0.01331,0.03842,0.01446,-0.05696,0.02227,0.13677,-0.04431,-0.01269,0.17397,-0.06414,0.02282,-0.13104,-0.0557,-0.087,-0.02634,-0.00641,0.07044,-0.02153,0.07246,0.11578,-0.11816,0.09304,-0.02697,0.00021,0.05754,0.05084,-0.03179,0.00163,-0.03576,0.10901,-0.02511,-0.09399,0.04901,-0.14022,0.00824,-0.04813,-0.08664,-0.1457,-0.07976,-0.01107,0.00515,-0.13418,0.08367,-0.09724,0.00795,0.00552,0.00535,0.01391,0.0751,-0.06102,-0.0244,-0.08059,-0.13731,-0.00515,-0.03305,0.01534,-0.03063,-0.00615,0.07034,0.02869]},{"domain":"chemical_engineering","key":"chemeng_combustion_flue_gas","name":"Combustion with excess air: air requirement and flue-gas composition","package":"chemical-engineering-ai999x","example":"Combustion flue gas: fuel = CH4, excess_air = 0.2","v":[0.01279,0.10137,0.02143,0.07758,0.08915,0.04434,-0.06628,0.01013,0.0037,0.00629,0.01483,0.07324,-0.08739,0.05638,0.01132,-0.01339,-0.01735,0.06917,0.05497,0.03752,-0.05343,-0.07467,0.00036,-0.13233,-0.01728,-0.0012,-0.05657,0.00129,-0.20374,0.05351,0.01697,-0.07543,0.07146,0.07381,0.03081,-0.07413,-0.01972,0.02295,0.04079,-0.09473,0.03254,0.03481,-0.02272,0.04198,-0.03396,-0.04736,-0.09893,0.04178,-0.06955,0.06155,-0.01981,0.08592,0.00893,0.07646,-0.01592,0.13793,-0.04367,0.02852,0.02558,-0.04896,-0.00618,-0.0481,0.06,-0.05667,0.02878,-0.03231,0.02587,-0.06956,-0.00297,-0.04666,-0.05916,0.00069,-0.09931,-0.00206,0.08154,0.06918,-0.0028,-0.01927,0.03487,-0.03057,-0.03449,-0.03812,-0.09947,0.01799,0.01475,0.11584,0.00485,0.00802,0.05164,0.00747,-0.02711,0.10169,-0.05927,0.11198,-0.01772,-0.05136,-0.02896,-0.0138,-0.1459,0.11254,-0.02992,0.08768,0.09491,-0.10128,0.04534,-0.12284,-0.0303,0.0201,-0.0627,-0.01107,-0.05418,-0.04156,-0.02024,0.12436,-0.1183,-0.00324,-0.02791,-0.08974,0.05519,0.05591,-0.03529,0.00685,-0.0381,-0.03563,0.00352,0.13674,0.15417,-0.03592,-0.01914,-0.02054,-0.08333,0.2067,-0.08862,-0.03891,0.02621,-0.00282,-0.01884,-0.03747,0.02287,-0.00685,0.00212,0.01631,0.01335,-0.04833,-0.03638,0.12046,0.06304,-0.04402,0.08541,0.01814,0.05475,0.00837,-0.06315,0.00299,-0.10259,-0.00671,-0.08592,0.05046,0.10935,0.03086,0.06297,-0.13775,-0.09148,-0.02618,0.04921,0.09905,0.01183,0.04092,0.08525,-0.00244,0.00912,0.10511,-0.01879,0.0347,0.12551,-0.00505,0.03105,-0.09273,0.03322,0.0127,-0.08627,-0.03088,-0.05242,0.0302,-0.05417,0.11344,0.03691,0.01543,0.05854,-0.03944,-0.00257,0.02209,-0.01592,-0.02214,-0.03265,-0.06885,-0.0346,0.03438,-0.08367,-0.02102,-0.00928,-0.01917,0.08475,-0.02179,-0.02547,-0.00368,0.06527,-0.00431,0.03417,-0.04971,-0.0368,0.05372,0.02192,0.03668,0.03423,-0.09065,0.03245,0.01877,0.07522,0.04851,0.09441,-0.0079,-0.10704,0.07424,-0.03075,-0.11295,-0.02879,0.04612,0.02339,0.01391,-0.07134,-0.01736,-0.01673,0.08712,0.13014,-0.08978,-0.07105,0.07247,0.04854,-0.08486,0.04671,-0.03449,0.02045,0.02364,-0.09546,0.08061,-0.04432,-0.01728,-0.00582,-0.02196,-0.01318,-0.07865,0.10366,0.02716,-0.10618,-0.06924]},{"domain":"chemical_engineering","key":"chemeng_countercurrent_extraction","name":"Countercurrent liquid-liquid extraction (N stages, immiscible solvents)","package":"chemical-engineering-ai999x","example":"Countercurrent extraction: F = 100.0 kg/s, S = 80.0 kg/s, K = 1.5, N = 4, XF = 0.1, YS = 0.0","v":[0.00754,0.02426,0.03506,-0.03054,-0.0065,0.03082,-0.09542,0.10816,0.05475,-0.06909,0.07903,-0.08645,-0.01268,-0.04394,-0.02494,-0.02667,-0.10822,-0.09588,-0.04811,0.01553,-0.06063,-0.04509,-0.01403,-0.12001,0.04214,0.03725,-0.0689,0.03847,0.00222,-0.07902,0.02363,-0.13912,0.01566,-0.06539,-0.01106,0.06744,0.02897,0.00678,0.01863,-0.06152,0.09523,0.10134,0.10216,0.03572,0.03458,-0.00843,0.02326,-0.04447,-0.02644,0.06537,-0.09514,0.15066,0.00927,0.00979,-0.04429,0.03723,0.01,-0.06269,0.03511,-0.07938,-0.03715,0.0237,0.06732,-0.10737,-0.03201,0.01221,-0.03356,0.0415,-0.04969,-0.08508,0.04807,-0.00788,0.03294,0.02157,0.01652,0.11979,-0.10548,-0.06017,-0.02921,0.061,-0.07963,0.014,-0.059,0.00797,0.00269,0.01925,-0.00501,0.13484,0.05859,0.00625,-0.03932,-0.00157,0.0871,0.00692,0.04175,0.05519,-0.12048,0.02154,-0.06222,-0.14894,0.07259,0.05559,-0.01846,0.09859,0.02202,0.0538,0.07369,-0.07711,-0.06358,0.1106,0.0146,-0.0306,-0.10156,-0.03818,0.0467,-0.038,0.09698,0.06019,0.00173,0.04049,-0.05215,0.03736,0.02475,0.12891,0.04523,0.05278,0.03101,0.08364,-0.02039,-0.05265,-0.09688,-0.05462,-0.08607,-0.01566,0.01886,0.07611,-0.07612,0.12666,-0.06814,-0.06838,-0.04909,0.01633,-0.05224,0.10626,0.02207,-0.00608,-0.12507,0.15353,0.14817,-0.05347,-0.05734,-0.10572,-0.03186,0.08259,0.05236,-0.09584,-0.05107,-0.00668,-0.00718,-0.01141,0.02595,0.0077,0.05743,0.01772,-0.05349,-0.09888,-0.07683,0.06771,0.11708,0.08924,0.06002,0.04461,0.03019,-0.029,0.10053,0.09676,-0.01519,0.00815,-0.00689,0.10068,-0.1261,0.01435,-0.02554,-0.0936,-0.04023,0.0583,0.01396,0.06852,0.01201,-0.11642,-0.02232,-0.04176,0.03032,-0.02037,0.0172,0.08729,0.06839,-0.02598,-0.05676,-0.10195,-0.02975,0.01118,-0.01355,0.04385,-0.04345,-0.05382,-0.0134,0.01834,-0.04961,0.00546,-0.04258,-0.02485,-0.04023,0.01054,0.06163,0.00332,0.08758,0.08825,0.03427,-0.06205,-0.00502,-0.04005,0.06369,0.11393,0.03483,0.04886,-0.07692,-0.03942,-0.05202,-0.04336,-0.06585,-0.10944,-0.06858,0.06432,0.03187,0.00963,0.01707,-0.12377,0.02336,-0.06186,0.03532,0.02057,0.02782,-0.01941,-0.02574,0.04552,0.06293,-0.00512,0.01159,0.00769,-0.00801,0.03371,0.05697,-0.06533,0.12276,0.02149]},{"domain":"chemical_engineering","key":"chemeng_crosscurrent_extraction","name":"Crosscurrent (multiple-contact) extraction with fresh solvent","package":"chemical-engineering-ai999x","example":"Crosscurrent extraction: F = 100.0 kg/s, S = 20.0 kg/s, K = 1.5, N = 4, XF = 0.1","v":[0.02964,0.02174,0.03403,-0.03577,-0.00347,0.05635,-0.10237,0.12127,0.04107,-0.08336,0.05792,-0.03304,0.04372,-0.02109,-0.01616,-0.05243,-0.1237,-0.03134,-0.03718,0.04861,-0.01175,-0.00736,-0.01197,-0.11546,0.03535,0.05851,-0.10093,0.03362,-0.00081,-0.08706,0.00691,-0.141,0.0016,-0.01337,-0.00767,0.01844,0.06172,-0.01693,0.01885,-0.03631,0.08453,0.10025,0.02419,0.00849,0.01253,-0.02223,0.01854,-0.01494,-0.03254,0.09288,-0.12448,0.14823,0.01055,0.01554,0.02505,0.03343,-0.01163,-0.06951,-0.02996,-0.0617,-0.03924,0.01365,0.06262,-0.13348,-0.02126,0.03326,-0.02227,0.01953,0.01089,-0.08445,0.08875,-0.00199,0.02672,-0.00337,-0.02262,0.13732,-0.08441,-0.06744,-0.01694,0.08867,-0.03862,-0.01696,-0.01262,-0.04104,0.00157,0.03824,-0.00175,0.17936,0.09386,-0.01654,-0.05159,0.00931,0.04994,-0.00521,0.03606,0.02075,-0.08899,0.01287,-0.08103,-0.14623,0.08466,0.008,-0.02242,0.08057,0.03703,0.02325,0.09099,-0.08258,-0.03533,0.12575,0.04204,0.0018,-0.06203,-0.04024,0.08189,-0.06777,0.09121,0.0605,0.01556,0.02582,-0.07045,0.03481,0.02515,0.13334,0.09214,0.05433,0.02678,0.05299,-0.02434,-0.03283,-0.12145,-0.0328,-0.08529,-0.01041,0.03523,0.06264,-0.08072,0.12327,-0.06546,-0.02859,-0.05615,0.01851,-0.08374,0.0983,0.06988,0.00051,-0.07351,0.15546,0.12227,-0.03424,-0.07642,-0.07277,-0.05144,0.06828,0.01238,-0.14461,-0.08339,-0.04433,0.01825,-0.0727,0.00262,-0.00062,0.05821,-0.00145,-0.05066,-0.10048,-0.07483,0.07289,0.09769,0.02192,0.05628,0.0395,0.02475,-0.03603,0.09517,0.07897,-0.01504,-0.02132,-0.03757,0.10847,-0.1094,0.01498,-0.01604,-0.12763,-0.07565,0.05496,0.02831,0.03538,0.01118,-0.11815,-0.06654,-0.0207,-0.024,0.0129,0.05885,0.08398,0.08035,-0.04323,-0.06744,-0.06995,-0.01687,0.01017,-0.02694,0.09354,-0.0486,-0.05669,0.01471,-0.00502,-0.04919,0.01333,-0.05097,-0.00561,-0.06369,-0.00605,0.03368,-0.01126,0.07215,0.09646,0.01897,-0.02683,-0.017,-0.01505,0.04998,0.07529,0.03369,0.05564,-0.11685,-0.05663,-0.02117,0.04034,-0.06952,-0.08216,-0.05955,0.09226,0.04647,0.03884,-0.01692,-0.13706,-0.01971,-0.04092,0.05106,-0.01732,0.02558,-0.01014,-0.05415,0.05713,0.06722,-0.0059,0.00662,0.04009,-0.01946,0.02731,0.06188,-0.04364,0.09581,0.04538]},{"domain":"chemical_engineering","key":"chemeng_cstr_conversion_first_order","name":"CSTR conversion for a volume (first order)","package":"chemical-engineering-ai999x","example":"First-order CSTR conversion: v0 = 0.01 m^3/s, V = 20.0 m^3, k = 0.001 1/s","v":[-0.03151,0.01002,-0.03845,0.02126,-0.01933,-0.11131,-0.08896,-0.05973,-0.02293,-0.07061,0.00535,0.03994,-0.09025,0.03631,0.01646,-0.01918,0.02719,-0.04852,-0.00445,0.00195,-0.11281,0.02767,0.00041,-0.06272,-0.12857,0.00501,0.04865,0.0234,-0.0182,-0.10793,-0.00549,-0.07248,0.03309,0.02103,-0.01981,-0.08731,0.00711,0.02437,-0.03182,-0.00463,0.01871,0.01765,-0.03419,0.1506,0.06245,-0.06384,-0.05874,0.03733,-0.07513,0.00731,0.0271,-0.01014,-0.01856,-0.06134,0.02359,-0.06882,0.09791,0.06411,-0.1216,0.01819,0.04319,-0.08465,-0.02432,0.03496,-0.13706,0.01982,-0.02894,-0.01669,-0.04918,-0.00476,0.05571,-0.00841,-0.08106,-0.03776,0.06548,0.11208,0.00839,0.01681,0.02724,0.00961,0.03642,0.08581,0.01527,0.04414,0.08894,-0.02313,-0.01711,0.05231,0.03296,-0.01643,-0.00048,-0.03303,0.07101,0.12652,0.12145,0.07403,-0.05797,-0.02359,0.06888,-0.05318,-0.00492,-0.0592,-0.01684,0.0778,0.03663,-0.02848,0.09445,-0.0099,-0.00395,0.02172,0.03571,0.06112,-0.08567,-0.00731,-0.04259,0.05191,0.03846,0.01394,0.02111,0.02899,-0.01243,-0.01249,-0.01163,-0.03279,0.02227,-0.00305,0.00989,0.06349,-0.00029,-0.06923,-0.04293,-0.09404,0.06385,-0.00065,0.08943,-0.06082,-0.11668,0.0165,-0.02873,-0.05939,-0.00639,0.09213,-0.01175,-0.06606,-0.10343,0.04404,-0.0949,0.06408,0.00808,-0.05239,-0.0443,0.00431,0.11057,0.04617,0.05892,0.02925,-0.01725,0.01715,0.00732,-0.1229,0.08015,0.03696,-0.1201,-0.05511,-0.02508,0.07991,-0.01721,0.00408,-0.0831,0.00955,0.04022,0.16118,0.03591,-0.04912,0.09645,0.01708,-0.06476,-0.08755,0.05157,-0.14685,0.02026,-0.04445,0.06448,0.04506,-0.0467,0.0968,0.03525,-0.0303,-0.05871,0.01949,0.02538,0.02463,-0.00935,0.11384,-0.09746,0.15436,0.03873,0.11427,-0.00832,-0.05085,-0.07558,0.03212,-0.04627,-0.06307,0.0429,-0.10823,0.01063,-0.05556,0.01372,-0.01703,0.05656,-0.04746,0.10676,0.02616,0.0088,-0.09865,-0.1134,-0.01006,-0.10021,-0.0751,0.03845,0.08759,-0.00851,0.07019,0.04917,0.12101,-0.0127,0.04854,0.1634,-0.00355,0.0198,0.1022,-0.0354,-0.04323,-0.04358,0.00771,0.11956,0.04599,-0.05002,0.01175,0.00554,-0.00727,-0.13995,-0.02669,0.07454,0.12133,-0.05132,-0.04524,0.0123,0.05119,0.02214,0.168,-0.1374,0.02465,-0.00046,-0.06484]},{"domain":"chemical_engineering","key":"chemeng_cstr_conversion_second_order","name":"CSTR conversion for a volume (second order)","package":"chemical-engineering-ai999x","example":"Second-order CSTR conversion: v0 = 0.01 m^3/s, V = 2.0 m^3, k = 1e-05 m^3/(mol*s), CA0 = 1000.0 mol/m^3","v":[-0.0639,0.03113,-0.0263,-0.08846,-0.00965,-0.04041,-0.11285,-0.03261,-0.00031,-0.04994,0.00833,-0.05615,-0.04001,0.01607,0.03902,-0.02799,-0.00139,0.02029,-0.06564,-0.0182,-0.07466,0.03599,0.04968,-0.06059,-0.09178,-0.01794,0.06492,0.1166,-0.0747,-0.07512,-0.00548,-0.12218,-0.01226,0.02093,0.08293,-0.01995,-0.06529,0.02272,-0.03742,-0.01386,0.05793,-0.02023,-0.08286,0.15064,0.01227,-0.05348,0.02616,0.03004,-0.077,-0.02906,0.12548,0.05698,-0.02767,-0.02313,-0.03167,0.05503,0.10558,0.06869,-0.16102,0.08579,0.07362,-0.07109,0.06807,0.06735,-0.17702,0.00524,0.05283,0.00975,-0.06976,-0.02699,0.04751,0.00319,-0.04293,0.01097,-0.01226,0.03455,-0.06037,-0.02694,0.0415,0.00137,0.00537,-0.01062,-0.04111,0.04466,0.01327,0.00529,0.07103,-0.00172,0.00215,-0.03961,-0.05918,0.08339,0.06971,0.16259,0.08659,0.02957,-0.03839,-0.0621,0.02915,-0.13018,0.02643,0.00781,0.06587,0.07857,0.07148,-0.01981,-0.01515,0.00608,-0.04677,0.0309,0.11808,0.01097,0.02113,-0.02727,-0.02542,-0.00783,0.09666,-0.02449,-0.0622,0.07689,-0.02691,0.03074,0.01079,0.00263,-0.01812,0.10971,0.03295,0.06079,0.02874,-0.05094,-0.04939,-0.17396,-0.04155,-0.02482,-0.04356,-0.03261,-0.14343,0.0203,0.0112,-0.06612,-0.04167,0.12797,0.05671,-0.02324,-0.04936,0.00632,-0.06537,0.06568,-0.00715,0.01894,-0.01561,0.04562,0.05995,0.06769,0.05141,0.05161,0.00285,0.03933,0.01583,-0.05132,0.05344,0.02699,-0.08388,-0.09296,-0.06241,0.11253,-0.04281,-0.01108,-0.06774,-0.02041,-0.00933,0.11259,-0.02344,-0.07622,0.01876,-0.06451,-0.06669,-0.01652,0.03285,-0.1155,0.06012,-0.01165,-0.05826,0.02332,0.02151,0.11075,0.00202,0.01746,-0.01642,0.05764,0.0858,0.02518,0.01199,0.07507,-0.04978,0.0328,-0.0399,0.05589,-0.00315,-0.07087,0.01311,0.03512,-0.0312,-0.07844,-0.05313,-0.06529,-0.02165,0.05927,0.05744,-0.09673,-0.03157,-0.12767,0.20543,-0.00438,0.04882,-0.04138,-0.07995,0.05894,-0.03188,-0.04178,0.1071,-0.00383,-0.02428,0.08159,0.07704,0.14019,-0.02803,-0.00422,0.08022,-0.01021,0.02135,0.05878,-0.01656,-0.02793,-0.03158,-0.05215,0.03954,0.09586,0.01008,-0.00839,0.05702,0.04197,-0.05495,0.03211,-0.01279,0.13697,-0.13574,-0.08714,0.0097,0.06784,-0.03147,0.12219,-0.10574,0.00323,-0.01026,-0.06943]},{"domain":"chemical_engineering","key":"chemeng_cstr_volume_first_order","name":"CSTR volume for a conversion (first order)","package":"chemical-engineering-ai999x","example":"First-order CSTR volume: v0 = 0.01 m^3/s, k = 0.001 1/s, X = 0.9","v":[0.00527,-0.07357,-0.06886,-0.0036,-0.04749,-0.04542,-0.00165,-0.00287,0.11231,-0.03537,0.10059,0.08592,-0.01112,0.06609,0.02714,0.01704,0.0678,0.05879,0.00546,-0.00634,-0.02034,-0.03921,-0.07566,-0.07797,-0.07891,-0.01312,0.04664,0.0204,-0.05546,-0.11286,-0.00011,-0.06791,0.05585,-0.01056,-0.01253,-0.10475,0.01732,-0.01041,0.0053,0.11836,0.01902,0.05022,-0.08638,0.09011,0.02086,-0.05108,0.01469,-0.04475,-0.02336,0.02156,-0.02356,0.00537,-0.06892,0.00752,-0.05684,-0.01566,0.09335,0.10853,-0.09208,0.02741,0.02537,0.04266,0.00758,0.13383,-0.07985,-0.01636,-0.02033,-0.10678,0.02585,0.03948,-0.01995,-0.01353,-0.1305,-0.02039,-0.01424,0.13815,0.02658,-0.02964,0.07422,0.09273,0.08539,0.06352,-0.00552,-0.06997,0.02901,0.07344,-0.04584,0.1051,0.04287,0.01633,-0.03225,-0.07163,0.02085,0.00084,-0.01981,0.11898,-0.07119,-0.01364,0.052,0.05341,-0.08238,-0.04695,-0.06588,-0.02039,0.04452,-0.04484,0.06752,-0.04246,0.04245,0.02141,-0.01703,-0.00419,-0.14258,0.05113,-0.02986,0.02094,-0.05726,0.08998,0.01976,0.12215,0.05114,0.0266,0.00078,0.00111,-0.00604,-0.09287,-0.01491,0.01275,0.02203,-0.04638,-0.11407,-0.04707,0.05898,-0.05038,0.10236,-0.06378,-0.00276,-0.01809,0.05818,-0.00853,0.04178,0.08147,-0.012,-0.07008,-0.14736,-0.05462,-0.06452,0.01859,0.0597,-0.06567,-0.01532,0.00549,0.17273,0.01672,-0.01391,0.06786,-0.01022,0.03202,0.04162,-0.09279,0.03099,0.01082,-0.08391,0.00871,-0.03048,0.12818,0.03133,0.04874,0.00155,-0.02219,0.03593,0.12423,-0.07224,-0.03424,0.13958,-0.01965,-0.05947,-0.0663,-0.01219,-0.10895,-0.01002,-0.06762,0.12698,0.00497,-0.04829,0.06121,0.03548,-0.02903,-0.07094,-0.03475,-0.01798,-0.03645,0.0312,0.15649,-0.05054,0.08874,0.04019,0.07593,-0.0628,-0.01954,-0.03098,-0.01569,-0.07003,-0.00908,0.04607,-0.08144,0.00624,-0.1291,-0.06368,0.02112,-0.00185,-0.04322,0.07736,6e-05,0.00527,-0.06607,-0.04977,-0.11121,-0.04651,-0.04825,-0.00953,0.11909,-0.0071,-0.02804,0.05241,0.0474,-0.00766,0.0533,0.14291,-0.03451,-0.01637,0.05135,-0.06011,-0.12302,-0.01381,0.09561,0.14458,0.01412,0.01491,0.00799,0.00652,-0.06035,-0.1276,0.02359,0.14586,0.08251,0.00231,-0.0433,0.01657,0.10173,0.00191,0.04366,-0.07782,-0.02424,-0.01966,-0.01852]},{"domain":"chemical_engineering","key":"chemeng_cstr_volume_second_order","name":"CSTR volume for a conversion (second order)","package":"chemical-engineering-ai999x","example":"Second-order CSTR volume: v0 = 0.01 m^3/s, k = 1e-05 m^3/(mol*s), CA0 = 1000.0 mol/m^3, X = 0.8","v":[-0.02572,-0.02909,-0.0771,-0.10315,-0.03044,0.01342,-0.02007,-0.02246,0.11548,-0.03061,0.07475,-0.00282,0.02358,0.09811,0.0284,0.02093,0.06822,0.06637,-0.02112,-0.02134,-0.02149,-0.08659,-0.00703,-0.05997,-0.01712,-0.03095,0.05062,0.09495,-0.11234,-0.07862,-0.01092,-0.12092,-0.0159,-0.01911,0.07364,0.00721,-0.04053,0.03431,0.02032,0.08572,0.02914,0.0237,-0.0744,0.06351,-0.02977,-0.04307,0.09368,-0.07731,-0.03588,-0.00959,0.07348,0.03781,-0.0505,0.07664,-0.10398,0.052,0.08947,0.15003,-0.13036,0.13204,0.07823,0.04963,0.1016,0.14279,-0.12663,-0.00427,0.00552,-0.09243,0.00546,-0.01696,-0.02043,-0.05929,-0.10088,-0.01167,-0.0303,0.04327,-0.03904,-0.05152,0.026,0.11908,0.04062,0.04641,-0.0138,-0.03438,0.00831,0.04393,0.02339,0.032,0.02899,-0.00868,-0.12505,0.07711,0.05924,0.06361,-0.03598,0.03004,-0.12208,-0.03215,-0.01553,-0.05097,-0.05923,0.03245,-0.03348,0.03258,0.06543,-0.06293,-0.02975,0.01028,-0.03538,0.01074,0.02819,-0.03283,-0.04519,0.0118,-0.02108,-0.06109,0.0836,0.0816,-0.06243,0.14835,-0.05279,0.0325,0.02753,-0.01477,-0.0859,0.00255,-0.01301,0.05275,0.08899,-0.05238,-0.1155,-0.1281,-0.04668,-0.06135,-0.0111,0.00057,-0.04298,-0.0336,0.07849,-0.0466,0.0357,0.11641,0.08779,-0.00677,-0.1037,-0.05722,-0.08205,-0.0109,0.0587,-0.02596,-0.00456,0.05487,0.13662,0.06928,-0.01297,0.1233,0.01606,0.0175,-0.00172,-0.02687,0.02499,0.02168,-0.01864,-0.01563,-0.01982,0.1206,0.04265,0.059,-0.00999,-0.05425,-0.00722,0.06912,-0.09187,-0.07575,0.06384,-0.08659,-0.04333,0.03524,-0.00139,-0.0607,0.05575,-0.03281,-0.02989,-0.0153,0.01369,0.08166,-0.0226,0.02755,-0.04628,-0.01965,0.02699,-0.05603,0.05644,0.09326,-0.006,-0.04159,-0.01896,-0.00927,-0.05322,-0.07505,0.03303,0.05856,-0.03961,-0.0651,-0.03551,-0.08902,0.01905,-0.00647,-0.03702,-0.08129,-0.03523,-0.11253,0.22455,-0.01602,0.0695,0.03781,-0.03433,-0.06431,0.01086,-0.00978,0.08496,0.0104,-0.03822,-0.01215,0.10979,0.09669,-0.02021,0.00824,0.03596,-0.0453,0.02174,0.04512,-0.03165,-0.13217,-0.08101,0.05988,0.07999,0.07387,0.0942,-0.02296,0.00208,-0.02162,-0.0755,0.09168,0.05859,0.11086,-0.0823,-0.05827,-0.008,0.0529,-0.04618,0.08083,-0.05414,-0.03043,0.0045,-0.01028]},{"domain":"chemical_engineering","key":"chemeng_cstrs_in_series_first_order","name":"Equal CSTRs in series: conversion (first order)","package":"chemical-engineering-ai999x","example":"First-order CSTRs in series: v0 = 0.01 m^3/s, V = 5.0 m^3, k = 0.001 1/s, N = 3","v":[-0.05349,0.01913,-0.07362,-0.01173,-0.03486,-0.09221,-0.04135,0.0047,-0.00077,-0.08351,0.00766,0.04774,-0.10716,-0.01004,-0.00506,-0.00195,0.03725,0.02136,-0.00181,-0.00328,-0.09427,-0.01753,-0.06146,-0.05555,-0.10298,-0.03277,0.04936,0.00117,-0.07195,-0.13992,0.00135,-0.13106,0.05662,0.00424,0.08689,-0.12271,0.07169,-0.01518,-0.02507,0.03545,0.02079,0.03076,-0.04913,0.09514,0.04153,-0.04403,-0.07709,0.06591,-0.07619,0.043,-0.03693,0.0488,-0.02005,-0.04113,0.03971,-0.09434,0.06553,0.03005,-0.07813,0.05361,0.02352,0.01772,-0.02111,-0.00033,-0.10605,0.04395,-0.00473,-0.10333,0.0152,0.0256,0.00123,0.04094,-0.07793,0.00054,-0.01938,0.10667,-0.00036,0.06321,0.09727,0.03303,0.06331,0.04108,0.02828,0.00293,0.06681,-0.00427,-0.0403,0.08448,0.03384,-0.01308,-0.02361,0.0321,0.05334,0.07228,0.10183,0.05623,-0.07656,-0.01861,0.03609,-0.03617,-0.01132,-0.08129,-0.06696,0.03551,0.08826,-0.0151,0.04093,-0.06121,-0.04894,0.04084,0.01536,-0.01953,-0.02929,0.02189,-0.06204,0.02908,-0.00399,-0.00422,0.05203,0.06656,-0.06848,-0.01078,-0.00129,-0.04032,0.0633,0.06023,0.05246,0.08515,0.01185,-0.09991,-0.08894,-0.08407,0.02327,-0.0338,0.06589,-0.11083,-0.15435,0.04355,-0.04017,-0.03404,-0.07205,0.11012,-0.03318,-0.00255,-0.03418,0.00288,-0.10226,0.0922,0.0555,-0.06871,-0.07674,0.07638,0.0843,0.03726,0.06116,0.0233,-0.07342,0.01653,0.02057,-0.05955,0.09508,0.05206,-0.13991,-0.04747,-0.00508,0.08997,-0.02478,0.06231,-0.04277,0.04687,0.02452,0.11945,0.00491,-0.03517,0.12152,-0.00236,-0.08097,-0.08,0.01147,-0.08063,-0.01055,-0.06064,0.05724,0.05951,-0.07395,0.11857,0.08343,-0.02435,-0.07854,0.02832,0.00796,0.07689,-0.0011,0.1985,-0.07506,0.09293,0.02946,0.02919,-0.03431,-0.08501,-0.06677,0.02854,-0.06982,-0.02369,0.0193,-0.05087,0.02199,0.0102,-0.0376,-0.00985,0.04726,-0.03771,0.05404,0.00426,-0.00231,-0.10582,-0.02368,-0.03071,-0.1053,-0.06757,-0.00325,0.13817,-0.00064,0.04229,0.05926,0.09447,-0.02574,0.07025,0.1468,0.01501,0.02804,0.04701,-0.04013,-0.03166,-0.04656,0.00304,0.13232,0.05606,-0.02366,-0.03888,0.02373,0.01303,-0.10158,-0.01121,0.06964,0.08572,-0.03575,-0.0666,0.04412,0.10349,0.0514,0.19088,-0.10033,0.01085,0.01862,-0.0704]},{"domain":"chemical_engineering","key":"chemeng_cstrs_in_series_second_order","name":"Equal CSTRs in series: conversion (second order)","package":"chemical-engineering-ai999x","example":"Second-order CSTRs in series: v0 = 0.01 m^3/s, V = 1.0 m^3, k = 1e-05 m^3/(mol*s), CA0 = 1000.0 mol/m^3, N = 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counterdiffusion flux","package":"chemical-engineering-ai999x","example":"Equimolar counterdiffusion flux: D = 2.3e-05 m^2/s, P = 101325.0 Pa, T = 298.15 K, L = 0.1 m, yA1 = 0.2, yA2 = 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pressure drop (Ergun equation)","package":"chemical-engineering-ai999x","example":"Ergun pressure drop: dp = 0.0008 m, eps = 0.4, vs = 0.05 m/s, rho = 1000.0 kg/m^3, mu = 0.001 Pa*s, L = 1.0 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decline curve: rate and cumulative production","package":"chemical-engineering-ai999x","example":"Exponential decline: qi = 0.0018401307283333335 m^3/s, Di = 9.506426344208685e-09 1/s, t = 63115200.0 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number of stages at total reflux (Fenske)","package":"chemical-engineering-ai999x","example":"Fenske minimum stages: alpha = 2.5, xD = 0.95, xB = 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cake and medium resistance from constant-pressure filtration data","package":"chemical-engineering-ai999x","example":"Filtration constants fit: t = [17.3, 41.3, 72.0, 108.3, 152.1, 201.7], V = [0.5, 1.0, 1.5, 2.0, 2.5, 3.0], t_unit = s, v_unit = L, A = 0.0439 m^2, dP = 338000.0 Pa, mu = 0.000895 Pa*s, c = 23.47 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gain and time constant from step-test data (least squares)","package":"chemical-engineering-ai999x","example":"First-order step test fit: t = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 8.0, 10.0, 12.0, 15.0, 20.0], y = [0.0, 0.0, 1.7, 3.1, 4.3, 5.2, 6.0, 7.1, 7.9, 8.4, 8.8, 9.1], t_unit = min, M = 5.0, theta = 60.0 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process: response to a step","package":"chemical-engineering-ai999x","example":"FOPDT step response: K = 2.0, tau = 300.0 s, theta = 60.0 s, M = 5.0, t = 360.0 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initially in place from the p/z plot","package":"chemical-engineering-ai999x","example":"Gas p/z material balance: p = [3200.0, 2925.0, 2525.0, 2125.0], z = [0.85, 0.84, 0.83, 0.82], Gp = [0.0, 15.0, 35.0, 55.0], p_unit = psi, gp_unit = 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deliverability from a back-pressure test (Rawlins-Schellhardt)","package":"chemical-engineering-ai999x","example":"Gas well back-pressure test: q = [4288.0, 9265.0, 15552.0, 20177.0], pwf = [403.1, 394.0, 378.5, 362.6], q_unit = Mscf_per_day, p_unit = psi, pr = 2814439.927071325 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decline curve: rate and cumulative production","package":"chemical-engineering-ai999x","example":"Harmonic decline: qi = 0.0018401307283333335 m^3/s, Di = 1.2675235125611581e-08 1/s, t = 94672800.0 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in place and gas-cap size from the material balance (Havlena-Odeh, gas cap)","package":"chemical-engineering-ai999x","example":"Havlena-Odeh gas cap: F = [5000000.0, 9300000.0, 14300000.0, 19500000.0], Eo = [0.01, 0.018, 0.027, 0.036], Eg = [0.025, 0.05, 0.08, 0.11], v_unit = bbl","v":[0.01312,0.05935,-0.07431,0.01139,0.02945,0.00905,0.00969,-0.00228,0.10092,0.04356,0.00283,0.0307,-0.05893,0.06676,-0.0399,0.13743,-0.00518,0.0006,0.06239,-0.05568,0.02376,-0.01844,-0.05345,-0.07813,-0.07504,-0.06747,0.0065,-0.07716,-0.05984,-0.08938,0.0637,-0.00275,0.11967,-0.01779,-0.02892,-0.0141,-0.01948,0.05304,-0.03222,-0.10485,0.05203,0.05077,-0.10094,0.05122,-0.00104,0.00929,-0.06944,0.02516,-0.07079,0.03906,-0.03857,0.01862,0.07721,0.00298,0.00831,0.03548,-0.00838,0.00093,-0.0134,-0.03374,0.03004,-0.05844,-0.10049,-0.07596,-0.00472,0.00964,-0.03501,-0.21022,-0.00992,-0.10121,0.06376,-0.05488,0.01121,-0.04652,0.07523,0.03164,0.01467,-0.00295,-0.07335,0.13091,0.00103,0.10566,-0.08853,0.0008,0.04371,-0.01629,-0.02297,0.07919,-0.00058,0.02515,-0.00592,0.06283,-0.0131,0.12593,-0.05541,0.07755,-0.03453,-0.03275,0.05072,0.00915,-0.03934,0.01662,0.01976,-0.05019,-0.0647,-0.08025,0.07601,-0.03666,0.07437,0.05388,-0.0786,-0.01279,-0.00058,0.07037,0.02134,-0.00778,-0.04348,0.04193,0.12873,-0.04669,0.11632,0.01194,-0.05823,0.07613,-0.05704,0.00643,-0.04275,0.00815,-0.01566,-0.12133,-0.019,0.03079,0.04398,-0.07739,0.01068,-0.1193,0.02695,0.05643,-0.04718,0.0154,0.05755,0.01599,-0.00022,0.06052,0.12514,0.05369,-0.03491,-0.04708,0.06102,-0.03549,-0.00605,0.00106,0.17512,-0.0202,0.01286,0.00292,-0.01471,-0.06147,0.11165,-0.01799,-0.06369,-0.12585,0.04199,0.05531,-0.04541,0.06019,0.01341,0.03605,0.08758,-0.05533,-0.05933,0.14959,-0.04627,0.01115,0.17536,0.04799,-0.03519,-0.02348,0.02881,-0.08983,-0.06031,-0.07143,0.03174,0.04468,-0.0033,-0.02526,-0.06384,0.07308,-0.025,-0.10143,0.00678,-0.06218,0.17991,0.03727,0.00638,0.11442,0.0709,0.12108,-0.02555,-0.12539,-0.06948,-0.04334,0.01794,-0.07498,-0.02326,-0.06972,-0.01608,-0.00614,0.06917,-0.0217,0.08674,0.07594,0.0732,0.07773,0.00168,-0.08834,0.01755,-0.0232,0.01933,-0.02171,0.0552,0.02957,0.006,0.07247,-0.08063,-0.06809,-0.02098,-0.00225,0.06948,0.10577,-0.10515,-0.06129,0.0015,-0.08271,-0.00549,-0.00309,-0.05545,-0.03616,0.05134,-0.03384,0.01307,-0.06296,0.04906,0.06282,0.05276,0.00442,0.03972,-0.02126,0.0608,-0.05137,0.04501,-0.18165,-0.02753,-0.00066,0.05181,0.10663]},{"domain":"chemical_engineering","key":"chemeng_havlena_odeh_oil_in_place","name":"Oil initially in place from the material balance (Havlena-Odeh straight line)","package":"chemical-engineering-ai999x","example":"Havlena-Odeh oil in place: F = [580700.0, 1600000.0, 2800000.0, 4100000.0], Et = [0.0101, 0.0278, 0.0485, 0.0712], v_unit = 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build-up test: Horner analysis for permeability and extrapolated pressure","package":"chemical-engineering-ai999x","example":"Horner build-up analysis: dt = [2.0, 4.0, 8.0, 16.0, 24.0], pws = [2960.0, 3015.0, 3069.0, 3122.0, 3150.0], t_unit = h, p_unit = psi, tp = 1800000.0 s, q = 0.0005520392185 m^3/s, mu = 0.0008 Pa*s, h = 6.096 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decline curve: rate and cumulative production","package":"chemical-engineering-ai999x","example":"Hyperbolic decline: qi = 0.0018401307283333335 m^3/s, Di = 1.5844043907014474e-08 1/s, b = 0.5, t = 94672800.0 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with N equilibrium stages (Kremser)","package":"chemical-engineering-ai999x","example":"Kremser absorber: N = 5, A = 1.4, m = 2.0, y_in = 0.05, x_in = 0.0","v":[0.01515,0.03963,-0.04251,0.01594,0.11725,0.02951,-0.00911,0.01536,0.10407,-0.04081,0.04249,-0.15582,-0.00663,-0.0244,-0.08975,0.05808,0.05669,-0.18488,0.057,0.07653,-0.01622,-0.04646,-0.0259,-0.02,-0.03686,0.07599,-0.01126,-0.03879,-0.00902,-0.08714,0.00109,-0.09009,0.04777,-0.03453,-0.04654,0.06956,-0.0532,0.01929,-0.00155,0.02474,0.01112,0.10282,0.09733,0.10125,0.05762,0.03495,-0.05357,0.0001,0.09491,0.06996,-0.03018,0.11534,0.01063,0.06792,0.0134,-0.03568,-0.11609,-0.0652,0.10008,-0.00741,-0.15693,-0.08053,-0.01234,-0.11998,0.05194,-0.00173,-0.107,-0.03277,-0.08438,-0.04207,0.0287,0.05392,-0.02906,0.03012,0.10063,0.11079,-0.00972,-0.09936,0.15647,0.07927,-0.056,-0.00598,-0.06499,0.03687,0.06966,-0.03645,0.06949,0.03569,0.04591,0.09241,-0.00375,-0.0165,-0.01063,0.00514,0.04249,-0.00861,-0.04041,-0.03706,0.01399,-0.03617,0.00513,-0.00748,-0.0717,-0.03076,0.04148,0.0846,0.06589,-0.10541,0.0604,0.04307,-0.0255,-0.00297,-0.04277,-0.07009,-0.02046,-0.03794,-0.03761,0.0553,0.02213,0.09006,0.04056,-0.00437,-0.02472,0.00671,0.10574,-0.06221,-0.00056,0.03266,0.03596,-0.02498,-0.03879,0.0167,-0.04095,-0.04562,-0.03005,0.07525,-0.05775,0.04993,0.05257,0.07359,0.03804,-0.04944,0.00217,0.05815,-0.00071,-0.02803,-0.09489,0.0417,0.04557,-0.07975,0.02574,0.03367,0.01547,0.0266,0.09991,0.03461,-0.07631,0.09345,0.03604,-0.04521,-0.05862,-0.06704,-0.01319,-0.02697,-0.05017,-0.15619,0.00921,0.01646,0.05712,0.08224,0.04067,-0.03276,-0.05302,-0.04671,0.13847,0.06008,-0.01063,-0.08623,0.09875,0.02964,-0.02163,0.07014,0.0121,0.00996,-0.08804,0.07743,0.1361,0.16215,-0.01269,-0.06359,0.01644,0.06726,-0.00265,0.04516,-0.03801,0.06524,0.02742,0.02459,-0.05493,0.00613,0.05876,-0.04093,0.01892,0.07756,-0.00972,-0.00087,0.00925,-0.07541,0.00845,-0.00289,-0.0806,-0.01524,-0.07407,0.03101,-0.03982,-0.07254,-0.00394,0.05946,-0.1339,-0.07662,-0.00608,0.05085,0.06822,0.10679,-0.06069,-0.04017,-0.0111,0.07805,-0.07943,-0.05175,-0.0546,-0.089,-0.08079,0.00027,0.03253,-0.0311,-0.0355,-0.07422,-0.0055,-0.12886,-0.066,0.05505,0.01345,-0.08922,0.07289,-0.06259,0.12027,-0.01416,-0.01034,-0.04263,0.06924,0.10114,-0.02291,-0.06234,0.04824,-0.10433]},{"domain":"chemical_engineering","key":"chemeng_kremser_stripper","name":"Stripper with N equilibrium stages (Kremser)","package":"chemical-engineering-ai999x","example":"Kremser stripper: N = 6, S = 1.5, m = 3.0, x_in = 0.01, y_in = 0.0","v":[-0.00845,0.02225,-0.01472,-0.06797,0.04127,-0.04757,-0.02113,0.03271,0.01786,0.00457,0.00044,-0.15863,-0.02797,-0.01919,-0.09663,0.06365,-0.06491,-0.15521,-0.10289,-0.03842,-0.08076,-0.02169,-0.03047,-0.0475,0.00126,0.0392,-0.02435,-0.08451,-0.06156,-0.14578,0.04451,-0.11649,0.03321,-0.06863,0.01582,0.07259,-0.00941,-0.0241,-0.06597,0.07068,0.01521,0.07681,0.14694,0.07169,0.01734,0.03749,0.01299,0.04863,-0.03592,0.04693,-0.06378,0.14699,-0.06877,0.02828,0.08339,0.09221,-0.10556,-0.00852,0.06805,-0.00794,-0.08534,-0.04659,0.02434,-0.12732,-0.01948,0.06448,-0.08319,-0.06183,-0.00418,-0.04968,0.01673,0.04009,-0.06255,0.1038,0.07645,0.11085,-0.04023,-0.04009,0.10704,0.02068,-0.02227,-0.00632,-0.02489,0.04081,0.03764,-0.08927,-0.06546,0.12164,0.06771,0.07625,-0.04286,0.03292,-0.00786,0.03521,0.06312,0.04097,-0.05839,-0.02454,-0.02945,-0.08328,0.01177,0.0167,-0.07906,0.04605,0.10018,0.03829,0.06653,-0.03501,0.03073,-0.035,0.01989,0.00257,-0.0276,-0.03341,-0.0017,0.08402,0.01008,0.0846,-0.01647,0.04122,-0.02547,0.05012,-0.01123,0.05965,0.00173,0.1214,-0.02001,0.10363,-0.04143,-0.00612,-0.07819,0.01519,0.06812,-0.02092,-0.04268,0.13955,0.00318,0.07781,-0.06303,0.01738,0.04163,-0.00364,-0.02074,0.04723,0.01668,0.00503,-0.06594,0.12332,0.05756,0.03667,0.01406,0.00914,0.0809,0.08382,0.12416,-0.12115,-0.06392,0.06209,-0.03622,-0.02405,-0.03231,-0.01126,0.021,-0.03516,-0.012,-0.13106,-0.04775,-0.01956,0.03573,0.11056,0.01975,0.03729,-0.03666,-0.06839,0.10453,0.09825,-0.0587,-0.12072,0.05026,0.05379,-0.08794,0.04768,0.01376,0.01705,-0.06656,0.08698,0.07859,0.0946,-0.01353,-0.019,-0.02522,0.03186,0.0195,0.04218,-0.03868,0.04631,0.02534,0.01256,-0.0308,-0.04172,0.07204,0.05699,-0.00805,-0.0143,-0.02856,0.038,0.00658,0.01845,-0.02912,-0.01023,-0.04858,0.02178,-0.08527,0.03358,-0.01645,-0.07203,0.11127,0.06121,-0.07895,-0.02478,0.00595,0.06274,0.05948,0.14088,-0.05455,-0.00557,-0.01541,0.04078,-0.00155,-0.02069,-0.10023,-0.12898,-0.07074,-0.00047,-0.00295,-0.06551,-0.03372,-0.03728,-0.08742,-0.08652,-0.05418,0.02874,0.05636,-0.12744,0.03108,-0.09604,0.13371,-0.03942,-0.05148,0.03561,0.04758,0.04241,-0.04865,-0.0439,0.07391,-0.11796]},{"domain":"chemical_engineering","key":"chemeng_lag_frequency_response","name":"Frequency response of first-order lags in series (amplitude ratio and phase)","package":"chemical-engineering-ai999x","example":"Lag frequency response: K = 2.0, taus = [10.0], t_unit = s, w = 0.1 rad/s","v":[0.00106,0.04019,-0.02026,0.08835,0.00735,0.00765,-0.10097,-0.03777,0.08169,-0.02508,-0.02432,0.03082,0.06389,0.03631,0.05273,0.06477,-0.00616,-0.03784,-0.00372,0.04197,0.04029,-0.02281,-0.03356,-0.02593,0.01836,-0.01533,0.1036,-0.00261,0.00722,0.08601,-0.0089,0.05707,-0.04764,0.02865,0.03353,0.01765,0.07536,0.08903,-0.07108,0.04201,-0.01009,-0.00672,-0.09213,0.03699,-0.04125,-0.02451,0.02067,0.1058,-0.04733,-0.02363,-0.18222,0.07651,-0.04457,0.03228,-0.02421,-0.02147,-0.04868,-0.0108,0.02514,0.04916,-0.00651,-0.04593,-0.07346,-0.02993,0.09886,-0.03564,-0.03827,0.02314,0.03813,-0.11663,0.02953,0.13971,-0.00734,-0.13005,0.04148,-0.09888,0.14473,0.0515,0.05172,-0.05962,-0.01534,-0.03339,0.05159,0.04856,0.02747,-0.02551,-0.02377,0.07577,0.06002,0.05327,-0.03098,-0.00253,0.03028,-0.15783,-0.03937,-0.07843,-0.03338,0.02765,0.14705,-0.0669,-0.0511,0.02502,-0.1257,-0.02163,0.09482,0.11542,-0.1154,-0.01108,-0.01809,0.08197,0.02113,-0.03964,0.0319,-0.01839,-0.10421,0.0857,-0.06222,-0.08562,0.02545,-0.04272,-0.02511,-0.04323,0.13265,0.02009,-0.04481,-0.08959,-0.10441,-0.05722,-0.09701,-0.08136,0.01699,-0.05062,0.0351,-0.02787,0.12602,0.03512,-0.06789,-0.03024,0.06235,0.00265,-0.04873,0.0338,-0.03355,-0.03105,0.08015,-0.06614,-0.0278,0.07596,0.05153,-0.03876,-0.03013,-0.06512,-0.04896,-0.1041,-0.0422,-0.03925,0.01476,0.08291,0.08543,-0.07528,0.00867,0.117,-0.03528,0.1114,0.09847,0.04021,-0.07102,0.11743,-0.0016,0.09861,0.0072,0.12217,-0.00448,-0.0463,0.08231,-0.01921,0.01464,-0.01914,-0.0613,0.04045,-0.03217,-0.05185,0.05523,-0.0266,-0.0009,-0.03004,-0.0871,-0.07447,-0.10895,-0.00052,-0.05651,0.08257,0.00427,0.07611,-0.07415,0.04436,0.00073,0.04285,-0.05289,-0.08262,-0.04681,-0.02399,-0.10749,0.02986,0.0331,-0.06029,0.11656,-0.02638,-0.0212,-0.02306,0.12978,-0.00031,-0.03689,0.02386,0.02067,-0.02211,-0.05652,-0.04049,0.0016,0.00451,-0.1024,0.04474,-0.01588,0.05156,0.00477,0.01265,0.10759,0.01946,0.10372,0.00521,-0.02207,-0.05129,-0.12001,0.07481,0.02284,0.06545,0.05135,-0.10972,-0.00373,-0.03243,-0.01901,-0.05231,0.03554,-0.03238,0.03299,0.03608,0.15646,-0.07178,0.04242,0.08883,0.0305,0.00104,-0.00153,-0.09075,0.07812,0.03146]},{"domain":"chemical_engineering","key":"chemeng_lee_kesler_vapour_pressure","name":"Vapour pressure by the Lee-Kesler correlation","package":"chemical-engineering-ai999x","example":"Lee-Kesler vapour pressure: T = 400.0 K, Tc = 568.7 K, Pc = 2490000.0 Pa, omega = 0.399","v":[0.04275,-0.05849,-0.08433,-0.06794,-0.0237,-0.04673,0.11673,0.01768,0.01537,0.00364,-0.03296,-0.10049,-0.06181,-0.07227,0.04303,0.01306,0.0298,-0.05534,-0.01029,0.04812,-0.01823,0.0355,-0.14146,0.02718,0.05561,0.00764,0.1593,0.00263,0.12623,-0.02845,-0.04176,-0.06689,0.00281,0.03175,-0.00945,-0.01038,0.06151,0.06547,-0.11587,-0.00393,0.04646,0.00326,-0.03917,0.11234,-0.01378,-0.06168,0.04363,0.02368,0.05061,0.00096,0.09207,-0.07861,-0.01679,0.00577,0.03368,-0.19042,-0.05892,0.01997,0.05248,0.0412,0.09037,-0.00586,-0.13412,-0.00327,-0.04089,0.02737,-0.04843,0.01008,-0.103,-0.05427,-0.06527,0.02882,0.1275,-0.05079,0.08616,-0.04633,0.0908,-0.08261,-0.07898,-0.00265,0.03497,0.05278,-0.00228,0.01157,0.01108,-0.09273,-0.05101,-0.02716,-0.00507,-0.02145,-0.00927,0.03892,-0.0645,0.00788,-0.01076,-0.00089,0.02804,-0.02804,0.08338,-0.05523,-0.00013,0.05451,-0.02853,0.03105,-0.00453,0.00461,-0.00583,0.01768,0.16241,-0.06833,0.08454,-0.07022,-0.02301,-0.1469,-0.03874,-0.00737,0.07328,0.11134,-0.04842,-0.02223,0.0727,0.06676,0.04174,-0.02634,-0.0966,0.05201,-0.02277,-0.02603,-0.04636,0.00967,0.03568,-0.05999,0.03316,-0.00106,0.03561,0.02974,-0.0597,0.0113,-0.06768,0.03033,-0.00436,0.02892,0.13424,0.18376,0.06659,-0.02799,0.0227,0.14424,-0.01373,0.06213,-0.02461,0.03625,0.10597,0.11825,0.02635,0.05198,0.02157,-0.03238,-0.01796,-0.04149,-0.15716,-0.0509,0.15889,-0.01166,-0.05481,0.02265,0.04222,0.06426,0.05512,-0.04534,-0.03474,0.01175,-0.07227,-0.03942,0.17529,0.08032,-0.07937,-0.00714,0.11593,-0.02634,-0.02152,0.00399,0.02489,0.03561,0.00282,0.02443,-0.00072,-0.08267,-0.14683,0.06187,-0.00469,0.03822,-0.03557,0.05218,-0.02156,0.02706,0.01683,0.04475,0.10039,-0.00417,-0.13575,0.00085,-0.09036,-0.0487,-0.06788,-0.0235,-0.02116,-0.10725,0.03278,-0.10041,-0.0114,0.0335,0.01241,-0.03473,0.06144,0.09081,-0.03518,-0.02571,-0.02014,-0.0455,-0.01783,-0.07028,0.05539,0.09151,-0.03271,-0.02622,0.03413,-0.01129,-0.0454,0.0159,0.02003,-0.00696,0.01949,-0.11733,-0.05115,0.04428,-0.07737,0.02717,-0.00145,0.04807,0.03046,0.08351,0.12746,0.02363,0.00958,-0.03306,0.01407,-0.06114,0.06933,-0.03633,-0.06159,0.03245,-0.07091,-0.04643,-0.06008,-0.03272]},{"domain":"chemical_engineering","key":"chemeng_line_source_drawdown","name":"Transient drawdown around a well (line-source solution)","package":"chemical-engineering-ai999x","example":"Line-source drawdown: q = 0.001 m^3/s, mu = 0.001 Pa*s, k = 1e-13 m^2, h = 10.0 m, phi = 0.2, ct = 1e-09 1/Pa, r = 0.1 m, t = 3600.0 s, pi = 30000000.0 Pa","v":[0.00372,-0.03503,-0.06865,-0.01121,-0.02349,0.12104,0.07319,-0.00234,0.05034,0.05193,0.05426,0.00284,0.05497,-0.00191,0.00331,-0.00194,0.05403,-0.01365,-0.02301,0.01461,-0.021,-0.04459,-0.03661,0.03433,-0.02728,-0.00605,-0.01511,0.01698,0.01253,0.02153,0.00052,0.04817,-0.04303,0.02231,-0.01716,0.06311,-0.0109,0.05827,-0.05948,0.04397,0.04088,0.05019,-0.0998,0.05615,-0.11353,0.08557,-0.01013,-0.10255,0.02775,0.00651,-0.00049,0.06627,0.05057,-0.04061,0.02386,0.08129,0.0286,-0.03652,-0.04707,0.00982,0.01583,0.0464,-0.03226,-0.01077,-0.00101,0.04459,-0.01399,-0.1135,-0.07058,-0.06344,0.01866,0.02367,0.01196,0.02556,0.05496,-0.03926,-0.08458,0.00354,-0.1547,0.01679,0.09902,0.02951,0.05602,-0.05002,0.01647,-0.10587,-0.08512,0.06306,-0.04889,0.02538,0.03936,0.02257,-0.03243,-0.01381,0.00649,0.02217,0.13436,-0.0336,0.01841,-0.00884,0.03986,-0.00574,-0.02154,0.06573,0.1283,0.04371,0.08698,-0.08129,0.0708,0.13236,0.00657,-0.01688,-0.07218,0.0078,-0.00069,-0.12007,-0.07161,-0.00799,0.03722,0.02615,-0.01262,-0.01892,-0.01571,0.07467,0.02834,-0.01911,-0.03955,0.10149,-0.03182,-0.02939,0.02433,-0.06412,0.05802,-0.02733,0.04449,-0.11972,0.0556,0.01814,0.06395,-0.00209,-0.12412,0.05881,-0.14863,-0.06345,0.01528,0.05541,-0.02573,-0.11541,-0.02428,-0.05599,-0.07781,-0.00489,0.10674,0.01581,-0.00249,0.03358,-0.02497,-0.02663,0.05085,-0.0512,-0.1556,-0.0988,0.01026,0.01606,-0.11173,-0.08411,0.03025,-0.03815,0.01264,-0.04232,0.02762,0.079,-0.01581,0.02287,0.06402,0.07091,-0.0922,0.02283,-0.01381,0.05742,-0.07568,-0.02662,0.00609,-0.12164,-0.00724,0.20055,-0.03196,0.03745,-0.01753,-0.13141,-0.0449,0.02458,0.0207,0.01955,0.00586,0.05123,0.02329,0.02249,-0.01541,-0.06584,-0.05695,0.08168,-0.02341,0.0474,0.05544,-0.06359,0.07723,-0.02805,0.01085,0.04346,0.11737,0.14077,0.04554,0.0533,-0.00541,-0.15382,0.01667,-0.05538,-0.05368,-0.0711,0.11135,-0.16067,0.06575,0.05099,0.02524,-0.02856,-0.05544,-0.0085,0.0534,0.05629,-0.09737,-0.18475,-0.0471,0.10521,-0.05081,-0.00966,-0.08165,0.02949,-0.0092,0.13904,0.01117,-0.00433,0.04741,-0.06517,0.02545,0.0984,-0.01467,-0.0093,0.11989,0.07614,0.02475,-0.14474,0.11923,0.02619,-0.01703,-0.00768]},{"domain":"chemical_engineering","key":"chemeng_mass_to_mole_fractions","name":"Mass fractions to mole fractions and mean molar mass","package":"chemical-engineering-ai999x","example":"Mass to mole fractions: w = [0.5, 0.5], MW = [32.042, 18.015]","v":[-0.09476,0.12992,0.09056,0.07752,-0.02276,-0.01372,-0.00735,-0.03478,0.05151,-0.065,0.08909,0.08362,-0.0277,-0.08482,-0.06396,-0.11014,-0.02824,-0.0474,-0.00841,0.0966,2e-05,-0.01352,-0.05452,0.02433,0.02103,0.02759,-0.02183,-0.04752,-0.03964,0.02901,-0.01697,-0.05267,-0.05865,-0.00013,0.08148,-0.13826,-0.04063,0.00382,0.13736,-0.06796,-0.08049,0.05131,0.04239,-0.03527,0.02099,0.03173,-0.07491,0.02128,-0.00154,0.02356,-0.13851,0.0387,0.02524,-0.00445,0.01661,0.14959,-0.0651,-0.10271,0.01221,0.00872,0.02327,-0.00855,-0.00816,-0.04046,0.10502,-0.00224,-0.01933,-0.02817,0.06013,0.0219,-0.10403,-0.02059,0.03074,-0.03017,0.05222,0.11437,-0.06212,-0.02769,0.00328,0.02156,-0.00714,-0.00846,0.06957,-0.04898,0.04896,0.00837,-0.00787,0.09646,0.0356,0.012,-0.06317,-0.00551,-0.07905,0.06452,0.00542,-0.04877,-0.08164,0.02571,-0.12443,0.03858,0.0032,-0.00871,-0.04179,-0.00904,0.03908,-0.05093,0.06908,0.09574,-0.04412,0.17176,0.03939,-0.07698,0.01356,-0.0215,-0.1046,-0.03741,-0.0033,0.00154,0.11989,0.04492,-0.00723,-0.0393,-0.06931,-0.01937,-0.03521,0.06594,0.1006,-0.11985,-0.04576,0.0081,0.0356,0.15745,-0.01358,-0.02317,0.02823,-0.07088,-0.02888,0.03896,-0.02986,0.00845,-0.00264,-0.07876,-0.04001,0.06533,-0.00888,0.03705,0.01708,0.04288,-0.00336,-0.01436,-0.10566,0.01667,0.02445,-0.0678,-0.00231,0.03211,0.00546,-0.05712,0.04816,0.03059,0.00355,-0.09173,0.02781,-0.05275,0.11502,0.09141,-0.04129,0.08852,0.12754,-0.01883,0.17003,0.01198,0.01698,-0.09231,-0.01873,0.04409,0.12474,-0.17272,-0.03489,-0.05555,-0.03465,0.07018,-0.04069,-0.03733,-0.10764,0.14365,0.02419,0.1212,0.03031,-0.1121,-0.12789,0.04126,-0.04437,0.07289,0.02446,-0.01575,-0.01936,-0.04854,-0.06316,-0.00856,-0.0892,-0.00751,-0.07712,0.01796,-0.07376,-0.04051,0.08343,0.03031,-0.03264,-0.03655,-0.02442,0.12693,-0.00345,-0.03962,0.05477,-0.01707,0.08798,-0.00244,0.02545,0.04199,-0.013,0.08319,-0.02659,0.04783,0.0351,-0.07964,0.04032,0.02176,0.07593,-0.07207,0.069,0.04939,-0.03602,-0.00247,0.08567,-0.10061,0.02221,0.01784,-0.00152,-0.05358,0.10518,-0.05076,-0.01373,0.0857,0.05198,0.03879,-0.0055,0.09307,0.0412,-0.01486,-0.07712,-0.02957,0.02734,-0.06088,-0.07977,-0.07079]},{"domain":"chemical_engineering","key":"chemeng_mass_transfer_coefficient","name":"Mass-transfer coefficient from a stated Sherwood correlation","package":"chemical-engineering-ai999x","example":"Mass-transfer coefficient: geometry = sphere, u = 0.1 m/s, L = 0.001 m, D = 5e-09 m^2/s, rho = 1000.0 kg/m^3, mu = 0.001 Pa*s","v":[-0.0445,-0.03494,0.05476,0.11586,-0.00212,0.03362,-0.01252,0.01598,0.07194,-0.09723,0.02399,-0.11596,0.05467,-0.01663,-0.07089,-0.03615,-0.00947,-0.11085,0.05041,-0.03832,0.05995,0.0383,0.01574,0.00448,0.04598,0.04049,0.0386,-0.11432,-0.03537,0.01379,0.02939,-0.09504,0.03273,0.04356,-0.09141,0.01379,0.0305,0.0363,-0.04521,-0.02018,-0.02205,0.12144,-0.02163,0.05044,0.00735,-0.08698,0.09311,0.03525,-0.01814,-0.04193,-0.03562,0.03138,0.10013,-0.09209,0.07072,-0.0345,0.1776,0.12617,0.00845,0.02077,0.01466,-0.01308,-0.0496,-0.01377,-0.03471,0.00338,-0.12802,-0.01792,0.1142,-0.09289,0.0709,-0.12445,-0.01029,0.01342,0.03927,0.10302,-0.04384,0.05151,-0.13327,-0.07685,0.0702,0.01765,0.03189,0.10536,0.12657,-0.08645,-0.03783,0.07121,0.11829,-0.09038,-0.03602,-0.09177,-0.07113,-0.03656,-0.02742,0.01859,0.00976,0.01506,-0.02563,0.03829,0.08563,-0.08409,-0.10249,0.06447,0.07668,0.08988,-0.02048,0.12335,0.00114,0.02673,-0.05396,-0.03338,0.00747,-0.05722,-0.01801,-0.05655,0.09968,0.02267,-0.03478,0.01001,-0.01776,0.00438,0.01745,0.10471,-0.00281,-0.03898,0.09208,0.06492,-0.05774,-0.04248,-0.04002,0.0183,0.04684,-0.0421,-0.05492,-0.02862,0.00815,0.05184,-0.09961,0.02514,-0.09485,-0.1101,0.06821,-0.0195,0.00013,-0.05069,0.03345,0.08801,-0.02023,0.08563,0.05053,0.00216,0.06728,0.03773,-0.11401,-0.01888,0.05821,-0.06152,-0.04669,0.05474,0.03108,0.05105,-0.11653,0.00183,0.11415,0.01807,-0.00934,-0.03281,-0.06618,0.06038,-0.08386,0.09361,-0.0686,-0.02684,-0.02107,0.03923,-0.04536,-0.0599,-0.01537,-0.06113,0.05511,0.09802,0.06163,0.03987,-0.00249,0.07897,-0.06489,-0.01229,-0.00234,0.02818,-0.0404,0.03734,-0.05166,-0.00351,-0.06384,0.01978,-0.01387,0.04589,0.10379,-0.00945,-0.06186,0.01604,-0.09291,0.00194,0.01632,0.0525,0.01868,-0.05169,0.00442,-0.09132,-0.05646,-0.01301,0.00616,-0.0028,-0.01039,-0.0532,-0.12806,0.10599,0.07638,0.06276,0.0387,0.0054,0.0801,-0.11117,-0.10268,-0.04519,-0.0431,0.09985,0.06961,-0.02091,-0.03017,0.07507,-0.0656,0.03667,0.07993,-0.0457,-0.07884,0.04756,0.00267,-0.08882,0.03187,-0.05582,-0.01515,0.02318,-0.00598,0.09904,0.04329,0.03459,-0.07395,0.15054,-0.01816,0.08603,0.0075,0.01443,-0.09656,-0.07206]},{"domain":"chemical_engineering","key":"chemeng_mccabe_thiele_stages","name":"McCabe-Thiele number of theoretical stages (binary)","package":"chemical-engineering-ai999x","example":"McCabe-Thiele stages: alpha = 2.5, zF = 0.5, xD = 0.95, q = 1.0, xB = 0.05, R = 2.0","v":[0.01685,0.02575,0.02487,-0.00714,-0.04569,0.04369,-0.04989,-0.02059,0.09218,0.03908,0.03477,-0.10519,-0.09614,-0.01,-0.13961,0.02912,0.07184,-0.11444,0.01669,-0.1175,0.0176,-0.05792,-0.07729,-0.09691,0.04282,0.06229,-0.03862,0.00798,-0.04758,-0.09858,-0.02148,-0.11895,-0.02971,-0.07626,-0.03014,0.01416,0.05752,0.04073,0.00855,-0.02338,-0.00408,0.05726,0.00752,0.0381,0.03443,-0.05392,0.0841,-0.00696,-0.07493,0.07816,-0.01374,0.08784,-0.05869,0.01709,-0.03051,0.08312,-0.08684,-0.03383,0.04024,-0.06981,-0.10252,-0.04538,-0.03091,-0.07279,0.06281,-0.06071,-0.02705,-0.02258,-0.10986,0.02522,0.01465,0.0664,0.02501,0.01815,0.05304,0.0607,-0.0767,-0.04382,0.18855,0.17861,-0.13456,0.03644,-0.06231,0.00287,0.09125,-0.01256,0.05959,0.10559,0.02,0.02169,-0.0966,0.02845,0.0631,0.0714,0.01903,0.01136,-0.0951,-0.10388,-0.08554,-0.1125,0.05535,0.00024,-0.05503,0.05375,0.09786,0.04762,0.03391,-0.05907,-0.03774,-0.07156,0.00783,0.00861,-0.0341,0.00962,0.01538,-0.02095,0.04922,0.02599,-0.02988,-0.03451,0.02423,-0.10534,-0.05136,0.05239,0.03562,0.10545,-0.01291,0.02331,-0.0804,-0.0342,-0.11769,0.06838,-0.04498,-0.03325,-0.00054,0.06593,-0.04465,-0.01564,0.01897,0.01945,0.00661,0.0364,0.01557,0.07362,-0.00953,-0.02807,0.03729,0.12118,0.07522,0.03089,0.05491,-0.02141,0.05184,0.03123,0.17473,0.03117,-0.03375,0.05079,-0.10496,-0.06504,-0.06058,-0.05541,0.0182,-0.00464,-0.06234,-0.02107,-0.08646,-0.02675,0.16403,-0.00949,0.05456,0.04494,0.02379,-0.07551,0.17049,0.05499,0.00212,-0.04733,0.01143,0.05828,-0.08112,-0.01533,0.06476,0.052,0.01894,0.0297,0.07264,0.08643,-0.03343,-0.08773,-0.04764,0.01416,0.02158,0.10283,-0.01025,0.07346,-0.02048,0.05121,0.02546,-0.03701,-0.01978,-0.01213,0.02251,0.01252,-0.01526,-0.0495,0.02802,-0.00118,-0.02104,-0.02319,-0.06253,0.01151,-0.01523,0.06427,0.03881,0.02451,-0.04153,0.08735,0.0374,-0.01906,0.07511,0.04151,0.04074,0.1182,-0.01196,0.07867,-0.04584,0.05042,0.03419,-0.07416,-0.10672,-0.1348,-0.13807,-0.00422,-0.04951,-0.07421,0.041,0.04796,0.02464,-0.04297,-0.0424,0.02305,0.04772,-0.0045,-0.03611,0.06205,0.0659,-0.04032,-0.03173,0.11365,0.01452,0.06678,-0.08403,-0.01235,0.10925,-0.09396]},{"domain":"chemical_engineering","key":"chemeng_modified_raoult_bubble_pressure","name":"Bubble-point pressure by the modified Raoult's law (activity coefficients)","package":"chemical-engineering-ai999x","example":"Modified Raoult bubble pressure: x = [0.4, 0.6], gamma = [1.8, 1.2], Psat = [55.0, 30.0], p_unit = kPa","v":[-0.0512,0.02377,-0.04927,0.03853,-0.11213,0.08778,-0.00836,0.0388,0.00977,-0.05969,-0.02392,-0.01861,-0.09485,-0.15736,-0.05912,-0.02922,0.07094,-0.09561,0.04179,0.10609,-0.00782,-0.04223,-0.08526,0.11115,0.0849,0.13146,0.09941,0.0565,0.11418,0.0284,0.01795,-0.02067,0.01615,0.01456,0.05447,0.02434,-0.00805,0.03932,-0.03181,0.05445,-0.00314,0.10303,0.05741,0.02789,0.03107,-0.02143,-0.00415,-0.0258,-0.07091,0.02171,0.03955,-0.05257,0.02575,0.01258,-0.07887,0.03532,-0.07487,-0.05311,0.06366,0.07616,0.05047,0.08792,-0.14975,-0.11797,-0.05111,-0.07983,-0.0598,-0.06191,-0.03739,-0.0603,-0.15087,-0.01143,0.11234,-0.0418,0.06258,0.03644,0.03225,-0.03742,0.00039,0.00327,-0.08507,0.05272,0.0161,-0.01456,0.00738,-0.00568,0.00888,0.09516,0.07498,0.10311,-0.02276,-0.00987,-0.08612,-0.02203,-0.05524,-0.03479,-0.04274,0.00329,0.00875,-0.09848,-0.01505,0.05636,-0.11029,0.02092,0.08029,-0.05192,-0.04104,0.06152,0.06616,0.0412,0.08913,-0.11313,0.02684,-0.05984,-0.04402,-0.12795,-0.00155,0.00409,0.06847,-0.02455,0.01735,-0.02516,-0.06691,-0.05192,-0.06959,0.0642,-0.03815,0.04366,0.0429,0.01466,-0.00821,-0.03491,-0.024,-0.02846,-0.0718,0.00622,-0.14364,0.13553,-0.08051,-0.01951,-0.06294,-0.03205,-0.03111,0.11826,0.08682,0.03897,-0.0277,0.05334,0.09409,0.07979,-0.10097,0.01963,0.10805,0.10765,0.11678,0.05246,-0.04368,-0.08623,0.0073,0.05912,-0.09411,-0.11039,0.04206,-0.01274,0.03009,-0.04416,0.01903,0.10069,0.04545,0.05613,0.01082,0.06172,-0.01932,-0.17549,0.12553,-0.00366,-0.01258,-0.05052,0.10696,0.05732,-0.06199,0.00401,-0.03876,-0.01046,-0.07798,-0.0317,0.00954,-0.05361,0.01281,0.03642,-0.02245,0.03858,-0.01801,1e-05,-0.00637,0.03593,-0.03812,-0.05344,0.05318,-0.00743,-0.07696,0.06727,0.01034,-0.03015,-0.08908,0.0317,-0.06791,-0.01639,0.03496,0.05435,0.08157,0.07374,-0.0159,-0.01146,0.04551,0.00691,0.03384,-0.09625,0.08664,0.04145,0.00595,0.01179,-0.03985,0.13671,-0.11939,-0.07554,0.04487,0.09712,0.00337,-0.01825,0.05176,-0.04246,-0.05235,-0.0366,-0.01413,0.01292,-0.10512,0.05979,-0.02383,0.01456,0.05493,0.06481,0.12193,0.09495,0.0346,-0.0442,-0.03633,0.04098,-0.00396,-0.03724,-0.03651,0.00029,0.0051,-0.00655,-0.02479,-0.01572]},{"domain":"chemical_engineering","key":"chemeng_multicomponent_underwood","name":"Minimum reflux of a multicomponent column (Underwood)","package":"chemical-engineering-ai999x","example":"Multicomponent minimum reflux: alpha = [2.5, 1.0, 0.5], z = [0.4, 0.3, 0.3], xD = [0.9, 0.1, 0.0], q = 1.0, lk = 1, hk = 2","v":[0.039,0.06999,-0.04313,0.08835,-0.14268,0.00409,-0.03098,0.04333,-0.00623,-0.11832,0.00575,-0.10001,-0.06038,-0.04296,-0.15289,-0.01602,0.12479,-0.12961,-0.01894,-0.0533,0.04807,0.04939,-0.0803,0.06806,0.15446,0.15537,-0.03387,0.06976,-0.04414,-0.00222,-0.01664,-0.04698,0.01106,-0.02703,0.03964,-0.00762,0.02355,0.03515,0.00978,0.06617,-0.02618,0.01574,-0.09133,-0.02919,0.01882,-0.01376,0.0487,-0.00812,-0.01607,0.06994,0.04171,0.12385,-0.0437,-0.02401,-0.10613,0.03378,-0.00902,-0.08192,-0.00305,-0.03528,0.02589,0.00919,-0.05085,0.03514,0.08351,0.02414,-0.00681,-0.01581,-0.07719,0.00949,-0.09178,0.05106,0.10968,0.03494,0.01205,0.07855,-0.0347,0.03917,0.1219,0.14414,-0.09107,0.10831,-0.06955,0.01514,-0.00443,0.00481,-0.0073,0.12494,0.00749,0.07526,-0.04694,0.0068,0.07473,-0.03172,-0.0098,-0.04481,-0.02343,0.02843,-0.04012,-0.04388,0.05299,0.05723,-0.04085,-0.01122,0.0519,-0.02243,-0.00511,0.00976,-0.03252,-0.01993,0.06495,-0.06341,-0.00748,0.02623,-0.07287,-0.04387,-0.07845,-0.11046,-0.04774,0.01294,0.07701,-0.02495,0.07381,0.09333,-0.03405,0.01506,-0.01744,-0.04228,0.04522,-0.05149,-0.14831,-0.0222,-0.01468,-0.00113,-0.03724,0.04316,-0.06389,0.04968,-0.00029,-0.01397,0.02463,-0.02231,-0.10933,0.09993,0.01449,-0.04836,0.06178,0.0445,0.14233,0.00644,-0.05034,-0.02845,-0.03827,-0.04427,0.12473,-0.01903,-0.07091,-0.06013,-0.05145,0.01566,-0.09904,-0.00869,0.02242,0.08747,-0.00487,0.0239,-0.0965,0.04507,0.0936,0.00612,0.03634,0.07651,0.10058,-0.06373,0.04514,0.03528,0.05157,-0.00683,-0.04124,-0.01132,-0.13399,-0.01909,0.0111,0.10927,0.06486,-0.03022,-0.05355,0.02797,-0.01878,0.07399,-0.18154,-0.07085,0.0091,0.03491,0.03718,0.05529,-0.00924,0.0333,0.05521,-0.11913,-0.10503,-0.04604,-0.02893,-0.05328,-0.07707,-0.06058,0.01335,-0.01779,-0.03035,-0.04657,-0.01921,0.03736,0.03288,0.12148,0.00216,-0.00636,-0.07823,-0.11594,0.05567,0.01878,0.00678,0.04015,-0.0509,0.0543,0.01774,0.04754,-0.03454,0.08138,0.00636,-0.00171,-0.03624,0.01171,-0.08232,-0.01593,-0.0313,-0.00043,-0.07112,0.1132,-0.01919,0.00581,-0.02761,0.06205,0.10798,-0.07978,0.00873,0.12348,-0.02516,0.07513,-0.09858,0.08944,-0.04658,0.00208,-0.03942,-0.07767,0.1398,0.0358]},{"domain":"chemical_engineering","key":"chemeng_npsh_available","name":"Net positive suction head available","package":"chemical-engineering-ai999x","example":"NPSH available: p_s = 101325.0 Pa, p_v = 2339.0 Pa, rho = 998.0 kg/m^3, z_s = 2.0 m, h_f = 0.5 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coefficients from the NRTL equation","package":"chemical-engineering-ai999x","example":"NRTL activity coefficients: x = [0.3, 0.7], tau = [[0.0, 0.8], [1.2, 0.0]], alpha = [[0.0, 0.3], [0.3, 0.0]]","v":[0.01571,0.02268,0.02287,0.11383,-0.15172,0.04068,-0.01358,0.01488,0.06039,-0.01914,-0.04263,-0.09759,-0.01486,-0.11298,-0.01669,-0.10633,0.08694,0.01451,0.04226,-0.00883,0.10185,-0.00071,-0.08479,0.05435,0.11878,0.06903,0.14478,0.05355,0.03751,-0.00277,-0.05753,-0.05349,0.05274,0.03398,0.09402,0.03863,-0.05268,0.02117,-0.00606,-0.02588,-0.00156,0.02768,-0.05417,0.04246,-0.06938,0.05556,-0.00806,0.0489,-0.0481,0.0364,-0.0426,-0.03223,0.00896,0.05279,-0.02979,0.08018,0.00898,-0.09051,-0.01666,0.04873,-0.0138,0.09951,-0.05401,-0.0569,0.07454,-0.12939,0.05318,-0.02579,-0.10911,-0.10662,-0.11243,-0.03518,0.05965,-0.0697,0.03302,-0.01152,-0.02682,0.02668,0.02558,0.04111,-0.08391,0.0607,-0.04052,-0.02466,-0.01192,0.06099,-0.00824,0.12078,0.02184,0.0824,-0.04348,-0.104,-0.01809,-0.08518,-0.15692,0.00933,-0.18208,-0.12242,0.03875,-0.14721,-0.0114,0.03678,-0.09693,0.04753,0.10511,-0.03768,-0.14784,-0.01246,0.07946,0.05992,0.08005,-0.00087,-0.046,-0.06668,0.03925,-0.13584,0.00863,-0.04079,0.05042,0.01588,-0.03794,-0.00065,0.02686,0.03845,-0.07693,0.03696,-0.06349,-0.007,-0.01163,0.01029,-0.06661,-0.04196,-0.11051,-0.01155,-0.06066,0.03036,-0.12761,0.00769,-0.04465,-0.07703,0.02685,-0.07266,-0.00374,0.09569,-0.0177,-0.02045,-0.00236,0.05344,0.07865,0.04495,0.01249,-0.11439,-0.00471,0.11676,0.0352,0.06877,0.02351,-0.13031,0.04907,0.1122,-0.00816,-0.12621,-0.11607,0.11208,0.03348,0.08528,-0.00289,-0.03407,-0.06417,0.06605,0.09848,0.05829,0.00081,-0.04122,0.01452,-0.01062,0.03916,0.01319,-0.00616,0.02606,-0.04435,0.0095,-0.06767,-0.02594,-0.00336,0.03207,0.03412,-0.00084,-0.03236,0.03207,0.06961,-0.01375,0.01578,0.05065,-0.03742,0.0104,-0.00538,0.04089,0.01208,0.06292,-0.03372,0.02592,0.08064,0.02347,-0.00723,-0.04463,0.05512,0.03358,-0.03736,0.0214,0.04245,-0.03287,-0.00701,0.04259,0.04665,-0.05738,0.00697,-0.11195,0.14177,0.0461,0.06684,-0.02642,-0.04201,0.097,-0.01394,-0.01341,0.09181,-0.04584,0.0451,-0.02106,-0.01698,0.0222,-0.03044,-0.07762,-0.02638,0.01965,0.06432,0.04832,-0.02456,0.03588,0.07593,0.084,0.10006,0.0627,-0.0091,0.04495,0.02188,0.09775,0.05665,-0.00262,-0.06085,0.08752,-0.05229,-0.08363,-0.02404,-0.0627]},{"domain":"chemical_engineering","key":"chemeng_p_control_offset","name":"Proportional control: steady-state offset after a set-point step","package":"chemical-engineering-ai999x","example":"P-only control offset: Kc = 2.0, K = 1.5, taus = [5.0, 2.0], t_unit = min","v":[0.07941,0.0002,-0.03953,-0.05772,0.01931,0.00026,-0.03393,0.01141,-0.04787,-0.00722,0.02712,0.04226,-0.06518,0.09162,0.05014,0.17869,0.00763,-0.05931,-0.11043,-0.03803,0.01664,-0.02465,-0.09312,-0.06804,0.02871,-0.01335,-0.03082,-0.06328,-0.00361,0.00526,0.00813,-0.00012,-0.04487,0.05365,0.00196,0.10613,0.05657,0.06648,-0.08024,-0.00427,0.07395,0.09628,-0.07351,0.11563,0.04068,0.0201,0.0359,0.08043,-0.01606,0.08324,-0.03216,0.0323,-0.03,0.04031,0.07676,-0.03348,-0.01029,-0.02918,0.10327,-0.01595,-0.09506,-0.03483,-0.01544,-0.02504,-0.01052,-0.00775,0.00155,0.03205,0.144,-0.05429,-0.00194,0.0674,-0.12291,0.00896,-0.07827,-0.06443,0.02947,0.01471,0.11077,-0.00103,-0.09632,-0.07226,0.03076,0.08028,0.00178,-0.04219,0.05013,-0.02809,0.02014,0.05357,-0.07564,0.00936,0.02341,0.02568,0.04722,0.06492,-0.05766,-0.09249,0.09387,0.03633,0.01218,0.03227,-0.01249,0.01829,0.04868,0.03263,0.00566,-0.08658,0.01257,0.02942,0.07225,0.0401,0.08156,-0.00279,-0.05112,0.0898,-0.0113,-0.0179,0.00545,-0.03318,0.0004,-0.05219,0.05626,0.03935,-0.07754,-0.03525,0.00118,-0.02165,-0.15311,-0.08502,-0.0658,-0.04563,0.0616,-0.10637,0.06994,0.0447,-0.03749,-0.02068,0.00478,-0.03651,-0.03526,0.04007,-0.00262,-0.07312,0.04222,-0.01835,-0.11263,-0.01665,0.01079,0.05864,-0.0314,-0.02838,0.04468,0.02932,-0.06243,-0.07025,0.08212,0.07596,-0.04763,-0.14551,-0.01641,0.16711,-0.03546,0.04617,-0.01831,-0.00145,0.05691,0.01666,0.045,0.05373,0.0442,0.11794,-0.02449,-0.05171,0.10896,0.0668,-0.02904,0.08598,-0.09595,0.02172,0.0189,-0.01814,0.09323,0.00335,0.0902,-0.02074,0.01923,-0.07103,-0.0973,0.01574,-0.01265,0.06828,0.02746,0.03318,-0.09868,0.06631,-0.01823,0.12731,-0.02669,-0.11267,0.00081,0.06653,-0.12449,-0.09503,0.08172,-0.0428,0.06352,-0.06003,0.03184,-0.0259,0.00695,0.01536,0.05126,-0.00175,0.04808,0.01684,-0.13441,-0.03017,-0.06469,0.04125,0.13575,0.07283,-0.07168,0.05414,0.05784,0.10656,0.04394,-0.01107,0.06652,-0.08137,-0.04845,-0.10828,-0.09561,-0.04643,-0.09415,-0.04853,0.05135,0.02657,0.00182,0.04887,0.01008,-0.09226,-0.00188,-0.06613,0.08078,0.05683,0.09918,-0.00565,-0.176,0.12417,-0.01482,-0.0131,-0.08042,-0.08542,0.06523,-0.03449]},{"domain":"chemical_engineering","key":"chemeng_peng_robinson","name":"Peng-Robinson equation of state: compressibility and fugacity coefficient","package":"chemical-engineering-ai999x","example":"Peng-Robinson: Tc = 507.6 K, Pc = 3025000.0 Pa, omega = 0.2975, T = 400.0 K, P = 1000000.0 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conversion for a volume (first order, liquid)","package":"chemical-engineering-ai999x","example":"First-order PFR conversion: v0 = 0.01 m^3/s, V = 20.0 m^3, k = 0.001 1/s","v":[-0.02127,-0.02441,-0.02377,0.00892,-0.01557,-0.15467,-0.07805,-0.06021,-0.10007,-0.06156,-0.05121,-0.00067,-0.06578,0.00331,0.05711,-0.03615,0.00732,-0.05891,0.03936,0.06307,-0.09747,0.07151,0.0017,-0.05032,-0.06531,0.03559,-0.02148,0.05302,-0.02651,-0.08364,0.0748,-0.04386,0.03174,-0.02769,-0.02018,-0.06594,0.05847,0.00421,-0.06717,0.04545,-0.03154,-0.00203,0.04027,0.04315,0.0922,-0.0566,-0.03619,0.0856,-0.06962,0.00936,-0.01631,-0.01116,-0.01995,-0.11726,-0.02902,-0.08384,0.08521,0.07655,-0.11037,-0.01001,0.08662,-0.09536,-0.03952,0.00274,-0.15531,-0.03375,-0.00488,-0.02556,-0.09829,-0.02532,0.09173,0.00167,-0.04029,-0.0549,0.07208,0.13894,0.07031,0.03893,0.07258,-0.10243,0.02204,0.04984,0.04036,0.07641,0.07721,-0.00373,0.01276,0.03812,0.07318,-0.00341,0.06305,-0.08965,0.08054,0.06571,0.09386,0.07287,0.02919,-0.01669,0.13018,-0.0286,0.02743,-0.07711,0.03002,0.0553,-0.01971,-0.00945,0.01958,0.0225,-0.0205,0.02526,0.01332,0.04824,-0.07155,0.01713,-0.03089,0.06607,0.02112,-0.00178,0.01219,-0.03767,-0.02751,0.01182,-0.04831,0.0118,0.03945,0.00103,-0.01599,0.04199,-0.01982,0.03106,0.02915,-0.03365,0.09328,-0.01819,0.07853,-0.03533,-0.06832,0.01338,-0.02219,-0.05217,-0.02282,0.06828,0.03291,-0.11132,-0.12204,0.03989,-0.09154,0.05336,-0.00624,-0.02261,-0.03517,-0.0035,0.10192,0.03388,0.10329,0.01985,-0.01065,0.05618,-0.01397,-0.09082,0.13776,0.00362,-0.03725,-0.08875,-0.0285,0.02532,-0.01834,-0.02318,-0.10404,0.03089,-0.03736,0.1937,-0.02088,0.01362,0.0821,0.02053,-0.05006,-0.08531,0.06701,-0.12004,-0.01696,-0.01989,0.02484,0.07082,-0.00501,0.08126,0.03273,-0.0578,1e-05,0.0241,0.03491,-0.00332,-0.06619,0.06866,-0.07561,0.11889,0.0329,0.0392,-0.01406,-0.02493,-0.08098,0.00029,-0.01041,-0.08836,0.09132,-0.15111,-0.03305,-0.02286,0.05448,0.01052,0.02907,-0.04459,0.10334,0.00756,-0.01483,-0.08752,-0.10659,0.03086,-0.11153,-0.08442,0.01282,0.04511,-0.00434,0.01839,0.0764,0.0952,0.00049,0.07135,0.13644,-0.00276,0.03125,0.13145,-0.08795,0.02032,-0.00773,-0.03136,0.04568,-0.00819,-0.12097,0.00917,-0.02383,0.01423,-0.07186,-0.05061,0.10356,0.09194,-0.06859,-0.06768,0.04342,0.10442,0.05291,0.13589,-0.1297,0.06472,0.04995,-0.05255]},{"domain":"chemical_engineering","key":"chemeng_pfr_conversion_second_order","name":"PFR conversion for a volume (second order, liquid)","package":"chemical-engineering-ai999x","example":"Second-order PFR conversion: v0 = 0.01 m^3/s, V = 2.0 m^3, k = 1e-05 m^3/(mol*s), CA0 = 1000.0 mol/m^3","v":[-0.07288,-0.01569,-0.03272,-0.11509,-0.00684,-0.10404,-0.06733,-0.06393,-0.07336,-0.04978,-0.0206,-0.08587,-0.01574,0.0095,0.07119,0.00111,0.00025,-0.02071,0.01769,0.06723,-0.01977,0.03046,0.00172,-0.04824,-0.01595,0.01086,-0.0386,0.11723,-0.07152,-0.03209,0.07508,-0.08484,-0.01379,-0.04594,0.09601,0.02446,0.04411,-0.01074,-0.05886,0.04286,-0.01783,-0.07118,0.05182,-0.00443,0.04429,-0.03404,0.06737,0.04653,-0.08971,-0.04493,0.03685,0.03091,-0.04193,-0.07721,-0.11567,0.01381,0.05441,0.10267,-0.11388,0.05287,0.13765,-0.06688,0.02733,0.0514,-0.16808,-0.02326,0.06322,-0.07055,-0.10308,-0.04151,0.12231,-0.01713,-0.03786,-0.02879,0.0054,0.088,0.02164,0.00511,0.06763,-0.0845,-0.04406,-0.01922,0.02943,0.04748,0.0678,-0.01305,0.06934,-0.04084,0.06573,-0.02031,0.00118,0.02749,0.04553,0.06866,0.01411,0.04384,0.0202,-0.02823,0.10895,-0.07695,0.03416,0.00364,0.08199,0.0714,-0.02989,-0.03737,-0.11723,0.02592,-0.03923,0.04553,0.07623,0.0066,0.02036,0.00812,-0.01245,-0.03758,0.08199,0.00786,-0.08348,-0.02985,-0.06204,0.04251,-0.04474,0.07027,0.00138,0.07042,-0.02733,0.05816,0.04765,0.06412,0.04854,-0.09724,0.0351,-0.0521,-0.06964,0.01867,-0.05105,0.01577,0.03055,-0.03413,0.01233,0.09349,0.16748,-0.07076,-0.05811,0.00295,-0.11517,-0.00463,-0.02942,0.06631,-0.02189,0.05792,0.11069,0.05975,0.07641,0.10052,0.00517,0.07647,0.0031,-0.04195,0.08682,-0.00404,0.01738,-0.13089,-0.02804,0.06105,-0.00963,-0.01209,-0.06648,-0.02766,-0.11828,0.15861,-0.1046,0.05044,0.05327,0.00486,-0.02093,-0.02566,0.04971,-0.07411,0.03326,0.03687,-0.06825,0.0518,0.07852,0.07673,-0.03935,-0.00585,0.02661,-0.00092,0.07627,-0.0109,-0.05355,0.04061,-0.01939,-0.02665,-0.03655,-0.03579,-0.02119,-0.03952,-0.00904,0.00423,0.01232,-0.09336,-0.00093,-0.16092,-0.08595,0.03788,0.07411,-0.03502,-0.04721,-0.12815,0.21466,-0.01087,0.05045,0.01257,-0.07564,0.06809,-0.05777,-0.07309,0.11175,-0.08717,0.00431,-0.00621,0.09171,0.05813,0.00117,0.03199,0.07616,-0.01217,0.0159,0.10088,-0.09745,0.01168,-0.04565,-0.0568,0.00837,0.00115,-0.0376,0.00196,0.00224,0.04462,0.00644,0.02516,0.05426,0.10128,-0.10816,-0.09153,0.0529,0.12352,0.00195,0.05792,-0.10037,0.04083,0.04342,-0.02712]},{"domain":"chemical_engineering","key":"chemeng_pfr_gas_volume_first_order","name":"Gas-phase PFR volume with volume change (first order)","package":"chemical-engineering-ai999x","example":"First-order gas-phase PFR volume: FA0 = 10.0 mol/s, CA0 = 40.0 mol/m^3, k = 0.05 1/s, eps = 1.0, X = 0.8","v":[0.02088,0.06812,-0.04044,0.04139,0.04156,-0.09238,-0.03662,-0.02387,0.02475,-0.0373,0.02232,-0.05037,-0.05419,0.07547,0.01611,0.07786,0.08412,-0.04014,0.09312,0.12283,0.08304,0.03327,-0.0658,-0.0171,-0.08897,0.007,0.00884,0.00563,-0.07633,-0.09472,0.02993,-0.08747,-0.0035,-0.00519,-0.04919,0.04853,-0.02108,-0.04351,0.01173,0.07515,-0.01517,0.06239,0.06931,-0.00287,0.12354,0.02916,0.03027,0.073,-0.00901,0.0271,-0.05237,0.07296,-0.0153,-0.03619,0.02964,0.06638,-0.08628,0.05036,-0.05251,-0.08826,-0.0699,-0.14349,-0.05348,0.00785,0.01165,-0.08643,-0.02961,-0.07774,-0.00609,-0.04532,0.06385,0.08574,-0.06409,0.00183,0.06281,0.10078,0.10442,-0.04204,0.07124,-0.03983,-0.04301,-0.0056,-0.03385,-0.00054,0.10659,0.02952,-0.04103,0.04401,0.012,0.00125,0.03577,-0.09044,-0.03927,0.05867,-0.01379,0.06606,-0.03587,-0.03707,0.10962,0.02469,0.04098,-0.04014,-0.05549,-0.01292,-0.01807,0.00099,0.04224,-0.04966,0.14063,0.11496,0.0314,0.05398,-0.0405,0.00888,-0.08643,-0.03323,-0.06024,0.05198,0.02923,-0.00019,0.1091,0.004,-0.08263,0.05249,0.07181,-0.09594,-0.06616,-0.01988,-0.00873,-0.04207,0.01492,-0.01652,0.11317,-0.08441,0.06047,-0.02176,-0.01886,0.00906,0.02284,0.04834,0.07799,-0.02439,-0.02406,0.01086,-0.03093,0.00274,-0.02745,-0.01728,-0.07237,0.04908,0.05942,-0.04198,0.09881,-0.06051,0.06109,0.08607,0.00753,0.07558,0.10531,-0.03285,-0.04205,-0.13037,-0.08534,-0.05661,0.02258,0.07064,0.02065,0.05341,0.03181,0.04017,-0.04263,0.15071,-0.02211,0.06,0.14511,0.07508,-0.02639,-0.09462,-0.01003,-0.06368,0.00504,-0.05111,0.06267,0.04352,-0.05517,-0.01211,0.01539,0.0844,-0.01884,-0.09439,0.04426,0.04881,0.02534,0.07621,-0.0648,0.07083,-0.03629,-0.01703,-0.06857,-0.01272,-0.05645,-0.03225,0.15335,0.05046,0.15488,-0.03837,-0.05916,-0.11507,0.00983,-0.02422,-0.10791,0.01498,-0.00859,0.05494,-0.12229,-0.07153,-0.11548,-0.05705,-0.09269,-0.07001,-0.01452,0.11037,0.05811,0.03653,-0.02972,-0.08069,0.06903,0.10628,0.08506,-0.02667,-0.04532,-0.00688,-0.06136,0.00896,0.01973,-0.02957,0.02672,-0.0245,-0.07645,0.0197,-0.03874,-0.02527,0.01669,-0.08514,0.17929,0.02733,-0.0256,0.02473,0.02413,0.06862,0.01138,-0.02197,-0.15403,0.00415,-0.03012,-0.11852]},{"domain":"chemical_engineering","key":"chemeng_pfr_gas_volume_second_order","name":"Gas-phase PFR volume with volume change (second order)","package":"chemical-engineering-ai999x","example":"Second-order gas-phase PFR volume: FA0 = 10.0 mol/s, CA0 = 40.0 mol/m^3, k = 0.001 m^3/(mol*s), eps = 1.0, X = 0.8","v":[-0.04704,0.08587,-0.04326,0.00614,0.06829,-0.07545,-0.04785,-0.04454,0.02586,-0.02872,0.03368,-0.11386,-0.01219,0.09351,0.0217,0.07258,0.1031,-0.0033,0.08966,0.13552,0.04044,0.01169,-0.02874,-0.06184,-0.0714,0.00251,0.03311,0.03443,-0.09088,-0.06689,0.04233,-0.10346,-0.07776,0.02597,0.00993,0.07384,-0.04875,-0.00315,-0.01122,0.0256,-0.01676,-0.01167,0.09056,-0.01141,0.06682,0.01848,0.09051,0.04316,0.01344,-0.02384,0.00498,0.11535,-0.01202,-0.01052,-0.03401,0.05932,-0.10005,0.08717,-0.08705,-0.04345,-0.03267,-0.16668,-0.02499,0.04412,-0.04635,-0.08104,0.01039,-0.05828,-0.08189,-0.06357,0.09049,0.04591,-0.07903,-0.00345,0.04523,0.06875,0.04851,-0.0318,0.08227,-0.05727,-0.06499,-0.00973,-0.0562,0.05561,0.11325,0.01336,0.01723,-0.03909,0.00367,-0.02326,-0.00413,0.02155,-0.03723,0.13175,-0.01702,0.00984,-0.04134,-0.04954,0.07756,-0.02931,0.06608,0.00519,0.00461,0.00059,-0.02691,0.00391,-0.02297,-0.02599,0.06527,0.13678,0.09655,0.02976,-0.00097,0.00117,-0.0735,-0.10435,0.0084,0.04019,-0.06992,0.02424,0.09693,0.05125,-0.07857,0.05994,0.08579,-0.06857,-0.01457,-0.00741,0.04552,-0.02123,0.01889,-0.08375,0.0495,-0.06315,-0.03329,-0.00494,-0.03887,0.02319,0.05447,0.0805,0.06438,-0.03728,0.0609,0.03613,-0.04777,0.00412,-0.06283,-0.0452,-0.11287,0.07942,0.0664,0.01574,0.10625,-0.03071,0.04446,0.18263,0.02012,0.06972,0.09064,-0.03383,-0.01146,-0.18192,-0.0612,-0.11211,0.00583,0.07729,0.01932,0.03723,0.01597,0.00981,-0.07699,0.1491,-0.00565,0.1004,0.08179,0.03047,0.00012,-0.04822,0.01389,-0.0435,0.03929,-0.00966,-0.02807,0.03894,0.02074,-0.01414,-0.03131,0.09693,0.00357,-0.07285,0.09184,0.05765,-0.00554,0.05144,-0.06283,0.01888,-0.09094,-0.03909,-0.04863,0.02198,-0.00614,-0.01647,0.18478,0.02176,0.07287,-0.05117,-0.05392,-0.05952,0.03494,-0.06776,-0.13115,-0.04043,0.07021,0.02028,-0.05398,-0.0051,-0.1497,-0.02108,-0.06812,-0.08915,0.06132,0.03296,0.03228,0.0385,-0.01709,-0.09296,0.07009,0.05477,0.03854,-0.04393,-0.0222,0.02704,-0.05012,0.00788,0.01494,-0.03937,-0.02645,0.04068,-0.04301,-0.0058,-0.05137,-0.02412,0.04241,-0.03836,0.14941,0.08238,-0.08905,-0.04192,0.02126,0.06502,-0.00604,0.01422,-0.14652,-0.02006,-0.04844,-0.12145]},{"domain":"chemical_engineering","key":"chemeng_pfr_volume_first_order","name":"PFR volume for a conversion (first order, liquid)","package":"chemical-engineering-ai999x","example":"First-order PFR volume: v0 = 0.01 m^3/s, k = 0.001 1/s, X = 0.9","v":[-0.0222,-0.11054,-0.05085,-0.01572,-0.00614,-0.09007,-0.02154,-0.00972,0.0158,-0.04768,0.06223,0.04262,0.00194,0.0255,0.02803,0.00681,0.04913,0.01301,-0.0017,0.06739,0.00286,-0.00157,-0.09759,-0.01508,-0.08817,-0.00871,-0.04363,0.01923,-0.05434,-0.10767,0.03633,-0.07197,0.06552,-0.04545,-0.02254,-0.06666,0.09702,-0.03283,-0.01475,0.15597,-0.03796,0.03376,-0.00215,0.01115,0.12371,-0.06062,0.01905,0.02844,0.01681,0.07522,-0.06929,0.03402,-0.02456,-0.05551,-0.04684,-0.04169,0.04147,0.07341,-0.05615,-0.03943,0.03476,-0.02066,-0.01934,0.12167,-0.08575,-0.03273,-0.02042,-0.09506,0.03193,0.0078,0.09555,-0.00398,-0.10265,-0.05704,-0.00016,0.21126,0.07639,-0.01152,0.09189,-0.00923,0.01125,0.03186,0.05501,-0.04477,0.09626,0.07668,-0.01092,0.08807,0.03468,0.06182,0.03906,-0.13508,0.01597,-0.00649,-0.07563,0.11337,-0.01806,0.00465,0.11794,0.07205,-0.06193,-0.06666,-0.00873,0.00844,0.00288,-0.03107,0.03217,-0.03168,0.0586,0.08199,-0.06183,-0.04166,-0.13793,0.04157,-0.04918,0.01338,-0.07054,0.05797,0.04761,0.02567,0.04906,-0.02031,-0.05193,0.00139,0.03076,-0.1458,-0.05623,0.01918,0.0404,0.02488,-0.03301,0.02666,0.10745,-0.06795,0.06402,-0.01257,0.00519,-0.02071,0.02383,0.00783,0.02875,0.05888,-0.01595,-0.08337,-0.13276,-0.03114,-0.05775,-0.04564,0.07085,-0.03925,-0.00305,0.05054,0.18688,0.01697,0.03729,0.06586,-0.01809,0.08092,0.02055,-0.08201,0.05991,-0.02771,-0.06372,-0.03679,-0.03689,0.06953,0.03488,-0.01199,0.01137,-0.00333,-0.03178,0.1375,-0.12189,-0.00724,0.13722,0.05081,-0.00782,-0.09664,0.03242,-0.08772,-0.02265,-0.0165,0.10147,0.0317,-0.01839,0.04614,-0.00183,-0.00124,-0.01502,-0.04762,-0.04451,-0.02216,0.01944,0.11407,-0.02824,0.09597,0.01614,0.03763,-0.07889,-0.03316,-0.0265,-0.05147,-0.02217,0.01008,0.06611,-0.12988,-0.08464,-0.12777,-0.02595,0.05803,-0.01958,-0.05729,0.04552,0.00334,-0.01624,-0.04588,-0.05034,-0.06369,-0.04673,-0.07875,0.0101,0.09699,-0.01106,-0.02403,0.0943,0.02982,-0.00563,0.1172,0.14221,-0.00701,-0.05761,0.06986,-0.07338,-0.01071,-0.02772,0.0413,0.0942,-0.04096,-0.09735,0.01553,-0.03363,-0.02685,-0.09491,-0.0548,0.14439,0.05848,0.02663,0.01133,0.01991,0.15206,0.00792,0.01175,-0.1191,0.03162,0.03326,-0.01042]},{"domain":"chemical_engineering","key":"chemeng_pfr_volume_second_order","name":"PFR volume for a conversion (second order, liquid)","package":"chemical-engineering-ai999x","example":"Second-order PFR volume: v0 = 0.01 m^3/s, k = 1e-05 m^3/(mol*s), CA0 = 1000.0 mol/m^3, X = 0.8","v":[-0.08052,-0.08602,-0.05077,-0.11868,0.00876,-0.07033,-0.04646,-0.06068,-0.01534,-0.05171,0.04951,-0.06756,0.01665,0.0544,0.02654,0.02628,0.046,0.03471,0.01143,0.07736,0.00698,-0.04414,-0.03058,-0.03368,-0.04734,-0.02634,-0.03317,0.09885,-0.09082,-0.04894,0.02729,-0.11879,-0.00716,-0.04533,0.08353,0.01284,0.03991,-0.00893,-0.02036,0.09577,-0.03311,-0.04719,0.02786,-0.01694,0.06493,-0.05099,0.10832,-0.00433,-0.01639,0.00188,0.01329,0.0468,-0.03341,-0.02556,-0.12087,0.02011,0.02395,0.10752,-0.0868,0.05221,0.11253,-0.02801,0.04376,0.1439,-0.16151,-0.02063,0.01908,-0.10943,-0.02337,-0.02353,0.12245,-0.05698,-0.08726,-0.06396,-0.04193,0.1297,0.01999,-0.01661,0.08167,-0.00388,-0.04929,0.02047,0.04244,-0.00588,0.0774,0.03079,0.05126,-0.00079,0.04782,0.0219,-0.0291,0.03113,0.03961,0.06623,-0.08673,0.04322,-0.04518,-0.02108,0.07878,-0.02628,-0.03431,0.0094,0.04407,0.04141,-0.03323,-0.0581,-0.11273,-0.00438,-0.01088,0.07695,0.02658,-0.0373,-0.02969,0.02478,-0.01717,-0.10255,0.04357,0.0414,-0.06369,0.01575,-0.01033,0.01291,-0.06123,0.04428,-0.00774,-0.04162,-0.0497,0.06495,0.12496,0.04101,-0.00472,-0.06312,0.02773,-0.05861,-0.08285,0.04439,-0.00622,-0.01605,0.06503,-0.00084,0.06303,0.06887,0.14869,-0.05041,-0.09541,-0.04488,-0.10331,-0.08696,0.02276,0.02884,0.01057,0.1377,0.17295,0.07746,0.04233,0.1831,0.00716,0.09714,0.00913,-0.02033,0.05844,-0.04743,-0.00628,-0.08443,-0.04714,0.06401,0.05406,0.00669,-0.02406,-0.03626,-0.11192,0.12163,-0.13118,0.04896,0.08462,0.01087,0.02355,-0.00605,0.02134,-0.06822,0.05189,0.02815,-0.0257,0.03049,0.07499,0.05763,-0.06352,0.02971,0.02176,-0.0151,0.02795,-0.04198,0.00137,0.05761,0.00302,-0.03391,-0.05864,-0.04899,-0.0436,-0.02087,0.04312,-0.00527,0.01614,-0.03632,-0.03819,-0.16286,-0.0774,-0.03438,0.02572,-0.02337,-0.0766,-0.14209,0.20275,-0.01517,0.04549,0.04112,-0.08263,-0.02968,-0.01206,-0.06698,0.13853,-0.04598,-0.01597,-0.0377,0.12287,0.03181,0.01984,0.05661,0.05718,-0.01628,-0.01569,0.09948,-0.08165,-0.02469,-0.07605,-0.00596,0.04158,0.01396,-0.02291,-0.01915,-0.01433,-0.00138,-0.0194,0.03418,0.07262,0.09635,-0.05921,-0.05281,0.00369,0.12629,-0.02539,0.01505,-0.08533,0.02142,0.02769,0.00205]},{"domain":"chemical_engineering","key":"chemeng_pi_loop_margins","name":"Gain and phase margins of a PI loop around lags in series","package":"chemical-engineering-ai999x","example":"PI loop margins: Kc = 1.0, tauI = 5.0 s, K = 2.0, taus = [1.0, 1.0, 1.0], t_unit = min","v":[0.01029,-0.03022,0.02627,0.05229,-0.0147,-0.00682,0.04638,0.00735,0.02433,0.04018,-0.02107,0.08478,0.07254,0.03011,0.01963,0.09129,-0.00531,-0.00945,-0.00082,0.04908,0.04889,-0.04909,-0.11655,-0.14628,0.0901,-0.00334,0.05037,-0.01652,-0.05136,0.09484,-0.06418,0.03295,-0.15695,0.11008,0.03933,0.03403,0.04164,0.02768,-0.05459,-0.03765,0.06022,0.04026,-0.06101,0.04282,0.06319,0.0603,0.092,0.03906,-0.03069,0.01953,-0.09405,-0.00756,-0.00171,0.0802,0.01706,-0.01929,-0.01462,-0.00846,0.07631,0.0593,-0.10456,-0.04766,-0.10197,-0.0196,0.00161,-0.06141,0.00066,0.03248,0.05896,-0.06838,0.08775,0.05892,-0.13582,-0.07834,-0.04141,-0.08445,0.01835,-0.00172,0.03227,0.01306,-0.01685,-0.02939,0.04498,0.07207,-0.01194,-0.00863,0.01799,0.00816,0.09108,0.04664,-0.1012,0.072,-0.03514,-0.03126,0.01458,-0.03455,-0.03729,-0.0616,0.04599,-0.0184,-0.00199,0.0411,-0.02939,0.04173,0.07028,0.00292,-0.06584,-0.09684,-0.02874,0.03991,0.07098,-0.06949,0.07547,0.02933,-0.08923,0.09544,-0.01302,-0.06656,0.02125,0.02528,-0.09421,-0.03431,0.05625,0.05422,-0.00656,-0.10226,-0.00302,-0.0515,-0.18718,-0.03395,-0.04926,-0.03278,-0.01577,-0.0258,0.09111,0.03991,-0.08035,0.03675,0.0935,0.07441,-0.0603,-0.02169,0.05754,-0.06029,-0.0266,-0.07946,-0.07014,-0.01632,0.08639,0.07128,-0.02732,-0.02928,0.01874,0.02666,-0.04475,-0.08042,0.14235,0.04448,-0.00314,-0.078,-0.02508,0.19926,0.01181,0.07256,0.05549,0.02034,0.02024,0.04832,-0.01195,0.14376,0.00717,0.078,0.01724,0.03497,0.08747,-0.00038,0.04929,0.0581,-0.11262,0.04428,-0.03055,-0.08565,0.05138,-0.05276,0.04655,-0.03906,0.04146,-0.13005,-0.11999,0.01162,0.00655,0.08901,-0.07474,0.10769,-0.0994,0.00344,-0.01192,0.07629,0.0383,-0.02834,0.08558,0.05818,-0.06659,0.00515,0.03861,-0.09978,0.10236,-0.1013,0.00797,-0.05797,0.04634,0.00322,0.01353,-0.04652,0.05933,0.07422,-0.17404,-0.02485,-0.03447,0.03693,-0.00113,0.07235,-0.10427,-0.03324,0.02481,0.04033,-0.01536,-0.05901,0.0341,-0.04389,0.01344,-0.0514,-0.09684,-0.10048,-0.02837,-0.03372,0.0124,-0.05765,0.03975,-0.00436,0.02642,-0.06594,0.02238,-0.01309,0.08715,-0.01603,0.08686,-0.15445,-0.07568,0.05256,0.04304,0.07892,0.0216,-0.07697,-0.00633,0.0432]},{"domain":"chemical_engineering","key":"chemeng_pid_controller_output","name":"Discrete PID controller output for an error history","package":"chemical-engineering-ai999x","example":"PID controller output: Kc = 2.0, tauI = 10.0 s, tauD = 1.0 s, dt = 1.0 s, e = [1.0, 0.8, 0.5, 0.3], bias = 50.0","v":[0.05368,-0.00298,0.10264,0.04063,-0.08578,0.02061,0.09366,0.0208,-0.13306,0.03082,0.0864,0.11487,0.001,0.09,0.02946,0.07504,0.05533,-0.01762,-0.08094,0.02957,0.08794,-0.06796,-0.02515,-0.06059,0.09862,0.11342,-0.01062,-0.09788,0.02189,0.00684,-0.03168,-0.03846,-0.03397,0.07376,0.13728,0.05028,0.05654,0.1183,-0.01267,-0.09341,0.08213,0.07493,-0.03225,-0.03313,0.03411,0.01147,0.06786,0.00304,-0.04689,0.03715,-0.07769,-0.03627,0.01495,0.08722,0.07827,-0.04286,0.07149,0.07058,0.0137,-0.00704,-0.06308,-0.03907,-0.03165,0.03889,-0.0488,-0.04297,0.05638,0.03474,-0.04217,0.02975,0.00042,-0.01827,-0.01197,0.13051,-0.03617,-0.01533,0.03729,0.08112,-0.05019,-0.08645,0.06415,-0.0707,0.02412,-0.03773,-0.09288,-0.01112,-0.01301,-0.01613,0.00283,0.00625,-0.02974,-0.03645,0.06285,-0.00224,-0.0428,0.01099,0.10532,-0.11998,0.03357,0.05911,-0.02996,-0.04332,-0.01038,-0.08165,-0.01481,0.05223,-0.0766,-0.057,-0.01295,-0.008,-0.02,-0.01343,0.06111,0.14747,0.01403,0.03839,-0.00321,-0.01723,0.03179,0.05254,-0.08015,-0.02272,-0.04107,0.04262,-0.00849,-0.09249,-0.00894,-0.03101,-0.1557,0.03436,0.04277,0.03186,-0.05339,-0.01011,0.06327,0.10384,0.02414,-0.02347,0.05714,0.03498,-0.08327,0.05734,0.04211,-0.0646,0.03815,0.04644,-0.04176,-0.01673,-0.00176,0.04181,-0.06178,-0.11374,-0.06436,0.05082,-0.01862,-0.03252,0.10891,-0.00208,-0.04491,-0.078,-0.00641,0.10761,0.02261,0.09643,0.05346,-0.02253,-0.10283,-0.0592,-0.04662,0.01887,-0.03899,-0.03234,-0.00354,0.05841,-0.0158,-0.01711,-0.01847,0.11475,-0.15426,0.04527,-0.09917,-0.00572,0.02101,0.03477,0.01192,0.1009,0.06255,-0.09964,-0.04177,0.01528,-0.00365,0.05433,-0.0755,0.04746,-0.05425,0.01048,-0.03325,0.05477,-0.00111,-0.06984,-0.00384,0.00529,-0.09003,0.02563,-0.00348,-0.03782,0.00458,-0.08439,0.10621,-0.08,0.02251,-0.08175,0.0948,0.00469,0.0881,0.00991,-0.11279,0.01932,-0.08068,-0.05201,0.20029,0.06665,-0.02599,0.02055,0.07984,0.03669,0.03894,-0.0452,-0.0345,-0.08812,0.05945,-0.05281,-0.15946,0.01713,0.00426,-0.0451,0.01526,-0.00869,0.08986,0.02096,0.00341,-0.03675,-0.02448,-0.01954,0.03791,-0.01434,-0.06509,-0.06523,-0.186,0.11595,0.04944,0.00614,0.02743,-0.14132,-0.05538,-0.07837]},{"domain":"chemical_engineering","key":"chemeng_pitzer_heat_of_vaporization","name":"Heat of vaporisation from the acentric factor (Pitzer)","package":"chemical-engineering-ai999x","example":"Pitzer heat of vaporization: T = 452.0 K, Tc = 645.6 K, omega = 0.35","v":[0.12781,-0.02872,-0.04545,0.06118,-0.00466,0.00723,0.02556,0.03683,0.06454,-0.0567,-0.02108,-0.09247,-0.0245,0.0391,-0.01913,0.06581,0.07831,0.01865,0.02999,-0.01873,0.10882,-0.01225,-0.17233,-0.03416,-0.03995,-0.08861,0.195,-0.03769,0.10612,-0.05444,-0.06908,-0.02423,-0.02152,0.02599,-0.01719,0.0147,0.06092,0.04033,-0.13371,0.0421,-0.0503,0.00633,-0.02841,0.1312,-0.05468,-0.04791,0.09634,-0.01118,-0.01093,0.01354,-0.01185,-0.09513,0.08321,0.03334,0.06318,-0.13573,-0.03401,-0.02045,0.00647,-0.03059,0.05731,-0.07556,0.00519,0.06479,0.01152,-0.07582,-0.01489,0.05071,-0.10076,-0.02687,0.00501,0.00776,0.04946,-0.03077,0.02706,-0.01342,-0.02367,-0.04926,-0.01493,0.08261,-0.05459,0.07756,-0.05469,-0.02677,0.04723,-0.12294,-0.0656,-0.05743,-0.00115,-0.09932,0.01244,0.05441,0.00396,0.02855,-0.06216,-0.02536,-0.06459,-0.023,0.03193,-0.12447,0.01477,-0.02105,0.02227,-0.02481,-0.03452,-0.05301,0.01461,0.01091,0.10053,-0.03907,0.04998,0.07681,-0.00297,-0.02639,-0.05543,-0.02805,0.02083,0.07243,0.05023,0.03072,0.03208,-0.05069,-0.04828,-0.01525,-0.04927,0.01802,-0.09283,-0.01013,-0.03425,-0.03672,0.01968,-0.05928,0.03465,-0.0228,-0.03054,0.04441,-0.02885,-0.02513,-0.03346,-0.04937,0.12451,-0.02386,0.14176,0.12233,0.06671,-0.01756,-0.0382,0.09949,0.02191,0.01722,-0.03442,-0.02155,0.03369,0.05956,0.00054,0.09924,-0.0535,-0.08498,0.02838,-0.01243,-0.10344,-0.14747,0.03933,-0.00457,-0.00703,0.05753,0.02125,0.04469,0.14183,-0.09917,-0.00452,-0.01755,-0.06122,0.14543,0.04928,0.06941,-0.09185,0.01946,0.11143,0.00956,0.0961,0.04602,0.03932,-0.03016,-0.03042,-0.03965,0.00183,0.07777,-0.15803,-0.02505,0.01576,-0.00475,-0.08462,0.11142,0.02097,-0.00414,-0.00249,0.11341,0.11572,-0.0179,-0.11005,-0.02919,0.01588,0.07711,-0.1007,0.02316,0.03312,-0.05276,0.05732,-0.12834,-0.07478,-0.02958,0.01019,0.04174,0.00208,0.04653,-0.05932,-0.07812,0.07694,0.02254,0.02516,0.0471,0.09861,0.00032,-0.06646,-0.03896,0.0976,0.03352,-0.07054,0.0331,0.01535,0.04638,0.0575,-0.04915,-0.00965,0.0409,0.0337,0.05058,-0.00389,0.04901,0.06128,0.08115,-0.01223,-0.02703,-0.01796,-0.09164,0.08345,0.03074,0.10414,-0.15269,0.02384,0.07582,-0.02227,-0.07985,-0.05153,-0.08719]},{"domain":"chemical_engineering","key":"chemeng_pump_head","name":"Pump total head and power","package":"chemical-engineering-ai999x","example":"Pump total head: p1 = 100000.0 Pa, p2 = 400000.0 Pa, rho = 1000.0 kg/m^3","v":[0.0221,-0.01773,-0.15171,-0.13821,0.10771,0.1175,0.13934,-0.00557,-0.03622,-0.07682,-0.05467,0.03346,-0.08404,0.06775,-0.02109,0.01788,0.05306,-0.01359,0.07435,-0.02438,0.01241,0.02808,-0.07076,0.02165,-0.01966,0.05328,-0.01824,0.01417,-0.00315,0.07867,-0.01631,0.0087,0.05076,-0.11558,-0.12433,0.07832,0.11151,0.02214,0.02461,-0.01818,-0.07951,0.04157,-0.12098,0.02562,-0.00508,-0.01486,-0.00133,-0.09878,0.06658,-0.04382,0.03564,-0.03429,0.04589,0.1021,-0.08508,-0.06794,-0.08561,-0.01584,-0.04657,0.07801,0.05105,-0.0241,-0.05365,-0.08253,-0.02351,-0.05582,-0.04125,-0.01781,-0.0541,-0.07263,0.0613,0.0889,0.06735,0.0013,0.07105,0.0724,0.00652,0.00626,0.01412,0.07929,0.02527,0.03886,0.07896,0.02637,-0.01617,-0.16357,0.12545,-0.01833,0.04185,-0.08481,-0.01823,-0.03183,-0.08411,-0.0171,-0.04292,-0.03667,0.10788,0.02484,0.07857,-0.05326,-0.00203,-0.05013,-0.0239,0.02393,-0.01697,0.01789,-0.0932,0.03552,-0.02962,0.01256,-0.02657,0.00207,0.01961,0.04698,-0.03534,-0.05629,-0.02167,0.07492,0.00877,-0.02742,-0.06555,-0.0502,-0.01297,-0.03061,0.00632,-0.01283,-0.07241,0.0393,0.14482,-0.07227,-0.00168,-0.00136,-0.02465,-0.04729,0.0551,0.0818,-0.00868,-0.01948,-0.06607,-0.0133,0.01,-0.00255,-0.0112,0.06564,0.12948,-0.01105,-0.09029,-0.03879,0.06108,0.01941,-0.08114,0.09591,-0.05908,0.06654,0.03573,0.01258,-0.03753,-0.05076,-0.05401,-0.10585,-0.01564,0.03177,0.07904,-0.01139,-0.01917,-0.03799,0.06579,0.0552,0.07291,0.00034,-0.04299,-0.07977,-0.04177,-0.07963,-0.04466,0.09372,0.03876,-0.04792,0.03399,0.12205,0.05828,-0.00593,0.01946,0.04437,-0.04337,0.03056,0.03795,-0.0877,-0.17883,-0.01568,0.02016,-0.01959,0.03889,0.17237,0.07855,-0.00213,0.04731,0.00808,-0.00968,-0.09526,-0.02242,0.10482,-0.04778,0.11025,0.04453,-0.05576,0.00993,-0.04258,-0.04299,-0.0586,-0.06838,0.01831,0.11604,-0.05666,0.03539,-0.03381,-0.04546,-0.09654,0.07291,-0.07797,0.16179,-0.03826,0.04412,-0.02093,-0.05988,-0.06146,-0.07387,0.10311,0.03448,0.09451,0.08617,-0.02429,0.03094,-0.04162,0.00075,0.16973,-0.03455,0.04161,0.02696,-0.0378,-0.04,0.0405,0.08257,0.10294,0.02474,-0.02514,0.00905,-0.00287,0.07771,-0.07018,-0.04916,-0.02809,0.06201,-0.03951,-0.00012,0.06545]},{"domain":"chemical_engineering","key":"chemeng_rachford_rice_flash","name":"Isothermal flash with given K-values (Rachford-Rice)","package":"chemical-engineering-ai999x","example":"Rachford-Rice flash: z = [0.5, 0.3, 0.2], K = [1.685, 0.742, 0.532]","v":[0.03929,-0.00134,-0.04248,-0.00106,-0.07546,-0.05195,-0.05869,0.04924,-0.00386,-0.10352,0.01111,-0.12269,-0.11601,-0.03351,-0.06148,0.01278,-0.10014,-0.08565,-0.12277,-0.01394,-0.06659,-0.00453,-0.06703,-0.04465,0.03004,0.00786,-0.09035,-0.09986,-0.00724,-0.10515,0.08553,-0.05823,-0.04058,-0.1015,0.07372,-0.05384,0.06904,0.04951,-0.02645,-0.0396,0.08721,-0.00802,0.09996,-0.00701,0.02107,0.00184,-0.01381,-0.00612,-0.06528,0.04355,-0.04769,0.11404,-0.06081,-0.0361,-0.00507,0.0421,-0.02629,-0.10939,0.00367,-0.05088,0.04977,-0.04452,-0.06943,-0.05736,0.02963,0.02541,-0.05111,-0.00164,-0.04799,-0.01902,0.09001,0.02524,0.0143,0.01633,0.01622,0.07543,-0.02572,-0.03444,0.09736,-0.00998,-0.07256,0.05766,-0.06854,-0.01655,0.04022,-0.02181,0.00691,0.03437,0.03931,0.01156,-0.03078,0.02543,0.01222,0.08797,0.01623,0.05576,-0.14309,-0.06599,-0.01191,-0.08293,-0.0083,0.08524,-0.00196,0.06626,-0.01319,-0.05655,0.08329,0.07156,-0.00014,-0.04953,0.06387,-0.10169,0.01425,0.01958,-0.0088,0.06515,0.03006,0.09182,0.11247,0.0115,-0.04181,-0.06588,-0.0079,0.01892,-0.03888,0.11428,0.03669,0.04163,-0.05019,0.01812,-0.03308,0.01646,0.02167,-0.02806,-0.04815,0.00929,-0.04238,0.14115,0.00091,-0.02328,0.07657,0.08126,-0.01573,0.03545,-0.04392,0.08424,-0.06608,0.15617,0.08056,0.06571,-0.00072,-0.04844,0.08256,0.03874,0.07389,-0.05646,-0.0084,0.03808,-0.0423,-0.11615,-0.0066,-0.08667,-0.02424,-0.11188,0.03469,0.07078,-0.05661,0.10449,0.14717,0.05765,0.07164,0.09048,-0.01259,0.06251,0.11163,0.04457,0.01034,-0.04624,0.02972,-0.04824,-0.03494,0.05344,-0.02466,-0.00664,-0.04595,-0.0456,-0.05196,0.14598,0.06152,0.05191,-0.04327,-0.02755,-0.01824,-0.01382,0.04623,0.09413,0.14942,0.07233,-0.06681,0.05263,-0.01068,-0.01451,0.05878,-0.04736,-0.12474,-0.16033,-0.08214,0.00654,0.02924,-0.01408,-0.02584,0.0289,-0.00369,0.1008,-0.01648,-0.01925,0.05307,0.05506,0.00344,-0.05688,0.06893,0.02283,0.00716,0.17717,0.02163,0.04066,0.0356,0.04813,0.08673,-0.01999,-0.13116,-0.04712,-0.07763,-0.02505,-0.03566,-0.14285,-0.02632,0.01579,0.02886,0.01731,0.11073,-0.01073,0.0948,-0.01716,0.05793,-0.02707,0.00384,0.00878,0.03909,0.00029,-0.03612,0.05257,-0.14958,-0.06601,0.02926,-0.03477]},{"domain":"chemical_engineering","key":"chemeng_rackett_liquid_volume","name":"Saturated liquid molar volume (Rackett)","package":"chemical-engineering-ai999x","example":"Rackett liquid volume: T = 272.03889 K, Tc = 369.83 K, Pc = 4248000.0 Pa, Zc = 0.2763","v":[-0.10437,-0.05071,-0.12931,0.04436,-0.05533,0.06005,0.07959,0.00815,0.12417,0.09224,0.05529,0.00271,0.03539,-0.04829,0.02251,-0.02548,0.06513,-0.0248,0.07084,0.04794,0.04174,0.04916,-0.16148,0.00837,0.03721,-0.05704,0.08495,-0.00922,0.0577,-0.14449,-0.05129,-0.08833,-0.0367,-0.05736,0.02884,-0.04344,0.1011,-0.01439,-0.02708,0.01842,0.00856,-0.02865,0.06315,-0.03935,-0.00146,-0.05668,0.0577,-0.07414,-0.05544,-0.06436,0.00737,-0.05559,-0.0186,-0.09963,0.03962,0.03511,-0.1341,0.00809,0.06853,0.04566,0.05031,0.01043,-0.02903,0.0676,0.03096,-0.02483,-0.08091,0.02424,-0.1501,0.03467,0.01974,0.026,0.02088,0.13619,0.06112,0.02205,-0.00721,-0.12333,0.05729,0.08206,-0.07766,0.14636,-0.04347,-0.0167,0.04564,0.05101,-0.0816,-0.00567,0.04114,-0.17122,0.06455,0.00207,-0.09203,0.05581,-0.08878,-0.01106,-0.04858,-0.16042,0.08837,-0.06136,0.02973,-0.03051,0.0121,0.00026,-0.08167,-0.00964,-0.0038,0.08838,0.02828,0.00544,0.00848,-0.03748,-0.09177,0.03367,-0.04183,-0.00046,-0.04775,0.04531,0.0063,-0.0109,-0.01583,-0.10953,0.00573,0.01343,-0.03068,-0.06885,0.03585,-0.06928,-0.06906,0.07006,1e-05,-0.01469,-0.01841,-0.04444,-0.00959,0.04516,0.03644,0.0628,-0.03038,-0.04637,0.04375,0.01922,0.05447,0.14457,-0.01987,0.03884,0.04518,0.01494,0.01582,-0.00164,0.00815,-0.03248,0.1112,-0.05303,-0.06805,0.03681,-0.0359,0.00135,-0.06783,-0.03188,-0.0306,-0.06911,0.12199,-0.02585,0.02511,0.17372,0.00436,0.02132,0.12327,-0.01733,0.02116,0.05745,-0.08394,0.03633,0.05271,-0.03613,0.06564,-0.02269,0.08756,-0.05994,-0.01704,0.04586,0.11199,0.00759,0.02173,0.00762,0.06381,0.14048,-0.0241,-0.00715,0.04543,-0.04227,-0.04118,0.00205,0.04362,0.06315,-0.05741,0.09647,-0.02932,0.03994,-0.11861,-0.00746,-0.0531,0.00568,-0.03524,-0.05611,-0.07386,0.01574,-0.03414,-0.0736,-0.0265,-0.01742,0.11803,0.00296,-0.0212,0.07313,-0.06724,-0.07444,0.04938,-0.0572,0.02075,-0.02834,0.03942,-0.02953,0.00908,0.07447,0.04346,0.01651,-0.06469,0.0852,-0.01775,-0.05097,0.02917,-0.17083,-0.05352,-0.04568,0.04,-0.02459,0.01014,0.02041,0.08305,-0.01507,0.02569,0.01385,0.06319,0.09477,0.10662,0.04519,0.1474,-0.00714,0.03143,0.05628,-0.02836,0.0012,-0.12506,-0.06619]},{"domain":"chemical_engineering","key":"chemeng_radial_darcy_flow","name":"Steady radial flow of oil to a well (Darcy) and productivity index","package":"chemical-engineering-ai999x","example":"Radial Darcy flow: k = 9.869233e-14 m^2, h = 9.144 m, mu = 0.0015 Pa*s, pe = 20684271.879505083 Pa, pw = 17236893.232920904 Pa, re = 304.8 m, rw = 0.09144000000000001 m","v":[0.09072,-0.0712,-0.07657,0.03937,-0.06348,0.01345,-0.00473,0.01527,-0.0241,0.02828,0.09219,0.00111,0.09203,-0.04597,-0.01903,0.11436,-0.02449,-0.00717,-0.02574,-0.02046,0.0035,-0.01754,0.01656,-0.04422,-0.09507,-0.05242,-0.07119,-0.05376,-0.03084,-0.05304,0.06182,-0.00243,0.00761,-0.0317,-0.05412,-0.01364,0.02299,0.04404,-0.02125,-0.05993,0.01793,0.05443,-0.07148,0.0612,-0.04294,0.0234,0.00983,-0.05339,-0.02464,-0.06087,-0.0135,0.06381,0.0338,0.04613,0.02009,0.05995,-0.02813,-0.02478,-0.05182,0.03168,0.05189,-0.10104,-0.04584,-0.01302,-0.05694,0.08465,-0.0717,-0.00413,-0.0854,-0.00827,0.07812,-0.01353,-0.03236,0.0152,0.03427,0.00712,-0.02758,-0.05245,-0.10703,0.0074,-0.05458,0.09261,0.08238,-0.0418,0.04329,-0.11266,-0.05546,0.02737,-0.10812,0.03571,-0.03701,-0.00632,-0.05299,0.03971,0.05054,0.04811,-0.00319,0.01615,0.09765,-0.02339,0.01714,0.01117,0.04615,0.06248,0.08821,0.08868,0.11211,-0.07749,0.04662,0.10236,0.05632,-0.047,0.00898,-0.0152,-0.01633,-0.00612,0.07238,-0.05321,0.03999,-0.08347,0.14132,-0.05115,-0.05026,0.06683,-0.09601,-0.04683,-0.16409,0.08784,-0.00247,-0.00411,-0.04152,-0.02616,0.14683,-0.02685,-0.03773,-0.01218,-0.08477,0.05746,-0.02597,0.02595,-0.04084,0.03238,-0.03904,0.0119,0.1187,0.00932,-0.05776,-0.08434,0.02825,-0.13146,-0.01813,0.119,0.01617,0.08298,0.04179,-0.03954,0.06688,-0.02348,-0.01734,-0.04866,-0.02831,0.0043,0.02034,-0.04716,-0.07987,-0.03436,-0.0195,-0.01285,0.00048,-0.00243,0.06531,0.18642,0.0745,0.01722,0.0724,0.10473,-0.00921,0.03001,0.10532,0.00143,-0.0282,-0.01092,-0.13017,0.015,0.06095,0.06555,-0.00674,0.00722,-0.11293,-0.07278,0.04648,0.02711,0.00053,0.03046,-0.03988,0.04052,0.03753,0.12406,0.04348,-0.11829,-0.00788,0.05865,0.00734,0.07504,-0.04661,-0.08658,-0.0077,0.09393,0.04992,-0.00276,0.16281,0.12064,0.09038,0.06014,-0.05722,-0.11913,-0.1247,-0.09645,-0.00366,-0.05419,0.09675,-0.05706,-0.01964,0.02833,-0.00835,0.01534,-0.07668,0.01777,0.04037,0.0192,-0.20562,-0.08096,0.05282,0.08705,-0.0379,-0.10228,0.03015,0.05828,0.01288,0.08936,0.01489,0.0853,-0.00544,-0.07143,-0.06941,0.09456,-0.07631,-0.00833,0.03039,0.01962,0.08985,-0.05431,-0.04691,0.03426,-0.07411,-0.00325]},{"domain":"chemical_engineering","key":"chemeng_raoult_bubble_pressure","name":"Bubble-point pressure (Raoult's law)","package":"chemical-engineering-ai999x","example":"Bubble-point pressure: ant = [[6.90565, 1211.033, 220.79], [6.95464, 1344.8, 219.482]], units = mmHg_degC, base = log10, x = [0.4, 0.6], T = 368.15 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temperature (Raoult's law)","package":"chemical-engineering-ai999x","example":"Bubble-point temperature: ant = [[6.90565, 1211.033, 220.79], [6.95464, 1344.8, 219.482]], units = mmHg_degC, base = log10, x = [0.4, 0.6], P = 101325.0 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pressure (Raoult's law)","package":"chemical-engineering-ai999x","example":"Dew-point pressure: ant = [[6.90565, 1211.033, 220.79], [6.95464, 1344.8, 219.482]], units = mmHg_degC, base = log10, y = [0.4, 0.6], T = 368.15 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temperature (Raoult's law)","package":"chemical-engineering-ai999x","example":"Dew-point temperature: ant = [[6.90565, 1211.033, 220.79], [6.95464, 1344.8, 219.482]], units = mmHg_degC, base = log10, y = [0.4, 0.6], P = 101325.0 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flash of an ideal mixture (Raoult's law)","package":"chemical-engineering-ai999x","example":"Raoult isothermal flash: ant = [[6.90565, 1211.033, 220.79], [6.95464, 1344.8, 219.482]], units = mmHg_degC, base = log10, z = [0.5, 0.5], T = 368.15 K, P = 101325.0 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of reaction at another temperature (Kirchhoff)","package":"chemical-engineering-ai999x","example":"Heat of reaction at temperature: nu = [-1.0, -3.0, 2.0], cp = [[27.27, 0.004927, 0.0, 0.0], [27.01, 0.003509, 0.0, 0.0], [24.62, 0.03753, -7.1e-06, 0.0]], dH0 = -92220.0 J/mol, T0 = 298.15 K, T = 700.0 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with recycle and purge","package":"chemical-engineering-ai999x","example":"Recycle and purge balance: F0 = 100.0 mol/s, zA = 0.98, X = 0.25, f = 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reactor with recycle: conversion (first order)","package":"chemical-engineering-ai999x","example":"Recycle reactor conversion: v0 = 0.01 m^3/s, V = 20.0 m^3, k = 0.001 1/s, R = 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of vaporisation at the normal boiling point (Riedel)","package":"chemical-engineering-ai999x","example":"Riedel heat of vaporization: Tb = 294.0 K, Tc = 466.0 K, Pc = 5550000.0 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distribution: mean, variance and tanks-in-series number from tracer data","package":"chemical-engineering-ai999x","example":"RTD moments: t = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0], C = [0.0, 1.0, 5.0, 8.0, 10.0, 8.0, 6.0, 4.0, 3.0, 2.2, 1.5, 0.6, 0.0], t_unit = 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heat with a polynomial heat capacity","package":"chemical-engineering-ai999x","example":"Sensible heat with polynomial cp: n = 10.0 mol, a = 29.0, b = 0.002, c = 0.0, d = 0.0, T1 = 300.0 K, T2 = 500.0 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equation of state: compressibility and fugacity coefficient","package":"chemical-engineering-ai999x","example":"Soave-Redlich-Kwong: Tc = 507.6 K, Pc = 3025000.0 Pa, omega = 0.2975, T = 400.0 K, P = 1000000.0 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of A through stagnant B (Stefan film)","package":"chemical-engineering-ai999x","example":"Stefan diffusion flux: D = 2.6e-05 m^2/s, P = 101325.0 Pa, T = 298.15 K, L = 0.1 m, yA1 = 0.0313, yA2 = 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coefficients from the UNIQUAC equation","package":"chemical-engineering-ai999x","example":"UNIQUAC activity coefficients: x = [0.3, 0.7], r = [2.1055, 0.92], q = [1.972, 1.4], tau = [[1.0, 0.9], [1.1, 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well-mixed tank (concentration change)","package":"chemical-engineering-ai999x","example":"Unsteady mixing tank: V = 10.0 m^3, q = 0.01 m^3/s, C_in = 500.0 mol/m^3, C0 = 0.0 mol/m^3, t = 1000.0 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or draining well-mixed tank (variable volume)","package":"chemical-engineering-ai999x","example":"Variable-volume tank: V0 = 1.0 m^3, q_in = 0.002 m^3/s, q_out = 0.001 m^3/s, C_in = 1000.0 mol/m^3, C0 = 0.0 mol/m^3, t = 1000.0 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of vaporisation at another temperature (Watson)","package":"chemical-engineering-ai999x","example":"Watson heat of vaporization: T = 298.15 K, T_ref = 373.15 K, Hvap_ref = 40656.0 J/mol, Tc = 647.1 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coefficients from the Wilson equation","package":"chemical-engineering-ai999x","example":"Wilson activity coefficients: x = [0.3, 0.7], Lam = [[1.0, 0.5], [1.5, 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velocity","package":"civil-engineering-ai999x","example":"Chezy velocity with Chezy C = 55 m^0.5/s, hydraulic radius = 1.1 m and slope = 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network flows by the Hardy Cross method (Hazen-Williams)","package":"civil-engineering-ai999x","example":"Hardy cross network with pipe list = [1-2, 2-3, 3-4, 4-1, 2-4], lengths = [600, 500, 600, 500, 780], diameters = [300, 250, 200, 250, 200], C factors = [120, 120, 120, 120, 120] and node demands = [0, 0.04, 0.05, 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type III design flood","package":"civil-engineering-ai999x","example":"Log pearson iii design flood with annual maxima = [420, 380, 510, 290, 640, 455, 370, 520, 600, 330, 880, 410] and return period = 100 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n from a Chezy coefficient","package":"civil-engineering-ai999x","example":"Manning n from chezy with Chezy C = 60 m^0.5/s and hydraulic radius = 1.2 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flow in a part-full circular pipe","package":"civil-engineering-ai999x","example":"Manning flow in a partially full pipe with diameter = 0.6 m, depth = 0.3 m, slope = 0.005 and Manning n = 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discharge in a rectangular channel","package":"civil-engineering-ai999x","example":"Manning discharge in a rectangular channel with width = 3 m, depth = 1.2 m, slope = 0.001 and Manning n = 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from steady pumping (Thiem, confined aquifer)","package":"civil-engineering-ai999x","example":"Thiem confined transmissivity with pumping rate = 2500 m^3/d, first distance = 15 m, second distance = 60 m, first drawdown = 2.8 m and second drawdown = 1.1 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conductivity from steady pumping (unconfined aquifer)","package":"civil-engineering-ai999x","example":"Thiem unconfined conductivity with pumping rate = 1500 m^3/d, first distance = 20 m, second distance = 80 m, first head = 18.2 m and second head = 19.6 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rainfall by Thiessen polygons","package":"civil-engineering-ai999x","example":"Thiessen polygon rainfall with gauge x = [2, 8, 5], gauge y = [2, 3, 9], rainfall = [45, 60, 38], boundary x = [0, 10, 10, 0] and boundary y = [0, 0, 10, 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problem (Hazen-Williams)","package":"civil-engineering-ai999x","example":"Three reservoir problem with levels = [120, 90, 40], lengths = [2000, 1500, 2500], diameters = [400, 300, 350] and C factors = [120, 120, 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channel: area, wetted perimeter, hydraulic radius","package":"civil-engineering-ai999x","example":"Trapezoidal channel section with width = 4 m, depth = 1.5 m and side slope = 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base conversion (binary, octal, decimal, hexadecimal)","package":"electrical-engineering-ai999x","example":"Convert 1011 from binary to 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operating point of a voltage-divider biased BJT","package":"electrical-engineering-ai999x","example":"A voltage-divider biased BJT has VCC = 12 V, R1 = 10 kohm, R2 = 2.2 kohm, RC = 3.6 kohm, RE = 1 kohm, beta = 100 and VBE = 0.7 V. Find the collector 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response (Bode magnitude and phase) at one frequency","package":"electrical-engineering-ai999x","example":"Find the Bode magnitude of G(s) = 10/(s+1) at 1 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of two Boolean expressions","package":"electrical-engineering-ai999x","example":"Is (A·B)' equivalent to A' + B'?","v":[-0.01646,-0.06572,-0.03859,0.10882,-0.01484,-0.00307,0.09832,0.0164,0.07726,0.1006,0.09129,0.02706,-0.08449,-0.01512,0.04748,-0.18357,0.06355,-0.17923,0.11237,-0.07973,0.00052,-0.01699,0.09242,0.12516,-0.02799,-0.01457,-0.06162,0.05239,-0.09215,0.1134,-0.08703,0.00067,-0.04161,-0.00533,0.05427,0.081,-0.02704,-0.01303,0.0753,0.00553,0.0271,0.07992,0.04946,-0.06133,-0.02273,-0.14754,-0.00915,0.06794,-0.00642,0.11392,-0.08672,0.05712,0.02984,-0.03053,-0.03044,0.1097,0.00779,0.07319,0.023,0.05901,-0.08821,-0.0153,0.00929,-0.08132,-0.11943,0.05463,0.13107,-0.02386,0.10435,-0.03937,0.01918,0.00597,0.04203,-0.09427,-0.00987,-0.0402,-0.0285,-0.10311,0.02994,0.01236,-0.00264,-0.02786,0.01463,-0.04917,-0.07188,0.03422,0.07933,-0.01853,-0.07065,0.10163,0.02982,0.02453,-0.01091,0.04518,-0.04373,-0.12859,0.08299,0.06802,-0.04673,0.07023,0.00445,0.00152,-0.06369,0.0947,-0.00479,-0.03018,-0.05885,-0.04468,-0.13645,-0.02294,0.0487,-0.03225,-0.03457,0.0098,-0.00612,-0.00503,-0.01551,0.02656,0.04356,-0.00655,-0.08738,-0.00073,-0.06495,-0.00531,0.06028,0.06865,-0.02202,-0.00839,0.06008,-0.02026,0.09543,-0.05856,-0.13728,-0.04378,-0.02127,-0.05602,-0.05637,0.04019,-0.04108,-0.02647,0.01481,-0.08718,-0.0529,0.00406,0.02096,0.08469,0.07041,0.06839,-0.04278,0.0109,0.00085,0.07345,0.01849,-0.06305,0.03455,-0.08609,0.04984,-0.0148,0.04216,-0.0826,0.0745,-0.02837,0.05206,-0.06909,0.08028,-0.04088,-0.07088,0.01851,0.0916,0.0366,-0.04415,0.0231,-0.0443,-0.00362,0.02603,0.06086,-0.03798,-0.0246,-0.02294,-0.15197,-0.06335,0.04874,-0.05678,-0.0398,-0.0174,0.02207,0.05198,0.05819,-0.12439,0.01629,0.01647,0.12068,-0.06006,0.06804,-0.05725,-0.10991,-0.04697,-0.04182,0.05739,-0.07043,-0.018,0.01553,-0.06078,-0.0109,0.07605,0.05875,-0.0727,0.01538,0.07393,0.02817,-0.05526,-0.09202,-0.12491,0.01598,-0.00548,0.0236,0.02755,0.01556,-0.02661,0.10017,0.09307,-0.03973,0.04719,-0.06841,0.06644,0.00225,0.04302,-0.04139,0.14758,0.00167,0.00923,0.12192,0.0191,0.04528,0.06765,-0.03792,0.01004,-0.02856,0.09503,-0.03316,-0.02886,-0.00403,0.03313,0.03062,0.04839,-0.09668,-0.06451,-0.04051,0.00108,0.09256,0.00695,0.11486,0.01476,-0.02177,-0.0227,0.02979]},{"domain":"electrical_engineering","key":"boolean_evaluate","name":"Evaluate a Boolean expression","package":"electrical-engineering-ai999x","example":"Evaluate A AND (B OR NOT C) for A=1, B=0, C=0.","v":[-0.0056,-0.07415,-0.07702,0.00854,0.14827,-0.01809,0.08343,0.00618,-0.0031,0.03975,0.10084,-0.01594,0.04687,-0.0377,0.07988,-0.02877,0.05556,-0.17878,-0.02124,-0.03746,-0.07732,-0.19316,-0.02374,0.12886,-0.0413,-0.0152,-0.0154,0.07068,-0.06147,0.06019,-0.10461,-0.05201,-0.00622,-0.02613,0.00736,0.01754,0.00305,-0.07066,0.10001,0.0038,0.00969,0.00389,0.03989,0.0002,0.05546,-0.08886,0.02157,-0.01167,-0.01115,0.02168,-0.06696,-0.0838,0.03243,-0.18682,0.00351,0.07845,0.03684,0.03263,0.03321,0.07279,-0.07334,0.00928,-0.02838,-0.10757,-0.12204,0.05702,0.03919,0.03926,0.00096,0.0097,0.02144,-0.01938,-0.028,-0.0798,0.01912,-0.0802,0.00094,-0.06308,-0.01999,0.04816,-0.03481,0.07836,0.01445,-0.05393,-0.04554,0.07952,0.0473,0.00661,0.03797,0.04133,0.10609,-0.02011,-0.00239,0.01405,-0.02177,-0.04681,0.00685,0.09356,0.02158,-0.02305,-0.02888,0.02837,-0.04603,0.06657,0.00238,-0.0066,-0.07262,-0.09672,-0.05819,-0.02915,0.10013,0.01762,-0.09966,0.07556,0.08441,-0.02774,-0.03618,-0.00445,0.11322,-0.05286,0.05553,-0.02501,-0.15106,-0.04731,0.1085,0.01745,-0.02381,-0.00829,0.0258,-0.10427,0.098,0.02272,0.04731,-0.12938,0.01392,0.05064,0.01901,-0.01533,0.04196,0.062,0.0339,-0.04341,-0.03834,0.01351,-0.08829,0.01799,0.04017,0.0568,-0.03534,-0.04119,-0.02272,0.04224,-0.01782,-0.03202,-0.04556,0.02087,0.04775,0.02018,0.07988,-0.05845,0.03233,0.0027,-0.01481,-0.02557,0.12046,0.00025,0.0263,0.08663,0.09253,0.00018,-0.01684,-0.0646,-0.04677,0.13282,-0.00203,0.00739,-0.09926,-0.09064,0.03021,-0.04265,0.03559,0.08014,0.0278,-0.07439,-0.00124,-0.03677,0.06633,0.10559,-0.15208,-0.01638,0.02231,-0.14234,-0.11073,-0.03365,-0.05791,-0.10249,-0.00189,0.04731,0.05428,0.02911,-0.05762,-0.0326,-0.05549,-0.02283,0.10269,0.0307,-0.03282,0.10471,0.11382,0.05817,-0.04235,0.01813,0.00455,-0.02821,-0.00078,0.00073,0.09522,0.05565,0.01764,0.08484,0.07316,0.03591,0.04926,-0.08237,0.05228,-0.07065,0.16389,0.01392,0.11685,-0.01713,0.09733,0.03778,0.04492,0.06953,-0.0433,0.00613,0.03639,0.03966,0.07271,-0.02807,-0.04424,0.04707,0.05929,0.01811,0.01197,-0.10772,-0.03204,0.02086,-0.03005,0.00771,0.12545,-0.02387,0.04546,0.01171,0.00963,-0.09836]},{"domain":"electrical_engineering","key":"closed_loop_poles","name":"Closed-loop poles with unity negative feedback","package":"electrical-engineering-ai999x","example":"Find the closed-loop poles of G(s) = 2/(s^2 + 3s).","v":[0.00412,-0.14019,-0.03327,0.04627,-0.00226,-0.06026,-0.02499,0.00585,-0.05278,-0.0784,-0.06153,0.08979,0.07238,0.11955,-0.00607,0.09949,-0.06087,-0.07376,0.02514,-0.03272,0.0119,-0.04167,0.01222,-0.0412,0.14514,-0.03651,-0.02048,0.01564,0.02727,0.07256,0.03434,0.05586,-0.02882,0.01693,-0.12732,0.00796,0.00408,-0.00751,0.10807,-0.04637,0.06365,0.02375,0.0306,0.13022,0.04168,0.08367,0.04767,0.01533,0.14322,0.10933,-0.0013,-0.05839,0.05177,0.07136,-0.00796,0.0207,-0.12586,0.09526,0.07132,0.0067,-0.06224,-0.02167,-0.07386,-0.13155,-0.03377,-0.08277,0.02151,-0.089,0.07695,-0.07051,0.03638,0.05566,-0.12723,-0.01173,0.06759,0.02922,-0.0811,0.04285,0.05265,0.0596,0.04511,-0.06045,-0.00378,0.0382,-0.01778,0.04273,0.05345,0.00927,-0.00328,-0.04632,-0.05905,0.02983,0.04266,-0.01194,0.04414,0.04679,-0.02689,0.00943,0.01089,0.01097,0.0231,-0.01863,-0.07045,0.10023,0.04414,-0.03001,0.09817,-0.0668,-0.02236,0.06618,0.04442,0.07401,0.04622,0.06873,-0.0425,0.09661,0.03488,-0.02462,0.01802,-0.01426,0.0751,-0.00113,0.04279,0.04452,-0.09198,-0.02023,0.05079,0.00389,-0.09948,-0.07769,-0.06688,-0.04404,0.04672,-0.11162,0.07541,0.07253,0.02261,-0.02792,0.00314,-0.02399,0.06203,0.01232,-0.06576,0.02219,0.03816,0.00874,-0.01317,-0.0123,0.12531,0.00991,0.02181,-0.00908,-0.0006,0.02945,-0.05579,-0.08089,0.0045,0.03677,-0.11919,-0.02784,0.02607,0.09545,-0.0344,-0.02764,0.03577,0.05084,0.00507,0.0035,0.06633,0.00934,0.11524,0.02034,0.00796,0.04607,-0.00187,-0.01228,-0.04307,-0.09431,-0.04918,0.11822,-0.1143,-0.08377,-0.04315,0.01191,0.03127,-0.09315,-0.00846,-0.04168,-0.0342,0.05603,-0.06078,0.09012,0.05769,-0.04619,-0.06196,0.00929,-0.02201,0.09047,0.07197,-0.05336,-0.04256,0.1516,-0.06405,-0.02613,0.168,-0.03357,0.02344,-0.10759,-0.04887,-0.08698,0.05814,0.06724,0.09295,0.0166,0.04238,0.10338,-0.12109,0.04083,-0.0127,-0.00488,0.01776,0.0784,-0.05974,0.01701,-0.10173,0.11088,-0.0097,-0.10979,0.02891,-0.04817,-0.02026,-0.05333,-0.06815,-0.16966,-0.09857,0.03471,-0.03671,-0.1432,0.03794,-0.03119,0.04438,0.03283,-0.00559,-0.01538,0.05998,-0.07579,0.02305,-0.07148,-0.08869,-0.01727,0.00722,0.04459,-0.0794,0.00528,0.05584,0.00373]},{"domain":"electrical_engineering","key":"complex_power","name":"Complex, real, reactive and apparent power from voltage and current phasors","package":"electrical-engineering-ai999x","example":"Find the complex power for V = 230∠0° V and I = 10∠-30° 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and observability of a single-input single-output system","package":"electrical-engineering-ai999x","example":"Is the system with A = [[0, 1], [-2, -3]], B = [0, 1], C = [1, 0] controllable and observable?","v":[0.03198,-0.08519,-0.01657,0.12497,-0.08119,-0.11258,0.00083,-0.0349,0.00936,-9e-05,0.06943,0.03089,-0.04377,0.02969,0.07726,0.02284,-0.04252,-0.12436,0.07391,0.0386,-0.02098,0.0172,0.02685,0.02642,0.01484,-0.08886,0.09544,-0.06622,-0.0065,0.06923,0.00797,0.0104,-0.0311,0.07016,-0.02403,-0.03698,0.00227,0.0812,-0.03562,-0.03597,0.15614,-0.01602,0.05853,-0.01846,0.04346,-0.09762,0.02796,-0.00807,-0.13708,0.05788,0.12315,-0.0339,-0.01808,0.0396,0.05429,0.05878,0.05739,0.01062,0.02973,0.05852,-0.03621,0.09979,-0.03134,-0.01529,-0.02373,0.0216,0.05601,0.04281,-0.00266,-0.00518,0.00491,0.02502,-0.0735,0.23191,0.04187,-0.0536,-0.03239,-0.03243,0.06007,0.00588,-0.0657,-0.08658,-0.04851,-0.18826,-0.03289,-0.00315,-0.04327,-0.0978,0.05955,0.05693,-0.09477,-0.03566,0.02528,-0.0535,0.01339,0.00638,0.04427,-0.03721,0.04558,0.16556,-0.03821,-0.00348,-0.03109,-0.07298,0.02862,0.05682,0.03536,-0.08414,-0.03186,0.01165,-0.07001,0.08721,0.0426,0.04556,-0.04145,0.10209,-0.0039,-0.08158,-0.05256,0.02988,-0.02841,-0.07534,0.03948,-0.05442,-0.04617,0.01371,0.07075,-0.00045,0.01976,0.09009,-0.01772,-0.07281,0.00333,0.01215,0.01896,-0.08828,0.0181,0.04906,0.06605,-0.08274,-0.13859,0.06677,0.04832,-0.00617,-0.084,-0.01566,-0.03564,0.02453,0.02803,-0.04966,-0.0356,-0.11194,-0.05815,0.03014,-0.0044,-0.06924,0.10743,0.03225,-0.04953,-0.01369,0.05262,0.01413,-0.00092,-0.10581,0.06873,0.06571,-0.05721,0.05006,0.02212,-0.00553,0.02122,0.00184,-0.04643,-0.04936,-0.03608,-0.1525,-0.00981,0.09895,-0.07544,0.04534,0.03165,0.02701,0.032,0.03988,0.03836,0.09524,0.01565,0.00564,-0.01565,0.12659,0.04092,-0.01653,0.00754,-0.09372,-0.15632,-0.03772,-0.02987,-0.04343,-0.06403,0.07537,0.00352,-0.05622,-0.00773,-0.08055,-0.01239,-0.15227,-0.03426,0.07863,-0.02129,-0.01618,-0.05494,-0.06857,-0.04519,-0.01369,0.1131,-0.08811,-0.04936,0.0371,0.00224,0.02757,0.16441,-0.04803,-0.08124,0.13868,0.05206,0.09161,-0.04063,-0.09241,-0.01143,-0.05624,0.01443,0.06678,-0.0195,-0.02483,0.03612,-0.05875,0.04856,-0.00191,-0.01489,0.0362,0.01746,-0.01727,0.03562,-0.05862,0.01134,0.10914,0.06042,-0.00213,-0.06274,0.11414,-0.02862,0.10287,0.03728,-0.01847,0.01677,-0.00996]},{"domain":"electrical_engineering","key":"current_divider","name":"Current divider","package":"electrical-engineering-ai999x","example":"Find the branch currents of a current divider with I = 6 A, R1 = 4 ohm, R2 = 2 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speed and current of a permanent-magnet DC motor","package":"electrical-engineering-ai999x","example":"Find the steady-state speed of a DC motor with V = 12 V, R = 1 ohm, Kt = 0.05, Ke = 0.05, T = 0.02 N*m, b = 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voltages of a DC resistive circuit from its netlist","package":"electrical-engineering-ai999x","example":"Find the node voltages of the circuit: V1 1 0 12; R1 1 2 1000; R2 2 0 2000.","v":[-0.08558,-0.07483,0.10167,-0.07664,-0.02657,0.03088,0.03939,-0.00878,0.01673,0.02521,0.03813,-0.05545,-0.0918,-0.01213,0.02352,0.02336,0.0259,-0.04367,-0.08886,0.01361,-0.06925,-0.03136,-0.01439,0.11683,-0.04014,0.05279,-0.02675,0.00321,-0.01508,0.00758,-0.14619,-0.03141,-0.06294,-0.08959,0.03027,0.08811,0.02263,-0.06808,0.0847,0.03364,0.02346,0.0533,-0.04423,-0.03432,-0.05387,0.0163,-0.07897,0.0115,-0.00183,0.09458,0.0117,-0.04248,-0.07676,0.0217,0.0297,-0.05599,-0.02107,0.01703,0.02443,0.0413,0.05473,0.18936,-0.04855,-0.05002,0.07344,0.09958,0.06143,-0.05217,0.03209,0.02605,-0.09213,0.04062,-0.03908,0.00542,0.01708,0.04011,-0.22493,0.02023,-0.02611,0.06147,-0.0249,-0.01376,0.03933,0.02613,-0.03052,0.00585,0.07974,0.03983,-0.06539,-0.04567,0.14654,0.04783,0.01755,0.01658,-0.03539,0.01284,-0.06451,0.02747,-0.057,-0.0399,-0.10145,-0.10801,0.08213,-0.10209,0.04084,-0.04331,0.07091,0.00722,-0.01991,-0.00304,0.08374,-0.03539,-0.1461,0.08315,-0.00249,-0.06009,0.01636,-0.03282,0.08647,0.02653,0.02355,-0.01617,-0.03139,0.01098,0.07377,-0.05371,-0.06037,0.00236,0.02575,-0.03658,0.00332,0.05213,-0.08472,-0.01198,-0.10717,0.03976,-0.04016,0.05479,-0.06209,0.02122,-0.08717,0.02648,-0.10488,-0.06871,0.02565,-0.0528,0.08122,-0.07749,0.04079,-0.00239,-0.0575,0.09891,0.01853,0.12894,-0.01405,0.06612,-0.03395,0.01762,-0.00816,0.04553,-0.02668,-0.03271,-0.00629,-0.01475,-0.00472,0.02632,0.00909,0.02118,0.01821,-0.03987,-0.03042,0.01675,-0.00686,-0.13941,-0.00695,0.00273,-0.14156,-0.0366,-0.05562,-0.16119,-0.07026,0.05517,0.04198,-0.04363,-0.0996,0.10533,0.05141,0.01184,-0.02311,0.06117,0.01434,-0.01908,0.06946,0.12992,-0.03189,-0.04123,-0.06464,0.09466,0.08296,0.01935,-0.08013,-0.02326,0.00113,0.00985,-0.05857,0.01564,-0.02048,0.00554,0.0485,0.04958,0.09797,-0.0104,-0.03775,0.05391,0.1561,-0.01296,-0.00717,0.0038,0.00471,-0.0745,0.11926,0.0958,-0.00441,0.03075,0.00455,0.00767,-0.05025,0.04233,0.07255,0.06495,0.0249,-0.02208,-0.07266,0.0174,-0.09528,-0.10676,-0.05915,0.02722,0.09417,0.05088,0.10537,-0.0121,-0.01955,-0.03117,0.05262,-0.05594,0.07614,-0.02262,0.08075,0.24409,-0.04502,-0.02076,0.00239,0.05925,-0.01061,0.06512]},{"domain":"electrical_engineering","key":"delta_to_wye","name":"Delta-to-wye (Pi-to-T) resistor transformation","package":"electrical-engineering-ai999x","example":"Convert a delta with Rab = 10 ohm, Rbc = 20 ohm, Rca = 30 ohm to a wye.","v":[0.09188,0.06802,0.02113,0.00471,-0.07195,0.12057,-0.00256,-0.09339,0.1069,-0.0154,0.02628,-0.0685,-0.17195,0.0977,-0.0488,-0.03376,0.07855,-0.0884,-0.11796,0.01106,-0.04291,-0.08701,-0.09109,0.05714,0.08462,-0.01284,-0.0082,-0.05806,0.00862,0.10365,-0.05732,0.00252,-0.08626,0.05131,0.08505,0.08372,-0.01491,-0.01483,-0.03473,-0.07004,0.03916,0.03158,0.05495,-0.05936,-0.09379,-0.12112,-0.03412,-0.05522,-0.00748,0.07402,0.03752,0.06013,-0.06757,-0.04009,0.0971,-0.01416,-0.01415,-0.02816,-0.03602,0.00384,0.00842,0.09537,0.03412,-0.0306,0.11014,0.00683,-0.01427,-0.02185,-0.04362,0.01277,-0.03097,0.06109,-0.01848,-0.05991,-0.06614,-0.09543,-0.17655,0.0052,-0.02189,-0.01731,0.0179,-0.06262,-0.02817,0.1021,-0.00164,0.02592,-0.00327,-0.11015,-0.05514,-0.06192,0.00982,0.04189,0.02465,0.06767,-0.0073,0.01389,-0.00777,0.01831,-0.12651,0.05125,0.00431,-0.00336,0.10978,0.00436,0.03361,0.01602,-0.04272,0.04226,0.01805,0.14285,0.03264,-0.06212,-0.07031,-0.10993,-0.08254,0.04474,0.02091,-0.05704,0.05457,0.01289,-0.01965,0.0583,-0.04839,-0.03765,0.03488,0.08845,-0.03246,-0.05606,0.0385,-0.11592,-0.0288,-0.03769,0.00298,-0.02776,-0.19853,-0.05058,-0.07592,-0.03849,-0.01334,0.05008,-0.07021,-0.03759,-0.06101,-0.09549,-0.01612,-0.02763,0.03746,0.03312,0.00892,-0.0789,0.03733,0.023,0.01973,-0.01248,0.13049,0.03325,-0.03959,-0.07818,0.07345,-0.05629,-0.02031,0.07673,0.02672,0.11005,0.10532,-0.03231,0.05315,0.07666,0.00213,0.05742,0.05724,0.05255,0.02579,-0.08021,-0.00331,0.04094,-0.00545,0.02867,-0.00042,-0.06126,0.00479,-0.06424,-0.05255,0.02377,-0.02015,0.06514,0.085,-0.01054,0.01717,0.06497,-0.00219,0.06973,0.13708,0.06092,0.02987,-0.0486,0.01243,-0.011,0.01662,0.09919,-0.07752,0.06161,0.06768,0.06862,-0.01078,0.05257,0.02884,-0.06939,0.01565,-0.04466,0.06103,0.07906,-0.16109,0.0388,0.01176,-0.05732,0.01382,-0.06737,-0.07744,0.06389,0.08688,0.05133,-0.10628,0.0652,0.08986,-0.0109,-0.05525,0.054,0.1011,-0.01917,0.05947,-0.04823,-0.01883,0.10062,-0.03648,-0.06512,0.00778,0.07033,0.04422,0.05841,0.02757,-0.00551,0.04233,-0.11673,-0.03978,0.08369,-0.05925,0.04,-0.02067,0.0853,0.04459,0.04982,-0.0086,0.07923,-0.07272,-0.06953]},{"domain":"electrical_engineering","key":"difference_amplifier","name":"Difference amplifier output (four-resistor op-amp circuit)","package":"electrical-engineering-ai999x","example":"A difference amplifier has R1 = 10 kohm, R2 = 100 kohm, R3 = 10 kohm, R4 = 100 kohm, V1 = 1 V and V2 = 1.5 V. Find the output voltage.","v":[-0.00235,0.07841,0.0062,0.10511,-0.08326,0.02033,-0.00583,0.03612,0.07231,-0.01323,0.07596,0.00979,-0.04768,7e-05,0.01959,-0.09166,0.02328,-0.00744,-0.11359,0.0665,0.0896,-0.07179,0.07975,0.06722,0.03718,-0.05213,0.00464,-3e-05,0.02753,0.07576,-0.04126,0.03235,-0.13182,-0.0301,0.00334,0.12569,0.03115,0.00306,0.09792,0.00611,0.12158,-0.00597,-0.06406,-0.04924,-0.04716,0.00613,-0.00519,0.03436,0.06432,0.05402,-0.01173,0.09518,0.00834,-0.04474,-0.00792,0.04064,0.05079,0.01569,0.15872,0.02027,-0.05547,0.04847,0.06163,-0.09187,0.117,0.04231,0.07378,-0.05687,0.06741,0.0182,0.00406,0.08665,0.00967,0.06294,-0.11439,-0.06392,-0.00678,-0.0008,0.0621,0.00177,0.04763,-0.03114,-0.05154,-0.07857,-0.07565,0.02934,0.0103,0.01262,0.03546,-0.01927,0.02882,0.04727,0.08386,-0.01135,0.01095,0.04018,0.09484,-0.04113,-0.06663,-0.14035,-0.04783,-0.01859,-0.02805,-0.11606,0.0332,-0.05445,-0.05638,0.00318,-0.0873,-0.01394,-0.02401,0.03308,-0.02105,0.02619,-0.03195,-0.01492,0.07678,0.01354,0.02994,0.02819,0.02072,0.04331,-0.06243,0.1352,0.02897,0.01169,-0.13176,-0.02556,-0.01722,-0.05874,-0.0616,-0.00447,-0.08623,-0.09661,0.07812,-0.08169,-0.02988,-0.09256,0.02962,-0.11802,-0.11781,-0.04206,0.00675,0.024,0.0801,-0.08378,0.06913,0.02711,0.07334,-0.02081,-0.12805,0.07715,-0.1263,0.05417,-0.00079,0.02178,0.04118,-0.00669,0.03998,-0.05547,0.00467,-0.11728,-0.09886,-0.0174,0.03562,0.04873,-0.14151,0.01026,0.02836,-0.02556,-0.16623,0.03757,0.10238,-0.03362,-0.02632,-0.0098,-0.12751,-0.10016,0.09548,-0.00163,0.00951,-0.02538,0.07375,-0.01594,-0.0267,0.10296,0.12166,-0.00101,0.00855,-0.07396,0.02322,0.0919,0.02894,0.00398,0.072,-0.10782,-0.15384,0.00929,6e-05,0.07348,-0.05399,-0.00846,-0.03835,0.03057,-0.01306,-0.02935,-0.05646,0.05713,-0.01235,0.07958,0.03522,0.0693,0.00104,0.01642,0.06117,0.03921,0.01439,0.09763,0.08586,-0.04861,0.1324,0.05461,0.07589,-0.05474,0.07005,-0.07639,-0.04857,0.02739,-0.03946,-0.02875,0.00298,-0.05164,-0.02595,0.08686,-0.05754,-0.07065,0.0304,-0.03432,-0.02502,-0.02092,-0.04537,-0.00141,0.05262,-0.01852,0.06894,0.11286,-0.11416,-0.06307,-0.03492,0.08395,-0.02567,0.0293,0.06014,0.03772,0.00632,0.03607]},{"domain":"electrical_engineering","key":"diode_circuit","name":"Operating point of a diode in series with a resistor (Shockley equation)","package":"electrical-engineering-ai999x","example":"Find the current of a diode circuit with Vs = 5 V, R = 1 kohm, Is = 1e-14 A, n = 1, VT = 25.85 mV.","v":[0.01201,-0.04501,0.06043,-0.08986,0.03473,-0.0509,0.01006,0.03203,-0.07997,-0.01511,-0.02836,-0.05618,-0.10947,-0.06477,0.04271,0.07942,-0.12132,-0.0424,-0.15336,0.07443,0.02569,0.03071,0.02141,0.06339,-0.05873,-0.01883,-0.07545,-0.02712,0.07055,-0.01704,-0.0416,0.00326,0.04913,-0.02315,0.0387,0.10569,0.04974,-0.05616,0.06323,0.01287,0.041,0.07076,0.00532,-0.11084,0.00743,-0.03304,-0.04508,0.10023,0.03133,0.01897,0.04012,0.04149,-0.0206,-0.09125,0.04986,-0.0089,-0.02422,0.08797,0.00617,0.04186,0.02324,0.08907,-0.02928,-0.05631,0.10325,0.03874,-0.03136,-0.05076,-0.07802,0.13575,0.03039,-0.00674,0.01251,0.00064,0.00944,-0.00796,-0.10887,-0.02612,-0.02746,-0.02668,-0.02979,0.0674,-0.10796,0.06192,0.02378,-0.0355,0.03135,-0.02638,0.04594,-0.04049,0.03953,0.00832,0.12502,0.00633,0.03503,0.07841,0.01965,0.03301,0.06659,-0.04461,-0.02104,-0.01069,0.03203,-0.07553,-0.03462,-0.09069,0.10324,0.13969,-0.0204,-0.04364,0.04176,0.02492,0.01454,0.00182,0.05037,0.05582,-0.07927,-0.02275,0.0365,-0.08644,0.01041,-0.02731,-0.02983,-0.01882,0.02684,0.01397,-0.12489,-0.00343,-0.04273,0.05713,-0.07218,0.01231,-0.03853,-0.08251,0.14087,0.13609,-0.03294,-0.00556,-0.10064,-0.07722,-0.08679,0.04752,0.03237,-0.01423,0.10342,0.02308,0.04074,-0.01802,-0.02681,0.04389,-0.02292,0.06007,0.02074,0.06868,-0.00684,-0.04301,-0.03534,0.04142,-0.01911,-0.04266,-0.01751,-0.08666,0.02357,-0.17125,-0.01229,-0.06371,-0.08871,-0.08586,-0.08018,-0.0607,-0.12536,0.10267,0.01787,0.02918,0.05968,0.01186,-0.17946,-0.0479,0.04429,-0.08025,-0.00401,0.0896,0.01285,-0.00833,-0.10538,0.03959,0.11491,0.12426,-0.00827,0.02091,0.12151,0.00606,-0.01364,-0.05882,0.08402,-0.03301,-0.01489,0.13771,0.07358,-0.00087,-0.09215,-0.07371,0.06643,-0.05956,0.0438,0.02669,-0.08342,0.06994,0.0425,0.03719,0.09482,0.04616,0.1038,-0.03878,0.12519,-0.04206,-0.06113,0.07313,-0.06696,-0.06693,-0.03832,0.06835,0.03554,-0.0501,0.03448,0.04681,-0.01664,0.11125,0.039,0.02067,0.04289,-0.05478,-0.13803,-0.06177,-0.0439,-0.04363,-0.0178,0.06156,0.10615,0.02543,0.04568,0.02989,0.02663,-0.0014,0.03051,-0.02896,-0.0414,0.00956,0.00822,0.07874,0.0842,0.03134,0.01112,-0.00104,0.03509,-0.12735]},{"domain":"electrical_engineering","key":"first_order_time_to_value","name":"Time for a first-order response to reach a value","package":"electrical-engineering-ai999x","example":"How long does a first-order response with V0 = 0 V, Vf = 10 V, tau = 2 ms take to reach v = 5 V?","v":[0.02298,0.01616,0.02973,-0.00171,-0.04666,-0.03652,0.10395,-0.0133,0.01636,-0.06859,0.08916,0.10153,0.00806,0.02026,0.09737,0.04622,-0.05602,-0.06515,-0.03362,0.01081,-0.01023,-0.03533,-0.04874,0.02879,0.16981,0.0266,0.00151,-0.01275,0.0359,0.01351,0.04022,0.05806,-0.00365,-0.05434,0.00602,-0.00636,0.1173,0.10218,0.02108,0.10931,0.06026,0.08483,-0.02731,-0.07184,-0.04165,0.00537,0.00654,0.01646,0.06612,0.01357,-0.11399,-0.02128,-0.14584,-0.08106,-0.01207,-0.03491,0.09454,0.07259,-0.0245,-0.01607,-0.08376,0.04261,-0.02866,0.0196,0.03148,-0.09116,-0.01401,0.03956,0.05816,-0.03131,-0.03723,0.07654,-0.07059,-0.05878,0.01321,-0.06598,-0.07414,0.01469,0.01378,0.00331,0.02899,0.02058,0.0032,0.03778,-0.04021,0.05216,0.02887,0.00645,0.09611,-0.00726,0.06637,-0.0126,-0.02591,-0.17201,-0.04687,0.02088,0.05859,-0.07295,-0.0311,0.10616,-0.01972,-0.02,0.00214,-0.08517,-0.00759,0.06791,0.00112,-0.06081,0.16688,-0.00265,-0.07594,-0.05754,-0.12037,-0.00409,-0.0714,0.11366,-0.02591,0.01326,0.00563,0.11598,0.00843,-0.02604,0.01454,-0.02835,-0.03023,0.03873,-0.04745,-0.01181,-0.05904,0.05121,0.00435,0.04257,0.04186,0.04485,0.07698,-0.08159,0.07148,-0.01606,0.1286,0.05148,0.07452,0.08884,0.11284,-0.07386,-0.1871,-0.09583,-0.00425,-0.00273,0.0609,0.09317,-0.05586,-0.09951,0.10164,-0.07901,-0.09563,-0.06177,-0.01735,0.01509,-0.01096,-0.11927,-0.02702,0.01565,0.04058,0.07583,-0.04175,-0.06856,-0.04494,-0.00476,0.08221,0.03644,-0.05088,0.0985,-0.03376,-0.02371,-0.00671,-0.10211,-0.06203,0.04056,0.03469,-0.08525,-0.07887,-0.04157,0.15028,-0.04035,-0.0812,-0.0169,-0.00373,0.00702,-0.07271,0.09752,-0.07013,-0.08887,-0.0047,-0.01078,0.00727,0.01099,0.01748,-0.06457,-0.00187,0.03523,-0.06349,0.02253,0.009,0.01411,0.00447,-0.07076,0.06231,-0.09039,0.04014,0.04827,0.02079,-0.00837,-0.03746,-0.06411,0.01815,-0.02224,0.02871,-0.07844,-0.10131,0.02781,-0.04805,0.10039,-0.02425,-0.05221,0.04516,0.00306,0.08266,0.0846,0.07719,-0.11214,0.02613,-0.01058,-0.11748,-0.01594,-0.07709,-0.0051,-0.04708,0.0365,0.03892,0.06069,-0.06781,0.01884,-0.03329,0.00236,0.16399,0.00673,0.04741,-0.06106,-0.04817,0.14136,0.01683,-0.0347,-0.12678,-0.03498,0.05356,0.0183]},{"domain":"electrical_engineering","key":"first_order_transient","name":"First-order (RC or RL) transient response","package":"electrical-engineering-ai999x","example":"Find the first-order transient value with V0 = 0 V, Vf = 10 V, tau = 1 ms, t = 2 ms.","v":[-0.01955,-0.02037,-0.01698,-0.05146,-0.04279,-0.01272,0.01777,-0.00365,0.00415,-0.03727,-0.00596,0.08574,-0.04289,0.02047,0.12147,0.01581,-0.03701,-0.14339,-0.08827,-0.08144,0.01543,-0.02314,-0.03199,0.06037,0.09366,-0.01714,0.01423,-0.01895,0.03264,-0.06997,0.01989,0.07175,0.0331,-0.09739,0.0216,0.06698,0.09703,0.03959,0.04613,0.06484,0.04769,0.01836,-0.01444,0.0566,-0.03286,-0.06184,-0.00699,0.00779,-0.01482,0.04104,-0.12947,-0.04662,-0.05575,-0.12938,0.07319,-0.00716,0.07865,0.02161,-0.00336,-0.00811,-0.0703,0.0091,0.04604,-0.03217,0.02177,-0.00268,-0.08267,0.04016,0.04147,-0.04947,-0.0339,0.08104,-0.03031,-0.02094,0.00279,-0.11445,-0.07666,0.03133,0.00021,0.03681,0.01141,0.03084,0.02601,0.05596,0.01774,0.01226,0.03649,0.02045,0.01687,-0.02201,0.07275,-0.0457,-0.04476,-0.04366,-0.06574,0.05001,0.0016,-0.12869,-0.02354,0.01115,-0.04296,-0.05384,0.03283,0.0048,0.02565,0.02528,0.08223,-0.06502,0.19825,0.01174,-0.01426,-0.01595,-0.12792,0.09596,-0.04778,0.10563,0.00853,-0.0428,0.06546,0.08077,0.02465,-0.10059,-0.03168,0.0222,-0.10296,0.06608,-0.03106,-0.02106,-0.10674,0.04379,-0.0143,-0.00541,0.04449,0.00667,0.03728,-0.07679,0.06388,-0.04764,0.01471,-0.01961,0.05264,0.03289,-0.01451,-0.07983,-0.13236,-0.04446,0.0299,0.0315,0.05094,0.04963,-0.07414,-0.07495,0.09821,-0.01645,-0.11915,-0.08461,0.01519,0.04433,-0.00872,-0.10623,-0.02797,-0.02715,-0.01613,0.09547,-0.06645,-0.05532,-0.06066,-0.03459,0.06408,0.01371,0.01408,0.096,0.01691,-0.03921,0.00648,0.00382,-0.105,0.02816,0.05038,-0.08945,0.02071,0.0551,0.17474,-0.07034,-0.052,-0.09106,-0.00517,0.04561,-0.05457,0.0953,-0.02624,-0.03755,0.02445,-0.00922,0.06197,0.07928,0.0303,0.03141,0.0233,-0.05446,-0.07659,0.04663,-0.097,0.00261,0.04717,-0.06477,0.06377,-0.08186,0.0766,0.03357,0.11054,0.0536,0.0378,-0.00319,0.00896,-0.09708,-0.0405,-0.1027,-0.16735,-0.01918,0.09803,0.11995,0.01226,0.04325,0.04975,0.08397,0.09035,0.04539,0.10461,-0.05459,0.01013,-0.07345,-0.0724,0.04412,-0.15179,-0.02176,0.01657,0.00874,0.03969,0.07261,0.03785,0.02912,-0.00238,-0.00491,0.09301,0.03859,0.1093,-0.01481,-0.06204,0.17784,0.0816,0.00386,-0.16812,-0.00834,0.0108,-0.04712]},{"domain":"electrical_engineering","key":"gain_margin","name":"Gain margin and phase-crossover frequency","package":"electrical-engineering-ai999x","example":"Find the gain margin of G(s) = 10/(s(s+1)(s+5)).","v":[0.06628,0.00439,0.04135,0.10731,-0.05124,-0.00561,-0.07772,0.04387,0.06617,-0.06085,-0.12708,0.03383,0.0432,0.06028,-0.02814,0.13882,-0.00969,-0.03797,0.003,0.00871,-0.05413,-0.03881,-0.06038,-0.07323,0.11932,0.0417,0.03722,-0.10566,-0.09519,0.1077,-0.00266,0.11745,-0.09868,0.07207,-0.11894,0.02154,0.01351,-0.00173,0.00916,-0.09259,0.01205,-0.00473,0.02344,0.18061,0.07453,0.0695,0.08258,-0.00684,-0.03185,0.08591,-0.03909,-0.02862,0.05281,0.07892,-0.0306,0.14225,-0.09335,-0.00436,0.00263,-0.02246,-0.10335,-0.04635,-0.01908,-0.16151,0.02123,-0.16466,0.0591,-0.03429,-0.07955,-0.1025,0.14292,0.09509,-0.09025,-0.10641,0.0081,-0.05841,-0.05211,0.05262,0.05207,0.09286,-0.01354,0.03417,-0.01187,0.04718,-0.01699,0.07987,0.03237,0.08309,0.06742,0.00595,-0.0446,0.03421,0.0682,-0.06743,0.00905,0.02148,-0.12058,0.01376,0.05955,-0.00838,-0.04277,0.02394,-0.00747,0.00777,0.10727,-0.08497,0.08169,0.04016,-0.03557,0.08248,0.01039,-0.06534,0.00928,-0.03404,-0.06783,0.13788,0.02126,-0.08882,0.0647,-0.12378,0.00078,0.03992,0.04491,0.07996,-0.05998,-0.01927,-0.02198,-0.03522,-0.16671,-0.06432,-0.0536,-0.00352,-0.04227,-0.03067,0.06368,0.05952,-0.07883,0.02554,0.08131,-0.04003,-0.02308,-0.01723,-0.01411,0.02685,0.00428,-0.03236,-0.01457,-0.0821,0.13504,0.03271,-0.01602,-0.06376,-0.01124,0.06651,-0.11914,-0.11508,0.05418,0.05144,0.04936,0.03237,0.03245,0.07818,0.01745,0.00603,0.10918,0.02562,0.01376,-0.0166,0.08091,0.06042,0.07981,0.0271,0.00144,0.00428,0.0528,-0.02987,0.04193,0.01588,0.01379,0.06599,-0.06575,-0.038,-0.00456,-0.054,0.03497,-0.10147,-0.051,-0.02216,-0.03287,-0.01238,-0.0496,0.03377,-0.06137,0.00056,-0.05111,0.04754,0.01995,0.13267,-0.02865,-0.03068,0.00894,0.08256,-0.04053,-0.0138,0.06795,-0.01902,0.04232,-0.06384,-0.00012,-0.02459,0.01275,0.04774,0.01558,-0.04577,0.01065,-0.02592,-0.09449,0.0099,0.01984,0.04284,0.0168,0.0939,-0.0703,0.05634,-0.07915,-0.03688,-0.00563,-0.00943,0.0897,0.0543,-0.00934,0.0019,-0.05543,-0.12149,-0.00968,-0.02881,-0.0247,-0.09348,0.01357,-0.05828,0.04346,-0.02347,-0.00701,-0.07733,0.06639,-0.02925,0.05323,-0.0424,0.01426,-0.07673,0.00866,-0.0092,-0.03627,-0.01414,0.1041,0.02145]},{"domain":"electrical_engineering","key":"gray_code","name":"Binary to Gray code and Gray code to binary","package":"electrical-engineering-ai999x","example":"Convert the binary number 1011 to Gray code.","v":[0.05626,-0.01541,0.04652,0.01282,0.15325,0.01331,0.0581,-0.09275,-0.08041,-0.00485,-0.04223,0.01707,0.04197,-0.0479,0.00387,-0.01943,0.02491,-0.05485,-0.11268,-0.00543,-0.08691,-0.10353,-0.06371,0.04497,0.06278,-0.02494,-0.03153,-0.00038,-0.06223,0.03994,-0.04044,0.01671,-0.10914,-0.03534,-0.06298,0.03788,-0.12629,0.08337,0.08842,-0.10712,-0.01068,0.01609,0.13687,-0.10172,0.0557,-0.04047,-0.00177,0.02766,-0.06197,-0.0152,-0.02051,-0.06487,0.00143,-0.16857,0.00827,0.11561,0.04086,0.04595,-0.02409,0.06681,-0.06948,-0.01064,0.05387,-0.09138,-0.04068,0.09593,0.04074,0.03473,-0.05469,0.09325,-0.01746,-0.05318,0.04973,0.0238,0.0663,-0.03838,-0.08933,0.11753,-0.06993,0.00555,-0.02895,0.13335,0.04171,0.11369,-0.01024,0.10032,0.05828,-0.03941,0.01894,-0.0488,0.06796,-0.00864,0.16055,0.02533,0.07016,-0.0118,-0.00125,0.0404,0.00756,-0.10779,0.03348,-0.02791,0.0058,0.02639,0.05565,-0.07774,0.00065,0.07703,-0.18559,-0.12259,-0.01041,0.04978,-0.07362,0.00142,0.12331,-0.057,0.08253,-0.09832,-0.00026,-0.07215,-0.02339,-0.08825,-0.05504,-0.06245,-0.00309,0.01845,-0.01629,0.02857,7e-05,-0.06655,0.15472,0.05057,0.03987,-0.01658,0.0135,0.09538,0.06097,-0.01845,-0.05287,-0.00142,-0.02768,-0.03284,-0.01902,-0.08083,-0.05446,0.00058,-0.02253,0.03213,0.03629,-0.07482,0.01599,-0.064,0.11342,0.02775,-0.02329,0.08553,0.04023,-0.08045,0.00418,-0.02511,0.05741,0.00173,0.11067,-0.01257,0.07434,-0.02371,-0.01683,0.13174,0.01545,-0.0253,-0.01918,-0.08788,0.0204,0.09256,-0.03108,0.0113,-0.02246,-0.01057,-0.00148,-0.15913,-0.022,-0.01303,0.03998,-0.06424,0.03593,0.00261,0.00335,0.08999,-0.10004,0.01792,-0.02627,-0.0581,-0.03489,-0.08877,0.00616,-0.03845,-0.07476,0.04577,-0.00894,0.02294,-0.06893,0.01489,0.08117,-0.04459,0.08645,-0.00355,-0.07261,0.05565,0.01337,0.01768,0.01896,0.00083,0.07622,0.03112,0.04572,-0.0574,0.0547,0.07779,0.01642,-0.04328,0.0745,-5e-05,0.00541,0.00095,0.03311,0.02257,0.16518,-0.02533,-0.0544,-0.04852,0.06522,-0.04266,-0.04933,0.04549,0.0477,0.0449,-0.00848,0.09684,0.06176,-0.03519,-0.00103,-0.04605,-0.06495,0.03441,0.02208,0.07794,-0.00556,0.06225,-0.05834,-0.01466,0.10543,0.0048,-0.16046,0.00459,0.01602,-0.06723]},{"domain":"electrical_engineering","key":"inductor_energy","name":"Energy stored in an inductor","package":"electrical-engineering-ai999x","example":"Find the energy stored in an inductor with L = 50 mH, I = 2 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amplifier gain and output","package":"electrical-engineering-ai999x","example":"Find the output of an inverting amplifier with Rin = 10 kohm, Rf = 47 kohm, Vin = 0.5 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phase lead of a lead compensator","package":"electrical-engineering-ai999x","example":"Find the maximum phase lead of a lead compensator with z = 1 rad/s, p = 10 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power transfer","package":"electrical-engineering-ai999x","example":"Find the maximum power transfer for Vth = 12 V, Rth = 6 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currents from the mesh equations (Kirchhoff's voltage law)","package":"electrical-engineering-ai999x","example":"Solve the mesh equations with resistance matrix [[10, -4], [-4, 8]] and source vector [12, 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equivalent of a DC circuit between two nodes","package":"electrical-engineering-ai999x","example":"Find the Norton equivalent between nodes 2 and 0 of the circuit: V1 1 0 12; R1 1 2 1000; R2 2 0 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integrator output for a constant input","package":"electrical-engineering-ai999x","example":"Find the output of an op-amp integrator with R = 10 kohm, C = 1 uF, Vin = 0.5 V, t = 5 ms, V0 = 0 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inductance of inductors in parallel","package":"electrical-engineering-ai999x","example":"Find the equivalent inductance of 10 mH and 40 mH inductors in 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kHz.","v":[-0.05973,0.00404,-0.02481,0.116,-0.0188,-0.05962,0.03458,0.02072,0.15938,0.09841,0.00748,0.02097,0.11982,0.05167,0.04462,-0.0522,-0.12701,0.03867,0.01278,0.16491,0.0187,0.03382,0.06257,0.03887,0.00036,-0.04818,0.0652,-0.0051,0.05752,0.00563,-0.10013,0.00982,-0.06285,-0.11676,-0.03537,0.16518,-0.04911,-0.10347,-0.06493,0.00111,0.08996,-0.04969,0.05329,0.00848,-0.02248,-0.17122,-0.01889,-0.00706,0.00701,-0.07662,-0.06506,0.01387,-0.01207,-0.00396,-0.15206,0.05689,-0.00159,0.08539,-0.02153,-0.01885,-0.01482,-0.07992,-0.07731,0.03679,0.00167,-0.03222,-0.02459,-0.02527,-0.08789,-0.10443,0.11864,0.10019,-0.03585,-0.11287,0.01237,-0.06953,-0.00898,-0.06847,0.07005,-0.10206,0.05277,0.00629,0.00832,0.06712,0.0403,-0.00671,0.04176,-0.0211,0.01149,-0.02829,-0.04388,0.0503,-0.09799,0.01879,-0.01239,-0.03494,-0.11101,-0.02906,-0.02981,-0.05102,-0.04997,0.05999,-0.10528,-0.00744,0.03788,0.0736,-0.02983,0.00232,-0.11714,0.0601,0.00393,0.00696,0.01169,-0.03779,0.04069,-0.07292,0.12858,0.0374,0.01119,0.05666,0.03546,-0.03374,0.12504,0.09324,-0.04051,0.00665,0.05363,-0.00851,0.04869,-0.0031,0.07723,-0.03131,0.07469,-0.00396,-0.06304,-0.07684,-0.04934,0.07058,-0.04866,0.07053,0.00723,-0.00832,-0.05742,0.01351,0.07849,-0.00109,0.03667,-0.03398,0.04664,0.00852,0.07035,0.09044,-0.03009,0.10243,0.04409,-0.10765,-0.0325,-0.04843,0.03929,0.0094,0.03853,-0.05429,-0.00188,-0.02639,-0.1219,0.05575,0.02661,0.04295,0.05847,-0.09703,0.00569,-0.06595,0.06248,0.02271,-0.00913,0.00219,0.11888,0.02141,0.04384,0.00105,0.01833,-0.01739,-0.00061,-0.09401,-0.02637,-0.03909,-0.08746,-0.0197,0.01282,0.01533,0.1433,-0.02416,0.04456,-0.09554,-0.08199,-0.04282,-0.0708,0.10536,-0.01087,-0.0158,-0.03512,0.00016,-0.00513,0.08691,-0.09934,0.04928,0.06492,0.03654,-0.01923,0.01953,-0.02333,0.03074,0.01135,-0.01648,0.01886,-0.00015,0.02901,0.1685,-0.02332,0.03096,-0.0121,-0.05009,-0.00304,0.01064,-0.05412,0.0093,-0.03025,-0.03741,0.11863,0.05825,-0.0157,-0.11239,0.04409,0.02099,-0.02719,-0.0724,-0.0644,-0.04541,0.00131,-0.02689,-0.03771,0.05331,0.0294,0.06479,0.00999,-0.06572,-0.00752,-0.11836,0.16902,-0.03947,-0.03353,0.01294,-0.00592,-0.05397,-0.03513,0.18204]},{"domain":"electrical_engineering","key":"parallel_rlc_resonance","name":"Resonance, Q factor and bandwidth of a parallel RLC circuit","package":"electrical-engineering-ai999x","example":"Find the resonance and bandwidth of a parallel RLC circuit with R = 10 ohm, L = 10 mH, C = 1 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margin and gain-crossover frequency","package":"electrical-engineering-ai999x","example":"What is the phase margin of G(s) = 4/(s(s+2))?","v":[0.05273,0.02751,0.04619,0.1201,-0.02004,-0.00261,-0.02479,-0.02343,0.08757,-0.10288,-0.12667,0.04793,0.01824,0.04056,-0.02349,0.06734,-0.00889,-0.06704,0.0756,0.01243,-0.02288,-0.00204,-0.0763,-0.02589,0.09708,0.05013,0.05437,-0.05478,-0.08447,0.11128,-0.00537,0.10235,-0.12991,0.07809,-0.13884,0.02578,-0.03391,-0.00668,0.00523,-0.04462,-0.0094,-0.02302,0.00582,0.18746,0.0596,0.02399,0.03035,0.01028,0.02213,0.0361,-0.05812,-0.02941,0.03272,0.07408,-0.06758,0.10199,-0.11826,0.05205,0.0338,-0.02787,-0.1279,0.01124,-0.10062,-0.16527,0.06068,-0.16899,0.05056,-0.07771,-0.04614,-0.12249,0.08071,0.09631,-0.12259,-0.10762,0.05012,-0.09361,-0.03794,0.03949,0.08214,0.08126,0.01688,0.00841,0.06653,0.04896,-0.02414,0.1005,0.02346,0.07739,0.09426,0.06298,-0.05016,0.00495,0.0188,-0.03027,-0.05197,-0.01839,-0.05901,0.04472,0.00752,-0.01734,-0.02926,-0.01554,-0.06231,-0.00356,0.13404,-0.03063,0.03081,0.02582,-0.04476,0.08592,0.02434,0.0208,0.00469,-0.02924,-0.04214,0.09555,0.06907,-0.09456,0.04658,-0.11247,0.02537,0.07308,-0.00201,0.06121,-0.04964,-0.05928,-0.01583,-0.01433,-0.11792,-0.0572,-0.0408,0.00075,-0.05942,-0.0294,0.08677,0.06628,-0.08087,0.00989,0.1247,-0.02636,-0.07518,-0.06162,-0.04441,0.02529,0.02906,-0.02515,0.03254,-0.04139,0.11934,0.01423,0.02014,-0.03202,-0.024,0.09877,-0.11525,-0.01164,0.023,0.04071,0.03531,0.0843,-0.01897,0.08739,-0.02884,0.03525,0.10669,-0.01258,0.01996,0.00174,0.08408,0.08576,0.10501,0.01194,0.02008,-0.02596,0.08963,-0.01233,-0.00146,-0.02603,0.01256,0.09361,-0.05362,-0.00363,-0.05976,-0.0426,-0.02523,-0.0608,0.01638,-0.0419,-0.01379,-0.0299,-0.02185,0.06478,-0.06891,0.00924,-0.05826,0.03147,0.02862,0.11483,0.0078,-0.01808,-0.04775,0.13553,-0.05426,-0.01975,0.05707,0.0184,0.06734,-0.06858,-0.00265,-0.04042,0.05173,0.05626,0.0473,-0.04348,0.00527,-0.01546,-0.10785,0.01488,0.03494,0.01595,0.02625,0.07668,-0.06393,0.00357,-0.11587,-0.03006,0.0116,-0.0094,0.07397,0.08795,0.00883,-0.05753,-0.01547,-0.07362,-0.02386,0.04161,-0.02265,-0.12167,0.00631,-0.0541,-0.01208,-0.0436,-0.04052,-0.05036,0.04,-0.09215,0.01398,-0.07834,0.0667,-0.09378,-0.00359,-0.00768,-0.01717,-0.02951,0.0979,-0.00051]},{"domain":"electrical_engineering","key":"phasor_sum","name":"Sum of sinusoids by phasor addition","package":"electrical-engineering-ai999x","example":"Find the sum of the phasors 3∠0°, 4∠90° and 2∠180°.","v":[-0.05364,0.09255,-0.02846,0.09632,0.0843,0.0011,0.02078,0.04219,0.07044,-0.06363,0.02303,0.01001,-0.02443,-0.03735,-0.06878,-0.06765,-0.08742,0.0244,0.07501,0.04546,-0.02623,-0.08819,-0.05387,0.0529,-0.05696,0.00901,0.06322,0.143,0.06251,-0.01849,-0.10443,-0.01045,-0.0161,-0.04229,0.05922,-0.05526,-0.00803,-0.00373,0.02746,0.10336,-0.00052,-0.0256,-0.02093,0.01181,-0.09516,-0.07578,-0.08641,0.00233,-0.02519,-0.04138,-0.15014,-0.00128,-0.0098,0.07336,-0.10859,-0.03039,-0.05588,-0.04182,0.02681,-0.01814,-0.00331,0.07043,-0.02308,-0.02373,0.05672,0.03712,-0.04714,-0.04857,-0.00552,-0.07912,0.0355,0.08962,0.01742,-0.06697,-0.01037,-0.03156,0.08319,0.00347,0.07647,0.05127,0.06332,0.05182,0.13109,-0.01326,0.07021,0.00464,-0.02676,0.19133,0.06175,-0.04197,-0.10562,0.01726,-0.06824,0.03967,-0.11262,-0.10901,-0.00753,0.07625,0.00102,-0.08852,-0.05814,0.02119,-0.05895,-0.00985,0.08305,0.05397,-0.03489,0.05081,-0.12694,0.04197,0.09579,-0.02133,0.04066,0.06087,0.01114,-0.03758,0.02334,-0.05453,0.03704,0.036,-0.08114,0.04935,-0.00841,-0.12255,0.12228,-0.04051,0.04223,-0.02656,0.04436,-0.09477,0.05172,-0.07666,-0.12928,-0.01291,-0.01402,-0.00957,-0.03271,0.07038,-0.02851,0.02706,-0.07459,0.00414,-0.14886,0.03735,0.12047,-0.02098,0.07147,0.0922,-0.03449,-0.11432,-0.08526,0.12351,-0.06367,0.01104,0.0069,0.13029,-0.05133,0.06473,0.0132,-0.01088,-0.08215,-0.05664,-0.105,0.09148,0.03368,0.0148,-0.03859,0.07236,0.04158,0.02748,0.05704,-0.01487,0.01873,-0.01625,0.0029,0.01306,0.03735,-0.15829,0.00058,0.09778,-0.08293,-0.0483,-0.0016,-0.04269,-0.09003,-0.03013,0.0009,-0.04982,0.06209,-0.04623,-0.00602,0.01206,0.02563,0.06315,-0.01798,0.03941,0.04905,0.04938,0.00207,-0.07973,-0.01484,0.03471,-0.0027,0.08545,-0.12463,0.02874,0.08278,0.00333,0.09992,0.06322,0.07309,0.01269,0.06883,0.07575,0.06447,0.05318,-0.06111,-0.0529,0.00735,-0.03208,-0.06539,-0.04349,0.03011,0.07542,-0.03663,-0.02382,-0.05273,0.00372,0.1235,0.1443,-0.02146,-0.05885,0.04901,0.05065,0.0151,0.035,0.01176,-0.051,-0.00313,-0.06571,0.03322,-0.09988,-0.01896,0.09408,0.00974,-0.06867,-0.00677,-0.05757,0.05202,-0.07275,-0.015,0.00539,0.0165,-0.11209,-0.01944,0.08126]},{"domain":"electrical_engineering","key":"polar_to_rectangular","name":"Phasor 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form.","v":[-0.06145,-0.00607,-0.01466,0.1013,0.10077,0.00468,0.0662,-0.08491,-0.02856,-0.03467,-0.00386,0.1067,0.04696,0.06052,0.06965,0.06075,-0.10762,-0.00936,-0.07866,-0.03506,-0.1781,0.01299,-0.01814,0.01711,0.00845,0.02057,-0.04045,0.05302,0.09784,-0.03678,0.00448,0.0553,-0.05987,-0.01978,-0.02528,-0.03921,-0.01724,-0.03647,-0.04541,0.00077,0.00407,-0.10533,0.13768,-0.06364,0.05122,-0.07954,-0.02742,-0.04706,0.00243,-0.02793,-0.03801,-0.02442,-0.04225,-0.04703,0.00317,-0.09395,-0.04566,-0.0345,-0.03006,-0.13318,0.01046,-0.02016,-0.04444,-0.0463,0.04177,0.00882,-0.13137,-0.01039,-0.1449,0.01342,0.01357,0.03949,-0.04161,-0.02578,0.0467,-0.07095,0.11551,0.02807,0.04064,0.00442,0.06155,0.03143,0.13697,0.07788,0.11471,0.02766,0.07068,0.07181,0.13492,0.03334,-0.0305,-0.08217,-0.0435,0.04041,0.00092,-0.00756,-0.02873,0.00048,-0.03257,0.04773,-0.01376,-0.05622,0.02675,-0.06341,0.02184,-0.05257,-0.02676,0.08716,-0.16048,0.01291,-0.00416,0.02782,-0.0974,0.02414,0.01713,0.02288,0.03044,0.01618,0.0053,0.04761,0.03477,-0.01379,0.01152,-0.15929,0.0966,0.06201,0.07097,0.1241,0.06473,-0.01663,-0.02239,-0.03338,0.07508,-0.03305,-0.02719,0.02278,0.01473,0.0511,-0.05175,0.05646,0.00311,0.00421,-0.10539,-0.03741,0.04386,-0.07459,0.10821,0.0863,-0.05799,-0.07191,0.04272,0.06012,0.02247,0.04087,0.03538,0.0262,-0.04325,0.01035,0.04513,0.03409,-0.00732,-0.01595,-0.08161,-0.02045,-0.03841,-0.02332,0.01463,-0.02002,-0.00963,0.01237,-0.05645,0.03154,0.05522,0.08481,-0.05814,-0.05872,0.08326,-0.04281,0.04855,0.0217,-0.02808,-0.02217,-0.01561,-0.08817,0.0187,-0.01934,0.019,-0.07346,0.07727,-0.07491,-0.00484,-0.0475,0.16416,-0.02162,-0.08694,0.11142,0.03974,0.06397,0.01815,0.10423,0.0073,-0.01096,0.08878,0.01189,-0.11232,0.08979,0.08948,-0.08412,0.08547,0.06538,0.09084,0.02253,0.03076,0.10484,0.07772,-0.03081,0.02881,0.01402,0.03302,-0.09319,-0.08555,-0.01059,-0.09538,0.08585,0.00345,-0.03895,0.11482,-0.03554,0.10315,0.0543,-0.04732,-0.02517,0.06052,0.07628,-0.14128,-0.03824,0.00342,-0.02966,-0.08841,-0.03986,0.01095,-0.02043,-0.09123,0.02708,-0.09978,-0.06685,0.06918,0.00586,-0.11942,-0.08175,0.00591,0.06707,0.02329,-0.12726,0.01875,0.07169]},{"domain":"electrical_engineering","key":"power_factor_correction","name":"Power-factor correction capacitor","package":"electrical-engineering-ai999x","example":"A load draws 10 kW at a power factor of 0.7 from a 230 V, 50 Hz supply. What capacitance corrects the power factor to 0.95?","v":[0.07534,0.02699,0.07194,-0.02391,0.01472,-0.05031,-0.10908,0.03305,-0.0465,-0.00128,-0.02791,0.03248,0.03092,0.07787,0.07771,0.03698,-0.0036,-0.10169,0.09507,0.12279,0.02468,0.0924,0.07088,0.00108,-0.10663,-0.01805,0.03877,-0.0504,-0.01801,-0.04912,-0.08256,0.0065,-0.03105,-0.08097,-0.00772,0.11123,0.06259,0.02346,-0.07402,0.04053,0.02872,-0.05239,0.02048,-0.04205,-0.00748,0.03595,-0.00453,0.04341,0.05981,0.00128,-0.01007,-0.00783,0.04656,0.0311,0.02502,-0.05456,-0.07801,0.03227,-0.02068,0.03265,0.0519,-0.09743,-0.09787,0.05109,-0.03825,0.00442,-0.02922,-0.09631,-0.12042,-0.04065,0.09653,0.04796,-0.0448,0.00832,0.00233,-0.02993,0.02414,-0.06205,-0.05682,0.05708,0.06446,-0.02584,0.05548,0.00144,0.03226,-0.19126,0.08469,-0.09799,0.05373,-0.04526,0.05385,0.06791,0.02448,-0.06539,-0.02103,-0.05159,-0.02265,-0.01335,-0.018,-0.07835,-0.05911,-0.00915,-0.07312,-0.03933,-0.11297,-0.03392,-0.07555,-0.01918,0.04443,0.12169,0.04929,0.09113,0.03085,0.01181,0.00616,0.03907,0.02856,0.03702,0.01125,-0.12104,0.01794,0.06047,0.10451,0.05962,-0.04916,-0.04448,-0.05911,-0.0225,0.03145,0.02085,0.08301,-0.04299,-0.0842,-0.04692,0.00631,0.0473,0.092,-0.08828,-0.07314,0.03304,0.02623,-0.03852,0.07361,-0.04074,0.07995,-0.06418,0.02116,0.07725,0.00763,0.05257,-0.01868,0.08492,0.05103,0.13276,-0.00289,-0.0417,0.03079,-0.04487,-0.04092,-0.01487,-0.04057,-0.01344,0.15253,0.05995,-0.07835,-0.06439,0.12497,0.1365,0.01071,-0.02285,-0.07548,0.05687,-0.0716,0.02069,-0.02688,0.13949,-0.0192,-0.03211,-0.04936,0.04739,0.05559,0.02716,0.03952,0.0665,-0.02325,-0.16247,-0.21229,-0.07625,-0.11779,0.0231,0.08561,-0.03414,-0.00618,-0.06712,-0.00511,0.13337,-0.02608,-0.02197,0.02147,-0.11639,0.03633,0.05312,0.0862,-0.04234,0.02312,0.05236,-0.04232,-0.07158,0.07799,-0.07314,-0.06558,-0.1639,0.09838,-0.02406,0.05765,-0.01364,0.00314,-0.00924,-0.00643,0.01663,0.1038,0.01335,0.0278,0.01961,-0.01378,-0.03249,0.0432,-0.02565,0.11309,0.06234,0.02899,-0.00791,0.06084,-0.01366,-0.10634,-0.00147,0.0487,-0.02062,-0.06167,0.04038,-0.02888,-0.08973,-0.02663,0.09397,0.03867,0.02735,0.07172,-0.03462,-0.01093,0.04307,-0.0789,0.01943,0.01671,0.06173,-0.01965,-0.0174]},{"domain":"electrical_engineering","key":"rc_filter","name":"First-order RC filter: cutoff, gain and phase","package":"electrical-engineering-ai999x","example":"An RC low-pass filter has R = 1 kohm and C = 100 nF. Find the gain at f = 2 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from rectangular to polar form","package":"electrical-engineering-ai999x","example":"Convert 3 + 4j to polar form.","v":[-0.01992,-0.04154,-0.07762,0.09768,0.12191,-0.0465,0.0563,-0.07321,-0.04478,-0.03213,-0.05544,0.10863,0.07461,0.03491,0.01295,0.01819,-0.15371,0.01153,-0.03547,0.01427,-0.08815,0.04352,-0.01709,0.02209,0.00315,0.04783,-0.0105,0.05405,0.07896,-0.00959,0.00785,0.07754,-0.07659,-0.0293,-0.01985,-0.06866,-0.02161,-0.05751,-0.02981,-0.00163,0.00048,-0.11969,0.13842,-0.05946,0.07607,-0.09605,-0.00637,-0.04502,-0.01088,-0.07535,-0.05391,-0.01247,-0.05077,0.01002,-0.03204,-0.05718,-0.05766,-0.05881,-0.03739,-0.13144,0.01052,-0.05351,-0.03629,-0.0272,0.05503,-0.06785,-0.15717,0.01721,-0.13267,-0.00392,0.05365,0.09313,-0.02978,-0.03804,0.06658,-0.07937,0.11903,0.01189,0.07617,-0.01826,0.08544,0.04546,0.14345,0.09229,0.11856,0.03555,0.03638,0.00256,0.06597,-0.02837,-0.00972,-0.08287,-0.0954,0.06648,0.00583,0.01217,-0.00554,-0.0707,0.03484,0.02786,-0.00674,-0.05764,0.01558,-0.07938,0.03644,0.00021,-0.04661,0.05222,-0.1928,-0.00263,0.02633,0.02848,-0.04771,0.02747,0.0284,-0.04344,0.0369,-0.00657,0.02753,0.07282,0.04379,-0.0247,0.01456,-0.1627,0.10236,0.10597,0.03915,0.1333,0.03713,-0.03894,-0.00761,-0.03086,0.10076,-0.03398,0.00587,0.01659,-0.00431,0.06313,-0.03577,0.08439,0.03675,-0.00417,-0.10389,0.00628,0.06625,-0.05073,0.08058,0.02838,-0.02153,-0.05829,0.02243,0.07432,-0.00661,0.06285,0.01167,0.03959,-0.0165,0.0809,0.01109,0.05061,0.00618,0.04376,-0.08129,-0.01169,-0.07237,0.02579,0.01057,0.01128,0.00761,0.02771,-0.03991,-0.01733,0.02495,0.06936,-0.10477,-0.10396,0.12211,-0.03259,0.0477,-0.00088,-0.02067,-0.04524,-0.00721,-0.09304,0.0187,-0.04035,0.01486,-0.05414,0.0832,-0.06078,0.0041,-0.03551,0.13158,-0.02017,-0.07054,0.03528,0.03379,0.07739,0.01924,0.09962,0.02213,0.00746,0.06515,0.01528,-0.0645,0.06893,0.07276,-0.05429,0.09788,0.077,0.08219,0.01766,0.08572,0.0564,0.066,-0.01492,0.0103,-0.02053,0.07788,-0.09086,-0.0935,0.03617,-0.11291,0.06602,-0.04455,0.00438,0.1023,-0.04793,0.08829,0.02497,-0.00339,-0.03353,0.07601,0.09576,-0.10261,-0.03351,-0.03413,-0.00966,-0.0387,-0.02345,-0.02465,-0.01437,-0.046,0.06244,-0.09242,-0.08299,0.03536,-0.05158,-0.12129,-0.10212,0.02898,0.01431,-0.00292,-0.0978,-0.0451,0.08727]},{"domain":"electrical_engineering","key":"resistor_network","name":"Equivalent resistance of a series-parallel resistor network","package":"electrical-engineering-ai999x","example":"Find the equivalent resistance of 10 + (20 || 30) ohm.","v":[-0.00725,-0.04037,-0.03714,-0.00389,-0.05877,0.02232,0.08071,-0.05508,0.09341,-0.01545,0.04832,0.01498,-0.06278,-0.01678,0.02525,-0.08314,0.04012,0.00695,0.00599,0.03114,0.0487,-0.14311,-0.0159,0.02389,0.01133,-0.00081,-0.07775,-0.02892,0.01086,-0.00269,-0.15043,-0.08567,-0.06145,-0.05012,-0.02752,0.01043,0.02518,-0.03809,0.04507,0.08247,0.0182,0.01445,-0.06422,-0.09366,-0.01106,-0.09742,0.01158,-0.01992,0.00567,-0.01334,-0.09519,0.03374,-0.01642,0.01292,0.07207,-0.06361,-0.08098,-0.01987,0.05218,0.04311,-0.03465,0.02519,-0.01045,-0.03529,0.03574,-0.03191,0.07485,-0.06054,0.06722,-0.00468,0.04442,0.04633,-0.02681,-0.03919,-0.06308,-0.0637,-0.05698,0.00201,0.06347,0.0273,0.02256,-0.05413,-0.00882,0.08602,0.05135,0.02279,0.08574,0.05764,-0.02976,-0.04481,-0.06617,0.16994,0.01464,0.07154,-0.05379,-0.10374,-0.08166,0.07113,-0.0795,0.04872,-0.02085,-0.06772,-0.00528,0.07744,0.05173,-0.02633,-0.05724,-0.0951,-0.12315,0.02373,0.07031,0.01144,-0.0263,0.03538,-0.00632,-0.01978,0.0439,0.01414,0.12141,0.02364,-0.03027,0.01501,0.00151,0.00087,0.06807,-0.00071,0.0561,-0.01897,-0.02481,-0.13719,-0.03099,-0.0201,-0.12219,-0.03135,-0.10383,-0.0501,-0.08088,0.04464,-0.0123,0.08608,-0.11815,-0.0532,-0.05768,0.11799,0.12479,-0.08097,0.06328,-0.03379,-0.00329,-0.01085,-0.07454,0.20201,-0.08763,-0.02008,0.05257,0.00516,-0.11744,-0.01986,0.00713,0.04643,0.04648,0.174,-0.02302,0.02851,0.00584,0.07828,0.01333,0.11199,0.00859,-0.1104,0.07183,-0.07801,-0.01571,0.1761,-0.10858,-0.03956,0.00769,0.04328,-0.00294,-0.05565,-0.01869,-0.05952,-0.05027,-0.0011,-0.00122,0.08945,0.06382,0.03392,-0.06499,-0.00907,0.08638,0.03377,-0.01931,0.02618,-0.03311,-0.17372,-0.06544,0.0146,0.09908,-0.02401,-0.01886,0.04457,0.06156,0.1048,-0.02113,0.04803,0.09918,0.04138,0.03062,0.00787,-0.00069,0.04691,-0.05529,-0.01211,-0.06041,-0.01407,-0.0406,-0.01129,-0.06462,0.10034,0.0226,0.05585,0.02846,-0.06905,0.03364,-0.0225,0.01821,0.03759,0.09609,-0.00332,0.06032,-0.05073,0.07496,0.00844,-0.0518,-0.10053,-0.07989,-0.00209,0.04202,1e-05,0.08018,0.03802,0.00756,-0.00274,0.0717,0.05181,-0.06895,-0.06931,0.01276,0.12279,0.08166,0.12978,0.07363,-0.00996,-0.07164,0.10436]},{"domain":"electrical_engineering","key":"rms_waveform","name":"RMS and average value of a periodic waveform","package":"electrical-engineering-ai999x","example":"Find the rms value of a square wave with amplitude = 5 V, offset = 0 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stability test","package":"electrical-engineering-ai999x","example":"Use the Routh-Hurwitz criterion on s^4 + 2s^3 + 3s^2 + 4s + 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Q factor and bandwidth of a series RLC circuit","package":"electrical-engineering-ai999x","example":"Find the resonance and bandwidth of a series RLC circuit with R = 10 ohm, L = 10 mH, C = 1 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response of a series RLC circuit","package":"electrical-engineering-ai999x","example":"A series RLC circuit with R = 10 ohm, L = 0.1 H and C = 100 uF is connected to a 12 V step. Find the capacitor voltage at t = 5 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error of a unity-feedback system","package":"electrical-engineering-ai999x","example":"Find the steady-state error of G(s) = 10/((s+1)(s+2)) for a step 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summing amplifier output","package":"electrical-engineering-ai999x","example":"An inverting summing amplifier has inputs of 1 V, 2 V and -0.5 V through input resistors of 10 kohm, 20 kohm and 10 kohm, and a feedback resistor of 100 kohm. 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represent?","v":[0.05244,-0.09157,-0.0286,-0.02644,0.19522,0.02262,-0.04396,-0.03964,-0.00567,0.00946,-0.07301,-0.01903,0.05095,-2e-05,0.02119,0.00115,-0.03733,-0.01634,-0.15143,-0.02027,-0.08276,-0.0106,0.0132,0.04595,-0.03755,-0.01125,-0.04483,0.00588,-0.10215,0.04444,-0.07209,0.0513,-0.10308,-0.09238,0.04645,0.01461,-0.10198,0.01039,0.06798,-0.03327,-0.07148,-8e-05,0.09768,-0.11728,0.01672,0.05348,-0.04847,0.09559,-0.08419,0.00267,-0.09898,-0.0396,0.00622,-0.08838,0.12505,0.08271,0.01526,0.07766,0.042,0.0233,-0.12502,0.0136,0.09612,-0.03827,-0.00487,0.03512,-0.02374,0.03676,-0.0032,0.07233,-0.00096,-0.02622,-0.05777,0.01528,-0.01331,-0.04098,-0.02481,0.02786,0.077,0.01041,-0.04877,0.10666,0.10648,0.01777,0.03498,0.0053,0.09474,0.05452,0.01036,-0.03368,0.09134,-0.02577,0.08781,-0.02159,-0.0165,-0.04449,0.00132,-0.03096,0.08098,-0.11272,-0.09126,-0.0106,0.10022,-0.00966,0.12444,-0.10139,-0.03051,0.05211,-0.09429,-0.05172,0.03087,0.00346,-0.15552,0.04971,0.11231,-0.14141,0.05035,-0.04239,0.00809,-0.04667,-0.03569,-0.14381,-0.05856,-0.02853,0.06537,0.04848,0.01845,0.06801,-0.00766,-0.11471,0.0264,0.09897,0.05688,0.01492,0.00075,0.08185,0.04927,-0.03372,-0.02993,-0.00171,0.00733,-0.05119,0.01921,0.0033,-0.02713,0.05979,0.07804,0.0114,0.00036,-0.10621,-0.04558,-0.02397,0.10455,-0.0076,-0.0053,0.0041,0.06351,-0.04835,-0.03481,0.02154,0.12442,-0.05282,0.01709,-0.00037,-0.00027,0.02257,-0.04941,0.08707,0.03319,-0.02283,-0.07364,-0.01714,0.02896,0.1001,-0.03482,0.03149,-0.00699,-0.03305,-0.01884,-0.09354,-0.02039,-0.00362,0.08578,-0.07034,-0.01411,0.02918,-0.01249,0.05471,-0.04931,0.08847,0.0342,-0.09677,-0.03553,-0.01723,0.05398,-0.03719,0.00858,0.04922,0.05768,-0.10237,-0.02406,-0.07679,0.07433,-0.06037,0.06263,0.01739,-0.06996,-0.01206,0.00229,0.03481,0.00771,-0.0721,0.05931,-0.00411,0.00904,0.02258,0.03167,0.08325,0.01347,-0.02296,0.13715,-0.02341,0.01958,-0.07694,0.02514,0.07138,0.15682,-0.02964,-0.00857,0.01104,0.06046,-0.07051,-0.04877,0.06854,0.00067,0.03037,-0.09262,0.18852,0.03577,-0.07627,-0.07831,-0.02686,-0.03496,0.05001,0.05492,0.01432,-0.04248,0.02849,-0.14161,-0.04897,0.08438,0.04753,-0.02022,0.08762,-0.0623,-0.11911]},{"domain":"electrical_engineering","key":"twos_complement_encode","name":"Two's complement representation of a signed integer","package":"electrical-engineering-ai999x","example":"Write -5 in 8-bit two's complement.","v":[0.12063,-0.07532,-0.07688,-0.01126,0.17236,0.02599,-0.05962,-0.07555,0.02873,-0.014,-0.02848,0.05294,0.07165,0.02604,0.01342,0.01327,-0.00211,-0.01872,-0.15279,-0.03186,-0.08082,-0.04188,-0.06601,0.02791,-0.00851,-0.03784,-0.00991,-0.00393,-0.05745,0.06894,-0.04111,0.08428,-0.12032,-0.06832,-0.00196,-0.04056,-0.06442,-0.02226,0.08099,-0.07585,-0.10176,-0.06416,0.05184,-0.07926,0.06147,0.04572,-0.06269,0.04681,-0.08982,-0.01592,-0.01531,-0.03212,0.0079,-0.00884,0.10305,0.00181,-0.00954,0.05869,0.03398,-0.01675,-0.11362,0.08199,0.11185,0.06544,0.03096,0.05281,-0.02567,-0.01728,-0.04126,0.04099,-0.05096,0.02905,-0.10279,0.05671,0.0321,-0.02698,-0.03072,0.02804,0.06242,0.0405,-0.04255,0.09466,0.0948,-0.02515,0.04451,0.03759,0.08035,0.03067,-0.01125,-0.08104,0.02371,0.00653,0.03448,0.02056,0.01327,0.01965,-0.0128,-0.03387,0.02457,-0.04962,-0.05357,-0.03776,0.07083,0.03844,0.1243,-0.12882,-0.02108,0.02967,-0.09743,-0.05637,0.02702,0.00334,-0.06681,0.08336,0.13862,-0.14972,0.0378,-0.07068,-0.03115,-0.05375,0.01721,-0.12301,-0.0662,-0.05443,0.04288,-0.01566,0.06456,0.07745,-0.01386,-0.17233,-0.00485,0.05623,0.02356,0.01961,-0.02529,0.04624,0.0224,-0.03782,0.00068,0.05054,-0.00363,-0.01221,-0.03582,-0.01985,-0.02887,0.0104,0.04619,0.03317,0.04999,-0.13222,-0.03896,0.0297,0.06774,0.00911,-0.06507,0.04597,0.05292,-0.05492,-0.01207,0.0019,0.04846,-0.01221,0.02825,0.04137,0.01432,0.04118,-0.00826,0.09885,0.01875,-0.04397,-0.04002,0.00525,0.06755,0.1761,-0.09881,0.04941,0.04589,-0.04866,-0.03919,-0.06669,0.00417,-0.0195,0.02659,-0.08664,-0.0183,0.04666,0.02658,-0.00404,-0.06226,0.0387,-0.04412,-0.11476,-0.0221,-0.02521,0.05887,-0.09324,0.04152,0.03277,0.06233,-0.03115,-0.03801,-0.05151,0.05949,-0.06826,0.04721,0.01054,-0.0511,-0.00316,-0.00316,-0.02596,0.02763,-0.01374,0.12901,0.00901,-0.00551,0.07501,0.04787,0.0358,0.03301,-0.01462,0.09249,0.009,-0.01726,-0.06047,0.07407,-0.01741,0.0537,-0.05236,-0.05062,-0.0671,0.08146,-0.14768,-0.01904,0.1375,0.05935,0.08113,-0.13057,0.20362,0.02192,-0.06853,-0.07722,0.0119,-0.01918,0.098,0.04921,0.05966,-0.02633,0.02606,-0.09409,-0.0543,0.14154,-0.00869,-0.04087,0.08246,-0.08128,-0.09218]},{"domain":"electrical_engineering","key":"voltage_divider","name":"Voltage divider","package":"electrical-engineering-ai999x","example":"Find the output of a voltage divider with Vin = 12 V, R1 = 1 kohm, R2 = 2 kohm.","v":[0.00172,0.02241,0.05819,-0.0506,-0.10111,-0.02038,0.08122,-0.00129,-0.01594,0.05099,0.06091,-0.02246,-0.10532,-0.02713,0.09376,-0.00086,-0.05267,0.00304,-0.13678,0.03741,0.05375,0.02129,0.07093,0.04669,0.07125,0.03258,-0.04783,-0.0005,0.00822,-0.03687,-0.12187,-0.00101,-0.09478,0.03383,0.01344,0.06682,0.07061,-0.00102,0.02388,0.03595,0.04906,0.04632,-0.04131,-0.06776,-0.06667,-0.08017,-0.01949,0.10132,-0.01434,0.06804,-0.00764,0.05803,-0.11287,-0.0532,0.06295,0.07055,0.05637,-0.01341,-0.03942,0.06557,0.00253,0.04705,-0.00506,-0.08659,0.07865,0.03671,0.10876,0.0286,0.09409,0.09041,0.03825,-0.02539,0.04158,-0.00063,-0.11626,0.00932,-0.10843,0.07031,0.075,-0.03744,0.08195,0.00563,-0.07268,0.03598,-0.05773,0.05694,0.06076,-0.00932,-0.04172,0.02312,0.03944,0.06847,0.02331,-0.04628,0.11428,0.08562,0.10108,-0.03082,-0.09229,-0.03809,-0.00793,-0.01518,0.09653,-0.06779,0.00644,-0.0598,0.00942,0.04251,-0.07834,-0.00171,-0.0153,-0.07016,-0.07272,0.03978,-0.04431,0.08256,0.08894,-0.0143,0.0074,-0.08082,0.03604,0.03416,0.00359,0.03438,-0.05088,0.13185,-0.08323,-0.00873,-0.01537,0.06795,-0.09397,0.00141,-0.01254,-0.02069,0.00621,-0.08384,-0.00571,-0.02969,-0.03357,-0.07272,-0.20662,0.09108,0.07211,0.00922,0.09001,-0.12335,0.10852,-0.04174,0.07265,0.08777,-0.15664,0.05343,-0.04096,0.03329,0.08739,-0.02584,-0.02249,-0.0168,0.01817,-0.01067,0.0072,0.00369,0.05309,-0.08897,-0.02982,-0.0016,-0.14826,-0.03239,-0.06232,-0.15569,-0.1078,0.06861,-0.0195,-0.0118,-0.05802,-0.06683,-0.07698,-0.05455,0.03047,-0.11421,-0.02251,0.0001,-0.00841,-0.01183,-0.0456,0.06186,0.03342,0.03061,0.0097,0.06406,0.0145,0.10256,0.02844,0.04349,0.00112,-0.12408,-0.15326,0.05902,0.03947,0.08797,-0.03308,-0.00951,-0.07689,-0.09239,0.02845,-0.03978,-0.10978,0.07592,-0.02805,0.00639,0.05393,0.0596,-0.03358,0.02958,0.06456,0.00521,-0.01553,0.06177,0.0119,-0.04088,0.04577,0.07935,0.0044,-0.00121,0.00868,0.08013,0.03824,0.04935,0.08242,0.00947,-0.00109,0.00477,-0.12716,-0.01739,-0.01669,-0.13307,-0.07261,-0.02551,-0.0059,-0.08133,0.03387,-0.00026,0.07244,-0.0876,0.06781,0.05056,0.00113,-0.01683,-0.0017,0.10699,0.01474,-0.00548,-0.04,0.02087,0.07719,0.07738]},{"domain":"electrical_engineering","key":"wheatstone_bridge","name":"Wheatstone bridge output","package":"electrical-engineering-ai999x","example":"Find the output of a Wheatstone bridge with Vs = 10 V, R1 = 100 ohm, R2 = 200 ohm, R3 = 150 ohm, R4 = 250 ohm.","v":[-0.01915,-0.03675,0.05291,0.0278,-0.0998,0.10034,0.05623,0.07473,0.02843,0.0887,0.00471,0.10098,-0.21087,0.04666,0.0875,-0.06573,0.01162,0.05431,-0.07739,-0.01111,-0.06524,-0.0579,0.01395,0.07608,0.00361,-0.05456,-0.04937,-0.07797,0.01566,0.03623,-0.0186,0.06153,-0.04292,0.00355,-0.07014,0.02441,0.08709,-0.04631,0.01764,-0.1656,0.11043,0.04193,0.09226,-0.06486,-0.02165,-0.04477,-0.06308,-0.02912,-0.009,0.11534,0.0108,0.05143,-0.05687,-0.09459,0.00876,-0.02374,0.00494,-0.00909,0.12229,0.06046,-0.01354,0.06688,-0.01077,-0.14503,0.0636,0.05896,-2e-05,-0.00991,0.03814,-0.02184,0.01492,0.02983,0.05833,0.0083,-0.06233,-0.0193,-0.14156,0.06805,0.07008,0.00822,-0.02733,-0.03376,0.00984,0.02826,-0.11147,0.07734,0.10169,-0.0126,0.00048,0.09243,0.00643,0.093,0.0692,0.10337,0.03931,0.02231,0.11384,-0.00765,-0.13896,-0.04224,-0.03978,0.00253,0.15793,0.00446,0.05936,-0.11544,0.0246,0.06332,-0.12804,-0.09649,-0.03785,-0.07709,-0.03577,0.03126,0.00495,0.10067,0.11189,-0.02141,-0.0065,-0.00201,0.03652,0.01935,0.02391,0.05412,-0.06204,0.11885,0.0764,-0.06237,-0.02505,0.0263,-0.0604,-0.01977,0.03019,-0.08335,-0.06079,-0.06564,0.01283,-0.01019,-0.04215,-0.08927,-0.016,0.02147,0.10152,-0.09166,-0.04294,-0.02419,0.11916,0.09438,-0.01803,-0.04073,-0.05257,0.05504,0.00963,0.06366,0.07381,-0.03004,0.08995,-0.06025,0.00924,-0.0222,-0.00464,-0.08202,0.03228,-0.02497,0.02422,-0.04254,-0.11221,0.06023,-0.0175,0.03744,-0.07152,0.07025,0.02202,-0.0954,-0.03313,-0.04022,0.02617,-0.00322,0.02634,-0.07986,-0.05357,-0.02667,0.02261,-0.05429,-0.01978,0.09394,0.08603,0.03748,-0.00661,0.09221,-0.01204,0.05297,0.05311,-0.03837,0.10893,-0.05985,-0.0508,-0.01239,-0.0368,0.05152,0.00446,0.00286,-0.11776,-0.01053,-0.02035,0.02179,0.01074,0.06329,-0.04914,0.00081,0.02033,0.05859,-0.06725,0.07188,0.13675,0.03545,-0.05178,0.00565,0.00378,-0.0634,0.07122,0.01073,-0.00565,-0.01348,0.11632,0.03136,-0.0913,0.06261,0.09606,0.00567,0.00122,-0.03379,0.01711,-0.04563,-0.04428,-0.06472,-0.04739,-0.06732,0.00877,-0.08156,-0.04691,-0.11463,-0.03423,-0.06092,-0.03188,0.08039,-0.02527,0.0259,0.01529,0.13424,-0.03736,-0.04951,0.0164,0.01385,0.03947,0.00534]},{"domain":"electrical_engineering","key":"wye_to_delta","name":"Wye-to-delta (T-to-Pi) resistor transformation","package":"electrical-engineering-ai999x","example":"Convert a wye with Ra = 5 ohm, Rb = 10 ohm, Rc = 20 ohm to a delta.","v":[0.09759,0.07232,0.01243,-0.01071,-0.07115,0.11692,-0.01121,-0.09046,0.09451,-0.01732,0.01559,-0.06653,-0.16896,0.09507,-0.04236,-0.02568,0.07247,-0.08732,-0.13432,0.002,-0.04282,-0.10306,-0.10272,0.05772,0.07515,-0.00553,-0.012,-0.05464,0.01573,0.09255,-0.0457,-0.00336,-0.08031,0.04561,0.08611,0.08333,-0.01428,-0.01416,-0.04722,-0.0679,0.05704,0.02876,0.05274,-0.06068,-0.08039,-0.10292,-0.02917,-0.05996,0.00155,0.08048,0.02644,0.05993,-0.0757,-0.04034,0.09118,-0.01505,-0.00117,-0.02713,-0.03739,0.00239,-0.0068,0.10505,0.04289,-0.04366,0.11574,-0.0018,-0.03628,-0.02185,-0.04997,0.0142,-0.03447,0.06767,-0.00541,-0.05704,-0.06119,-0.08931,-0.16396,0.00663,-0.02138,-0.01776,0.01439,-0.04717,-0.02187,0.09415,-0.00854,0.03548,0.00194,-0.09468,-0.04714,-0.06022,0.00726,0.04352,0.03656,0.07282,-0.01526,0.02896,-0.00824,0.01656,-0.12302,0.05413,-0.00628,-0.01065,0.11093,-0.0015,0.04025,0.01623,-0.03798,0.05261,0.02351,0.15373,0.01911,-0.06879,-0.07768,-0.10995,-0.08119,0.05068,0.02248,-0.0678,0.06544,0.01368,-0.00931,0.04747,-0.0494,-0.03767,0.03975,0.08636,-0.03173,-0.04596,0.04323,-0.11444,-0.02905,-0.03448,0.01399,-0.0411,-0.19525,-0.0514,-0.06439,-0.03869,-0.01557,0.05105,-0.0598,-0.0403,-0.06569,-0.1104,-0.01329,-0.02485,0.0463,0.02796,0.008,-0.08655,0.04831,0.01937,0.03542,-0.01211,0.13712,0.03551,-0.04868,-0.06726,0.08322,-0.05949,-0.02653,0.06998,0.02077,0.11734,0.0943,-0.04453,0.06325,0.07548,0.00908,0.06737,0.06908,0.04002,0.02748,-0.09219,0.00656,0.04214,-0.00238,0.01319,0.00746,-0.0605,0.00709,-0.06456,-0.04713,0.02637,-0.01504,0.06255,0.07852,-0.00804,0.02612,0.05122,-0.00316,0.0599,0.14536,0.05548,0.032,-0.03256,-0.00245,-0.0074,-6e-05,0.10231,-0.07926,0.06646,0.06411,0.06955,-0.00791,0.05963,0.03107,-0.05779,0.00838,-0.03126,0.06291,0.08159,-0.16278,0.05283,0.02159,-0.05696,0.01673,-0.07856,-0.07159,0.06804,0.08673,0.05768,-0.10298,0.0784,0.08066,-0.0105,-0.05175,0.04649,0.09088,-0.01375,0.06362,-0.05513,-0.01391,0.10449,-0.05244,-0.05669,-0.00082,0.06475,0.02911,0.0539,0.0245,-0.01743,0.03685,-0.12522,-0.03611,0.08065,-0.04688,0.06012,-0.02003,0.0897,0.02925,0.03902,-0.01938,0.07126,-0.065,-0.07399]},{"domain":"electrical_engineering","key":"zener_regulator","name":"Zener diode shunt regulator","package":"electrical-engineering-ai999x","example":"A Zener regulator has an input voltage of 20 V, a series resistor of 1 kohm, a Zener voltage of 12 V and a load resistance of 2 kohm. Find the Zener current.","v":[-0.03244,-0.03036,0.07084,-0.05513,-0.10259,0.00194,0.0358,0.03268,-0.00166,0.10225,-0.00185,-0.13911,-0.06142,-0.02162,0.02113,0.04445,0.02816,0.04622,-0.17002,0.09121,0.1428,-0.04918,-0.00172,0.08309,0.05423,0.03166,-0.08958,0.0973,0.09316,-0.06444,-0.08186,-0.03277,-0.05921,-0.00481,0.01331,0.0422,0.06561,-0.05168,0.05979,0.03556,0.0551,0.0215,-0.08791,-0.00645,0.02018,-0.09136,-0.01047,0.0442,0.08898,-0.03444,-0.02549,0.02936,0.03121,-0.09578,-0.02961,0.06905,-0.01228,0.00269,-0.05855,0.05202,0.0216,0.06564,-0.05864,0.0908,0.05625,-0.02526,-0.04571,0.0041,-0.04248,0.02155,0.09703,-0.00146,0.07318,0.03055,-0.0527,-0.03389,0.04344,-0.01226,0.05402,-0.10498,0.02367,0.06546,-0.03998,0.04514,-0.0762,0.01105,0.0148,-0.0396,-0.01577,-0.08049,-0.03887,0.00995,-0.0002,-0.06568,0.11806,0.09835,0.0607,0.05043,-0.09978,-0.016,0.03363,-0.00671,-0.01601,-0.0064,-0.05151,-0.05712,0.05138,0.04082,-0.05919,0.08619,-0.02964,0.03123,-0.02322,-0.00952,-0.00482,0.0287,0.06812,-0.03991,0.00339,-0.03978,0.08177,0.03093,0.06322,0.03504,-0.02895,0.00237,0.01097,0.02113,0.0125,-0.07204,-0.14244,-0.0247,-0.01851,-0.01733,0.12985,-0.10685,-0.00716,-0.04057,-0.0657,-0.02601,-0.11549,0.05088,-0.01908,0.09007,0.12506,-0.02545,0.01906,0.01961,0.0906,0.08709,-0.04458,0.17017,-0.09012,0.07026,0.03862,-0.0686,-0.06757,0.00457,0.01146,-0.0735,0.04136,0.01531,0.00272,-0.08652,-0.13287,-0.02519,-0.0969,0.05011,-0.02808,-0.20681,-0.05801,-0.01196,0.02871,-0.02734,-0.02917,0.02373,-0.04962,-0.08497,0.01859,0.06874,0.04772,0.02216,0.04016,-0.09173,0.02299,0.09675,-0.06998,0.10142,0.0298,0.03064,0.00941,0.03139,0.02407,-0.01311,-0.00282,-0.11125,-0.1719,0.04962,0.04234,0.0025,-0.08043,-0.05311,-0.05976,-0.07646,0.11541,-0.05599,-0.06634,0.08757,-0.04691,-0.09325,0.0052,0.06027,0.03693,-0.06086,0.03582,0.03704,-0.03018,0.151,0.03026,-0.03994,0.04893,0.09448,0.02515,-0.03406,0.0137,0.06955,-0.04665,-0.05359,0.0206,0.03843,0.03481,-0.10397,-0.06808,-0.05024,0.0695,-0.06897,-0.11101,0.06486,0.0178,-0.02305,-0.05599,0.10745,0.01561,0.06985,-0.00631,0.04175,0.03191,-0.01443,0.02842,0.04366,0.02912,0.03641,0.03709,0.07723,0.02707,-0.07149]},{"domain":"energy_systems","key":"energy_actuator_disc","name":"Actuator-disc (momentum theory) rotor performance","package":"energy-systems-ai999x","example":"Actuator disc: a = 0.25, rho = 1.2 kg/m^3, D = 10 m, v = 8 m/s","v":[0.13101,-0.03736,-0.00058,0.06715,0.01153,0.10256,-0.03215,0.01483,-0.0093,0.04674,0.00715,0.01219,-0.13488,0.12671,-0.04325,0.00719,-0.08027,-0.06769,0.02608,0.02848,-0.00837,0.06668,0.04491,0.02283,-0.00103,0.00987,0.02875,0.01038,0.0451,-0.05092,0.02106,-0.086,-0.02174,-0.06107,-0.03032,0.06267,-0.10664,0.0047,-0.08406,0.00793,-0.08244,0.06822,0.07001,-0.05299,0.0067,-0.06055,0.1189,-0.0952,0.08282,-0.05892,0.07724,0.02934,0.0307,0.04202,-0.04943,0.01564,-0.02493,0.06399,-0.07519,-0.02302,0.07071,0.02294,-0.05541,-0.18264,-0.11013,0.01543,0.02677,0.07307,-0.17601,-0.0641,0.09262,0.05175,-0.0387,0.04838,0.05638,0.04856,-0.005,0.01774,-0.0004,0.00374,0.02308,0.04357,-0.065,0.03814,-0.11458,-0.13679,0.04737,0.02179,0.08145,-0.1237,-0.15605,-0.01556,0.06133,-0.05012,-0.00857,-0.06216,0.01888,0.04277,0.05802,0.04072,0.0133,-0.01767,-0.02333,-0.0006,-0.00099,-0.00392,-0.02018,-0.05909,0.08175,0.01926,0.07741,0.03231,0.0263,0.01093,-0.02947,-0.00582,-0.025,-0.09344,-0.00585,0.00371,0.07584,0.02606,-0.01186,0.05486,-0.13993,-0.0022,-0.07744,0.13796,-0.03131,0.08491,-0.11502,-0.08036,-0.0336,-0.06727,-0.02787,0.05052,0.05217,-0.08359,-0.0761,-0.00468,0.06099,-0.0264,0.03709,0.04486,0.02916,0.11696,-0.00624,-0.05475,0.03572,0.05566,0.0265,-0.04302,-0.06712,0.10395,-0.01441,-0.02722,-0.00216,-0.00212,-0.06504,0.01252,0.00142,-0.08464,-0.03926,0.01454,0.02067,-0.00934,0.09732,0.00051,-0.03934,0.10034,0.04177,0.0037,0.01302,-0.07005,0.06379,0.02073,0.06161,0.09233,0.07548,-0.00185,-0.02638,-0.00124,-0.04325,0.06162,-0.02064,0.00756,-0.09453,0.05262,-0.03723,0.09428,0.10794,-0.12365,0.0632,-0.00402,-0.03452,0.08854,0.02332,0.03597,-0.0839,0.02225,0.01231,0.02627,-0.05768,-0.0105,0.03656,0.08214,-0.09465,-0.04403,-0.10523,-0.129,0.00321,-0.02758,0.09512,0.0608,0.05963,-0.04835,0.03375,-0.04098,0.06735,-0.01714,-0.02348,-0.00978,-0.01629,0.02458,-0.05543,0.01176,-0.0205,0.17562,0.06551,-0.01981,0.0031,0.05325,-0.03238,0.07834,-0.04516,0.04494,-0.06514,-0.07916,0.04478,-0.00252,0.08857,0.14435,0.10731,0.00818,-0.04816,0.0513,-0.03096,0.05274,-0.09892,-0.12694,-0.04064,0.07227,0.02956,-0.01878,0.04349,-0.07233]},{"domain":"energy_systems","key":"energy_air_mass","name":"Optical air mass","package":"energy-systems-ai999x","example":"Air mass: zenith = 60, model = simple","v":[0.07029,0.04283,0.04681,-0.10425,0.07138,0.08123,-0.00342,0.01942,0.04129,-0.06704,0.04506,-0.04765,0.03653,0.02261,0.0307,0.01306,0.1542,0.05988,0.14948,0.06516,0.0305,-0.03238,0.09488,0.05385,-0.01811,0.04474,0.06639,0.05649,-0.03431,-0.04143,0.0307,-0.04492,-0.10355,0.0802,-0.05114,-0.017,-0.01327,0.05884,0.01302,0.03091,0.04247,0.0531,-0.16392,0.03341,-0.05415,0.05158,-0.09374,-0.04829,0.10411,-0.0323,-0.02749,-0.0421,0.03949,0.018,-0.03062,-0.10112,0.06772,-0.00778,0.06529,0.02729,-0.05227,-0.00485,-0.05255,-0.03574,0.00303,-0.05046,0.02036,0.04382,0.0212,0.10014,0.03753,-0.03425,0.19421,-0.06957,0.05937,0.02799,0.17367,-0.04335,0.07344,0.05645,0.02149,-0.00707,-0.01486,0.0363,0.03237,-0.07274,0.14766,-0.0309,0.12997,0.03485,-0.03166,-0.07977,-0.10047,0.01692,0.04942,-0.08529,0.06305,0.08072,0.00677,0.04224,0.04236,-0.04846,-0.06042,-0.06895,-0.01924,-0.04078,-0.03841,0.01451,0.03229,-0.03271,-0.01573,-0.01961,0.05798,-0.11704,-0.02222,-0.09437,0.03158,0.00359,-0.06742,0.03118,0.04158,0.00282,0.04361,0.07012,0.03206,-0.03939,0.01403,0.00378,0.01412,-0.02202,-0.04928,-0.02087,-0.02769,-0.00132,0.01596,-0.05353,-0.12915,-0.09494,0.0775,0.08807,-0.02027,-0.02623,0.10586,0.02108,0.07678,0.0068,0.08365,0.00569,-0.09043,-0.00332,-0.08628,0.06788,-0.07777,0.03926,-0.05333,0.07948,-0.07629,0.02616,-0.0337,0.01253,-0.03354,-0.02999,-0.02867,-0.05641,-0.06214,0.00959,-0.03494,-0.09339,-0.0241,-0.04954,-0.07719,-0.11374,0.06315,-0.1072,0.10779,0.04239,-0.05855,-0.10714,0.02698,0.06776,0.03413,0.14349,-0.0506,-0.01569,-0.05737,0.07798,-0.08397,-0.10133,-0.10598,-0.06788,0.00751,0.06831,-0.00109,-0.03983,-0.09452,-0.00209,0.06088,0.07343,-0.0527,0.05346,-0.04047,-0.04842,-0.01641,0.03498,-0.01263,0.02698,0.06763,0.01187,-0.0744,-0.02799,-0.09201,-0.00748,0.01915,-0.00313,0.00555,-0.05208,-0.04626,-0.01122,-0.06535,0.01372,0.10291,-0.07808,0.00373,-0.02164,-0.10274,-0.02139,-0.01528,-0.07538,-0.0274,-0.00421,0.11956,0.0983,-0.04794,0.04688,0.11619,-0.05482,0.04592,-0.04411,-0.00484,-0.04659,-0.05368,-0.01494,0.02425,0.09491,-0.01601,0.03543,0.03845,0.0094,-0.06895,-0.02605,-0.12274,0.07984,0.11481,0.00382,-0.10941,-0.00651]},{"domain":"energy_systems","key":"energy_angle_of_incidence","name":"Angle of incidence of the sun on a tilted surface","package":"energy-systems-ai999x","example":"Angle of incidence: tilt = 0, surface_azimuth = 180, zenith = 60, azimuth = 100","v":[0.0622,0.06171,0.03155,0.09134,-0.00539,0.05463,0.01736,0.06543,0.06703,-0.04521,0.03856,-0.06687,0.0063,0.09211,0.08107,0.10877,0.00028,-0.00928,-0.06707,0.10983,-0.00573,0.00844,-0.07677,0.00227,-0.0184,-0.05046,-0.01091,0.1603,0.02075,-0.07589,-0.04801,-0.01087,0.00105,0.01694,-0.01613,0.04717,0.02896,0.0264,0.01699,0.00182,-0.00254,0.01423,0.01291,0.01986,0.02495,0.04048,-0.01466,0.09648,0.04114,0.0544,0.07901,-0.02586,0.02884,-0.01152,-0.05024,0.0791,-0.02706,-0.03945,-0.12928,0.06686,-0.04614,0.11715,-0.11136,-0.08271,0.13161,0.01418,0.04747,-0.05458,-0.00398,0.02288,-0.06894,-0.09677,0.14182,0.10702,-0.0356,-0.04255,0.03154,0.11517,0.00754,-0.03708,0.00534,0.07543,-0.0074,-0.01325,0.0681,-0.07606,-0.00383,-0.04289,0.10095,-0.005,0.01408,-0.00712,-0.04337,-0.11854,0.03882,-0.05107,0.0607,-0.02185,0.04071,0.11164,0.0035,-0.01333,0.02028,-0.01767,-0.01573,-0.04039,0.13369,0.06082,-0.03084,-0.06418,0.06122,0.05295,0.0876,-0.08395,0.02375,0.05263,-0.05038,-0.11339,-0.06825,0.00069,-0.00265,0.01558,0.02974,-0.15089,-0.0083,0.11177,-0.0676,-0.02669,0.06603,-0.00684,0.05926,-0.04137,-0.0169,-0.06755,0.00888,0.02261,-0.03508,-0.00932,-0.04109,-0.09618,0.01001,0.04756,-0.02885,0.03258,0.11506,-0.08472,0.02231,0.06552,-0.04214,-0.08145,-0.08371,-0.05988,0.04092,0.05203,-0.06463,0.09235,-0.16451,0.00145,0.09535,-0.02404,0.0383,-0.0561,-0.02616,-0.00259,-0.08112,0.01906,-0.10048,-0.02078,-0.05427,-0.0633,0.10474,0.03041,0.02961,0.02478,0.04219,-0.02564,-0.04167,-0.07815,-0.04795,-0.12085,-0.00895,0.00615,-0.07047,-0.15599,0.02512,-0.08207,-0.01269,0.00459,-0.0058,-0.07529,-0.00956,-0.03089,-0.04289,-0.08806,-0.01808,0.07624,-0.04423,0.12455,-0.01237,0.07244,-0.01324,-0.13622,0.08289,-0.01728,0.02922,0.08266,0.05314,0.08534,-0.04852,-0.03753,-0.01118,-0.06492,-0.03393,0.04276,-0.01338,-0.08333,0.05796,0.04309,0.04188,-0.03995,0.00556,-0.09741,-0.0274,-0.00845,-0.10141,0.04246,0.01613,-0.04884,0.04891,0.07696,-0.01934,0.12165,-0.09615,0.00167,-0.04837,0.00791,0.07254,-0.05461,0.07484,-0.02513,0.0458,0.09433,0.0774,0.07867,-0.01294,-0.00358,0.07068,0.00198,0.00725,-0.10511,-0.07159,0.07965,0.08687,-0.14406,-0.03162,0.02758]},{"domain":"energy_systems","key":"energy_battery_pack_sizing","name":"Battery pack series-parallel sizing","package":"energy-systems-ai999x","example":"Battery pack sizing: V_target = 48 V, E_target = 10 kWh, V_cell = 3.2 V, Q_cell = 100 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terminal voltage under constant current (one-RC equivalent circuit)","package":"energy-systems-ai999x","example":"Battery RC model: OCV = 4 V, R0 = 10 mohm, R1 = 20 mohm, C1 = 1000 F, I = 10 A, t = 0 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module temperature (Faiman model)","package":"energy-systems-ai999x","example":"Module temperature (Faiman): poa = 1000 W/m^2, T_air = 25 degC, wind = 0 m/s","v":[0.03297,-0.01192,0.06192,0.00542,-0.05581,-0.02636,0.00323,0.06255,-0.01317,0.03045,-0.00097,-0.04747,0.07733,-0.01766,-0.11152,-0.03659,0.09672,0.03438,0.15291,0.08314,0.06137,0.01176,-0.02038,-0.04453,0.06077,-0.06166,0.11337,-0.02014,-0.04138,-0.05721,0.08938,-0.08419,-0.08355,0.14341,0.01784,0.01998,0.01099,0.01828,-0.01655,0.07033,0.07101,-0.15595,0.01244,0.01242,-0.02649,-0.00068,-0.02759,0.02319,0.04957,0.01,-0.0844,-0.01386,0.06717,-0.07052,0.0255,-0.06449,0.15023,-0.04658,-0.05288,-0.00565,-0.09538,-0.00378,-0.05098,0.02863,-0.00759,-0.09873,0.06754,0.07806,-0.02538,-0.04174,0.07181,0.10725,0.10602,0.02806,-0.05792,0.04138,0.11334,-0.05267,0.06193,-0.06018,0.12775,-0.04808,-0.02097,0.04563,-0.08218,-0.05061,0.12458,-0.00325,0.08262,0.04583,-0.08443,0.02481,-0.10279,0.04262,-0.09609,0.01046,-0.00175,-0.02457,0.03375,-0.05068,-0.0299,-0.0904,0.02613,-0.03193,-0.04532,0.01535,-0.05756,-0.01958,-0.05373,0.02122,0.10254,0.01685,0.01978,0.05348,0.05472,-0.02286,-0.03474,-0.0977,-0.05565,0.02561,-0.00907,-0.07136,-0.03167,-0.02128,0.00763,-0.04181,-0.02544,0.12087,-0.0874,0.00824,0.00763,0.0562,0.0951,-0.05123,-0.07877,-0.06167,-0.03341,-0.08918,0.07243,0.09225,0.14061,-0.05356,0.0917,-0.00595,0.04836,0.02511,-0.01266,-0.09068,-0.0647,0.11724,-0.00776,0.05539,-0.03282,0.06869,-0.07757,0.01018,-0.06775,-0.04543,-0.02711,0.08355,0.00765,0.0486,-0.05401,0.02699,-0.04429,0.03916,-0.01611,-0.10018,-0.05771,-0.04156,0.01988,-0.05429,-0.04027,-0.06768,-0.04188,0.01997,0.00412,-0.08616,0.0013,-0.04654,0.03094,-0.00819,-0.10246,-0.04018,-0.13136,0.01663,0.07484,-0.01344,-0.09016,-0.00396,0.01436,0.02936,-0.09143,0.06972,-0.08407,0.03619,0.03803,0.18162,0.03992,0.11408,0.01612,-0.07587,0.09473,0.03082,0.06591,0.02965,0.02101,0.10681,-0.0167,-0.10663,0.07832,0.00859,0.06101,0.00435,0.10097,0.02502,-0.01445,0.05391,0.04852,0.01641,-0.02224,0.01488,-0.08789,-0.02561,-0.06395,-0.00335,0.08746,0.00726,-0.00782,-0.06065,0.1019,0.06235,-0.15086,0.09296,0.05392,-0.09263,-0.06992,0.00591,-0.00244,0.07205,-0.00416,-0.09627,0.01393,0.04802,0.00593,0.05216,0.06194,0.04068,-0.03443,-0.0404,-0.0308,-0.04302,-0.05445,-0.00691,-0.04693,-0.002]},{"domain":"energy_systems","key":"energy_cell_temperature_noct","name":"PV cell temperature from NOCT","package":"energy-systems-ai999x","example":"Cell temperature (NOCT): poa = 800 W/m^2, T_air = 25 degC, noct = 45 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cell and module temperature (Sandia SAPM model)","package":"energy-systems-ai999x","example":"Cell temperature (SAPM): poa = 1000 W/m^2, T_air = 10 degC, wind = 0 m/s, mount = open_rack_glass_glass","v":[-0.03233,0.0128,0.05011,0.0499,-0.04456,0.04173,0.03347,0.08946,-0.00157,0.06287,-0.06916,0.00122,0.05205,0.00571,-0.0874,-0.0494,0.05267,0.07594,0.19288,0.07646,0.0468,-0.01069,-0.01305,-0.02665,-0.03335,-0.08352,0.06928,0.05026,-0.023,-0.04364,0.08426,-0.05227,-0.06776,0.16445,-0.06629,0.03725,-0.04426,0.02471,-0.00631,0.01121,0.07292,-0.09181,-0.01074,0.03663,-0.03433,0.01423,-0.07269,0.01522,0.07363,0.0307,-0.07217,-0.00861,0.09284,-0.03178,-0.00071,0.00532,0.1239,-0.07077,0.00415,0.03648,-0.10779,-0.02705,-0.04348,-0.0578,0.00594,-0.10087,0.00086,0.08164,-0.02157,-0.07379,0.01972,0.10732,0.12698,-0.00858,-0.00653,0.02376,0.07641,-0.03203,0.04293,-0.10591,0.08434,-0.0155,-0.02192,0.09536,-0.06161,-0.0162,0.05333,-0.01536,0.05489,0.04364,-0.06134,0.04122,-0.06775,0.10531,-0.02028,-0.00261,0.0402,0.01862,-0.01963,-0.0457,0.00719,-0.04104,0.02447,-0.00341,-0.04744,0.03426,-0.09402,-0.04644,-0.03117,0.07194,0.08449,0.02463,-0.06648,0.06859,0.06945,0.01281,-0.02811,-0.10974,-0.04228,0.0387,0.07473,-0.03604,-0.05587,0.04921,-0.0145,-0.08987,0.00329,0.13762,-0.10011,-0.00294,-0.02376,0.07308,0.08605,-0.04682,0.01096,-0.02663,-0.0942,-0.14104,-0.01602,0.08154,0.09221,-0.044,-0.02308,-0.03209,0.02633,0.02728,0.01642,-0.01179,-0.10941,0.12497,0.01706,0.02192,-0.07763,0.0967,-0.08761,0.06233,-0.05422,-0.02785,-0.00358,0.09228,-0.00656,0.02757,-0.0748,-0.01898,-0.04367,-0.00498,-0.01474,-0.1384,-0.10891,-0.05373,0.04124,-0.08141,-0.0557,-0.13679,-0.01302,0.02552,0.0047,-0.06157,-0.04629,0.03251,0.01148,0.01316,-0.09982,-0.01872,-0.08264,0.09686,0.09406,0.04644,-0.04511,-0.0335,-0.03424,0.00817,-0.08382,0.07928,-0.01819,0.11163,0.04142,0.12093,0.01097,0.13206,0.02009,-0.10295,0.0668,0.06159,0.086,0.03906,0.01189,0.03175,-0.10718,-0.08098,0.07663,0.00472,0.01055,-0.02255,0.10074,-0.0257,-0.08171,-0.00474,0.04025,0.00414,0.06282,-0.00699,-0.12187,0.04734,-0.00401,0.01899,0.049,-0.00748,-0.04018,-0.01373,0.05439,0.0209,-0.12725,0.1223,0.03578,-0.07446,-0.04889,-0.02108,0.01453,0.12143,-0.02697,-0.03979,-0.00632,0.0573,-0.06638,0.02851,0.06255,0.08144,-0.07526,-0.04995,0.00702,-0.00409,-0.03316,-0.02782,-0.1025,0.02751]},{"domain":"energy_systems","key":"energy_clear_sky_haurwitz","name":"Clear-sky global horizontal irradiance (Haurwitz)","package":"energy-systems-ai999x","example":"Clear-sky GHI (Haurwitz): zenith = 0","v":[0.14835,-0.0123,0.03436,0.02761,0.01222,0.02343,-0.01909,0.0602,0.02826,-0.0215,-0.05221,-0.10252,0.04384,0.05661,0.0172,-0.05748,0.01818,0.02026,-0.02471,0.03858,-0.03522,-0.098,-0.0116,-0.09278,0.09166,-0.00814,0.04611,0.1165,0.00456,0.01357,0.00545,0.04238,-0.18437,0.08315,-0.1072,-0.01429,-0.01673,0.03997,-0.02879,-0.02437,0.07365,-0.05953,-0.20949,0.13984,0.02654,0.02982,-0.06185,-0.03767,0.0388,-0.00045,0.09429,-0.01086,0.13212,0.06451,-0.04518,0.06252,0.08367,-0.04369,-0.07758,0.0556,-0.06669,0.05985,-0.06255,-0.00609,-0.08185,-0.03671,0.02861,-0.04186,-0.02064,-0.08006,0.12117,-0.00702,0.14536,0.0418,0.03605,-0.0036,-0.00472,0.03084,0.10444,-0.06356,0.00652,0.0756,-0.0093,-0.0308,-0.00673,-0.06387,-0.08664,0.02723,0.08829,0.03317,-0.06164,-0.00158,-0.07063,-0.03607,0.00401,0.05317,0.05644,-0.01444,-0.03802,0.04371,0.00688,0.00189,-0.06644,-0.02255,-0.05103,-0.00177,0.07291,-0.04326,0.07168,-0.04598,0.01542,0.01291,0.12688,0.02199,0.07528,0.05627,-0.05864,-0.06211,-0.10277,0.01999,0.07489,-0.0969,-0.10495,-0.00678,0.01324,-0.07894,0.03911,0.06151,-0.00539,-0.04434,0.00364,-0.0154,-6e-05,0.02097,0.01012,-0.01247,-0.07952,-0.08736,0.03105,0.0269,0.1131,0.05238,-0.01331,-0.01898,0.08156,-0.03615,0.01431,0.03807,0.00209,0.07628,-0.02906,0.09176,-0.05957,0.11339,-0.08134,0.07707,-0.00644,0.03313,0.04848,0.00729,0.08514,-0.11111,-0.03469,-0.04215,-0.11838,0.03704,-0.11986,-0.00185,-0.07118,-0.04743,0.07766,0.0138,0.04679,0.02669,-0.04439,-0.03689,-0.02678,0.05476,0.06456,-0.00109,-0.0725,0.06669,-0.03977,-0.04868,-0.04331,0.00715,0.05034,-0.00647,0.01496,-0.04947,-0.1028,-0.09619,-0.04034,-0.03397,-0.02464,0.03427,-0.00157,0.12681,-0.02238,0.07607,-0.01037,0.03432,-0.00117,0.05193,-0.0093,0.02249,0.05698,0.06197,-0.06856,-0.15016,-0.05046,0.06799,0.01238,-0.02906,-0.03731,-0.0364,-0.03452,0.10001,0.0087,-0.03071,-0.0412,-0.04642,-0.04475,-0.01536,-0.04566,0.01639,-0.0128,-0.06544,-0.03989,-0.05185,0.1117,0.01917,-0.0549,0.00599,0.12025,-0.02056,0.05216,-0.00869,-0.05325,0.06893,-0.21011,0.08228,-0.03266,0.12758,-0.01658,0.10637,0.06026,-0.02163,0.05986,-0.09656,0.01711,-0.06662,0.00913,-0.0396,-0.08548,0.04361]},{"domain":"energy_systems","key":"energy_clear_sky_ineichen","name":"Clear-sky irradiance (Ineichen-Perez with Linke turbidity)","package":"energy-systems-ai999x","example":"Clear-sky irradiance (Ineichen): zenith = 30, linke_turbidity = 3, altitude = 500 m, n = 172","v":[0.03263,-0.01408,0.11464,-0.05952,0.00391,0.03147,-0.06106,0.07981,0.07576,0.0338,-0.02387,-0.0432,0.02747,0.01257,-0.00288,-0.14626,0.1257,0.0453,0.02012,-0.04177,0.03062,-0.11561,0.03099,-0.06697,0.06352,0.05602,0.09562,-0.02294,-0.02648,-0.01127,-0.12095,0.00439,-0.09974,0.09307,-0.04823,0.06643,-0.00297,0.05992,0.03075,0.04152,0.00809,-0.0154,-0.11335,0.07859,-0.05744,0.05884,-0.08287,-0.09854,0.09959,-0.05929,0.01792,0.04129,0.05415,0.05439,-0.08038,0.01052,0.14416,-0.01483,0.01648,0.12804,-0.07094,0.04117,-0.09442,-0.04076,-0.09422,-0.00112,0.06875,0.06888,0.03469,-0.03139,0.04709,-0.05664,0.14103,0.04416,0.06535,-0.04294,0.0784,-0.00769,0.0974,-0.0289,0.02885,-0.01177,0.0671,0.00084,-0.031,-0.10688,-0.06056,-0.03266,-0.01895,0.10127,-0.06984,-0.02782,-0.10476,-0.02291,-0.01471,0.04095,0.12252,-0.00764,0.01635,0.03321,0.04949,0.07718,-0.10357,-0.04031,-0.01057,-0.03023,-0.03292,-0.07449,0.14447,-0.04904,0.01666,-0.0305,0.05651,-0.03638,0.02281,-0.09053,0.00068,0.02589,-0.01628,0.05139,0.1033,-0.04639,-0.10368,0.09139,-0.02131,-0.12543,0.05249,0.07637,0.02843,4e-05,-0.03588,0.02231,0.0515,-0.06145,0.02293,0.0341,-0.08358,-0.18826,0.03529,0.04781,0.03581,0.04903,0.07513,-0.04005,0.0604,-0.03752,0.02353,-0.03403,0.02006,0.02922,-0.07604,0.04467,-0.04983,0.11288,-0.08351,0.0443,-0.02286,-0.04196,-0.01049,0.04915,-0.0765,0.02358,-0.0406,0.04851,-0.0006,-0.01283,0.00256,-0.10056,-0.08288,-0.04654,-0.04388,-0.07901,-0.03102,-0.05493,0.03157,0.05238,-0.00369,0.02861,-0.00835,-0.01711,-0.01045,0.05462,0.05077,-0.01617,-0.0726,0.10118,0.10415,-0.01151,-0.04719,-0.00901,-0.09268,0.0996,-0.01771,0.08041,-0.06297,-0.00419,-0.02537,0.07695,0.03077,-0.03195,0.00013,0.06236,-0.09775,0.04795,-0.01155,-0.03484,0.08739,0.01949,-0.08597,-0.03211,-0.00797,0.04382,-0.0125,-0.00153,-0.07561,-0.06155,-0.0034,0.11376,0.01734,-0.02062,0.04174,-0.02757,0.01987,-0.00998,-0.06475,-0.00673,-0.01108,-0.05871,-0.1264,-0.04387,0.08485,0.00439,-0.10353,-0.01347,0.13005,-0.05692,0.06617,-0.00203,0.00032,0.11466,-0.16658,0.0132,0.04294,0.06171,-0.01524,0.09432,0.05927,0.02679,0.03051,-0.03786,0.04191,0.03313,0.01248,0.005,-0.13065,-0.00635]},{"domain":"energy_systems","key":"energy_coulomb_counting","name":"State of charge by coulomb counting","package":"energy-systems-ai999x","example":"Coulomb counting: SOC0 = 90%, Q = 50 Ah, currents = [10, 20, -5], dt = 1 h","v":[-0.05749,0.12591,-0.02284,-0.04329,-0.04464,-0.05604,0.08812,0.07915,-0.07155,0.00155,-0.01265,0.04332,-0.05455,0.05598,0.06993,0.10105,-0.13307,-0.07375,-0.01646,-0.02104,0.10202,-0.04901,-0.05451,-0.03659,-0.01915,-0.00169,-0.06913,0.07336,-0.02865,-0.10509,-0.00288,-0.0475,0.07506,-0.01674,-0.00082,0.11498,-0.05486,-0.06058,0.01649,-0.0049,0.00473,0.03768,-0.01826,0.03784,-0.05112,-0.04393,-0.10007,0.11568,-0.00049,-0.09703,-0.04895,-0.03495,0.02023,-0.06389,-0.00303,0.04177,-0.03134,0.05106,-0.03069,0.00141,-0.03793,0.02448,0.02819,-0.07781,-0.00665,-0.08488,0.05878,0.12631,-0.07581,0.08503,-0.02586,0.03106,-0.01414,-0.01468,-0.04611,0.06793,-0.06833,0.10407,-0.01651,0.1303,-0.02209,-0.04306,0.00426,0.0662,0.05054,-0.04175,0.03431,-0.02968,0.06843,3e-05,0.06453,0.07095,0.05838,0.07801,0.03436,-0.04633,-0.08738,-0.1098,0.00716,-0.01757,-0.01594,-0.15813,0.01661,-0.01139,-0.06129,-0.0412,-0.07238,0.0916,0.09383,-0.0081,-0.04258,0.03786,0.01847,0.05306,0.05206,0.11658,0.02348,0.01751,0.03074,-0.00784,-0.05511,-0.02352,0.07604,0.01561,-0.16012,-0.05294,-0.02484,0.01292,0.00534,0.04976,0.00211,0.00051,-0.00928,-0.07443,0.03134,-0.04302,0.04288,-0.05036,-0.00277,-0.11068,0.01923,-0.01316,-0.0107,-0.0418,0.02198,-0.01675,-0.02751,0.08313,-0.02128,0.03152,0.03379,-0.17884,-0.0289,-0.07952,-0.10254,-0.01923,-0.03148,-0.04562,0.00475,0.05784,0.06933,0.05819,0.13731,0.04138,-0.02581,0.03186,0.04695,0.04168,-0.05693,-0.05094,0.08958,-0.01151,-0.03465,-0.09196,-0.13798,0.05177,-0.07561,-0.03725,0.05513,0.01645,0.04551,0.14004,0.0626,-0.00057,-0.04647,-0.03981,-0.08455,0.09459,-0.04136,-0.02956,0.07613,-0.1057,0.05181,0.06862,-0.05376,0.05219,-0.00874,-0.01643,0.09827,-0.04329,-0.00881,0.03283,0.06283,-0.03403,0.0893,0.00964,-0.11116,-0.00564,0.07232,-0.05877,0.01873,-0.11045,0.1264,-0.00746,0.0221,0.01133,-0.02832,-0.05682,-0.10825,0.07279,0.15547,0.05026,0.00531,0.12495,0.10498,0.04837,-0.00855,-0.05934,-0.02243,0.0543,0.01199,-0.06375,-0.03493,-0.03895,0.0764,-0.00252,0.08456,0.03275,0.07904,-0.11774,0.04357,0.00576,-0.02334,-0.0181,0.00671,-0.01879,0.05856,-0.03708,-0.11813,0.10105,0.08849,0.03999,0.03538,0.08384,-0.00581,0.01752]},{"domain":"energy_systems","key":"energy_critical_clearing","name":"Critical clearing angle and time (equal-area criterion)","package":"energy-systems-ai999x","example":"Critical clearing: Pm = 1, Pmax_pre = 2, Pmax_fault = 0, Pmax_post = 2","v":[-0.02901,-0.11531,0.0729,-0.00922,0.0146,0.15672,-0.04724,-0.01255,0.06332,-0.00893,0.0645,0.11393,-0.11516,0.03642,0.12588,0.04752,0.01222,-0.01167,0.09937,0.07975,-0.05225,0.10362,0.00074,0.04282,0.03191,-0.0081,0.11011,0.10698,0.07793,0.03651,-0.05612,-0.04746,-0.09724,0.0154,-0.06681,0.02317,0.0462,-0.01196,-0.09201,-0.09621,0.06947,-0.06583,-0.00276,0.09526,0.07006,-0.06018,0.02519,-0.11006,0.07096,-0.01583,0.04697,0.01836,0.00338,0.05033,0.0102,0.06521,7e-05,0.02778,-0.02844,-0.02783,0.05917,0.11209,-0.07422,-0.01997,0.07001,-0.0438,0.00462,0.02455,-0.07875,-0.08226,0.10574,0.01003,-0.02722,0.02639,0.06312,-0.0753,-0.00145,0.00506,0.00762,0.14325,0.04277,-0.06503,0.00805,-0.00576,0.00509,-0.05734,-0.09242,0.04073,-0.01521,-0.00841,-0.03564,0.04534,-0.04167,-0.07028,-0.09791,-0.04272,0.0328,-0.01211,-0.08846,-0.10852,0.00117,0.08814,-0.10363,0.01342,-0.11573,0.04949,-0.1331,-0.03471,-0.06828,-0.00587,-0.03459,0.06838,0.0462,0.06989,0.03383,0.00551,-0.06304,-0.112,0.00799,0.0044,-0.07951,0.00229,0.07213,0.04688,-0.04878,-0.07168,-0.05533,-0.0556,0.10062,-0.02041,0.01775,0.00851,-0.04485,-0.04824,-0.09316,0.02942,0.04227,0.00376,0.07869,-0.00428,0.01136,-0.0121,0.04743,-0.04346,-0.05112,-0.01983,0.068,0.06129,-0.00508,0.03151,0.10646,-0.01064,-0.10418,0.07987,-0.0953,-0.00615,-0.04537,-0.01533,-0.04492,-0.008,0.03885,0.15772,0.01869,0.06703,-0.00169,-0.03733,0.07566,0.03902,0.00941,-0.0226,-0.01585,0.0589,0.00502,0.06466,0.04861,0.03817,-0.06788,0.0563,-0.09224,0.052,-0.06505,-0.01752,0.08949,-0.02444,-0.07462,0.01483,-0.08684,0.01779,0.02011,0.0104,-0.0467,-0.1196,-0.03077,-0.03447,-0.07375,0.07144,-0.05229,0.06782,0.02989,0.07299,-0.04257,0.00444,-0.10358,0.13295,-0.0014,-0.01704,-0.04799,-0.12764,-0.02832,-0.06071,-0.0227,-0.00641,0.05937,-0.00491,-0.01624,0.04475,-0.06004,0.01435,-8e-05,-0.01516,0.01404,-0.14166,-0.04893,0.00514,0.00862,0.02159,-0.10371,-0.08924,0.12138,0.10457,-0.00429,-0.00594,0.02012,0.00811,0.06381,0.06988,-0.09718,-0.07051,0.00473,0.03757,0.03677,0.00781,0.00311,0.05331,-0.06813,0.10491,0.00744,-0.03598,-0.06215,-0.1136,-0.01906,0.14963,0.11403,0.05842,0.03468,0.08127]},{"domain":"energy_systems","key":"energy_dc_power_flow","name":"DC power flow","package":"energy-systems-ai999x","example":"DC power flow: lines = 1-2 0.1; 2-3 0.2, P = [0, 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module single-diode parameters at operating conditions (De Soto)","package":"energy-systems-ai999x","example":"De Soto parameters: G = 1000 W/m^2, T_cell = 25 degC, alpha_sc = 0.004, a_ref = 1.9 V, IL_ref = 9 A, I0_ref = 1e-10 A, Rsh_ref = 400 ohm, Rs = 0.3 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normal irradiance from global horizontal irradiance (DISC model)","package":"energy-systems-ai999x","example":"DISC model: ghi = 709.0092500000001 W/m^2, zenith = 0, n = 1","v":[0.07738,0.0414,0.05815,-0.0898,-0.00993,0.09486,0.01848,0.06815,-0.056,-0.00816,-0.05327,0.00403,-0.0043,0.05125,-0.02661,-0.04423,0.02336,0.03379,0.02794,0.02831,-0.0611,-0.12474,0.08669,0.00062,0.07824,0.02066,0.02617,0.02565,-0.02602,-0.11136,0.01128,-0.00809,-0.0317,0.092,-0.01983,0.0658,-0.07727,0.09377,0.01705,-0.05103,0.02807,0.0073,-0.08595,0.04046,0.02039,0.01885,0.00737,-0.11485,0.06063,-0.01089,0.0281,0.02179,0.09305,0.07613,-0.07638,-0.00112,0.11396,0.0326,-0.02335,0.03837,0.022,0.03454,-0.0698,-0.11967,-0.10331,-0.03156,0.0299,0.10848,-0.0034,0.04252,0.02538,-0.07748,0.18478,0.06824,0.02582,-0.04127,0.04698,0.01191,0.1067,-0.00356,0.05777,0.0588,0.04828,0.02631,-0.06174,-0.06865,-0.03178,0.02963,0.05758,-0.01776,-0.06966,-0.05737,-0.01327,-0.0328,0.03665,-0.05539,0.0542,-0.04278,0.01595,0.00068,0.07649,-0.03218,-0.15302,-0.03546,-0.03976,0.04525,-0.04239,-0.01941,0.07095,-0.10674,-0.07564,0.02315,0.09423,0.01211,0.03086,-0.00671,0.0484,-0.07328,-0.032,0.05892,0.09558,-0.04518,-0.06521,-0.00825,-0.05914,-0.14131,-0.00614,0.12163,-0.05796,0.04208,-0.08507,0.0342,-0.02831,-0.05523,0.06437,0.0738,-0.08904,-0.07598,-0.00252,0.13237,0.05274,0.05295,0.04384,-0.04279,0.12453,-0.01332,0.03621,-0.04517,-0.07901,0.04755,-0.02639,0.01314,-0.08806,0.18111,-0.03842,-0.05395,-0.01203,-0.05117,-0.0598,0.08902,0.03585,0.05288,-0.01946,-0.07669,-0.0192,0.06464,-0.03821,-0.05402,-0.07401,0.03079,-0.08155,-0.0984,0.00878,-0.0546,-0.00359,0.00468,-0.01962,0.09774,-0.00662,-0.02312,0.04201,0.12533,-0.12479,0.03817,-0.035,0.01834,0.10572,-0.02822,-0.09062,-0.01239,0.01023,-0.04624,0.05242,0.03845,-0.07562,-0.00382,-0.03325,0.05371,-0.08723,0.0449,0.01464,0.08551,0.00472,0.10466,0.01922,-0.0265,-0.02004,0.04841,-0.1324,-0.12969,0.03234,0.05241,0.0066,-0.07259,0.03504,-0.03131,0.01077,0.02117,-0.03959,0.01333,0.04221,-0.05353,-0.0518,0.0295,0.0251,0.0533,-0.03711,-0.05409,-0.06792,-0.0304,0.12005,0.07622,-0.06142,0.05008,0.15948,-0.06555,0.14252,0.02809,-0.07908,0.08387,-0.0903,-0.01851,0.01213,0.04691,-0.04493,0.0533,-0.00639,-0.0155,-0.06166,-0.0721,0.0446,-0.04909,-0.01174,0.06276,-0.10348,0.00803]},{"domain":"energy_systems","key":"energy_dlg_fault","name":"Double line-to-ground fault (symmetrical components)","package":"energy-systems-ai999x","example":"DLG fault: X1 = 0.1, X2 = 0.1, X0 = 0.1","v":[-0.05717,-0.01963,0.14902,-0.02732,0.08706,0.03075,0.03428,0.07037,0.07893,0.00531,0.03117,-0.0496,-0.177,-0.03658,0.0774,-0.0072,-0.07844,0.04155,-0.04422,0.13835,0.0189,-0.04966,0.03034,0.02353,-0.01631,-0.08176,0.0344,0.02392,-0.05386,0.00258,-0.12189,-0.02675,-0.04501,-0.04153,0.07559,0.06723,0.0406,-0.04993,-0.0383,-0.10727,0.06873,0.07709,0.05088,0.0783,-0.08292,-0.06079,-0.01406,0.04912,0.03688,-0.00404,-0.06944,0.10644,-0.01403,0.0362,-0.05646,-0.03631,0.00445,0.06538,-0.01804,0.01592,-0.03789,0.03332,-0.05337,-0.00244,0.0515,0.01682,0.06803,0.0146,0.00068,-0.02473,0.14169,-0.10765,-0.03761,-0.08129,-0.02854,-0.06565,-0.13404,-0.02926,0.17011,0.02371,0.001,0.00136,0.05283,-0.01552,-0.0046,0.0214,-0.01145,0.0098,0.00246,-0.00214,0.00724,-0.00557,-0.05002,0.07349,0.04179,0.04178,-0.13846,0.01673,-0.086,-0.07365,-0.01359,-0.0122,-0.12007,-0.04554,-0.0252,-0.04392,-0.02743,-0.08859,-0.07685,0.01641,-0.0363,0.01372,0.06992,-0.05247,0.0569,-0.06669,0.0297,-0.04362,0.03724,-0.08726,-0.0533,-0.01901,0.01407,-0.0278,-0.03415,0.0281,0.05081,0.04585,0.15676,-0.00892,0.05809,0.04429,0.01501,-0.07734,-0.04055,-0.05487,0.00702,-0.02524,0.10052,-0.00545,-0.03982,0.00824,-0.03481,0.04175,0.00296,0.07107,0.08093,-0.03797,0.09213,-0.05649,0.03423,0.00807,-0.05542,0.20193,-0.02064,0.05493,-0.05397,0.03344,-0.04769,-0.04541,0.05201,-0.02284,-0.00857,-0.17726,-0.00169,0.03931,-0.00034,-0.02771,0.05742,0.00674,0.02192,0.02945,0.10511,0.04318,0.03761,-0.04043,-0.0342,0.00596,-0.08979,0.01032,0.03244,0.04284,-0.06837,-0.07343,-0.1342,0.02217,-0.0573,0.04938,-0.00983,-0.00684,0.15511,-0.00121,-0.02595,0.04941,-0.05037,-0.09233,0.04412,0.11809,-0.01616,0.12718,-0.07302,-0.02403,0.06365,0.07631,-0.0163,0.01096,-0.04105,0.00215,-0.06494,0.01893,-0.02171,0.05235,0.00871,-0.05114,0.03462,0.00216,0.02956,0.11441,0.01295,-0.00424,0.14619,-0.06219,0.02331,0.02829,0.09304,0.03298,-0.09645,-0.12274,0.11266,-0.02407,-0.00301,-0.12866,0.00755,0.07247,0.02338,-0.03808,-0.15108,0.05181,0.02718,0.05966,0.04593,0.1157,0.05485,-0.05391,0.01486,-0.02053,0.03125,-0.08951,0.0695,-0.06131,0.01651,0.06407,-0.00885,0.01097,0.03709,-0.00048]},{"domain":"energy_systems","key":"energy_droop_sharing","name":"Frequency deviation and load sharing under governor droop","package":"energy-systems-ai999x","example":"Droop sharing: R = [0.05, 0.05], ratings = [500, 500], dP = 100 MW, f0 = 50 Hz","v":[-0.05621,-0.00577,0.0426,0.01256,-0.00673,0.04685,-0.04656,0.04062,0.01719,0.01806,0.11562,-0.05526,-0.06929,0.03155,-0.00244,0.04852,0.00028,0.00545,0.00608,-0.01493,-0.0116,0.00794,-0.05245,0.05806,-0.01703,0.03903,-0.0117,-0.06402,-0.05103,-0.11062,-0.06582,-0.04706,0.01555,-0.00742,-0.03361,0.10401,-0.05698,0.06752,0.02665,0.02554,-0.02605,0.02623,-0.02818,0.08052,0.00972,-0.07313,-0.01987,-0.04537,0.16402,0.06012,0.0093,0.16583,-0.07432,0.0303,0.00077,0.05405,-0.05324,-0.10603,-0.05017,-0.07072,-0.02078,-0.03276,-0.04996,0.07441,0.00829,0.01548,-0.04614,0.15098,0.07363,-0.06617,0.09903,0.06357,0.01094,0.08283,0.10813,-0.03814,-0.1529,-0.02197,-0.07009,0.02287,0.01915,0.03802,0.05843,0.01302,-0.04362,-0.06257,-0.01911,-0.02423,-0.16259,0.11021,-0.05108,-0.04609,0.00124,-0.00857,-0.10121,0.0006,-0.03428,0.01701,-0.09113,-0.05754,-0.01854,0.0381,-0.06821,-0.00722,0.00612,0.04884,0.11811,0.02577,-0.0104,0.10772,0.06211,0.04282,-0.06738,0.05475,-0.05486,0.04183,0.06935,-0.07366,0.01613,-0.11739,0.03681,0.04909,-0.07227,-0.00012,0.00366,-0.1133,-0.01381,0.04046,-0.02095,-0.06227,0.00176,-0.07374,-0.03515,-0.03625,-0.0172,0.08604,-0.0153,-0.02197,-0.0276,-0.00015,-0.09217,0.01778,-0.05975,-0.0195,0.07315,0.06922,-0.01804,-0.05246,0.04908,0.04675,0.08064,-0.07005,-0.03015,0.0724,-0.03398,-0.00702,0.02059,0.01843,0.05465,-0.03291,-0.01202,0.08576,-0.0044,0.13236,-0.011,-0.13337,0.1397,0.07363,-0.00934,-0.03326,0.1115,-0.03443,0.01764,-0.07064,0.09827,0.07712,0.00026,-0.00975,-0.04524,0.08411,-0.05117,0.01563,0.04033,-0.00077,0.08228,0.00302,-0.04282,0.04335,0.06763,0.0429,-0.15695,0.05342,-0.00947,-0.0321,-0.08358,0.08488,-0.01819,0.07232,-0.05605,-0.06226,-0.00635,0.00373,-0.03369,-0.04654,-0.01282,-0.00133,-0.05299,-0.08958,-0.05903,-0.10324,0.02583,-0.02452,-0.00994,-0.0067,-0.03206,-0.00615,-0.08156,0.03707,-0.00089,-0.06932,0.10295,0.10794,0.01755,0.13848,0.02576,-0.01683,-0.01947,-0.0973,0.07292,0.12814,-0.02726,-0.02614,-0.0157,-0.00444,0.0279,0.05391,-0.19135,0.09395,-0.10939,0.04928,0.05022,0.02645,0.02877,-0.04159,0.10584,0.10176,0.10224,0.01736,-0.07768,-0.03376,-0.03109,-0.03247,-0.08368,-0.01908,0.10474,0.02158]},{"domain":"energy_systems","key":"energy_economic_dispatch","name":"Economic dispatch with quadratic costs and limits","package":"energy-systems-ai999x","example":"Economic dispatch: costs = [500 5.3 0.004 200 450]; [400 5.5 0.006 150 350]; [200 5.8 0.009 100 225], demand = 800 MW","v":[-0.10723,0.01924,-0.08605,-0.08766,-0.01458,0.0152,0.09428,-0.0742,0.04445,-0.00836,0.00999,-0.00825,-0.03502,-0.03096,0.01564,-0.08141,0.04903,0.05727,0.00417,0.0338,-0.10156,0.01321,-0.06967,-0.02945,-0.00762,0.08612,0.05452,0.01891,-0.00813,0.02959,-0.09203,0.00233,-0.06831,-0.01367,-0.04209,-0.01305,0.0299,0.07285,0.05776,-0.11961,-0.06558,0.01237,-0.05341,-0.03323,0.09166,-0.03947,0.01609,0.02913,-0.01502,0.06702,0.0763,0.0297,-0.01708,-0.02079,0.0247,0.02281,0.09091,-0.04228,-0.06206,0.084,0.02605,-0.02381,-0.05539,0.07046,0.02234,-0.00877,0.06585,-0.04187,-0.02848,-0.05139,0.09547,0.04903,0.11721,0.11147,0.00095,0.01337,0.00241,0.01227,-0.02742,0.01358,0.11751,-0.0068,0.04544,-0.02635,-0.09473,-0.10736,0.02208,-0.08657,-0.1105,0.09465,-0.0255,-0.0026,0.04535,0.0302,-0.0395,-0.18746,-0.0201,0.04914,-0.10599,0.07311,0.02941,0.03802,-0.11837,0.0067,-0.09782,-0.00233,-0.03625,-0.04253,-0.08366,0.10738,0.04277,0.01031,0.11461,0.04303,0.00513,-0.03239,-0.02091,-0.05998,-0.00726,0.1105,0.00252,0.02823,0.0625,-0.0442,-0.03119,-0.05835,-0.03603,0.09065,0.05762,-0.00429,0.02609,0.03591,0.02772,-0.0097,-0.10069,-0.02065,0.02192,-0.06947,-0.00488,-0.00578,-0.06484,-0.11266,0.02648,-0.02392,-0.01005,0.15654,0.00462,-0.02726,-0.01416,0.00434,0.02675,0.03671,-0.01822,0.00426,0.02081,-0.0769,0.07251,-0.00246,0.02279,0.0569,-0.13778,0.08896,0.02113,0.10091,0.02491,-0.0223,-0.00186,0.02734,-0.00227,-0.03041,0.03484,0.06921,0.02803,-0.09214,-0.08907,-0.05145,0.10522,-0.03776,-0.0779,-0.01374,0.02435,-0.09644,-0.08992,0.00331,-0.03093,0.01927,-0.03466,-0.02248,-0.06334,0.09852,-0.10878,-0.01288,0.11706,0.1241,-0.05121,0.06281,-0.00696,0.03099,0.1457,-0.05417,0.02529,0.08181,-0.01767,-0.0319,-0.06841,-0.0763,0.03257,0.02728,0.06066,-0.232,-0.04612,0.02616,0.02546,0.04903,0.03681,0.0939,-0.12178,0.00081,0.05039,-0.05062,-0.02088,0.02925,-0.02045,0.09438,0.0985,-0.02039,-0.22374,0.02791,0.00931,0.03941,0.11355,0.03734,0.0433,-0.03073,0.05876,0.04936,-0.04088,0.0321,0.01298,-0.03037,0.08098,0.0519,0.03374,-0.00744,-0.09741,0.07454,0.04688,-0.02212,-0.07987,0.03276,0.02828,0.03741,-0.00264,0.02592,-0.02453,-0.05294]},{"domain":"energy_systems","key":"energy_electrolyser","name":"Water electrolyser: hydrogen production and energy per kilogram","package":"energy-systems-ai999x","example":"Electrolyser: I = 192970.66424 A, N = 1, V_cell = 2 V","v":[0.09843,-0.00214,-0.07176,-0.11911,0.06325,0.04524,0.046,0.07491,-0.10034,0.05453,-0.03002,0.06629,0.08031,-0.02835,-0.01058,0.04841,-0.11125,0.05924,-0.00628,0.07706,-0.02227,0.082,-0.08532,-0.02975,-0.05764,-0.00931,-0.00954,-0.05154,-0.09259,-0.04079,-0.06404,-0.1025,0.04242,0.01004,0.03461,-0.00643,-0.00811,0.04418,0.0024,-0.03906,0.04458,0.08765,0.00407,0.08791,-0.03349,0.01202,-0.12262,-0.01809,-0.01581,0.00028,0.08738,-0.00806,0.02017,0.01302,-0.04247,-0.00733,0.02406,-0.0706,-0.10752,-0.04752,-0.02138,-0.07831,-0.02607,-0.04867,0.02294,-0.00355,-0.0517,0.03391,0.03592,0.0348,0.04158,0.07234,-0.02878,0.01538,0.05297,0.12408,0.06116,-0.02191,-0.07533,-0.07203,0.02788,0.02673,-0.03925,0.08,-0.06882,-0.06829,0.07024,-0.03231,0.08772,0.10087,-0.04631,0.0462,0.07122,0.05063,0.05415,0.05395,-0.13684,-0.08854,-0.0894,-0.00655,-0.06043,0.01737,-0.02457,-0.0574,-0.11624,-0.05939,-0.01292,0.04269,-0.03521,-0.07922,0.02958,0.02702,0.06866,0.06403,-0.01045,0.00025,0.02897,-0.0002,0.08985,0.02176,0.03282,-0.04815,0.03271,0.03266,-0.09583,0.15224,-0.20602,0.15666,0.01757,-0.01664,-0.10275,0.06759,0.08288,-0.05307,0.03816,0.0278,-0.02685,-0.09323,0.01428,0.02438,0.0852,0.00276,-0.03064,0.02529,0.08933,-0.06062,-0.00456,0.00506,0.12921,0.09575,0.02773,0.01527,0.02036,0.01096,0.00048,-0.07552,0.10421,-0.03489,0.02086,-0.03969,0.04279,0.10128,0.04975,-0.02022,-0.0756,-0.06142,-0.02871,0.03087,-0.1017,-0.01919,0.00076,0.03979,-0.09204,0.03113,-0.03255,0.02319,0.00704,-0.04777,0.03338,-4e-05,-0.08148,-0.02572,-0.12628,-0.01628,-0.16007,0.13833,0.03106,0.0487,0.04363,-0.03688,-0.08513,-0.02363,-0.04883,0.08485,-0.00109,0.07702,-0.03768,0.06021,-0.01692,-0.0546,-0.02135,0.09953,0.01625,0.06317,-0.04253,-0.13103,0.13059,0.09973,-0.08226,-0.12821,0.0423,-0.06151,0.01334,0.08198,-0.03674,-0.04628,-0.01016,0.0687,0.06731,-0.03995,0.05781,0.00472,0.04429,0.14758,0.04877,0.02046,0.05136,0.02419,0.01924,-0.06993,0.01897,-0.03624,-0.0271,-0.00401,0.04467,0.10312,-0.06689,-0.00528,-0.03872,-0.06639,-0.07874,0.03558,0.05471,-0.01317,-0.09254,3e-05,0.03769,-0.0089,0.05034,0.01747,-0.01585,0.02764,-0.06664,0.07656,0.05244,-0.03327]},{"domain":"energy_systems","key":"energy_equation_of_time","name":"Equation of time","package":"energy-systems-ai999x","example":"Equation of time: n = 81, method = pvcdrom","v":[0.11841,-0.00469,-0.00036,0.10275,0.08155,0.00878,0.10417,0.15058,0.05756,0.07563,0.07117,-0.08007,-0.00979,0.03804,-0.04803,0.00817,0.00318,0.0429,0.03188,-0.11015,0.02944,-0.10969,-0.00513,-0.06176,0.16662,-0.00325,0.04153,0.00461,0.01073,-0.03365,0.01006,-0.01741,0.00494,-0.00353,0.05396,-0.07328,0.05077,0.01019,-0.03977,0.04317,-0.061,-0.06524,-0.07371,-0.03137,-0.05258,-0.05256,0.01311,-0.08893,0.10358,0.01573,-0.00486,0.00964,-0.04847,0.08861,-0.0876,-0.08471,-0.01138,0.11769,0.00246,-0.00158,0.02885,0.07893,0.0309,0.06328,0.0329,0.01112,0.0211,-0.0663,-0.07679,0.07158,-0.02202,-0.01762,0.0471,-0.05513,-0.03047,-0.02341,0.07945,-0.0313,0.12397,0.03643,-0.03626,-0.00428,0.03493,-0.07069,0.05096,-0.09987,0.02231,-0.06495,0.07236,-0.10117,-0.00166,-0.07708,-0.00455,-0.13735,-0.16804,-0.02631,0.07599,-0.06833,0.04729,0.09989,0.03218,0.01378,-0.05618,-0.14165,-0.04718,-0.05948,-0.07552,0.01234,0.17195,-0.07899,0.04736,0.00153,0.03913,-0.03777,0.05947,0.09546,-0.0324,0.0861,-0.01724,0.07177,-0.03571,-0.0571,-0.04726,-0.03113,-0.02132,-0.03024,-0.01034,-0.02474,-0.05603,0.02344,-0.02229,0.04877,0.09707,-0.03607,0.02136,0.04767,-0.02345,0.016,0.01931,0.19699,-0.00124,0.0213,0.15761,-0.0269,-0.0275,-0.00736,-0.0461,-0.06986,-0.08923,0.08514,-0.01504,-0.10484,2e-05,-0.0686,-0.04709,-0.00937,0.07124,-0.03725,0.00604,-0.06644,0.02585,0.01478,0.02824,0.01555,0.06779,-0.00958,-0.0477,0.10794,-0.04519,0.03295,0.02311,0.04951,0.00826,-0.01245,-0.02215,0.04863,-0.02391,0.01165,0.02777,-0.06575,-0.02593,-0.01737,-0.00145,0.06496,0.02233,0.03891,-0.03162,-0.00316,-0.122,-0.00789,0.06891,-0.02676,0.00642,0.01897,0.03561,0.01771,0.17535,-0.00448,-0.07501,-0.02896,0.0669,0.01385,-0.04463,0.08885,-0.046,-0.00491,-0.07244,0.03594,0.01019,0.02064,-0.0182,-0.1074,0.00326,-0.00987,0.06132,-0.03678,0.01725,-0.05932,0.00014,0.01693,0.00713,-0.00245,-0.0084,-0.07484,0.00693,-0.08613,-0.00399,-0.05793,-0.00459,0.04586,0.01558,0.01204,-0.03725,0.02005,0.05688,-0.05273,0.01896,0.01615,0.05373,0.07839,0.00809,0.02199,-0.08691,0.1354,0.09303,-0.10928,-0.00539,-0.17244,-0.07712,0.00055,0.16875,0.01028,-0.00573,-0.02881,-0.16342,-0.04993]},{"domain":"energy_systems","key":"energy_erbs_decomposition","name":"Diffuse and direct irradiance from global horizontal irradiance (Erbs)","package":"energy-systems-ai999x","example":"Erbs decomposition: ghi = 141.3981805 W/m^2, zenith = 0, n = 1","v":[0.1202,0.00701,0.11236,-0.01305,0.01274,0.01071,-0.02702,0.01628,-0.01611,-0.0743,-0.0476,-0.05202,0.05146,0.03116,-0.05822,-0.13896,0.01672,0.01089,0.02798,0.01412,0.04367,-0.10682,0.06605,-0.06069,0.17017,0.0249,-0.00276,0.0524,-0.08817,-0.03648,-0.06778,0.01931,-0.04698,0.01518,-0.02025,0.0604,-0.04466,0.04014,0.06198,-0.09626,0.02,0.01616,-0.14563,0.08554,0.03245,-0.03934,0.02495,-0.04497,0.03507,-0.06879,0.02531,0.06387,0.09958,-0.01983,-0.08692,0.03847,0.12703,0.00037,-0.03338,-0.00386,0.00871,0.06267,-0.05191,-0.10269,-0.13445,-0.05705,0.03118,0.0394,0.00735,0.04236,0.07197,-0.08772,0.14504,0.03812,0.01635,-0.08484,0.01488,0.0525,0.13366,-0.03687,0.04802,0.00889,0.04279,-0.00488,-0.00957,-0.04887,-0.08856,-0.02434,0.01318,0.04924,-0.12035,-0.07397,0.02844,-0.0344,-0.03885,-0.02751,0.01901,-0.11321,0.01589,-0.01781,0.04862,0.02098,-0.10274,0.00303,-0.09366,-0.04257,0.03147,-0.01297,0.16457,-0.07148,-0.03446,0.03241,0.19082,-0.02345,0.04359,0.03193,0.05917,-0.00488,-0.03668,-0.03468,0.04825,-0.01981,-0.12198,0.06929,-0.05134,-0.15667,0.04739,0.00453,-0.104,0.02164,0.05386,-0.02627,-0.04479,-0.04671,0.02876,0.06473,-0.01278,-0.03314,-0.02128,0.09278,0.09542,0.03386,0.01172,0.04608,0.12599,-0.0879,0.02732,-0.02246,-0.02276,0.15492,-0.0137,-0.01786,-0.08704,0.07242,-0.02921,-0.03129,0.0441,-0.03578,-0.03245,0.05755,0.07819,0.03103,-0.03824,-0.09051,0.0765,0.07529,-0.128,-0.03624,-0.08312,0.05073,-0.02803,-0.06473,-0.05465,0.03147,-0.01251,0.00702,-0.01603,0.09531,-0.04612,-0.0335,-0.00606,0.05682,-0.07866,-0.00227,0.00783,0.06024,0.0666,-0.0006,-0.05425,-0.00585,-0.04016,-0.03814,0.04592,0.04591,-0.03693,0.01834,-0.06625,0.07057,-0.02131,0.05388,-0.03886,0.07795,0.01832,0.03578,0.00888,-0.03015,-0.01785,0.03328,-0.05761,-0.07224,-0.01117,0.04687,-0.06623,-0.01307,0.00296,-0.07231,-0.07467,0.05657,0.02156,0.02564,0.00283,-0.01186,0.06481,0.00327,0.03481,0.04144,-0.00917,-0.08081,-0.04765,-0.01907,0.02534,0.0648,-0.06027,-0.01843,0.16,-0.06055,0.15995,-0.03214,-0.0056,0.13687,-0.10037,-0.00112,0.00626,0.13525,-0.02053,0.08456,0.01215,-0.022,0.02817,-0.00629,0.07104,-0.02034,-0.08046,0.02892,-0.08443,0.0353]},{"domain":"energy_systems","key":"energy_extraterrestrial_irradiance","name":"Extraterrestrial (top-of-atmosphere) normal irradiance","package":"energy-systems-ai999x","example":"Extraterrestrial irradiance: n = 365, method = asce, solar_constant = 1367 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fuel-cell stack: consumption, power and efficiency","package":"energy-systems-ai999x","example":"Fuel-cell stack: I = 192970.66424 A, N = 1, V_cell = 0.7 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mean distance of a three-phase line","package":"energy-systems-ai999x","example":"Geometric mean distance: D_ab = 4 m, D_bc = 4 m, D_ca = 8 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density at hub height","package":"energy-systems-ai999x","example":"Air density at hub height: p = 1013.3 hPa, h_p = 0 m, T = 288.15 K, h_T = 0 m, hub = 0 m","v":[-0.03254,-0.03406,-0.04375,-0.09178,0.02279,0.09256,0.01919,0.02781,0.09955,0.02707,0.01478,0.06613,-0.03989,0.13745,0.00895,-0.08222,0.0707,0.07879,0.1497,0.02727,0.00331,-0.06937,0.03415,-0.04272,0.04324,0.078,0.06945,-0.02734,-0.07279,-0.05082,-0.04128,-0.00552,0.03816,-0.04588,0.03263,0.10253,0.05792,-0.00375,-0.03664,0.04531,-0.01131,0.03295,-0.02624,0.03,-0.06561,0.00122,-0.09867,-0.16045,0.03978,-0.06664,-0.03801,-0.0808,0.02246,-0.00481,-0.06274,-0.05896,0.13303,0.0064,0.01937,-0.04544,-0.08952,-0.08199,0.01518,-0.07812,-0.03675,-0.03405,0.0279,0.04566,-0.09907,0.09169,0.01565,0.06342,-0.03729,-0.05144,0.06367,-0.00469,0.10395,-0.04597,-0.08628,0.04003,0.02735,6e-05,-0.01402,0.03433,-0.09843,-0.08708,0.1021,-0.02482,-0.01774,0.10218,-0.05786,0.01229,-0.02969,0.00036,-0.08672,0.06534,0.1629,0.02934,0.05931,0.07042,0.02314,-0.03823,0.00485,0.10634,0.05889,-0.03146,0.01021,0.03689,0.05736,-0.02369,-0.0646,-0.11611,-0.06315,0.00213,-0.05102,-0.01991,0.08202,0.08517,-0.01372,-0.03471,-0.04647,-0.02192,0.00977,-0.10128,-0.02127,0.01334,-0.01177,-0.01639,0.07694,-0.04384,-0.04581,-0.00659,0.08202,-0.07902,-0.03021,0.04309,-0.06982,-0.08077,0.063,0.08735,-0.02599,-0.0002,0.02001,-0.03424,0.08058,0.11451,0.04402,-0.09442,0.07,-0.01592,-0.04275,-0.03601,0.02639,0.09036,0.07682,0.02707,0.01196,-0.00536,-0.0911,-0.01813,-0.04019,0.08138,0.00553,-0.06372,-0.02044,0.0074,0.04034,-0.14091,-0.0169,-0.0225,-0.00989,-0.11198,-0.01876,-0.08494,-0.02003,0.06372,-0.00977,0.00141,0.0469,0.15172,0.02192,0.05492,0.00918,0.07034,-0.03044,0.03953,0.12906,-0.03637,-0.08116,-0.04457,0.08459,0.14339,0.02352,0.04022,0.03244,-0.00159,-0.0175,0.07701,-0.02129,-0.06781,-0.05891,0.06614,-0.07652,-0.04857,0.00298,-0.06094,0.05688,0.0508,0.0305,-0.01468,0.03891,0.04379,0.04475,-0.04675,-0.01093,0.05191,0.03139,0.01104,0.02563,0.00131,-0.06116,-0.05807,0.13484,-0.02128,-0.10359,-0.12514,0.02819,0.01643,-0.07514,-0.05931,0.1106,0.01712,-0.08445,-0.00746,0.09649,-0.02187,-0.05278,0.0367,0.04867,0.0781,-0.05226,-0.13224,0.12638,0.01368,-0.07676,-0.03424,0.01952,0.07543,-0.04609,-0.09827,-0.05045,0.121,-0.08059,0.06832,0.01617,-0.03413]},{"domain":"energy_systems","key":"energy_hydrogen_isentropic_compression","name":"Isentropic (adiabatic) compression of hydrogen","package":"energy-systems-ai999x","example":"Hydrogen isentropic compression: p1 = 30 bar, T1 = 300 K, p2 = 100 bar","v":[0.00368,0.03602,-0.12216,-0.10537,0.07883,0.07168,-0.0065,-0.07199,-0.10184,0.0459,-0.13361,0.03234,0.03154,0.01147,0.05063,0.04507,-0.0009,0.03619,0.03386,0.01061,-0.00268,-0.00062,-0.01066,0.04426,-0.05812,0.01408,-0.01694,-0.04295,-0.04935,0.05549,0.04679,-0.04755,0.03795,-0.01004,0.09589,0.13163,-0.06203,0.01393,-0.11883,0.00127,0.00499,0.0164,-0.10375,0.08097,-0.04477,-0.00897,-0.06028,-0.11209,0.02213,-0.02792,0.07407,-0.02939,0.05712,0.02362,-0.0718,-0.07186,0.01185,0.02973,-0.00157,0.03361,0.02378,-0.10571,-0.03046,0.00756,0.01795,-0.00182,-0.02689,-0.00734,-0.00996,0.05282,-0.02801,0.10508,0.03345,-0.05046,0.06168,-0.05081,0.05516,0.04051,0.13119,0.02257,-0.07696,-0.04729,-0.00649,0.10045,-0.07825,-0.15277,0.01421,-0.06137,0.02109,0.03449,0.14877,0.01763,0.03306,0.09139,0.00644,-0.05004,0.09697,-0.11717,0.03122,-0.01469,0.12383,0.01702,0.01041,-0.08287,-0.10527,-0.11094,-0.04717,0.03362,0.02029,0.00318,-0.01677,0.03549,-0.00375,-0.00469,-0.02099,-0.02083,0.01992,-0.00307,0.05924,-0.02369,-0.03926,0.02485,-0.00212,-0.01139,0.03121,0.07783,0.00793,-0.01552,0.02283,-0.00476,-0.06174,-0.01694,0.00956,-0.08199,0.00773,0.08175,-0.0987,-0.04721,-0.09044,-0.06873,-0.03244,-0.10089,-0.00209,-0.01503,0.19563,0.1111,-0.03479,-0.02091,0.06584,-0.036,-0.01801,-0.02309,0.01567,0.02931,0.03199,0.0644,0.05761,-0.01721,0.06354,-0.0299,-0.0067,-0.03329,0.00882,0.02798,-0.03214,-0.00337,0.11839,-0.10333,0.06382,0.11796,0.01742,0.04756,-0.08041,0.03006,-0.10559,0.06063,0.02189,0.03131,0.07112,-0.08325,-0.00425,0.01939,0.0038,0.11087,-0.06107,0.06852,0.09719,0.05516,0.01421,-0.05264,0.03284,0.06467,0.03393,0.12632,-0.03903,0.06237,-0.13793,0.10696,-0.05465,-0.09953,0.04105,0.06929,0.00341,-0.06918,0.05242,-0.07912,0.02215,0.05472,-0.09812,-0.07313,0.01085,-0.12723,0.03378,-0.00348,0.01661,-0.02031,-0.05948,0.0348,0.00779,-0.06499,0.15375,0.00617,0.03991,0.02742,0.02635,0.00233,0.00993,0.11419,-0.08545,-0.03944,-0.02621,-0.08639,-0.02925,-0.01322,0.06362,-0.08509,0.02026,0.13757,-0.09253,0.03063,0.06825,-0.05592,0.13722,0.04757,-0.05237,0.04749,-0.01645,-0.00771,-0.00359,0.01229,-0.04857,0.04402,-0.1069,0.09153,-0.0779,-0.07013]},{"domain":"energy_systems","key":"energy_hydrogen_isothermal_compression","name":"Minimum (isothermal) work to compress hydrogen","package":"energy-systems-ai999x","example":"Hydrogen isothermal compression: p1 = 1 bar, p2 = 2 bar, T = 300 K","v":[0.0086,-0.05121,-0.09536,0.01957,0.00024,0.11024,0.06218,-0.0339,-0.07826,0.01868,-0.18171,0.01393,0.05883,-0.06857,-0.01867,0.01432,0.02093,-0.03093,0.081,0.13074,0.00357,0.06602,-0.03374,0.07544,0.0056,0.06911,-0.02476,0.03841,-0.02649,0.1065,0.00533,0.02085,0.05209,0.03316,0.03863,0.08917,-0.1488,0.09128,-0.06634,-0.06103,0.01453,-0.00453,-0.10176,-0.00504,0.02017,-0.038,-0.06383,-0.10004,0.05659,-0.03651,0.13681,-0.03803,0.05416,-0.00187,-0.09583,-0.03882,-0.01004,0.01401,0.00669,0.05008,0.05195,-0.01552,-0.08499,0.03491,0.0315,-0.00623,-0.0628,-0.02822,-0.049,-0.02576,-0.00227,0.08001,0.01334,-0.05539,0.01713,-0.02193,-0.00383,0.07757,0.01735,-0.00778,0.03177,0.06014,0.05833,0.03216,-0.13444,-0.11554,-0.04379,-0.02739,0.07171,0.15081,0.04985,0.05015,0.02464,0.03309,-0.00179,-0.05505,0.09167,0.00072,-0.00164,0.06411,0.02604,-0.00193,-0.01694,0.04779,-0.08528,-0.07704,-0.05971,-0.05525,0.01103,0.04451,-0.00293,-0.02266,0.05638,-0.05148,-0.06952,-0.02701,-0.10166,-0.04883,0.05644,0.04323,0.00558,-0.02589,0.05391,-0.07723,-0.03729,-0.07362,-0.03762,0.01813,0.09304,0.05175,-0.02964,-0.00773,0.00722,-0.00417,-0.02746,0.01462,-0.09802,0.01057,-0.0199,-0.03583,-0.00501,-0.10618,-0.12761,0.06747,0.14585,0.06172,0.02875,-0.06735,0.07422,-0.05667,0.00203,-0.0116,0.02682,0.09079,0.02691,0.00855,0.11961,0.00252,0.07177,-0.04305,0.01726,0.04111,0.04335,-0.00726,-0.10266,-0.08687,0.08338,-0.0562,-0.04603,0.12001,0.02874,0.06324,-0.04121,0.09483,-0.06419,-0.01173,0.06245,0.05413,0.0547,-0.02037,-0.03389,-0.02034,-0.07283,-0.02874,-0.09074,0.00244,-0.0206,-0.06086,0.03721,-0.02279,-0.12173,0.03737,-0.00029,0.11131,0.04728,0.07587,-0.12137,0.042,-0.02867,-0.04238,-0.00564,0.09566,-0.05423,-0.1679,-0.05014,-0.09388,0.06498,0.00349,-0.11266,-0.13974,0.11743,-0.01281,0.05032,0.01388,0.06747,-0.01649,0.04219,-0.05971,0.00934,-0.06739,0.092,-0.01948,-0.00479,0.01025,0.0538,-0.02229,0.02192,0.06298,-0.14502,-0.01961,0.09577,-0.08199,-0.01373,0.02728,0.03842,0.04534,-0.08819,0.10194,-0.0667,-0.0455,0.04309,-0.04115,0.12655,0.08417,-0.06451,0.08833,0.00608,-0.00244,-0.05593,-0.01449,-0.00862,0.02522,-0.07479,0.08786,0.02504,0.02584]},{"domain":"energy_systems","key":"energy_hydrogen_tank","name":"Hydrogen stored in a tank at pressure (real gas)","package":"energy-systems-ai999x","example":"Hydrogen tank: V = 1 m^3, p = 700 bar, T = 288.15 K","v":[-0.03121,-0.01083,-0.12024,-0.09191,0.11485,0.07561,0.17968,0.05033,0.07992,0.05061,-0.01831,0.08099,0.06667,0.02848,0.01611,0.06473,0.05494,0.03712,0.08708,0.11638,0.04127,0.0018,-0.09771,0.01312,0.01712,0.03142,0.04975,-0.01057,-0.05724,-0.06729,-0.03036,-0.02257,0.10378,-0.0169,0.00629,0.08345,-0.03248,0.08444,-0.04795,0.03766,0.01665,0.04422,-0.10865,0.0602,-0.03511,0.00892,-0.12502,-0.13055,0.09551,-0.06302,0.09038,-0.08339,0.0588,0.09284,-0.07453,-0.12999,-0.00771,-0.00658,0.00937,0.05491,-0.00529,-0.08991,0.00033,0.04012,0.0786,-0.03715,-0.0662,-0.06881,0.02932,0.00017,-0.08724,-0.01678,0.00325,0.02534,0.05868,0.01346,0.14472,-0.0291,-0.01971,0.0528,0.08578,-0.00173,-0.00399,0.00271,0.0102,-0.06834,0.03544,0.03066,0.00443,0.05433,0.01255,0.05463,-0.08305,0.01928,0.01686,0.02657,0.02678,-0.07691,0.03424,0.1203,-0.01882,-0.13942,-0.0908,-0.0814,-0.09745,-0.08605,0.03317,0.03126,-0.01008,0.01774,-0.15322,-0.00317,0.0288,0.01218,-0.05963,-0.11193,0.05317,0.12746,0.07037,0.03579,-0.03527,-0.01925,0.01993,-0.09813,-0.02269,-0.0243,-0.05391,0.01424,0.14733,-0.06111,-0.15331,0.00568,0.06571,-0.06527,0.02859,-0.0048,-0.13826,-0.07103,-0.00858,0.0247,0.0293,-0.03124,-0.00128,0.0657,0.12464,0.08494,0.06269,-0.0281,0.03674,-0.05498,0.03001,0.02947,0.11524,-0.00597,-0.01793,-0.01931,0.05062,0.03029,-0.00128,-0.05047,-0.01352,0.0503,0.04149,-0.01458,0.00908,-0.01204,0.01487,-0.04262,0.0343,-0.02922,-0.07833,-0.00541,-0.14782,-0.02486,-0.02424,0.05961,0.04877,-0.04613,0.08093,0.04682,0.02945,0.1242,-0.00144,0.05505,-0.07554,0.023,0.03246,-0.04163,-0.08265,-0.08556,-0.04748,0.0201,0.08624,0.0797,0.07894,0.01241,-0.06653,0.0914,-0.09425,0.02735,0.01325,-0.01188,-0.0322,0.03489,-0.02936,-0.04614,0.01184,0.03991,-0.05003,-0.06109,0.05723,-0.00918,0.09164,-0.03675,-0.04206,0.01271,-0.02253,-0.02103,-0.04192,-0.10734,0.10394,0.03608,-0.07349,0.00397,-0.07493,-0.08069,0.05082,-0.00015,-0.11177,-0.04964,0.1337,-0.04783,0.05334,-0.01114,0.02467,0.01717,-0.00285,0.12783,-0.01379,-0.00767,-0.03351,0.01762,0.06047,0.02209,-0.0309,-0.02118,-0.01741,0.01247,-0.00872,-0.05095,-0.01278,-0.02505,-0.09504,0.08473,-0.06353,-0.0207]},{"domain":"energy_systems","key":"energy_iam_ashrae","name":"Incidence angle modifier (ASHRAE)","package":"energy-systems-ai999x","example":"Incidence angle modifier (ASHRAE): aoi = 60","v":[0.13271,0.03939,0.00294,0.02945,0.01401,-0.02086,0.0017,0.0269,0.04046,-0.02059,-0.04419,-0.10442,0.01737,0.03942,-0.04513,0.10504,0.07376,-0.00955,0.05194,0.10045,0.03819,-0.04848,-0.0158,0.08374,0.10124,0.00985,0.00126,0.08834,-0.03194,-0.06869,0.05887,0.05442,-0.12071,0.09033,-0.05716,0.027,0.02488,0.02862,-0.07173,0.156,0.02433,0.04036,0.08555,-0.01667,0.12393,-0.06105,0.02005,0.00787,0.07521,0.01862,0.06016,0.0691,0.02625,-0.03446,-0.0144,0.08336,0.08415,0.00447,-0.12972,0.03794,-0.00595,0.0637,-0.08827,-0.03235,-0.04354,-0.03385,0.01835,0.0367,0.05834,-0.04543,0.05575,-0.08082,0.16306,-0.01127,0.00614,0.00277,0.08836,0.00688,-0.00191,0.00249,0.03725,0.05051,0.03497,0.06545,0.05214,-0.11076,0.04296,-0.06427,0.0407,-0.02247,-0.01548,0.00976,-0.0223,-0.07591,0.01626,0.04501,-0.02643,-0.03518,0.11394,-0.01718,0.00679,-0.04469,-0.0213,-0.04659,-0.0516,-0.03129,0.08051,0.06586,0.01812,-0.0325,0.10515,0.07742,0.04775,-0.08382,0.02833,-0.01948,0.01429,-0.0856,-0.03741,-0.03961,-0.03251,-0.02098,-0.06135,-0.0574,-0.03664,-0.04162,-0.11364,-0.01498,-0.06245,0.0136,0.07675,0.07102,0.13451,-0.11188,-0.05201,0.02841,-0.02093,-0.06682,-0.0453,0.11232,0.20294,-0.11192,0.03681,-0.02393,0.12913,-0.09683,-0.00668,0.00088,-0.08009,0.05009,0.01906,-0.00099,0.04836,-0.00497,-0.03542,0.04158,-0.13753,-0.0796,0.07519,0.10373,0.04434,-0.06991,-0.0267,-0.00035,0.07973,-0.02833,0.03928,-0.03932,-0.08438,-0.05838,0.02334,0.02831,-0.06913,-0.09419,0.07557,-0.07628,-0.00397,0.02947,0.01473,-0.13043,0.02995,0.04683,-0.11047,-0.07164,-0.03471,-0.07688,-0.07918,0.04139,-0.02297,-0.0061,-0.07524,-0.07584,0.0365,-0.03227,-0.11779,0.12842,-0.05789,0.10412,0.05326,0.09312,0.00069,-0.01442,0.09961,0.02886,0.01651,-0.00037,-0.06728,-0.03724,0.01351,-0.02526,0.00581,-0.0477,0.01849,0.00634,-0.02691,-0.00436,0.01436,0.05441,0.06789,-0.09527,-0.01725,-0.04333,-0.06415,0.05638,-0.11612,-0.02948,0.11198,-0.0082,0.05926,-0.07156,0.07504,0.0388,-0.06104,-0.06605,0.08375,-0.08809,-0.04196,-0.01346,0.03681,0.04494,-0.01306,-0.01405,0.02861,0.01889,0.06595,-0.00878,0.08328,-0.04296,-0.05091,-0.06727,-0.00709,-0.00619,-0.13243,-0.03036,-0.01324,0.03104]},{"domain":"energy_systems","key":"energy_iam_physical","name":"Incidence angle modifier from Fresnel reflection and absorption","package":"energy-systems-ai999x","example":"Incidence angle modifier (physical): aoi = 0","v":[0.14113,0.0217,0.06776,0.01146,-0.02926,0.04908,0.03086,0.01366,0.08368,-0.05173,0.036,-0.07934,0.01423,-0.01893,-0.0477,0.02512,0.06598,-0.09106,0.04032,0.12578,-0.02561,0.00967,-0.05823,0.08636,0.03776,0.00867,0.03146,0.12671,-0.05174,-0.03855,0.14121,-0.0106,-0.04225,0.11712,-0.0595,0.02856,0.09664,-0.06407,-0.00991,0.06359,-0.03327,0.00162,0.0906,-0.00193,0.02797,0.01129,-0.03758,0.03609,0.03979,-0.05232,-0.00797,0.08912,0.06057,0.0244,-0.09219,0.01491,-0.00972,-0.04637,-0.06679,0.02062,0.02414,0.08921,-0.02207,-0.16562,-0.03301,-0.02798,-0.05668,0.002,0.03847,-0.05867,0.01134,-0.08142,0.14098,0.02798,0.12954,-0.07622,0.06094,0.03758,0.09445,0.06035,0.08641,0.01023,-0.04907,0.05035,0.09827,-0.01032,-0.02728,-0.09103,0.12127,0.05802,-0.06865,0.00248,-0.00515,-0.08304,0.07247,-0.01466,0.05242,-0.00419,0.03545,-0.08789,0.06945,0.00043,-0.08343,-0.01062,-0.06067,0.01166,0.0292,0.01506,0.15605,-0.04386,-0.00258,0.05551,0.00336,-0.10479,-0.05514,-0.06571,-0.00186,-0.12025,-0.06525,0.00714,0.04738,0.02859,-0.02497,0.02793,0.03705,-0.0822,-0.09336,0.01389,-0.14218,0.06832,0.07082,0.00378,0.06017,-0.11792,0.04398,0.04929,-0.03866,-0.03561,-0.14678,0.1023,0.06771,-0.03337,0.00045,0.03495,0.08025,-0.12679,0.0798,-0.03248,-0.11496,0.03889,0.07915,0.00922,-0.00671,-0.03424,-0.08423,-0.03113,-0.08398,-0.06986,0.0237,-0.00811,-0.03511,0.03148,0.06402,-0.05247,0.119,0.00016,-0.06761,-0.12128,0.00582,-0.04113,0.04105,0.02866,-0.02992,-0.04718,0.03925,-0.09283,-0.05344,-0.02581,0.05684,-0.11024,0.03381,0.00055,-0.07894,-0.10051,0.00205,-0.01518,-0.03756,0.00237,-0.04134,0.0357,-0.03961,0.04134,0.01618,-0.10107,-0.04218,0.08982,-0.02553,-0.02118,0.00157,0.08802,0.0133,-0.00752,0.13798,0.05748,0.03652,0.02846,0.05651,0.00153,-0.08181,-0.02684,0.04151,0.0166,0.05357,0.00184,-0.09178,-0.02787,0.01966,0.08331,0.05305,-0.12818,0.06218,-0.10984,-0.04174,0.00755,-0.12736,0.00596,0.04889,0.02626,-0.01246,-0.04243,0.08854,-0.03376,-0.02692,-0.01093,0.0966,-0.04214,0.08853,-0.07422,0.00289,0.11073,0.02007,0.06892,0.04149,0.06613,0.02138,-0.00606,0.00564,-0.01289,-0.029,-0.06553,0.0157,-0.0008,0.05703,-0.05118,0.00901,0.02491]},{"domain":"energy_systems","key":"energy_induction_max_torque","name":"Induction motor breakdown (maximum) torque and starting torque","package":"energy-systems-ai999x","example":"Induction motor maximum torque: VL = 460 V, f = 60 Hz, poles = 4, R1 = 0.641 ohm, X1 = 1.106 ohm, R2 = 0.332 ohm, X2 = 0.464 ohm, Xm = 26.3 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motor performance from its equivalent circuit","package":"energy-systems-ai999x","example":"Induction motor: VL = 460 V, f = 60 Hz, poles = 4, R1 = 0.641 ohm, X1 = 1.106 ohm, R2 = 0.332 ohm, X2 = 0.464 ohm, Xm = 26.3 ohm, slip = 2.2%, connection = 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capacitance and surge impedance of a three-phase overhead line","package":"energy-systems-ai999x","example":"Line parameters: D_ab = 5 m, D_bc = 5 m, D_ca = 5 m, r = 1 cm, f = 50 Hz, gmr = 5 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fault (symmetrical components)","package":"energy-systems-ai999x","example":"LL fault: X1 = 0.1, X2 = 0.1, X0 = 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transmission line (exact distributed parameters)","package":"energy-systems-ai999x","example":"Long line: Vr = 400 kV, P = 1 MW, pf = 1, R = 0 ohm, X = 100 ohm, B = 400 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transmission line (nominal pi)","package":"energy-systems-ai999x","example":"Medium line: Vr = 132 kV, P = 50 MW, pf = 1, R = 0 ohm, X = 40 ohm, B = 500 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load flow by Newton-Raphson","package":"energy-systems-ai999x","example":"Load flow: lines = [1 2 0 0.5 0], loads = [2 0 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sharing between two transformers in parallel","package":"energy-systems-ai999x","example":"Parallel transformers: S1 = 500 kVA, vk1 = 5%, vkr1 = 1%, S2 = 500 kVA, vk2 = 5%, vkr2 = 1%, V_lv = 400 V, P = 600 kW, Q = 200 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impedance on a new base","package":"energy-systems-ai999x","example":"Per-unit change of base: R_pu = 0.01, X_pu = 0.1, S_old = 10 MVA, V_old = 11 kV, S_new = 100 MVA, V_new = 11 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impedance and per-unit impedance","package":"energy-systems-ai999x","example":"Per-unit impedance: R = 5 ohm, X = 20 ohm, S_base = 100 MVA, V_base = 132 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on a tilted plane (isotropic sky)","package":"energy-systems-ai999x","example":"Plane of array irradiance (isotropic): tilt = 30, surface_azimuth = 180, zenith = 30, azimuth = 180, dni = 800 W/m^2, ghi = 792.820323027551 W/m^2, dhi = 100 W/m^2, albedo = 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on a tilted plane (Klucher sky model)","package":"energy-systems-ai999x","example":"Plane of array irradiance (Klucher): tilt = 30, surface_azimuth = 180, zenith = 30, azimuth = 180, dni = 800 W/m^2, ghi = 792.820323027551 W/m^2, dhi = 100 W/m^2, albedo = 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on a tilted plane (Reindl sky model)","package":"energy-systems-ai999x","example":"Plane of array irradiance (Reindl): tilt = 30, surface_azimuth = 180, zenith = 30, azimuth = 180, dni = 800 W/m^2, ghi = 792.820323027551 W/m^2, dhi = 100 W/m^2, albedo = 0.2, n = 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transfer and power angle between two voltages","package":"energy-systems-ai999x","example":"Power angle: V1 = 100 kV, V2 = 100 kV, X = 100 ohm, P = 50 MW","v":[-0.15237,-0.10867,0.07918,0.00653,-0.01908,0.08068,-0.00352,0.01392,0.06863,0.01942,0.02607,0.04265,-0.04151,-0.08262,0.10444,-0.01877,-0.07346,-0.07505,0.01493,0.0581,-0.08765,0.13638,-0.01193,-0.05084,0.01344,-0.04809,0.17015,0.05538,-0.10587,0.07996,-0.09886,-0.0377,-0.07912,0.02116,-0.03537,0.06734,-0.05202,0.05597,-0.03285,0.06504,0.06554,0.01171,0.10846,0.18383,-0.02456,-0.08561,-0.03571,-0.06742,0.05068,0.04998,0.02811,0.09093,-0.09833,0.01763,0.03191,0.03916,0.01666,-0.00949,-0.04012,0.03968,-0.01664,0.00607,-0.07678,0.00488,0.00864,0.00767,-0.00698,-0.00126,0.03912,-0.12704,0.08888,0.04587,-0.03895,0.00279,0.13905,-0.08805,-0.1642,0.03536,0.04404,0.08743,0.05818,-0.08792,-0.01987,-0.01375,0.04417,-0.12342,-0.01549,-0.0155,0.00908,0.08104,-0.0239,-0.03795,-0.00299,0.01731,-0.03705,-0.09296,-0.01155,-0.07086,-0.0411,0.00256,0.00938,0.07454,-0.02588,-0.01413,0.011,0.02606,-0.0513,-0.00572,-0.07011,0.00165,-0.02802,0.07263,-0.02474,-0.0212,-0.00584,-0.01838,0.02212,-0.10512,-0.04657,-0.03693,-0.04719,0.00905,-0.02945,-0.02114,0.0239,-0.05163,0.02671,-0.00713,0.06946,0.0142,0.04216,-0.03993,-0.00072,0.05046,-0.1291,0.05194,0.07759,-0.12211,-0.00538,-0.0623,-0.11127,0.01085,-0.03463,-0.10628,0.02906,0.06412,-0.04261,-0.05106,0.04722,-0.00034,0.02571,0.09876,0.04198,0.08246,-0.07808,-0.02974,0.00869,0.05381,0.02689,0.04367,-0.03644,0.12257,0.0543,0.00431,-0.04028,-0.07916,-0.00287,-0.0504,-0.01024,-0.03286,-0.06154,0.08504,-0.02657,-0.11543,0.02143,0.05564,0.02568,-0.01016,-0.1237,0.07716,0.02143,-0.03287,0.0023,-0.07833,0.01556,-0.01359,-0.05099,-0.0996,0.04365,0.0329,-0.0646,-0.00141,-0.07168,0.05705,-0.04401,0.06922,-0.05885,0.12243,-0.00011,0.07081,0.00049,0.03736,0.01694,-0.08066,-0.03945,0.08271,0.00845,-0.11982,-0.00395,-0.06282,-0.04368,-0.05641,0.05047,-0.01916,0.14098,0.04609,-0.01293,0.00301,0.02391,-0.08896,0.17691,0.01116,0.02246,0.11336,0.00312,-0.02412,-0.10713,-0.00652,0.17116,0.09324,-0.01567,-0.04404,-0.10065,0.04713,-0.02648,-0.04325,-0.08555,-0.01199,-0.05389,0.00865,0.04047,0.03574,0.08457,0.01259,0.02179,0.05504,0.06685,0.00443,0.01571,-0.04157,-0.05998,0.02347,-0.00189,0.06189,0.04309,0.03907]},{"domain":"energy_systems","key":"energy_power_curve_density_corrected","name":"Turbine output from a density-corrected power curve","package":"energy-systems-ai999x","example":"Density-corrected power curve: speeds = [3, 5, 8, 12, 25], powers = [0, 150, 800, 2000, 2000], v = 6.5 m/s, rho = 1.225 kg/m^3","v":[-0.025,-0.03929,0.09831,-0.05841,0.03664,0.04885,-0.01484,0.05435,0.10117,0.00997,0.0338,0.08948,-0.13863,0.02609,-0.02202,-0.09231,0.0267,-0.03405,0.18198,-0.04311,0.08247,0.05432,0.09819,-0.0569,-0.0462,0.02564,0.05434,0.01813,-0.09289,-0.02394,-0.04708,-0.15883,-0.0214,0.00747,0.03911,0.01553,0.08082,-0.01513,0.05712,-0.02472,-0.08189,0.03244,-0.08906,-0.02205,-0.0376,-5e-05,0.00584,-0.03005,0.12404,-0.10132,-0.04718,-0.03442,0.00218,-0.00284,-0.06625,0.05333,0.0954,-0.02787,0.02558,-0.00851,0.07659,-0.02073,0.00381,-0.04769,-0.07346,-0.0498,0.11419,0.04116,-0.02535,0.0109,0.0863,0.03226,-0.00394,-0.03645,0.08545,-0.01597,0.13642,-0.01088,-0.04032,0.03527,0.02232,-0.0674,-0.0672,0.00888,-0.06371,-0.1446,0.08396,-0.00746,0.03928,-0.06353,-0.10303,-0.01199,0.03204,0.06294,-0.0834,-0.03208,0.21509,0.0272,0.03329,0.09798,-0.01795,-0.05764,-0.01712,0.01104,0.02803,-0.11129,-0.13919,-0.0084,0.0746,0.10437,-0.03319,-0.06716,-0.00797,0.04589,-0.06899,0.0856,0.00235,-0.04959,0.06302,0.01425,0.00348,0.04861,-0.04219,0.01817,-0.06438,-0.04133,0.00474,0.01185,-0.09424,-0.08243,0.02641,0.00159,-0.06141,-0.07587,-0.02633,0.03877,-0.00237,-0.02326,-0.03161,0.07862,0.0292,0.04929,0.04224,0.06205,0.03223,0.10165,-0.02662,-0.05888,0.06345,0.10654,-0.02299,0.01747,-0.07876,0.02436,-0.06308,0.04972,-0.02466,-0.1233,-0.02252,0.03636,-0.09046,0.03005,-0.05835,0.0266,0.14803,-0.06161,0.0105,-0.02699,-0.0228,-0.01291,-0.0033,-0.03324,-0.03218,-0.16468,-0.0154,0.08811,0.09238,0.00759,0.00265,0.0191,-0.02734,-0.07774,-0.04675,0.02202,0.05885,0.09879,0.01223,0.04277,-0.13033,0.009,0.074,-0.01546,0.03421,0.06142,0.03168,0.07309,-0.04567,-0.01273,0.07185,-0.10823,-0.06024,-0.00611,-0.01763,0.05611,-0.00057,0.07297,-0.01817,-0.04209,0.00544,-0.05572,0.00996,-0.01319,0.04465,-0.00501,0.14306,-0.01843,-0.1162,-9e-05,0.04362,0.07963,0.01157,0.0275,0.08199,-0.04983,0.003,-0.01803,0.01155,0.03291,-0.01846,-0.01498,0.0546,0.06517,-0.03465,0.0602,0.01031,-0.0919,-0.05422,0.01916,0.09078,-0.01613,-0.02761,-0.05659,0.04436,0.06334,-0.09665,0.05763,-0.00288,0.16289,-0.02341,-0.00923,-0.0566,0.087,-0.03122,0.06728,-0.0502,-0.107]},{"domain":"energy_systems","key":"energy_power_curve_output","name":"Turbine output from its power curve","package":"energy-systems-ai999x","example":"Power curve output: speeds = [3, 5, 8, 12, 25], powers = [0, 150, 800, 2000, 2000], v = 6.5 m/s","v":[-0.06669,-0.02707,0.08922,-0.13024,-0.01037,0.05013,-0.02607,0.03765,0.05918,0.02151,0.03885,0.08899,-0.15817,-0.00275,0.02794,-0.09911,0.02963,-0.02923,0.13322,-0.02371,0.05786,0.09267,0.07822,-0.06337,-0.09838,0.0218,0.13026,-0.00748,-0.018,-0.01475,-0.12293,-0.08767,-0.03383,0.02302,0.02097,-0.06842,0.05317,0.00638,0.00819,-0.1173,-0.11062,-0.0069,-0.09012,0.00207,-0.07197,0.01708,-0.03614,-0.03595,0.0819,-0.08102,-0.01399,-0.03067,-0.03187,0.0114,-0.08923,0.05028,0.08418,-0.14345,-0.01178,-0.00071,0.03684,-0.01497,-0.09057,-0.07126,-0.04308,0.01189,0.0729,0.04603,0.00857,0.01091,0.07854,0.07844,-0.06498,-0.00985,0.11338,0.00313,0.04005,0.02446,0.00989,-0.02186,-0.00483,-0.06013,-0.03051,0.02143,-0.10963,-0.13626,0.04775,-0.03398,0.01093,0.00869,-0.05314,-0.00208,-0.00422,0.08283,-0.04555,-0.04481,0.25578,0.04997,0.05974,0.07862,-0.02926,-0.02155,0.01941,0.00959,-0.01073,-0.05093,-0.10506,-0.07163,0.06051,0.1321,0.01086,-0.05503,-0.01147,0.07661,-0.0182,0.05892,-0.06854,-0.10909,0.1054,-0.01273,0.06459,0.05448,-0.10034,-0.03972,-0.02661,-0.02348,0.07374,0.05744,-0.08713,-0.05409,-0.00737,0.01198,-0.0402,0.00284,0.01376,0.0064,0.03729,-0.02652,-0.00232,0.03903,0.03353,0.06042,-0.01444,0.02894,0.01483,0.06708,-0.08244,-0.01629,0.06823,0.09621,-0.09317,0.056,-0.09604,0.04234,-0.06598,0.06286,0.00589,-0.09706,0.03098,0.01143,-0.06868,0.01957,-0.0356,0.06892,0.0761,-0.02305,-0.01691,-0.03101,-0.07875,-0.01642,0.0342,-0.01255,-0.04017,-0.1184,-0.0364,0.02624,0.0707,-0.04567,-0.01289,-0.01514,-0.0817,-0.07868,0.02366,-0.00081,0.03961,0.10733,0.06204,0.00813,-0.07798,0.04247,-0.01539,0.04789,-0.02741,0.12594,-0.00357,0.07336,-0.08912,0.04207,0.06545,-0.04081,-0.04669,-0.02317,-0.03935,-0.01951,0.00906,0.08835,-0.04381,-0.04477,-0.00097,-0.06135,0.07437,-0.01244,0.101,-0.0124,0.13724,-0.06622,-0.10816,-0.0138,0.05801,0.03953,0.0065,0.03474,0.00864,0.03129,0.01891,0.03717,0.02031,0.06516,0.03755,0.03068,-0.01603,0.07956,-0.05429,0.09264,0.07403,-0.05708,-0.04617,0.02065,0.07742,-0.05756,-0.04798,-0.03558,0.02138,0.04222,-0.15348,0.0725,0.00568,0.14781,0.03901,-0.04282,-0.04625,0.05882,0.01032,0.06683,-0.01159,-0.05581]},{"domain":"energy_systems","key":"energy_pv_array_output","name":"PV array output at operating temperature","package":"energy-systems-ai999x","example":"PV array output: poa = 800 W/m^2, T_air = 25 degC, noct = 45 degC, pdc0 = 10 kW, gamma = -0.4%","v":[-0.03025,-0.09786,0.07621,-0.11381,-0.07113,0.00823,-0.06323,0.06928,-0.01731,0.04664,0.02498,-0.01815,0.00745,-0.06376,-0.06215,-0.05128,0.09672,-0.00097,0.08658,0.04228,0.07521,-0.0198,-0.03018,-0.11728,0.0104,-0.04268,0.0306,-0.07767,-0.04572,-0.10781,0.02962,-0.0562,0.01379,0.09755,0.04532,0.03273,0.04821,0.03462,0.0206,-0.06075,-0.00052,-0.0483,-0.02972,0.01916,-0.03232,-0.03904,0.03529,0.02251,-0.09656,0.08981,-0.01295,0.03193,0.1164,-0.04094,0.05523,-0.04934,0.12036,-0.00158,0.00197,-0.03594,-0.10329,0.01684,0.02139,-0.03154,0.00993,0.00207,-0.05724,0.02553,0.00061,-0.00582,0.04681,0.07436,0.10571,0.05253,-0.03182,0.01549,0.04262,-0.04607,-0.00108,-0.03296,0.08685,-0.02757,0.10349,-0.00015,-0.05177,0.03639,0.07651,-0.00145,-0.01528,-0.01112,0.01538,0.0124,-0.05122,0.01589,-0.12309,0.01814,0.03599,-0.01207,-0.00115,-0.04854,-0.09068,-0.07555,0.02112,-0.06212,-0.03307,0.08229,-0.08155,-0.00722,-0.05538,0.03604,0.05272,0.06351,0.03167,0.06399,0.11525,0.02925,0.03128,-0.10953,-0.04061,0.00657,-0.03202,-0.0275,-0.06315,-0.05777,-0.03068,-0.01467,-0.07328,0.13067,-0.14559,0.02139,-0.01456,0.07126,0.12324,-0.06862,-0.09793,-0.01696,-0.06101,-0.11909,-0.02485,0.04868,-0.0151,0.00687,0.07426,-0.06727,0.05884,0.0424,0.03557,-0.03758,0.0072,0.09631,0.0813,0.01047,-0.03452,0.11791,0.03283,-0.0984,0.03471,0.01734,0.02804,0.05418,0.04341,0.07638,-0.07013,0.06129,-0.03185,0.06068,0.01694,-0.1045,-0.12691,-0.00802,0.02468,-0.09077,-0.11413,-0.10793,-0.04199,0.05568,-0.06207,-0.04397,0.01908,-0.03471,0.06016,0.07811,-0.05952,0.0344,-0.0369,0.09252,0.07812,-0.00619,-0.02217,0.05537,0.07297,-0.06986,-0.0317,0.10482,-0.07947,0.09409,0.08412,0.18896,0.01187,0.02957,-0.02126,0.00627,0.04971,-0.02353,0.06511,0.04955,0.02956,0.07542,-0.0587,-0.05203,0.10845,-0.04318,0.00889,-0.03907,0.16999,0.02584,-0.02712,0.03346,-0.01261,-0.0003,0.10111,0.06286,-0.04802,0.02932,-0.01186,-0.00384,0.06546,-0.017,-0.02499,0.03727,0.05879,0.0596,-0.16709,0.02457,-0.00985,-0.06804,0.02854,0.02871,0.03512,0.03487,-0.00019,-0.06989,0.02938,-0.03434,-0.00073,0.10315,0.0428,-0.10714,-0.16716,0.06149,-0.03241,0.04023,-0.15957,0.0033,-0.06311,-0.03524]},{"domain":"energy_systems","key":"energy_pv_module_at_conditions","name":"PV module maximum power at an irradiance and temperature","package":"energy-systems-ai999x","example":"PV module at conditions: G = 1000 W/m^2, T_cell = 25 degC, alpha_sc = 0.004, a_ref = 1 V, IL_ref = 5 A, I0_ref = 1e-10 A, Rsh_ref = 1e15 ohm, Rs = 0 ohm","v":[0.01623,-0.0577,0.07216,0.00901,-0.08725,-0.06499,-0.03528,0.06848,-0.01598,0.03648,-0.13188,-0.06931,0.03005,-0.00428,-0.07589,0.02186,0.03992,0.01193,0.05806,0.11703,0.09623,0.00912,0.0027,-0.014,0.04662,0.00426,0.0542,-0.00929,0.00483,0.00175,0.01643,0.00764,-0.10108,0.12042,-0.00166,-0.02055,0.01513,0.04456,-0.01445,-0.03562,0.05517,-0.0137,0.06063,0.03866,-0.00112,0.01016,-0.02368,0.06944,0.07295,-0.02336,0.04281,0.09883,0.08165,-0.07873,0.0102,-0.00361,0.05936,-0.00453,-0.01516,0.06467,-0.0606,-0.00159,-0.06371,-0.00519,-0.04871,-0.1393,-0.03114,0.02721,-0.00136,-0.00867,0.06147,0.00992,0.03753,-0.02024,-0.01042,0.05886,0.0251,-0.00225,0.01881,-0.0168,0.08514,0.11409,0.03996,0.02421,0.07358,-0.06234,0.06087,-0.02131,0.10541,-0.06967,0.03614,0.11079,0.00459,0.01468,-0.07075,0.00837,-0.08847,-0.02323,-0.00315,-0.09684,-0.04844,-0.01174,-0.00493,-0.00077,-0.16056,-0.05541,-0.08396,-0.00678,-0.06352,0.00669,0.08859,0.14801,0.05177,0.0171,0.0198,0.00863,-0.01883,-0.03885,-0.0554,-0.09158,0.01384,-0.05836,-0.10743,0.04898,-0.06613,-0.14572,-0.03658,0.08054,-0.08247,0.04567,-0.0465,0.05375,0.03381,0.01499,-0.01255,0.01499,-0.10707,-0.09475,-0.04223,0.05445,0.13879,-0.0365,0.10582,0.00908,0.08424,0.02338,-0.03329,0.02104,-0.02545,0.11704,0.03094,0.03189,-0.08813,0.11155,-0.06937,-0.05803,-0.05158,-0.09981,-0.03805,0.07175,0.06604,-0.02482,-0.07311,-0.02752,-0.08815,0.04974,0.0143,-0.04546,-0.0865,-0.05992,-0.01842,0.04378,-0.07158,0.07551,-0.05204,-0.00235,-0.10401,0.04245,0.01634,-0.04609,0.07241,0.1113,-0.06287,-0.03744,-0.09216,0.01378,-0.01006,0.05653,-0.06202,0.04103,0.01994,-0.12382,-0.1019,0.09429,0.02316,0.06846,0.06793,0.11936,0.08999,0.02876,-0.02306,-0.03641,0.13301,0.07383,0.0402,-0.00594,-0.02253,0.06614,-0.0516,-0.16119,-0.01245,-0.0273,0.08395,-0.12902,0.15192,0.09979,-0.10509,0.04709,-0.0277,-0.0386,0.04214,-0.05001,-0.08188,0.02968,-0.04575,0.0498,0.06505,0.02686,0.01872,-0.06286,0.05005,0.0532,-0.06492,-0.05404,0.00479,-0.01697,-0.03246,0.01429,0.02992,0.11211,-0.05073,0.01286,-0.02531,0.08157,-0.01192,0.04463,0.03836,-0.0919,-0.12005,-0.08996,0.01023,0.00931,-0.00773,0.04234,-0.02881,-0.05577]},{"domain":"energy_systems","key":"energy_pvwatts_dc","name":"PV array DC power with temperature derating (PVWatts)","package":"energy-systems-ai999x","example":"PVWatts DC power: G_eff = 800 W/m^2, T_cell = 45 degC, pdc0 = 5 kW, gamma = -0.4%","v":[0.00103,-0.10934,0.10353,-0.0394,-0.04257,0.00977,-0.02727,0.06744,-0.01551,0.06931,-0.07799,-0.03299,0.01188,-0.09789,-0.11194,-0.04047,0.04237,-0.04707,0.08425,0.09521,0.06777,0.0045,-0.05987,-0.08012,0.00065,0.00915,-0.0053,-0.00975,-0.00931,-0.04614,-0.06966,-0.0428,0.00416,0.05891,0.03963,0.06206,0.03547,0.03606,-0.02899,-0.13406,0.04539,-0.0058,0.07746,-0.03738,-0.01717,-0.03831,0.01394,0.00572,-0.01121,0.09066,0.03322,0.10334,0.11049,-0.09326,0.02448,0.00869,0.0737,-0.02697,-0.05494,-0.00249,-0.06292,-0.01343,-0.0038,-0.04386,-0.02565,-0.0431,-0.04389,0.03625,-0.0696,0.01467,0.06045,0.0826,0.10294,0.02769,-0.06196,-0.0052,-0.03909,0.015,-0.04986,-0.03695,0.12278,0.06538,0.11199,0.01386,-0.03896,-0.05465,0.03544,0.0091,0.00593,-0.07134,0.02083,0.10965,0.0353,0.03535,-0.12943,-0.04288,-0.0201,0.03335,0.04658,-0.00911,-0.06484,-0.04448,-0.00885,0.03652,-0.08743,0.02242,-0.00882,-0.0025,-0.03617,0.05927,0.05654,0.05627,-0.03575,0.07166,0.0247,0.10199,0.01485,-0.1235,-0.00688,-0.03508,0.01796,-0.09164,-0.13775,-0.07528,0.00315,-0.11921,-0.06743,0.10779,-0.13027,0.04024,0.0495,0.08604,0.04516,-0.06486,-0.13851,0.10317,-0.02105,-0.09664,-0.07084,0.0555,0.05033,-0.00142,0.01365,-0.06303,0.11606,-0.02354,-0.0071,-0.00049,0.02387,0.08488,0.04806,-0.01725,0.0163,0.10063,0.01989,-0.14286,-0.00053,-0.08039,0.03583,0.00328,0.07858,0.06406,-0.02748,0.04356,-0.06852,0.05982,0.02058,0.01846,-0.12488,-0.09094,0.02997,0.00016,-0.10232,-0.07586,-0.07989,0.05113,-0.05718,-0.03056,0.00066,-0.04,0.09291,0.06469,-0.04829,-0.02298,-0.03019,0.05819,0.02256,0.07136,-0.08901,0.02555,-0.03199,-0.0864,-0.09258,0.13949,0.02102,0.1211,0.07968,0.09544,0.07343,-0.0239,-0.02148,0.00896,0.04958,-0.01736,0.06018,0.05907,-0.01759,0.04436,-0.01765,-0.07851,0.11252,-0.0513,0.02442,-0.04906,0.22911,0.00508,0.01315,-0.03977,-0.05744,-0.06225,0.06009,0.02475,-0.07113,0.06273,0.06261,0.01726,0.05229,-0.02511,-0.00269,0.06148,0.07791,0.04841,-0.08185,0.00674,0.02543,-0.03815,-0.00189,-0.00168,0.06714,0.14528,0.02027,-0.02732,-0.04122,0.01182,0.01539,0.06952,0.0034,-0.08339,-0.08559,-0.02917,-0.00255,0.0418,-0.09865,0.05469,0.00431,-0.02944]},{"domain":"energy_systems","key":"energy_pvwatts_inverter","name":"Inverter AC output and efficiency (PVWatts)","package":"energy-systems-ai999x","example":"Inverter output (PVWatts): pdc = 6 kW, pdc0 = 5 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PV system losses (PVWatts)","package":"energy-systems-ai999x","example":"PVWatts losses: soiling = 0%, shading = 0%, snow = 0%, mismatch = 0%, wiring = 0%, connections = 0%, lid = 0%, nameplate_rating = 0%, age = 0%, availability = 10%","v":[0.01284,-0.03467,-0.00453,0.0706,0.04435,-0.07339,0.02053,0.03734,0.01706,0.09212,-0.03624,0.02997,0.00874,-0.0841,-0.088,-0.01082,-0.01614,-0.02223,-0.04897,0.08381,0.00902,0.01557,-0.04612,-0.02203,-0.01641,0.02765,0.07217,0.03347,-0.02234,0.0392,-0.04968,-0.11161,-0.07575,0.09086,0.04378,-0.03282,0.04258,-0.02075,0.00948,-0.06828,-0.01015,-0.00543,0.06629,-0.04386,0.08341,0.01327,-0.0038,0.0079,-0.00208,0.004,-0.03771,0.08549,0.02121,-0.06823,0.10721,-0.01372,0.05048,-0.01266,-0.02758,-0.01818,0.01491,0.02136,-0.11316,0.02943,-0.02753,-0.07736,0.02394,0.053,-0.0173,-0.02742,0.10905,-0.0299,0.05319,0.0084,-0.07823,-0.06687,-0.06619,0.05373,-0.03031,0.01112,0.07895,0.08452,0.11372,-0.02994,0.03441,-0.09389,-0.03128,-0.05603,0.07592,0.01123,-0.05039,0.04875,-0.03001,0.00638,-0.04552,-0.07484,0.02116,0.04504,0.01699,0.05924,-0.03954,-0.07323,0.07008,0.00348,-0.13812,-0.10376,-0.00059,-0.00333,-0.01449,0.08625,0.15408,0.00448,0.04185,-0.01158,-0.09185,0.06835,0.03662,-0.12145,0.06744,-0.02848,0.01154,0.00031,-0.09805,-0.06957,0.07063,-0.04145,-0.01303,0.10228,-0.09453,0.04246,0.10961,0.10741,0.0315,-0.12197,-0.10158,0.03045,-0.09594,-0.08846,0.04559,0.06017,0.01374,-0.0502,-0.02557,0.00485,0.08131,-0.02023,0.03156,-0.07651,-0.00874,0.07958,-0.0629,0.07645,0.1067,0.04872,0.00832,0.02995,0.04181,-0.13345,-0.00867,0.05135,0.08848,0.02049,-0.03606,0.05235,-0.0043,0.0302,0.05961,0.02998,0.0013,-0.09137,0.02305,0.01582,-0.06489,-0.09702,0.08199,-0.01495,0.00519,-0.13912,0.036,-0.08703,0.03774,0.0081,-0.00626,-0.08777,-0.04455,0.03473,0.1129,0.00035,-0.15213,0.08274,-0.11756,-0.05474,-0.05976,0.12443,-0.06574,0.00107,0.11394,-0.02912,0.11071,0.02466,0.06099,0.00241,0.03776,0.06885,-0.00148,-0.00314,-0.02708,-0.02483,-0.06735,-0.02163,0.07307,0.0226,0.04115,-0.08886,0.11525,-0.00799,0.05179,0.08317,-0.04078,0.06478,0.08359,-0.05429,-0.08956,-0.00168,-0.03641,-0.01696,-0.06614,0.02697,0.10731,-0.04787,0.03204,0.00498,-0.09479,0.10253,0.10375,-0.12006,-0.10683,0.06367,-0.01922,0.02019,0.16381,0.02182,-0.03331,0.04113,-0.03699,0.07696,0.09041,0.05993,-0.03834,-0.07972,-0.08954,-0.00957,0.03256,0.01315,-0.00915,0.07606]},{"domain":"energy_systems","key":"energy_short_line","name":"Short transmission line: sending-end voltage, regulation and efficiency","package":"energy-systems-ai999x","example":"Short line: Vr = 33 kV, P = 10 MW, pf = 1, R = 0 ohm, X = 0 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single-diode model: current at a voltage","package":"energy-systems-ai999x","example":"Single-diode current: V = 1 V, IL = 5 A, I0 = 1e-10 A, Rs = 0 ohm, Rsh = 100 ohm, nNsVth = 1 V","v":[-0.10708,-0.06905,0.02214,-0.0339,0.06946,-0.03209,0.10595,0.07437,-0.11823,-0.02144,-0.06712,-0.10712,-0.06611,-0.10902,-0.03672,0.12738,-0.08124,-0.02197,-0.00951,0.0104,0.07243,0.02063,0.02525,0.0576,-0.03087,0.04019,-0.03147,0.08326,0.07461,-0.04808,0.04066,-0.04394,-0.01217,0.12691,0.03034,0.06744,0.02201,-0.0033,0.00061,0.09579,0.03586,0.0372,0.01844,-0.09217,-0.0267,-0.03664,-0.08298,0.05408,-0.014,-0.04561,0.05138,0.04512,-0.04526,-0.10204,-0.0231,0.04639,0.07151,0.01424,0.01568,0.06291,0.02323,0.06846,-0.0228,0.05184,0.07146,-0.0982,0.0193,-0.01719,-0.05299,0.01706,0.02184,0.02416,0.09466,-0.0034,0.0009,-0.00814,-0.01134,-0.01353,-0.02545,-0.09597,-0.06104,-0.00514,0.05131,0.12157,0.00785,-0.04292,0.10732,-0.01246,0.06874,0.00495,0.11102,-0.02031,-0.0452,-0.03503,-0.02354,0.11803,-0.02613,0.00425,0.07349,0.0268,-0.01137,0.01622,0.10052,-0.09675,-0.09937,-0.05789,0.04288,0.03773,-0.04193,0.03651,0.0705,0.03027,-0.00227,0.02882,-0.00301,0.11192,0.00159,-0.08617,-0.00028,-0.04148,0.015,0.0158,-0.04412,0.06973,-0.00071,0.00597,-0.04023,0.12316,-0.1037,0.0269,-0.05143,0.10825,0.01355,-0.10279,0.00025,0.12739,-0.0543,-0.00498,-0.09429,0.02117,0.05513,0.07609,0.06763,-0.05535,0.09113,-0.01387,-0.00089,0.04042,-0.01841,0.10984,-0.01122,0.02199,-0.00692,0.08112,0.02133,0.01025,-0.08879,-0.01922,-0.02385,-0.03492,0.00054,0.01954,0.00174,-0.13475,0.00977,0.00736,-0.13577,-0.12417,-0.17589,-0.07336,-0.16257,0.09666,-0.06917,-0.07002,-0.02579,-0.01665,-0.12599,-0.0528,-0.02463,-0.05324,-0.01502,0.11024,-0.03201,0.01772,-0.06782,0.04128,0.09406,0.14469,-0.0395,0.00674,0.0978,0.01007,-0.00739,0.01702,0.05719,-0.01081,-0.01816,0.01298,0.06296,-0.03645,-0.01893,-0.03225,-0.01592,0.01432,0.05508,-0.00251,-0.04771,0.00887,-0.03327,0.06602,0.02363,0.03111,0.08003,-0.06624,0.09487,-0.01932,0.06072,0.11591,-0.03372,-0.05975,0.04888,0.04063,-0.13716,-0.02079,-0.00463,0.00446,0.01118,0.01262,0.0414,-0.01815,0.05279,-0.01746,-0.1525,-0.07086,0.09571,-0.0931,-0.01338,-0.00799,0.11825,0.07598,-0.02234,-0.00902,0.01621,0.04557,0.0033,-0.07881,0.05924,-0.04921,-0.11049,0.07485,0.06422,0.00553,0.00728,0.05015,0.06624,-0.09506]},{"domain":"energy_systems","key":"energy_single_diode_mpp","name":"PV single-diode model: short-circuit, open-circuit and maximum power point","package":"energy-systems-ai999x","example":"PV MPP: IL = 5 A, I0 = 1e-10 A, Rs = 0 ohm, Rsh = 1e15 ohm, nNsVth = 1 V","v":[-0.0487,-0.04825,0.04625,0.02781,-0.0092,-0.08711,0.04378,0.02355,-0.06065,-0.0203,-0.15174,-0.0709,-0.03624,-0.00744,-0.02296,0.10821,-0.05813,0.01899,-0.03838,0.0734,0.07514,-0.00473,0.0759,0.00038,-0.02854,0.00206,-0.03544,0.01323,0.01047,0.02225,0.02942,0.00103,-0.02563,0.05604,-0.01488,-0.01286,0.03257,0.00842,0.01114,0.00472,0.05871,0.05463,-0.00165,-0.02401,-0.03494,0.03787,-0.06977,0.1215,0.07938,-0.04564,0.06541,0.04497,-0.00765,-0.0758,-0.00733,-0.0421,0.02019,0.0515,0.04412,0.03897,0.03522,0.03199,-0.08551,0.00733,0.00807,-0.10378,-0.03064,-0.00678,-0.03978,0.00697,0.02887,0.03519,-0.02993,0.01654,0.06452,0.06569,0.00388,-0.04025,-0.05515,-0.02792,-0.02181,0.10161,-0.0276,0.05104,0.04816,-0.09787,0.09599,-0.02169,0.11926,-0.09101,0.03734,0.06216,0.03838,-0.02508,0.01798,0.06004,-0.03876,0.08791,0.02558,-0.00513,-0.0528,0.03238,0.00279,-0.09604,-0.14042,-0.0909,-0.0096,0.01375,-0.07223,-0.0003,0.02502,0.09676,0.10258,0.07935,-0.00045,0.03406,-0.04899,-0.03253,0.04101,-0.07353,0.05471,-0.01403,-0.05876,0.10087,-0.12195,-0.11644,-0.08297,0.06748,-0.06482,0.06815,-0.10871,0.04448,-0.0281,0.02875,0.10748,0.11383,-0.05763,-0.0115,-0.06802,0.04887,0.01877,0.01832,0.13529,0.03449,0.11462,0.06093,-0.04128,-0.02594,0.04755,0.07785,-0.07031,-0.02461,-0.08479,0.11619,-0.05572,-0.02692,-0.08517,-0.04345,-0.07157,0.04358,0.05599,-0.04986,-0.00523,-0.14263,-0.05656,0.01563,-0.04993,-0.06525,-0.07288,-0.09898,-0.11522,0.07206,0.02525,0.03793,0.05124,-0.01553,-0.11742,0.01665,0.04814,-0.05495,-0.04802,0.12929,-0.03482,0.02654,-0.10725,-0.00599,-0.02234,0.06038,-0.0812,0.01223,0.06491,-0.14058,0.01052,-0.00502,0.07678,0.01874,0.07018,0.0472,0.07865,-0.06986,-0.0129,-0.03639,0.08057,0.06208,0.01606,-0.00623,-0.06112,0.06051,-0.0368,-0.06187,-0.00601,0.01979,0.16244,-0.16307,0.05552,0.06284,-0.10477,0.12407,-0.06487,-0.06719,0.03799,-0.01169,-0.05824,-0.01707,-0.03785,0.08384,-0.01782,0.06666,0.05391,-0.04686,0.00958,0.07389,-0.09627,-0.06931,0.05292,0.02529,-0.06308,0.01192,0.05392,0.01602,-0.01634,0.02572,-0.01341,0.1104,-0.05142,-0.04922,0.03193,-0.04565,-0.12523,-0.06395,0.08008,0.04252,0.07577,0.08363,-0.01418,-0.09933]},{"domain":"energy_systems","key":"energy_single_diode_voltage","name":"PV single-diode model: voltage at a current","package":"energy-systems-ai999x","example":"Single-diode voltage: I = 0 A, IL = 5 A, I0 = 1e-10 A, Rs = 0 ohm, Rsh = 1e15 ohm, nNsVth = 1 V","v":[-0.0893,-0.05487,0.00268,-0.02043,0.0572,-0.0462,0.14064,0.05459,-0.09614,0.00363,-0.09847,-0.09445,-0.07236,-0.07869,-0.03032,0.13168,-0.0847,-0.01673,-0.02358,0.03791,0.07557,0.01256,0.03582,0.05202,-0.02533,0.0264,-0.0268,0.0501,0.07481,-0.04648,0.02226,-0.05224,-0.02985,0.13904,0.01975,0.05152,-0.00097,-0.03882,-0.01076,0.07324,0.04817,0.04731,0.00313,-0.06566,-0.06222,-0.0287,-0.09386,0.07925,0.04369,-0.04082,0.06307,0.04748,-0.06146,-0.10047,-0.00859,0.03501,0.05298,0.0065,0.02586,0.05162,0.01934,0.07556,-0.04029,0.01936,0.07651,-0.09823,0.01418,-0.00216,-0.04544,0.00722,0.0118,0.0193,0.06657,0.01386,0.02774,-0.00419,-0.00611,-0.01933,-0.03563,-0.07576,-0.09058,0.04532,0.03566,0.12804,0.01784,-0.02288,0.09936,0.00172,0.07588,-0.01517,0.08059,-0.01344,-0.04665,-0.01603,0.00023,0.12382,-0.06232,0.03459,0.0529,0.03358,0.00452,0.00725,0.06491,-0.09982,-0.11139,-0.06843,0.04015,0.06002,-0.04839,0.05325,0.07662,0.0303,-0.01874,0.03785,0.00503,0.09692,0.03617,-0.114,0.0176,-0.05698,0.04223,0.02675,-0.0525,0.09848,-0.05064,0.00375,-0.03697,0.11415,-0.0846,0.02508,-0.08609,0.08,0.01295,-0.069,0.02929,0.11561,-0.04644,-0.00027,-0.09979,0.00463,0.00402,0.0531,0.07218,-0.04951,0.13358,-0.0225,-0.01598,0.02744,0.00429,0.08537,-0.0225,0.00642,-0.03104,0.10996,0.01448,-0.01092,-0.11235,-0.03451,-0.02622,-0.01513,-0.01187,-0.00227,-0.00878,-0.12388,-0.04064,0.00351,-0.10141,-0.11311,-0.18993,-0.08392,-0.13157,0.08735,-0.03727,-0.05922,-0.01839,-0.01905,-0.14656,-0.04562,-0.00313,-0.04772,-0.01329,0.08212,-0.04388,0.02597,-0.07484,0.03594,0.0936,0.14337,-0.04295,-0.00701,0.11514,-0.01827,-0.01017,0.00573,0.0726,-0.00333,0.00678,0.02373,0.05611,-0.03881,-0.02263,-0.00414,0.00591,0.00185,0.03661,0.0137,-0.03302,0.02117,-0.06381,0.04543,0.01371,0.041,0.12672,-0.06584,0.07693,-0.03199,0.03344,0.12914,-0.03085,-0.06469,0.08072,0.04274,-0.13357,0.00147,-0.04409,0.00102,-0.00969,0.00239,0.04159,0.0128,0.05815,-0.01744,-0.12529,-0.10204,0.09818,-0.08143,-0.03655,-0.02103,0.13222,0.05511,-0.01449,-0.01649,0.01762,0.07723,-0.00731,-0.0793,0.05426,-0.0512,-0.10282,0.06277,0.07014,0.03412,0.0322,0.06271,0.06938,-0.10604]},{"domain":"energy_systems","key":"energy_slg_fault","name":"Single line-to-ground fault (symmetrical components)","package":"energy-systems-ai999x","example":"SLG fault: X1 = 0.1, X2 = 0.1, X0 = 0.1","v":[-0.06498,0.00528,0.11765,-0.03416,0.09665,0.00287,0.03166,0.05813,0.05412,-0.02358,0.0048,-0.05116,-0.19215,-0.03831,0.07359,-0.01452,-0.06742,0.00883,-0.06027,0.08206,0.01825,-0.06161,-0.00246,0.02623,-0.0436,-0.06891,0.02262,-0.00673,-0.02982,-0.03452,-0.10032,-0.00552,-0.02931,-0.06875,0.07479,0.02695,0.08975,0.00932,-0.03923,-0.10359,0.05266,0.03507,-0.01388,0.13472,-0.06123,-0.01769,-0.0051,0.05259,0.04424,-0.02024,-0.09231,0.15245,0.00209,0.01773,-0.05163,-0.09855,0.00305,0.01751,-0.00123,0.02449,-0.03081,0.03522,-0.06608,-0.01117,0.09158,-0.00762,0.04595,0.02765,-0.00972,-0.01454,0.13494,-0.10563,-0.02741,-0.04081,-0.01611,-0.03671,-0.11897,-0.01206,0.15422,0.02991,0.011,0.03078,0.06993,-0.00158,0.02102,0.04803,-0.03083,0.0077,0.00336,-0.03887,0.03427,-0.02668,-0.0519,0.07064,0.06781,0.03149,-0.15196,0.02213,-0.05423,-0.08957,0.00263,-0.0547,-0.08899,-0.04838,-0.0336,-0.04707,-0.06695,-0.08745,-0.06135,0.03704,-0.04262,0.01149,0.0608,-0.00848,0.0611,-0.04277,-0.01012,-0.04806,0.08347,-0.14533,-0.04476,-0.05178,0.03013,-0.03558,-0.03242,-0.01245,0.06279,0.05664,0.16,-0.02055,0.02082,0.02371,0.01112,-0.06957,-0.00541,-0.03014,-0.00773,-0.05567,0.10149,-0.02797,-0.10355,0.00186,-0.07375,0.05258,-0.00187,0.04655,0.06544,-0.0323,0.09996,-0.06355,0.01754,-0.0308,-0.06093,0.19301,-0.0476,0.08849,-0.07469,0.05008,-0.03454,-0.04671,0.028,-0.01223,-0.01229,-0.14792,-0.01528,0.05162,-0.0172,-0.03587,0.06209,0.04324,0.03055,0.01675,0.09989,0.07918,0.04623,-0.02708,-0.03953,0.03298,-0.07872,0.03694,0.04272,0.06167,-0.05953,-0.06589,-0.13623,-0.00219,-0.03347,0.02793,-0.01035,-0.00467,0.15675,-0.02688,0.00753,0.07342,-0.04371,-0.04297,0.06249,0.12447,-0.01358,0.12086,-0.0975,-0.02693,0.05633,0.02754,-0.03685,0.01977,-0.05999,-0.00233,-0.06404,0.00675,0.06084,0.04275,0.0497,-0.06468,0.01967,-0.02432,0.02831,0.07451,0.03265,-0.04639,0.10096,-0.00704,0.01878,0.05413,0.10966,0.05199,-0.07016,-0.09398,0.13311,-0.06827,0.01383,-0.15213,-0.00359,0.09778,0.0111,-0.01731,-0.10011,0.02441,0.00067,0.06368,0.04899,0.10847,0.03047,-0.05797,0.00808,0.01727,0.05907,-0.04435,0.09202,-0.02368,0.06202,0.06695,-0.05856,0.03752,0.05165,-0.0107]},{"domain":"energy_systems","key":"energy_solar_declination","name":"Solar declination on a day of the year","package":"energy-systems-ai999x","example":"Solar declination: n = 172","v":[0.13724,-0.01005,-0.05186,0.0622,0.05482,0.01841,-0.05449,0.07245,0.04014,0.10114,-0.03911,-0.13663,0.00051,0.00179,-0.00379,-0.01989,0.03056,0.03203,0.07941,-0.09218,0.00892,-0.03014,0.03903,-0.07177,0.18872,0.00521,-0.03862,0.0139,-0.02539,-0.07558,-0.07702,-0.0061,0.05154,-0.0111,0.059,-0.06124,0.00741,-0.02527,0.01401,0.03204,-0.02149,-0.00805,-0.03968,-0.04707,-0.01726,0.02012,0.01218,-0.0424,0.15459,0.09104,0.00153,0.03955,0.02382,-0.04397,-0.07786,-0.0145,0.00136,0.07101,0.03376,-0.04164,0.036,0.12592,0.00548,-0.00864,-0.08865,0.0441,-0.01455,-0.08235,-0.05916,0.04261,0.04071,-0.06074,0.04867,-0.00686,-0.02885,-0.00402,0.03429,0.00024,0.11458,0.03901,0.02323,-0.03063,0.04857,-0.06028,0.05454,-0.07258,0.01563,0.01824,0.07647,-0.06567,0.0494,-0.02467,-0.00249,-0.12099,-0.19913,-0.02087,-0.00877,-0.02351,0.06245,0.05487,0.02378,-0.01932,0.01191,-0.0995,-0.07529,-0.0664,0.05352,0.04791,0.12525,-0.06795,0.0616,0.08247,-0.00609,-0.03078,0.12005,0.06071,0.01076,0.03069,-0.03012,0.00329,-0.02437,-0.06847,-0.01389,0.02785,-0.01645,0.05415,-0.02264,0.00107,-0.06869,0.04473,-0.03,0.00457,0.08026,-0.08444,-0.03696,0.07589,-0.04249,-0.00772,0.00841,0.20105,0.03647,0.02079,0.06292,-0.01401,0.11908,0.03571,-0.01933,-0.10977,-0.05021,0.0414,0.01542,-0.14117,-0.00951,0.05219,-0.02689,-0.04274,-0.0156,-0.0836,-0.0474,-0.02363,0.10738,0.0144,-0.03943,0.0057,0.05633,0.01145,0.03358,0.03916,-0.04101,0.07191,0.03273,0.0756,-0.00426,-0.22084,-0.05425,0.01635,-0.02752,0.01975,0.06428,-0.12632,-0.03932,0.03483,-0.01837,0.03476,0.0328,-0.03911,0.05688,-0.03767,-0.10712,-0.0164,0.11075,0.05538,0.0325,-0.03078,-0.04212,-0.01895,0.1202,0.08131,-0.09522,-0.05637,0.06545,0.03842,-0.00528,-0.03969,-0.01948,0.03455,-0.07145,0.07396,-0.0638,0.00673,-0.01339,-0.1475,-0.0216,-0.0095,0.08172,-0.03421,0.03632,0.0649,-0.03626,0.1224,-0.07744,-0.00431,0.10231,-0.01233,0.00577,0.01619,-0.04141,-0.07943,-0.01294,0.02769,-0.01179,0.02363,-0.10671,-0.05479,-0.00116,-0.03062,0.12058,-0.05608,-0.00635,0.03636,-0.06397,0.05057,-0.0738,0.0292,0.00743,-0.04856,0.11943,-0.14391,-0.05847,-0.0082,0.05955,0.10163,0.03375,0.07169,-0.078,-0.00249]},{"domain":"energy_systems","key":"energy_solar_position","name":"Sun position at a place and local time","package":"energy-systems-ai999x","example":"Solar position: latitude = 40, longitude = -105, n = 172, clock = 13:00, utc_offset = -7","v":[0.01228,0.08622,-0.09633,0.04425,0.0042,0.02495,0.03047,0.04122,0.07044,0.01591,-0.03644,-0.05384,0.05075,0.07706,0.02598,0.07472,0.05632,0.08042,0.03426,-0.09459,-0.06443,-0.13561,0.01449,-0.08123,0.12023,0.04112,-0.03862,0.00761,-0.02556,0.0078,-0.02022,0.01572,0.01199,0.00843,0.07697,-0.03718,0.11954,-0.03777,-0.01713,-0.07746,0.09715,-0.05457,-0.11102,-0.00094,-0.04714,0.09247,0.00221,-0.15851,0.07524,0.01264,0.07205,4e-05,0.02604,0.06156,-0.13136,-0.00604,-0.00689,0.05887,-0.0501,0.07135,-0.05015,0.11732,-0.02518,-0.02841,0.04028,0.01526,0.01147,-0.08633,-0.06627,0.04288,-0.07724,-0.11863,0.07235,-0.01898,0.05279,-0.0997,0.07345,0.01529,0.11699,0.03109,-0.04271,-0.01656,0.03824,-0.03043,0.00025,-0.0343,0.07059,-0.05436,0.0992,-0.06616,0.02754,-0.04491,-0.15374,-0.0211,-0.17331,-0.02497,0.03617,-0.01876,-0.03293,0.03106,0.01892,0.0455,0.0246,-0.13579,-0.06001,-0.03525,0.00081,0.02476,0.00172,-0.05776,0.10219,0.05836,-0.03144,0.00222,0.14346,0.058,-0.02767,0.0719,-0.08274,0.06651,-0.01779,-0.07417,0.00972,-0.06851,0.04748,-0.01961,0.05349,0.00116,0.0673,0.05719,0.04068,-0.01068,0.05359,-0.02312,0.02165,0.08794,-0.08195,0.00693,0.05803,0.09791,0.08997,0.12555,0.00325,-0.06131,0.02713,-0.0172,-0.01033,-0.03929,-0.00478,0.03355,-0.03806,0.00377,0.02613,0.07099,-0.06215,0.09222,-0.06442,0.0275,-0.01353,-0.00758,0.13975,-0.03407,-0.03671,0.04354,0.05245,0.0674,-0.0219,0.11783,-0.05793,0.03485,0.03129,-0.01161,0.03925,-0.09751,-0.09803,-0.02912,-0.02676,0.03079,0.07572,-0.10857,-0.05446,0.06109,-0.01242,-0.05873,0.00822,-0.00549,0.04001,0.02809,-0.11763,-0.05059,0.05672,0.00486,0.01728,0.02373,-0.06407,-0.00962,0.11291,0.00657,0.02648,0.01279,-0.04976,-0.02986,0.04519,0.06928,-0.09298,0.03233,0.05577,0.06439,-0.04008,-0.02864,0.00533,-0.07927,0.00231,0.00213,0.01043,-0.00785,-0.07191,-0.01918,-0.0818,-0.0404,-0.12261,0.01883,0.00183,-0.02611,0.04244,-0.03916,0.02738,-0.13867,-0.03033,0.04324,0.00879,-0.04436,-0.05498,-0.11556,0.0702,-0.06532,0.11843,-0.00446,0.06325,0.01865,-0.11611,0.01284,-0.11924,0.02536,0.04929,-0.06268,0.09462,-0.1621,0.04787,0.00825,0.07665,0.01821,0.05883,-0.06791,-0.04186,0.03532]},{"domain":"energy_systems","key":"energy_solar_time_hour_angle","name":"Solar time and hour angle from clock time","package":"energy-systems-ai999x","example":"Hour angle: n = 172, clock = 14:30, longitude = -75, utc_offset = 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power of a fuel-cell or electrolyser stack","package":"energy-systems-ai999x","example":"Stack electrical power: I = 200 A, N = 100, V_cell = 0.7 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zenith, elevation and azimuth from latitude, declination and hour angle","package":"energy-systems-ai999x","example":"Sun angles: latitude = 40, declination = 0, hour_angle = 0","v":[-0.00298,0.04428,0.01015,0.02264,-0.01576,0.04354,-0.07396,-0.05223,0.0244,-0.02829,-0.05674,-0.06645,0.04438,0.06261,0.0397,0.04292,0.11026,0.07801,0.02528,0.01056,-0.06394,-0.06638,-0.07148,-0.04093,0.05189,0.0453,0.0048,0.05421,-0.04384,-0.09079,-0.13078,-0.01459,-0.11267,-0.00104,-0.00893,0.03667,0.0616,-0.13341,0.00319,-0.12072,0.03439,0.04193,-0.12473,0.0592,-0.00916,0.08439,-0.02711,-0.0276,0.01611,0.04569,0.10391,-0.05321,0.00765,-0.0021,-0.06417,0.074,-0.0277,-0.01779,-0.04804,-0.01612,-0.07218,0.08343,-0.07141,-0.12622,-0.00355,0.02067,0.04997,-0.1347,-0.08877,0.0313,0.04523,-0.00762,0.17705,-0.00155,0.08346,-0.04543,0.01327,0.1188,0.09572,0.01348,-0.05618,0.02666,0.03913,0.00329,0.01034,-0.05562,0.10143,0.00685,0.06279,0.03033,0.08117,0.03068,-0.07788,0.00416,-0.08602,-0.02681,0.00493,-0.01347,-0.01629,-0.01123,-0.03593,0.00376,0.05898,-0.01148,-0.06559,0.02338,0.03538,0.03152,-0.04649,-0.00677,0.12627,0.08994,-0.08678,0.02318,0.0888,0.05642,0.00408,-0.02737,-0.05527,-0.04836,-0.01511,-0.06631,0.02625,-0.07669,0.08563,0.06173,0.05729,-0.00507,0.0863,-0.00202,0.07985,-0.08758,-0.07002,0.02357,-0.04786,-0.00349,-0.11671,0.03754,0.03003,-0.04623,0.00692,0.10748,-0.07844,0.01066,0.11101,-0.02041,0.02009,0.09901,-0.03655,0.00467,-0.03921,-0.01195,0.00555,0.0722,0.00602,0.07884,-0.08539,0.04391,0.02481,0.0003,0.13229,-0.11544,-0.09046,0.0478,-0.08676,0.05582,-0.12496,-0.01187,-0.1103,0.05191,0.11225,0.01886,0.05698,-0.11121,-0.07804,0.00353,-0.07279,-0.04285,0.03723,-0.10769,-0.02538,0.08868,0.00606,-0.12008,0.0611,-0.01524,0.07552,-0.06878,-0.02307,-0.04642,-0.01583,-0.02956,-0.04111,0.04977,-0.03632,0.08691,0.07363,0.09722,0.07817,0.02509,-0.08835,-0.06351,0.03556,0.00818,-0.1054,0.06186,0.11706,0.06695,0.00741,-0.12183,-0.05757,-0.04776,0.03369,0.06395,0.01612,-0.07187,-0.06811,0.05897,-0.03092,-0.01509,-0.05916,-0.05725,0.04431,-0.00479,-0.0395,0.06262,0.00504,-0.0317,-0.00763,0.053,0.00303,0.02796,-0.07309,-0.08683,0.01526,-0.12134,0.08422,-0.0155,0.02087,-0.03354,-0.05641,-0.04698,-0.03435,0.01815,-0.00826,-0.01009,0.13664,-0.05979,0.09632,0.01025,-0.00825,0.07175,0.09028,0.00924,0.00151,0.06461]},{"domain":"energy_systems","key":"energy_sunrise_sunset","name":"Sunrise, sunset, solar noon and day length","package":"energy-systems-ai999x","example":"Day length: latitude = 0, longitude = 0, n = 81, utc_offset = 0","v":[0.02883,0.05081,-0.05055,0.00015,0.02845,-0.00585,0.06702,0.07483,0.03775,0.04525,-0.02457,-0.04848,0.08171,0.10549,0.03347,0.04688,-0.02329,0.0601,-0.06712,-0.03056,-0.07873,-0.125,-0.01292,-0.0627,0.1238,0.02014,-0.07438,0.01991,0.00013,-0.0262,0.05895,0.02928,-0.00465,-0.02297,0.04266,-0.02417,0.09989,-0.01902,-0.04702,-0.0144,0.08235,-0.03385,-0.02354,-0.00301,0.00986,0.08382,-0.03771,-0.09377,0.07079,0.04895,0.00427,0.06057,0.05936,0.07135,-0.09872,-0.0202,0.01454,0.03101,0.01024,0.02903,-0.08872,0.11431,-0.02685,-0.00375,0.04569,0.08913,0.02914,-0.06366,-0.13268,0.01825,-0.0452,-0.13217,-0.02661,-0.00693,0.03561,-0.06439,0.01916,-0.00428,0.07025,0.03666,-0.01705,0.03658,0.05132,-0.04498,0.05189,-0.06691,0.0579,-0.03367,0.11393,-0.0856,0.01337,-0.03488,-0.05714,-0.0746,-0.13018,0.04989,0.05463,0.02859,-0.05529,0.11268,0.03121,0.0281,-0.03425,-0.11571,-0.04307,-0.05687,-0.03882,0.01797,0.0233,-0.08828,0.02133,-0.021,0.06344,-0.02888,0.08243,0.08951,-0.03454,0.0129,-0.13542,0.07939,-0.00456,-0.0909,-0.03881,-0.10147,0.08534,-0.02702,0.06704,0.04756,-0.00042,0.03328,0.00627,0.00149,0.12257,-0.0123,-0.00602,0.10247,-0.01663,0.02069,0.02962,0.08077,0.1171,0.12706,0.04948,-0.15439,-0.02217,-0.01436,-0.00533,-0.06891,-0.05316,0.02821,0.03121,-0.02714,0.02476,0.01522,-0.06852,0.07195,-0.10167,0.00796,-0.07497,-0.00546,0.15464,-0.03854,-0.07764,-0.06747,0.04417,0.06517,0.03399,0.0307,-0.01286,-0.01701,-0.03317,0.01525,0.04775,-0.00966,-0.11886,-0.09712,0.04787,0.05143,0.11783,-0.12639,-0.06053,0.11852,-0.02089,-0.0451,-0.02793,-0.05813,0.0662,0.09005,-0.07794,-0.049,0.04036,-0.06373,0.06184,-0.07542,-0.08831,-0.00359,0.09275,0.06732,-0.06309,0.07936,-0.02085,0.01881,0.03719,0.07899,-0.11811,0.04805,0.08824,0.0948,-0.10032,-0.01328,-0.0185,-0.10489,0.00407,0.01401,0.02698,0.0301,-0.02093,0.03287,-0.04928,-0.0545,-0.07297,0.00268,-0.03189,-0.04718,0.04859,-0.01189,0.02983,-0.11194,0.02493,0.05386,-0.03539,-0.09805,-0.02922,-0.01184,0.02893,-0.05553,0.0735,-0.00527,0.03052,0.05896,-0.07651,-0.02588,-0.10218,-0.02368,0.03709,-0.09036,0.16098,-0.0879,-0.02377,-0.00254,0.10019,0.00468,0.0469,-0.06187,-0.04616,0.01853]},{"domain":"energy_systems","key":"energy_symmetrical_fault","name":"Three-phase (symmetrical) fault current by the bus impedance matrix","package":"energy-systems-ai999x","example":"Symmetrical fault: network = 0-1 0.2; 1-2 0.3, fault_bus = 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in the wind and the Betz limit","package":"energy-systems-ai999x","example":"Power in the wind: rho = 1.225 kg/m^3, D = 80 m, v = 10 m/s, cp = 0.4","v":[-0.00734,-0.10195,0.08626,0.08285,0.06421,0.07117,0.01392,0.0137,0.02122,0.08659,0.03773,0.05185,-0.1074,0.02574,0.00702,-0.09287,-0.0613,-0.03449,0.05455,0.00891,-0.01985,0.1178,0.09562,-0.08109,-0.0198,-0.01163,0.06683,0.05937,-0.03533,0.06023,0.00804,-0.11241,-0.07799,-0.02262,-0.00708,-0.04038,-0.02679,-0.09041,0.01591,0.01031,0.03051,0.01918,0.00536,-0.08499,-0.04307,0.0298,0.01355,-0.09589,0.05985,-0.09464,0.06521,0.04006,0.01187,-0.01632,0.00438,0.0342,0.07492,0.01424,-0.06678,0.01647,0.1199,-0.00743,-0.03235,-0.06772,-0.01713,-0.10766,0.04108,0.0594,-0.0297,0.04149,0.09636,0.0584,-0.1525,-0.02625,0.0265,0.02647,0.01704,-0.03495,-0.02649,-0.00753,-0.02651,-0.05013,-0.11042,-0.06216,-0.05006,-0.07833,0.1219,0.01971,0.11989,-0.14099,-0.07774,-0.03865,-0.02717,0.01167,-0.02277,-0.0653,0.14573,0.06314,0.01334,0.01623,-0.01515,-0.01984,0.08739,0.06071,0.0348,-0.06744,-0.05565,-0.03112,0.10241,0.04001,-0.01841,0.01766,0.02253,0.07069,-0.02104,-0.03277,-0.02668,-0.11014,-0.00481,-0.02572,0.02153,-0.01052,-0.06859,0.0427,-0.11978,-0.0374,-0.00417,0.07548,-0.00452,-0.05011,-0.0592,0.02603,0.01686,-0.07681,-0.06892,0.07098,0.11976,-0.1418,-0.05407,0.03029,0.01602,0.07323,0.06058,0.04321,0.04493,0.08666,-0.03082,-0.08,-0.01813,0.10003,-0.01112,0.11262,-0.09144,0.03118,-0.0486,0.02064,-0.02074,-0.06511,-0.02076,0.08971,-0.01641,0.07604,-0.06899,0.03385,0.06405,0.02533,0.11135,-0.00394,-0.04445,-0.11066,-0.00226,-0.0019,-0.10326,-0.11848,-0.01421,-0.02186,0.07186,0.05805,0.08637,-0.00424,-0.04728,-0.03871,-0.02771,0.02006,-0.00352,0.02354,-0.05522,0.01664,-0.06499,0.02169,-0.026,-0.0943,0.0607,-0.03027,-0.0549,0.04117,0.06893,0.05298,0.02595,0.02055,0.00312,0.0358,0.0131,0.03454,0.0414,0.09002,-0.07718,-0.0819,-0.0158,-0.12904,0.08,-0.03921,0.0995,0.00472,0.09058,0.07432,-0.07,0.0493,0.10801,0.04809,-0.1035,0.0677,-0.05105,-0.06391,0.03726,0.0209,-0.00573,0.04287,0.08761,0.01698,-0.03046,0.12785,-0.08898,0.06407,-0.05082,0.05299,-0.07098,-0.09723,0.04283,-0.0066,-0.00939,0.00909,0.03799,0.09301,-0.10324,0.06158,0.04845,0.10741,-0.0735,-0.10508,-0.06926,0.04699,0.06079,0.10252,0.02777,-0.0098]},{"domain":"energy_systems","key":"energy_wind_shear_log","name":"Wind speed at another height (logarithmic profile)","package":"energy-systems-ai999x","example":"Wind shear (log profile): v1 = 5 m/s, h1 = 10 m, h2 = 100 m, z0 = 1 m","v":[-0.00658,0.02831,0.11935,-0.01932,0.10819,0.02768,-0.06985,0.01873,-0.07393,-0.03963,0.03749,-0.00648,-0.09261,0.12444,0.01901,-0.01453,0.05455,0.00875,-0.04201,-0.10251,-0.07359,0.00424,0.0675,-0.07938,-0.04452,0.0078,0.07132,-0.09035,-0.01598,-0.00306,-0.01738,-0.00932,0.04253,-0.03972,-0.03839,0.0369,0.06631,-0.00735,0.01454,0.02419,-0.06452,-0.1185,0.00511,-0.03567,-0.13353,0.02872,-0.01912,-0.10878,-0.03477,-0.04134,-0.05734,-0.05901,0.01994,0.00736,-0.00086,-0.00888,0.13252,0.10376,-0.05158,-0.03548,-0.03132,0.03058,-0.0023,-0.0797,0.00489,-0.00726,0.06935,0.18809,-0.03071,0.06427,0.15423,-0.00466,-0.07587,0.03154,0.03201,0.03484,-0.00239,-0.04323,-0.00503,-0.00981,0.04483,0.07128,-0.10041,0.1084,-0.03746,-0.03974,0.10391,0.00099,0.10056,0.11665,-0.10311,0.00085,-0.0586,0.04931,0.0796,-4e-05,0.13458,0.0555,0.03835,0.05231,0.00254,-0.0187,-0.05625,-0.03409,0.02637,-0.07474,-0.16595,0.0884,0.07288,-0.09198,-0.0027,-0.0827,0.06179,0.07767,-0.05714,0.01857,-0.07669,0.00284,0.0229,0.00419,0.1222,0.01982,-0.0279,-0.01101,0.00451,0.0042,0.00816,0.07691,-0.00899,-0.00543,-0.07046,0.01625,-0.02643,-0.05638,-0.03681,0.08983,0.03262,-0.06204,0.10132,0.03077,-0.01633,0.06216,0.04215,-0.04055,-0.04373,0.04643,-0.03178,-0.02795,-0.09258,0.0534,-0.09228,-0.05858,-0.05345,0.07779,-0.00794,-0.00586,0.0192,-0.04749,0.00087,0.0582,-0.09501,0.04962,0.00481,0.04616,-0.07497,-0.02353,0.07509,-0.15238,-0.00822,-0.01636,-0.00716,0.00027,0.05296,-0.11872,-0.05171,-0.06099,0.05384,0.06739,0.02388,-0.01412,-0.03991,-0.01431,0.04903,0.07653,-0.03886,0.01468,0.07054,0.00385,-0.0208,0.10072,0.06099,-0.05929,0.09454,-0.03339,-0.079,-0.08254,-0.15513,0.0587,-0.07373,0.03326,-0.028,-0.01115,0.00191,-0.0546,0.01821,0.062,0.03392,0.05391,-0.01255,-0.09633,-0.02014,-0.06404,0.06993,-0.05061,0.03395,-0.02719,0.01494,0.03166,0.00266,0.04131,-0.00045,0.05894,-0.02865,-0.04283,0.06316,0.051,-0.0097,0.16848,-0.00229,-0.13104,-0.03964,0.12201,-0.06306,0.04522,0.06532,-0.02943,-0.01798,0.10617,-0.01516,0.02948,-0.11275,-0.08602,0.05274,-0.06468,-0.01176,-0.01665,0.03928,0.18597,-0.0178,-0.05615,0.03612,0.01616,0.04852,-0.03697,0.03213,0.02038]},{"domain":"energy_systems","key":"energy_wind_shear_power_law","name":"Wind speed at another height (power law)","package":"energy-systems-ai999x","example":"Wind shear (power law): v1 = 6 m/s, h1 = 10 m, h2 = 1280 m","v":[-0.01052,0.03999,0.03511,0.0185,0.06374,0.09518,-0.10306,0.11943,-0.04984,0.03,0.00969,-0.01621,-0.10031,0.03624,-0.03687,-0.11377,0.05107,0.00347,0.13742,-0.05666,-0.04878,0.13135,0.12857,-0.02466,-0.07384,-0.05587,0.10894,0.02041,-0.08733,0.05747,-0.08823,-0.02271,0.03181,0.02619,-0.00033,-0.01817,0.01168,-0.06756,-0.06109,0.0588,-0.0526,-0.00069,-0.09574,-0.01255,-0.10572,0.076,-0.07387,-0.08096,0.01012,-0.0757,-0.00273,0.01675,-0.02674,-0.0026,-0.01562,0.043,0.09908,0.02617,-0.09237,-0.0302,-0.03835,-0.00456,-0.01335,-0.15951,-0.06165,-0.06512,0.13473,0.12323,-0.06035,0.03117,0.1666,0.04334,-0.04099,-0.05151,0.00854,-0.02667,0.02977,0.03749,0.04548,0.00247,-0.03501,-0.01207,-0.09854,0.0363,-0.10693,-0.08839,0.09578,0.05138,0.09741,0.13084,-0.06466,-0.01945,-0.02049,0.01787,0.01525,-0.02207,0.10145,0.08732,0.01769,-0.03455,-0.02887,0.00598,0.07369,0.07253,0.08015,-0.07863,-0.04224,-0.00784,0.13604,0.03158,0.08865,-0.05919,-0.02358,0.07726,-0.03348,-0.02339,-0.0342,-0.02667,0.04441,-0.03148,0.04967,0.01658,-0.00196,0.03514,0.03381,0.08909,-0.00553,0.05468,-0.01964,-0.05574,-0.06154,-0.01731,-0.05955,-0.08408,-0.08048,0.02817,0.00936,-0.01344,0.03682,0.0325,0.10106,0.06029,0.00392,0.00212,0.03102,0.04561,-0.02135,0.03966,-0.04261,0.09206,-0.07694,0.08061,-0.10019,0.11571,-0.07002,-0.00839,-0.05488,-0.05701,0.00596,0.03676,-0.02412,-0.09213,-0.06533,0.02291,-0.05791,-0.03654,-0.11628,-0.11014,-0.03071,-0.03487,0.02187,0.09348,0.02984,-0.06666,-0.04347,-0.01838,0.03959,0.03028,-0.0093,0.00274,-0.11452,-0.05485,0.04765,0.00774,-0.00465,0.00308,0.06374,-0.06765,-0.12115,0.10068,0.02641,-0.02839,0.03633,0.02652,0.02707,0.03337,-0.09373,0.00854,0.01349,0.01668,-0.02949,-0.07282,-0.01634,-0.04254,0.0145,0.0393,0.01796,-0.02316,0.07935,-0.0686,-0.04674,0.03374,0.03302,-0.04353,0.05059,0.00737,-0.00347,-0.01448,0.16235,0.07989,-0.02301,-0.04662,0.03602,0.0112,0.01634,-0.04374,0.07494,0.09426,0.09611,-0.03923,-0.08029,0.1134,-0.03119,0.07623,0.06359,0.00313,0.05511,-0.00028,-0.06181,-0.01054,-0.06684,-0.08141,0.07049,-0.00874,-0.11292,-0.01691,0.06154,0.13371,0.04,-0.04665,-0.11155,0.01207,0.08284,0.01898,0.06295,0.03314]},{"domain":"mechanical_engineering","key":"angle_section_properties","name":"Section properties of an angle (L) section, with principal axes","package":"mechanical-engineering-ai999x","example":"Angle section: b = 100 mm, h = 100 mm, t = 10 mm","v":[0.00852,-0.0461,0.0863,0.01125,0.04424,-0.08665,-0.00699,0.01104,0.00976,0.02752,-0.04348,0.0388,0.00889,0.0773,0.0308,0.06793,-0.07883,0.09665,-0.06099,-0.02396,-0.029,-0.04912,0.07444,0.01969,0.06521,-0.02917,-0.03874,0.10419,-0.02107,0.09399,-0.03557,0.10343,-0.00017,-0.06185,0.14249,-0.05474,0.0834,-0.03037,-0.08822,0.07835,0.03367,-0.01423,0.00494,0.11267,-0.08769,-0.13008,0.01583,-0.06386,0.03052,-0.0682,0.00274,-0.01337,0.05115,-0.01875,-0.01256,0.02526,0.01846,-0.00243,0.01403,-0.00182,-0.01251,0.01301,-0.11417,0.12404,0.04976,0.0122,0.06394,0.00282,0.03596,0.03115,-0.13303,0.00398,-0.05302,-0.03768,-0.09321,-0.12689,0.09278,0.03373,-0.02642,-0.04425,0.00316,-0.00651,0.11768,0.11659,0.01338,0.06201,0.00034,0.00128,-0.09136,0.12074,-0.06187,-0.01909,-0.03106,-0.02567,-0.02498,-0.05962,-0.06541,0.0009,0.00069,0.01337,-0.00119,0.05312,0.06021,0.01292,0.04124,-0.07454,-0.0558,0.00385,-0.05911,-0.02708,-0.01212,0.00387,0.18695,0.07801,-0.1042,-0.09332,-0.01423,0.0281,0.00456,-0.01484,0.03995,0.07966,0.05469,0.02576,-0.05856,0.10139,0.05895,0.02776,0.12038,-0.07902,0.04612,-0.05113,0.02554,-0.10068,0.00255,0.02939,-0.07347,0.11844,0.02272,-9e-05,0.1299,-0.02376,0.08167,-0.06595,-0.02812,-0.01565,-0.0454,0.13818,0.08362,0.03058,0.02148,0.1805,-0.09615,0.00509,0.10854,-0.02944,0.02897,0.01341,0.00145,0.05461,0.04389,-0.0019,-0.03957,0.01795,-0.0082,0.06193,-0.12239,0.09772,-0.05224,0.08333,-0.05945,0.06703,0.06066,0.05449,-0.04501,-0.11141,0.0244,-0.00659,-0.02603,-0.14945,-0.00193,0.07099,-0.04399,-0.04515,-0.05937,-0.00769,0.0173,-0.04239,-0.02387,-0.14558,-0.02345,-0.01754,0.01883,0.04458,0.00341,-0.03538,-0.03524,0.00281,0.07934,-0.08179,0.06965,-0.01462,-0.03583,-0.04087,-0.01665,-0.05415,0.0116,-0.04038,-0.02662,-0.03924,-0.05318,0.0348,0.04479,-0.05221,-0.00292,-0.00124,-0.01827,0.05149,0.15943,-0.11874,-0.0771,-0.04554,-0.09787,0.00222,-0.00783,-0.08137,0.1157,0.09142,0.03236,-0.03996,-0.00132,0.065,0.06419,-0.08086,0.00715,0.00064,0.03571,-0.02202,-0.0396,-0.05933,0.07446,-0.00509,0.1174,0.07176,-0.11156,-0.01516,0.01843,-0.00841,-0.0153,-0.08321,-0.01523,-0.03872,0.00086,-0.07411,-0.04754,0.0278]},{"domain":"mechanical_engineering","key":"asme_elliptic_fatigue_safety_factor","name":"Fatigue safety factor by the ASME-elliptic criterion","package":"mechanical-engineering-ai999x","example":"ASME-elliptic safety factor: sa = 100 MPa, sm = 60 MPa, Se = 220 MPa, Sy = 450 MPa","v":[0.01152,-0.03231,0.0365,-0.06783,0.06307,-0.01989,-0.08236,0.04319,0.03552,-0.00736,0.02674,-0.13089,0.02287,0.05295,-0.02386,0.0385,-0.03101,0.10244,-0.0411,0.03277,-0.01804,0.04698,-0.01638,0.12719,0.01185,-0.00339,0.11976,-0.06794,0.05443,0.09679,-0.05549,-0.09297,-0.00394,0.06678,-0.04561,0.02592,0.00185,-0.01617,0.01834,0.01224,0.13329,0.13356,-0.12206,0.01103,0.06541,0.01324,0.09092,-0.05603,0.00291,-0.08694,-0.02305,-0.1233,-0.02447,0.11809,-0.01292,0.07215,-0.12131,0.03881,-0.03081,-0.01563,-0.02957,0.01695,-0.0074,-0.03906,0.03341,0.03389,-0.10984,-0.06377,0.07375,-0.01732,0.12591,-0.01452,0.06227,-0.04853,-0.03194,0.0107,0.02809,-0.0072,-0.09666,-0.07155,-0.0013,0.0575,-0.04524,0.0505,0.03934,-0.06097,-0.06822,-0.03029,-0.08442,-0.06569,0.03357,0.01419,-0.01965,0.06145,0.04826,0.04649,-0.06469,0.03077,0.05852,0.07187,0.09833,0.09892,0.05466,-0.01782,-0.04346,-0.01945,-0.07917,-0.02144,-0.05915,-0.00829,-0.0668,-0.04005,0.03621,-0.08235,0.03079,-0.00865,0.0539,0.08174,-0.00525,-0.07967,-0.09061,0.04515,-0.02757,-0.03006,-0.07986,-0.03579,-0.08848,0.04848,0.09016,-0.03039,0.04766,-0.0903,-0.09475,-0.02217,-0.03971,0.02726,-0.02817,-0.02729,-0.0583,0.12084,0.03117,-0.01001,0.07011,0.05668,0.00511,0.04333,0.02153,0.07726,0.05518,0.15084,0.10325,0.03348,-0.08913,-0.05174,-0.01003,-0.05955,0.0646,0.01014,-0.05401,-0.02879,-0.02267,0.06216,-0.07122,-0.05477,-0.04359,-0.00688,-0.08683,0.05582,0.04591,0.13551,0.01423,0.01102,-0.11098,0.04847,0.07405,0.06578,0.04253,-0.03518,0.07188,-0.01479,-0.01665,-0.0451,-0.06559,0.02636,0.03373,0.14437,-0.10354,0.05364,-0.03754,-0.10129,-0.00591,0.00867,0.0727,-0.00692,0.0517,0.01212,-0.04739,-0.03198,0.13464,0.02976,0.06438,-0.00822,-0.02239,0.00451,0.07798,-0.1021,-0.05965,0.00347,-0.14162,-0.13204,-0.04627,-0.0898,0.05077,0.07633,-0.02739,0.07077,-0.06184,-0.03491,-0.11255,0.08622,-0.08643,0.00176,0.05056,0.00893,0.07222,0.08605,-0.01137,-0.05159,0.01363,0.03981,0.05333,0.02151,0.16402,-0.07976,0.05428,-0.11609,-0.02161,0.02417,-0.0359,-0.02573,0.02169,-0.03119,-0.01992,-0.06171,0.08638,-0.02886,0.01745,-0.07403,-0.0362,-0.07797,0.07862,0.04622,-0.00048,0.0264,-0.0354,-0.06006]},{"domain":"mechanical_engineering","key":"axial_bar_segments","name":"Stepped bar under axial loads at its joints","package":"mechanical-engineering-ai999x","example":"Stepped bar: lengths = [300, 500], areas = [400, 200], loads = [-20, 30], E = 200 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fixed at both ends with an axial load at a step","package":"mechanical-engineering-ai999x","example":"Bar fixed at both ends: P = 60 kN, L1 = 0.4 m, A1 = 500 mm^2, E1 = 200 GPa, L2 = 0.4 m, A2 = 500 mm^2, E2 = 200 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life at a given reliability","package":"mechanical-engineering-ai999x","example":"Bearing life: C = 30 kN, F = 4 kN, n = 1500 rpm, R = 0.95, kind = ball","v":[-0.02756,-0.11206,0.00633,-0.01401,0.01306,-0.06523,0.02178,0.08348,-0.07324,0.05396,0.05385,-0.0385,-0.0281,0.01556,-0.02837,0.00633,-0.04668,-0.07828,-0.1085,-0.09105,0.00045,-0.05835,-0.00277,0.00873,0.06102,0.00235,0.10156,-0.07169,0.05592,-0.08897,0.04766,0.01698,0.04199,-0.01432,-0.01275,-0.01168,0.03185,0.12675,-0.01161,-0.0207,0.10195,0.03522,-0.01478,-0.02632,0.04589,0.00876,0.0695,-0.00359,0.06487,-0.16799,0.03203,-0.08422,-0.00443,0.02055,-0.07694,0.08656,0.03687,-0.03825,-0.0563,0.15728,-0.0157,0.13732,0.0198,-0.01416,0.0277,0.09591,-0.14229,-0.04593,-0.08258,0.06184,-0.00118,-0.02784,-0.01344,-0.05626,0.0745,-0.02823,-0.09187,0.01174,-0.02194,0.02362,0.09017,0.08246,0.0186,-0.02557,0.0819,-0.06511,-0.0301,-0.06302,0.03626,0.0369,-0.06038,0.00794,-0.02191,-0.01364,0.0336,0.04405,-0.05841,0.02369,-0.07518,0.00313,0.00788,-0.04675,0.05304,-0.03621,-0.01739,0.06877,-0.03445,0.02549,0.02165,0.02555,0.09114,0.0031,-0.02875,-0.06493,0.0534,-0.04539,0.00579,-0.08341,-0.02684,-0.01462,-0.05966,-0.08379,-0.04671,0.08735,0.00059,-0.05516,0.00585,-0.02311,0.00755,-0.04954,0.05109,-0.00377,-0.06879,-0.046,-0.04156,-0.01721,-0.05316,0.00317,-0.01049,0.08818,-0.0743,0.05336,0.039,-0.03408,-0.14716,-0.05389,0.02628,0.01378,0.00786,0.01178,0.11653,-0.04931,0.0231,-0.01574,0.0199,-0.09635,0.01468,0.04556,-0.01556,-0.11736,0.00107,-0.06324,0.02395,-0.08062,-0.01172,0.00744,0.00993,-0.05005,0.11656,0.02961,-0.1085,0.02974,-0.13802,-0.00881,-0.17055,0.14447,0.05201,0.05672,0.03633,-0.00466,0.04315,0.09398,0.14223,0.08901,0.10033,-0.03948,-0.07378,0.06286,-0.11699,0.04024,-0.09947,0.05191,0.04678,0.06049,-0.07748,-0.0289,0.02747,0.00811,0.07456,0.01927,-0.01523,-0.05519,-0.04983,0.04951,-0.0033,0.00428,-0.0703,-0.00323,-0.02991,0.04689,0.05128,-0.06033,-0.04245,-0.00211,0.10576,-0.00763,-0.02143,0.03245,0.0211,0.04891,0.03649,0.02752,0.01372,0.06272,0.02192,-0.01131,0.09036,0.05331,-0.00733,0.04519,-0.08502,0.01716,0.02758,0.03773,-0.02581,-0.09803,-0.07686,0.02938,-0.19795,0.096,0.01081,0.02603,-0.00934,0.0449,-0.0212,0.14729,0.04547,0.10191,0.0278,0.12062,0.01502,-0.04061,0.16145,0.07736,-0.14013,0.04271]},{"domain":"mechanical_engineering","key":"belt_drive_power","name":"Power of a belt drive with centrifugal tension","package":"mechanical-engineering-ai999x","example":"Belt drive power: T1 = 1.2 kN, m = 0.4 kg/m, v = 20 m/s, mu = 0.3, theta = 160 deg","v":[-0.06032,-0.0655,0.03956,-0.07209,-0.06305,-0.09419,0.05872,0.12383,-0.04286,0.07612,0.02967,0.01112,-0.04625,-0.10314,0.09544,0.00721,-0.03374,-0.08927,0.0662,0.04546,-0.0653,0.07712,0.05063,-0.01919,-0.03623,-0.02117,0.07484,-0.01795,-0.11836,0.00876,0.03917,-0.06333,-0.07841,-0.07605,-0.08396,-0.0133,0.00717,0.05066,-0.01123,0.06108,0.00096,0.06162,-0.04304,0.04181,0.09403,0.06794,-0.05089,-0.04462,0.09786,-0.061,0.0108,0.02162,-0.12994,0.02514,0.00868,0.06236,0.01855,-0.02591,0.03786,0.06794,-0.03487,0.08205,-0.08352,0.05613,0.04683,0.08758,0.00983,0.05048,-0.0344,-0.08107,0.06324,-0.02387,0.06125,0.00075,0.07403,-4e-05,-0.03598,-0.08278,0.00989,0.08108,-0.02282,-0.02932,-0.00156,-0.13786,0.01576,-0.03917,0.00784,-0.01411,0.08153,0.08734,-0.02714,-0.03921,-0.02543,0.02218,-0.06253,-0.01479,-0.02531,0.0183,0.08316,0.05571,-0.02694,0.12288,0.13453,-0.00842,0.03917,-0.00597,-0.04362,-0.03822,-0.02238,0.02012,0.01388,0.11513,-0.02992,-0.16855,-0.01554,-0.07868,-0.02896,0.00264,0.03789,-0.05632,-0.08513,-0.03635,0.00906,0.17576,0.01233,0.05843,0.02268,0.00201,-0.06554,-0.03687,0.03174,-0.08652,-0.03713,-0.01198,-0.05639,0.09216,0.0861,-0.06573,0.04989,-0.02543,0.00129,0.06225,0.11101,-0.05656,0.08856,0.00104,-0.10507,0.10586,-0.0398,-0.00849,0.01999,0.05003,-0.09929,0.10924,-0.08129,-0.06338,0.03177,0.02272,-0.01346,-0.04247,0.09821,-0.05215,-0.10569,0.0068,0.00781,-0.03078,0.04039,0.01063,0.02477,0.05153,-0.05376,0.01948,-0.12543,-0.01011,0.02207,0.05993,-0.02852,0.03569,-0.07902,-0.00282,0.10235,0.08375,0.0542,0.04183,0.00046,0.06863,-0.06505,-0.07707,-0.02738,0.01946,0.03017,0.06401,-0.07219,0.03623,0.01212,-0.02888,-0.06603,0.02484,0.10987,0.05437,-0.00643,-0.04705,-0.05334,-0.09356,-0.04484,-0.02892,0.01319,-0.05121,-0.02283,0.03699,-0.09595,-0.01841,-0.01221,-0.08092,0.13484,-0.04738,-0.02898,-0.02649,0.0753,0.02264,-0.07068,-0.03513,-0.0978,-0.03699,0.002,-0.02767,0.08008,0.15251,0.06761,0.05033,-0.00964,-0.03137,-0.06936,-0.06284,-0.02019,-0.07994,-0.12519,0.02009,-0.05434,0.06741,0.01665,0.11759,0.1424,-0.03342,-0.04419,0.06719,-0.02686,-0.088,-0.07778,0.0605,-0.06067,0.00441,0.10471,0.05508,-0.01975,0.10176]},{"domain":"mechanical_engineering","key":"belt_friction_capstan","name":"Belt or rope friction on a drum (capstan equation)","package":"mechanical-engineering-ai999x","example":"Capstan equation: T2 = 200 N, mu = 0.3, theta = 180 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tightening torque and preload (T = K F d)","package":"mechanical-engineering-ai999x","example":"Bolt torque: K = 0.2, d = 12 mm, F = 25 kN","v":[0.07103,-0.00956,-0.04388,-0.11312,0.02015,0.06446,-0.03296,0.06674,0.03822,0.06323,-0.00059,-0.02611,0.00946,0.10351,0.03378,0.0332,-0.03394,0.00228,-0.02156,0.08427,-0.01184,-0.02052,-0.01861,0.00246,-0.00913,0.04775,-0.00256,-0.04421,0.03828,-0.08507,0.07276,-0.09695,0.06778,-0.02805,-0.13204,0.09561,-0.0079,0.03974,0.04006,0.02534,0.02691,0.04188,-0.12336,-0.0135,0.06458,-0.0486,-0.02845,-0.06138,0.10717,-0.01237,-0.06223,-0.02416,-0.06591,0.04773,0.08125,-0.00394,-0.1018,0.03724,-0.04146,-0.02573,-0.02842,0.02656,-0.11745,0.02468,-0.05583,0.10009,-0.06415,0.10964,-0.03057,-0.01208,0.05634,-0.11958,-0.05162,-0.01228,-0.05679,-0.01579,-0.08632,-0.03556,-0.01512,0.08163,-0.00022,0.0865,-0.05207,-0.12602,0.05564,-0.0556,-0.1062,0.08047,-0.03236,-0.07995,0.03848,0.03604,0.03063,-0.01224,-0.00888,-0.02883,-0.05633,-0.07643,0.04042,0.02767,0.02273,-0.04466,0.06307,-0.03448,-0.01173,-0.02819,-0.02543,-0.05217,0.03577,-0.0084,0.00447,0.05863,-0.01237,-0.05008,0.01517,-0.01482,0.02146,0.01399,0.09484,-0.07669,-0.05904,-0.08258,0.03447,0.07964,0.10855,-0.06338,-0.07709,0.00629,-0.0487,-0.10315,-0.11028,0.0526,-0.07581,0.01285,-0.0086,0.0572,0.16229,0.00208,0.08172,0.09839,0.00775,0.05212,0.04333,0.07151,-0.03534,-0.01166,0.09282,0.04172,-0.0203,-0.04435,0.17869,-0.04989,-0.079,0.15382,-0.06348,-0.01624,0.02225,0.05416,-0.06314,-0.06143,-0.03385,-0.08907,-0.05486,0.07591,-0.01946,0.0331,0.05678,-0.02925,-0.08274,0.02327,-0.02057,-0.04907,-0.0457,0.14677,-0.028,0.05731,-0.06457,0.01529,-0.00657,0.01087,-0.0198,0.02701,0.0135,0.09364,0.01688,-0.08061,-0.00507,0.08074,-0.05059,-0.023,0.11392,-0.07149,-0.05425,-0.07833,0.00736,0.04564,0.04777,0.08032,-0.16291,0.10669,0.08944,-0.00814,-0.02218,-0.05935,0.18848,-0.00787,-0.01239,-0.01117,0.03376,0.04123,0.10558,0.01598,-0.03227,0.03554,-0.03137,-0.07573,-0.05991,-0.03995,0.05505,0.02366,-0.08683,-0.02243,0.00462,-0.06066,0.0078,0.05529,0.08068,-0.01622,0.04979,0.09796,-0.05017,0.00405,-0.11492,-0.16723,-0.14212,-0.00674,-0.00854,0.01508,-0.04831,0.02522,0.07881,-0.0234,0.02526,-0.00648,-0.03561,0.04683,0.01655,0.08071,-0.06148,0.07401,-0.0215,0.03055,0.02783,-0.01852,0.00305,0.09248]},{"domain":"mechanical_engineering","key":"brittle_failure_mohr","name":"Safety factors of a brittle material (maximum normal stress, Coulomb-Mohr, modified Mohr)","package":"mechanical-engineering-ai999x","example":"Brittle failure: sA = 90 MPa, sB = -50 MPa, Sut = 210 MPa, Suc = 750 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with a point load","package":"mechanical-engineering-ai999x","example":"Cantilever with end load: L = 2 m, P = 5 kN, E = 200 GPa, I = 8e-6 m^4","v":[0.06309,0.03927,0.0605,-0.00411,-0.08705,-0.02603,-0.08533,0.04174,-0.06159,-0.03102,-0.05325,-0.05458,-0.0391,0.06852,0.03812,0.02481,-0.01951,0.01389,0.00099,0.10891,-0.00686,0.09688,-0.04422,0.05692,0.04847,-0.01925,-0.06936,0.04504,0.05361,0.00332,0.08316,0.06286,0.01882,0.0185,0.06402,0.0608,0.04633,0.00451,-0.07048,0.04295,0.03483,-0.00385,0.00115,0.0408,-0.03193,0.13531,-0.03508,-0.10203,0.01805,-0.01213,0.05011,-0.05196,-0.0655,-0.08577,-0.00806,0.07257,-0.1303,-0.04446,0.07869,-0.09388,0.0056,0.06531,-0.1235,-0.02544,-0.16911,-0.02493,-0.01259,0.04816,0.00335,-0.03751,-0.02586,0.07732,-0.11468,0.07903,0.06179,-0.02135,0.02991,-0.08937,0.02064,-0.10767,-0.12788,-0.04191,-0.03578,0.03771,0.02089,0.03252,-0.13358,-0.11326,0.00669,-0.02038,-0.05119,0.04048,0.00889,0.09238,-0.03711,-0.04471,-0.05685,0.0408,-0.0116,-0.02846,-0.0402,-0.06032,-0.02079,0.09496,0.04556,0.0879,-0.07262,-0.01691,-0.12497,0.00929,-0.0442,-0.03466,0.04591,-0.00114,0.02838,0.04803,0.01554,-0.10929,0.03984,0.0138,0.04,-0.00602,-0.04141,0.0113,0.02526,0.13945,-0.00951,-0.02738,0.0782,0.0885,0.06887,0.05753,0.018,-0.10928,0.03827,0.00144,0.06013,-0.0692,-0.08334,-0.0449,-0.01075,0.08619,0.09718,-0.0771,-0.08682,0.06075,0.02788,0.04674,-0.02617,0.05831,-0.02168,-0.06904,-0.03647,-0.00903,-0.01458,0.06305,0.06003,0.00177,0.11048,0.02083,0.02824,0.03014,0.01518,0.12367,-0.03307,-0.03971,-0.10937,-0.03792,-0.08097,0.11875,-0.00898,0.01438,0.04574,0.08968,0.00427,-0.04599,-0.07565,0.00586,0.08664,0.01344,-0.02974,-0.07274,-0.03415,-0.02384,-0.0175,0.02314,0.02958,-0.09254,0.12033,-0.02396,0.05677,-0.03357,-0.01672,-0.01875,-0.06251,0.12551,-0.13553,-0.06209,0.06209,-0.05232,0.0371,-0.16243,0.05108,-0.08944,-0.01201,0.01601,-0.02218,0.0179,-0.05864,-0.02034,0.04517,-0.04113,0.12571,-0.05136,0.01749,-0.10539,-0.08303,0.11498,0.01131,-0.06128,0.0345,0.08665,0.08602,0.05377,0.19552,0.0875,0.05809,0.01755,-0.03095,0.04751,0.11454,-0.07722,0.06375,0.01481,0.0224,0.02264,-0.01299,-0.01419,-0.03921,0.06158,0.06817,0.03699,0.03754,-0.03257,0.002,-0.01267,-0.00961,0.10089,0.00764,-0.04586,0.02171,-0.0949,0.02648,0.0161,0.00683,0.03574]},{"domain":"mechanical_engineering","key":"cantilever_triangular_load","name":"Cantilever with a triangular (linearly varying) load","package":"mechanical-engineering-ai999x","example":"Cantilever with triangular load: L = 3 m, w = 6 kN/m, E = 200 GPa, I = 2e-5 m^4","v":[0.06461,0.07729,0.10026,0.00879,-0.11869,-0.025,-0.06095,0.00156,-0.01892,-0.02924,0.02369,-0.086,-0.04559,0.06171,0.00623,0.04765,-0.00076,-0.02547,-0.04464,0.08999,0.02835,0.11625,-0.03455,0.04854,0.05994,0.00711,-0.02585,0.03592,0.04214,-0.06785,0.02953,0.04515,-0.01715,0.05339,0.04464,0.08211,-0.01389,0.00267,-0.0607,-0.027,0.04492,-0.06502,-0.01099,0.01051,-0.02659,0.10193,-0.01203,-0.04347,-0.01686,-0.03626,-0.01226,-0.06995,-0.05881,-0.12908,0.00704,0.1044,-0.12197,-0.05529,0.07763,-0.0114,0.01421,0.08708,-0.05744,0.01175,-0.14296,-0.03745,0.00913,0.04031,0.02119,-0.06008,-0.02932,0.1242,-0.02266,0.11377,0.04175,-0.01623,-0.05221,-0.04944,0.00744,-0.13139,-0.07936,-0.01674,-0.01427,0.05141,-0.00975,0.00915,-0.13587,-0.10426,-0.03067,-0.01879,-0.04195,0.0401,-0.0373,0.05685,-0.03383,-0.06258,-0.02248,-0.01355,0.00479,-0.00263,-0.04579,-0.03436,-0.03097,0.12248,0.13645,0.11121,-0.03036,0.0095,-0.0943,0.0596,-0.10616,-0.07122,0.01744,-0.01564,-0.03136,0.10006,-0.03857,-0.14706,0.0736,0.04303,-0.00202,-0.04061,-0.06293,-0.00941,0.02879,0.14215,0.01352,-0.02093,0.04492,0.06688,0.07583,0.02772,0.01717,-0.08244,-0.00609,-0.06583,0.05553,-0.11982,0.01191,-0.10019,-0.00668,0.05062,0.04277,-0.03898,-0.11091,0.06195,-0.01191,0.04218,0.01139,0.05683,-0.0308,-0.08456,0.0237,-0.05168,-0.06794,0.00855,0.03802,-0.02958,0.13785,0.03972,0.05808,0.10201,0.04667,0.08716,-0.03646,0.00536,-0.07905,-0.0244,-0.09035,0.16735,0.02893,0.01543,0.0441,0.03906,-0.05143,0.00439,-0.05662,0.01921,0.06749,-0.0878,-0.05934,-0.06564,-0.06331,-0.07906,-0.04777,0.05998,0.05472,-0.03355,0.11392,-0.0357,0.04024,0.00625,-0.01575,0.03675,-0.0587,0.05983,-0.11286,-0.04859,0.00349,0.00868,0.03728,-0.12526,0.0463,-0.06786,0.01518,0.03053,-0.00289,0.01256,-0.10807,-0.06161,0.09152,-0.01883,0.11321,0.00372,0.04798,-0.09162,-0.01037,0.04163,-0.0,-0.08872,-0.04033,0.12323,0.02779,0.0827,0.12139,0.0826,0.03524,0.04547,-0.03257,0.0415,0.13272,-0.1289,-0.0052,-0.00952,0.11757,0.00634,0.02894,0.01102,-0.05119,0.05621,0.03279,0.07636,0.08231,-0.02355,0.01866,-0.01358,-0.00709,0.08876,0.01303,0.0052,0.00434,-0.10195,0.05644,0.02731,0.0394,0.0237]},{"domain":"mechanical_engineering","key":"cantilever_udl","name":"Cantilever with a uniformly distributed load","package":"mechanical-engineering-ai999x","example":"Cantilever with uniform load: L = 3 m, w = 2 kN/m, E = 200 GPa, I = 1e-5 m^4","v":[0.08437,-0.01123,0.14648,0.05077,0.0009,-0.0211,0.00756,0.00887,-0.03804,-0.07594,0.0827,-0.0588,0.02808,0.04744,0.07737,0.03511,0.02083,-0.03736,-0.05713,0.04984,0.01949,0.07445,-0.07952,0.05446,0.08645,-0.00235,-0.04359,-0.02096,0.02194,-0.0835,0.04958,0.15099,0.06524,-0.04443,0.01285,0.03204,0.04192,0.02742,-0.00227,0.04358,0.01766,-0.03388,0.01571,0.02475,0.01297,0.09936,-0.0775,-0.05447,0.07829,0.05524,-0.06197,-0.03438,-0.10635,-0.06693,0.04182,0.04603,-0.03135,-0.05081,0.03393,-0.02895,-0.00671,0.073,-0.07689,0.02438,-0.102,-0.00453,0.00173,0.06191,-0.04588,-0.07016,0.01185,0.1044,-0.12402,0.16961,0.01131,0.09964,0.02555,-0.0686,0.07405,-0.06896,-0.11104,-0.04971,0.02189,-0.02497,-0.03451,0.03837,0.01861,-0.01718,0.04714,-0.00237,-0.04749,0.01953,-0.01544,0.05626,-0.0999,0.04336,-0.08313,-0.05245,0.05097,0.0085,-0.06511,0.03695,-0.00537,0.08717,0.10307,0.0661,-0.01122,-0.048,-0.08152,0.03622,-0.06287,-0.04993,-0.00895,-0.0616,-0.02095,0.06843,-0.04956,-0.08155,0.022,-0.02805,0.01242,-0.01135,-0.07747,-0.0127,0.0684,0.08973,-0.00278,-0.02862,-0.03125,0.06237,0.12916,0.06231,0.04213,-0.10689,-0.02749,-0.06171,0.0564,-0.06539,0.03418,-0.0037,0.08693,0.01705,0.09015,0.0195,-0.08654,0.08197,-0.01519,-0.01494,0.03871,0.06439,-0.01167,-0.07406,0.02643,0.00524,-0.0118,-0.02882,0.01964,-0.04667,0.12631,0.02474,-0.01747,0.06896,0.13048,0.12821,-0.00503,-0.0597,-0.03571,-0.03992,-0.06688,0.13738,0.05766,0.00567,0.0346,0.04167,-0.09779,-0.00516,-0.00462,-0.03574,0.08644,-0.06829,-0.05337,-0.04915,0.02047,-0.05823,-0.04327,0.0004,0.0648,-0.11536,0.05961,0.00171,-0.03466,-0.00747,-0.05718,-0.10069,-0.09853,0.01878,-0.13867,0.00404,-0.01353,-0.04913,-0.00824,-0.13705,-0.06944,-0.13554,-0.04864,0.01656,0.01519,-0.03157,-0.10915,0.01119,0.05904,-0.01494,0.05891,0.00397,0.06775,-0.06078,-0.02784,0.04492,-0.01053,-0.04225,-0.11398,0.12598,0.09388,0.06705,0.17313,-0.0295,-0.05372,0.04096,-0.01577,0.0015,0.09483,-0.07314,0.00885,0.01656,0.07247,0.02152,-0.09762,0.01965,-0.02759,0.07536,-0.07726,0.10546,0.05808,-0.0936,0.09731,-0.03673,0.06862,0.0652,-0.03629,-0.04907,0.04878,-0.07056,-0.05546,-0.01577,0.0192,0.06859]},{"domain":"mechanical_engineering","key":"channel_section_properties","name":"Section properties of a channel (C) section","package":"mechanical-engineering-ai999x","example":"Channel section: b = 80 mm, h = 200 mm, tf = 10 mm, tw = 7 mm","v":[0.04312,0.01175,0.08797,-0.02929,0.00712,-0.06363,-0.02061,-0.00951,-0.00058,0.06752,-0.09638,0.04054,0.01361,0.03459,-0.0082,-0.01448,-0.09981,0.09005,-0.01342,-0.04832,-0.00643,-0.14553,0.02015,0.03005,0.06459,-0.1055,-0.04277,0.13174,-0.0805,0.02648,-0.03044,0.1242,0.0416,-0.13593,0.01675,-0.02936,0.00817,-0.06016,-0.09957,-0.03931,-0.05247,-0.06073,0.07993,0.10799,-0.13067,-0.12148,0.0305,-0.14597,0.09903,0.05348,0.02861,-0.02357,0.05388,0.00188,-0.04501,0.02634,0.00579,0.0542,-0.01434,0.01883,0.01995,-0.01584,-0.00879,0.04947,-0.02051,-0.02879,0.11444,0.01001,6e-05,-0.01523,-0.02363,0.0165,-0.03869,0.09377,-0.08492,0.00655,0.04044,0.05907,0.03121,-0.06273,0.02285,-0.13385,0.08182,0.03508,0.01726,0.04967,-0.03438,0.00783,-0.0523,0.10099,-0.03768,0.07514,0.00016,0.12848,-0.01707,-0.14329,-0.04048,-0.05223,-0.02465,-0.01194,-0.03998,0.0381,-0.01026,0.12184,0.06333,-0.01881,-0.10609,0.0542,-0.03463,0.08136,-0.01375,-0.01604,0.06683,0.0647,-0.0249,0.04814,0.0404,-0.03242,0.01121,-0.0456,0.03797,0.05828,0.00372,0.03901,-0.01943,0.05961,0.09083,-0.0925,0.03074,0.00854,0.02137,0.08836,0.00243,-0.05947,0.03258,-0.04376,-0.03273,-0.0345,0.02017,0.00054,-0.05086,-0.03591,0.01053,-0.12346,-0.08518,-0.08818,-0.03954,0.09381,0.04974,-0.00257,0.01148,0.04729,-0.02031,0.09155,0.03953,0.01305,0.01411,-0.03408,-0.0038,0.0732,0.04237,-0.10908,0.01446,-0.04971,0.01098,0.02293,-0.10021,0.09067,-0.01832,0.06528,0.06021,0.02849,0.01581,0.08666,-0.04002,-0.13839,0.05029,-0.08214,-0.0132,-0.04001,0.01267,0.02264,-0.1084,-0.14421,0.01419,0.04331,0.09738,-0.03651,0.0411,-0.14667,-0.06779,0.02172,-0.13432,0.04716,-0.01792,-0.0598,-0.10722,0.04337,0.0692,-0.07064,0.00678,0.08853,-0.0171,-0.11382,-0.02561,-0.06037,-0.04189,-0.00792,0.01747,0.01894,-0.09623,0.0758,0.04777,-0.00118,-0.01997,-0.05447,-0.04694,0.03098,0.16155,0.01543,-0.00623,0.04334,-0.04971,0.03224,0.04955,-0.07627,0.0531,0.02323,-0.00877,0.11965,0.01764,0.02699,0.09356,0.11236,0.04741,-0.02206,0.02423,0.04955,0.08496,-0.09642,0.15605,0.06462,0.02334,0.01011,-0.04682,-0.05624,-0.02094,0.0145,0.08049,-0.05745,0.06132,0.02473,-0.04904,0.05162,-0.0357,-0.00818]},{"domain":"mechanical_engineering","key":"circular_section_properties","name":"Section properties of a solid circle","package":"mechanical-engineering-ai999x","example":"Circular section: d = 50 mm","v":[0.02788,-0.08741,-0.01837,0.00707,0.05651,-0.04012,-0.0387,0.06884,-0.03642,0.05495,0.02511,-0.04411,0.0358,0.00027,-0.0515,0.13101,-0.03314,-0.01108,-0.08141,0.077,0.0576,-0.09502,0.04353,-0.04354,-0.06562,0.01519,0.0048,0.12231,0.03924,0.08989,0.00346,-0.01741,-0.0032,0.024,0.01876,-0.01683,0.03663,-0.01868,0.053,0.00233,0.06766,0.06749,-0.06965,0.08286,-0.04225,-0.03084,0.09058,-0.12671,0.02543,-0.07984,0.00649,-0.00057,0.07513,0.04806,-0.08438,0.10458,-0.03887,-0.03093,-0.1385,0.05895,0.00295,-0.0615,-0.09829,0.1164,-0.0753,-0.07306,-0.00646,0.083,-0.02823,0.05033,0.03406,-0.02472,-0.12571,-0.00229,-0.01116,-0.06196,-0.06912,-0.02868,-0.00919,-0.09765,-0.03495,0.05299,0.08418,0.14294,0.06652,0.1079,-0.00834,-0.0197,-0.02795,-0.01935,-0.08963,-0.02681,-0.03479,0.02214,-0.03332,-0.07053,-0.13254,0.02999,0.01756,-0.10447,-0.02634,0.00172,0.0209,0.02121,-0.0493,0.07291,0.016,-0.01964,0.01226,0.06761,0.01664,0.07138,0.02464,0.04659,-0.09776,-0.06691,0.00283,-0.07639,-0.05288,-0.0013,0.03625,-0.03477,-0.04014,0.04718,-0.07071,-0.09642,-0.04585,0.01842,-0.00678,-0.01014,-0.03203,0.06887,0.07295,-0.00546,0.08285,0.13658,-0.01889,-0.02257,0.01789,0.11265,0.02204,-0.01133,0.08095,-0.00956,0.00175,0.04061,0.04023,-0.01439,0.03571,0.05452,0.09115,0.14373,-0.12968,0.03758,0.08121,0.06396,0.01487,0.04141,0.07277,-1e-05,-0.02381,0.02332,0.00339,-0.04545,0.06893,0.03251,-0.10882,0.05182,-0.00039,0.05069,-0.04811,-0.07241,0.04045,0.06511,-0.00906,-0.13374,0.02072,0.14077,0.07211,-0.16404,0.11567,-0.00188,0.05849,-0.00063,0.02563,-0.09172,-0.00693,0.04244,-0.03805,-0.17232,0.03265,0.03738,-0.04365,-0.06073,-0.05972,-0.04114,0.01446,0.04561,0.0764,-0.02308,0.00748,-0.00806,0.02112,-0.09483,0.0366,-0.08724,0.03615,-0.06399,0.0045,-0.10356,0.04161,0.02287,0.17634,0.00142,-0.03476,-0.03384,-0.08295,-0.02191,0.07624,-0.07652,-0.09056,0.04992,-0.01099,-0.06566,0.09252,0.0266,0.08852,-0.03696,-0.00896,0.02034,0.01932,0.08974,0.12437,-0.06576,-0.04657,-0.0124,-0.03497,0.00426,-0.00199,-0.02406,-0.04966,0.08301,0.04717,-0.02243,-0.01232,0.00525,-0.00241,-0.04277,-0.12596,-0.05898,-0.04511,-0.03412,-0.00107,-0.06986,-0.06337,0.09517]},{"domain":"mechanical_engineering","key":"combined_axial_and_bending_stress","name":"Combined axial force and biaxial bending of a rectangular section","package":"mechanical-engineering-ai999x","example":"Combined axial and bending stress: b = 100 mm, h = 200 mm, N = -50 kN, Mx = 8 kN*m, My = 2 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section of rectangles (parallel-axis theorem)","package":"mechanical-engineering-ai999x","example":"Composite section: rects = [200 20 0 10; 20 300 0 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90","v":[-0.05286,-0.01581,0.01927,-0.04225,0.00195,-0.07312,-0.04524,-0.04474,-0.02316,-0.03077,0.01919,-0.03236,0.03115,0.06035,-0.00288,-0.04222,-0.07853,-0.02286,-0.07865,-0.13204,-0.05211,-0.01379,-0.03579,-0.0154,0.04447,0.0016,0.04627,-0.04145,0.00397,-0.0013,-0.06139,-0.01132,-0.05545,-0.03644,-0.03326,-0.04613,0.07849,0.09551,0.11595,0.05243,-0.01763,0.05133,-0.07796,0.09431,0.05254,-0.00275,-0.07161,0.13602,0.10133,-0.12013,-0.11187,0.02013,-0.01541,0.05281,0.10718,0.0606,-0.09558,-0.01102,0.03162,-0.01477,-0.00196,0.03435,-0.06207,0.02656,-0.00547,0.05479,-0.06573,0.03265,-0.04412,0.0801,0.10935,0.03662,0.09348,-0.02218,0.05281,0.07436,-0.05541,0.0121,0.00063,0.00448,0.07454,-0.03905,0.01377,-0.00165,0.04026,-0.05005,-0.01528,0.00451,-0.07514,0.05131,-0.03138,0.0339,0.04221,0.00336,0.07719,-0.0597,0.0735,0.0675,0.04008,0.03933,0.05319,0.03321,-0.04633,0.03171,-0.00845,-0.00554,-0.08622,-0.02824,0.03055,0.06075,-0.06084,-0.05043,0.0588,0.06033,-0.06821,-0.02779,-0.02771,-0.06995,-0.01318,0.02148,-0.16086,0.00183,0.05534,-0.04047,0.04187,-0.12433,-0.03997,0.04703,0.03222,-0.00225,0.0563,0.05891,-0.04383,-0.00785,-0.03502,0.05598,-0.00781,-0.07127,0.05493,0.20995,-0.08841,0.00906,0.01552,0.02529,-0.05513,-0.02167,-0.02602,0.01681,0.04322,0.0429,0.10938,-0.03245,-0.10751,-0.03928,-0.10355,-0.06193,-0.02681,-0.13386,0.09087,0.09548,-0.10504,0.17161,-0.06059,0.02275,-0.01573,-0.14038,-0.06333,-0.04668,0.0818,0.06079,0.02954,-0.05281,-0.05198,-0.06689,-0.01026,-0.01088,0.04936,-0.06223,0.05809,-0.0023,-0.11731,-0.01192,0.05295,0.0306,0.05625,0.09945,0.07406,0.06266,-0.0191,-0.00849,-0.11931,0.01215,0.0104,0.12166,0.01499,0.03029,-0.00291,0.06067,0.09376,-0.00746,0.0109,0.06084,0.04828,-0.03399,-0.02922,-0.02141,-0.08537,-0.08237,-0.06787,-0.03224,0.04689,-0.08816,-0.05522,0.03689,0.0135,-0.0215,-0.07141,0.04582,-0.10399,0.04809,-0.02888,0.12048,0.15225,0.01443,0.01102,0.11195,-0.03156,-0.00426,-0.10415,0.06681,-0.02227,-0.05859,0.05522,0.03456,0.10459,-0.02235,0.02291,0.0256,-0.13104,-0.00042,-0.01507,-0.06765,0.0229,-0.04245,0.04509,0.05596,-0.02939,0.01796,-0.02529,0.08517,0.05887,0.00344,-0.02062,0.10532,-0.05865,-0.16601]},{"domain":"mechanical_engineering","key":"fatigue_life_mean_stress_correction","name":"Fatigue 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(built-in) beam with a point load","package":"mechanical-engineering-ai999x","example":"Fixed-fixed beam with point load: L = 6 m, P = 30 kN, a = 2 m, E = 200 GPa, I = 5e-5 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(built-in) beam with a uniformly distributed load","package":"mechanical-engineering-ai999x","example":"Fixed-fixed beam with uniform load: L = 6 m, w = 12 kN/m, E = 200 GPa, I = 6e-5 m^4","v":[0.0324,-0.0489,0.16132,0.04174,0.08949,0.05596,0.05817,-0.03058,-0.01813,-0.01155,0.1075,0.0004,0.08191,0.05455,0.12633,0.04346,0.04554,-0.05203,0.058,0.08499,0.04845,0.01929,0.01331,0.03014,0.1161,-0.03801,-0.02111,0.06298,0.0123,-0.01493,0.06794,0.12423,0.03498,-0.03165,-0.05265,0.00146,0.01596,0.02093,0.0371,-0.04807,-0.03978,-0.04751,-0.08342,0.0339,-0.0557,0.06319,-0.08609,-0.0421,0.09663,0.03668,-0.06867,-0.02963,-0.06659,0.01428,0.01331,0.05414,-0.11248,-0.0201,-0.06896,-0.00364,0.01198,-0.0298,-0.03993,0.02562,-0.04427,0.03422,-0.01564,-0.00796,-0.02628,-0.09935,0.02999,0.11352,-0.05959,0.08245,-0.01134,0.08447,0.02223,-0.03211,0.07274,-0.01056,0.02291,-0.04767,0.02208,0.06088,0.06323,0.06678,0.10086,0.00032,-0.01444,-0.02542,-0.05764,0.00273,-0.04657,0.01803,-0.082,-0.01956,0.00966,-0.05369,-0.01944,-0.12665,-0.02965,0.00635,-0.04054,0.02214,0.07525,-0.06098,-0.02898,-0.06912,-0.09664,0.01933,-0.03673,0.05259,0.02146,0.02767,-0.00216,-0.03692,0.01775,-0.07976,-0.08034,-0.03969,-0.00239,-0.00125,-0.14992,-0.00521,0.04306,-0.04847,-0.0243,-0.01202,-0.04128,0.03182,0.11141,0.0911,0.00594,-0.06927,-0.05767,-0.08828,-0.037,-0.10835,0.0052,0.02972,0.01096,-0.02,0.13174,0.03932,-0.06684,0.16064,0.032,-0.07846,0.04198,0.05382,-0.01374,-0.02226,0.05203,-0.01754,0.0339,-0.0421,-0.02708,-0.05232,0.12617,-0.01806,0.01467,-0.04175,0.15009,0.0519,-0.00472,-0.09816,-0.05752,-0.02958,-0.02502,0.10743,0.03339,0.01241,0.04916,0.01081,-0.111,0.13281,0.01365,-0.09774,-0.00235,-0.05359,0.05889,-0.04365,-0.01034,-0.0199,-0.04749,-0.07442,0.05658,-0.02612,0.03747,-0.09997,-0.0639,0.13491,-0.11718,-0.03253,-0.0859,-0.00293,-0.13368,-0.00243,-0.0608,-0.03374,-0.00255,-0.0592,-0.02027,-0.03759,0.0504,-0.02966,-0.03793,0.0146,-0.11522,0.03381,0.04058,0.03663,-0.05173,0.04208,0.07134,0.1126,-0.04678,0.06831,0.03307,-0.02658,-0.01925,0.11099,0.11425,-0.03287,0.08607,-0.01148,-0.1041,0.05481,-0.03019,-0.07014,0.08631,-0.0777,-0.02118,-0.04772,0.10059,0.01635,-0.0822,0.00559,-0.03238,0.11056,-0.09693,0.13501,0.00348,0.0603,0.09361,-0.00329,0.16191,0.02028,-0.06962,-0.07191,0.01546,-0.09148,-0.01514,-0.00803,-0.03954,0.02935]},{"domain":"mechanical_engineering","key":"forced_vibration_amplitude","name":"Steady-state response to a harmonic force","package":"mechanical-engineering-ai999x","example":"Forced vibration: m = 10 kg, c = 40 N*s/m, k = 4000 N/m, F0 = 100 N, omega = 20 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linkage position analysis","package":"mechanical-engineering-ai999x","example":"Four-bar linkage: a = 2 m, b = 7 m, c = 9 m, d = 6 m, theta2 = 30 deg, branch = open","v":[-0.16343,-0.04089,0.00707,-0.0377,-0.1033,-0.01849,0.03106,0.00441,0.04129,0.0196,0.04104,0.07819,-0.00057,-0.00213,0.16011,-0.03035,0.00325,0.02792,0.0029,-0.02645,-0.08005,0.01325,0.05176,-0.06453,0.1103,0.00293,0.05301,0.05139,-0.03816,0.05571,-0.00336,0.01325,-0.18591,0.00377,-0.01398,0.01881,0.07582,0.01445,-0.07623,-0.10126,0.12765,-0.02978,0.06965,0.0451,0.00375,-0.16356,-0.02418,0.02512,0.01351,0.07653,-0.04027,0.01803,-0.10398,0.1234,-0.03114,0.04006,0.0133,0.12178,0.04201,-0.04343,-0.03888,0.04668,-0.17974,-0.0954,0.013,0.07797,0.04371,-0.0105,-0.09936,-0.10807,0.01247,0.01356,-0.01813,-0.0128,-0.00819,-0.05445,-0.01057,0.07471,0.09935,0.06719,-0.03478,-0.08091,0.0423,-0.06265,0.066,0.01684,0.01386,0.00587,0.03394,0.08541,0.00105,0.00414,0.00898,0.02098,0.03606,-0.02378,0.07001,-0.00804,-0.04046,0.03135,0.04587,-0.00139,-0.03356,0.01664,0.05998,0.01282,-0.17436,0.00998,-0.11997,0.00048,-0.01433,0.00653,0.14482,0.00033,-0.03131,-0.04143,0.06541,-0.08031,-0.03171,-0.08066,-0.07978,0.08565,-0.02546,0.06739,-0.03372,0.08911,0.09048,-0.01897,0.07075,-0.0039,0.00853,0.03156,-0.04106,-0.04249,0.04456,0.01632,0.03305,0.06998,0.07367,-0.05051,-0.14813,0.01806,0.04088,-0.06974,-0.03618,-0.01068,0.016,0.17389,-0.01347,-0.02701,-0.01169,0.00303,-0.09363,-0.03794,0.09154,-0.02678,0.07348,-0.01283,0.04082,-0.01211,0.0508,0.09889,-0.09042,0.09081,0.0483,0.0105,0.04319,-0.04998,-0.03587,0.00522,-0.06147,0.03173,0.05037,-0.04101,-0.03335,-0.19073,-0.01919,0.02755,-0.01918,-0.00938,-0.00975,-3e-05,0.02163,-0.00696,-0.01532,0.0945,0.1262,-0.04194,0.02454,-0.02585,-0.01143,-0.03381,0.07602,0.00977,-0.05797,0.0138,-0.03804,0.02353,0.03133,0.0168,0.06367,-0.02609,-0.10712,0.0036,-0.04599,0.0205,-0.03519,-0.00083,-0.02547,0.04403,0.00697,-0.04411,-0.10362,0.08575,0.11045,0.02072,-0.00971,0.14805,-0.03259,-0.06483,0.09132,-0.09361,-0.03702,0.05957,0.03671,-0.01484,0.04253,0.04804,0.00837,0.04595,-0.05763,0.06588,-0.03918,-0.05306,0.02093,-0.04558,-0.01938,-0.05666,0.01263,-0.10628,0.01146,0.05761,0.13567,-0.02136,-0.12056,0.05058,-0.07126,-0.02111,0.00101,-0.0262,-0.03831,0.0704,0.04774,-0.12128,-0.00688,-0.02096]},{"domain":"mechanical_engineering","key":"generalized_hookes_law","name":"Generalized Hooke's law: strains from a 3D stress state","package":"mechanical-engineering-ai999x","example":"Generalized Hooke's law: sx = 100 MPa, sy = 50 MPa, sz = 0 MPa, txy = 30 MPa, tyz = 0 MPa, tzx = 0 MPa, E = 200 GPa, nu = 0.3","v":[-0.05446,-0.04811,0.0151,-0.09465,-0.08885,-0.00977,-0.09599,0.01968,0.03928,0.00954,-0.05619,-0.07334,-0.0001,0.09108,-0.02553,0.08522,0.01182,0.04074,-0.06345,-0.07112,0.05755,0.04711,-0.09816,0.00405,-0.02042,-0.00992,-0.00567,0.04945,-0.0341,-0.06262,0.04233,-0.03914,0.0173,0.04848,0.00445,-0.05554,0.00569,-0.05134,0.02089,-0.05523,0.06568,0.04964,-0.14648,-0.03625,-0.1063,0.03168,-0.00314,0.04165,-0.03289,-0.07792,0.03699,-0.11016,-0.0255,0.05288,-0.08521,0.10418,-0.03983,-0.03313,-0.02569,0.04431,0.08387,0.00564,0.04718,0.09907,-0.01577,-0.08566,0.03101,-0.00033,-0.0256,-0.04441,0.01648,-0.14316,0.07156,0.03165,0.01752,0.01463,-0.03023,-0.02825,0.00995,-0.06304,0.04475,0.09721,-0.12315,0.00549,-0.04121,-0.00619,-0.11802,-0.03456,-0.07063,-0.02534,-0.01141,-0.03338,-0.08304,0.04332,0.00197,0.01135,-0.12554,-0.0881,0.10431,0.04609,0.00742,-0.00382,0.11277,0.0202,0.02363,0.0978,0.03614,-0.0812,-0.06605,-0.01772,-0.00563,0.02513,0.00715,0.07776,-0.08941,-0.1165,-0.00162,0.06128,0.00479,-0.10893,-0.07738,0.04368,-0.04579,-0.03379,0.11175,-0.05217,0.05178,0.06149,0.04767,-0.0087,0.03353,-0.08738,0.03495,0.0361,0.00938,0.07145,-0.09307,-0.05878,0.00948,0.01145,0.04872,0.01263,0.0007,-0.00327,0.11639,0.01693,-0.0515,0.09041,0.01266,0.05893,0.05182,-0.06423,-0.04235,0.00471,-0.10305,0.02135,-0.09896,0.02067,0.1285,-0.02957,-0.0334,-0.04019,-0.02773,0.03338,-0.04138,0.0363,-0.15755,-0.00594,-0.01078,0.05921,0.04507,-0.16218,-0.07771,-0.00282,0.05558,-0.01565,0.01866,0.01966,0.07947,-0.10015,0.02063,-0.01974,-0.05608,0.04532,0.06691,0.00189,0.07912,0.07672,0.02393,-0.03665,0.09703,0.00949,-0.05331,0.02355,0.03783,-0.03539,0.02,0.04606,-0.07656,0.1442,-0.00495,0.02493,0.0859,-0.05252,-0.01624,-0.0926,-0.06208,0.02003,-0.01015,-0.09287,0.10186,0.01121,0.05471,-0.0631,0.06224,-0.01732,-0.07103,-0.01645,-0.05263,-0.01375,0.02086,0.06711,0.03876,-0.00801,0.04433,0.08594,0.1577,-3e-05,-0.02081,0.07137,0.11449,-0.06001,0.00053,-0.02582,0.00264,0.02453,0.03118,0.08099,0.00019,0.14648,0.08304,0.04795,0.09145,-0.06217,0.07738,-0.00796,0.05179,0.01495,0.09147,0.09267,0.10386,-0.14037,-0.04162,-0.09799,-0.11152,0.0469]},{"domain":"mechanical_engineering","key":"gerber_fatigue_safety_factor","name":"Fatigue safety factor by the Gerber criterion","package":"mechanical-engineering-ai999x","example":"Gerber safety factor: sa = 120 MPa, sm = 80 MPa, Se = 250 MPa, Sut = 700 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90]","v":[-0.01675,-0.01559,0.02962,0.02409,0.00835,0.05379,-0.01543,-0.08782,0.02662,-0.06586,-0.00429,0.10035,-0.07951,-0.04345,0.07734,-0.12871,-0.14996,0.08887,0.01008,0.00418,-0.10846,-0.00537,0.02908,0.04562,0.00809,0.01072,-0.09015,0.11258,-0.08853,-0.00684,0.03875,-0.02702,0.01088,-0.00542,-0.00445,0.00969,-0.03726,0.01886,0.0139,0.09797,0.11421,0.06046,0.0823,-0.03024,0.00696,0.00879,0.0096,0.03915,0.01716,0.03333,-0.08535,0.00128,-0.0203,0.03269,0.02228,-0.03874,-0.10686,-0.05767,0.06763,-0.01806,0.03764,0.14533,-0.08897,-0.12191,0.05871,-0.05255,0.00114,-0.0289,-0.05611,-0.01607,0.031,-0.0005,-0.0042,-0.03843,-0.06367,0.02958,-0.03375,0.01079,-0.00032,0.00032,-0.06844,-0.02371,0.05948,-0.05214,0.0,0.09874,-0.07943,0.07558,-0.00572,-0.05024,-0.1251,-0.03746,0.04764,0.02541,-0.08939,-0.13503,-0.00114,0.07225,-0.01263,-0.05143,-0.00201,-0.04691,-0.01505,0.04968,0.10679,0.04521,-0.02231,-0.0226,-0.05517,0.00347,-0.02124,-0.02933,0.10226,-0.04567,-0.02517,0.05487,0.06324,-0.10813,0.0536,0.11177,-0.08526,0.09994,0.00388,-0.10199,0.03671,0.04312,0.11876,0.04598,0.09963,-0.03701,0.00623,-0.08101,-0.15659,-0.02051,-0.14782,-0.05219,-0.01154,0.00037,0.02701,-0.09246,-0.14538,-0.02915,-0.11288,-0.02357,0.11738,-0.00571,0.03687,0.06582,0.0474,-0.08659,-0.06994,0.12935,-0.05697,0.11598,0.01532,0.10615,-0.07291,0.00517,-0.03088,0.04996,0.04466,-0.06524,-0.11004,0.02668,-0.10482,0.01761,0.03544,-0.00249,-0.00802,0.03839,0.05934,-0.07593,-0.00924,0.08356,-0.01619,0.03325,0.07687,-0.02653,-0.01409,0.02443,-0.02578,-0.06067,0.01706,-0.07726,-0.01215,0.0071,0.05451,-0.03082,-0.0114,-0.06702,0.08709,0.00677,0.01175,0.05559,-0.00421,0.00244,-0.0826,0.11352,-0.07683,0.00242,0.03533,0.01715,0.04398,0.12067,-0.13704,0.08276,0.00114,0.12096,0.01526,0.08994,-0.0016,0.03436,-0.023,0.03132,-0.02466,-0.09903,0.05609,0.00038,-0.02298,0.01736,-0.0264,-0.00837,0.0418,0.0227,0.07396,0.08625,0.06047,0.03392,0.04324,0.16203,-0.04792,0.00044,0.02617,0.11104,-0.14164,-0.02386,0.04654,-0.01278,0.02128,-0.00752,-0.00833,-0.01588,-0.0544,0.0462,0.0375,0.05036,-0.01859,0.01348,-0.00316,-0.01029,-0.05635,0.08216,0.03055,-0.03224,-0.11797,0.03654]},{"domain":"mechanical_engineering","key":"rotating_disk_stresses","name":"Stresses in a rotating disk (solid or with a central hole)","package":"mechanical-engineering-ai999x","example":"Rotating disk: rho = 7800 kg/m^3, omega = 3000 rpm, nu = 0.3, ro = 250 mm, ri = 50 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loaded column (secant formula)","package":"mechanical-engineering-ai999x","example":"Secant column: P = 200 kN, e = 10 mm, L = 3 m, A = 4000 mm^2, I = 1.2e-5 m^4, c = 75 mm, E = 200 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fatigue safety factor (DE-Goodman)","package":"mechanical-engineering-ai999x","example":"Shaft fatigue safety factor: d = 40 mm, Ma = 150 N*m, Mm = 0 N*m, Ta = 0 N*m, Tm = 200 N*m, Kf = 1.6, Kfs = 1.4, Se = 200 MPa, Sut = 700 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of an undamped isolator for a target transmissibility","package":"mechanical-engineering-ai999x","example":"Vibration isolator design: m = 200 kg, omega = 1500 rpm, TR = 0.1","v":[0.0568,-0.05565,-0.05052,0.00979,-0.08723,0.03868,-0.03814,-0.0349,-0.01799,-0.01174,-0.03058,0.00791,0.02288,0.05176,-0.04724,0.00205,0.012,-0.04189,0.05913,0.01645,-0.10147,0.02868,-0.00293,0.04327,0.05433,-0.04241,-0.06858,-0.06134,0.07946,-0.1013,0.05177,0.02876,-0.07116,0.02204,-0.09712,0.12126,0.04364,0.10933,0.03846,0.05741,0.07945,-0.05448,-0.02778,0.05135,0.0101,0.06761,-0.06703,0.05305,0.07536,0.04392,-0.0478,-0.09717,-0.02242,-0.00605,0.04152,0.05494,-0.06657,-0.03262,0.07806,0.01433,0.0516,-0.02843,-0.09263,0.01197,0.00365,0.05472,-0.05874,0.07474,0.06842,-0.04722,0.10386,0.08848,-0.0072,0.06825,0.01922,-0.05087,-0.11335,0.0198,0.02415,0.0496,0.0974,0.03486,-0.01078,0.10081,-0.01968,-0.1809,-0.04546,-0.04681,-0.01666,0.01552,-0.04161,-0.02014,0.0767,0.02182,0.10202,-0.0231,-0.14778,-0.01492,0.08231,0.02032,0.04913,-0.04834,-0.01446,-0.00903,0.00553,0.06921,0.11769,-0.02257,-0.13663,0.08959,0.05677,0.05291,-0.05443,-0.04772,-0.03587,0.02177,0.02023,-0.01431,-0.00484,0.00296,-0.09009,0.07556,0.0624,-0.002,0.02108,0.05194,-0.03806,-0.09282,0.02596,-0.00284,0.00761,0.06509,-0.08092,0.0391,-0.06571,0.03875,0.00302,-0.02397,0.04869,0.1964,-0.0209,0.07307,-0.05825,-0.10804,-0.00742,-0.02579,0.08062,-0.06719,-0.0462,-0.02395,-0.00119,-0.0326,-0.04818,0.07326,-0.06465,0.08792,0.03609,0.02642,-0.01528,0.00946,0.07468,-0.00592,0.04988,0.01888,-0.04211,-0.00158,0.10314,-0.0224,-0.0337,0.09007,-0.01713,-0.03434,0.0318,0.07083,0.03765,-0.04022,0.00289,0.13814,-0.04472,-0.03505,-0.02413,-0.01233,0.04899,-0.07633,-0.01778,-0.01237,-0.05184,-0.04736,0.04346,0.05822,-0.10914,-0.10909,-0.10953,0.0035,-0.1174,0.01887,-0.07655,0.02646,-0.05238,0.08818,-0.01382,0.01549,-0.1319,-0.17266,-0.02816,-0.04975,0.07982,-0.0329,-0.13028,-0.01713,0.07001,-0.02947,0.0214,-0.02265,0.08323,-0.01655,-0.05464,-0.04967,0.04248,-0.11156,-0.0358,0.0514,-0.09831,0.06258,0.06983,0.06891,-0.01584,-0.05063,-0.09514,0.03492,0.11372,0.04294,-0.10005,-0.01653,-0.02401,0.03225,-0.02733,-0.04786,-0.14566,0.01702,-0.09829,-0.03006,0.01105,-0.04946,0.01036,0.15611,0.09377,0.02191,0.03597,-0.02868,-0.00991,0.00287,0.02039,-0.03314,0.00538,0.11841]},{"domain":"mechanical_engineering","key":"vibration_transmissibility","name":"Force (or base-motion) transmissibility of a vibration isolator","package":"mechanical-engineering-ai999x","example":"Transmissibility: zeta = 0, r = 2","v":[0.07345,-0.04616,-0.05422,0.10813,-0.09967,0.03133,-0.07849,-0.02519,-0.01703,0.0187,-0.04229,-0.01924,-0.01711,0.00896,-0.09229,-0.01451,-0.01755,-0.05887,0.05766,0.07802,-0.01998,-0.0224,0.05506,0.03441,0.02533,-0.05029,-0.08488,-0.0657,0.10072,0.0191,0.09441,0.03395,-0.04996,0.05361,-0.08165,0.11176,0.02237,0.09126,0.00807,0.05938,0.04897,-0.05757,-0.00554,0.01081,-0.05864,0.00193,-0.0084,-0.00493,0.03521,0.02597,-0.00057,-0.02949,0.02642,-0.01624,0.13625,0.07059,-0.00508,-0.03433,0.05148,-0.07801,0.09471,-0.12291,0.01317,0.01031,0.01605,-0.04484,0.03549,0.10158,0.0432,-0.00689,0.15513,0.08255,0.11603,-0.00292,-0.06819,-0.11034,-0.12825,0.01504,0.05713,-0.0087,0.05176,0.04453,-0.05179,0.01946,0.00778,-0.12614,-0.11685,-0.01367,0.0174,-0.02394,-0.03113,0.02692,0.09572,0.00312,0.12021,-0.03749,-0.05615,0.05274,0.11118,0.02249,0.01725,-0.0596,-0.01193,-0.04774,-0.04335,0.09387,0.05168,-0.05094,-0.13009,0.04892,0.01469,0.0352,-0.0491,-0.10348,-0.08228,0.04539,-0.04785,-0.08486,0.00662,-0.0282,-0.12787,-0.02361,0.08578,-0.02473,0.03386,0.05536,-0.04056,-0.03261,-0.00843,-0.00178,0.01274,0.01101,-0.06205,0.01722,-0.15054,0.01464,0.00328,0.02464,0.02734,0.0874,-0.02486,0.08499,-0.00308,-0.05231,-0.01011,-0.01142,0.06035,-0.02826,-0.05093,-0.00742,-0.0771,-0.00632,-0.12562,0.0225,-0.01148,0.04904,0.03522,0.0715,-0.03163,-0.01281,0.18057,-0.01495,0.0267,-0.0565,-0.00697,0.00898,0.09125,-0.05676,0.03137,-0.01904,-0.06402,-0.0357,0.07003,0.00985,0.10914,0.00726,0.06202,0.07295,-0.02373,0.07752,0.01509,0.00888,0.03555,-0.09102,-0.03719,-0.06222,-0.13732,0.04072,0.04748,0.03352,-0.03484,-0.15249,-0.03995,-0.04518,-0.04407,0.00815,-0.07047,-0.04304,-0.13213,0.16371,-0.02652,-0.05804,0.00422,-0.08582,-0.00641,-0.08952,-0.00997,-0.00908,-0.11887,-0.01554,-0.07263,-0.04409,-0.02518,0.03143,0.13218,0.00014,-0.01857,-0.01128,-0.03551,-0.07878,0.05231,0.00041,-0.05304,0.06378,0.09526,0.10309,0.01569,-0.01796,-0.03306,0.07758,0.13335,0.07952,-0.09558,0.03884,0.00618,0.00505,-0.0677,-0.02527,-0.01524,-0.00332,-0.06731,-0.02013,0.01386,-0.06333,0.04122,0.16867,0.05505,0.02071,0.07097,-0.02497,-0.00923,-0.03906,0.02473,-0.00435,0.0571,0.06788]},{"domain":"mechanical_engineering","key":"wahl_factor","name":"Wahl curvature factor of a helical spring","package":"mechanical-engineering-ai999x","example":"Wahl factor: d = 3 mm, D = 24 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Mises and Tresca equivalent stresses and safety factors","package":"mechanical-engineering-ai999x","example":"Yield safety factor: Sy = 350 MPa, sx = 120 MPa, sy = -40 MPa, txy = 60 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number of collisions to slow a neutron down","package":"nuclear-engineering-ai999x","example":"Collisions to thermalize: A = 12.0, E0 = 2 MeV, Ef = 0.025 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effective dose from a dose coefficient","package":"nuclear-engineering-ai999x","example":"Committed dose from a dose coefficient: I = 1 MBq, e = 2.2e-8 Sv/Bq","v":[0.02275,0.0978,-0.07218,0.01097,0.01834,0.02889,-0.10807,0.0009,0.01429,-0.04057,-0.01467,-0.01509,-0.04486,-0.07672,-0.03793,-0.0436,0.0592,0.05284,0.02685,0.03158,-0.02492,-0.02407,-0.061,0.08627,-0.00397,0.05842,-0.01636,-0.02477,0.07681,-0.01468,0.02688,0.01654,0.06537,-0.07103,0.0311,0.0113,0.05876,0.04457,0.01247,0.05248,-0.03354,-0.07351,-0.09595,-0.0231,0.04625,-0.00783,-0.12993,0.021,-0.07612,-0.08522,0.04609,0.1198,0.08652,-0.01278,0.02772,0.023,-0.01564,0.11873,-0.08,0.13057,0.00123,0.01207,-0.08691,-0.08717,-0.06609,0.05104,0.05921,-0.01135,-0.02894,0.01198,0.03999,-0.02997,0.03657,-0.02129,0.0187,0.06244,0.10454,-0.07924,0.01896,-0.00767,-0.07653,-0.04462,0.04778,-0.06839,-0.11262,-0.05888,-0.00296,-0.01584,-0.05125,-0.09428,-0.00941,-0.02361,0.05326,0.02674,0.0208,-0.03189,-0.06679,-0.10821,0.13832,-0.10567,0.00351,-0.16886,0.02288,0.07673,0.10007,-0.08312,0.02868,-0.08551,0.09763,-0.01899,0.0183,0.02425,0.03393,0.0264,0.07026,-0.06769,-0.08279,-0.12771,-0.01105,-0.02679,-0.05885,-0.04129,0.03271,-0.00938,-0.04177,-0.12349,-0.05961,0.058,-0.03683,-0.02959,-0.03171,0.1004,-0.00212,-0.00963,-0.00573,0.032,-0.01261,0.00213,-0.06314,-0.02025,-0.01101,-0.0542,-0.03862,0.02646,-0.00674,-0.02449,0.11083,0.0848,-0.08153,0.00928,0.01,0.10779,0.08972,0.00523,0.0506,-0.04813,-0.03556,-0.04327,0.02535,0.13029,0.0599,-0.02973,-0.04567,0.17771,0.13466,0.00951,-0.00044,-0.04378,-0.06656,-0.02489,-0.05149,-0.04772,-0.01819,-0.01447,-0.04299,-0.0185,0.05062,0.07268,0.07167,0.06988,0.00604,0.09253,-0.05652,0.00264,-0.01458,0.08667,-0.03358,-0.04576,0.10017,0.03314,0.00996,0.00444,0.0056,0.04432,-0.14191,0.06264,-0.00324,0.11003,0.14389,0.04672,-0.0221,0.06624,0.11287,0.0006,-0.06737,-0.10035,-0.15144,-0.02811,0.02965,-0.07323,-0.0056,-0.02567,0.02309,0.07224,-0.02179,0.00172,-0.00131,-0.12054,-0.03427,0.03724,-0.06356,0.00167,-0.00687,0.04057,0.02484,0.02043,0.09788,0.07535,-0.01089,0.1196,0.01858,0.09421,0.01293,-0.09387,-0.04927,-0.06126,0.03824,-0.04729,0.0125,0.01149,0.01739,-0.03248,0.10927,-0.04304,-0.03511,0.02493,0.00216,-0.06211,0.114,0.13201,0.03893,0.00803,-0.08402,0.05978,-0.1013,-0.07746]},{"domain":"nuclear_engineering","key":"nuc_committed_dose_retention","name":"Committed equivalent dose to an organ from an intake (retention compartments)","package":"nuclear-engineering-ai999x","example":"Committed dose: I = 1 MBq, f = [0.3], Tb = [80.0], t_unit = d, T_p = 8.0207 d, E = 0.18 MeV, w_R = 1.0, m = 20 g, tau = 50 y","v":[-0.04178,0.06588,-0.11592,0.03197,0.04246,0.08703,-0.09237,0.00882,-0.02263,0.07039,0.03207,0.05769,-0.06478,-0.10341,-0.06681,-0.04537,0.02205,0.01073,0.04899,0.04598,-0.08925,-0.02263,-0.14696,0.16869,-0.04285,0.0791,-0.07952,-0.05047,-0.03624,0.02792,0.0141,-0.03809,0.0435,-0.0721,0.09195,-0.00034,-0.03924,0.03062,-0.00684,0.16554,0.03717,0.01972,-0.02244,-0.06225,-0.01757,0.04035,-0.0982,0.0471,-0.08467,-0.04804,-0.04428,0.12721,0.06869,-0.02033,0.06794,-0.04733,-0.07234,0.0281,-0.04787,0.16978,-0.00435,0.00323,0.03437,-0.04494,-0.04448,0.07309,-0.06186,-0.01601,0.01005,-0.01833,-0.02731,0.04383,-0.00188,-0.06426,-0.02548,0.03004,0.04215,-0.03292,0.05382,0.06651,0.03779,-0.04802,-0.0331,-0.02698,-0.05526,-0.09863,-0.04857,0.01583,0.02315,-0.09617,-0.00249,0.05546,-0.01931,-0.01071,-0.00731,-0.01837,0.01223,-0.11005,0.0849,-0.00722,0.02486,-0.09842,0.01078,0.03139,0.07902,-0.08439,0.02401,-0.07109,-0.02829,0.01056,-0.05457,0.02888,0.00449,0.03073,-0.00524,-0.03133,-0.0068,-0.06243,0.09961,0.07323,-0.13924,0.01141,-0.0181,0.04055,-0.04776,-0.03124,-0.10307,-0.02759,-0.09362,0.00212,-0.01085,0.16183,-0.00692,-0.11278,0.10037,0.03856,-0.0908,-0.08859,-0.00939,0.03474,0.08133,-0.09163,-0.03657,-0.01702,-0.07949,0.05085,0.03505,0.11101,-0.02519,0.01569,0.03711,0.01584,0.06727,-0.09675,0.04073,-0.07461,-0.05392,0.02965,-0.01259,0.09348,0.09529,0.08571,0.00476,0.14447,0.13331,0.03159,0.01132,0.00758,0.03852,-0.0142,0.01839,-0.0174,-0.08598,-0.01994,-0.08832,0.09596,0.09807,0.10384,0.03077,-0.01649,0.00743,0.06209,0.00084,-0.02371,0.06893,0.10621,0.08974,0.10601,0.02294,-0.03931,0.04948,-0.02611,-0.00855,0.05393,-0.02521,0.04953,-0.07091,0.01674,0.04372,0.07881,-0.03568,-0.08833,0.10121,0.09033,-0.01586,-0.02605,-0.08797,-0.01173,-0.02451,-0.06247,0.00307,-0.03087,0.05837,0.02553,-0.00154,0.02699,0.10768,-0.06267,-0.06683,0.04891,0.01609,-0.00474,-0.06406,0.02757,0.0675,0.02642,0.05966,0.07305,-0.04565,0.02531,0.02443,0.0349,-0.05875,0.00858,0.05678,-0.1549,0.05951,-0.04159,-0.01184,0.0002,0.0026,-0.01889,0.17012,-0.06485,-0.04649,-0.02721,-0.04488,-0.0681,0.02673,0.06947,0.07108,-0.02527,0.02826,-0.0019,-0.11846,-0.06076]},{"domain":"nuclear_engineering","key":"nuc_compton_edge","name":"Compton edge and backscatter peak of a gamma line","package":"nuclear-engineering-ai999x","example":"Compton edge: E = 662 keV","v":[0.05585,0.02652,0.10153,0.1426,0.00432,0.10699,-0.02902,0.00152,-0.03655,0.05368,-0.02809,0.1092,-0.05939,0.02398,0.01388,0.1559,0.03308,0.01075,-0.06152,-0.02917,0.02853,0.02146,-0.02515,0.02331,0.06669,0.07656,-0.07122,-0.00677,-0.03083,0.01907,0.02672,-0.01791,0.02851,-0.00035,0.02434,0.00176,-0.04312,0.03432,-0.10881,0.01586,-0.12281,0.00609,0.11941,0.02917,0.02924,0.0613,-0.05073,-0.09799,-0.0469,0.04813,0.07629,-0.00501,0.04672,-0.00374,-0.05184,0.0565,-0.01625,0.08218,0.01355,0.11224,-0.01772,0.05471,0.09216,0.06261,-0.05096,-0.01929,-0.10643,-0.01877,-0.01574,-0.06582,-0.0164,-0.01524,0.06993,-0.12313,0.00504,-0.01926,0.02868,0.03336,0.0609,0.14228,0.10218,0.07743,0.01024,0.03289,-0.04841,-0.0572,-0.09566,-0.02349,0.09974,-0.02989,0.16141,0.10598,0.06033,0.04384,-0.02613,-0.07373,0.00252,-0.10012,0.05103,0.10837,0.03306,0.04419,-0.13708,-0.03004,-0.01575,-0.05983,-0.10799,0.01785,-0.16167,-0.08796,-0.05282,0.0937,0.0322,0.01088,0.00254,-0.0297,-0.04344,-0.15377,0.01423,-0.05644,0.05097,0.08688,-0.04941,-0.048,-0.17681,-0.05664,0.00149,0.04889,0.08537,0.05889,-0.08802,0.04782,-0.04899,-0.05217,0.04536,-0.02119,-0.07027,-0.0633,0.05023,0.00837,-0.01041,-0.00038,0.06452,0.04615,0.03478,-0.0439,-0.01069,-0.10725,-0.08897,0.06821,-0.02531,0.10455,0.08859,-0.0019,-0.04244,0.04381,-0.04686,-0.00808,-0.02702,0.01037,-0.02507,0.11447,-0.03104,0.07351,-0.09858,0.04169,0.06604,0.07356,-0.03775,0.0273,-0.03125,-0.00815,-0.0316,-0.00638,0.01801,-0.03322,0.02506,0.12184,0.0209,-0.08843,-0.06961,-0.06953,0.06872,0.05918,-0.09328,-0.0031,0.00045,-0.00308,0.04912,0.06926,-0.09254,-0.01994,-0.05148,-0.01437,-0.00832,-0.02267,-0.06967,-0.06573,0.01268,-0.04267,0.05442,-0.02366,0.09433,0.0168,-0.03071,-0.05498,-0.03668,0.08373,0.01728,-0.00359,-0.04531,-0.02627,-0.05301,-0.0098,-0.07631,-0.02776,0.01041,0.07724,0.02145,0.00922,0.0213,-0.08802,-0.10813,-0.01098,-0.00608,0.07852,0.05018,0.09077,0.02175,0.07681,-0.00431,0.08076,0.00906,0.02199,0.01978,-0.12299,-0.08473,0.08959,0.0068,-0.12018,-0.00322,0.04731,-0.02275,0.03174,-0.08127,-0.05415,0.02025,0.06465,0.03694,-0.0137,-0.08483,-0.0845,-0.0107,0.07403,-0.07626,-0.03303]},{"domain":"nuclear_engineering","key":"nuc_constant_power_depletion","name":"U-235 depletion at constant power","package":"nuclear-engineering-ai999x","example":"Depletion at constant power: m0 = 100 kg, P = 30 MW, t = 1 y, E_f = 200 MeV, sigma_a = 680.9 b, sigma_f = 582.6 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and differential control-rod worth (sine-squared weighting)","package":"nuclear-engineering-ai999x","example":"Control rod worth: rho_tot = 1000 pcm, H = 3.66 m, x = 1.83 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power from the peak flux (or peak flux from power) of a bare core","package":"nuclear-engineering-ai999x","example":"Core power from flux: geometry = cylinder, Sigma_f = 0.002 1/cm, E_f = 200 MeV, phi_max = 1e13 1/(cm^2*s), R = 170 cm, H = 370 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count rate from a point source on a detector's axis","package":"nuclear-engineering-ai999x","example":"Count rate from a point source: A = 1 uCi, y = 85.1%, d = 10 cm, a = 2.54 cm, eps_int = 60%","v":[0.05781,-0.0769,-0.02437,-0.01443,0.15448,-0.00481,-0.02021,0.03904,-0.00583,0.04171,0.03506,-0.00847,-0.06775,-0.00868,-0.05194,0.13562,0.04355,0.01559,-0.00939,0.04633,-0.01178,0.01035,0.00764,0.04304,-0.09389,0.08072,-0.05188,0.02678,0.10242,0.04275,0.05268,-0.00575,0.05178,-0.11961,-0.0125,0.06917,-0.01273,-0.03597,-0.09222,0.0032,0.0394,0.04461,0.05712,-0.00941,-0.07523,0.04164,-0.01569,0.03812,0.01979,0.04956,0.08738,0.06972,0.12305,-0.02247,-0.16497,0.04216,-0.08025,-0.04984,-0.05906,0.07374,0.00466,-0.01585,-0.02384,-0.02959,-0.07585,0.04908,-0.0809,0.0236,-0.06092,-0.04157,-0.02618,-0.04585,0.06467,0.11141,0.11826,0.07476,0.11694,0.01845,-0.16992,-0.1257,0.04499,0.01489,0.02946,0.06983,-0.07767,-0.08057,0.00539,-0.00222,-0.02192,-0.0441,0.02279,-0.01044,0.04873,-0.01101,-0.08294,0.13597,-0.03945,0.00358,0.10934,0.01097,0.00388,-0.0519,-0.03269,-0.06712,0.09951,-0.03345,0.02766,-0.03818,0.00919,0.05751,-0.03417,-0.02416,0.00839,0.05398,-0.04493,-0.02678,-0.04662,-0.03697,-0.00155,-0.01261,0.0337,0.00248,0.01235,-0.00542,0.00029,-0.07141,-0.11376,0.02827,-0.07274,-0.14404,-0.00491,0.01673,0.05956,-0.022,0.03742,0.08979,0.0255,0.0303,-0.08175,0.06351,0.05743,0.04701,-0.10419,-0.10329,-0.00811,0.03732,-0.02088,0.03315,0.04786,-0.01819,-0.08015,-0.01982,0.06856,-0.03743,0.13483,0.15355,-0.0174,0.06924,0.0278,0.01097,-0.05261,-0.13658,-0.06128,0.0341,0.14578,-0.12586,-0.03888,0.03036,0.01458,0.00014,0.00853,-0.01807,-0.04614,-0.00437,-0.00416,0.03921,-0.09721,0.04666,0.0126,0.01756,-0.03083,0.00636,0.12958,0.00067,-0.12016,0.0925,0.00034,0.0222,0.01998,-0.00193,0.02519,-0.04674,-0.01915,0.05325,0.06931,0.04908,0.00253,-0.01921,0.02026,-0.04219,-0.06466,-0.06552,0.1231,0.10563,-0.019,-0.09986,-0.15551,0.04573,-0.00643,0.06677,-0.06778,-0.00485,0.00757,-0.02554,-0.01869,-0.06404,0.03263,-0.00292,-0.02477,-0.02803,-0.02833,0.06407,0.03116,0.13935,-0.01026,-0.10468,0.05504,0.02005,0.00669,-0.02575,0.03621,0.08495,-0.0312,0.02204,-0.1369,-0.02919,0.07375,-0.03274,-0.06977,0.04267,0.05379,-0.00834,0.10116,-0.01277,-0.0003,-0.04309,-0.01482,-0.00435,0.11331,0.02762,0.0314,-0.15298,0.01252,-0.05112,-0.10497,-0.06257]},{"domain":"nuclear_engineering","key":"nuc_count_time_for_precision","name":"Counting time for a target precision of the net count rate","package":"nuclear-engineering-ai999x","example":"Counting time for precision: Rg = 100 cps, Rb = 25 cps, r = 1%","v":[0.06145,0.05342,-0.04818,0.10019,0.01133,0.07405,-0.01518,-0.00548,0.08586,0.07775,0.10578,0.11806,-0.06188,-0.0423,-0.04846,0.07034,0.07568,-0.00403,-0.01966,-0.01553,-0.02001,-0.12958,0.09178,-0.11043,-0.04154,0.12476,-0.04254,-0.04361,0.02313,-0.00072,-0.02855,-0.06435,-0.01615,-0.0652,0.02073,0.01243,-0.01618,0.02987,-0.03804,-0.03987,0.02042,0.02103,-0.07554,0.02194,-0.00853,0.07002,0.01991,0.03048,0.02339,0.00297,-0.08122,0.05322,0.1077,0.09391,-0.00124,-0.02282,-0.04499,0.01983,0.10232,0.02176,-0.01883,0.1715,0.08585,-0.01698,0.03255,-0.00905,-0.03698,0.01013,-0.06541,0.0151,-0.03883,-0.0962,0.06184,0.01582,0.01792,-0.01746,-0.0006,0.00305,-0.03683,0.09556,0.01608,-0.09128,-0.07983,0.1022,-0.00848,0.05622,0.01216,0.02963,-0.05826,-0.04209,-0.01079,0.01249,0.00013,-0.01743,-0.07178,0.00792,-0.04682,-0.03991,-0.11143,-0.0064,0.01504,-0.13322,0.00887,-0.01903,0.01397,-0.06001,-0.08045,-0.07356,0.01688,0.04709,-0.05479,-0.10308,-0.03081,0.0085,-0.10105,-0.07741,0.00958,0.02913,0.05964,0.11976,0.0317,0.06944,0.07174,0.04861,0.01642,-0.04219,-0.02537,0.0721,0.00517,-0.02767,0.01103,0.0349,-0.16778,0.05374,-0.12246,-0.03559,-0.02664,-0.0423,-0.00813,0.05625,-0.1127,0.05783,-0.05293,-0.05255,-0.1071,-0.02526,-0.05004,-0.0182,0.10917,0.03867,-0.04347,0.00154,0.04884,0.10203,0.03468,0.06139,0.00575,0.05782,0.00225,-0.07425,0.00273,0.0004,-0.03408,0.13199,-0.09362,-0.03396,-0.00213,0.0716,0.08959,-0.03288,0.06052,-0.07857,-0.00277,-0.04963,0.04566,0.03985,-0.09659,0.09144,-0.05021,0.02335,-0.04907,-0.03343,0.10379,-0.08485,-0.03108,0.1629,0.01698,0.03868,-0.04121,0.05291,-0.03672,0.06453,0.06403,0.03865,0.10089,-0.00239,0.02504,-0.03937,-0.00881,0.05465,0.11099,0.06824,0.04668,0.08929,-0.08888,0.02702,-0.08977,-0.10724,-0.04026,-0.00288,0.02589,-0.03799,-0.07759,-0.05716,0.04699,-0.09583,-0.10393,-0.11743,0.03365,-0.03933,0.08323,0.01921,-0.06483,0.00475,-0.06664,-0.05311,0.09405,-0.06785,-0.05973,0.05143,-0.02568,0.03962,0.02619,-0.04037,-0.05604,-0.03918,0.08152,0.00091,-0.07542,-0.03415,0.11434,-0.01535,-0.00625,0.07987,-0.04009,0.02577,0.02245,-0.01947,0.02084,0.1144,0.01546,-0.07276,0.02414,-0.14227,-0.14995,0.0529]},{"domain":"nuclear_engineering","key":"nuc_count_time_split","name":"Optimal division of counting time between sample and background","package":"nuclear-engineering-ai999x","example":"Counting time split: T = 1 h, Rg = 100 cps, Rb = 25 cps","v":[0.03525,0.1216,0.00231,0.17005,-0.0451,-0.03934,0.06759,-0.04491,0.0841,0.05981,0.04507,0.06485,-0.03322,-0.12406,-0.00801,0.04096,0.03338,0.00688,-0.10491,0.02207,-0.05435,-0.08294,0.06221,-0.12771,0.05821,0.11199,-0.0431,-0.0012,0.06035,0.07022,-0.06204,-0.03814,0.00291,-0.01721,0.03581,-0.04831,-0.05298,-0.02684,-0.00366,-0.07213,-0.01947,0.01808,-0.05329,0.0088,0.05607,0.00676,-0.02923,0.06786,0.0221,0.03604,-0.06023,0.04009,0.06087,-0.04022,-0.02052,0.03544,-0.01363,-0.00252,0.0969,0.05325,0.019,0.17308,0.02438,0.05818,-0.02843,0.01016,-0.06158,0.04834,-0.10334,-0.01986,-0.05671,-0.11258,0.07332,0.0584,0.02599,0.04701,-0.06594,0.14859,-0.07099,0.07916,0.12298,-0.09471,-0.05951,0.10227,-0.00488,0.07172,-0.07757,-0.00379,0.00963,0.02192,-0.02679,-0.01141,0.00782,-0.0594,-0.04571,0.02375,-0.06193,0.00378,-0.04233,-0.01512,-0.01589,-0.0872,-0.00071,-0.0108,-0.01433,-0.06072,-0.05442,-0.08749,0.03402,0.0294,-0.07287,-0.09635,0.00486,0.0025,-0.12439,-0.06228,-0.04832,-0.02094,0.03472,0.14652,0.04961,0.12505,0.05371,0.02557,0.00127,-0.0584,-0.03488,0.06989,0.06113,0.02275,0.03856,0.05018,-0.06643,0.06735,-0.03206,-0.03813,-0.01944,-0.04706,-0.03634,0.09124,-0.10621,0.0303,-0.06274,-0.08422,-0.1073,-0.02245,-0.08102,-0.00056,0.05135,0.04012,-0.04698,-0.08052,0.00797,0.02421,0.01726,-0.02916,0.02821,0.02451,0.01856,0.00625,0.0264,0.13378,0.01127,0.12348,-0.14394,-0.05187,0.00045,0.0253,0.03461,0.00558,0.08813,-0.03857,0.03733,0.07256,-0.04437,0.02799,-0.13121,0.03893,-0.07034,0.02668,-0.0627,-0.03222,0.02962,-0.09685,-0.05928,0.04257,0.03518,0.06266,0.01837,0.08343,-0.11486,0.04041,0.0129,0.03326,0.10835,0.00396,0.0463,-0.02887,0.04443,0.06237,0.07605,0.03936,-0.06641,-0.03871,-0.01924,0.00586,-0.08169,-0.11042,-0.07866,-0.07496,-0.0343,-0.01988,-0.04235,-0.06948,0.11197,-0.033,-0.0536,-0.02907,0.10168,-0.01161,-0.03546,0.07712,-0.05842,-0.03352,-0.05706,-0.01302,0.08971,-0.04468,-0.12455,0.06035,0.01731,0.01079,0.01579,-0.02514,-0.00651,0.03743,0.05278,-0.05654,-0.08251,0.01371,0.06208,-0.03345,0.05113,0.0872,0.0725,0.05551,0.04505,-0.012,-0.02673,0.02117,0.05528,-0.07778,-0.01775,-0.1621,-0.12952,0.08012]},{"domain":"nuclear_engineering","key":"nuc_counts_during_decay","name":"Counts recorded from a decaying source (decay during counting)","package":"nuclear-engineering-ai999x","example":"Counts during decay: A0 = 100 kBq, T_half = 6586.2 s, tc = 1 h, eff = 20%, y = 96.7%","v":[0.06753,0.05225,-0.0808,0.04494,0.16887,-0.01001,-0.03868,0.06131,0.02999,0.08406,0.10306,0.06012,-0.13882,-0.0524,-0.08267,0.03644,-0.0148,-0.03744,0.03585,0.11089,-0.04691,0.03174,0.02953,0.02431,-0.00381,0.06115,-0.00772,-0.02646,0.11482,0.04619,-0.00116,0.09287,0.04822,-0.11569,-0.01824,0.03354,-0.00555,-0.05163,-0.04719,0.03643,-0.03605,0.05927,0.08675,-0.03055,-0.07201,0.00123,-0.0253,0.10327,-0.05734,-0.01867,-0.02737,0.02262,0.10352,-0.10064,0.00058,0.04917,-0.08829,-0.0196,-0.05044,0.01194,0.00701,0.08886,0.00423,-0.03835,-0.06971,0.02793,-0.02954,0.02412,-0.01643,-0.03523,-0.09379,-0.09947,0.05902,0.10656,0.08242,0.00862,0.00726,0.10985,-0.13103,-0.03508,0.06844,-0.049,0.01718,0.11045,0.00182,-0.09704,0.06302,-0.01538,0.01776,-0.04167,-0.01258,-0.06273,0.06765,-0.03622,-0.10195,0.11737,-0.02516,-0.05867,0.05417,0.03946,-0.01815,-0.11281,-0.09887,0.03093,0.09333,0.01818,-0.0673,-0.03615,-0.0187,-0.02352,0.0075,-0.01029,0.03802,-0.07644,-0.12083,0.04493,0.01663,-0.02647,0.01495,0.03714,-0.01657,-0.03895,0.02222,0.02056,-0.03546,0.03601,-0.10362,0.03551,-0.08164,-0.01668,0.08999,-0.0364,0.09533,-0.00525,-0.02806,0.04176,0.03171,-0.02835,-0.04895,0.05204,0.03599,0.02243,0.0208,-0.05067,-0.14423,0.08945,-0.03806,0.15553,0.01551,-0.0268,-0.06917,-0.12137,0.10482,-0.05438,0.15307,0.03535,0.01616,0.01827,-0.04074,0.03916,-0.0199,-0.0038,-0.0483,-0.01776,0.058,-0.16143,0.00874,0.021,-0.01693,0.05298,0.0477,0.04721,-0.00284,0.04289,-0.0534,0.07608,-0.13248,0.01757,0.02223,0.02871,-0.01124,0.02081,0.09007,-0.00042,-0.04964,0.02819,0.03693,0.01637,0.04809,0.08563,0.05598,-0.06024,-0.04708,-0.05928,0.07913,0.12866,0.02973,0.00282,-0.01593,0.0058,0.00992,0.04605,0.08652,0.05937,0.02241,-0.01714,-0.04647,0.01411,0.00277,-0.00199,-0.0854,-0.05289,0.04464,-0.00691,0.05078,-0.06718,-0.0134,0.02973,-0.1161,0.06284,-0.05427,0.08631,0.05169,-0.00376,-0.09022,-0.0987,0.17033,0.00962,-0.05802,-0.08122,0.03402,0.075,-0.00562,0.05287,-0.08993,-0.11862,0.0562,-0.03749,-0.04195,-0.04134,0.06747,0.03151,0.01692,0.01554,0.01643,-0.07525,-0.04646,-0.0328,0.00527,0.03415,-0.0341,-0.07136,-0.06247,-0.02221,-0.12843,-0.1115]},{"domain":"nuclear_engineering","key":"nuc_critical_cuboid","name":"Critical third side of a bare rectangular reactor (one group)","package":"nuclear-engineering-ai999x","example":"Critical cuboid: D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = 2.13D, a = 60 cm, b = 60 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radius of a bare cylindrical reactor of given height (one group)","package":"nuclear-engineering-ai999x","example":"Critical cylinder: D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = 2.13D, H = 50 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critical bare cylinder (one group)","package":"nuclear-engineering-ai999x","example":"Minimum volume critical cylinder: D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = none","v":[-0.03746,0.03035,-0.05074,0.04228,0.01689,0.05391,-0.07579,0.06994,0.06909,-0.03435,0.00188,-0.05964,0.05402,-0.04208,-0.06529,0.03759,0.1124,0.10924,0.04527,0.01452,-0.03402,-0.00911,-0.10238,-0.05591,0.14619,-0.02222,-0.07571,-0.00332,0.0309,0.0195,-0.05853,0.01977,0.04166,0.00624,-0.00162,-0.04092,0.08917,-0.0483,0.01796,0.08659,0.02844,-0.0627,-0.03329,0.00763,0.01166,-0.07958,0.02026,-0.10802,-0.05761,-0.15771,0.11063,-0.10975,0.06103,0.086,-0.11779,-0.01509,0.09188,-0.00264,-0.0764,-0.01249,-0.04731,0.08046,-0.04294,0.08983,-0.02188,0.0592,-0.01318,0.0131,-0.08584,0.0654,-0.00895,0.05886,-0.04659,-0.00177,0.00455,0.00957,-0.09661,-0.0646,-0.02408,0.08517,0.12352,-0.01446,-0.09164,0.02621,0.01116,0.07916,-0.06196,-0.02385,-0.00538,0.01929,-0.03599,0.05265,0.0689,0.03709,0.04816,0.10277,-0.13934,-0.06622,0.05625,0.05334,-0.11393,0.00706,-0.02963,-0.06291,-0.02077,0.02315,0.00905,-0.04186,0.05004,0.03144,-0.02464,-0.04515,0.02414,0.02261,-0.12608,-0.11254,-0.02722,-0.07075,-0.04746,-0.04204,0.0755,-0.06094,-0.0196,-0.00465,0.00214,0.02684,0.02987,-0.00519,0.02414,-0.06729,-0.11831,-0.09591,0.00477,0.00784,0.02137,0.01542,-0.0226,0.05809,0.02382,0.1082,0.03143,-0.02875,0.06721,0.02848,-0.00407,0.02731,0.1191,0.00066,0.02076,0.0724,-0.01034,-0.01519,0.03889,0.06502,0.11198,-0.01232,0.04609,0.04777,0.01474,0.03191,0.01889,0.15758,0.07172,-0.03471,-0.01469,-0.00326,-0.06228,-0.00914,-0.02208,0.00206,-0.01435,0.04344,-0.04325,0.024,-0.03079,-0.13485,0.03086,-0.02099,0.1465,-0.0359,-0.1707,-0.0682,0.04051,0.01857,-0.05307,-0.01414,0.02986,0.06353,0.03477,0.03558,-0.08644,-0.06922,0.04277,-0.01068,-0.0526,-0.05181,-0.01384,-0.05096,0.00901,-0.01119,-0.0084,0.04186,-0.03565,-0.06737,-0.06889,-0.11052,0.08189,-0.0412,0.02039,-0.04169,-0.14655,-0.08456,0.12181,-0.04317,-0.09687,-0.04873,0.08059,-0.09001,0.10768,0.06228,-0.15601,-0.01245,-0.06752,-0.04025,0.01105,0.09327,-0.01068,0.06328,-0.02103,0.00085,0.01098,0.17574,0.00403,-0.09129,-0.0421,0.08552,0.03901,0.0865,-0.03215,-0.01914,0.03319,0.07742,0.07352,-0.02777,0.06494,-0.00837,-0.01366,-0.043,-0.03227,-0.04332,0.04526,0.0481,0.09697,0.02884,0.07924,0.00565]},{"domain":"nuclear_engineering","key":"nuc_critical_slab","name":"Critical thickness of a bare slab reactor (one group)","package":"nuclear-engineering-ai999x","example":"Critical slab: D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = 2.13D","v":[-0.01141,0.00368,-0.00894,0.08578,0.10497,0.07959,-0.03246,0.00291,0.00761,-0.03098,-0.01073,0.05809,0.10215,-0.04019,0.00068,-0.06059,0.00683,0.0351,0.1182,0.0984,-0.08949,-0.03679,-0.01862,0.02429,0.06616,-0.07259,-0.02654,-0.013,0.09885,-0.01497,-0.05424,0.08155,-0.03312,-0.01042,-0.08061,0.00903,0.0388,-0.03153,-0.08231,-0.04965,-0.0644,-0.10452,-0.01417,0.04486,-0.01939,-0.06364,-0.06164,-0.06742,-0.02725,-0.05261,0.08251,-0.06986,0.0324,0.05788,0.00399,-0.08998,0.03262,0.05372,0.02402,-0.02499,-0.09583,0.01917,-0.07461,-0.11529,0.03029,0.11685,-0.02835,0.03505,-0.0077,-0.05654,0.04315,-0.01637,0.00747,0.0504,0.0899,-0.01102,-0.0274,-0.1084,-0.09933,0.0657,0.19194,-0.06568,-0.07246,0.08452,-0.0536,0.05507,-0.07779,-0.05602,-0.03984,0.09026,-0.15919,0.03494,0.03749,0.05553,0.03428,-0.00795,-0.0877,-0.0019,0.02824,-0.07635,-0.06729,0.10877,-0.10711,-0.03601,0.04321,0.06621,0.12262,-0.02167,0.02849,0.04972,-0.00499,0.00687,-0.00679,-0.01958,-0.07631,-0.1132,-0.01526,-0.11628,0.01671,0.01343,0.03837,0.01609,-0.02754,0.03468,0.07371,0.08576,0.05295,0.03055,-0.0404,0.03334,-0.05841,0.03042,-0.00957,0.04656,-0.01995,0.02645,0.0418,0.01125,-0.04837,0.06264,-0.05707,-0.08885,0.07484,0.0403,-0.01289,-0.04735,0.13916,0.00793,0.00366,0.09069,-0.01352,-0.03299,-0.02743,0.13036,0.01379,-0.06249,0.03789,0.02591,-0.01388,-0.01744,-0.00932,0.06904,0.08746,-0.05851,0.04788,-0.06417,-0.03659,-0.06085,-0.05543,0.03167,0.11608,0.00336,-0.04006,0.0733,0.02298,-0.23097,-0.01813,-0.12827,0.07604,-0.02464,-0.08693,-0.03307,-0.04198,-0.05053,-0.02848,0.04405,0.06193,0.01233,0.07396,-0.03089,-0.02923,0.00875,-0.06602,-0.03143,-0.02369,-0.02326,0.00834,0.00563,0.08441,-0.02113,-0.0209,0.06603,-0.01531,-0.12838,-0.07411,-0.04534,0.08675,-0.05504,-0.02362,0.06563,-0.10721,-0.00363,0.07442,-0.09986,-0.09107,0.00691,-0.07544,-0.05368,0.00671,0.06962,-0.03884,-0.104,-0.01053,-0.0462,0.04112,-0.00585,-0.03064,-0.00634,0.02661,0.00838,0.01409,0.05036,0.01433,-0.0988,-0.02911,0.11266,0.00232,0.1187,0.02479,0.02937,0.01048,0.10441,0.07262,0.0069,0.02093,0.0228,-0.03012,-0.00859,0.11141,-0.07137,0.01093,0.06973,0.08193,0.12465,0.06685,-0.043]},{"domain":"nuclear_engineering","key":"nuc_critical_sphere","name":"Critical radius of a bare spherical reactor (one group)","package":"nuclear-engineering-ai999x","example":"Critical sphere: D = 0.9 cm, Sigma_a = 0.15 1/cm, nuSigma_f = 0.18 1/cm, extrapolation = 2.13D","v":[-0.05421,-0.05773,-0.05334,0.05541,0.09863,0.1516,-0.06413,0.00194,0.08652,-0.13293,-0.01766,-0.01601,0.09963,-0.06589,-0.00926,-0.02259,0.05708,0.0575,0.16632,0.02975,-0.03156,-0.0894,-0.04725,-0.00811,0.05082,-0.03371,-0.00094,-0.02883,0.14518,-0.07132,-0.09481,0.00289,0.01087,-0.02203,-0.0554,-0.05605,0.01358,0.03858,0.00463,0.00144,-0.03574,-0.04361,-0.08175,0.08764,0.0096,-0.05476,0.06975,-0.00577,-0.00489,-0.08705,0.07274,-0.07592,0.07725,0.04794,-0.05336,-0.12964,0.03792,0.07752,0.00107,-0.00847,-0.04213,0.04427,-0.08482,-0.02863,0.04748,0.07985,-0.03832,-0.0708,-0.10067,-0.02291,0.03985,0.00966,-0.07845,-0.00547,-0.00701,0.04572,-0.0588,-0.06136,-0.0354,0.06863,0.06015,-0.01523,-0.01239,0.04307,0.03215,0.03657,-0.03692,0.01182,-0.00557,-0.05307,-0.0576,0.03488,0.07064,0.0118,0.0036,0.00974,-0.15392,-0.07979,0.02218,-0.09844,-0.05243,0.01654,-0.0345,-0.05358,0.00709,0.00967,0.01446,-0.05009,0.09864,0.05755,-0.0155,-0.03596,0.03885,0.06936,-0.04247,-0.16133,0.02628,-0.02587,-0.05676,-0.05014,-0.01612,-0.08119,-0.16111,-0.00355,0.09116,-0.04892,0.10426,0.02628,-0.0125,0.03391,-0.10738,-0.10209,0.00103,0.01448,-0.0418,-0.00242,0.00793,0.02851,-0.042,0.06213,-0.06671,-0.02433,0.09645,0.07079,0.02866,-0.00347,0.20179,0.03266,-0.02372,0.14308,0.0606,0.04111,-0.00947,0.07283,0.0578,0.01518,0.02693,0.01721,-0.00444,0.04881,0.01701,0.03875,0.02415,-0.00616,-0.00441,0.00918,0.01001,-0.01693,0.01423,0.04591,0.00646,0.0524,-0.03722,0.04883,-0.04717,-0.16269,0.00613,-0.05954,0.1435,0.01178,-0.04956,0.01957,0.01666,-0.00163,0.02422,0.0588,0.12148,0.03688,0.0298,0.00377,-0.00154,0.00737,-0.01748,0.04984,-0.02145,0.0315,0.01763,-0.10225,0.01769,0.00451,-0.08386,0.06549,-0.03915,-0.03001,-0.09247,-0.07237,0.08042,-0.07922,0.02364,0.03721,-0.05879,-0.05383,0.07742,-0.06321,-0.11764,-0.00552,-0.07658,-0.04852,0.09443,0.0742,-0.05678,-0.04282,0.03054,-0.0363,0.04618,0.00082,-0.08502,-0.01626,0.08671,0.03475,-0.00733,0.18921,0.00327,-0.15162,-0.07436,0.05732,-0.03823,0.01753,-0.12622,0.06406,0.04547,0.04946,0.08681,0.04814,0.01664,0.06919,-0.07357,-0.05399,0.0599,0.01791,0.02646,0.03491,0.02711,0.08469,-0.05868,-0.00016]},{"domain":"nuclear_engineering","key":"nuc_currie_detection_limits","name":"Currie critical level, detection limit and minimum detectable activity","package":"nuclear-engineering-ai999x","example":"Currie detection limits: B = 100.0","v":[0.01886,-0.04985,-0.00468,0.12265,0.0158,0.03173,0.03194,0.0379,0.08542,0.17027,-0.02772,0.03924,-0.14375,-0.04277,-0.09272,0.15465,0.0014,-0.00644,-0.06562,-0.03567,-0.04149,0.01261,0.02498,-0.045,-0.05179,0.08187,-0.02513,0.04778,0.04506,-0.03746,-0.04484,-0.02439,0.08251,-0.07755,0.02482,0.04477,-0.0334,-0.02753,0.00655,-0.02284,-0.01165,0.06476,-0.00498,-0.07718,0.1066,-0.06598,0.022,0.16851,-0.00997,-0.0265,0.03324,0.08998,0.07751,-0.06153,-0.03372,0.00818,-0.06847,0.10112,0.12332,0.14465,-0.0049,0.08851,0.00592,-0.03554,-0.07194,0.03295,-0.14629,0.08156,-0.08551,-0.03493,0.05361,-0.02464,0.20867,0.02061,0.09928,0.04716,0.03376,0.00435,-0.0919,-0.02571,-0.04667,-0.03427,-0.03872,0.0054,-0.02793,-0.06183,0.03323,0.05005,-0.03313,-0.00977,-0.05568,0.04789,0.08391,0.01406,0.02475,0.0755,0.02008,-0.04536,0.03038,0.03225,-0.01102,0.01466,-0.14255,0.05021,0.00338,0.03057,-0.06977,-0.02876,-0.0077,0.00677,-0.07666,-0.103,0.06261,-0.01129,-0.10582,0.01346,0.01809,-0.06366,-0.02287,0.10489,0.04288,-0.03788,0.15654,0.06706,-0.1187,-0.02508,-0.03519,0.07433,-0.04518,-0.09374,-0.02972,0.06422,0.02115,-0.00843,-0.09071,-0.08812,-0.07681,0.03713,-0.06124,0.02754,0.00967,-0.02857,0.07496,-0.07679,-0.07286,-0.01954,-0.00332,0.05132,0.04679,-0.07315,0.04475,-0.01253,0.04428,-0.00694,0.02553,-0.11911,0.0146,0.00546,-0.0964,0.10546,-0.01471,0.02622,-0.00396,-0.00367,0.04511,-0.03228,-0.01679,0.03105,-0.01015,-0.03276,-0.00671,0.07786,-0.02096,-0.06721,0.00927,0.0342,-0.03382,0.04174,0.1244,-0.02726,-0.05038,-0.05905,0.08725,0.03846,-0.04538,0.02674,-0.03172,0.03081,0.01017,0.07071,-0.01918,-0.10939,-0.02722,0.1016,0.06697,0.00536,-0.00557,0.01322,0.10309,-0.08871,0.04986,0.0334,-0.06769,-0.02761,-0.0257,-0.09615,-0.07317,0.02456,-0.03415,-0.07122,-0.06003,0.00291,0.00406,0.01286,0.02071,0.10143,-0.03035,0.04653,-0.06339,0.03359,-0.10286,0.07325,-0.02906,0.09439,-0.05258,0.04829,0.02931,-0.03185,-0.0308,0.14757,-0.1032,0.0632,0.01019,-0.13773,-0.00159,-0.09235,0.04279,-0.00108,0.00316,0.02985,-0.04723,0.02563,0.06066,-0.02805,-0.09967,0.00351,-0.00807,0.03457,-0.03779,0.05927,-0.0166,-0.04547,0.00756,0.05691,-0.11949,-0.03742]},{"domain":"nuclear_engineering","key":"nuc_daughter_max_activity_time","name":"Time of maximum daughter activity","package":"nuclear-engineering-ai999x","example":"Daughter maximum activity time: T_P = 65.94 h, T_D = 6.015 h","v":[-0.04244,0.04652,0.00305,0.09253,-0.08232,0.01509,0.02034,0.04936,0.00352,0.03481,0.09487,0.12058,-0.00624,0.0137,0.005,0.0345,0.02187,-0.03529,0.05189,0.00405,0.03636,-0.00245,-0.02647,-0.01818,0.09331,0.07451,-0.13571,0.05036,0.15559,0.04951,0.06562,0.05737,0.06208,0.00011,-0.07787,0.00901,-0.0934,-0.00773,-0.07835,-0.01762,0.00693,0.00442,0.06495,-0.03876,-0.01993,0.03221,0.04749,-0.01903,-0.03967,-0.05808,-0.0488,0.15066,0.09442,0.01734,-0.01949,0.09417,-0.05706,-0.01704,-0.05992,0.10896,0.02525,0.01311,0.07283,-0.06801,-0.05769,-0.05902,-0.01781,-0.05603,-0.07264,-0.05577,-0.02979,0.00903,-0.02643,0.00034,-0.06569,-0.0447,-0.05977,0.00859,-0.00246,0.00533,-0.02209,-0.01337,-0.05791,-0.0509,-0.06729,0.03056,0.01406,0.06037,-0.05114,-0.121,0.00587,0.08648,0.02264,0.01895,-0.01609,0.05765,0.11441,-0.01951,0.01591,0.03238,-0.00779,8e-05,-0.13418,0.0671,-0.07827,0.09601,-0.13517,-0.04726,-0.04271,-0.0191,-0.10232,0.09747,0.11847,0.03444,0.05897,0.03612,-0.08497,-0.03682,-0.04491,-0.07813,0.17342,0.01093,0.05151,0.00836,-0.13738,0.02325,-0.05252,0.01534,0.03927,0.02743,-0.05426,0.0138,0.06062,-0.05654,-0.08187,0.0496,0.11475,-0.06497,0.02862,-0.00075,0.06456,0.08091,0.21861,-0.07863,-0.02413,0.02574,0.00636,-0.04503,-0.00436,0.09154,-0.14615,0.00559,-0.06754,0.05668,0.0581,-0.01753,-0.03532,0.06297,-0.03419,0.03452,0.0315,0.04109,-0.02074,-0.03959,-0.14993,0.00982,0.10248,0.0303,0.06678,-0.05364,-0.07636,-0.03786,-0.01233,-0.05599,-0.04173,-0.02443,0.04286,0.05122,0.08325,-0.01733,-0.01806,0.04637,0.00727,0.08387,-0.09011,-0.10005,-0.03943,0.01023,0.01309,-0.04584,0.00494,0.05517,0.01512,-0.02005,-0.02205,0.03904,0.00855,-0.03497,0.00092,0.04966,0.09659,0.03832,0.03036,0.10357,0.06381,-0.07449,-0.02145,0.00494,0.07698,-0.05885,-0.03021,-0.06427,0.05125,-0.06283,0.00516,0.06032,-0.15006,-0.00233,-0.08297,0.01445,0.03583,-0.05232,-0.01051,-0.07357,0.00404,-0.02254,-0.00706,-0.00392,0.0135,-0.03595,-0.00872,0.11767,-0.03873,-0.03331,0.0272,0.00486,-0.02729,0.06638,0.0669,0.00749,0.00073,0.1744,-0.01819,0.12558,-0.1215,-0.09336,-0.09096,-0.02983,-0.06254,-0.06138,0.02984,-0.07744,0.07918,0.02134,-0.06866,0.01518]},{"domain":"nuclear_engineering","key":"nuc_dead_time_nonparalyzable","name":"Dead-time correction, non-paralyzable detector","package":"nuclear-engineering-ai999x","example":"Non-paralyzable dead time: m = 50000 cps, tau = 5 us","v":[0.14917,-0.03009,-0.00816,0.09457,-0.00503,0.06143,0.04284,0.05439,0.04364,0.12395,0.10309,0.02231,0.05504,-0.00961,-0.03364,0.07266,0.0718,-0.06077,-0.04397,0.09,0.04499,-0.04209,0.03431,0.00992,0.00332,0.00344,-0.01613,-0.03477,0.06337,-0.06272,-0.02647,-0.05806,0.04712,-0.01789,0.02484,0.01155,-0.01972,0.00597,-0.0499,0.02852,0.05855,-0.07258,0.07577,0.06052,-0.069,-0.018,0.05353,0.04275,0.01669,-0.00318,-0.08472,-0.00901,0.0865,0.01401,0.02383,-0.02589,-0.09295,0.09272,-0.08788,0.02157,0.00876,0.05133,0.00536,0.04182,-0.13916,-0.02978,-0.09335,0.01533,-0.09137,0.0024,0.11343,-0.05732,0.14417,0.05049,0.04414,-0.03888,0.12657,-0.06203,-0.06526,0.03475,0.07403,-0.09402,0.01693,-0.05923,-0.06085,-0.10906,0.03621,-0.02843,0.10184,-0.00214,-0.06804,0.00319,0.01893,-0.07927,-0.07344,0.06758,-0.05187,-0.02902,0.01429,0.04532,-0.03603,-0.1001,-0.18427,0.03982,-0.04217,-0.00229,-0.11458,-0.0375,0.01925,0.07053,0.01086,0.02505,0.04729,-0.03201,-0.07242,0.09931,-0.03699,0.0229,0.06546,0.07562,-0.05017,-0.02194,-0.00546,0.04853,0.04834,-0.1456,-0.13056,0.00436,-0.05402,-0.02505,0.04455,-0.03831,-0.02614,0.01402,-0.03529,-0.03656,-0.0129,-0.01463,0.004,0.05737,-0.00606,0.00026,0.03688,0.03208,-0.08954,0.02314,-0.05347,0.01792,0.01267,-0.0117,0.06144,-0.08452,-0.00351,0.01493,0.00098,-0.00261,0.02526,0.02948,0.02106,-0.06425,-0.01985,-0.04708,0.08337,-0.01049,0.02977,-0.0315,0.01666,0.09165,0.07434,-0.06794,0.08392,0.063,-0.04848,0.03848,0.01991,0.15346,-0.1147,0.05583,0.0868,0.07473,-0.03815,-0.09234,0.10549,-0.02955,-0.01921,0.04808,0.05323,-0.06097,-0.09538,0.03868,0.04092,-0.12583,-0.03624,-0.05461,-0.0456,0.06496,0.00634,-0.04827,0.02605,-0.07331,0.10396,-0.02599,0.08227,0.07551,0.01333,0.03772,0.01411,0.03312,0.00822,0.00091,-0.11749,-0.01108,0.03111,-0.03995,-0.04872,-0.11132,-0.00034,0.06696,-0.09043,-0.00464,0.05345,0.01876,0.02481,0.00552,-0.03361,-0.13809,0.1542,-0.15549,-0.08639,0.00374,-0.01194,-0.04541,0.04921,-0.10763,0.01874,0.00852,-0.00344,0.06168,-0.13368,-0.02355,0.06152,0.04595,0.07773,0.05184,0.09486,-0.00042,0.02788,-0.10997,-0.00989,0.02603,0.0827,-0.05768,0.06312,-0.04227,-0.09582,-0.06036]},{"domain":"nuclear_engineering","key":"nuc_dead_time_paralyzable","name":"Dead-time correction, paralyzable detector","package":"nuclear-engineering-ai999x","example":"Paralyzable dead time: m = 50000 cps, tau = 5 us, branch = low","v":[0.02148,-0.04188,0.07471,0.01736,-0.11011,0.07761,-0.00643,-0.04186,0.02872,0.09799,0.0334,0.14394,-0.03216,-0.0509,0.06243,0.04414,0.07292,-0.08244,-0.0185,0.01733,0.05404,-0.05344,0.01302,-0.0727,0.06805,0.01253,-0.03014,0.03942,0.0984,0.04993,-0.05068,-0.01522,0.09352,0.01254,-0.07989,-0.04745,-0.01474,-0.00417,-0.03139,-0.07609,0.01031,0.06468,0.11237,0.05583,-0.01261,-0.05694,0.1289,-0.06207,0.02386,-0.07325,-0.05126,0.01003,0.03526,-0.06404,-0.11044,0.06835,-0.06236,0.05181,0.0111,-0.01467,0.02926,0.05492,0.0327,0.00116,-0.11492,-0.07266,-0.10667,-0.02335,-0.13733,-0.03534,0.10624,-0.1276,0.12613,0.03753,0.04133,-0.08556,0.03295,0.03829,-0.13206,-0.04315,0.00631,-0.04439,0.0223,-0.03926,-0.02321,-0.00017,0.06079,-0.04102,0.01602,-0.0496,-0.0077,0.12085,0.08344,0.01617,-0.06979,0.10239,-0.02887,-0.02005,-0.00773,0.09307,-0.02203,-0.09456,-0.14554,0.09011,0.04096,-0.00615,-0.12789,0.00494,-0.10223,-0.01391,-0.00586,0.01046,0.05681,0.1444,-0.03428,0.02208,-0.01445,-0.05687,0.05471,0.05339,0.08096,0.0371,0.03411,0.06246,-0.04823,-0.10928,-0.01384,-0.07882,-0.04181,-0.05538,0.00947,0.00147,0.00271,0.02894,0.03195,-0.02053,-0.00164,-0.03462,-0.03833,0.06767,0.0743,0.08522,0.03706,-0.0662,-0.09612,0.08098,-0.022,0.0726,0.06324,-0.00563,0.01872,-0.06185,-0.02554,0.02777,-0.0083,-0.0567,-0.05708,-0.04331,-0.05515,-0.08293,-0.01454,-0.01415,0.05339,-0.02638,-0.04525,-0.04711,-0.02527,0.02793,0.13134,-0.04364,0.11398,0.0008,-0.00621,-0.03761,-0.03558,0.10077,-0.0434,0.08737,0.09629,0.11057,-0.04014,-0.0769,0.06756,-0.07406,-0.01853,0.07169,0.04684,-0.02807,-0.04711,0.1072,-0.00533,-0.11735,-0.03162,-0.04934,0.0255,0.02429,-0.06062,-0.05063,0.09675,-0.03084,0.0413,0.08038,0.00057,0.07605,0.02838,0.02457,0.00433,0.05365,-0.01274,-0.04352,-0.11506,-0.00748,-0.00659,-0.03511,0.05957,-0.05906,-0.11699,0.13155,-0.05557,0.08583,0.05663,-0.04063,0.0082,-0.01778,-0.03533,-0.02261,-0.00256,-0.09068,-0.05546,-0.04574,0.05938,-0.03304,0.0334,-0.14087,0.10419,-0.00201,-0.00987,0.10415,-0.06331,-0.05143,-0.06133,0.0828,0.09103,0.03271,-0.01713,-0.00976,-0.00756,-0.04198,0.02891,0.00675,0.07379,-0.04936,0.09308,-0.02297,-0.08365,0.0497]},{"domain":"nuclear_engineering","key":"nuc_decay_curve_fit","name":"Half-life from a measured decay curve (weighted log-linear fit)","package":"nuclear-engineering-ai999x","example":"Decay curve fit: t = [0.0, 1.0, 2.0, 3.0, 4.0], C = [10000.0, 7100.0, 5000.0, 3540.0, 2500.0], t_unit = 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heat energy released between two times after shutdown","package":"nuclear-engineering-ai999x","example":"Decay heat energy: P0 = 3000 MW, T_op = 1 y, t1 = 10.0 s, t2 = 1 d","v":[-0.00531,-0.07722,-0.02488,-0.09566,-0.04326,-0.00283,0.03958,0.0639,0.01935,0.03258,0.02819,0.1301,-0.04358,-0.13314,-0.0459,-0.0667,0.0027,-0.00879,-0.01776,0.00805,-0.03799,-0.00763,-0.02862,0.15248,0.01296,0.01979,0.01572,0.00538,-0.06023,0.05222,0.00555,0.01318,-0.06851,0.02529,0.04283,0.00254,0.04105,0.01821,0.02531,-0.10164,0.01882,0.01515,-0.03292,-0.0069,0.00827,0.05044,-0.07589,0.00432,0.02936,0.08371,-0.12389,0.09501,0.06278,-0.03779,-0.00846,-0.08235,0.01374,-0.03394,-0.03007,-0.00096,0.02579,0.02118,-0.07685,-0.01722,0.02156,0.12347,-0.0579,-0.03932,0.01358,-0.15398,-0.00686,-0.01881,-0.05637,0.07553,-0.09695,-0.05422,-0.0401,0.05979,-0.12793,-0.01756,0.09513,-0.12868,0.02962,-0.01884,-0.05288,-0.1113,0.00755,0.03333,0.06293,-0.00462,-0.06255,0.01247,-0.00232,0.01524,-0.03178,0.00853,0.23408,0.01269,-0.06289,0.13257,-0.01464,-0.05278,-0.02122,0.02371,-0.1203,-0.00248,-0.02113,0.00391,-0.10544,0.08334,-0.00406,0.0561,0.01741,0.02879,-0.08335,0.01792,-0.04936,-0.06141,0.13329,0.11794,-0.00106,-0.02687,-0.04772,-0.0291,-0.01503,-0.00718,-0.09052,0.01296,-0.08453,0.05488,0.11475,0.03598,-0.06179,-0.0392,0.06519,-0.09929,0.08228,-0.00049,0.00477,0.02241,-0.10513,-0.0702,0.00428,0.00154,-0.08996,0.18058,-0.00775,0.08481,0.05433,0.00066,0.02587,-0.04395,0.04603,-0.00966,0.00082,0.01183,0.04728,-0.01627,0.03107,0.01162,-0.02489,0.08998,0.04236,0.14774,-0.07426,0.00764,0.04052,0.16064,0.04719,-0.01485,0.10832,0.07375,0.03563,-0.01801,-0.07205,-0.01615,0.0147,-0.02741,-0.03303,-0.03882,-0.05286,0.00727,-0.08589,-0.02816,-0.09175,0.00931,0.0153,0.02072,0.08089,0.00528,-0.12792,-0.0273,0.05412,0.10034,0.05027,0.03724,-0.06399,-0.02439,0.07767,-0.0296,-0.0016,0.02774,0.08693,-0.10113,0.0641,-0.01991,-0.10163,-0.06843,-0.03919,-0.16655,-0.00774,-0.00897,0.00725,-0.03927,0.078,0.01212,-0.0752,0.01217,0.01231,0.00343,0.07097,-0.03689,0.0438,-0.01101,-0.00722,-0.02588,0.12795,-0.06117,0.03568,0.04317,-0.02204,-0.00515,-0.09493,0.0234,0.05465,0.0383,0.06407,0.00995,0.02325,-0.01577,0.10246,0.04326,0.03611,0.12002,-0.01593,0.00947,0.00136,0.01064,0.11116,0.00281,0.05403,-0.1132,-0.00574,0.0879,0.01581,-0.07067]},{"domain":"nuclear_engineering","key":"nuc_decay_heat_power","name":"Decay heat after shutdown (Way-Wigner)","package":"nuclear-engineering-ai999x","example":"Decay heat: P0 = 3000 MW, T_op = 1 y, t = 1 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depletion and energy released at constant flux","package":"nuclear-engineering-ai999x","example":"Depletion at constant flux: m0 = 1 kg, sigma_a = 680.9 b, sigma_f = 582.6 b, phi = 3e13 1/(cm^2*s), t = 1 y, E_f = 200 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and intrinsic efficiency of a slab detector for a point source on axis","package":"nuclear-engineering-ai999x","example":"Detector efficiency for a point source: d = 10 cm, a = 3.81 cm, t = 7.62 cm, mu = 0.28 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diffusion length and migration length","package":"nuclear-engineering-ai999x","example":"Diffusion length: D = 0.16 cm, Sigma_a = 0.0197 1/cm","v":[-0.06119,-0.04265,0.06022,0.01082,0.07464,0.07414,-0.00335,-0.03987,0.0053,0.0064,0.07351,-0.02705,0.11322,0.03686,-0.01989,-0.00221,0.04453,0.03392,-0.03813,0.01575,-0.04986,0.05406,-0.04946,0.05956,0.13876,-0.01662,-0.07655,-0.07393,0.03625,0.18615,-0.06339,0.06057,-0.08169,0.06652,0.05763,-0.00897,0.05684,-0.0095,0.07665,0.0589,0.01473,0.01076,0.15506,-0.04943,-0.04149,-0.05457,0.03612,-0.01597,0.00952,-0.04154,-0.05736,0.03498,0.12353,0.06879,-0.0521,-0.04139,0.07717,0.05863,0.12614,0.04108,0.0121,0.02104,-0.0598,0.05673,-0.00202,-0.01568,0.01503,0.03677,-0.01833,-0.06482,-0.04732,-0.00024,-0.13049,-0.02986,0.07818,-0.07131,-0.05917,-0.01124,-0.06205,-0.05158,0.07082,-0.0147,-0.0169,0.06336,0.04453,0.0283,-0.00993,-0.08232,0.02812,0.03338,-0.09323,-0.1144,0.00454,-0.02745,-0.0455,-0.03608,0.00499,-0.01771,0.06011,-0.03077,-0.03432,0.10008,-0.09932,-0.08579,0.02232,-0.0338,-0.07466,-0.05488,0.03619,-0.04017,-0.03792,0.0276,0.14331,-0.01137,-0.0864,-0.17332,-0.02811,-0.00495,-0.06326,0.07525,0.06759,0.01663,-0.06775,0.05962,-0.02285,-0.01767,-0.01031,-0.0138,-0.03669,-0.00659,-0.02598,-0.01108,0.02001,-0.08006,0.01499,0.03627,0.04049,-0.04966,0.0649,0.02474,0.05014,-0.03556,0.10801,-0.06496,-0.12981,-0.06835,-0.03141,0.04522,-0.08971,0.08118,0.08573,-0.06956,-0.04956,-0.02326,0.02356,-0.01334,0.03077,0.02887,-0.04629,-0.01981,0.01625,0.11604,-0.0528,0.04127,0.01563,-0.04671,0.0172,0.01097,-0.07128,-0.04399,-0.05308,0.03923,0.0225,0.09252,0.00859,-0.08554,0.01756,0.05855,0.09928,0.04134,0.1118,0.03367,-0.04821,-0.02818,-0.1013,0.11334,0.09613,0.03629,0.01586,-0.02107,0.037,0.05458,0.01396,-0.04271,-0.08867,-0.06728,-0.00024,-0.03139,-0.02782,0.05182,0.03528,-0.07264,0.05656,-0.04348,0.01181,-0.09638,0.15729,-0.00627,-0.02129,0.0541,-0.02081,-0.02578,0.04355,-0.09916,0.0377,0.01787,-0.0082,-0.01201,-0.04679,0.00348,-0.10168,0.00484,-0.05417,-0.19816,0.11489,-0.04764,0.01878,0.07069,0.02011,-0.03522,-0.00165,0.07055,0.01841,-0.08237,0.03352,0.00983,0.03562,0.06514,0.07854,0.00792,-0.04352,0.14951,0.02351,-0.03286,0.05037,0.13854,0.00329,-0.04392,0.0167,-0.10636,0.08881,0.0463,-0.00332,-0.01823,-0.02666,-0.19809]},{"domain":"nuclear_engineering","key":"nuc_disk_source_flux","name":"Uncollided flux on the axis of a shielded disk source","package":"nuclear-engineering-ai999x","example":"Disk source flux: S_A = 1e7 1/(m^2*s), R = 1 m, h = 50 cm, mu = 0.1 1/cm, t = 5 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dose from organ equivalent doses and tissue weighting factors","package":"nuclear-engineering-ai999x","example":"Effective dose: H = [10.0, 5.0, 2.0], w = [0.12, 0.04, 0.01]","v":[0.06602,0.11915,0.00612,0.03302,0.04737,0.05172,-0.03627,0.00276,0.01808,-0.03964,-0.01143,0.07855,-0.07472,-0.04591,-0.12382,0.04678,-0.06078,-0.01637,0.0139,0.02284,-0.00663,-0.03291,-0.19751,0.05952,-0.06622,0.04183,-0.02215,-0.05855,0.02616,-0.00011,-0.0106,-0.02272,0.08431,-0.07524,-0.01591,-0.00799,0.04668,0.0753,0.06479,0.03048,-0.00071,0.01077,0.06703,-0.06212,-0.16226,-0.08107,-0.05007,-0.00915,-0.053,-0.05517,-0.0444,0.0197,0.03574,-0.05791,0.05009,-0.02562,-0.12303,0.06203,-0.10948,0.15282,0.00256,-0.01183,0.03961,-0.00822,-0.11193,0.07354,-0.02574,0.00771,0.07725,0.06645,-0.00091,-0.00629,-0.0423,-0.10089,-0.06624,0.06594,-0.00683,-0.01388,-0.0249,0.03206,-0.01084,0.0305,-0.06101,0.05727,-0.0372,0.01185,0.00148,-0.07297,0.01528,-0.04915,-0.03493,0.06437,-0.0342,-0.01365,0.04022,-0.02744,-0.07403,-0.0181,-0.04527,0.07754,0.0118,-0.07355,-0.0597,-0.02322,0.05201,-0.06099,-0.01078,-0.07764,-0.01414,-0.05352,0.00493,-0.08955,0.11584,0.0058,-0.07809,0.01843,-0.06569,-0.08112,0.15126,0.04401,-0.06931,-0.01463,-0.00504,-0.15737,-0.0278,-0.14328,-0.0303,-0.03137,-0.06049,0.03886,0.08594,0.14862,-0.03994,-0.02867,-0.03054,0.06014,-0.06899,-0.08424,-0.04774,0.13019,0.15556,-0.09475,-0.00044,0.03536,-0.02628,0.05879,0.06455,0.03847,-0.03296,-0.04718,0.02113,0.03268,0.05062,-0.02781,0.02706,-0.14544,-0.03087,-0.0264,-0.08637,0.04146,0.02482,0.06917,0.0147,0.10196,0.11001,-0.01132,-0.02302,0.06145,0.04301,-0.00587,0.08326,0.05632,-0.01736,-0.0136,-0.02191,0.06495,0.11579,-0.04743,0.095,0.036,0.03927,-0.01256,-0.09339,-0.03757,0.03026,0.02404,0.08634,0.15678,-0.03574,0.05513,0.04285,0.04618,-0.06332,0.11053,-0.05343,0.03009,0.05718,0.00533,0.08154,0.04803,-0.06637,-0.07442,0.00599,0.07407,-0.07068,0.0772,-0.10063,0.06984,-0.06038,-0.07114,0.06065,0.04161,-0.01732,0.05045,0.02305,0.00568,0.09184,-0.04814,-0.09384,-0.00402,0.00993,0.02898,0.02466,-0.08974,-0.03249,-0.00049,0.07705,0.04238,0.00763,0.04911,0.04214,0.07425,0.0629,0.05634,0.09828,-0.00048,0.0556,-0.08455,-0.04719,-0.02452,0.0349,-0.0071,0.12971,-0.04731,-0.02353,0.01069,0.01291,0.01156,0.04657,-0.00143,0.07924,0.01225,-0.02572,-0.04564,-0.12374,-0.02852]},{"domain":"nuclear_engineering","key":"nuc_effective_half_life","name":"Effective half-life (physical and biological removal)","package":"nuclear-engineering-ai999x","example":"Effective half-life: T_p = 8.0207 d, T_b = 80 d","v":[0.03469,-0.03657,-0.06484,0.05269,0.14121,0.03732,-0.02994,0.0307,0.02407,0.01181,0.04727,0.08205,-0.03713,-0.20767,-0.08953,-0.01572,-0.01249,0.01487,0.1395,0.13094,0.02526,0.02226,-0.07951,0.10923,0.0324,0.02838,0.0015,0.08568,0.14135,-0.01657,-0.05369,0.055,0.06525,-0.08798,-0.06932,0.03129,0.06321,0.02345,-0.0099,-0.01519,0.04073,-0.03529,0.15959,-0.10679,-0.07747,0.00183,-0.02597,0.06681,-0.09888,-0.01965,-0.07966,0.06276,0.08725,-0.12556,0.06618,0.05302,-0.0288,0.05772,-0.14695,0.09077,-0.00814,0.02886,0.02898,-0.05051,-0.06157,0.104,0.05957,-0.03175,-0.00305,-0.09222,-0.01207,0.02657,-0.05164,0.00068,0.00016,-0.02696,0.03973,-0.02441,-0.02006,-0.049,-0.00317,0.03858,0.00743,0.05057,-0.05411,-0.09632,0.05063,-0.03532,0.09371,-0.00811,-0.03214,-0.03285,-0.03399,-0.05991,-0.03141,0.08983,0.00582,-0.00604,-0.00887,-0.03595,0.01564,-0.04449,0.00408,0.15256,-0.03665,0.04871,-0.03564,-0.15582,-0.04654,-0.07553,0.04166,0.00326,0.07211,0.06652,-0.03089,-0.04144,-0.05864,-0.0232,0.04509,0.00168,0.04257,0.06671,-0.01452,0.084,-0.07539,-0.03353,-0.04728,0.00907,-0.01636,-0.0636,0.11939,0.04817,0.07812,-0.02264,-0.01453,-0.08123,0.0686,0.00355,-0.07242,-0.00432,-0.02672,-0.04016,0.03951,-0.01515,-0.05088,0.0345,0.09544,0.06863,0.04899,-0.02954,-0.01931,0.0983,-0.03408,-0.0335,0.07595,-0.0579,0.02817,0.04569,-0.07375,0.00464,0.0031,-0.09935,-0.06743,0.03393,-0.01794,-0.07384,0.00347,0.06596,-0.01561,-0.04711,-0.01693,0.00181,0.02322,-0.04536,-0.09873,-0.03092,-0.00981,-0.08614,0.02897,0.05435,0.07166,-0.03413,0.0418,-0.11376,0.03637,0.0036,0.0345,-0.0462,-0.03146,-0.05451,0.03417,0.02555,-0.07892,-0.06392,0.01321,0.04977,0.0138,0.01033,0.10872,0.06483,0.03659,0.04027,0.00996,0.05456,0.11489,-0.10902,0.07373,0.10319,-0.0194,-0.07126,-0.10317,-0.03316,0.06007,0.0723,0.05776,0.02322,0.01524,-0.07075,-0.07151,0.02941,-0.05743,-0.05608,0.06103,-0.13355,-0.04719,-0.03075,0.10543,-0.0583,-0.02608,0.127,0.0946,0.04826,-0.03344,0.12565,0.00089,-0.00647,-0.01194,-0.06226,-0.09768,0.05417,-0.02942,0.05045,0.06814,0.02766,0.03847,0.03047,-0.01898,-0.08175,0.09267,-0.02805,-0.02725,-0.06963,0.03066,-0.02486,-0.1253,-0.0524]},{"domain":"nuclear_engineering","key":"nuc_elastic_scattering","name":"Neutron energy and lab angle after an elastic collision","package":"nuclear-engineering-ai999x","example":"Elastic scattering: A = 12.0, E = 2 MeV, theta = 90 deg","v":[0.0871,0.01134,0.09545,-0.12653,0.09506,0.11941,-0.02483,0.01386,0.03832,-0.00103,0.09753,0.08027,-0.04217,0.01438,0.0648,0.11306,-0.01415,0.05888,0.00987,0.05189,0.0533,0.12138,-0.00108,0.01582,-0.04655,-0.03035,-0.01643,0.01365,0.00627,0.04372,-0.07618,-0.00426,-0.03731,0.01447,-0.07569,0.03104,-0.06455,-0.01105,0.0139,-0.05027,-0.01581,0.06096,0.00058,-0.00722,0.00681,0.01339,-0.03749,0.00473,0.02419,-0.03314,-0.01385,-0.01195,0.02219,0.04788,-0.0056,0.04832,-0.07026,0.00773,-0.15301,0.0252,-0.03513,0.04177,0.05083,-0.06548,0.12073,0.04001,-0.05655,0.0317,0.04072,0.03754,0.01015,-0.1371,0.07538,-0.00431,-0.02485,0.02761,0.0266,0.0372,-0.0211,0.06471,0.05206,-0.05682,-0.01318,0.08907,-0.02291,-0.08422,0.0188,-0.05633,-0.01652,-0.10484,0.10946,-0.05293,0.1779,-0.09097,-0.02022,0.06947,-0.03625,0.00313,-0.00956,-0.01474,0.07635,-0.01035,-0.06322,0.0001,-0.05099,-0.15637,0.06264,0.06627,-0.11366,-0.12392,0.03982,0.09279,0.10821,-0.13594,-0.1034,-0.01078,0.08506,-0.06128,0.06211,-0.04832,-0.14645,0.00056,0.08671,0.06488,-0.01228,-0.0875,0.04214,0.02624,0.04958,-8e-05,-0.0221,-0.11974,-0.01438,-0.09621,0.00287,0.05268,0.06966,0.04367,-0.02975,-0.06329,0.06254,0.00068,0.12223,0.02081,0.04726,-0.00552,0.00166,0.08029,-0.11386,-0.08181,0.06937,0.02997,0.00491,-0.00084,-0.00619,0.00455,-0.04243,-0.03866,0.06766,-0.00522,-0.04548,0.04686,0.02405,0.08739,-0.03868,-0.01734,-0.05679,-0.07118,0.03589,-0.01034,-0.00888,0.05643,0.08815,-0.05356,0.06509,-0.01522,-0.05693,0.03771,-0.11481,-0.05226,-0.00866,0.08139,-0.06278,-0.09004,0.03327,-0.01209,-0.0188,-0.09064,0.02262,0.02036,-0.05322,0.00827,0.05186,0.00375,-0.00759,-0.01676,-0.0393,-0.0169,-0.041,0.00096,-0.11063,-0.03107,-0.03341,-0.02396,-0.05859,-0.04292,0.08252,0.08204,0.0431,-0.06727,-0.03575,-0.11404,-0.00348,-0.02511,-0.17714,-0.1064,-0.02148,0.04599,0.09579,0.03433,0.00054,-0.13434,0.09905,0.05455,0.00502,0.03092,0.08087,0.04647,0.08538,0.05124,0.01313,0.0714,0.06261,0.01715,-0.02122,-0.10081,-0.02925,0.0208,0.02583,-0.04324,0.03903,0.05014,0.08347,0.09453,-0.00839,-0.0141,0.10099,0.08665,0.04177,0.05362,-0.15555,0.02853,0.00034,0.01279,0.05509,-0.06575]},{"domain":"nuclear_engineering","key":"nuc_enrichment_swu","name":"Uranium enrichment: feed, tails and separative work (SWU)","package":"nuclear-engineering-ai999x","example":"Enrichment SWU: x_p = 4.5%, x_f = 0.711%, x_w = 0.25%, P = 1 kg","v":[0.12439,0.02336,-0.03152,0.00073,-0.01997,0.12863,-0.148,-0.06686,-0.00807,-0.05849,0.00363,0.1543,-0.01451,0.06799,-0.11317,0.02047,-0.09211,-0.00899,-0.00344,0.02143,0.06492,-0.00644,-0.07132,-0.04904,-0.00991,0.0482,-0.04942,-0.08191,0.01854,-0.01618,-0.02056,-0.02981,0.01523,0.02481,0.01045,0.00763,-0.12166,0.02867,-0.00025,-0.0607,0.03737,0.05723,-0.111,0.04712,0.10663,0.02063,-0.03915,0.06686,0.02498,-0.00491,-0.10866,0.03526,0.05578,0.04881,0.01852,0.01022,-0.03435,-0.0101,-0.0546,-0.08613,-0.07361,0.04875,-0.04758,-0.17249,0.01586,0.11862,-0.0717,-0.10356,0.07539,-0.04958,0.01592,0.01542,0.06171,-0.04886,-0.02521,0.10226,-0.00807,-0.01367,-0.01801,0.13245,0.02021,-0.00288,0.00316,0.00197,-0.0733,-0.02149,0.06036,0.1072,0.02903,-0.032,-0.05416,-0.00168,0.09499,0.07339,-0.00798,0.03396,-0.13348,-0.02597,-0.06508,-0.09889,0.05791,-0.03128,-0.01082,0.05962,-0.03498,-0.1417,0.0536,-0.08961,-0.06371,0.06657,-0.027,0.01692,0.00209,-0.01435,0.0328,-0.06409,-0.00099,0.06327,0.07366,-0.00795,0.03728,-0.05176,-0.00727,0.08684,-0.00175,0.0432,0.04264,0.05684,0.04065,0.00595,-0.05862,-0.05971,-0.08019,-0.04217,-0.03034,-0.03668,0.04194,0.0128,-0.01163,-0.00965,0.051,-0.09693,-0.03338,0.1067,0.06425,0.00021,-0.0739,0.02493,0.10931,0.05404,0.05625,0.01629,0.03861,0.11785,0.00332,0.00094,-0.01437,-0.08711,0.05211,-0.08147,0.02453,0.01542,0.08313,-0.01197,0.01373,0.01153,0.03951,0.13607,0.04456,0.04233,0.0591,0.05407,0.03293,-0.05345,0.09287,0.08585,0.07071,-0.08429,0.07801,-0.00993,-0.0465,0.01581,-0.0702,-0.07592,-0.04033,0.11743,0.04946,0.01844,0.02148,0.01581,-0.15615,-0.08232,-0.04511,0.06935,0.0266,0.06288,0.04506,0.02786,-0.09112,-0.05649,-0.06738,0.10546,-0.11524,-0.08575,0.01471,-0.07182,-0.00344,-0.0268,-0.08453,-0.04218,0.03763,0.00638,0.01122,-0.00652,0.02074,-0.05279,0.01414,-0.0206,0.07633,-0.00447,-0.01027,-0.05597,0.00773,0.07829,0.00698,0.04686,-0.06657,0.00515,-0.02663,-3e-05,0.02261,0.03228,-0.08539,-0.10383,-0.05694,-0.04804,-0.02949,-0.13406,0.05196,-0.02573,0.12311,-0.03225,0.02494,0.06756,-0.11716,0.04731,-0.03045,0.10958,0.13916,0.08517,-0.03061,0.03664,-0.05614,0.07524,0.11117,0.0078]},{"domain":"nuclear_engineering","key":"nuc_equilibrium_ratio","name":"Transient and secular equilibrium: activity ratio and approach","package":"nuclear-engineering-ai999x","example":"Equilibrium ratio: T_P = 237384.0 s, T_D = 21654.0 s","v":[-0.05063,-0.0244,-0.05916,0.07578,0.03756,0.01277,0.02492,0.06211,-0.01014,0.01539,0.07399,-0.03658,-0.0909,0.02314,-0.07021,0.00655,0.00565,-0.05224,-0.02472,-0.06895,-0.03377,-0.05992,0.01612,0.01627,0.14266,-0.01788,-0.1162,-0.04987,0.04627,0.04482,0.10447,0.06339,0.05729,-0.02907,0.03052,0.0606,0.03271,-0.00745,-0.00106,0.02667,0.09521,0.03446,0.03715,0.01605,-0.04817,0.07898,-0.01179,0.00992,-0.08781,-0.01208,-0.06301,0.177,0.07726,-0.00336,0.07868,0.05074,-0.03422,-0.09812,-0.03052,0.06283,-0.03344,-0.067,0.02325,0.00554,-0.02286,0.00671,-0.02466,-0.14987,-0.076,-0.14429,0.08764,0.02793,0.09737,-0.01845,-0.02437,-0.0018,-0.04789,0.07487,0.09179,0.05163,-0.09959,-0.03866,-0.08309,0.05398,-0.04414,-0.02256,0.05977,0.01,-0.0537,-0.0532,0.01794,-0.00609,0.02461,-0.03049,0.02489,0.10796,-0.01252,-0.04095,0.02501,0.0755,-0.01105,0.03443,0.03555,0.0804,-0.08289,-0.06118,0.00815,-0.04826,0.05419,0.01547,0.06237,-0.01925,0.13056,-0.1277,-0.00531,0.07345,-0.12584,0.07947,-0.09733,-0.01175,0.00471,-0.01565,0.11627,0.03445,-0.04724,0.12136,-0.04424,0.02159,-0.0656,0.00717,0.07381,-0.04239,0.05425,-0.10497,-0.08483,0.0366,0.01573,0.0883,-0.02117,-0.01189,0.09476,0.03137,0.13839,-0.08046,-0.02841,0.09442,-0.07107,0.05707,0.01009,0.09001,-0.0321,0.07378,-0.00946,-0.01372,0.1735,-0.06643,0.09124,0.04237,0.0275,-0.1179,0.04235,-0.05695,-0.01633,-0.01931,-0.08392,-0.0053,0.02439,0.03837,0.06699,-0.04221,-0.01779,0.02859,-0.05547,-0.03031,0.00265,0.04517,0.06904,0.0797,0.09058,-0.00762,-0.04986,0.01328,0.03788,0.02421,-0.04012,-0.03894,-0.04118,0.07331,0.07347,-0.03742,0.00229,0.08001,0.05414,-0.03457,-0.04349,0.04479,0.03635,0.02926,-0.01572,-0.00326,0.10474,-0.08844,0.05306,-0.04343,-0.04035,-0.07836,-0.01659,-0.11475,0.0133,0.00748,-0.12942,-0.08088,0.00223,0.05723,0.03692,-0.02298,-0.071,-0.02747,-0.14758,0.00243,0.07718,-0.08765,0.0051,0.00029,0.08504,-0.01466,-0.02072,-0.09783,0.07052,0.11642,-0.03375,-0.02776,-0.09872,-0.05296,-0.08303,-0.05425,-0.12901,0.04207,0.0879,-0.03672,0.03937,0.10686,0.07801,0.00509,0.05562,-0.0323,-0.02684,-0.09927,-0.03837,0.02295,0.07454,-0.03105,-0.02243,-0.00799,-0.02291,-0.00372]},{"domain":"nuclear_engineering","key":"nuc_escape_peaks","name":"Single and double escape peaks of a gamma ray","package":"nuclear-engineering-ai999x","example":"Escape peaks: E = 2614 keV","v":[0.0336,0.01266,0.05426,0.11663,-0.0106,0.00599,-0.00691,-0.01558,0.00773,-0.00427,0.00748,0.07187,-0.07247,0.01814,0.02065,0.06512,0.04555,0.11202,-0.0518,0.02945,-0.00078,0.06969,0.01595,0.02946,-0.06826,0.10819,-0.0236,0.0788,-0.08486,0.06856,0.01941,-0.04104,-0.05268,0.04781,-0.0106,-0.00538,-0.07143,0.0294,-0.03808,-0.14346,-0.03042,0.09189,0.01916,0.00953,-0.00289,0.01747,-0.0906,0.07694,-0.05777,0.1279,0.04715,0.0346,0.02609,0.12956,-0.02804,0.03789,-0.01113,0.06035,-0.06627,0.04642,-0.05231,-0.03551,0.03186,-0.04309,-0.06186,-0.00577,-0.08356,0.01781,0.04165,-0.07713,0.01917,0.04059,0.09852,-0.03989,0.08156,0.0559,-0.04931,-0.00066,0.00125,-0.0486,0.05561,0.04063,0.00539,-0.01694,-0.16627,-0.04045,-0.12597,-0.01108,0.01801,0.03506,0.06483,0.04119,0.11417,0.04116,0.06414,-0.00617,0.02452,-0.03915,0.06911,0.04016,0.03267,-0.05117,-0.16302,0.00023,-0.02472,-0.06641,0.03575,0.00056,-0.1466,0.01857,-0.0458,-0.01284,0.01543,-0.03683,-0.02237,0.016,0.00518,-0.18262,-0.00274,-0.0224,0.0457,-0.00437,-0.06303,-0.08968,-0.12589,0.09226,-0.04959,0.06811,0.03641,0.06595,0.02475,-0.01549,-0.11115,-0.01298,0.02325,-0.04329,-0.0408,-0.01876,0.01162,0.04926,-0.00048,0.03495,0.04707,0.02656,0.05391,0.06001,0.04533,0.02942,0.01917,0.10247,-0.00081,0.03309,0.04279,0.06544,0.00438,0.07786,-0.07341,0.04627,0.03802,-0.00701,0.03176,0.03305,0.01744,0.02128,-0.08812,0.00945,-0.14994,0.10644,-0.01528,0.04837,0.02679,0.0441,0.03301,-0.06516,0.06992,-0.10231,6e-05,0.11235,-0.00502,0.03382,-0.0981,-0.0519,-0.08249,-0.0128,-0.04041,0.08564,0.0054,-0.06731,0.1081,0.08914,-0.12263,-0.03806,0.00481,0.07776,0.04569,-0.03223,-0.03161,-0.11232,0.09201,-0.07491,-0.02102,-0.10148,0.11394,0.03145,-0.01202,-0.08115,-0.01901,0.00088,0.03975,-0.05462,-0.11053,0.12019,-0.03797,-0.11646,-0.06435,-0.04269,-0.08635,0.01932,0.01691,0.04455,-0.05324,-0.02657,-0.0101,0.02945,-0.01441,0.0271,0.04632,-0.02364,0.03111,0.03532,0.03563,0.04698,0.01776,0.00105,0.03521,-0.05132,-0.0374,0.04089,0.05825,-0.09433,-0.03397,0.14509,0.11764,-0.05467,-0.15649,-0.03714,-0.10514,-0.03091,0.08251,-0.04718,-0.05564,-0.02967,-0.0717,0.09708,0.0893,-0.10135]},{"domain":"nuclear_engineering","key":"nuc_exponential_pile","name":"Diffusion length from an exponential pile measurement","package":"nuclear-engineering-ai999x","example":"Exponential pile: z = [20.0, 40.0, 60.0, 80.0, 100.0], phi = [10000.0, 6200.0, 3850.0, 2390.0, 1480.0], a = 2 m, b = 2 m","v":[-0.15578,0.02813,-0.04249,0.06464,-0.0118,0.00233,-0.0964,0.01578,-0.00488,0.12016,-0.03657,-0.06826,0.00764,0.00469,-0.06154,-0.01214,0.05423,0.09528,0.01653,-0.02278,0.16753,0.03082,-0.0508,0.04491,0.1214,-0.04172,-0.13784,0.0523,0.05311,0.18604,-0.02041,0.09088,-0.00369,0.01473,0.15081,0.07036,0.06465,0.05856,0.01157,0.00714,-0.05264,-0.07964,0.06356,-0.0695,0.01624,-0.06789,0.0524,-0.04209,0.04484,-0.03169,-0.02093,0.14253,0.10498,0.0591,-0.15126,0.0404,0.10496,0.12881,0.04226,0.00255,-0.02457,0.00774,-0.02196,-0.00816,-0.09659,-0.008,0.00544,-0.01577,-0.06042,-0.02574,0.02669,-0.02256,-0.00317,-0.03274,-0.00699,0.04543,-0.02617,0.0023,-0.0141,-0.13241,0.00797,-0.07244,-0.02224,0.07041,0.01281,-0.00882,-0.09687,-0.05082,0.05228,0.01291,-0.03508,-0.06392,0.00453,0.07223,0.00785,-0.05596,0.05909,-0.0515,0.07459,0.08384,-0.03863,0.15041,-0.07055,0.01344,0.08292,0.01436,-0.05201,-0.11781,-0.05532,0.0692,-0.00121,0.00074,0.11636,0.10031,-0.03901,-0.09962,0.02191,0.01074,-0.04036,0.07392,0.09571,0.02479,-0.06981,0.09551,-0.05768,0.1145,0.01729,0.04416,-0.03328,-0.03772,0.03039,-0.05017,-0.00229,-0.09938,0.00742,0.08673,0.02227,-0.02415,0.00329,0.02237,-0.00026,-0.03981,0.03796,-0.04796,-0.06257,-0.00631,-0.0033,0.02917,0.01341,0.10966,-0.0849,-0.04903,0.0476,0.03016,0.01296,-0.0155,-0.06013,0.06455,-0.02856,-0.02912,-0.00986,-0.0217,-0.11021,0.02508,0.02269,-0.03077,-0.06358,-0.00203,-0.07577,0.02183,-0.09457,0.0599,0.03013,0.11321,-0.00948,0.00041,0.02114,0.0226,0.03365,-0.01601,-0.08133,-0.0483,-0.07228,-0.07975,0.00791,0.09294,-0.01507,0.03537,0.04479,0.00599,-0.0201,-0.01555,0.07874,0.011,0.00269,-0.06263,-0.00873,-0.08893,0.00023,-0.04461,0.0858,-0.1367,-0.00731,-0.1245,0.05124,-0.09515,0.04343,-0.00504,0.13332,0.04605,-0.12474,0.01097,0.03492,-0.07018,0.08358,0.04945,0.09531,0.00484,0.029,-0.05521,-0.06045,-0.07664,-0.02359,-0.01319,-0.00321,-0.10647,-0.04014,0.05966,0.03956,-0.05203,-0.02697,0.05594,0.02666,-0.00691,0.01691,-0.04226,0.00884,0.05734,0.0293,-0.00595,0.01637,0.05485,0.07588,-0.05017,-0.0007,-0.0801,-0.04799,0.05049,0.01976,-0.05195,0.06065,-0.11181,0.03815,-0.00717,0.12701,-0.08903]},{"domain":"nuclear_engineering","key":"nuc_flux_from_foil_activation","name":"Neutron flux from a measured foil activation","package":"nuclear-engineering-ai999x","example":"Flux from foil activation: A_d = 20 kBq, m = 0.1 g, M = 196.97 g/mol, theta = 1.0, sigma = 98.65 b, T_half = 2.695 d, t_irr = 1 h, t_d = 30 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flux shape of a bare reactor at a point","package":"nuclear-engineering-ai999x","example":"Flux shape: geometry = cylinder, R = 1.5 m, H = 3 m, r = 75 cm, z = 50 cm","v":[-0.05207,-0.01445,-0.02714,-0.03773,0.02037,-0.00716,-0.119,0.01262,0.05719,0.01189,-0.01094,-0.11635,-0.04746,0.0191,-0.01171,0.05315,-0.00364,0.07698,0.02651,0.02792,0.10143,-0.11293,-0.03533,0.00753,0.04484,-0.06411,-0.14564,-0.03795,0.0583,-0.04931,0.08192,0.05897,0.06332,-0.08119,-0.00755,-0.01831,0.07266,-0.05729,-0.13802,0.02376,-0.04037,-0.02319,0.02808,0.12817,0.01844,-0.06354,0.02549,-0.01477,-0.06749,-0.10936,0.00958,-0.02615,-0.0361,-0.00086,-0.10355,0.02878,0.00709,0.04963,-0.10139,-0.01935,-0.0151,-0.01305,0.02001,-0.09221,-0.00131,0.04241,-0.03307,-0.01519,-0.04515,0.03542,0.00855,0.03052,-0.00655,0.01537,-0.00617,0.10934,-0.05114,-0.0556,-0.05119,-0.12769,0.04055,-0.03239,-0.10359,0.1028,0.03589,-0.06211,-0.04437,-0.08621,0.03959,-0.08421,-0.00083,0.00687,0.09089,0.08305,0.06654,0.1988,-0.00446,-0.05953,0.05754,0.02121,-0.0292,-0.03308,-0.0508,-0.04628,0.02904,0.0401,0.01891,-0.01755,0.01603,0.0818,-0.10359,-0.01549,0.08951,0.02646,0.02816,-0.07485,0.12088,-0.02144,-0.09336,-0.011,0.0532,-0.11494,-0.03767,-0.0044,0.03831,0.06344,0.10249,0.01932,0.0669,-0.0044,-0.03378,-0.02862,0.11469,-0.01067,0.00247,0.02887,0.03861,-0.01753,-0.04747,0.06964,-0.10166,-0.10046,0.00189,-0.04877,-0.0885,0.05676,0.09792,0.04989,-0.01489,0.12677,-0.07741,-0.02566,0.08254,0.08099,0.02779,0.02946,-0.0521,0.13329,-0.00032,-0.00186,0.00041,0.00522,-0.0618,-0.07813,0.01552,-0.05718,0.01479,-0.08844,0.04372,0.06062,0.05417,0.00226,0.00843,-0.07498,-0.04449,-0.01503,-0.0453,-0.03737,-0.00515,-0.04766,-0.06388,0.04422,-0.01326,0.06793,0.0448,-0.07885,-0.0646,0.12279,0.16852,0.03997,-0.02337,-0.04144,0.08957,0.07311,-0.07426,0.05126,0.0968,0.00016,0.02266,0.06995,-0.02023,0.06191,0.0792,-0.07981,0.04234,-0.0963,-0.0624,0.03978,0.06409,0.04972,-0.06917,0.01201,0.15542,-0.04398,-0.11926,-0.08894,-0.0019,-0.00098,0.08542,-0.101,0.02297,-0.0961,-0.00914,0.06663,-0.00738,0.06166,-0.01399,-0.00784,0.07756,0.00133,-0.04395,0.05517,-0.00144,0.01334,-0.0189,-0.00621,-0.02675,0.11685,-0.03891,0.01719,0.04495,0.064,0.10889,0.03376,-0.05101,-0.119,-0.01905,0.05959,-0.01099,0.00092,0.07154,-0.08463,0.05468,0.06278,-0.04316,-0.06152]},{"domain":"nuclear_engineering","key":"nuc_fuel_cross_sections","name":"Number densities and macroscopic cross sections of UO2 fuel","package":"nuclear-engineering-ai999x","example":"Fuel cross sections: rho = 10.4 g/cm^3, w = 3%, sigma_a5 = 680.9 b, sigma_f5 = 582.6 b, sigma_a8 = 2.68 b, sigma_aO = 0.00019 b, nu = 2.43","v":[0.07922,-0.00661,-0.08888,-7e-05,0.06953,0.03534,-0.03214,-0.0355,0.06273,-0.01241,0.05145,0.01914,0.03028,0.0835,-0.05049,0.07024,0.02591,0.01614,0.11584,0.07453,0.02523,-0.08748,-0.0228,-0.01352,0.07228,-0.01689,-0.0366,-0.0635,-0.05849,0.04601,0.019,0.00578,-0.00961,-0.00693,0.05923,0.08435,0.0922,0.00694,0.10394,0.07556,0.01679,0.08047,-0.01128,0.03029,-0.00638,-0.0016,-0.11963,0.02822,0.07769,-0.09795,-0.07211,0.02421,0.11513,0.18631,-0.11379,-0.12229,0.01443,0.00522,-0.00252,0.02565,-0.03763,0.07835,0.00883,0.00862,0.06874,0.07441,0.0227,-0.09627,-0.00866,-0.07141,-0.07391,0.02216,-0.05369,-0.06412,0.08062,0.12134,0.091,0.00452,0.07365,0.10247,0.08038,-0.15374,-0.10378,-0.00309,0.00999,-0.01694,0.0753,0.03461,-0.04867,0.02663,-0.04552,-0.02908,0.09274,-0.00991,-0.15998,0.03495,-0.15655,-0.07659,0.03912,-0.011,-0.00408,-0.01579,-0.04594,-0.15831,0.07673,-0.11104,0.06262,-0.00918,0.04824,0.0325,-0.01743,-0.02707,-0.02235,-0.00567,-0.0688,-0.09571,0.00067,0.02459,0.00402,-0.02671,0.00963,-0.05699,-0.08323,0.08829,0.05425,-0.00479,0.0773,-0.01557,0.05346,-0.00443,-0.07574,0.01901,-0.09933,-0.04749,0.01943,-0.02094,0.03315,-0.10053,0.12567,0.05525,0.0585,-0.06355,0.08217,0.0296,-0.06537,0.03394,-0.05572,-0.07871,0.09808,0.01505,-0.00075,0.07686,0.01341,-0.03023,0.02843,-0.03828,-0.04489,-0.05865,-0.00446,0.00566,-0.02984,-0.00799,0.08536,-0.00017,0.06102,-0.03035,0.02788,-0.00715,0.00104,-0.01134,-0.06463,-0.00196,-0.03048,0.04273,0.04076,0.00265,0.09651,-0.01815,0.1731,0.00879,0.00029,-0.00018,-0.0678,0.06342,-0.0782,-0.02444,0.05324,0.09318,0.0504,0.03902,-0.0509,0.0261,0.0138,-0.08417,-0.04428,-0.02718,0.08093,-0.08708,-0.19347,0.0045,-0.13102,0.0397,0.04143,-0.0292,-0.09877,-0.0931,0.09189,-0.03879,-0.03183,0.03078,0.00311,0.01882,0.04155,0.01965,-0.14305,0.00377,-0.01584,0.0158,0.00493,0.07232,-0.07378,-0.00805,-0.05491,0.01177,-0.05184,0.01849,-0.03462,0.03522,-0.00734,0.07497,-0.01253,0.16885,0.00112,-0.11508,-0.04614,-0.06976,-0.02188,-0.04622,-0.02919,-0.02131,-0.013,0.02513,-0.00279,0.05545,0.00949,-0.03026,0.03117,0.0308,0.09273,-0.03688,0.01834,-0.03343,-0.05212,-0.0022,0.05968,-0.02009]},{"domain":"nuclear_engineering","key":"nuc_fuel_rod_temperatures","name":"Fuel-rod radial temperatures: centreline, pellet surface and cladding","package":"nuclear-engineering-ai999x","example":"Fuel rod temperatures: q_lin = 200 W/cm, R_f = 4.1 mm, k_f = 3 W/(m*K), h_g = 5000 W/(m^2*K), t_c = 0.57 mm, k_c = 15 W/(m*K), h = 34000 W/(m^2*K), T_cool = 580 K","v":[-0.06516,0.01482,-0.00994,-0.11281,-0.02926,-0.07988,-0.05743,0.06221,0.04217,0.04091,0.05691,-0.04877,0.04953,-0.04902,-0.06269,0.10282,0.04454,0.0007,-0.00641,0.04601,0.07514,-0.01616,-0.09022,-0.06198,0.07553,0.01585,-0.03642,-0.01337,0.07052,-0.0744,0.06441,-0.02379,0.05432,-0.02859,-0.0193,0.06731,0.09931,0.03856,-0.04901,0.03376,0.03388,-0.10106,-0.05236,0.11339,0.02018,0.09211,0.0504,-0.05492,0.01322,-0.07992,-0.0548,0.05477,0.09283,0.07245,-0.15114,-0.0819,0.05059,0.05958,0.05784,0.00056,-0.08775,0.03302,0.01251,-0.03552,0.04423,0.07809,-0.02729,-0.01337,0.0157,0.0179,0.00156,-0.01421,-0.05107,0.0478,0.02424,0.09093,-0.04926,-0.01208,-0.09466,-0.07269,0.06052,-0.07201,-0.03333,0.0436,0.03453,-0.10401,-0.13274,0.03132,-0.11088,-0.01822,-0.03464,0.11661,-0.03403,0.0886,-0.06736,0.09276,-0.03081,-0.0809,-0.01777,-0.0246,0.03622,-0.11375,0.00617,0.00451,0.07696,0.10455,0.05884,-0.07858,-0.05349,0.13267,-0.10708,-0.00536,-0.01858,0.05819,-0.03359,-0.01051,0.12416,-0.07614,-0.04982,-0.11643,-0.02021,-0.03517,-0.0125,0.08332,-0.07407,-0.08388,0.07212,0.11444,-0.0554,-0.12587,-0.11209,-0.07034,-0.01279,0.0637,0.00788,-0.01086,0.06169,-0.08411,-0.05612,-0.10873,-0.09952,-0.08878,-0.02328,0.01845,-0.00803,0.11527,-0.05954,0.04241,-0.03029,0.10327,0.03003,0.0445,0.05659,0.0567,0.04246,-0.1185,0.01898,0.06145,-0.06153,-0.01876,-0.03632,0.05482,-0.00035,-0.00349,0.00582,0.00016,-0.04357,-0.08977,0.05194,0.05692,-0.09672,0.01776,-0.02803,-0.04233,-0.0293,0.05126,-0.02171,-0.11247,-0.02223,0.08664,-0.01899,-0.01401,-0.03167,0.04322,-0.00731,-0.03346,0.02093,0.02015,0.08594,0.06612,-0.13119,0.10489,-0.05711,0.04638,0.04038,0.06225,-0.02977,0.0131,0.07129,0.00398,-0.0004,0.00788,0.05598,0.03652,-0.06425,-0.03221,-0.02987,0.0948,-0.03634,-0.03986,0.10083,-0.01858,0.08588,0.06021,-0.10981,-0.06851,0.02643,-0.04642,0.01547,0.02652,0.01124,-0.02706,-0.05928,0.11199,-0.05632,0.03696,0.03255,0.05918,-0.03654,0.02724,-0.04329,-0.01101,0.02026,-0.01403,-0.09314,-0.0936,0.03726,0.05284,-0.0947,0.1357,0.03294,-0.03285,0.02302,0.0186,-0.02399,0.02638,-0.13347,-0.013,-0.00556,0.08511,0.06054,0.03723,0.0218,0.04803,0.03096,0.08932]},{"domain":"nuclear_engineering","key":"nuc_generator_daughter_activity","name":"Radionuclide generator: daughter activity after elution (with branching)","package":"nuclear-engineering-ai999x","example":"Generator daughter activity: A_P0 = 1 Ci, T_P = 65.94 h, T_D = 6.015 h, b = 0.8773, t = 24 h","v":[0.01823,0.03604,0.01676,-0.08997,-0.06524,-0.02546,-0.05721,0.03078,0.05389,0.0125,0.1325,-0.03171,0.00065,-0.01069,0.06581,0.04365,0.03804,0.03383,-0.05432,0.06453,0.06782,-0.02967,-0.13935,0.03821,0.05536,0.07195,-0.12927,0.01084,0.20035,0.06462,0.06763,-0.04406,0.07092,0.0212,-0.10215,0.08298,-0.04505,-0.04829,-0.03362,-0.04843,-0.00376,0.09276,0.01205,0.02264,-0.01577,0.00221,0.09796,0.01238,-0.12814,-0.07736,-0.1099,0.15757,0.07765,-0.04439,-0.00821,0.12693,-0.0926,-0.06025,-0.04462,0.11497,0.0247,0.00743,0.06768,-0.17219,-0.08638,-0.01691,-0.11161,-0.03364,-0.08893,-0.15856,-0.03113,0.01245,0.06124,0.01564,0.07285,-0.01134,-0.0067,0.01604,-0.06489,-0.0358,-0.00252,0.01206,-0.00848,0.07419,-0.13662,0.00653,-0.02741,0.0158,-0.04612,-0.06004,-0.07995,0.00438,0.03159,0.07078,0.01404,0.14301,0.01417,0.01469,0.0186,-0.00026,0.00922,-0.05149,-0.02809,0.07546,-0.01615,0.04819,-0.075,-0.0109,-0.01695,0.05499,0.00672,0.05926,0.02912,0.0476,0.03365,0.04107,-0.03148,-0.0417,-0.01118,-0.07932,0.11145,0.03306,-0.00588,0.10157,-0.16443,-0.01294,0.00569,0.02808,0.04179,-0.03111,-0.03666,-0.04454,0.11947,-0.01359,0.04112,0.03917,0.03257,-0.05964,-0.06613,-0.00552,-0.00236,-0.00493,0.06016,-0.06489,-0.04465,0.02929,-0.02275,0.1057,0.06347,0.1659,-0.10107,-0.00435,-0.02125,0.0665,0.0777,-0.07245,0.01013,0.05559,-0.00661,-0.03824,-0.08387,-0.00941,0.0617,0.04497,-0.029,0.01089,-0.03093,0.06133,-0.02015,0.03179,0.0249,0.00786,0.07539,-0.02209,-0.06422,0.03464,0.0198,0.04478,0.06726,0.13443,-0.06569,-0.04238,0.04131,-0.02141,0.02466,0.01963,0.00316,-0.06006,0.07957,-0.01643,-0.07971,0.02934,-0.0086,0.08396,0.01435,0.0834,-0.0175,-0.00337,0.15553,0.06172,0.00691,-0.01098,-0.03659,0.01503,0.0623,-0.06977,-0.01117,0.008,0.12499,-0.10128,-0.0507,-0.0223,-0.06238,0.00306,-0.06992,-0.07028,-0.1174,0.0044,-0.01216,-0.02701,-0.01343,-0.03886,0.0305,0.02778,-0.05633,-0.0541,0.00832,-0.03336,-0.02116,0.0087,0.02117,0.01699,-0.02909,-0.05726,0.09051,-0.01438,-0.01609,0.02986,0.02356,-0.02793,0.00966,0.08846,0.02756,0.01936,-0.07547,-0.08455,-0.15058,0.03883,0.06448,0.00573,0.03668,-0.11109,-0.03268,0.00431,-0.07101,-0.09343]},{"domain":"nuclear_engineering","key":"nuc_half_value_layer","name":"Half-value and tenth-value layers","package":"nuclear-engineering-ai999x","example":"Half-value layer: mu = 0.656 1/cm","v":[0.01188,0.06642,0.00884,0.02692,0.06761,0.05997,-0.01897,0.08416,0.06472,-0.00126,0.11054,-0.02915,-0.04356,-0.03774,-0.03521,0.10681,0.08732,0.01866,0.08832,0.03852,-0.05221,-0.03423,-0.10449,0.00568,0.05522,-0.00441,-0.00744,0.00884,-0.05018,0.02496,-0.03341,0.12607,0.0423,-0.03156,-0.00749,-0.04741,0.03019,-0.01422,0.02295,0.15035,-0.133,0.0011,0.08695,-0.05013,-0.05943,0.03574,-0.06626,-0.03905,-0.13666,-0.04759,0.01943,-0.04599,-0.02148,-0.01274,-0.00457,-0.03406,0.10095,0.0441,-0.02597,0.07825,-0.07522,0.02283,0.06403,0.01379,0.03058,0.06777,0.04966,0.0273,0.13663,-0.02838,-0.03265,-0.02097,-0.06016,-0.0309,0.1008,-0.00978,-0.13858,0.01282,0.07705,-0.01825,-0.02458,-0.02014,-0.05042,0.06862,0.02922,-0.08597,-0.03262,-0.02922,0.06274,0.02841,0.00448,-0.05779,-0.02299,-0.11345,-0.00289,-0.04294,-0.10351,-0.01806,0.0288,0.03702,-0.02051,-0.05488,-0.01578,-0.11467,0.11319,0.00553,0.06001,-0.09423,0.00489,-0.06644,0.04237,-0.02402,0.04487,-0.059,-0.13332,-0.06098,-0.04302,-0.11237,0.02799,0.01,0.02976,0.03723,0.01345,0.08675,-0.0738,-0.02057,0.0295,0.04517,0.03918,0.02805,-0.05169,0.09417,0.07475,0.01885,-0.05872,-0.01796,0.04051,-0.11906,0.02026,0.09403,0.0323,-0.06328,0.15239,0.00836,-0.07833,-0.13161,0.02136,-0.01122,-0.02181,-0.07712,-0.07083,0.01956,0.09069,-0.01229,-0.0165,0.0804,-0.03737,0.03978,-0.08049,0.00756,-0.02122,-0.05539,0.02023,-0.02239,-0.05295,-0.16655,-0.01354,-0.18528,-0.02239,-0.02036,0.01039,-0.02601,-0.05645,-0.03471,-0.00387,-0.13586,0.02321,0.04379,0.05012,0.00666,0.03462,0.03625,-0.05456,-0.05831,0.06429,0.0784,0.03888,0.0481,0.09231,0.08429,-0.00933,0.11592,-0.09899,-0.05601,-0.03107,-0.06018,-0.03783,0.01302,-0.02173,0.10925,0.05292,-0.02164,-0.01166,0.00964,0.05165,-0.04307,0.1231,-0.01447,-0.01048,0.06105,-0.02735,0.06548,0.09161,-0.05061,-0.06829,-0.00328,0.0607,0.00837,-0.03003,-0.02284,-0.00408,-0.03723,-0.02371,-0.12139,-0.08074,-0.07411,0.14588,0.09856,0.04158,-0.02877,0.04119,0.0743,-0.03513,-0.02792,0.11381,-0.03875,0.01176,0.02141,0.11344,-0.11655,-0.09065,0.11676,0.02304,-0.00368,0.02076,-0.04002,0.00234,0.01008,0.05339,-0.04188,-0.05961,0.07114,0.08373,-0.01529,-0.01432,-0.03379]},{"domain":"nuclear_engineering","key":"nuc_inverse_multiplication","name":"Approach to criticality: inverse multiplication (1/M) extrapolation","package":"nuclear-engineering-ai999x","example":"Inverse multiplication: x = [0.0, 20.0, 40.0, 60.0, 80.0], C = [100.0, 125.0, 167.0, 250.0, 500.0]","v":[-0.10952,0.16256,-0.07095,0.02706,0.10148,0.06409,-0.13373,0.04181,0.10975,-0.08819,-0.00357,0.12037,-0.09772,-0.04615,-0.00324,0.11456,-0.00904,0.06084,0.06213,0.05749,0.02237,-0.00218,-0.06186,-0.00776,-0.00395,0.03864,-0.02834,0.02894,0.08298,-0.00012,-0.10817,-0.0388,0.00493,0.09723,0.03682,0.03784,0.04053,0.08431,0.0303,-0.02696,0.00462,0.00519,-0.05021,-0.02296,-0.00511,-0.04531,-0.03974,-0.00926,-0.03229,-0.09191,0.01923,0.01185,0.05702,0.03235,-0.12621,-0.03165,-0.00468,0.05432,0.01136,0.00154,0.01687,0.08029,-0.10071,-0.06417,-0.00253,0.10168,-0.08177,0.08114,-0.01786,0.02496,-0.01548,-0.06754,0.11184,-0.01081,0.05639,0.1369,-0.00036,0.07682,-0.03518,0.10809,0.09964,-0.07649,-0.12789,0.04482,-0.00188,-0.05124,-0.16363,-0.02075,-0.11963,-0.0497,0.00515,-0.01427,0.09142,0.02705,-0.04541,0.06473,0.01801,-0.02413,-0.00612,-0.02607,0.01506,-0.04255,-0.15151,-0.05243,0.04475,-0.07646,0.01298,-0.0455,-0.08812,0.05063,-0.13612,-0.01456,-0.03924,0.01221,-0.02382,0.0111,0.01796,-0.02054,0.06047,0.00618,0.01881,-0.03503,0.06124,0.03544,-0.03213,0.1178,0.03989,-0.00075,-0.03873,-0.08296,-0.05839,0.04526,-0.03583,-0.06708,0.0459,-0.04924,-0.06356,0.02082,-0.00019,-0.03327,-0.05269,0.01915,0.03144,0.04636,-0.10654,0.04708,0.02081,0.08306,0.15202,0.01622,-0.09186,-0.06365,0.05336,-0.01557,0.08246,-0.06968,-0.10236,-0.03445,-0.00239,0.05682,-0.02366,0.06314,0.04792,-0.01769,0.09657,0.02619,-0.03692,-0.03056,0.02459,0.0664,-0.05863,-0.00903,0.02649,0.04367,0.10259,0.03012,0.0039,-0.11129,0.06315,0.04598,-0.09674,-0.05316,0.05388,-0.07492,0.00644,0.04605,0.01039,0.06344,0.0182,0.13344,-0.04065,0.00286,0.01693,0.07531,-0.00492,0.06502,-0.02684,-0.04462,0.03991,-0.03846,-0.01014,-0.06351,-0.07745,-0.04451,-0.086,0.00618,-0.10016,-0.03792,-0.06211,0.01346,-0.01748,0.03952,0.00623,-0.06486,0.00749,0.07238,0.06085,-0.02473,-0.02316,0.16715,-0.00724,-0.03413,-0.02206,0.10653,0.03067,0.09866,-0.07676,0.01561,-0.04696,0.08219,-0.05456,0.11881,0.04917,-0.10961,0.01498,-0.04146,0.13569,0.04576,-0.08702,-0.02861,0.03833,-0.00449,0.04291,-0.0213,-0.10872,-0.05711,-0.00046,0.04079,0.03926,0.02161,-0.05987,0.03911,-0.00336,0.05445,0.05804,-0.03947]},{"domain":"nuclear_engineering","key":"nuc_irradiation_time_for_saturation","name":"Irradiation time to reach a fraction of saturation activity","package":"nuclear-engineering-ai999x","example":"Irradiation time for saturation: T_half = 15 h, f = 90%","v":[0.06389,0.05369,-0.07183,0.03256,-0.11601,0.08649,-0.04513,-0.06038,0.04291,0.05595,0.0482,0.1772,0.03071,0.00342,-0.09501,0.00138,-0.03131,0.0553,0.04558,0.08495,-0.00809,-0.00785,-0.13455,0.00839,0.12889,0.01834,-0.13588,-0.01174,0.11366,0.02757,-0.05335,0.1085,-0.07454,-0.03695,0.01118,-0.02463,0.0412,-0.02474,-0.07078,0.09667,0.03683,-0.03157,0.03312,-0.02461,0.05417,0.04847,0.02832,0.02929,-0.00029,0.03955,-0.04958,-0.0503,-0.04363,0.01059,-0.01428,0.08731,-0.05457,0.07958,-0.08214,0.08366,-0.00796,0.17859,-0.05282,-0.04055,-0.1354,0.03801,-0.04671,-0.04895,0.11035,-0.08464,-0.04768,-0.01666,-0.08765,0.00536,-0.04785,0.00225,-0.10055,0.03374,-0.05806,-0.00115,-0.0285,0.0508,-0.02352,0.06897,0.02462,-0.06049,0.06356,-0.0479,-0.01569,-0.00772,0.00221,-0.00392,0.05706,-0.06504,0.09558,0.06182,0.02202,-0.09143,0.00903,0.02915,0.00096,-0.03098,-0.06086,0.0162,-0.07559,-0.0248,-0.06893,-0.0892,-0.01081,-0.06788,-0.06137,-0.03029,0.04657,-0.01105,0.03334,-0.03828,-0.05956,0.02094,-0.07211,0.08034,0.02977,0.01958,0.01244,-0.08781,-0.14763,0.08356,-0.03625,0.05979,-0.04743,0.09278,0.01686,0.0233,-0.01624,0.01066,-0.03562,0.02013,0.04494,-0.01852,0.04067,0.10554,0.02436,0.03177,0.03218,-0.03468,-0.17485,-0.06607,0.01469,-0.04226,0.07762,0.05122,0.01514,0.01388,0.05753,0.05254,-0.0055,-0.03499,-0.01263,0.04988,-0.02136,-0.02216,0.02099,0.08232,0.0003,-0.06305,-0.08063,-0.09597,0.12503,0.1094,0.00641,0.09012,-0.03653,0.01236,-0.04147,-0.03384,-0.0297,-0.0762,0.08385,0.12475,0.13917,-0.04827,-0.05972,-0.0121,-0.06758,-0.03281,0.00568,0.04077,0.11254,0.07513,0.04183,0.057,-0.19011,-0.05464,-0.03391,-0.0908,-0.00917,0.05845,0.06344,-0.05116,-0.01132,0.17257,0.02314,0.11547,0.04708,-0.00879,0.00102,-0.0977,0.03139,0.03399,-0.07222,-0.02722,0.02301,0.00233,0.07954,-0.03422,-0.02623,0.08088,-0.06523,-0.01697,-0.05414,0.06662,-0.06254,-0.06167,-0.0412,-0.12667,0.00837,-0.02962,0.12069,-0.00514,0.04729,-0.07226,0.04299,0.05733,-0.09398,0.01081,0.00023,-0.06704,-0.02628,0.03417,-0.04,-0.09074,-0.02416,-0.02147,-0.03923,0.07661,-0.00843,0.00327,-0.03908,-0.02449,0.04865,0.0116,0.03537,-0.00941,0.02303,0.04392,0.01358,-0.0042]},{"domain":"nuclear_engineering","key":"nuc_klein_nishina","name":"Klein-Nishina Compton cross sections per electron","package":"nuclear-engineering-ai999x","example":"Klein-Nishina cross section: E = 0.662 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flux from a shielded line source (Sievert integral)","package":"nuclear-engineering-ai999x","example":"Line source flux: S_L = 1e8 1/(m*s), h = 1 m, y1 = -2 m, y2 = 2 m, mu = 0.1 1/cm, t = 10 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logarithmic energy decrement and mean scattering cosine","package":"nuclear-engineering-ai999x","example":"Logarithmic energy decrement: A = 12.0","v":[0.03501,-0.01618,0.08123,-0.02279,0.01734,0.02054,-0.09137,0.06237,0.01025,0.05406,0.12844,-0.02972,-0.04989,-0.02359,0.02111,0.14783,0.08138,-0.00898,-0.03344,-0.00474,0.06407,0.08228,-0.01564,0.00118,-0.00712,0.05242,-0.03226,0.01367,-0.00638,0.0461,-0.09521,0.00865,0.05649,-0.03764,0.01503,0.02214,-0.01282,-0.05169,0.06626,0.07949,-0.12062,0.07118,0.02317,-0.04775,0.02613,0.0369,0.00893,-0.0393,-0.0103,-0.04102,0.00363,-0.01266,-0.00471,0.04845,-0.03828,-0.04169,0.00261,0.02104,-0.11299,0.01593,0.00655,0.08618,0.0015,0.11239,0.1219,0.09159,-0.06639,0.03032,0.03223,0.01984,-0.00915,-0.03865,0.07731,-0.06825,0.00104,0.06725,-0.02214,0.07319,-0.01219,0.05038,0.05322,0.01876,0.003,0.04465,-0.05998,-0.06461,0.02248,0.04664,0.05468,-0.05345,0.05972,-0.05838,0.14961,-0.15147,-0.04788,0.04687,-0.02737,0.02082,0.06454,0.06538,0.00075,-0.00078,-0.13292,-0.05665,0.01318,-0.12375,0.02054,0.00729,-0.04532,-0.06122,0.02642,0.05077,0.14007,-0.15456,-0.16903,-0.02258,-0.02749,0.00542,-0.04053,-0.01234,-0.02368,-0.03182,0.09071,0.12147,-0.15128,-0.04217,-0.07568,-0.01255,-8e-05,0.01046,-0.04737,-0.05246,0.00633,-0.11819,-0.05037,-0.01018,-0.01456,-0.00147,0.01822,0.0219,0.1304,0.00416,0.16232,0.01466,-0.04169,0.01176,0.04663,0.06314,-0.09808,-0.03407,0.00311,-0.0394,0.0491,-0.12457,0.09323,-0.02478,-0.01383,-0.05361,0.05249,0.05864,-0.01352,0.08943,0.07561,0.1159,-0.027,-0.01154,-0.06102,-0.10207,0.07805,-0.00344,-0.02487,0.03245,0.03387,-0.08884,-0.00417,-0.10781,0.07438,0.05659,-0.08368,-0.04596,-0.05682,0.07797,-0.0473,0.01085,0.07463,-0.01489,-0.10167,0.02841,0.06975,0.13735,-0.13687,-0.0624,0.08827,0.02264,-0.03133,-0.05152,-0.06741,-0.04922,0.00582,-0.03663,-0.07526,-0.07822,-0.11056,-0.06437,-0.02387,-0.07653,0.09075,0.05345,0.03417,-0.0418,-0.08975,-0.01918,0.00788,-0.06109,-0.06684,-0.07566,0.0425,0.01602,0.05967,0.08759,-0.06624,-0.01852,0.06187,0.02374,0.04247,-0.03651,0.02288,0.07326,0.00126,-0.01381,0.07868,0.11965,0.03034,0.02328,0.0179,-0.06206,-0.00735,0.0272,0.04043,-0.01641,-0.00558,0.09867,0.08778,0.05289,0.02439,0.01124,0.08034,0.02029,-0.06978,0.01284,-0.1099,0.07644,-0.01711,-0.0137,0.03897,-0.03925]},{"domain":"nuclear_engineering","key":"nuc_mass_for_activity","name":"Mass 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power and ratio of a compound moderator","package":"nuclear-engineering-ai999x","example":"Moderator mixture: n = [2.0, 1.0], A = [1.0, 16.0], sigma_s = [20.0, 3.8], sigma_a = [0.332, 0.00019], rho = 1 g/cm^3, M = 18.015 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transmission through a multilayer shield","package":"nuclear-engineering-ai999x","example":"Multilayer transmission: mu = [0.656, 0.149], x = [5.0, 30.0]","v":[0.06429,0.04389,0.03953,-0.02141,0.06167,0.03363,-0.03655,0.06218,0.05059,0.02686,0.13705,-0.03659,0.04394,-0.11861,-0.03131,0.03865,0.06471,0.01669,0.03756,0.11906,-0.03246,-0.10326,-0.04851,0.0294,0.05215,-0.02246,-0.00389,0.02238,-0.04349,0.00227,0.08505,0.05337,0.00973,-0.06182,-0.06672,0.02855,0.05468,-0.00459,-0.03401,0.15293,-0.07882,0.03373,0.01668,-0.06539,-0.04158,0.05887,-0.12805,0.0206,-0.04267,0.07169,0.00462,-0.05675,-2e-05,-0.04305,0.08908,-0.02747,0.10704,0.02238,-0.08234,0.05522,-0.08738,0.07885,0.04259,-0.00823,-0.05229,0.14706,0.03301,0.00239,0.09652,-0.04273,0.08266,-0.06136,0.01957,0.00508,0.0092,0.00515,-0.04627,0.05488,0.01698,0.07571,0.09886,-0.075,0.00347,0.09998,-0.05264,-0.12752,-0.09699,0.04967,0.12814,0.02367,-0.03419,-0.0237,-0.0734,-0.11112,0.03812,0.04113,-0.102,0.04467,0.06018,-0.03062,0.07384,-0.09178,-0.03357,-0.10406,0.07927,-0.06738,0.1127,-0.12464,0.0255,0.05613,0.03013,0.01393,0.03872,-0.04151,-0.08996,-0.00423,-0.09973,-0.15809,0.0053,0.01107,-0.05195,0.13052,0.01172,0.07827,0.00679,-0.06922,-0.04458,0.05491,0.03619,-0.02253,-0.02791,0.0722,0.00746,-0.03175,-0.07264,-0.05221,-0.00859,-0.05221,-0.05049,0.1015,0.02408,-0.09767,0.00983,0.04177,0.00517,-0.03427,0.03612,0.01868,-0.08062,-0.03879,-0.06228,0.05865,0.03612,0.022,0.0423,0.02671,-0.08478,0.01447,-0.02641,0.0312,0.02095,-0.07752,0.06476,0.02816,0.00928,-0.08653,0.01054,-0.12327,-0.07872,-0.07605,0.03194,-0.00754,-0.10704,-0.01002,-0.01586,-0.0494,-0.00521,-0.10673,0.04498,0.05035,0.00953,0.02851,-0.03453,-0.11113,0.02138,0.0349,0.06201,-0.02171,0.06807,0.07906,-0.10948,0.08081,-0.08879,-0.09644,-0.03305,-0.03535,0.02557,-0.01332,0.03988,0.08096,0.00395,-0.0053,0.04797,0.01028,0.04483,0.03119,0.06266,-0.01934,-0.0277,0.03321,0.07176,0.01291,0.00215,-0.04414,-0.13594,-0.01948,0.04206,-0.00195,-0.04619,0.00372,-0.00342,-0.05821,-0.0151,-0.08672,-0.06571,-0.04301,0.11684,-0.00813,0.05114,0.06913,-0.01759,0.13624,9e-05,-0.06148,0.06756,-0.0525,0.0332,-0.02903,-0.05911,-0.1324,-0.09267,0.03779,0.09768,-0.0309,0.00915,-0.01889,0.07767,0.04899,0.10888,-0.06866,-0.03201,0.0584,0.122,0.0618,0.03377,-0.0354]},{"domain":"nuclear_engineering","key":"nuc_plane_source_slab_flux","name":"Flux from a plane neutron source at the centre of a slab","package":"nuclear-engineering-ai999x","example":"Plane source in a slab: S = 1e8 1/(cm^2*s), D = 0.16 cm, Sigma_a = 0.0197 1/cm, a = 1 m, x = 10 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rate from a shielded point gamma source with buildup","package":"nuclear-engineering-ai999x","example":"Point source dose rate: Gamma = 0.351 uSv*m^2/(MBq*h), A = 10 Ci, r = 2 m, mu = 0.0656 1/cm, x = 10 cm, buildup = 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from a point neutron source at the centre of a sphere","package":"nuclear-engineering-ai999x","example":"Point source in a sphere: S = 1e9 1/s, D = 0.16 cm, Sigma_a = 0.0197 1/cm, R = 50 cm, r = 10 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after a reactivity step (one delayed group, exact)","package":"nuclear-engineering-ai999x","example":"Power after a reactivity step one group: rho = 100 pcm, beta = 0.0065, lam = 0.08 1/s, Lambda = 1e-4 s, t = 10 s","v":[-0.06742,0.04065,-0.06172,-0.11697,0.09167,0.09081,-0.05232,0.08167,0.01523,0.03814,0.00422,-0.02941,-0.13296,0.0157,-0.03037,0.10452,0.08361,-0.10359,0.05337,-0.02274,0.02776,-0.07662,-0.04494,0.0496,-0.00667,0.03872,-0.01309,0.00353,0.05249,0.01021,0.0395,-0.01858,-0.02987,0.03538,0.09763,0.14005,-0.06334,0.07689,-0.02716,0.08396,0.03632,0.01058,-0.0341,0.09936,-0.01417,-0.01614,-0.01009,0.03366,0.00311,-0.02507,-0.04441,0.11365,-0.11187,0.05631,-0.00471,-0.03019,-0.04955,-0.02765,-0.00699,-0.16337,-0.05605,-0.07367,0.09638,-0.07321,0.02075,-0.01936,0.0591,0.02968,0.08342,-0.05882,0.02801,0.05476,0.03888,-0.0934,-0.02236,-0.04756,0.00278,-0.01106,0.08721,0.00118,-0.0323,-0.12211,0.00692,0.03485,0.07907,-0.03067,0.12804,-0.07587,-0.07995,0.00633,-0.09646,-0.01818,0.03767,0.0459,-0.00928,0.02801,0.02485,-0.10344,-0.03605,-0.02971,-0.04904,0.02415,-0.03855,0.01352,0.03638,0.0697,-0.01244,-0.03989,0.04669,0.13542,0.07522,0.04584,-0.07125,-0.05244,-0.0079,-0.06607,0.02689,-0.00562,-0.09104,-0.04474,0.04284,-0.10502,0.01739,0.03093,0.04131,-0.00125,-0.00161,-0.00414,-0.01691,0.01061,-0.04608,-0.00175,-0.00861,-0.04642,-0.04302,0.0557,0.03065,-0.06995,-0.04721,-0.02498,-0.00324,-0.03774,0.01118,-0.07659,-0.03109,0.04145,-0.05601,-0.07906,-0.07406,0.01925,-0.0783,0.03149,0.07144,0.13433,0.01752,-0.00867,0.01415,0.0222,-0.01815,-0.07311,-0.09345,0.00824,-0.01448,0.09522,-0.05643,-0.06644,0.11046,0.0562,0.05725,0.02125,-0.00328,-0.00136,0.05117,-0.13272,0.05845,0.13121,0.05264,0.05781,0.06642,0.04879,-0.00123,0.04328,0.05988,-0.02363,0.13365,-0.03055,0.05545,-0.00133,-0.02818,-0.02079,0.04001,-0.06032,0.05453,-0.02004,-0.04768,0.17013,-0.03176,-0.00329,-0.01444,-0.0389,0.01074,0.06452,0.07976,-0.04709,-0.05912,0.03749,0.06849,-0.07479,0.00677,0.0255,-0.04507,-0.07326,0.04827,-0.02485,-0.00458,0.00114,-0.07753,-0.13228,0.01475,-0.03881,0.2569,-0.05621,-0.03329,0.12006,-0.06007,0.03128,0.07531,-0.01867,0.10036,0.03906,-0.03181,-0.05222,-0.03013,-0.04204,-0.08767,0.00062,-0.0435,0.0986,-0.05905,-0.00571,0.0725,0.02741,0.00637,0.0799,-0.04475,0.01364,0.0356,-0.03903,-0.16277,0.119,-0.07826,-0.10466,0.00776,0.01752,0.0288,-0.04768]},{"domain":"nuclear_engineering","key":"nuc_power_after_step_six_group","name":"Power after a reactivity step (six delayed groups, exact)","package":"nuclear-engineering-ai999x","example":"Power after a reactivity step six groups: rho = 100 pcm, beta = [0.000215, 0.001424, 0.001274, 0.002568, 0.000748, 0.000273], lam = [0.0124, 0.0305, 0.111, 0.301, 1.14, 3.01], Lambda = 50 us, t = 10 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density and power from the fission reaction rate","package":"nuclear-engineering-ai999x","example":"Power from reaction rate: E_f = 200 MeV, N = 1e21 1/cm^3, sigma = 582.6 b, phi = 3e13 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unit conversion (Bq and Ci, Gy and rad, Sv and rem)","package":"nuclear-engineering-ai999x","example":"Radiation unit conversion: A = 10 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from a measured stable period or doubling time (inhour)","package":"nuclear-engineering-ai999x","example":"Reactivity from period: beta = [0.000215, 0.001424, 0.001274, 0.002568, 0.000748, 0.000273], lam = [0.0124, 0.0305, 0.111, 0.301, 1.14, 3.01], Lambda = 50 us, T = 60 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reactor period after a reactivity step (one delayed group)","package":"nuclear-engineering-ai999x","example":"Reactor period one group: rho = 100 pcm, beta = 0.0065, lam = 0.08 1/s, Lambda = 1e-4 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and specific activity of a mass of a radionuclide","package":"nuclear-engineering-ai999x","example":"Specific activity: nuclide = Co-60, m = 1 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period and prompt root of the inhour equation (six delayed groups)","package":"nuclear-engineering-ai999x","example":"Stable period six groups: rho = 100 pcm, beta = [0.000215, 0.001424, 0.001274, 0.002568, 0.000748, 0.000273], lam = [0.0124, 0.0305, 0.111, 0.301, 1.14, 3.01], Lambda = 50 us","v":[-0.03145,0.08995,-0.07846,0.02368,0.0487,0.07112,0.02287,0.05835,0.04328,0.00238,0.11776,0.04365,-0.05409,0.03927,-0.00775,0.11794,0.04986,0.03631,0.07425,0.04975,-0.00988,-0.12146,-0.10813,0.04896,0.17712,-0.00468,-0.08675,-0.00091,0.105,-0.00553,0.02261,0.02738,-0.00894,-0.02684,0.08628,0.03849,-0.02298,0.08642,-0.05342,0.03855,0.07446,-0.00161,0.07014,0.0933,0.00139,-0.06586,-0.01987,-0.00099,0.01161,0.00013,-0.05098,0.06449,-0.07944,0.09405,0.02529,-0.06784,-0.0526,0.02634,-0.11016,-0.09125,-0.10875,-0.043,-0.02508,-0.02279,0.05908,-0.00162,0.00669,0.03987,0.06372,-0.07885,-0.05076,0.01718,-0.00058,-0.14538,-0.0105,-0.01168,-0.04631,0.02588,0.1175,-0.0107,0.05037,-0.15365,-0.01511,0.03853,0.06689,-0.03338,0.05832,-0.09081,-0.09889,-0.04976,-0.17317,-0.00204,0.05702,0.05617,-0.00945,0.09834,-0.09351,-0.14101,0.00227,-0.02458,-0.07524,0.07715,-0.09107,0.03033,0.04586,0.06941,-0.02429,-0.04705,-0.01576,0.11316,-0.01764,-0.07782,0.02832,-0.02748,-0.05858,-0.02502,-0.03261,0.00391,-0.0886,-0.01011,0.03873,-0.04279,0.04299,-0.02704,-0.01508,0.0437,0.08428,0.02558,0.03432,0.04789,-0.07004,0.06473,-0.02926,-0.01401,0.07234,-0.02099,0.00681,-0.00382,0.07138,0.0201,0.0378,0.03042,0.01782,-0.0586,-0.08314,-0.03968,-0.07823,-0.02596,0.00705,0.04259,-0.072,-0.04263,0.01253,0.04334,0.03567,-0.05865,0.03957,0.06696,-0.07276,-0.04755,-0.07865,0.06207,-0.00054,0.01946,0.01182,-0.04401,0.13147,0.04332,0.11118,0.06618,0.04425,-0.0612,0.04134,-0.05542,0.01285,-0.03816,0.07103,-0.0046,0.13054,0.02464,-0.06927,-0.01145,-0.01814,-0.04357,0.15211,-0.01259,0.10778,0.0241,0.05316,-0.00901,-0.07594,-0.04559,0.09788,-0.07377,-0.06839,0.07941,-0.03648,-0.00747,0.03139,0.08383,0.00232,0.06638,0.11134,-0.0732,-0.15321,-0.0017,0.10017,-0.00171,-0.05654,-0.03282,-0.03472,-0.02342,-0.01114,-0.04197,-0.07209,0.02664,-0.06601,-0.07675,0.04407,0.03453,0.04305,0.00042,-0.05112,0.09326,-0.00646,0.07381,0.00875,-0.04747,0.05035,-0.05362,-0.00794,-0.03495,-0.07983,-0.04732,-0.09207,0.0173,-0.08082,0.13835,-0.02037,-0.02367,0.0728,0.10172,0.02623,0.0613,-0.01909,-0.04421,-0.04601,-0.10229,-0.12473,0.01399,-0.06621,-0.05601,-0.03881,0.01245,0.03308,-0.01099]},{"domain":"nuclear_engineering","key":"nuc_stay_time_decaying_source","name":"Stay time to a dose limit near a decaying source","package":"nuclear-engineering-ai999x","example":"Stay time: H0 = 2 mSv/h, T_half = 6586.2 s, D_lim = 1 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and mean energy of thermal neutrons (Maxwell distribution)","package":"nuclear-engineering-ai999x","example":"Thermal neutron speeds: T = 293.6 K","v":[-0.11262,-0.06083,0.10623,0.0319,-0.01561,0.01625,-0.03181,0.02559,0.03716,0.07095,-0.0031,0.00891,-0.05954,-0.02395,-0.00846,0.02771,0.02016,-4e-05,-0.02171,-0.03557,0.01152,-0.05455,-0.04143,0.08975,0.06215,0.04053,-0.05426,-0.05567,0.1156,-0.0144,-0.02325,0.00463,0.01566,-0.0099,-0.01986,0.00122,0.01551,-0.0642,0.03504,-0.04725,0.00668,0.00981,0.12148,0.02357,-0.03898,-0.03227,0.07173,-0.11863,0.11093,-0.00039,-0.04287,-0.02147,0.05799,0.04481,-0.06884,-0.09701,-0.00593,0.05529,0.03305,-0.02551,-0.01794,-0.02089,-0.0564,-0.05716,0.01338,0.08931,-0.04414,-0.00331,-0.02038,0.09814,-0.10721,0.02301,-0.0541,-0.11242,-0.02243,0.0895,-0.02402,0.03655,0.08004,-0.05157,0.05598,-0.04798,-0.08185,0.15144,-0.13099,-0.0414,0.02846,0.05338,-0.08619,-0.09797,0.07338,0.06833,0.09877,-0.01522,-0.03695,0.00169,0.04336,-0.08336,0.02625,0.08098,-0.01829,0.04736,0.00568,-0.03851,0.00603,-0.13899,-0.00477,0.02719,-0.04829,0.0275,0.02284,-0.02726,0.15547,-0.04056,-0.08324,-0.02761,0.10463,-0.01228,-0.03057,0.0466,0.07324,0.05323,0.04405,-0.07641,-0.0056,-0.08232,0.16996,0.01705,-0.04504,-0.0292,-0.00592,-0.0398,-0.10546,0.02492,0.02832,0.02859,0.0574,0.06234,-0.00554,0.01971,0.03858,0.08894,0.08499,0.09176,-0.15585,0.0878,-0.04302,0.09557,-0.05779,-0.02551,0.01677,0.10995,-0.05711,0.03436,-0.03451,0.04041,-0.07726,0.0004,-0.12362,-0.03502,-0.01691,-0.00238,-0.05839,-0.05868,-0.05361,0.02848,-0.08331,-0.03025,0.01423,0.00987,0.01676,0.02082,0.05672,-0.05495,-0.02134,-0.06944,0.10112,0.05037,-0.00362,-0.04128,0.05803,-0.07405,-0.1079,0.04202,-0.0252,0.07728,-0.04858,0.06866,-0.00764,0.08964,-0.09495,-0.03137,0.02379,0.06405,0.02081,-0.00994,-0.00011,-0.00973,-0.0436,0.07065,-0.00068,-0.04566,0.02764,-0.00237,-0.04353,-0.0269,0.00589,0.07412,0.02899,-0.06683,0.05716,0.01915,-0.04873,-0.05161,-0.03937,-0.03919,-0.02901,0.0295,0.06383,-0.00324,-0.15491,-0.01906,0.03764,-0.033,-0.01957,0.0074,-0.06235,-0.07453,0.05168,0.01343,0.05332,0.14533,0.10567,0.02022,0.02691,-0.0569,-0.1613,0.13961,0.03837,-0.01086,0.07894,0.12249,-0.02439,0.14894,-0.00787,-0.07317,0.01367,-0.01256,0.034,-0.0753,0.00679,0.04722,-0.18922,-0.05951,0.02376,-0.08411]},{"domain":"nuclear_engineering","key":"nuc_three_member_chain","name":"Three-member decay chain with initial activities (Bateman)","package":"nuclear-engineering-ai999x","example":"Three-member chain: T1 = 100.0 s, T2 = 10.0 s, T3 = 1.0 s, A10 = 1000.0 1/s, A20 = 0.0 1/s, A30 = 0.0 1/s, t = 50.0 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received passing a point source","package":"nuclear-engineering-ai999x","example":"Transit dose: Gamma = 0.351 uSv*m^2/(MBq*h), A = 100 Ci, d = 2 m, v = 1 m/s, L = 20 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decay curve: amplitudes of two known half-lives","package":"nuclear-engineering-ai999x","example":"Two-component decay fit: t = [0.0, 1.0, 2.0, 4.0, 8.0, 16.0], C = [11000.0, 6000.0, 3500.0, 1625.0, 1062.0, 844.0], T1 = 1 h, T2 = 10 h, t_unit = 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after shutdown: concentration and peak","package":"nuclear-engineering-ai999x","example":"Xenon after shutdown: Sigma_f = 0.1 1/cm, phi = 3e13 1/(cm^2*s), gamma_I = 0.0639, gamma_X = 0.00237, sigma_X = 2.65e6 b, t = 10 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iodine-135 and xenon-135 concentrations","package":"nuclear-engineering-ai999x","example":"Xenon equilibrium: Sigma_f = 0.1 1/cm, phi = 3e13 1/(cm^2*s), gamma_I = 0.0639, gamma_X = 0.00237, sigma_X = 2.65e6 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What is the modulation index?","v":[-0.05863,0.14748,0.00956,0.13378,-0.11461,-0.0717,0.11864,0.04915,0.0746,0.07193,0.03719,0.00305,0.02506,-0.02326,-0.02185,0.07292,0.09132,-0.01278,0.07535,-0.00312,0.08365,-0.00903,0.05298,0.06508,0.03159,0.00539,0.02741,0.03549,0.04563,0.02343,0.01902,0.06165,0.05512,0.02028,-0.11114,-0.03424,-0.08363,-0.05898,0.12607,0.1372,-0.05723,-0.0067,0.01227,-0.01836,0.06451,0.03762,0.02098,-0.05801,0.00175,-0.10439,0.05012,0.03795,-0.1289,0.01446,-0.02776,0.01992,-0.04058,-0.00286,0.00377,0.022,-0.02303,0.0224,0.04625,0.03764,-0.02996,-0.0162,-0.14504,0.06308,-0.03394,0.01048,0.03394,0.07104,0.14823,0.02057,0.05023,0.01262,-0.04031,-0.0078,-0.02912,0.00326,0.07734,0.09428,-0.05965,-0.19945,0.03546,0.02703,0.03898,0.07765,-0.02593,-0.0501,0.00614,0.08163,-0.06028,0.06634,-0.03489,-0.01439,0.0472,-0.05484,0.10731,0.02332,-0.03988,0.04789,0.05865,-0.08305,0.06345,-0.08819,-0.0521,0.06317,-0.11504,0.0031,0.01715,0.08427,0.01674,-0.01,0.00092,-0.03455,0.00512,-0.02697,-0.07359,0.04455,0.10869,-0.04021,-0.04926,0.04221,-0.14811,-0.0183,-0.02015,-0.10702,-0.02287,-0.023,-0.0988,0.01376,0.05385,-0.03405,0.01072,0.03521,0.09476,-0.01234,-0.037,0.08678,0.11233,0.03175,0.09187,-0.03082,0.14425,0.00139,0.04833,-0.00348,-0.09013,-0.04867,-0.01799,0.01686,-0.07613,-0.06494,-0.02203,-0.00561,-0.02827,0.08685,-0.02326,-0.02704,-0.06255,-0.01294,-0.00144,-0.05482,0.03314,-0.03912,-0.05908,-0.01851,0.12753,-0.03971,-0.16565,-0.01808,0.06868,-0.00391,-0.0025,-0.01905,-0.00303,-0.14562,0.08648,0.03901,0.05397,-0.09144,-0.09409,0.00151,-0.02028,-0.02746,-0.08155,-0.04736,-0.00346,-0.01499,-0.08202,-0.06832,-0.01593,-0.0006,-0.01262,-0.04913,-0.02238,0.01656,0.0209,-0.06339,-0.0,0.00439,-0.05054,0.04119,-0.11969,-0.08148,-0.01496,0.04007,-0.02327,-0.043,-0.04612,0.01083,0.03235,0.08266,0.0103,0.06902,-0.17788,0.04095,-0.01238,-0.10642,-0.00089,0.03386,0.03683,0.02341,-0.07295,0.01108,-0.08158,0.036,-0.02707,-0.07792,0.00966,0.01086,0.07936,0.10041,0.13737,-0.00031,-0.06804,-0.03403,-0.04318,0.00657,0.0986,0.04124,-0.05921,0.0787,0.00506,-0.05619,0.02819,0.09586,-0.11902,-0.05141,0.05961,0.04428,0.00252,0.01776,-0.02139,0.00998]},{"domain":"signal_processing","key":"am_power","name":"Power in an AM (DSB full-carrier) signal","package":"signal-processing-ai999x","example":"An AM transmitter has a carrier power of 1000 W and a modulation index of 0.8. What is the total transmitted power?","v":[-0.10241,0.05991,-0.03913,-0.04423,0.00492,-0.02698,0.07234,0.11485,0.00513,0.02196,0.00483,-0.00974,0.01583,-0.08437,-0.11114,0.02427,0.0541,-0.0228,0.14337,0.0606,0.04951,-0.00977,0.07332,0.07879,-0.12286,-0.05129,0.00586,0.07331,0.05471,0.06194,-0.01514,-0.03901,0.02525,0.02809,-0.001,0.07406,-0.0359,-0.06063,0.04097,0.0624,-0.08879,-0.00175,0.03915,0.03718,-0.02394,0.02129,-0.08089,-0.01294,0.07997,-0.1312,-0.0059,0.07153,-0.03356,0.08318,-0.06556,0.05384,-0.03371,-0.10667,-0.02628,0.01143,-0.05703,-0.0585,0.01866,-0.05342,-0.07178,-0.00573,-0.02878,-0.04916,-0.05491,-0.06435,0.01885,0.02873,0.07693,0.04585,-0.0167,-0.05945,0.00134,-0.07433,-0.04541,-0.03343,-0.02501,0.00801,0.0727,-0.03715,0.05095,-0.14088,0.0569,-0.01258,0.03034,-0.06167,0.03694,0.04968,-0.12713,0.07674,-0.05075,-0.0808,0.04487,0.03473,0.11784,-0.1291,-0.02057,0.11558,0.00781,-0.03356,0.04106,-0.00716,-0.04141,0.04456,-0.10013,0.06271,0.1239,0.11545,0.03614,0.01066,0.06002,-0.04822,0.0254,-0.0305,-0.08677,-0.03348,-0.03262,0.02616,-0.06399,0.01899,0.01747,0.01658,0.02641,-0.02171,-0.05467,-0.05256,0.05742,0.02509,-0.08978,0.09318,0.01958,0.14407,0.09542,-0.00652,-0.09869,0.1364,-0.03379,0.03577,0.03229,-0.0263,0.16248,-0.00536,-0.01643,0.02063,-0.04952,-0.11157,-0.09973,0.13673,-0.09421,-0.02973,0.02524,-0.02416,0.02219,0.06921,-0.0008,-0.0513,-0.06672,-0.07751,-0.026,0.04256,0.08376,-0.11276,-0.06001,0.06984,0.03424,-0.00156,-0.04064,-0.06825,0.085,0.00583,-0.01173,0.01178,0.05817,-0.09193,-0.02787,0.11512,0.09147,-0.05197,-0.0326,0.03646,-0.06527,-0.00922,0.02217,-0.04094,-0.09498,-0.0197,-0.07126,0.04775,-0.09141,0.07295,-0.03084,-0.01094,-0.00942,-0.00604,-0.0244,-0.07269,-0.00881,0.04314,-0.00372,0.08099,-0.09806,-0.01404,-0.02421,0.02809,0.01954,-0.03936,-0.12304,-0.03312,0.0499,-0.04152,0.07984,0.01113,-0.15341,-0.00142,-0.01512,-0.15637,0.11099,-0.07226,-0.03281,0.00637,-0.10821,-0.01157,0.00679,-0.02237,0.03716,0.0719,0.02566,0.01173,0.07221,0.06594,0.07248,0.01177,0.03556,-0.07978,-0.03948,0.06871,0.06506,-0.01835,0.00154,0.14177,0.02373,0.02459,0.05891,0.02327,0.01405,-0.03105,0.02802,-0.02629,0.02978,0.01327,-0.12776,-0.0287]},{"domain":"signal_processing","key":"amplitude_ratio_to_db","name":"Amplitude (voltage) ratio to decibels","package":"signal-processing-ai999x","example":"Express a voltage ratio of 50 in 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order of a analog Butterworth filter","package":"signal-processing-ai999x","example":"What Butterworth filter order is needed for a passband edge of 1 kHz with at most 1 dB ripple and a stopband edge of 2 kHz with at least 40 dB attenuation?","v":[-0.04211,-0.04525,0.06278,-0.01773,-0.0467,-0.04097,0.04312,-0.09826,-0.00741,-0.00692,-0.01971,0.05967,0.09905,0.01899,-0.0528,-0.01816,0.12642,-0.04184,0.03769,-0.02803,-0.05359,-0.04515,-0.09973,0.06715,-0.09599,0.00281,0.09367,0.02446,-0.03828,0.06936,0.01012,0.06089,0.02269,-0.04472,0.0058,-0.01474,0.00806,-0.05675,-0.06006,0.10963,-0.01956,-0.03967,0.02544,0.07264,0.1533,0.06318,-0.006,-0.10927,0.05374,0.13724,0.05399,-0.09703,-0.04038,0.00813,-0.1409,0.06269,-0.10637,0.02726,0.09008,0.026,-0.1291,0.07893,0.02486,-0.00319,-0.00907,0.03846,0.02964,-0.03012,-0.00924,-0.03773,0.0194,0.11559,-0.07682,-0.07331,-0.08707,-0.03727,0.1214,-0.01778,0.12797,-0.03747,-0.02868,-0.08201,-0.04099,-0.00669,0.07083,-0.01279,0.0215,0.0493,0.03406,0.07546,0.10921,0.06007,-0.00103,-0.02026,0.04851,-0.04266,0.01464,0.00573,0.03662,0.0828,0.01604,0.10209,0.03626,-0.03657,0.09026,0.03216,-0.03153,-0.11582,-0.00582,0.02811,-0.03122,-0.00844,-0.02118,-0.01838,-0.04883,-0.00556,-0.13636,0.05765,0.03821,0.05305,0.05704,0.10542,0.06169,0.07333,-0.11347,-0.01148,-0.04674,-0.02703,0.04051,0.02118,0.01064,-0.04502,0.03592,0.03638,-0.04737,-0.04968,-0.01883,-0.01678,0.08335,0.12365,-0.15072,0.03096,-0.02985,0.04777,0.0019,-0.05872,-0.01809,-0.09668,-0.02583,-0.00695,-0.01316,0.09917,-0.0996,-0.02858,-0.08316,-0.01775,0.05532,0.05825,-0.00763,0.04025,0.02007,-0.01383,-0.08109,0.10667,-0.0707,0.044,0.05993,-0.07652,0.15538,-0.05477,-0.05149,-0.0719,0.00938,-0.07179,-0.02096,-0.00251,0.03527,-0.00035,0.04695,0.05697,-0.07304,0.09333,0.02472,0.02164,-0.01381,-0.02496,-0.09435,0.08763,0.06963,0.04219,-0.0512,0.07795,-0.09327,-0.02219,-0.0288,-0.05729,-0.05784,-0.02885,0.07355,-0.07346,0.03127,-0.00805,0.04991,0.05568,-0.06274,-0.05639,0.04138,-0.07076,-0.10807,-0.03542,-0.07839,-0.01554,0.01264,-0.01264,0.02379,-0.00102,-0.04322,-0.0311,0.0491,-0.0191,0.01594,0.07699,-0.01638,-0.08165,0.06473,-0.0287,-0.02916,0.05919,-0.02746,0.04511,-0.02553,0.05825,-0.01265,0.08091,-0.03993,0.04141,-0.14758,-0.05964,-0.11203,-0.03543,-0.09023,0.06955,-0.02333,-0.12166,0.0282,0.10859,-0.00985,-0.12289,0.0207,0.0242,-0.05637,-0.02723,0.16739,0.02312,-0.04189,-0.02137]},{"domain":"signal_processing","key":"butterworth_order_digital","name":"Minimum 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order of a analog Chebyshev type I filter","package":"signal-processing-ai999x","example":"What Chebyshev filter order is needed for a passband edge of 1 kHz with at most 1 dB ripple and a stopband edge of 2 kHz with at least 40 dB attenuation?","v":[-0.05419,0.03193,0.0884,0.00309,-0.0606,-0.09507,0.10899,-0.02573,0.02248,-0.05802,-0.04044,-0.00692,0.03855,0.03564,-0.0488,-0.04648,0.14278,-0.01907,0.07049,-0.00303,-0.02812,-0.06429,-0.0885,0.06264,-0.03207,-0.00649,0.02135,0.04852,-0.04469,0.00765,-0.06112,0.04336,0.10493,-0.02076,-0.06777,-0.00596,-0.01705,0.00939,-0.02999,0.01881,-0.0205,-0.05467,0.08853,0.12207,0.1017,-0.01511,0.04166,-0.02813,0.14489,0.02331,0.03454,-0.03091,-0.07435,0.01265,-0.10468,0.04085,-0.11906,0.02964,0.05476,-0.02349,-0.12037,0.00319,0.01187,0.05848,-0.0181,-0.01006,0.01502,-0.041,-0.00116,-0.02141,-0.0209,0.14466,-0.03729,0.0329,-0.04743,-0.01839,0.03154,0.01949,0.05679,-0.10565,0.0111,-0.12938,-0.02088,0.04317,0.07154,0.01075,0.02288,-0.00709,-0.02385,0.02964,0.07348,0.01636,0.00299,-0.00779,-0.00887,-0.02187,0.02543,0.07731,0.1203,0.07879,0.00191,0.0541,-0.02656,-0.01639,0.11778,0.00024,0.02251,-0.09791,0.03898,0.07338,-0.08017,0.04757,-0.03089,-0.00026,-0.00977,0.0307,-0.09772,0.06486,0.00198,0.01501,0.1559,0.09351,0.04518,0.05354,-0.15053,0.0405,-0.07329,-0.10553,0.04611,0.07309,0.09193,-0.07747,-0.02717,0.07853,-0.02791,0.00062,0.00437,-0.07559,0.06053,0.08717,-0.028,-0.00149,0.02826,-0.00674,0.02627,-0.07602,-0.04368,-0.1086,-0.08368,-0.00257,-0.04572,0.02067,-0.09118,-0.04404,-0.12155,0.11834,0.05367,0.06568,-0.02601,0.02989,-0.02123,-0.10529,-0.03786,0.07954,-0.0411,0.03821,-0.01204,-0.08695,0.1688,-0.04787,0.00306,-0.06298,0.05269,-0.03585,0.05612,0.01528,0.01369,0.04547,0.00071,-0.02505,-0.06015,0.08534,-0.04273,0.06296,-0.05302,-0.03193,-0.11762,0.03167,0.11612,0.11681,-0.07594,0.06164,-0.01361,0.04609,0.00467,-0.07044,-0.01114,-0.07111,0.09075,-0.08349,-0.0433,-0.01093,0.01933,0.04478,-0.0877,-0.08934,-0.01731,-0.10694,-0.03292,0.02976,-0.07138,-0.0104,-0.00453,-0.09505,0.04286,-0.06812,-0.08676,0.02365,0.0743,-0.06037,0.00422,0.07825,-0.00216,-0.12321,0.00974,-0.11606,0.04464,0.02307,-0.04803,0.00262,-0.01084,0.05126,-0.01927,0.00903,0.0671,0.03898,-0.13746,-0.10157,-0.02931,-0.04027,0.01151,0.07876,-0.00126,-0.03707,0.0613,0.06051,-0.04222,-0.17903,0.02333,0.00592,-0.0303,0.0507,0.09295,0.00546,-0.03608,0.03558]},{"domain":"signal_processing","key":"circular_convolution","name":"Circular 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1].","v":[-0.11237,0.07107,0.04803,-0.04877,-0.02487,-0.05113,-0.0681,0.05624,-0.01525,0.04349,0.051,0.02541,-0.06917,0.01681,-0.0004,-0.03684,-0.09654,-0.06317,-0.05909,0.05886,-0.03042,0.00808,-0.02338,-0.06721,0.03108,0.02526,-0.07496,0.0798,-0.03713,-0.01227,0.03462,-0.0532,-0.0223,0.00683,0.09947,-0.06895,-0.10459,0.06606,0.08618,0.05874,0.13403,0.0274,-0.07355,-0.05229,0.05583,0.07859,0.06094,0.09989,-0.10312,-0.04244,-0.11253,0.04388,0.04512,0.06455,0.00865,0.03533,-0.05501,0.03831,0.00173,0.0106,-0.04336,0.04047,-0.00427,-0.02446,-0.07515,-0.01344,-0.02728,0.06866,0.04447,0.05007,-0.02848,-0.01362,-0.11006,-0.0514,-0.00091,0.05354,-0.18549,0.06753,0.0423,-0.07376,0.00071,0.03933,0.05649,0.02504,0.09495,-0.02322,-0.0455,0.09544,0.04525,-0.02732,-0.00093,-0.03194,0.03649,0.10652,0.04701,-0.0812,0.05544,0.0018,-0.00861,0.00324,-0.01616,-0.05499,0.00669,0.03899,-0.04684,-0.01826,-0.14683,-0.04279,0.00193,-0.01173,-0.04675,-0.08656,0.03383,0.00422,0.00902,0.14969,0.05446,-0.0793,0.10803,-0.01397,-0.07199,-0.12332,-0.03127,0.01542,0.01524,-0.04648,-0.09477,-0.01515,0.09299,-0.0153,0.05996,-0.15234,-0.01784,-0.05354,0.00507,-0.01402,-0.09596,0.11289,0.01199,-0.02635,-0.13302,0.00052,0.00268,-0.03356,0.12441,0.01313,-0.04771,-0.08779,-0.03438,-0.02677,0.07286,0.03645,0.00458,-0.0273,0.02638,-0.02463,0.04843,-0.01243,-0.02707,0.01975,0.01978,0.12694,0.00059,-0.06575,0.04763,-0.0222,-0.04494,-0.04387,0.0232,0.08838,0.12588,-0.00574,-0.05239,-0.06844,0.03775,0.01693,-0.07338,0.02622,0.11214,-0.0206,-0.00642,0.02836,0.00644,-0.09203,-0.06203,0.01664,0.08725,-0.02706,-0.07863,0.08853,0.11807,0.07534,0.00514,0.07971,0.0064,-0.07426,-0.0123,-0.1102,0.109,-0.03888,0.00743,0.05132,-0.01738,0.01944,-0.00535,0.03403,0.09403,0.01436,-0.03221,-0.007,0.13728,-0.15329,0.11148,0.01414,-0.02555,-0.02159,0.02952,-0.03952,0.10492,-0.00405,-0.02731,-0.02823,0.03207,0.04037,0.08491,0.04056,0.17371,0.06243,0.0618,-0.04613,-0.14791,0.04124,0.01829,-0.02885,0.00359,-0.05345,0.00252,0.00035,0.04118,-0.02742,0.13397,0.03132,-0.1175,-0.0532,-0.02883,-0.04963,-0.07472,0.05494,-0.03467,0.02633,0.00078,0.08158,-0.02498,0.03797,-0.01597,-0.04209]},{"domain":"signal_processing","key":"coax_impedance","name":"Characteristic 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combined?","v":[-0.10734,-0.02558,-0.02626,-0.00042,-0.02762,0.00502,0.03241,0.03164,-0.04773,-0.01637,0.06347,0.04248,-0.0262,-0.09246,-0.09071,-0.17527,0.02747,0.02394,0.07751,0.08076,-0.04518,-0.10828,0.03287,0.07024,-0.08462,-0.02001,-0.00853,0.03546,0.01504,0.04911,-0.04604,-0.06185,-0.02627,-0.04834,0.08214,0.02485,-0.06204,-0.03702,0.08671,-0.02792,-0.08027,0.04376,-0.07418,-0.07237,-0.04867,-0.02317,-0.08772,-0.07197,-0.0672,-0.04481,-0.08046,-0.04492,0.02117,0.0625,-0.03659,-0.00741,0.0012,-0.06193,0.05996,0.07185,-0.01906,0.16114,-0.0116,-0.05048,-0.10109,0.00083,0.03512,-0.09537,0.10254,-0.04459,0.00532,0.04086,-0.00703,0.05937,-0.02359,-0.10628,-0.05852,0.04074,-0.04972,0.04691,-0.00953,-0.03744,0.09146,-0.11749,-0.00301,-0.09232,0.01062,0.14539,0.02459,0.01427,-0.01352,0.05268,-0.07037,0.04054,-0.03941,-0.04483,0.05098,0.16282,0.02352,-0.02229,-0.00612,-0.00801,-0.04458,-0.01619,0.01718,-0.01977,-0.06288,0.05915,-0.09833,0.08438,0.02657,0.00812,0.04801,0.01244,-0.01057,0.02913,0.00776,-0.10999,-0.02291,-0.00246,-0.08527,0.12322,-0.03146,-0.10287,0.08094,0.02324,0.0492,-0.01973,0.00703,-0.05528,0.05775,-0.00497,-0.13511,0.04531,0.04023,-0.04679,0.01022,-0.01685,-0.00476,0.04041,-0.08229,0.06328,-0.12194,0.07156,0.09483,-0.05438,-0.0012,0.05233,0.07962,-0.08895,-0.1359,0.17972,-0.03974,-0.00973,-0.02409,-0.03457,0.00841,-0.09619,0.03595,0.12309,0.05212,-0.00152,0.01803,0.08233,0.09772,0.07303,0.02303,0.01709,-0.03268,-0.04818,0.11295,-0.07858,-0.0263,-0.00078,-0.05288,-0.00314,0.03702,-0.08651,-0.06133,0.06206,-0.06054,-0.03447,0.0041,0.03975,-0.02133,0.06794,0.07131,-0.04368,-0.01935,0.00271,-0.1312,0.0732,-0.07616,0.14816,-0.00798,-0.04814,-0.06092,-0.00413,0.05864,-0.11426,-0.06012,0.05062,-0.02589,-0.01195,-0.03672,0.06397,0.02831,0.00749,0.00288,-0.04894,-0.02678,0.04834,0.02098,-0.06331,0.04848,0.01798,-0.06,-0.09784,-0.06295,0.04377,0.06621,-0.02421,-0.05612,0.01486,0.0232,-0.03306,0.03711,0.07514,0.02977,0.16061,0.05818,0.03553,0.11745,-0.04114,0.04147,0.08413,0.12606,-0.01517,0.01463,0.0118,0.0446,-0.02311,-0.06926,0.08178,-0.02259,0.07119,0.03646,0.04141,0.06322,0.01377,0.01218,-0.02225,0.07567,0.07393,-0.06329,-0.03608]},{"domain":"signal_processing","key":"dbm_to_watts","name":"Power 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gain of a digital filter","package":"signal-processing-ai999x","example":"What is the DC gain of the filter with b = [1, 2, 1] and a = [1, -0.5, 0.25]?","v":[0.04173,-0.079,0.04201,-0.02457,0.05564,0.00717,-0.07283,0.02344,-0.13715,0.03695,0.02194,-0.00754,-0.05966,0.01162,0.01853,0.03565,0.046,-0.01889,-0.04689,0.04625,-0.05554,-0.06815,0.0052,-0.0121,0.0405,-0.03138,-0.01379,-0.00816,0.09007,-0.03112,-0.07047,0.07116,-0.00717,-0.06226,-0.01595,0.07753,0.01731,0.02786,0.01792,-0.10669,-0.00276,0.0185,0.05072,0.03349,0.10699,-0.00261,0.07031,-0.10038,-0.11862,0.00118,-0.01312,-0.04859,0.1168,-0.05903,0.01367,0.16449,-0.1103,0.01109,0.02543,-0.01363,-0.0858,-0.02943,0.09341,-0.14457,-0.01962,0.00684,-0.04752,0.01499,-0.02434,-0.03259,0.13406,-0.00657,-0.07316,-0.01131,0.05316,-0.08224,-0.08411,-0.00205,0.02349,-0.0792,0.01304,-0.00086,-0.00014,0.04928,0.02125,-0.00184,0.03184,0.05431,-0.01886,0.0251,0.06497,-0.14297,0.07548,-0.15684,0.08429,0.0241,0.04326,-0.04755,0.13019,-0.08396,0.01977,0.00036,-0.07635,-0.02007,0.03363,-0.02133,0.04789,0.06553,-0.00357,0.01751,-0.05702,0.10926,0.02778,0.01923,0.01052,0.10046,-0.0242,-0.07007,-0.08029,-0.00271,-0.00222,-0.03384,0.03449,-0.01857,-0.02204,0.03455,-0.14681,-0.01303,-0.03691,-0.06168,0.01518,0.05934,0.0765,-0.09658,-0.02246,0.12193,-0.02141,-0.02897,-0.0756,-0.0203,-0.12033,0.02093,-0.03096,0.02972,0.04371,-0.05592,0.08323,-0.04845,0.0428,-0.00087,0.03641,-0.03452,0.06887,0.00144,-0.03864,-0.1904,0.14565,0.0056,-0.02789,-0.01492,0.14528,0.08368,0.0755,0.01675,0.12062,-0.03412,0.00611,-0.13588,0.03086,-0.03624,0.08537,-0.03092,0.01888,-0.06669,-0.07964,-0.0592,0.0264,-0.04823,0.00897,0.08773,-0.02132,0.04948,0.01783,0.11082,0.02568,-0.05345,-0.01194,0.0144,-0.00673,0.08257,0.04196,0.03058,-0.02498,-0.02314,-0.08118,-0.01979,-0.04265,0.09736,-0.03276,-0.04293,-0.0639,0.07331,-0.09413,-0.01472,0.14293,0.01874,0.1,-0.08696,0.07749,0.00239,0.04194,0.02387,0.03352,0.03794,0.11455,-0.04761,-0.0013,0.07024,0.02608,0.02277,0.1105,0.04487,0.00071,0.02246,0.03389,0.00451,0.06676,0.11549,0.04004,0.09019,0.0569,-0.01631,-0.0613,-0.0364,-0.02534,0.02977,-0.0298,-0.02954,0.06973,0.02246,-0.01762,0.0526,-0.01545,-0.17263,0.1264,-0.03293,-0.00805,-0.0627,-0.04032,-0.01077,0.01563,-0.00487,-0.05192,0.05059,-0.02408,-0.08876]},{"domain":"signal_processing","key":"dft_bin","name":"One 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spectrum of a sequence (FFT)","package":"signal-processing-ai999x","example":"Compute the DFT of x = [1, 2, 3, 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55%?","v":[0.08681,-0.07401,-0.02811,0.05538,0.08004,-0.01744,-0.0154,0.02294,0.0256,0.00362,-0.02024,-0.11082,-0.00509,-0.02351,-0.10027,0.10754,0.08699,-0.01358,0.01519,0.05504,-0.04578,-0.01494,0.064,-0.04209,-0.05749,-0.00834,-0.05829,-0.12777,0.0636,0.07874,-0.00704,0.02799,0.04568,-0.00433,-0.00741,0.08062,-0.09705,-0.10432,0.00461,-0.00913,-0.00571,0.05368,0.01051,-0.02829,-0.01425,0.03636,0.15337,-0.03935,-0.01234,0.00134,0.06471,0.02901,0.06699,0.09964,-0.0469,0.14788,-0.04669,-0.10409,-0.14912,-0.05178,-0.00246,-0.09327,0.04202,-0.02331,-0.14753,0.00988,-0.09127,-0.007,-0.06517,-0.00165,0.12275,0.12326,-0.07344,0.01929,0.01172,-0.10807,-0.10632,-0.06816,-0.07847,-0.02224,-0.12119,0.04377,0.03513,0.04111,-0.00229,-0.09226,0.04775,-0.0444,-0.00055,0.01693,-0.0557,0.01605,0.06048,0.00099,-0.03286,-0.02098,-0.10538,0.04206,0.10703,-0.06075,-0.05592,0.06516,-0.01742,0.01211,0.06437,0.02623,0.08244,0.05804,0.01173,-0.03686,0.14217,0.02017,0.04765,0.02635,0.01064,0.06452,-0.01706,-0.05808,0.05783,-0.04359,0.07983,-0.06153,-0.042,-0.02807,-0.04263,-0.06438,-0.15615,0.08767,-0.10324,-0.07609,0.05154,0.03424,-0.0065,-0.05676,-0.01349,0.08115,-0.00028,0.10192,0.0189,0.11647,0.07169,-0.0097,0.01186,0.01301,0.20844,0.01008,0.03671,-0.06261,0.09279,0.01324,0.06131,0.10602,-0.00199,0.00078,0.01645,-0.08699,0.03863,0.02023,0.03656,-0.0752,-0.01703,0.05956,-0.02864,0.0099,0.01826,0.02778,0.10941,0.06605,-0.02513,0.02732,-0.02317,0.01282,0.09871,-0.06757,0.00347,-0.07634,-0.02033,0.03734,0.07189,-0.06088,0.04021,-0.06983,0.0093,0.02179,-0.02594,-0.02092,-0.03147,-0.0007,-0.0619,-0.05626,-0.01255,-0.02221,0.01546,-0.06596,-0.06085,0.02992,0.12676,-0.00076,-0.00627,-0.05963,-0.06946,0.04826,0.10013,0.01695,0.05844,-0.13423,0.07841,0.02326,0.0055,-0.08064,-0.01211,0.01716,0.03704,-0.04431,-0.05672,-0.01378,-0.05185,-0.08213,0.04184,-0.01471,-0.10519,0.12966,-0.04737,0.02098,-0.01177,-0.05116,0.07393,0.04351,0.06801,-0.03168,0.07489,0.09087,0.04507,-0.11191,0.03892,6e-05,0.07887,-0.05395,-0.02729,-0.02719,-0.00601,0.02523,0.04609,-0.01728,0.07067,0.08528,-0.00599,-0.02047,0.00422,-0.11619,-0.07121,-0.01653,-0.02292,-0.03449,-0.01545,0.06533]},{"domain":"signal_processing","key":"exponential_pulse_spectrum","name":"Fourier transform of a decaying exponential","package":"signal-processing-ai999x","example":"What is the Fourier transform of a decaying exponential with amplitude 2 and time constant 0.5 s at 0 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filter output","package":"signal-processing-ai999x","example":"Filter x = [1, 2, 3, 4] with the FIR filter b = [0.5, 0.5].","v":[-0.02546,0.00394,0.06473,0.03901,-0.00499,0.04365,-0.07798,0.00076,-0.02174,-0.01235,-0.03705,-0.03228,0.02084,-0.071,0.08196,-0.05675,0.0535,0.04939,-0.01791,-0.00994,0.02082,-0.07994,0.00036,0.02126,-0.03563,-0.05922,0.03775,0.08815,0.07457,-0.0933,0.03938,-0.04626,-0.0198,-0.02195,0.07015,-0.09341,0.09653,0.03307,-0.03682,-0.03076,0.04759,-0.08354,-0.0535,0.0293,0.02868,-0.06306,-0.1036,-0.05211,-0.00012,0.03787,-0.02758,-0.02024,0.09712,0.00503,-0.03919,0.09683,0.01223,0.01389,0.03708,0.02312,-0.02835,0.00263,4e-05,-0.00333,-0.06863,0.12278,0.00428,-0.01195,-0.04155,-0.04264,-0.0262,0.03349,0.00914,-0.02821,-0.01747,0.0453,0.1526,0.00964,0.03109,-0.16478,0.10412,-0.14992,0.05745,0.04022,0.03569,-0.03682,0.00043,-0.03674,-0.04507,0.01909,0.09853,-0.07384,-0.03475,-0.05705,0.02282,0.02651,0.10877,-0.09677,0.05697,-0.00239,0.0405,0.00173,-0.09752,-0.05768,-0.03608,-0.01868,-0.13439,-0.14746,0.03261,0.04455,-0.07975,0.00429,0.06101,0.00352,0.06166,0.04478,-0.061,-0.0065,0.00486,0.11209,-0.0383,0.05952,0.04428,-0.09465,-0.01788,0.0571,-0.07214,-0.036,0.06443,0.03479,0.16113,0.08836,-0.07098,0.08966,-0.0585,-0.05966,-0.08307,-0.02597,-0.01836,-0.04711,-0.25977,0.02853,-0.01971,-0.0004,0.08266,0.03451,-0.00605,0.04694,0.07544,-0.11861,-0.04322,0.07891,-0.10555,-0.09176,-0.0586,-0.01466,-0.00845,-0.08461,-0.06129,0.04119,0.0238,-0.04703,-0.05608,0.0073,0.07089,0.01503,-0.0005,-0.02038,-0.04316,0.00334,0.05112,-0.05704,0.00402,-0.01519,-0.01967,-0.03517,-0.01701,-0.21474,0.09191,0.11484,-0.01627,0.03739,-0.01517,0.05306,-0.09222,0.06882,-0.01654,-0.01562,0.00173,0.1249,-0.01708,0.0955,-0.01452,0.04182,0.0038,0.0005,0.0428,-0.12992,-0.03001,-0.03956,-0.0024,0.03259,-0.01526,0.14578,-0.03774,-0.05548,0.01597,-0.01279,0.04822,-0.06047,0.06124,-0.04974,0.01609,0.05436,0.01697,-0.04892,-0.0005,0.01809,0.08689,0.02463,0.02915,-0.0501,-0.02466,0.04903,0.03462,0.0227,0.09992,0.03975,0.00896,0.05996,-0.10436,0.04096,-0.00921,0.08364,-0.02212,0.04461,0.02973,-0.01079,0.03258,0.04103,0.01052,0.10215,-0.02077,-0.0647,0.04117,-0.03316,0.01452,-0.10764,0.00968,-0.04276,0.12172,0.0128,0.00884,0.07014,-0.1481,-0.07588]},{"domain":"signal_processing","key":"fir_window_design","name":"FIR low-pass filter design by the window method","package":"signal-processing-ai999x","example":"Design a 5-tap FIR low-pass filter with a Hamming window, a cutoff frequency of 1 kHz and a sampling rate of 8 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spectrum: Carson bandwidth and Bessel sideband amplitudes","package":"signal-processing-ai999x","example":"An FM signal has a peak frequency deviation of 75 kHz and a modulating frequency of 15 kHz. 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amplitude of a square, triangle or sawtooth wave","package":"signal-processing-ai999x","example":"What is the amplitude of the 3rd harmonic of a square wave with amplitude 2?","v":[0.03915,0.08612,0.02336,0.04759,0.02705,-0.01101,-0.07623,-0.03555,-0.00476,-0.04522,0.03087,-0.03434,0.0143,0.03127,-0.08311,0.0892,0.07451,-0.01087,-0.00251,0.04589,-0.05981,-0.13465,0.0481,0.00753,-0.02573,0.08,0.05703,-0.01266,0.08779,-0.08278,-0.17603,0.03818,0.08958,0.00525,-0.00629,-0.06235,0.02131,0.04171,0.08884,-0.04489,0.01564,-0.09689,-0.00889,-0.00014,0.01853,-0.03221,-0.07824,0.03836,-0.07835,-0.05371,-0.10319,0.03633,0.00697,-0.06111,-0.00481,-0.16929,-0.10519,-0.07303,0.02944,-0.01572,0.05394,-0.03651,0.11042,0.03764,0.12931,-0.01304,-0.15427,0.02741,-0.03684,-0.03437,0.08361,0.09721,0.06765,-0.0738,-0.06499,0.03852,-0.13425,0.02564,0.00834,-0.02409,-0.044,0.0934,0.02442,-0.09124,0.07554,-0.06125,-0.10971,0.07726,0.042,-0.14796,0.05361,0.08778,0.00695,-0.00051,-0.03595,0.00082,0.09934,0.05311,0.12738,0.01728,-0.01303,0.04738,0.0211,-0.02058,-0.02392,-0.03865,-0.10998,0.10546,-0.05138,-0.02185,-0.09163,-0.14422,0.01368,0.03083,0.00254,0.11062,-0.06277,-0.05623,0.03046,-0.05922,0.0123,-0.07316,-0.05055,-0.09799,-0.07933,0.03656,-0.01172,-0.13092,0.10451,-0.0355,0.00995,-0.03571,-0.06012,-0.01054,-0.00985,0.04279,0.02301,-0.03401,0.10028,0.01131,-0.09227,-0.02827,0.03173,0.05503,0.09173,-0.0561,-0.00615,0.06123,0.01792,0.0257,-0.02418,0.01939,-0.10571,0.02171,-0.05644,0.14453,0.01739,0.02565,-0.00327,-0.00331,0.01186,-0.00376,-0.03143,0.04045,-0.07849,0.01897,-0.07479,-0.08143,0.12094,0.03893,0.03708,0.0018,-0.04874,0.01416,-0.00418,0.03535,0.00397,0.01858,-0.07472,-0.01065,-0.04611,0.06637,-0.04652,0.06858,-0.03598,0.06543,-0.03106,0.04523,-0.02355,0.00825,-0.08416,-0.05297,0.02617,0.09896,0.08987,0.02294,-0.00788,0.00107,-0.08558,0.07376,0.04322,-0.03137,-0.11391,0.02388,0.01005,0.00388,0.0687,0.01545,0.02704,-0.03243,0.0525,0.00208,0.00336,0.06186,0.03448,-0.00169,-0.1071,-0.04851,0.03356,-0.05112,-0.08722,0.04019,-0.0017,0.10946,0.08262,-0.01697,-0.01231,0.07444,0.04724,-0.02746,0.11236,0.00218,0.07346,0.0704,0.0807,0.0483,-0.12871,0.03692,0.07007,-0.02677,0.02801,-0.01962,-0.02647,0.0526,0.00839,-0.02691,0.01243,0.09192,0.00332,0.12296,0.07317,0.02411,-0.11278,-0.04172,0.00057,-0.03372]},{"domain":"signal_processing","key":"free_space_path_loss","name":"Free-space path loss","package":"signal-processing-ai999x","example":"What is the free-space path loss at 2.4 GHz over a distance of 100 m?","v":[0.04601,-0.03132,-0.00868,-0.03222,-0.00442,-0.03685,-0.01916,0.16097,0.06151,-6e-05,-0.07451,-0.01022,0.04716,0.09751,-0.12584,0.04451,0.00787,0.0299,0.01676,0.08578,-0.18597,0.01258,0.04316,-0.11041,0.03345,-0.12118,-0.08421,-0.10377,-0.02218,0.0812,0.074,0.07759,-0.04172,-0.01555,0.121,0.06063,0.00472,-0.00539,-0.02185,0.0961,-0.05421,-0.06801,0.11092,-0.02037,-0.12337,0.04361,-0.00726,-0.0047,-0.03953,-0.10573,0.05126,0.00074,-0.04606,0.05693,0.01656,0.00918,0.01061,0.0338,-0.10124,-0.13655,0.07492,-0.04196,0.07248,0.0048,-0.10738,-0.03133,0.03603,-0.00681,-0.07531,-0.11445,0.09375,0.13703,-0.11125,0.02368,0.02807,-0.12265,-0.05235,-0.11792,-0.00666,-0.04079,0.06765,0.01891,0.01661,-0.01882,0.02465,-0.07656,-0.12804,-0.03818,0.10449,0.01246,-0.01848,0.05233,-0.01683,0.00022,0.04874,-0.01745,-0.111,0.04795,0.05673,-0.02685,-0.04074,0.08955,-0.01007,-0.05007,-0.05756,-0.04318,0.03315,0.03503,-0.06451,-0.03088,0.05495,-0.00725,0.02502,-0.03026,0.06774,0.07974,-0.02515,0.01934,-0.04955,0.02879,0.01594,0.06414,0.00282,0.02869,0.02956,0.06204,-0.03077,0.08112,-0.11425,-0.01928,0.04522,0.07829,0.02157,-0.01128,-0.04832,0.10306,0.07144,0.02764,0.04738,0.01218,0.0091,0.15076,-0.01408,-0.0748,0.08715,0.01221,0.05235,-0.03797,-0.07642,-0.05578,0.09113,-0.06353,0.00953,0.02367,0.0341,-0.10431,0.06743,-0.04992,0.08196,0.0339,0.02372,-0.01474,0.1161,-0.02626,-0.03505,-0.01087,0.07964,-0.03953,0.01004,-0.05274,0.045,-0.02192,0.03505,0.13978,0.02295,-0.17932,-0.01463,-0.03918,0.03675,0.01725,-0.01541,-0.04139,-0.02207,0.03448,0.02947,-0.03877,-0.00162,-0.04201,0.0306,-0.01183,-0.06815,-0.09459,-0.01671,-0.04792,-0.02966,-0.07154,-0.00465,-0.07809,-0.07169,-0.07119,0.05028,0.05168,0.10904,-0.17844,-0.02789,-0.04302,0.05729,0.02478,0.0189,-0.00509,-0.03881,0.054,0.03512,-0.0902,0.02648,0.03028,0.04075,0.07934,0.05557,0.04827,-0.0679,0.05289,-0.02834,0.08359,-0.01134,-0.02957,0.02228,0.07589,0.10579,-0.04384,0.05856,0.07467,-0.06231,0.01412,0.00614,0.04318,0.01349,-0.10139,-0.00377,-0.03656,0.06233,-0.01739,0.03748,-0.05142,-0.00633,0.0835,0.02353,-0.06158,0.0537,-0.03855,-0.0033,-0.07044,0.01323,-0.03335,-0.05649,0.07727]},{"domain":"signal_processing","key":"frequency_from_period","name":"Frequency and angular frequency from period","package":"signal-processing-ai999x","example":"What is the frequency of a signal with a period of 2 ms?","v":[0.10467,0.0818,-0.07673,0.05498,-0.06523,0.007,-0.03917,0.00438,0.0473,0.07242,-0.01578,0.05488,0.07711,0.05987,0.01372,0.01422,-0.04359,-0.0346,0.04904,-0.02919,-0.05678,-0.08643,-0.05614,0.0109,0.07662,-0.09517,0.04294,-0.073,0.016,0.04963,0.03561,0.09172,-0.01802,-0.01985,-0.09354,-0.06853,0.01734,0.02028,-0.03321,0.00221,-0.09032,-0.07395,0.05772,0.05923,-0.03028,-0.03302,-0.08786,0.2365,-0.00298,-0.04641,-0.10084,0.03979,-0.13216,0.02019,-0.02001,0.01209,-0.05064,-0.01764,-0.17032,0.00617,-0.01449,-0.01973,-0.08922,0.08671,0.11388,-0.01198,-0.02399,-0.06141,-0.06022,-0.0846,-0.01401,-0.00328,-0.04468,-0.03288,0.0922,0.00778,-0.01694,0.00261,-0.03182,0.02681,0.10211,0.04347,0.07858,0.01301,0.01488,-0.05571,0.00796,-0.015,0.02677,-0.0362,0.0096,-0.11304,-0.08933,-0.02851,-0.0712,-0.02799,0.01539,-0.00736,0.0432,0.10255,-0.07064,0.09792,-0.03277,0.02805,0.01678,-0.0278,0.07514,0.05647,0.02712,-0.01173,-0.02011,-0.07045,-0.06813,0.01435,0.09635,0.08062,-0.00602,0.02961,0.00331,0.07236,-0.06155,-0.04664,-0.03953,-0.09058,0.01001,0.00152,-0.04707,-0.10618,-0.00596,0.04436,0.04206,0.04548,-0.03133,0.01392,0.09439,0.0756,0.00099,0.00598,0.12961,0.08648,-0.03404,0.08982,-0.10193,-0.0389,-0.05857,-0.03825,-0.03385,0.0515,-0.00054,0.0115,0.154,-0.13443,-0.02718,-0.02595,0.01364,-0.02179,0.0225,0.02574,0.03234,-0.02194,0.00946,-0.01213,0.07723,0.10728,0.01924,-0.0228,-0.02307,0.15511,0.03084,-0.06586,0.09716,0.07736,0.08625,0.24862,-0.08016,0.00037,0.01826,-0.02755,-0.03201,0.00097,-0.08788,0.00202,-0.0149,0.02101,-0.01809,0.04144,0.04198,0.01399,0.03921,-0.00256,-0.06136,-0.03592,-0.03924,-0.07399,0.04476,0.06567,0.08149,0.03407,0.04274,0.04604,-0.00412,0.03834,-0.02966,-0.02175,-0.00647,0.01357,0.00299,0.00478,-0.00278,-0.06313,0.12353,-0.05104,-0.01698,-0.00724,-0.0234,-0.02064,-0.05257,-0.02536,0.09349,-0.16589,-0.11307,0.00382,-0.00548,0.01076,-0.00201,-0.06915,0.09739,-0.02422,0.06318,-0.01161,-0.00241,-0.02443,-0.05296,0.1328,-0.00726,0.12569,-0.01225,-0.1435,0.0154,0.0035,0.04194,-0.00447,0.04004,-0.028,-0.02292,-0.01963,-0.02597,-0.12408,0.03868,-0.07426,0.07546,-0.00121,-0.07208,-0.06348,-0.07222,-0.04564]},{"domain":"signal_processing","key":"frequency_resolution","name":"Frequency resolution of an N-point DFT","package":"signal-processing-ai999x","example":"What is the frequency resolution of a 1024-point FFT at a sampling rate of 48 kHz?","v":[0.03875,0.07636,0.08943,-0.022,-0.00865,0.0715,0.01424,-0.01748,-0.04482,0.01092,0.07758,0.04873,-0.0627,0.01247,0.03448,0.03763,-0.02876,0.12746,-0.04281,0.07655,-0.04011,-0.06435,0.05329,-0.1514,0.03331,-0.01649,-0.0388,-0.15799,0.05154,-0.11605,-0.01487,-0.00645,-0.00541,-0.05358,-0.011,0.0393,-0.05359,0.07466,0.0399,0.12211,-0.04279,-0.02577,0.05588,-0.05838,-0.07281,0.05654,-0.03281,0.02435,-0.07385,-0.0489,-0.0557,0.02623,-0.10688,0.07017,0.03015,0.05652,0.02495,0.08176,-0.04513,0.00607,-0.01423,0.03078,-0.0577,-0.0794,-0.0238,0.05222,-0.0382,0.04938,-0.11729,0.01912,0.01775,0.03809,0.02653,0.07007,-0.00664,0.07782,-0.0064,-0.00949,-0.03201,-0.05704,0.10278,-0.05946,-0.07797,-0.05337,0.10234,-0.0663,-3e-05,0.03849,-0.03401,-0.08304,0.02814,-0.01909,0.02783,-0.07853,0.02367,0.05334,0.04045,0.0956,0.14468,0.02185,-0.05806,0.03001,0.03046,-0.09772,0.0048,0.01591,0.0423,0.07099,-0.10869,-0.05095,-0.096,-0.09843,-0.10619,0.00881,0.07939,0.11406,0.04883,0.11905,0.05852,0.01052,-0.05264,-0.00361,0.02866,0.10983,0.01078,0.03087,-0.16754,-0.03454,-0.03912,-0.07654,0.01436,0.03554,-0.05404,0.01117,0.06068,0.12742,0.06919,0.06051,0.0376,0.02856,-0.17455,0.12155,-0.04487,-0.01551,-0.01673,0.01275,-0.03369,-0.0841,-0.00089,-0.02395,0.13338,-0.16681,-0.01577,0.03569,0.00961,-0.05106,0.04523,0.07998,-0.00371,-0.02873,-0.01278,-0.01565,0.13809,0.02779,0.08088,-0.05068,-0.03525,0.0118,0.02046,-0.09017,0.05776,-0.09099,0.02369,0.07643,0.00244,0.05664,-0.05971,0.0493,-0.03833,0.03913,-0.09891,0.01593,-0.00729,0.06794,-0.00461,0.03833,0.03668,0.01197,0.04468,-0.00012,-0.03301,0.00348,-0.04267,0.0583,0.06045,-0.03386,-0.02116,-0.1008,-0.01347,-0.0525,-0.03569,0.03672,-0.053,-0.08341,0.01217,-0.02016,-0.0678,0.02983,-0.01979,0.01207,0.08147,-0.05885,-0.0024,0.05909,-0.00497,0.00594,0.03502,0.09434,0.02325,-0.09136,0.00569,-0.00159,0.06486,0.07126,0.03195,0.02735,0.07458,-0.00118,-0.09641,-0.01279,-0.04808,-0.06629,-0.15618,-0.04279,-0.12555,0.14515,-0.02966,-0.06069,-0.01779,0.13333,0.02856,-0.01845,-0.07922,-0.04036,0.01742,0.01311,0.00255,-0.03279,0.07033,-0.03976,0.07579,-0.04209,-0.05276,-0.02494,0.01781,-0.08251]},{"domain":"signal_processing","key":"frequency_response","name":"Frequency response of a digital filter at one frequency","package":"signal-processing-ai999x","example":"What is the magnitude response of the filter b = [1, 1] at 1 kHz with a sampling rate of 8 kHz?","v":[0.03105,0.06228,0.0556,0.01786,0.0988,-0.00022,-0.06734,-0.0131,-0.08695,-0.05941,-0.06904,-0.00915,0.06155,0.01665,-0.01922,0.00785,0.05551,0.0463,0.05537,0.10241,-0.04142,-0.04351,0.02337,0.00709,-0.0125,-0.04683,0.03872,-0.13181,0.0307,-0.02658,0.08464,0.02852,-0.04002,-0.0065,0.02553,0.01282,0.03484,0.06785,0.01801,-0.0058,0.0195,-0.03612,0.05473,0.01477,0.12422,0.00376,-0.06547,-0.06356,-0.11225,-0.11691,0.00222,-0.0396,0.00063,-0.07026,-0.00317,0.09193,-0.08715,0.00604,-0.03476,-0.07192,-0.02788,-0.09569,0.01197,-0.0768,-0.04487,-0.0907,-0.00315,0.02468,-0.02358,-0.01943,0.1251,0.05473,-0.05171,-0.07584,0.05926,-0.05277,0.01272,-0.0171,0.00185,-0.06117,0.07221,-0.06896,0.00211,0.0182,0.06171,-0.03449,0.06398,-0.03979,-0.01541,-0.05574,0.18422,-0.13073,0.03533,-0.06456,-0.02504,0.04154,0.00069,-0.04169,0.18051,-0.08311,0.04417,-0.04553,-0.0056,-0.0729,-0.01531,-0.02737,0.00176,0.04625,-0.05735,0.02665,-0.08747,0.05388,0.03081,-0.03122,0.00668,-0.00154,0.01491,0.02455,-0.03101,-0.02388,0.00773,0.03734,0.00591,-0.02768,0.07995,0.02197,-0.08765,-0.00602,0.00171,-0.04887,0.12064,0.08129,-0.01123,-0.03219,-0.0345,0.11929,-0.04091,0.00638,-0.01685,0.05339,-0.10648,0.04031,-0.03604,-0.00486,0.08458,0.07835,0.06169,-0.08887,-0.03822,-0.09201,0.08099,-0.03769,-0.03649,0.02436,-0.0633,-0.01642,-0.00986,0.04993,-0.02213,0.09862,0.14799,0.00084,0.09292,-0.02177,0.05926,-0.03267,-0.11401,-0.07817,0.08603,-0.03199,0.05419,-0.06256,-0.0232,0.05255,-0.0972,0.00204,0.03795,-0.05461,-0.00593,0.07523,-0.12443,0.12525,-0.03119,0.04783,-0.10209,0.01709,-0.03224,0.04601,0.01872,0.07179,0.06222,0.08629,-0.03655,-0.00644,-0.04391,-0.03532,0.01052,-0.02779,-0.03674,0.02476,-0.06784,0.06081,-0.00824,0.05936,0.02727,0.00362,0.08225,-0.06352,0.00464,0.06909,0.03713,0.03669,-0.0187,0.06889,0.06179,-0.06946,-0.06077,0.08213,0.12458,-0.07031,0.03996,0.02382,0.02368,0.09975,0.0164,0.03724,0.12513,0.03983,0.05145,0.07092,0.02741,0.02568,-0.0497,0.10902,-0.10394,0.09281,-0.04072,-0.17804,0.00525,0.07785,-0.08216,-0.00567,-0.08532,-0.09804,0.08774,-0.12785,-0.04794,-0.15343,0.08847,-0.03386,0.0641,-0.06786,0.03379,0.02503,-0.05423,-0.02361]},{"domain":"signal_processing","key":"friis_received_power","name":"Received power of a radio link (Friis transmission equation)","package":"signal-processing-ai999x","example":"Find the received power for a transmit power of 1 W, a transmit antenna gain of 10 dBi, a receive antenna gain of 5 dBi, a frequency of 2.4 GHz and a distance of 1 km.","v":[-0.07896,-0.02697,0.0111,-0.08554,-0.0289,0.03129,0.01388,0.11487,-0.00571,-0.00461,-0.09558,0.01367,-0.00312,0.02373,-0.0707,-0.07589,0.07679,-0.0004,0.07694,0.0659,-0.09787,-0.08006,0.094,0.03572,-0.04888,-0.04976,-0.04953,-0.08712,0.03597,0.09376,0.02376,0.02715,-0.01209,0.01543,0.03607,0.14944,-0.06083,-0.01923,-0.04415,0.02008,-0.03971,-0.00673,-0.0074,0.05964,-0.15072,0.0199,0.03238,-0.04214,-0.05025,-0.09235,0.00305,0.07202,0.04471,0.05013,-0.02843,0.04124,0.003,-0.01172,-0.05127,-0.05415,0.00073,-0.11574,0.04744,-0.07826,-0.11427,-0.02728,0.02823,-0.00296,-0.06885,-0.05741,0.02652,0.00107,-0.07156,0.05682,0.02804,-0.13641,0.01173,-0.02722,-0.0429,0.0491,0.01228,0.02289,0.04028,-0.0181,-0.01685,-0.05879,-0.01449,0.00799,0.05403,-0.01265,-0.01604,0.02132,-0.04278,0.12277,0.03109,0.00121,-0.03185,0.10701,0.08932,-0.12352,0.03375,0.02278,-0.01559,0.07837,0.04553,-0.03298,-0.01854,0.03046,-0.02807,-0.02021,0.05461,0.09909,-0.00932,0.02154,0.13468,0.04073,0.01826,-0.13097,-0.08033,-0.06831,0.01949,0.00268,-0.1046,0.00277,0.0529,-0.08002,-0.04153,0.08046,-0.0667,-0.06096,0.0674,0.06713,-0.04265,-0.02533,-0.01145,0.18996,0.08281,0.02291,-0.05734,-0.02159,-0.03033,0.11657,-0.04174,-0.06349,0.06402,-0.05224,-0.02044,-0.00099,0.05408,-0.04697,0.03687,0.08332,-0.01503,0.07077,-0.083,-0.01162,0.08383,-0.06766,0.07674,0.02107,-0.04131,0.05282,0.01345,0.04114,0.0854,0.03245,0.05154,0.10703,-0.10401,-0.04777,0.01679,-0.09225,0.02062,0.10796,-0.0481,-0.09602,-0.01526,-0.05008,-0.03178,0.08063,0.02326,-0.04657,0.07561,0.05421,0.08605,-0.03595,0.0525,-0.07,-0.03987,-0.08765,-0.00851,-0.02271,-0.08672,0.10398,0.02655,0.00533,-0.01505,0.04718,-0.06871,-0.11708,-0.05972,0.08971,0.13402,-0.06869,-0.00505,-0.03308,0.03239,0.00836,0.08166,-0.0526,0.01049,0.02346,0.11912,-0.07479,0.04944,-0.05954,-0.04863,-0.00441,0.06595,-0.04835,0.11658,0.02034,-0.04339,0.02254,-0.10714,-0.07223,0.08788,0.07804,0.08101,0.1215,0.00744,0.09586,-0.00313,-0.0517,0.00959,-0.00091,0.16153,-0.06425,-0.05316,-0.01222,0.06046,-0.11888,-0.00993,-0.07022,-0.07655,0.0607,-0.00143,0.00459,0.04635,0.01478,0.01919,-0.03827,-0.0287,0.05073,-0.09587,-0.00212]},{"domain":"signal_processing","key":"group_delay","name":"Group delay of a digital filter","package":"signal-processing-ai999x","example":"Find the group delay of the FIR filter b = [1, 2, 3, 2, 1] at 500 Hz with a sampling rate of 8 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discrete wavelet transform","package":"signal-processing-ai999x","example":"Compute the 2-level Haar wavelet transform of x = [4, 6, 10, 12, 8, 6, 5, 5].","v":[-0.01303,0.02785,0.03301,0.05738,0.00579,0.10143,-0.10169,0.05785,-0.09413,-0.00196,-0.04435,0.04677,-0.09752,-0.02492,-0.00209,-0.0202,0.06748,-0.01123,-0.03206,-0.03792,-0.07362,0.07521,0.0184,-0.0186,-0.07156,0.06488,0.021,0.0057,-0.09888,-0.06656,0.03698,0.00882,0.01772,0.0238,0.1026,-0.04187,-0.02973,0.14234,0.03709,0.03214,0.0676,0.02279,-0.03364,-0.05035,0.03309,-0.02728,0.00831,0.06524,-0.1066,-0.06917,-0.0697,0.09271,0.00319,-0.06804,-0.06288,-0.06052,0.1273,-0.06338,0.0996,-0.05633,0.03712,0.02218,0.08766,0.06353,0.09054,0.03452,-0.05326,0.04988,0.02339,-0.01335,0.04558,-0.07348,0.0264,-0.02684,-0.06614,0.11975,-0.0162,-0.00105,0.03664,0.02851,0.04769,0.07373,0.03767,-0.02982,0.06735,-0.0246,-0.00423,0.06923,0.04988,-0.01234,-0.02706,-0.01433,0.03173,-0.01838,-0.09747,0.0339,0.08881,0.04773,0.04828,0.00421,0.02479,-0.06495,0.00111,-0.03614,-0.03643,-0.07377,-0.132,-0.02093,0.07484,-0.10121,-0.01361,-0.13351,-0.02467,-0.0068,-0.01546,-0.02188,-0.04078,-0.02066,0.07545,-0.06302,0.00808,-0.02536,0.05551,-0.04023,0.03199,0.05234,-0.08151,0.03031,0.0601,-0.1329,-0.03654,-0.05842,0.06588,-0.10989,0.02119,-0.00338,-0.12639,0.02371,0.07453,-0.04634,-0.15717,-0.11305,-0.01678,0.06129,0.09815,0.01843,-0.02965,-0.03841,0.06934,-0.12791,-0.04729,0.00949,-0.03124,0.09836,-0.04999,0.0391,0.07261,-0.01286,-0.01513,0.14241,-0.01694,0.05814,0.08264,0.08116,-0.06364,0.00452,-0.07422,0.02779,-0.00999,0.07813,0.0817,0.04699,0.0332,-0.06872,-0.04087,-0.02673,-0.03366,0.08521,-0.04664,-0.12676,-0.04875,0.08616,-0.13284,-0.0233,-0.05967,-0.06545,0.02476,0.05225,0.06793,0.11903,0.00043,-0.10344,0.05292,0.06956,0.07764,0.0149,0.04444,-0.05194,-0.05544,0.02849,0.02352,-0.05729,-0.06857,0.0345,0.05954,0.00938,0.09742,-0.0427,-0.06089,-0.06067,0.07211,-0.12105,0.05113,0.00327,0.07756,0.00754,-0.05888,-0.09864,0.04696,-0.03193,0.07953,0.03093,-0.07306,0.12963,0.07073,0.03891,0.12701,0.09154,0.06083,-0.02711,-0.08862,0.01613,0.01583,-0.02722,0.01525,0.05568,-0.01658,0.00021,0.0074,-0.0659,0.00984,0.01088,-0.1035,0.02241,-0.00662,0.0252,-0.03681,0.11613,-0.00991,0.04992,0.07838,-0.06032,-0.08788,0.1118,0.04212,-0.02011]},{"domain":"signal_processing","key":"haar_idwt","name":"Inverse Haar wavelet transform (one level)","package":"signal-processing-ai999x","example":"Compute the inverse Haar transform with approximation coefficients [16, 12] and detail coefficients [-6, 2].","v":[0.118,0.11551,0.03321,0.1172,0.00977,0.09325,-0.10309,0.03506,-0.08668,-0.03193,-0.07138,0.0369,-0.0714,-0.12263,-0.03249,-0.02441,0.058,0.00385,-0.06915,0.01686,-0.0705,0.06814,0.02739,-0.00259,-0.06802,-0.00123,0.09545,-0.04481,0.01499,-0.03689,0.02748,0.00447,-0.03006,-0.00339,0.02631,-0.04704,-0.05452,0.07393,0.01816,0.01853,0.08764,-0.02103,-0.08283,-0.05716,0.02352,-0.03026,-0.05985,0.04965,-0.08188,-0.07858,0.00681,-0.0455,-0.02029,-0.01665,-0.0646,0.02733,0.09823,-0.03055,0.04107,-0.03193,0.01746,0.02973,-0.02309,0.0409,0.052,-0.01199,-0.09632,0.00714,0.08077,0.01847,0.03348,-0.06731,0.1195,-0.12086,-0.06949,0.0482,-0.0424,0.01429,0.0568,-0.02393,0.08477,0.08013,0.05005,0.03216,0.10884,-0.0008,-0.02726,-0.04149,0.00425,0.05423,0.01919,-0.00637,0.03463,0.03068,-0.02514,0.03444,0.04279,-0.02582,0.05539,0.00186,0.03404,-0.0359,-0.03639,-0.03927,-0.07537,-0.09506,-0.04657,0.02193,0.0061,-0.06995,0.03869,-0.09122,-0.03575,-0.02523,0.02098,-0.05962,-0.01659,-0.04308,0.00208,-0.03812,-0.07849,-0.11772,0.05851,-0.10279,0.0743,0.10244,-0.05322,0.06139,0.04787,-0.11156,-0.04334,-0.08867,0.01678,-0.05254,0.08022,-0.05852,-0.17695,0.0516,0.00854,-0.09318,-0.03326,-0.17443,-0.01062,0.0286,0.11188,0.00947,0.01254,-0.03349,0.08009,-0.105,-0.04993,0.00034,0.09798,0.03712,0.0117,0.0149,0.06899,-0.04103,-0.01413,0.09031,0.00405,-0.02111,0.00986,0.03156,-0.01657,-0.04978,-0.02702,0.01342,-0.04714,0.12591,0.08735,0.06955,0.11773,-0.10526,-0.04388,0.0019,-0.00226,0.03941,0.00988,-0.09128,-0.09833,0.04481,-0.11385,-0.04805,-0.02705,-0.01362,0.06106,0.04042,0.09371,0.13119,0.06769,-0.01927,0.02448,-0.04868,0.10424,-0.00747,0.08719,0.02927,-0.03892,0.09452,-0.03868,-0.03722,-0.02376,-0.03288,-0.0744,-0.03579,0.11871,-0.02038,-0.05597,-0.03331,0.14503,-0.07611,0.03281,0.02975,0.13937,-0.01407,-0.01704,-0.01371,0.12091,-0.03839,0.07285,0.07414,-0.08201,0.05639,-0.05812,0.0155,0.10166,0.13177,0.08857,0.00816,0.04131,-0.00233,-0.02242,-0.03228,0.04044,0.02209,-0.09302,0.02155,-0.03031,-0.06405,-0.00245,0.01474,-0.09943,0.04684,0.06164,0.06101,-0.03613,0.05925,0.02796,-0.04409,-0.02028,-0.01688,-0.12018,0.11421,-0.01839,0.02433]},{"domain":"signal_processing","key":"iir_filter_output","name":"IIR filter output (difference equation)","package":"signal-processing-ai999x","example":"Find the output of the IIR filter with b = [1] and a = [1, -0.5] for the input x = [1, 0, 0, 0].","v":[0.06836,0.05084,0.05679,0.05173,-0.03337,0.07444,-0.17255,-0.03937,-0.05671,-0.03805,0.03148,-0.01418,-0.11233,0.00042,0.09275,-0.07997,0.01734,-0.05849,-0.06454,0.03951,0.0274,0.00033,0.029,0.04881,0.04203,-0.03006,-0.00614,0.06011,0.03321,-0.04502,0.09567,-0.05391,-0.00635,-0.04239,0.0701,0.01917,-0.0068,0.10017,-0.02774,-0.02698,0.04101,-0.04374,-0.04528,-0.01379,-0.01048,-0.01076,-0.04263,-0.05135,-0.03369,0.02311,-0.00784,0.02376,0.08399,0.01425,-0.03141,0.15965,0.03057,0.00783,0.11757,-0.0042,-0.06786,0.03192,0.05205,-0.12469,0.02236,0.07817,0.04894,-0.03484,0.03271,-0.12401,0.00195,0.05251,-0.03857,0.02799,-0.0883,-0.03817,0.0314,0.04765,0.04008,-0.12982,0.02943,-0.08005,0.02691,0.02504,-0.00543,-0.01069,-0.03699,0.00475,0.05533,0.01116,0.0602,-0.0602,0.07221,-0.0223,0.00481,-0.00552,0.11292,-0.09575,0.07008,-0.09645,0.0799,-0.04136,-0.09418,-0.00971,-0.05089,0.00312,-0.04683,-0.0755,0.08233,0.01126,-0.03023,0.02716,0.0402,-0.03085,0.09933,0.10724,-0.03378,-0.02632,-0.00758,0.03736,-0.04914,8e-05,0.04833,0.02056,0.04737,0.01813,-0.13621,0.01243,0.08693,-0.01698,0.02569,-0.01485,0.03766,-0.03674,-0.02533,-0.03971,-0.04914,-0.03032,-0.01228,-0.19855,-0.1963,0.03229,-0.01478,0.05946,0.11526,0.01212,0.04202,-0.0016,0.0425,-0.08874,0.00633,0.02984,-0.08999,-0.06511,-0.03813,-0.08029,-0.0411,0.00261,-0.06743,0.04091,0.07471,0.0225,-0.01044,-0.07166,0.07507,0.00519,-0.05158,-0.02809,-0.07161,0.02935,0.1001,0.00211,0.06179,-0.0901,-0.00305,0.00629,-0.07291,-0.18994,0.03439,0.09201,-0.03237,0.08298,-0.07896,0.01863,-0.06817,0.06986,-0.0206,-0.03914,-0.01122,0.07977,0.06889,0.13088,-0.02019,-0.01927,0.04972,0.03983,-0.025,-0.05869,-0.04065,0.00875,-0.01145,0.00732,-0.0383,0.06311,0.02725,-0.06031,0.03219,-0.02116,-0.03163,-0.02234,0.08219,-0.12225,0.09122,0.05404,0.09208,-0.06178,0.01568,0.01923,0.10655,0.04299,0.17723,-0.02754,-0.04169,0.05623,0.01978,0.03826,0.12089,0.07534,0.0565,0.07693,-0.09865,-0.01612,-0.0736,0.0328,-0.09291,-0.03043,-0.01531,-0.02198,0.04944,0.10326,0.02858,0.08573,-0.05424,-0.10954,0.00336,0.05665,-0.01189,-0.07046,-0.01981,0.11568,-0.00482,0.00587,-0.04694,0.06296,-0.03423,-0.10157]},{"domain":"signal_processing","key":"impulse_response","name":"Impulse response of a digital filter","package":"signal-processing-ai999x","example":"Find the first 5 samples of the impulse response of the filter with b = [1] and a = [1, 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figure of cascaded stages (Friis formula)","package":"signal-processing-ai999x","example":"Find the overall noise figure of a cascade with noise figures [2, 6, 10] dB and gains [15, 20, 10] 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error rates of DPSK and noncoherent BFSK","package":"signal-processing-ai999x","example":"What is the bit error rate of DPSK at Eb/N0 = 8 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IIR notch filter design","package":"signal-processing-ai999x","example":"Design a notch filter at 60 Hz with a quality factor of 30 for a sampling rate of 1 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rate","package":"signal-processing-ai999x","example":"What is the Nyquist rate for a signal with a maximum frequency of 4 kHz?","v":[-0.02771,0.13005,0.06946,0.08915,-0.08889,0.02346,-0.0084,-0.01821,0.02462,0.03263,-0.0555,0.06667,0.1095,0.02686,-0.03383,0.02008,0.03309,0.0547,-0.03399,0.03144,0.0196,0.0029,-0.0029,-0.10082,0.06939,0.00293,-0.02237,-0.02318,0.01883,0.04434,-0.07059,0.02936,-0.0346,0.03527,-0.07258,-0.04228,-0.05263,-0.03854,-0.04804,-0.00613,0.00874,-0.09033,0.07041,-0.0145,0.01202,0.06903,-0.05533,0.01261,0.03736,-0.02571,0.08416,-0.02447,-0.11159,0.00212,-0.02678,0.07619,-0.00717,-0.00319,-0.08267,0.0386,-0.04186,-0.0343,-0.00418,0.09133,-0.01524,0.01385,0.00078,0.0635,-0.03387,0.01661,-0.00793,0.04669,-0.01697,0.04804,-0.05503,0.04327,-0.08419,0.02985,-0.01431,-0.0178,0.16253,0.03606,-0.13631,-0.04314,-0.00237,0.00077,-0.01698,-0.02067,0.00966,-0.08137,0.13262,0.07312,0.06876,-0.04387,-0.00654,0.08981,-0.0177,0.05204,0.1309,0.03953,-0.11031,0.05809,-0.01843,-0.04771,0.0168,0.01853,-0.07394,0.04285,-0.10212,-0.11385,-0.11521,0.01543,0.01299,0.04141,-0.00034,-0.0753,-0.02819,0.04956,-0.04013,0.04496,0.02966,0.01796,0.0434,-2e-05,-0.06139,0.03494,-0.07174,-0.07556,0.00699,-0.05758,0.096,0.01679,-0.15654,0.11768,-0.02401,0.05608,0.05618,0.033,0.05169,0.11398,-0.05165,0.1617,-0.01122,-0.0011,-0.00917,0.00486,-0.01756,-0.05618,-0.04291,-0.00793,0.08959,-0.1559,-0.1705,0.00742,-0.02621,-0.08162,-0.00614,0.07712,-0.07385,0.01832,0.0454,0.0881,0.12602,-0.01315,-0.01764,-0.00057,-0.03613,-0.05772,0.14124,-0.08155,0.00785,-0.11721,0.04617,0.03816,-0.06791,0.01664,0.00282,0.04094,-0.03985,-0.00573,-0.1719,0.01677,-0.02627,0.05172,-0.04334,0.00381,-0.01628,0.05291,0.02453,0.10102,-0.14658,-0.03185,-0.00334,-0.01022,0.01428,-0.0691,0.06789,-0.06236,-0.02169,-0.01048,-0.00695,0.0481,0.00665,0.04313,-0.06256,-0.0183,-0.07852,0.09049,-0.0466,-0.09224,-0.05419,-0.01785,0.00271,0.08617,0.0118,0.09577,-0.04623,0.17902,0.05897,-0.06695,-0.04759,-0.01969,0.02157,-0.0473,-0.00626,0.04146,0.00101,0.03542,-0.03202,-0.1426,-0.00018,-0.03513,-0.08628,0.08868,0.02059,0.1622,-0.08321,-0.05332,-0.08188,0.00186,-0.04155,0.02485,-0.04444,-0.06319,0.04243,0.01124,-0.01685,-0.0699,-0.04118,-0.07551,0.04957,0.0847,0.07712,-0.02923,-0.04307,-0.01247]},{"domain":"signal_processing","key":"period_from_frequency","name":"Period 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zeros and stability of a digital filter","package":"signal-processing-ai999x","example":"Find the poles and zeros of the filter with b = [1, -1] and a = [1, -0.9].","v":[-0.04255,-0.05945,0.0324,0.09976,0.01994,-0.02819,-0.09416,-0.02863,-0.07481,-0.04093,0.02811,0.08882,-0.0155,0.02724,0.03308,0.09719,-0.01004,0.0379,0.00517,0.03485,-0.02858,-0.14226,-0.03514,-0.0965,0.03546,-0.04444,0.0219,0.11832,0.07763,0.01865,0.0181,0.01668,0.00154,-0.00148,0.01406,-0.05875,0.03443,0.07461,0.12227,-0.07526,0.06147,0.03589,0.13242,-0.00794,0.03204,-0.03301,-0.03481,-0.13184,0.03928,-0.04054,0.04427,-0.06532,0.08014,-0.01124,0.01246,0.07306,-0.12294,0.13514,0.09081,0.02253,-0.02266,0.02683,-0.00633,-0.09487,-0.02076,-0.01397,0.0015,-0.07367,0.04709,-0.0739,0.00102,0.04655,-0.08247,0.01791,-0.01399,0.01061,-0.04015,0.04495,0.07749,-0.06037,0.03728,-0.11586,-0.06339,0.00788,0.07454,0.00895,-0.02967,-0.0055,0.00472,-0.11176,0.11929,-0.01286,-0.02327,-0.10075,0.06854,-0.00344,0.1051,0.0039,-0.01144,0.02447,0.08246,-0.04787,-0.07047,0.06569,-0.09417,0.02823,-0.022,-0.10215,-0.06261,0.07226,-0.08021,0.08288,0.05955,-0.00734,-0.00302,0.06594,0.02768,-0.03157,-0.02437,0.09775,0.06823,0.01751,0.06483,-0.00079,-0.06097,0.05607,-0.02879,0.00257,0.09573,-0.03735,0.03754,-0.00643,0.08199,-0.09336,-0.09352,0.05741,0.07352,-0.07735,-0.01859,0.00077,0.01639,0.05795,0.0367,0.09176,0.0761,0.06673,0.11914,-0.01928,0.01955,-0.01181,0.05842,0.02929,-0.05806,-0.02278,-0.02176,-0.06073,-0.03721,0.0622,-0.1544,0.05447,0.10483,0.06686,-0.03737,-0.09812,0.15893,0.06518,-0.00948,-0.047,0.08644,-0.07908,0.05186,-0.05382,-0.0251,-0.06499,-0.03201,-0.00512,-0.0375,-0.0761,0.03013,0.11511,-0.06582,0.04206,0.00929,0.03909,-0.01436,-0.02017,-0.09707,0.10041,0.0169,0.09657,0.01609,0.09106,0.06155,0.00345,-0.09283,-0.10238,-0.03818,-0.10726,0.059,-0.00407,0.01288,0.01283,-0.03959,0.05963,0.09987,0.04503,0.05983,-0.09748,-0.06051,-0.05667,0.03246,0.00716,0.05455,0.02497,0.07329,0.03796,-0.0719,0.07462,-0.00204,-0.04634,0.05426,0.02032,-0.01337,-0.0356,-0.00069,0.06583,0.08763,-0.01536,-0.01221,-0.04126,0.00691,-0.02825,-0.05419,-0.1191,-0.1157,0.09492,-0.08779,-0.11208,0.05274,0.02197,-0.01728,0.09072,-0.0248,-0.06833,0.01063,-0.07654,0.00502,-0.13724,-0.0823,0.01462,-0.04277,-0.02789,0.04175,0.02393,-0.00984,-0.06225]},{"domain":"signal_processing","key":"power_ratio_to_db","name":"Power ratio to decibels","package":"signal-processing-ai999x","example":"Express a power ratio of 200 in decibels.","v":[-0.06406,-0.10055,-0.04938,-0.03183,0.05092,-0.0314,-0.07359,0.07081,-0.10146,0.01493,-0.04901,-0.04734,-0.01962,-0.00314,-0.12188,0.09908,0.07365,-0.01708,0.03938,0.09961,-0.0534,-0.08234,0.04355,-0.03067,-0.12164,0.03665,-0.00681,-0.0223,-0.00142,0.13355,-0.02949,0.0072,-0.06274,0.01573,0.008,0.08215,-0.04341,0.01753,0.02337,-0.01685,-0.04563,-0.01054,0.0603,-0.01271,-0.0041,0.06973,0.08689,-0.04563,-0.04417,0.05445,0.07523,0.00166,-0.01267,0.00983,-0.00631,-0.05694,-0.02754,-0.14076,-0.01304,-0.10964,-0.02718,-0.05905,0.09603,0.00207,-0.04662,-0.00172,-0.01327,-0.04361,0.02211,-0.02605,0.10262,0.02381,-0.08516,0.00513,0.07036,-0.14093,0.05556,-0.06547,0.01639,-0.05047,-0.1174,0.02267,0.00113,-0.09969,0.04565,-0.07123,0.0386,-0.01704,0.08262,-0.09055,0.01754,0.0358,0.01417,-0.06717,-0.02852,-0.00217,0.02335,0.02756,0.18443,-0.08406,-0.03606,-0.01413,0.04301,-0.05341,-0.02741,0.0307,0.06863,0.04712,-0.04533,0.11095,0.0267,0.05343,-0.01535,-0.05152,-0.07197,0.02013,-0.0325,0.04953,-0.07188,-0.0931,0.00461,0.01231,0.07958,0.00745,-0.00075,0.03842,-0.10175,0.02449,-0.00305,-0.0251,0.04796,0.00043,0.00296,0.00539,0.02597,0.10796,-0.0596,-0.04121,0.00102,0.06687,-0.00996,0.13693,0.01309,-0.02635,0.0674,-0.04577,-0.06402,-0.0786,-0.01621,-0.01474,-0.14169,-0.00926,-0.00551,0.01504,0.0628,-0.04619,0.09483,0.02158,0.14783,-0.00123,0.11869,0.03163,0.10444,0.06986,0.03268,-0.02997,0.01887,-0.08233,-0.00603,-0.04666,-0.02966,-0.07015,-0.01021,-0.01972,-0.02917,0.02209,0.04605,0.01471,-0.05532,0.05958,0.00932,-0.02045,0.08981,0.08838,0.12102,-0.05863,-0.04613,-0.03632,0.00758,0.03505,0.00173,-0.03704,-0.10954,0.02166,-0.03336,0.03232,-0.08832,0.03945,-0.05722,-0.01931,0.02188,-0.08562,0.14025,0.03879,0.0023,-0.01926,-0.05257,-0.15999,0.0385,0.0936,-0.13312,0.01238,0.01441,-0.12389,0.16986,-0.05228,-0.09484,0.02187,-0.08507,0.01208,0.12896,-0.04947,-0.09491,0.04615,0.0652,-0.09594,0.1122,0.01104,0.01295,0.04982,0.03798,0.01171,0.05221,0.03908,-0.04906,-0.03183,0.05418,0.00771,0.04043,0.00688,0.03266,0.12228,-0.01914,0.00871,0.01607,0.08266,0.03493,-0.049,-0.09232,-0.00078,0.02881,0.07058,0.07022,0.08395,0.09486,-0.04318]},{"domain":"signal_processing","key":"qpsk_error_rates","name":"Bit 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dB?","v":[0.03429,-0.05527,0.09065,-0.09653,0.03772,-0.0399,0.11297,0.03798,-0.0616,-0.0306,-0.03532,-0.04799,0.08072,0.03693,-0.10337,-0.06181,0.08454,-0.06334,-0.08181,0.00604,-0.03485,-0.04627,-0.09519,0.027,-0.09869,-0.00791,-0.00305,-0.0462,-0.01031,0.12152,0.05789,0.06296,0.00319,0.04574,-0.05707,-0.01765,-0.01881,-0.03104,0.05771,-0.02004,0.08194,-0.01768,0.03064,0.13017,0.00718,0.01698,-0.01872,-0.01925,0.06872,-0.05752,-0.01625,-0.00142,0.08056,0.03799,0.09607,0.17223,0.01132,0.13007,-0.09901,-0.00766,-0.06667,-0.10043,0.01688,0.01229,0.03288,-0.06392,0.10759,-0.09077,-0.1837,0.08194,0.12452,0.00235,0.10286,-0.01757,0.0956,-0.0371,0.01081,-0.01026,0.00597,-0.03891,0.05522,0.07598,0.03331,0.05593,-0.0454,0.03707,0.07109,0.02669,-0.01251,0.04477,-0.07481,-0.00613,0.06378,0.05381,-0.00802,0.01993,-0.04582,-0.01517,0.06243,-0.11115,-0.08671,-0.06925,0.0412,0.07772,-0.037,-0.10278,-0.03411,-0.02111,-0.0884,-0.14555,-0.03149,0.06609,0.0765,-0.03506,0.072,0.02265,0.01388,-0.01173,-0.0543,-0.02845,0.03158,-0.0225,-0.04457,-0.04512,-0.02356,-0.12249,-0.03399,0.00929,-0.05695,-0.0656,0.18672,-0.02978,-0.14302,0.02372,0.06867,-0.03664,0.00751,0.04438,-0.06543,-0.01392,-0.05561,0.05425,-0.14366,0.05233,0.01965,-0.02894,0.07653,-0.08635,0.00722,-0.01224,0.0967,-0.00204,-0.00936,-0.05505,0.05716,0.05169,0.10644,0.06566,-0.01472,-0.06521,-0.02298,0.00815,0.03685,-0.01137,-0.01354,0.01201,-0.02061,0.17107,0.02559,-0.08545,0.02252,-0.19481,-0.09063,-0.08764,0.04036,-0.01825,0.0297,0.05017,-0.05892,-0.05519,-0.11254,-0.03209,-0.07354,-0.01771,0.07772,-0.00237,-0.04175,0.0569,-0.05591,0.02957,0.00187,0.00613,-0.02269,0.07646,-0.02207,0.03218,0.02256,0.08359,-0.01904,-0.00429,-0.03527,0.11049,0.05944,-0.00313,0.02624,0.03014,-0.09098,-0.00588,0.02708,0.04433,0.01767,-0.01764,0.03858,0.00467,-0.00822,-0.06507,-0.09641,-0.00889,0.01313,-0.09933,0.05353,-0.01894,0.02045,0.02532,-0.05852,-0.01303,0.08172,-0.05353,0.01964,0.03284,-0.02582,0.02163,0.00528,0.00355,0.08318,0.08241,0.02105,0.01609,-0.04734,-0.07527,0.10104,-0.06746,-0.01593,-0.03324,-0.00761,0.06604,0.09103,-0.05432,0.01384,0.0081,0.04538,0.06351,-0.05808,-0.06081,-0.03523,0.06163]},{"domain":"signal_processing","key":"quantization_snr","name":"Signal-to-quantization-noise 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shift of a radar echo","package":"signal-processing-ai999x","example":"A 10 GHz radar sees a target approaching at 30 m/s. What is the Doppler shift?","v":[0.07904,0.0259,0.02108,0.03794,0.09064,0.03531,-0.04925,0.05286,-0.02681,-0.0689,0.10104,0.04854,-0.02879,0.03052,-0.07435,0.04719,-0.05138,-0.05475,-0.03723,0.04042,-0.03133,0.03011,-0.01721,-0.02794,-0.04595,-0.03337,-0.11172,-0.16287,0.0574,-0.00743,0.03959,-0.06361,0.0007,-0.01717,-0.07138,0.04421,-0.02294,-0.00606,0.01405,0.0501,-0.04826,0.03086,0.15148,-0.14055,-0.06537,0.05555,0.07127,0.02673,-0.07717,-0.11515,0.00748,0.01806,-0.08118,0.02522,0.04597,-0.00988,-0.06515,0.01047,-0.06056,-0.02288,0.04324,0.02725,0.17898,0.01821,0.00144,-0.01312,-0.01568,-0.00964,-0.01019,0.02932,0.0618,0.11117,-0.0192,-0.00555,0.06963,-0.16225,-0.08614,-0.02039,-0.0393,0.02287,0.11533,0.09239,0.01047,0.00925,-0.03151,-0.03035,-0.0724,-0.10998,-0.00997,0.00218,-0.09196,0.061,0.05364,0.03149,-0.00121,0.11622,-0.02574,-0.01805,-0.02448,-0.06905,0.04736,0.01585,0.07354,-0.05684,0.05922,0.00176,0.03895,0.06179,0.08325,-0.02452,0.12033,-0.06395,-0.05419,-0.05238,0.03616,0.07386,0.05751,-0.06931,0.02356,-0.01547,0.00548,-0.17235,-0.058,-0.00432,-0.03371,0.0862,-0.00583,0.04253,0.03059,-0.01597,0.01655,0.00472,0.01692,-0.06647,-0.04822,0.07044,0.00522,0.04011,0.05606,0.06564,0.02721,0.15595,0.00828,-0.09879,0.09186,0.04415,-0.04801,-0.03026,-0.07904,-0.04285,0.12596,-0.01342,0.09071,-0.03663,-0.05031,-0.02732,0.01936,0.00957,-0.02514,-0.08548,-0.10792,-0.08058,0.02988,0.02916,-0.06804,-0.02049,-0.02995,0.00649,0.0931,0.04131,0.00615,0.08906,0.04988,0.01481,0.03879,-0.00656,-0.02319,-0.00546,0.03114,-0.08645,0.02156,-0.05649,0.04381,-0.02246,0.06676,0.00427,0.06318,0.00939,0.03471,0.02075,-0.10876,-0.00331,0.00179,-0.05254,0.07592,-0.03436,0.13769,0.04933,0.06309,-0.00749,-0.12256,0.06052,0.17175,-0.04285,-0.09336,0.00935,-0.02319,0.03874,-0.00497,0.03002,0.09287,0.01915,0.02377,-0.04327,0.01499,-0.0787,-0.04436,0.02896,0.09452,-0.12997,0.06277,0.06145,-0.0186,-0.01373,-0.04275,-0.01762,0.08718,0.1073,0.11161,-0.11196,-0.05764,-0.00155,-0.03528,0.00649,0.00108,0.00712,-0.0301,0.05205,-0.0803,0.0442,0.00131,-0.02274,0.09472,-0.04603,0.03513,-0.0681,-0.11864,0.08501,0.00229,0.06485,-0.14383,-0.02681,-0.09731,-0.03751,-0.0634,0.02353]},{"domain":"signal_processing","key":"radar_max_range","name":"Maximum detection range of a radar","package":"signal-processing-ai999x","example":"What is the maximum range of a radar with a peak power of 1 MW, an antenna gain of 40 dBi, a frequency of 3 GHz, a radar cross-section of 1 m^2 and a minimum detectable signal of 1e-13 W?","v":[-0.02864,-0.04838,0.06984,0.04882,-0.06205,-0.00016,0.00446,0.0553,-0.01197,-0.05029,-0.00703,0.12136,-0.03927,0.03615,-0.00154,0.09123,0.08591,-0.01149,0.03844,0.04787,-0.05394,0.05295,0.079,-0.08745,-0.01577,0.03234,-0.07625,-0.07168,0.03996,0.06556,-0.08193,0.05429,0.01381,-0.0321,-0.0055,-0.01109,-0.08242,-0.01991,0.00853,0.00147,0.01388,0.03021,0.1096,-0.05368,-0.00988,0.06847,0.10599,-0.01432,-0.05139,-0.12915,0.02419,0.03758,0.03127,0.10778,-0.05259,-0.02872,-0.0652,0.03138,0.02335,0.05946,-0.00242,-0.02199,0.0736,0.008,-0.04356,-0.06357,-0.14884,0.00028,-0.02993,0.00803,0.06934,0.02759,-0.09215,0.06832,0.00963,-0.06173,-0.01984,-0.03159,-0.10705,0.00802,0.04723,0.05765,-0.00556,-0.06557,0.02006,0.00145,0.00425,-0.04579,0.06435,-0.05648,-0.03655,0.13946,0.04075,-0.04707,0.02936,0.01596,0.05888,0.00018,0.03615,-0.02438,-0.04312,0.09523,-0.01541,-0.04024,0.01315,0.04454,-0.07824,0.09273,-0.03173,-0.06204,0.01144,0.08604,0.09852,0.07786,-0.05451,-0.05687,0.00278,-0.11532,-0.11244,-0.02715,0.1023,-0.08529,-0.05643,-0.00903,-0.16537,-0.12283,-0.00108,0.05455,0.06926,-0.02926,-0.07174,0.03594,-0.05327,0.00824,-0.04167,0.07473,0.08033,-0.00826,-0.01928,0.18466,0.09254,0.15238,0.01806,-0.04717,0.0187,-0.06364,-0.004,-0.01345,-0.00179,-0.05964,-0.00175,0.0489,-0.12764,0.05012,-0.02307,-0.08464,0.03207,0.04212,-0.02068,0.0801,-0.05506,0.08309,0.02551,-0.03133,-0.03736,0.06569,0.0066,0.04308,0.04947,0.07898,-0.07923,0.01817,0.02113,0.06564,-0.0249,-0.12407,0.03383,0.09219,0.03385,0.03374,-0.05621,-0.05968,0.12712,0.08121,0.05894,-0.04613,0.02835,-0.03566,0.02635,0.01175,-0.11923,-0.07638,-0.0443,0.01779,0.04867,-0.02421,0.00336,0.05257,-0.04966,-0.10957,-0.04062,0.0238,0.09922,-0.02041,-0.0186,-0.10091,-0.04849,0.05175,0.00043,-0.04434,-0.00748,0.00644,0.08164,-0.1425,-0.03234,0.07375,-0.11313,0.01818,0.06689,-0.07721,0.01532,0.08438,-0.13618,-0.03451,-0.02032,0.01554,0.01674,0.03235,0.06824,-0.06407,0.02606,0.10573,0.07043,-0.08228,-0.01009,0.00058,0.00497,-0.05791,-0.11644,0.02091,-0.03183,0.02461,-0.03162,-0.04732,-0.07521,0.12029,-0.0118,0.04098,-0.12775,0.01561,0.03696,0.03184,0.04059,0.01833,-0.12097,0.09313]},{"domain":"signal_processing","key":"radar_received_power","name":"Received echo power (radar range equation)","package":"signal-processing-ai999x","example":"A radar with a peak power of 1 MW and an antenna gain of 40 dBi operates at 3 GHz. What is the received echo power from a target with a radar cross-section of 1 m^2 at a range of 100 km?","v":[-0.00166,-0.07407,0.00021,-0.04419,0.0417,0.01504,-0.01927,0.00263,-0.03072,-0.05221,0.03545,0.06547,-0.01681,0.03163,0.01227,0.07793,0.10309,-0.0661,0.03264,0.04946,-0.01954,-0.07662,0.08806,-0.04298,-0.06287,0.02836,-0.09077,-0.13121,0.12032,-0.00245,0.0057,0.00351,-0.0334,0.00198,-0.05593,0.14384,-0.07317,0.04509,0.02382,-0.01278,0.00365,0.02129,-0.0012,-0.01386,-0.14519,0.08354,0.12851,-0.03192,-0.04472,-0.13746,-0.02254,0.08762,0.03761,0.1197,0.01473,-0.0124,-0.05253,0.01553,0.00691,-0.02185,0.02211,-0.04803,0.0581,-0.04096,-0.03242,-0.09867,-0.06308,-0.03398,-0.07661,-0.02702,0.05582,0.06257,-0.0721,0.07688,0.0379,-0.16077,-0.00141,-0.06779,-0.09768,0.07746,0.00223,0.03451,0.02882,-0.00468,0.02302,-0.04805,-0.0049,-0.05883,0.03294,-0.07111,-0.05163,0.07731,0.00617,-0.0041,0.00899,0.01692,0.00607,0.00871,0.03123,-0.07449,0.01063,-0.02179,0.04093,-0.05694,0.04596,-0.0223,-0.00786,0.06148,0.0335,-0.05509,0.11457,0.1214,0.02592,0.04716,0.02193,-0.01975,0.094,-0.15825,-0.11391,-0.08587,-0.00468,-0.13023,-0.0702,-0.02818,-0.11486,-0.04072,-0.00257,0.05848,0.03271,0.03384,-0.02915,0.01784,0.01227,0.01099,-0.04663,0.06011,-0.00031,-0.0115,-0.03363,0.1448,-0.06447,0.14566,0.02701,-0.00036,0.06417,0.03009,0.01163,-0.03856,-0.01259,-0.02711,0.0418,0.14759,-0.02253,0.1142,-0.01601,-0.00714,-0.00658,0.02699,0.002,-0.00781,-0.06437,0.02875,0.02383,-0.00808,-0.03224,0.00257,-0.09987,0.01218,-0.02964,0.0833,-0.04035,-0.03675,0.03902,0.02784,-0.00906,-0.08534,0.07103,0.09358,-0.04455,0.02754,0.01182,-0.0288,0.08166,0.0676,0.08584,0.01688,0.0028,-0.04522,-0.01931,-0.03753,0.00861,0.01357,-0.05465,0.08463,0.0308,0.01568,0.02509,0.01638,-0.09832,-0.04465,-0.07185,0.06344,0.15817,0.04651,-0.0319,-0.08801,-0.02388,0.01341,-0.00885,0.02529,0.04478,0.00151,0.10141,-0.13144,0.00595,0.00365,-0.0182,-0.08364,0.13048,-0.13468,0.10471,0.02719,-0.10475,-0.04172,-0.05658,-0.05725,0.08829,0.05848,0.06145,-0.05599,-0.02905,0.11309,0.03645,-0.04535,-0.00048,0.00285,0.08918,-0.0057,-0.15331,-0.00871,-0.01764,-0.04569,0.01375,-0.03267,-0.09038,0.07959,-0.01102,0.13636,-0.02553,0.09401,0.00959,0.0254,-0.04275,0.03324,-0.15878,0.02293]},{"domain":"signal_processing","key":"rect_pulse_spectrum","name":"Fourier transform of a rectangular pulse","package":"signal-processing-ai999x","example":"What is the Fourier transform of a rectangular pulse of amplitude 2 and width 1 ms at 250 Hz?","v":[-0.01604,-0.03029,0.0028,0.05141,-0.00474,-0.03551,0.03195,-0.09841,-0.11736,0.00573,0.02255,0.09565,-0.08788,0.05648,0.09709,0.02907,0.01814,-0.08644,-0.00622,0.04629,-0.02047,-0.07504,0.04632,-0.00046,-0.10135,0.06982,-0.02619,-0.05023,0.02074,-0.08522,0.02739,0.04537,0.078,-0.03278,0.00637,0.0802,0.06678,0.02086,0.0111,0.07927,-0.00922,-0.04195,0.10162,0.05546,0.01989,-0.01741,-0.03732,0.07764,0.01939,-0.0121,-0.25522,0.06778,-0.09515,-0.01429,-0.00322,-0.11249,0.00633,-0.03256,0.06048,0.01294,-0.04684,-0.04293,0.05922,0.0081,-0.01561,-0.01004,-0.12405,-0.00063,-0.10888,-0.10177,-0.00043,0.0389,0.03954,-0.10035,0.01571,0.00955,0.08343,-0.01922,0.00255,-0.00723,0.10203,0.00165,0.09563,-0.017,0.08777,-0.02698,-0.06151,0.24653,0.02838,-0.02357,0.03488,-0.0719,-0.0403,-0.03901,-0.09033,-0.04569,0.1209,-0.03437,0.14999,0.08918,-0.07429,-0.01705,-0.03354,-0.05262,-0.02169,0.00688,-0.1269,0.02659,-0.00799,-0.05121,-0.148,0.03441,0.00933,0.0102,-0.01253,0.03254,-0.03165,0.02975,0.03987,0.09363,-0.0649,-0.05654,0.02779,0.0858,-0.02211,0.04921,-0.11801,-0.02466,0.06392,-0.03447,0.02449,0.01131,0.03211,-0.04191,-0.04094,0.02844,0.08073,-0.00738,0.09946,0.06097,0.10212,-0.01013,-3e-05,-0.0876,-0.03916,-0.09018,0.06567,-0.0553,0.03606,-0.05298,-0.00137,-0.09308,0.01893,0.0138,-0.01964,0.00094,0.01649,0.07984,0.01478,-0.03158,-0.0856,-0.06114,-0.00738,0.02545,-0.04325,0.00096,-0.04648,0.02372,0.0333,0.08803,0.00105,0.09999,0.00372,0.08447,-0.02499,0.06536,0.02407,-0.03037,-0.04935,0.04352,0.04817,0.04773,0.09582,-0.02332,-0.07107,-0.01531,0.09823,-0.04938,0.00172,-0.01455,0.017,-0.04925,0.00181,0.02506,0.03656,-0.02198,0.17693,-0.09318,-0.07786,-0.008,-0.02015,-0.0497,-0.12104,0.06408,0.06406,-0.06261,0.02272,-0.0895,-0.03349,0.06045,0.06115,-0.01418,0.00297,0.02143,-0.03191,-0.02064,-0.04049,-0.0778,0.09706,0.00361,0.05098,-0.0161,-0.06663,0.02667,-0.01056,-0.04474,0.10128,0.03815,0.09911,-0.0322,0.0132,-0.05545,-0.03643,0.09052,-0.03159,0.01963,0.01306,-0.08633,-0.00043,0.0946,0.06096,0.00795,-0.09675,-0.02984,0.05275,-0.08231,0.10519,0.00746,0.00221,0.13775,0.07659,-0.01969,-0.01472,-0.02623,-0.07877,-0.00591]},{"domain":"signal_processing","key":"reflection_coefficient","name":"Reflection coefficient, VSWR and return loss of a load","package":"signal-processing-ai999x","example":"A 50 ohm line is terminated in a load of 75 + j25 ohm. Find the reflection coefficient and the VSWR.","v":[0.07551,0.05192,0.00772,0.08029,-0.05827,-0.02449,0.01927,0.01871,0.0959,0.03091,-0.10821,0.0044,0.04192,0.07804,0.0248,0.01564,0.00979,-0.04923,-0.07171,0.01464,0.02786,0.05228,0.02409,0.02726,0.04979,-0.05342,0.05768,-0.04,0.01677,-0.03293,0.0242,0.10775,-0.0096,-0.00944,0.06521,-0.01544,0.00765,0.01363,0.01617,0.08749,-0.04143,-0.12497,0.06702,0.06426,0.00872,-0.05973,0.02975,-0.05661,0.03433,-0.05735,0.03242,0.0964,0.03621,-0.01668,0.0094,0.08779,-0.06551,0.06031,-0.04805,-0.03488,0.01844,-0.06557,-0.00593,0.03031,0.0658,-0.12608,-0.05658,-0.03709,-0.08954,-0.03813,0.04966,0.01971,-0.01114,0.01389,0.10899,-0.08759,-0.05808,0.00653,0.15705,-0.04304,0.03124,0.0898,-0.07592,-0.0075,0.11162,0.00029,-0.01797,-0.11337,-0.0167,0.03482,-0.00438,-0.0942,-0.08344,0.0285,0.07308,-0.05429,-0.07417,-0.13093,-0.0395,-0.00509,0.04169,-0.0675,-0.04965,-0.1194,0.03142,-0.05126,-0.0573,0.08387,-0.16682,-0.04391,-0.05188,0.094,-0.0337,-0.08999,0.0145,0.00638,-0.00432,-0.0874,0.01068,-0.12887,0.14959,-0.039,0.01895,0.02637,0.01542,0.03465,-0.04724,0.0297,-0.00287,0.05072,0.06428,-0.01512,0.08531,-0.05622,0.03654,-0.10488,0.00401,-0.13418,-0.05754,-0.00026,-0.04261,-0.06594,-0.05604,0.01201,0.0816,-0.05563,-0.01964,-0.00906,-0.04167,-0.0343,0.06425,0.08741,0.07876,0.06112,-0.03261,-0.04998,-0.01108,0.05324,0.0041,0.01463,0.03757,-0.02023,-0.01122,-0.02873,-0.21052,0.02178,0.10573,-0.07178,-0.00105,0.00472,0.00239,-0.07319,-0.03301,0.04994,0.0577,0.02155,0.07606,-0.0956,0.07676,-0.06723,0.1321,-0.07387,0.05876,-0.06286,-0.01967,0.04443,-0.05673,0.00828,-0.06124,0.1106,0.01839,0.01285,0.04552,-0.09114,-0.07004,-0.00294,-0.08869,0.03051,0.00317,-0.0026,0.00762,0.09766,0.08116,0.02069,0.00688,0.07949,0.00482,-0.01544,-0.03122,0.06685,0.06404,0.06991,0.05017,-0.01876,-0.02752,-0.01837,-0.00987,0.06939,0.00349,-0.01187,0.01586,0.05057,0.02161,-0.00092,-0.04704,-0.01928,0.01932,0.15357,0.19418,-0.00048,0.02613,0.02577,0.02044,0.00505,-0.02118,-0.19671,-0.03871,-0.02521,-0.09686,0.03005,0.12022,0.09712,0.05178,-0.02409,0.01261,-0.03737,0.08956,-0.00607,0.09602,-0.0581,-0.05331,-0.02854,-0.02975,0.03006,-0.0503,0.01576]},{"domain":"signal_processing","key":"reflection_from_vswr","name":"Reflection coefficient and return loss from the VSWR","package":"signal-processing-ai999x","example":"What reflection coefficient and return loss correspond to a VSWR of 2?","v":[0.07228,-0.00037,-0.05236,0.09319,-0.01262,-0.04718,-0.02627,0.05153,0.0216,-0.01682,-0.11125,0.01007,-0.00271,0.08803,-0.06557,-0.0343,0.04291,-0.05736,-0.10129,0.06674,-0.03112,0.01763,0.01846,-0.03615,0.02615,-0.02911,0.07096,-0.13146,-0.01773,0.02448,0.07615,0.04898,-0.05155,-0.02167,0.01351,-0.03928,-0.02013,-0.02929,0.03465,-0.00865,-0.01258,-0.09927,0.10928,0.07116,0.01082,0.02556,0.04354,-0.04042,-0.04859,0.0301,0.05632,0.08877,0.02232,0.03102,0.11783,0.08816,-0.03899,-0.0213,-0.078,-0.05728,-0.00902,-0.06611,0.04855,0.00561,0.00907,-0.1067,-0.01084,-0.00649,-0.05675,-0.04332,0.09972,0.09061,0.00154,0.00692,0.03218,-0.17026,-0.08922,-0.04805,0.06004,0.03088,0.04313,0.13295,-0.07064,-0.07326,0.10713,0.02585,-0.05106,-0.10469,0.03649,0.05903,-0.01123,-0.00947,-0.02804,0.04185,0.01078,-0.02056,-0.11071,-0.11488,-0.01995,0.02331,0.00859,-0.06216,0.04063,-0.03153,-0.01555,-0.18554,4e-05,0.09178,-0.09471,-0.03095,0.04559,0.00896,-0.04752,-0.10652,-0.07185,0.08185,0.02131,-0.1114,-0.01501,-0.08135,0.12416,-0.04177,-0.06898,-0.0011,-0.02368,0.08351,-0.04074,0.0888,-0.08236,0.0401,0.08689,0.01335,-0.03573,-0.06515,-0.01103,-0.03669,-0.0415,-0.11204,0.0217,0.05406,-0.07121,0.01803,-0.03083,0.04698,0.11916,-0.09618,-0.0425,-0.02103,-0.04751,-0.04864,0.04365,0.05867,0.13567,0.06298,-0.05281,-0.02157,0.06561,0.02127,0.01592,0.02573,0.04451,-0.02852,-0.06529,-0.01381,-0.09399,0.04482,0.1114,-0.05957,0.06233,0.00586,0.0026,0.01045,-0.07115,0.00157,0.07204,-0.10904,0.06374,-0.0809,0.08477,-0.08622,0.10063,-0.08373,0.0502,-0.05894,0.05462,0.05436,0.02376,0.00049,-0.03138,0.12615,-0.06327,-0.01413,0.0073,-0.01574,-0.0115,-0.00458,-0.01035,0.00282,0.05156,-0.03368,0.02168,0.13047,0.16308,0.00236,-0.01979,0.0527,-0.05346,-0.0321,-0.01161,0.0565,0.07353,0.05977,0.05328,-0.08959,-0.01428,-0.04046,-0.04373,0.00841,0.00625,-0.01179,0.01243,0.10833,-0.03276,0.03272,-0.03292,0.00395,0.08539,0.1865,0.16072,-0.06544,0.00816,0.00374,-0.00512,0.00645,0.0027,-0.08894,-0.05258,0.0292,-0.03237,0.01468,0.17558,0.06848,0.00559,-0.047,0.00515,-0.01694,0.04591,0.02368,0.05809,-0.02085,0.00742,-0.00949,-0.02382,0.03414,-0.05669,-0.01398]},{"domain":"signal_processing","key":"second_order_poles","name":"Poles 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stable.","v":[-0.07582,-0.08676,-0.04796,0.10428,0.01107,-0.04791,-0.06223,-0.01444,-0.03434,-0.0062,0.05011,0.02845,-0.01507,0.04231,0.0037,0.08647,-0.01607,0.04989,0.05106,0.00209,0.10054,-0.06825,0.01393,-0.04302,0.02673,-0.03373,-0.06274,0.09027,0.0902,0.09362,0.03305,0.07987,-0.0471,0.00909,0.00173,-0.00878,0.03806,0.02367,0.11271,-0.05563,0.05735,0.02085,0.01949,0.01123,0.00783,-0.04353,0.02279,-0.11388,0.02651,-0.06261,0.05259,0.04682,0.07,0.12653,-0.02185,0.07343,-0.08736,0.13971,-0.05628,0.07478,-0.01435,-0.04553,-0.01285,0.04711,0.04672,-0.06377,0.03276,-0.06273,0.00639,-0.09458,0.05926,0.05712,-0.09536,0.04907,0.01911,-0.00057,-0.00425,-0.02671,0.15677,-0.03327,-0.02143,-0.03451,-0.08001,-0.0625,0.02746,0.03846,-0.07031,-0.02237,0.01924,-0.14456,0.00015,-0.00278,-0.07575,-0.04277,0.1199,-0.02131,0.05094,-0.0001,-0.0085,0.06641,0.04036,-0.04315,-0.01761,0.07134,-0.06604,0.1,-0.0011,-0.05407,-0.05832,0.08332,-0.02795,0.05515,0.09282,0.01975,0.03076,-0.00957,0.00476,-0.01405,-0.04609,0.05984,0.09485,-0.06062,0.10738,0.04185,-0.08377,0.04158,-0.00708,0.06025,0.08358,-0.08002,-0.07525,-0.02988,0.12437,-0.1251,-0.0366,0.10772,0.02026,-0.10814,0.01845,-0.04009,0.12413,0.09391,-0.0172,0.0466,0.07839,0.00232,0.05276,0.00906,0.03588,0.08261,0.07201,0.08387,-0.02374,-0.00692,0.0215,-0.02612,-0.03083,0.13356,-0.12327,0.0509,0.09064,0.01011,-0.07785,-0.1073,0.03167,0.09335,-0.05792,0.08702,0.14935,-0.07448,-0.0147,-0.01614,-0.0048,-0.04281,-0.02184,-0.06284,0.05921,0.03562,-0.00054,0.13255,-0.01264,-0.02253,-0.00151,-0.0098,-0.01583,-0.06646,-0.07601,0.07072,0.0016,0.03134,0.00071,0.06447,0.0519,-0.0876,-0.08419,-0.11829,-0.1191,-0.05501,0.06012,-0.00429,0.04951,0.01358,-0.01785,0.01306,0.10585,0.00973,0.03065,-0.03294,-0.05378,-0.14444,-0.01971,0.02722,0.09474,-0.0321,0.01959,0.05055,-0.08428,0.04419,-0.04836,-0.0168,0.01909,0.03885,-0.04832,-0.10434,-0.0391,0.03508,-0.00367,-0.10466,-0.01728,-0.02981,0.02849,-0.09657,0.00704,-0.11076,-0.09055,0.00999,-0.10676,-0.06609,0.04006,0.05381,-0.01194,0.09348,0.02771,-0.02507,-0.00346,-0.03638,-0.011,-0.10817,-0.10959,6e-05,-0.05892,0.00892,0.03787,-0.05845,0.02771,0.06464]},{"domain":"signal_processing","key":"shannon_capacity","name":"Shannon 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SNR for a data rate (Shannon limit)","package":"signal-processing-ai999x","example":"What minimum SNR is needed to send 10 Mbit/s over a bandwidth of 2 MHz?","v":[-0.10206,-0.03914,0.00245,-0.01595,-0.04473,-0.01844,0.01691,0.02751,0.04292,-0.02262,-0.16571,0.01909,0.04139,0.019,-0.08812,-0.05622,0.10197,-0.03165,-0.00828,0.01484,0.00032,-0.02515,-0.02089,-0.01679,0.05004,0.01169,0.03601,0.02238,-0.00176,0.1079,-0.07013,0.03468,0.05073,0.01583,-0.05369,-0.05345,-0.06837,-0.06534,0.00151,0.01269,-0.00441,-0.05886,-0.10303,0.03942,0.04259,-0.00242,-0.02841,-0.05752,0.0163,0.05342,0.09798,-0.08347,-0.06799,0.03999,-0.01757,0.06888,0.05658,0.02319,-0.03843,0.07779,0.00129,0.04766,0.03587,0.14498,-0.08499,0.05954,0.00409,-0.05086,-0.12943,0.03538,-0.05491,0.0407,0.11115,0.03457,-0.03508,-0.05098,-0.02704,-0.02578,0.0211,0.06783,0.06428,0.09925,-0.06463,-0.03007,0.00876,0.00598,-0.07736,0.12522,-0.04171,0.05367,0.00539,0.08608,0.036,-0.00897,-0.02632,-0.04112,-0.07999,-0.00506,0.07168,0.04631,-0.06077,0.02759,0.04142,-0.0194,0.0438,-0.16518,-0.04906,0.02016,-0.00031,-0.0901,0.02822,0.08894,0.04612,-0.10015,-0.0314,-0.01659,-0.09962,-0.02895,-0.08853,0.09311,0.07502,0.03257,0.00145,0.10299,-0.04357,-0.07267,0.00661,0.05693,0.06926,-0.10489,0.06637,0.05778,-0.09038,0.02374,0.03161,-0.04151,0.00755,0.03125,-0.08088,0.05183,-0.02124,0.13391,-0.08999,0.05213,0.00968,-0.0548,0.04882,-0.01626,-0.00634,-0.14243,0.03362,0.01095,-0.08381,-0.07769,0.02426,-0.11855,0.0703,0.0296,0.06518,0.07501,0.00023,0.10699,0.01772,0.04246,-0.02531,0.04395,0.02767,0.01305,0.05323,-0.05304,-0.01552,-0.15555,0.04971,-0.03096,-0.08582,-0.03371,-0.00547,0.04268,-0.02761,-0.0293,-0.09744,-0.045,-0.00562,0.02539,0.02081,-0.00578,-0.06325,0.02707,-0.00199,0.16789,-0.18359,-0.04501,-0.00131,0.01494,0.05247,-0.08166,0.01794,0.05043,0.09046,-0.09233,-0.00736,0.0696,-0.06706,-0.06663,0.07121,0.00498,-0.04111,0.03935,-0.06545,-0.03872,-0.07042,0.04693,-0.00473,-0.03153,0.01611,-0.05874,-0.09747,-0.00561,0.03691,0.0442,-0.07576,0.03464,-0.02517,-0.00841,0.01507,-0.0014,-0.01605,0.09377,0.01235,0.08592,-0.01391,0.04275,0.03576,0.10303,-0.04745,0.0379,0.05644,0.00896,-0.18491,-0.06177,0.04048,-0.01933,-0.03223,-0.08131,0.05756,0.15405,0.04808,-0.05799,-0.07813,0.06729,0.05556,0.10279,0.11613,0.10328,-0.00082,-0.02725]},{"domain":"signal_processing","key":"signal_statistics","name":"Mean, 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V?","v":[-0.03149,0.00804,0.02129,0.05971,0.00083,-0.06168,-0.06909,0.04067,-0.06479,0.0016,0.00786,-0.06583,0.01667,0.0023,0.00344,0.12156,0.0527,-0.04744,-0.06747,0.05065,-0.01254,-0.12574,0.01505,0.04993,-0.00534,0.06516,0.02638,0.02621,0.06149,-0.01006,-0.14478,0.09276,0.08122,-0.00181,-0.03522,-0.03095,0.04659,-0.01184,0.09789,0.0321,0.0074,-0.02527,0.1195,0.03697,0.05346,-0.03621,0.01171,-0.03686,-0.06738,-0.05977,-0.01956,0.02993,0.02273,0.0708,0.03104,-0.19599,0.03325,0.0065,0.0891,0.01116,0.07351,-0.03452,0.0452,0.00937,0.11787,0.00789,-0.15207,0.03204,-0.02502,-0.066,0.06235,0.08726,0.03958,-0.10611,-0.02302,0.02559,-0.03774,-0.01877,0.03438,0.01681,-0.09076,0.05092,0.03004,-0.18559,0.03218,-0.06259,-0.0589,0.02948,0.02746,-0.07485,0.08791,0.10068,-0.0011,0.03051,0.00965,-0.00069,0.1021,-0.02035,0.14587,0.10545,-0.09496,0.03839,0.03491,-0.0548,-0.0002,-0.01609,-0.06067,0.0297,-0.07255,0.01733,-0.1047,-0.06032,-0.01332,0.09642,-0.02025,0.04769,-0.07501,-0.04384,-0.03099,-0.09491,0.17325,-0.01524,-0.11115,-0.09544,-0.15932,0.0015,-0.03194,-0.03537,0.09668,0.01919,-0.09468,-0.00188,0.02591,-0.00963,-0.03944,-0.0371,-0.03243,0.01672,-0.00211,0.09206,0.01953,0.09153,0.08052,0.01284,0.08266,0.00436,-0.00716,0.02603,0.03157,0.11946,-0.08963,0.0933,-0.03322,0.00929,-0.06446,0.06383,0.00223,0.05603,-0.0451,-0.02943,0.02175,0.02805,0.06602,-0.0086,-0.1176,-0.02684,-0.12019,-0.01897,0.01044,-0.00537,-0.10738,0.0201,-0.05717,-0.03039,-0.01809,-0.01513,0.05723,-0.02907,0.00766,0.03053,-0.03048,0.01682,-0.00932,0.10071,0.01907,0.03644,-0.09079,-0.01116,0.04751,0.00726,-0.14258,-0.03276,0.02468,0.08507,0.06526,0.00309,-0.02434,0.04713,0.01298,0.03576,0.06238,-0.07204,-0.11543,0.0652,-0.02022,-0.08747,-0.0117,-0.01028,0.06492,0.00313,0.02862,-0.02464,-0.0421,-0.03853,-0.03547,0.06697,-0.09358,-0.01465,0.04046,-0.07361,-0.05074,0.08012,-0.04153,0.06127,0.03119,0.03182,-0.04988,0.03738,0.0146,-0.05248,-0.00799,0.09022,0.07132,0.09453,0.03511,-0.00734,-0.12008,-0.00939,0.13535,0.01429,0.0517,0.08467,-0.09212,0.05282,0.02624,-0.06072,-0.00865,-0.02652,-0.10549,0.02247,0.06621,0.04516,-0.08726,-0.01604,-0.09158,-0.0575]},{"domain":"signal_processing","key":"snr_from_powers","name":"Signal-to-noise ratio from signal and noise powers","package":"signal-processing-ai999x","example":"What is the SNR in dB for a signal power of 2 mW and a noise power of 10 uW?","v":[-0.07485,0.02552,-0.03271,-0.00654,-0.02388,0.00029,-0.05961,0.15057,0.01141,0.00249,-0.02144,-0.00494,-0.01574,0.03079,-0.09542,-0.01017,0.0179,-0.03293,0.0176,0.0598,-0.0442,-0.0973,0.07154,-0.07224,-0.09317,0.03497,-0.0231,-0.10368,0.07289,0.03479,-0.04983,0.04173,0.02876,-0.03645,-0.00794,-0.02722,-0.04578,0.04076,0.06401,-0.02494,-0.01013,0.02495,0.0115,-0.02855,0.00595,0.05588,0.06679,0.04165,-0.07349,0.02683,-0.01536,0.03874,-0.00133,0.129,-0.01378,0.0504,0.00514,-0.08588,-0.03521,0.06726,0.03255,-0.0644,0.04895,0.06275,-0.02879,0.03657,0.02397,-0.09423,-0.07091,-0.03417,0.02252,0.01923,-0.00644,0.19756,0.00734,-0.06837,0.0128,-0.07319,-0.04373,-0.02726,-0.05888,0.124,-0.06588,-0.14925,0.02864,-0.10543,-0.05632,0.15231,0.00943,-0.16526,0.01741,0.07851,0.03915,-0.04662,-0.03087,0.07855,-0.00439,0.06626,0.12407,0.00663,-0.07259,0.02352,0.03012,0.09289,0.04148,-0.07631,0.08424,0.06872,-0.05904,-0.01034,-0.01524,0.05372,-0.03407,-0.03202,-0.01415,-0.02164,-0.074,-0.04959,-0.05466,-0.0248,-0.01412,-0.04028,0.00608,-0.02803,0.04438,-0.01057,-0.0309,0.09892,-0.01655,-0.03655,0.04114,0.07256,-0.13626,0.05112,0.1199,0.04522,0.02929,0.06108,-0.02917,-0.01565,0.00098,0.15528,-0.0807,0.03048,0.08139,-0.10118,-0.01779,0.05839,0.00648,-0.11662,-0.06447,0.02346,-0.1042,-0.03529,-0.06913,-0.08679,0.02003,-0.00714,0.0911,0.05976,0.06209,-0.04657,0.04437,0.02322,0.09531,0.06373,-0.10239,-0.01896,0.07233,-0.12392,0.01087,-0.11934,-0.00977,0.0273,-0.0317,-0.02037,0.04144,-0.03713,-0.00562,-0.0017,-0.1328,-0.01278,0.08833,0.0012,0.05921,0.00663,0.0328,0.05825,0.01233,0.12382,-0.16293,-0.05846,0.01158,0.08303,0.16232,-0.02319,0.00998,0.06266,-0.07081,-0.07815,0.02532,-0.05934,0.03401,-0.00883,0.07112,-0.01665,-0.05695,-0.04566,0.01477,-0.04755,-0.08048,0.0729,0.00863,-0.10233,0.01957,-0.06347,-0.09401,0.01595,-0.03334,-0.04859,0.01463,-0.05095,-0.01189,0.04847,0.06259,-0.10922,0.0408,0.04048,0.07083,0.07855,-0.06222,0.0282,0.08045,0.03708,-0.06782,0.00135,0.01186,-0.01573,-0.04388,0.02869,0.08339,-0.01975,-0.02157,-0.02946,-0.06252,0.13414,0.01192,0.03057,-0.00493,0.0426,0.04418,-0.02124,0.03821,0.06874,-0.06115,-0.10741]},{"domain":"signal_processing","key":"step_response","name":"Step response of a digital filter","package":"signal-processing-ai999x","example":"Find the first 4 samples of the step response of the filter with b = [1] and a = [1, -0.5].","v":[0.03499,0.03661,0.11682,0.00938,0.00546,0.00592,-0.05146,-0.06036,-0.08236,0.00248,0.03009,0.00443,-0.10343,0.12722,0.09976,0.05427,0.01614,0.03463,-0.03107,0.00165,-0.00958,-0.12352,-0.02994,-0.03216,-0.02473,0.04441,-0.04336,-0.02408,0.02708,-0.06096,0.07312,0.03095,-0.04848,-0.00432,0.01424,0.08404,0.03628,0.11136,-0.01198,-0.06616,0.04151,0.07594,0.01155,0.05912,0.01108,0.00608,-0.05641,-0.00206,-0.09625,0.05017,-0.02196,0.01046,-0.0536,-0.03561,0.00225,0.1144,-0.00611,0.05583,0.03689,-0.11112,-0.09892,-0.02263,0.03717,-0.11727,-0.14816,-0.04558,0.103,0.01672,0.03098,-0.01555,-0.03552,0.06522,-0.01192,-0.02466,-0.04105,-0.02445,-0.02676,0.07328,0.02055,-0.04552,0.00371,-0.13417,-0.04103,0.06117,0.04266,0.0358,0.03499,-0.04528,-0.03343,-0.00114,0.11241,-0.10001,0.11526,-0.14542,0.06214,0.05065,0.0026,-0.10455,0.11947,-0.01956,0.08391,-0.01877,0.00506,-0.06699,0.002,0.0168,0.02815,-0.04395,0.07621,-0.05845,-0.08673,0.04254,-0.06936,-0.0454,0.02914,0.08902,0.03405,0.03241,-0.04745,-0.03677,0.01072,0.01795,0.05096,0.02958,-0.0144,0.03562,-0.06845,0.05022,0.04065,0.00042,0.11032,0.0225,0.06577,-0.02467,-0.00533,0.10022,0.06812,-0.01878,-0.04323,-0.06597,-0.15554,0.02611,-0.00626,0.04146,0.07819,0.01615,0.04481,-0.04677,-0.12599,-0.08299,-0.01428,-0.10702,0.01544,-0.00806,-0.05347,-0.04117,-0.04574,0.00194,-0.05704,0.08639,0.1031,0.08029,0.06683,0.03674,0.10861,-0.0514,-0.05213,-0.09884,-0.01604,-0.00342,0.06533,-0.00344,-0.05364,-0.10335,0.02947,0.00286,-0.02003,-0.09152,-0.04342,0.04606,-0.03447,0.08971,0.04328,0.06706,-0.05017,0.05691,0.00593,-0.0173,-0.04431,0.12177,0.00686,0.08003,-0.04619,-0.05847,-0.12319,0.05331,0.00296,-0.02588,-0.03254,0.06119,-0.04409,0.07977,-0.09914,0.00258,0.16035,0.0695,0.04361,-0.07322,0.01111,-0.02423,0.0272,-0.03152,-0.03843,0.06298,0.00358,-0.06491,0.06269,0.01052,0.07439,0.06039,0.11511,0.00168,0.07064,0.05789,0.00828,0.09045,0.1239,0.03915,0.02443,0.00285,-0.06567,-0.05087,-0.14098,0.04707,-0.12015,0.0744,-0.03957,-0.08216,0.06876,0.03347,-0.0337,-0.04292,-0.08209,-0.12359,0.05127,-0.06821,0.06343,-0.03223,-0.01477,0.06173,-0.03658,-0.07094,-0.0751,0.06382,-0.01779,-0.06623]},{"domain":"signal_processing","key":"thd","name":"Total harmonic distortion","package":"signal-processing-ai999x","example":"What is the total harmonic distortion of a signal with harmonic amplitudes [10, 0.5, 0.3, 0.1]?","v":[-0.00589,0.08602,0.04982,0.05683,0.00445,0.00834,-0.01914,0.10254,0.06485,-0.04368,0.07884,0.01293,-0.03444,0.00576,-0.10529,0.07321,-0.03187,-0.01178,0.01186,0.06456,-0.07577,-0.12261,-0.01595,-0.08698,-0.0021,-0.00088,-0.05036,-0.06274,0.04303,-0.07755,-0.19039,0.01217,0.17303,0.02135,0.00374,-0.0739,0.03451,-0.00183,0.08489,0.03554,-0.00633,-0.097,-0.04409,-0.00282,-0.01543,-0.05186,-0.03886,-0.00974,-0.12554,0.02834,-0.05325,0.02562,-0.0957,-0.06553,0.00153,-0.02173,-0.06857,-0.09095,-0.03046,0.00507,0.04184,-0.09871,0.11362,0.01313,0.01321,-0.05314,-0.05548,0.06459,0.0275,0.04315,0.11175,0.02646,0.04624,-0.0675,-0.08419,-0.03895,-0.10977,0.0205,-0.07134,0.03326,-0.07468,0.08772,0.00469,-0.09862,0.03354,-0.04116,-0.13378,0.07586,-0.05246,-0.10023,-0.00339,0.08482,0.00582,0.01217,-0.00897,0.03839,-0.1257,0.04856,0.10389,-0.04935,0.03021,0.02131,0.11055,-0.03116,-0.06251,-0.02865,0.03002,0.10892,-0.02351,-0.02623,-0.0115,-0.11787,0.00267,0.05038,-0.08492,0.11895,0.01855,-0.02434,0.0497,-0.10073,0.00293,0.00909,0.06482,-0.07166,-0.00165,0.12918,-0.01349,-0.03601,0.01926,-0.03879,0.04869,-0.02638,-0.07535,-0.02756,-0.01295,0.06876,-0.03501,-0.04704,-0.03041,0.01496,-0.03923,-0.02081,-0.01901,0.06807,0.19648,-0.06389,0.03012,-0.0111,0.02926,0.00869,-0.10003,0.01044,-0.08505,0.02469,-0.01668,0.00828,-0.00717,0.00802,-0.00154,-0.03722,0.01286,-0.05445,-0.01104,0.00793,-0.00781,0.00806,-0.09268,-0.1239,0.17828,0.02603,0.09949,-0.06927,0.01394,-0.07107,0.04614,0.06063,-0.02227,-0.03257,-0.04765,-0.00657,-0.04515,0.01926,0.04505,0.02657,-0.06255,-0.02087,0.08611,0.05329,-0.04953,-0.00836,-0.08632,-0.00641,-0.01302,0.13886,0.04005,-0.01149,-0.02669,0.06116,-0.02736,-0.00795,0.06484,-0.05096,-0.10917,0.05287,-0.09883,-0.01307,0.05647,-0.01107,0.02005,0.00498,0.00988,0.05575,0.0273,0.046,0.08207,-0.00531,-0.05941,0.04944,-0.00386,-0.04795,-0.01136,0.03361,0.07987,0.04949,0.06982,-0.06598,0.01438,0.10653,0.05367,0.07367,0.16159,-0.02865,0.0623,-0.06008,0.01073,0.02127,-0.03753,0.03114,0.0949,0.03947,0.13915,0.00456,-0.01301,0.07875,0.03229,0.03666,-0.00061,0.03264,0.10126,0.03927,0.04933,0.01796,-0.09829,-0.10698,-0.00543,0.07541]},{"domain":"signal_processing","key":"vswr_from_reflection","name":"VSWR and return loss from the reflection coefficient","package":"signal-processing-ai999x","example":"What is the VSWR for a reflection coefficient of 0.2?","v":[0.09384,0.00641,-0.04708,0.09756,-0.00491,-0.04013,-0.0328,0.04664,0.01307,-0.03318,-0.12477,0.00117,0.01463,0.07527,-0.0437,-0.02064,0.03645,-0.06913,-0.08207,0.06373,-0.02054,0.02326,0.03184,-0.01926,0.05078,-0.02315,0.04767,-0.10391,-0.00642,0.03993,0.09339,0.05959,-0.059,-0.01474,-0.00143,-0.0327,-0.01211,-0.02629,0.03323,0.00429,-0.02754,-0.07497,0.13002,0.05737,0.02182,0.01244,0.05305,-0.03531,-0.06636,-0.01215,0.04878,0.08775,0.02217,0.01996,0.07038,0.07674,-0.05729,-0.035,-0.05309,-0.07787,-1e-05,-0.07383,0.05148,-0.01733,0.00364,-0.13759,-0.01259,-0.01196,-0.04481,-0.04292,0.10543,0.07755,-0.00981,-0.02413,0.0766,-0.17739,-0.10329,-0.03647,0.06603,0.03329,0.0433,0.14773,-0.05588,-0.05099,0.11542,0.06028,-0.02052,-0.09035,0.03257,0.06746,0.00083,-0.03421,-0.04619,0.05119,-0.0037,-0.03092,-0.10784,-0.10862,0.00832,0.01498,0.01331,-0.06183,0.01067,-0.04602,0.00044,-0.17653,-0.03189,0.08912,-0.08642,-0.05407,0.06183,0.01378,-0.02492,-0.10722,-0.06281,0.05933,0.01551,-0.10865,-0.00442,-0.07727,0.11822,-0.0636,-0.03056,0.00609,-0.01912,0.07147,-0.05478,0.07465,-0.09027,0.0354,0.08383,0.02238,-0.01921,-0.07266,-0.02909,-0.04311,-0.02506,-0.09153,0.01641,0.06988,-0.0402,-0.00897,-0.0209,0.05818,0.11196,-0.0897,-0.03518,-0.02305,-0.04742,-0.03964,0.05407,0.05063,0.12595,0.04127,-0.04614,-0.05448,0.05713,-0.00259,-0.01406,0.03966,0.04336,0.01392,-0.04191,-0.02446,-0.07169,0.03834,0.10658,-0.05437,0.05534,0.02705,-0.00081,0.02131,-0.07944,-0.0035,0.04917,-0.12197,0.07518,-0.06487,0.11193,-0.08713,0.08859,-0.0727,0.03022,-0.06286,0.03812,0.04584,0.02896,-0.01399,-0.02737,0.16194,-0.04845,-0.03993,0.03484,-0.0285,-0.01149,-0.01746,-0.02012,-0.00393,0.04966,-0.01781,0.01447,0.11774,0.18757,0.002,-0.01314,0.05502,-0.02438,-0.03355,-0.00792,0.07066,0.07895,0.06551,0.0553,-0.09572,-0.00618,-0.06199,-0.08178,-0.01199,0.02809,-0.00956,-0.01477,0.09231,-0.03947,0.03879,-0.07865,0.00535,0.10075,0.19669,0.17259,-0.06584,0.00442,0.00085,0.00309,-0.01101,0.00467,-0.09086,-0.03485,0.01305,-0.0277,0.00944,0.16251,0.06924,0.01338,-0.0229,0.01346,-0.03676,0.044,0.00399,0.04331,-0.02294,0.00071,-0.01516,-0.0114,0.03527,-0.06523,0.01061]},{"domain":"signal_processing","key":"watts_to_dbm","name":"Power in watts to dBm and dBW","package":"signal-processing-ai999x","example":"Convert 2 W to dBm.","v":[0.00759,-0.03584,-0.05458,-0.02782,0.0093,0.0382,-0.01844,-0.06108,-0.05693,-0.01433,-0.0909,0.0456,-0.06643,-0.02915,-0.08786,-0.06917,0.04416,-0.01632,0.0021,0.01475,-0.06664,-0.01564,-0.01358,0.06747,-0.15036,-0.02667,0.05076,-0.04303,0.02024,0.17236,0.04911,-0.03412,-0.07641,0.01326,0.09422,0.0286,-0.10699,-0.0235,0.05,-0.09916,-0.09231,-0.00428,-0.02787,-0.01532,0.03667,-0.05233,-0.06403,-0.06418,-0.01579,-0.02116,0.01119,0.00994,0.01964,0.01391,0.0112,0.04443,-0.03234,-0.08219,-0.09129,0.04247,0.0242,0.0414,-0.01869,0.02613,-0.00407,0.04187,-0.07893,-0.07617,0.02441,-0.03085,-0.02605,0.0315,-0.01687,0.04399,0.07332,-0.12104,-0.03649,-0.02534,-0.00646,-0.0127,-0.08108,0.06451,0.04286,-0.10623,-0.01324,-0.08728,0.0107,-0.02297,0.00579,-0.01733,0.04686,0.01407,0.00188,0.03548,0.03829,-0.02358,0.05053,0.11151,0.04816,0.05981,-0.02567,-0.03033,0.0375,0.008,0.00806,-0.09834,0.00789,0.1037,-0.01359,0.07474,0.07299,-0.02831,-0.02712,-0.05344,-0.03332,0.00239,-0.05091,-0.13731,-0.02045,-0.00785,0.01441,-0.00358,-0.10379,-0.14361,-0.00807,-0.00263,0.04641,0.02182,-0.06043,-0.0615,0.00984,0.06673,0.0114,-0.05945,0.06601,0.02512,0.01023,-0.02584,0.00877,0.03039,-0.03114,0.04756,-0.10956,-0.05098,0.02856,-0.08034,-0.03738,-0.0122,0.0538,-0.123,0.03463,0.11918,0.04168,0.06873,-0.05468,0.01986,0.1074,-0.11956,0.17154,0.10127,0.05859,0.00209,0.00607,0.07317,0.01198,0.04991,0.0801,0.07783,-0.04529,-0.06548,0.10259,0.0397,-0.0353,0.06824,-0.08712,-0.01978,0.07916,-0.08361,-0.00139,-0.08767,0.04108,-0.00474,-0.00542,0.03411,0.06079,0.02777,0.02582,0.09638,0.02793,0.03396,-0.10432,-0.01084,-0.07446,0.04305,-0.03869,0.04018,-0.01572,0.04492,0.05065,-0.02335,-0.11425,0.02992,0.0302,-0.13964,0.0866,0.03059,-0.03139,-0.07414,-0.0045,-0.10183,-0.02127,0.05481,0.09423,-0.07678,0.13836,-0.01189,-0.10135,-0.10935,0.00311,-0.00517,0.07597,0.03545,-0.12266,0.06942,0.12734,-0.04154,0.1005,0.05962,0.07975,0.11835,0.02158,0.07553,0.10896,0.05433,-0.00944,0.02335,0.06215,0.02439,0.0417,0.0096,0.07211,-0.03208,-0.13932,0.02058,-0.04374,0.12937,-0.03051,0.12726,0.05186,0.02187,0.035,-0.02639,0.07366,0.13893,-0.00991,-0.03757]},{"domain":"signal_processing","key":"window_coefficients","name":"Coefficients of a window function","package":"signal-processing-ai999x","example":"Give the coefficients of a 4-point periodic Hann 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width of a spectral window","package":"signal-processing-ai999x","example":"What is the main-lobe width of a 256-point Hann window at a sampling rate of 8 kHz?","v":[0.0256,0.00186,0.06002,-0.06114,0.08944,0.00315,0.13973,-0.11663,-0.07413,0.0474,0.06096,-0.00215,0.01532,-0.03125,-0.01811,0.00861,0.052,0.04729,-0.05002,0.09084,-0.04847,-0.08396,0.01199,-0.09565,-0.00106,0.00478,0.06345,-0.08386,-0.02532,-0.09692,0.02521,-0.00819,0.00585,0.04385,0.06889,0.01361,-0.06954,0.0464,0.00227,0.06033,0.02407,-0.18253,0.01137,-0.15495,0.04092,0.03034,-0.04372,-0.08014,-0.10769,0.03971,-0.09129,0.05875,-0.03193,0.05008,0.014,-0.01628,0.00544,0.02026,0.0459,0.05144,-0.07149,0.08359,0.01063,0.051,0.08144,0.10175,-0.00266,-0.01634,-0.13263,-0.07674,0.02865,0.06385,0.08385,0.05434,-0.06242,-0.02019,-0.01861,0.02978,0.00762,-0.06334,0.13912,-0.02804,0.00609,0.00539,0.06216,-0.08312,-0.04968,0.1639,-0.06181,-0.00527,-0.03535,0.04258,-0.04211,-0.06164,0.00944,0.00039,0.12331,-0.04656,0.11113,-0.04352,-0.04595,0.02255,0.06433,-0.06327,0.02295,0.01592,-0.09902,-0.00742,-0.09914,-0.00887,-0.11,-0.05853,-0.06437,0.0152,-0.01244,0.0409,-0.01856,0.03281,-0.00095,-0.00408,-0.07385,-0.02017,-0.02593,0.08147,0.05513,0.10412,-0.02618,0.00143,0.02051,-0.13063,0.05042,0.04944,-0.02049,-0.04306,-0.03066,0.00701,0.00421,0.02944,-0.00052,0.04951,-0.09364,0.12508,-0.04571,0.03445,-0.01841,-0.01979,0.03617,-0.05446,-0.08894,-0.04502,0.13724,0.01529,0.02757,0.0128,-0.0689,-0.00109,0.1278,0.10274,0.07192,-0.01939,0.02477,-0.16119,0.04071,0.00565,0.00257,-0.0702,-0.02829,-0.08243,0.07212,-0.08208,0.02877,-0.01995,-0.00627,-0.07239,-0.07436,0.03933,-0.00581,0.00472,0.014,-0.03913,-0.06097,0.04033,0.07357,0.04528,0.01755,-0.01275,0.06243,-0.01744,0.02502,-0.02603,-0.11304,0.09648,-0.06405,-0.02156,-0.01019,-0.06922,0.03485,-0.18981,-0.05648,0.00161,-0.01074,0.03202,-0.12528,-0.02405,0.04557,-0.0136,0.01422,-0.00947,-0.12245,-0.07015,0.05748,-0.01071,0.03489,0.09573,0.10383,0.08573,0.03295,0.04406,0.05775,-0.04227,0.0073,0.05353,-0.06642,0.0251,0.05579,-0.03288,0.07256,-0.01995,-0.00507,0.06932,0.07509,-0.05942,-0.02486,-0.03037,-0.06076,-0.00533,-0.03744,0.00257,-0.05621,0.12098,0.01573,-0.00987,-0.07594,-0.00075,0.09936,0.06049,0.07004,0.11578,0.06629,0.07713,0.0247,-0.09416,0.10889,0.01796,0.00573,0.01424]},{"domain":"thermofluids","key":"hydrostatic_gauge_pressure","name":"Gauge pressure at a depth in a liquid","package":"thermofluids-ai999x","example":"What is the gauge pressure at a depth of 12 m in a lake of water with density 1000 kg/m^3?","v":[0.08894,0.05349,-0.0838,-0.077,0.05215,0.12891,0.10746,-0.03655,-0.05396,0.02362,0.00245,0.05007,-0.01902,0.02473,0.00744,-0.04315,0.0094,0.07117,0.01544,0.05994,-0.04571,-0.03227,-0.0386,0.01061,0.06309,0.08981,-0.03244,0.06952,-0.05403,0.04959,-0.01205,0.11547,0.00563,-0.06018,0.06364,0.14605,0.04701,0.06031,-0.05356,0.09052,-0.10755,0.03525,-0.03202,-0.06296,-0.034,0.08405,-0.06516,-0.09877,-0.04975,0.01923,0.10024,-0.08794,-0.04682,0.05366,-0.16778,0.00158,-0.01775,-0.04516,-0.0192,0.08019,0.08523,0.00486,-0.00386,0.00762,-0.08636,0.02028,0.00971,-0.06464,0.01436,-0.01601,-0.06224,-0.00864,0.00197,0.09425,0.07856,-0.02988,0.03911,-0.01619,-0.18014,-0.05622,0.0622,0.04765,0.02971,-0.01909,0.01168,-0.03994,-0.1055,-0.03123,0.05893,0.08039,-0.07511,0.00493,-0.04633,-0.02325,-0.07251,-0.01313,-0.04164,0.02852,0.06552,-0.04285,-0.06277,-0.01199,-0.03725,0.03169,0.06201,0.02573,0.11459,0.1046,0.01173,-0.09421,-0.02627,-0.04371,-0.02073,0.0633,-0.08198,-0.0207,0.10138,-0.0367,0.0091,-0.01372,-0.10688,-0.02424,-0.05892,0.03775,-0.08656,0.07168,-0.08624,0.05873,0.10756,-0.02264,-0.01078,-0.05353,0.12034,-0.03912,0.00325,0.04333,-0.00044,0.03985,-0.02563,-0.15318,-0.01706,0.10779,-0.05689,0.01818,0.00983,-0.10236,0.0467,-0.02829,0.05075,-0.02468,0.04027,-0.04523,-0.08798,0.07133,0.00403,-0.02379,-0.01827,-0.02358,-0.07862,-0.06975,-0.02768,0.13406,0.13932,-0.01302,-0.06409,-0.01135,-0.01151,-0.05498,0.01835,0.01101,-0.03454,0.03443,0.02603,0.04927,-0.00109,-0.0189,0.02452,0.03615,0.02438,0.16769,-0.02228,0.01735,-0.02802,-0.02378,0.10588,-0.021,0.01054,-0.11185,-0.00159,-0.04314,-0.03969,0.0547,-0.0289,-0.15544,-0.04566,0.04561,0.00491,0.05571,-0.04426,-0.02326,-0.11276,0.04728,-0.04749,-0.1351,0.04788,-0.08325,-0.1266,0.04979,-0.10279,0.08494,0.05646,-0.00302,-0.02415,-0.07522,0.00607,-0.05995,0.02165,-0.07191,0.04002,0.03253,0.10343,-0.0794,-0.07687,0.02934,-0.01673,0.01014,0.01285,0.00325,0.01999,0.02391,0.0841,-0.00803,0.06286,-0.00131,-0.05001,0.11877,-0.02594,0.07317,0.05941,-0.00312,0.01254,-0.07144,0.06182,-0.04835,0.11916,0.0016,0.001,0.05803,0.00665,-0.05721,-0.01096,0.05014,0.0393,0.10265,0.10345,0.03799]},{"domain":"thermofluids","key":"absolute_pressure_depth","name":"Absolute pressure at a depth in a liquid","package":"thermofluids-ai999x","example":"A diver is at a depth of 20 m in seawater of density 1025 kg/m^3. The atmospheric pressure is 101325 Pa. What is the absolute pressure on the diver?","v":[0.0548,0.0288,-0.11473,-0.09607,0.10212,0.19424,0.0698,0.00379,-0.00546,0.00242,-0.02204,0.08332,-0.02509,0.02346,-0.02855,-0.04749,0.09983,0.01196,0.10549,0.0363,-0.03184,-0.10274,-0.02754,0.06005,0.04736,0.09782,-0.00249,0.11234,0.01379,0.06443,0.03748,0.06433,0.04105,-0.05513,-0.00869,0.11425,0.03844,0.06607,-0.02093,0.08912,-0.1081,-0.03132,-0.02579,-0.01427,0.00223,0.02586,-0.08973,-0.12234,0.01958,-0.03491,0.10892,-0.15686,-0.00415,0.11055,-0.18223,-0.17534,-0.02365,0.0109,0.05977,0.08155,0.03841,0.00272,0.00264,0.00632,-0.00045,-0.09304,0.00961,-0.05282,0.01985,-0.02241,-0.08225,0.00227,0.07258,0.01069,0.04143,-0.0201,0.08881,-0.07454,-0.07392,0.00063,0.03621,0.02378,0.01846,-0.04041,0.04918,-0.00379,-0.01364,-0.06077,0.01919,0.04318,0.00777,0.04456,-0.07414,0.00332,-0.06782,-0.08792,0.03478,0.04315,0.05804,0.00472,-0.06266,-0.08981,-0.09431,-0.00761,0.01616,0.01478,0.02649,0.08388,0.02623,-0.0052,-0.04953,-0.01965,-0.03374,-0.00148,-0.05761,-0.07041,0.04717,0.02555,0.0155,0.03596,-0.02976,-0.03288,-0.05289,-0.0087,0.03569,0.02149,-0.0476,0.04034,0.13853,-0.02884,-0.03171,0.02241,0.06394,-0.031,-0.04981,-0.02481,-0.02743,-0.03189,0.05737,-0.12569,-0.06774,0.05936,-0.01977,0.03125,-0.00361,-0.08048,0.06094,-0.03248,0.0337,-0.07881,-0.03803,0.05638,-0.12408,0.04787,-0.02412,0.12655,-0.06903,0.02361,-0.04777,-0.06733,-0.02132,0.09014,0.12954,-0.03007,-0.11839,-0.04086,0.03686,-0.03166,0.0797,-0.03283,-0.02169,-0.06221,-0.00225,0.00819,0.04307,-0.02531,0.0127,-0.03942,0.05846,0.1687,0.02207,0.0321,-0.08825,-0.00199,0.0456,0.05093,-0.00818,-0.04187,-0.06554,-0.11424,-0.03106,0.07291,-0.00979,-0.12043,-0.0494,-0.01142,0.00438,0.04566,-0.07464,-0.01133,-0.03516,0.06833,-0.05071,0.00104,0.04906,-0.01764,-0.05849,-0.01626,-0.10535,0.11379,-0.01791,-0.04066,0.00788,-0.05391,-0.01917,-0.05595,-0.00539,-0.12918,-0.00724,0.01083,0.0759,-0.04306,-0.08483,-0.01591,-0.05826,0.06109,-0.04124,-0.03106,0.0278,0.01715,0.11589,-0.01492,0.06848,0.03978,-0.06103,0.15321,-0.01521,0.04235,0.04455,-0.03312,-0.04063,0.02292,0.07562,0.06074,0.10509,0.00079,0.02706,0.01226,-0.02447,-0.04738,-0.00335,0.03257,0.15739,0.10636,0.07973,-0.01586]},{"domain":"thermofluids","key":"buoyant_force","name":"Buoyant force (Archimedes' principle)","package":"thermofluids-ai999x","example":"A solid block with a submerged volume of 0.02 m^3 is fully immersed in water of density 1000 kg/m^3. What is the buoyant force on it?","v":[0.15274,-0.05398,-0.05355,0.0224,0.06836,0.20901,0.08828,-0.05754,0.04364,0.0496,-0.01024,0.11186,-0.09286,0.00988,0.09051,-0.02208,-0.07206,0.08442,0.07183,-0.03767,0.04544,-0.05458,-0.07987,0.09336,-0.03224,0.05378,0.02752,0.13241,-0.06916,-0.07476,0.03473,0.02386,-0.02208,-0.03905,0.01116,0.06829,0.02093,-0.08748,-0.06117,0.10027,0.00795,0.03047,0.00094,-0.1183,0.01321,0.07994,-0.02446,-0.11416,0.05141,0.07463,0.04027,-0.11264,0.02688,-0.02398,-0.11348,0.01538,-0.09818,0.04141,0.02683,0.0975,0.10537,0.03118,-0.00563,0.03243,-0.03098,0.00778,0.08719,-0.05919,-0.00041,-0.05293,0.05925,-0.06484,0.00302,-0.02942,0.00818,0.05647,-0.04914,-0.0465,-0.064,-0.05091,-0.0474,0.02731,-0.03446,-0.01196,-0.01653,0.02912,0.02093,-0.11194,0.05255,0.0007,-0.0748,-0.10038,0.02103,0.03994,-0.06271,-0.04102,-0.02925,-0.06373,0.09398,-0.05808,-0.01226,-0.03257,0.00333,-0.0513,0.03962,-0.084,0.10323,0.04206,-0.01906,-0.05287,0.01589,-0.05417,-0.00911,0.01181,-0.03603,-0.07728,0.09979,0.03131,0.00617,0.0607,-0.10023,-0.02121,-0.01027,-0.02249,0.00696,0.02652,-0.06387,-0.01052,0.08062,0.01518,0.02657,-0.03051,0.0755,-0.04254,-0.06046,0.00326,-0.01972,-0.0037,-0.03348,-0.21789,0.04734,0.11069,-0.0239,0.03584,0.00081,-0.01221,0.04598,-0.0651,0.01317,-0.08674,0.07271,0.00383,-0.08627,-0.04534,-0.02126,-0.03918,-0.01963,-0.10133,-0.04666,-0.0141,0.02529,-0.00764,0.02226,-0.01579,-0.00964,0.1287,0.09961,0.06712,0.02066,-0.02232,-0.08965,0.01401,-0.11291,-0.0106,0.00177,0.01343,0.00998,-0.04251,0.00803,0.11369,0.11832,-0.02535,0.05938,0.00885,0.10182,-0.08676,0.00156,-0.02312,-0.04843,-0.05302,0.05401,-0.02183,-0.02755,-0.14854,0.07016,0.08793,0.00635,0.04605,-0.10169,-0.01341,-0.09637,0.06281,-0.01867,-0.01856,-0.00231,0.05056,-0.14037,0.02469,-0.07427,0.04809,0.00998,-0.04534,0.06931,-0.00738,0.07332,0.01402,-0.02365,0.01104,0.00264,0.05979,0.07968,0.01812,-0.07063,-0.07389,0.00656,0.10326,-0.04316,0.07379,0.04331,0.09648,0.0283,0.08178,0.00922,0.047,-0.06362,0.02864,-0.08337,-0.08585,0.01893,0.04846,-0.05149,-0.05843,-0.0109,-0.0015,0.1008,-0.04436,0.02451,0.13253,0.00992,-0.04259,0.00877,-0.09219,0.04894,0.12046,0.01592,0.05444]},{"domain":"thermofluids","key":"continuity_speed","name":"Continuity: speed after a change of pipe diameter","package":"thermofluids-ai999x","example":"Water enters a reducer with an inlet diameter of 0.1 m at an inlet velocity of 2 m/s. The outlet diameter is 0.05 m. What is the outlet velocity?","v":[0.04938,-0.00999,0.06402,-0.02348,0.00233,-0.01675,-0.05627,0.02009,-0.03713,0.03862,0.01626,-0.04749,-0.05957,-0.0522,0.00555,-0.06404,-0.10807,-0.00544,0.03017,-0.00874,0.04206,0.03133,0.04416,0.00648,-0.09245,0.00812,0.00402,-0.02166,-0.02573,-0.0001,0.05418,-0.03523,0.03886,-0.09575,-0.06062,0.01295,-0.00697,-0.09221,0.08132,0.07963,0.01619,0.08837,-0.0269,-0.01084,0.09538,0.03783,0.09156,-0.05326,0.01393,-0.03646,-0.01294,-0.04469,0.03013,-0.01029,0.03564,0.02248,0.04038,-0.00046,-0.09579,-0.07216,0.05144,-0.05272,-0.07718,-0.13656,-0.00065,0.0607,0.01946,-0.0127,0.08178,0.05056,-0.00638,0.03925,-0.00983,0.02285,0.01008,-0.05506,-0.0075,0.00538,0.02443,-0.02037,0.0447,0.01002,0.02885,0.07487,-0.03481,-0.00306,-0.05979,-0.0247,-0.12368,-0.00201,0.02722,-0.01987,0.01211,0.10045,0.06774,-0.02545,0.1016,-0.0434,0.05942,0.04624,0.12647,0.03866,-0.01488,-0.05632,-0.02332,0.04233,0.01218,0.07012,-0.01925,0.05539,-0.00656,-0.04028,-0.02072,-0.09136,-0.13512,0.05525,0.08068,0.06228,0.06724,-0.15608,0.05673,0.03452,-0.04927,0.13087,0.06487,0.05462,0.00153,-0.04342,-0.04958,-0.03637,-0.04928,-0.10591,0.08556,-0.08013,0.042,0.00443,0.01615,0.03695,-0.0602,-0.18112,-0.16223,0.14499,0.03433,-0.06547,0.03621,0.10356,0.02764,0.07086,-0.05203,0.04564,0.07413,-0.03807,0.03639,-0.02948,0.08147,0.00989,0.10155,-0.05631,-0.00693,-0.07467,0.05457,-0.03266,0.07236,-0.13828,0.00187,-0.01081,0.05497,-0.13333,0.01102,0.05049,-0.01402,0.03554,0.03285,-0.03971,-0.00893,-0.09414,-0.04625,0.02744,0.04646,-0.12565,0.05519,0.03381,-0.0124,0.05677,0.05202,0.06252,-0.01355,0.07272,-0.0015,-0.06158,-0.02752,-0.02701,0.07233,-0.01834,0.11802,0.04394,-0.01741,0.00959,0.07348,-0.05853,-0.0204,0.02848,-0.0789,-0.1695,0.07427,0.0495,-0.0467,0.01303,-0.01495,0.02115,-0.02463,-0.00387,0.08576,0.01738,-0.05328,-0.17172,-0.03967,0.09878,-0.02306,-0.00042,0.0501,-0.04431,0.03597,0.00884,0.03286,0.03467,-0.02245,0.11221,0.06548,0.01003,-0.07932,0.05424,0.00479,-0.01557,0.07139,-0.1389,-0.00428,0.00029,0.05697,-0.0208,0.13101,0.04624,-0.02968,-0.00151,0.1424,-0.03239,-0.1246,-0.03331,0.04256,0.00397,-0.04773,0.06195,-0.13057,-0.13829,0.12316,0.00546]},{"domain":"thermofluids","key":"bernoulli_horizontal","name":"Bernoulli's equation along a horizontal streamline","package":"thermofluids-ai999x","example":"Water of density 1000 kg/m^3 flows without losses through a horizontal pipe. The inlet pressure is 200 kPa and the inlet velocity is 2 m/s. The outlet velocity is 6 m/s. What is the outlet pressure?","v":[0.06363,-0.0258,-0.0716,-0.09472,0.04827,0.06799,0.04439,0.00045,-0.01244,0.05393,-0.09456,0.00469,-0.04884,0.00894,0.00176,0.02664,-0.02592,0.04331,0.02535,0.03447,0.04384,-0.00524,0.09343,0.0379,-0.03986,0.0072,-0.03465,0.04008,-0.0618,0.00315,0.05692,-0.00663,0.02924,-0.08871,-0.00198,0.15919,0.04845,-0.03275,-0.01431,0.10782,0.04508,0.03015,-0.07689,-0.01855,-0.05344,0.04291,0.04895,-0.08684,0.08134,-0.01432,0.02368,-0.08472,-0.05073,-0.0227,-0.04126,0.04651,0.02269,0.08327,0.00338,0.03747,0.07301,-0.05268,-0.05139,-0.1055,-0.05919,-0.0096,0.11611,-0.09901,0.03711,-0.03267,-0.12161,-0.01347,0.08286,-0.00327,0.01789,-0.02803,0.19579,-0.03989,-0.01305,-0.03424,0.01386,-0.07367,0.05195,0.03912,-0.02251,-0.13832,0.01952,-0.00849,-0.06453,0.03014,0.05518,-0.10482,0.02532,-0.07683,-0.00884,0.04315,0.14771,-0.06388,0.08659,-0.03215,0.04099,0.01483,-0.05435,-0.03525,0.0776,-0.07856,0.01893,0.06311,0.00327,0.0225,-0.0399,-0.01865,0.04977,-0.01988,-0.05355,-0.07499,0.17333,0.05023,-0.04929,-0.1101,-0.16206,0.00036,0.02213,0.06691,0.01055,0.0498,-0.06497,0.07156,0.06074,-0.01005,-0.06527,-0.04516,0.07705,-0.07911,-0.04711,0.04771,-0.06897,0.12138,-0.10243,-0.13325,-0.18115,0.08602,-0.03583,-0.01874,0.09293,0.05825,-0.00706,0.00961,0.01794,0.01221,-0.0313,0.04217,-0.0581,0.05527,0.06933,-0.04083,-0.02384,-0.04895,0.00146,-0.03281,-0.0196,0.014,0.08733,-0.09374,0.01948,-0.0141,0.06186,-0.09877,0.00448,-0.01949,-0.11323,-0.02596,0.05838,-0.10623,0.02936,0.05199,0.00389,0.07288,-0.0226,0.01562,0.00238,0.04077,-0.05533,0.11888,0.03868,0.12086,0.02758,0.01228,-0.10173,-0.03011,0.04769,-0.04101,0.06494,-0.00595,0.07284,0.0359,-0.06465,-0.09292,-0.01174,-0.11572,0.02609,0.08227,-0.11087,-0.02374,0.1089,-0.02507,-0.03957,0.06347,0.02988,0.14114,0.0144,-0.01508,0.06683,-0.04676,0.00017,0.00815,-0.02915,0.04352,0.00134,0.00914,0.05453,-0.14453,0.02246,-0.01101,-0.07534,-0.01559,-0.03585,0.12151,0.01604,0.05537,-0.03165,-5e-05,0.00794,0.03322,0.02488,-0.07192,-0.04411,0.03934,-0.04115,0.02251,-0.05818,-0.0224,0.10157,0.01367,0.08176,-0.0755,0.01801,-0.02497,0.01978,0.0568,-0.02237,0.06793,-0.04133,0.00721,0.07097,0.09543]},{"domain":"thermofluids","key":"torricelli_efflux","name":"Speed of efflux from a hole (Torricelli's law)","package":"thermofluids-ai999x","example":"Water leaves a small hole in the side of a tank 2 m below the surface of the water. What is the speed of efflux?","v":[0.0631,0.03137,-0.06342,-0.04815,-0.01119,0.12046,0.04986,-0.05003,0.00289,0.10937,-0.04257,-0.05427,-0.00084,-0.03681,-0.08708,-0.02678,-0.01562,0.02908,0.06247,-0.10556,0.0289,0.00685,0.01002,-0.05049,-0.0596,0.01805,0.01925,0.1382,-0.09205,0.04817,0.07143,0.07385,0.09397,-0.0719,-0.11008,-0.0058,0.10521,-0.04068,-0.03355,0.08314,0.05415,-0.09701,-0.11941,-0.03863,0.00259,0.03595,0.01929,-0.09942,0.03309,0.06689,0.01698,-0.11263,-0.01892,0.04796,-0.0917,0.02871,0.05201,-0.03549,-0.08965,-0.0128,0.00263,-0.02934,-0.04299,-0.0035,-0.20296,-0.01701,0.07431,-0.02844,0.06405,0.00744,0.00043,0.00455,0.0647,-0.02375,-0.00856,-0.03218,0.1033,-0.0582,-0.07223,-0.03113,0.04679,0.0064,-0.01785,0.04564,-0.12756,-0.00377,-0.02145,-0.02915,-0.02105,0.02772,-0.01091,-0.00642,-0.14278,0.08706,-0.03629,0.04635,0.1075,-0.12226,0.11553,0.02712,-0.03555,0.00422,0.07888,-0.16569,-0.00064,-0.01186,0.04074,0.03744,-0.0865,0.02905,0.02965,-0.0312,0.07528,0.06665,0.02016,0.04493,-0.02794,0.00763,0.07054,-0.03664,-0.09984,0.01179,0.01607,0.09049,-0.00538,0.0283,-0.00692,0.02125,-0.07874,-0.03642,-0.05984,-0.01242,0.1332,-0.07584,0.09252,-0.09348,-0.02174,0.13482,0.03704,-0.09921,-0.08749,0.12749,-0.04881,0.03516,0.05151,0.05051,0.01166,0.02225,0.0317,-0.01143,-0.03159,0.03176,-0.11386,0.05985,-0.02423,0.04202,-0.01734,-0.05566,-0.04924,-0.0051,0.03253,-0.03494,0.03226,-0.06415,-0.10588,0.06813,0.05149,-0.02441,0.13719,-0.01846,0.01398,0.08148,0.02589,0.04041,-0.00682,-0.10554,-0.01286,0.06376,0.09469,0.09578,-0.06917,0.02032,-0.02561,-0.00151,0.09518,0.11972,0.00957,-0.00185,-0.00301,0.00114,-0.01166,-0.04593,-0.02012,-0.08174,0.07765,0.02552,0.01497,0.04875,-0.0039,-0.02981,0.0435,0.03683,-0.11214,0.01769,0.10904,-0.0182,-0.01555,0.0333,0.03135,0.06705,-0.04593,0.05355,0.08199,-0.0755,-0.03981,-0.10063,-0.0003,-0.05912,0.02443,-0.0533,-0.00592,-0.08035,-0.01874,-0.02893,-0.01383,0.002,-0.03813,0.07334,0.05815,-0.04274,0.01657,0.00525,-0.00983,-0.07267,-0.007,0.03084,-0.09341,0.1124,-0.016,0.01515,-0.03304,0.13327,0.02034,0.00908,0.14714,-0.0294,-0.05941,-0.05206,0.08176,0.02902,-0.02793,0.03847,0.13225,-0.04516,0.07943,-0.03131]},{"domain":"thermofluids","key":"dynamic_pressure","name":"Dynamic pressure of a moving fluid","package":"thermofluids-ai999x","example":"What is the dynamic pressure of air with density 1.225 kg/m^3 moving at 40 m/s?","v":[0.05707,-0.04928,-0.05141,0.01104,0.00201,-0.01405,0.10793,0.08765,-0.03211,0.03346,-0.04558,-0.00603,0.01181,0.0583,-0.01554,-0.01393,-0.00806,-0.02369,-0.02446,-0.00073,0.06118,-0.01757,0.01352,0.01815,-0.05395,0.05357,-0.00586,-0.00633,-0.04057,-0.03634,0.1916,0.02203,-0.01701,-0.0732,-0.05328,0.14998,0.00868,0.03028,0.08767,0.09785,0.08519,0.09431,-0.04677,-0.04792,-0.13806,0.11716,0.0212,-0.06743,0.06331,-0.04502,-0.02587,-0.0626,0.01786,0.01353,0.0526,-0.01054,0.03892,0.04168,-0.02186,0.02258,0.0375,-0.07272,-0.04308,-0.08004,-0.01429,-0.00285,0.03444,-0.05214,0.03713,0.05887,-0.0452,0.02556,-0.02718,-0.07817,0.09425,-0.03549,0.20749,-0.04088,-0.05605,0.00472,0.01988,-0.03125,-0.0478,0.04523,0.00207,-0.11278,0.03127,-0.05011,-0.05926,-0.01805,-0.03605,-0.07187,-0.00704,-0.03965,0.06948,-0.01818,0.03724,0.10106,0.0529,0.01727,-0.0024,-0.03658,-0.00656,0.09157,0.1083,-0.04035,0.12257,0.09659,0.01203,-0.02643,-0.04417,-0.08311,0.02541,-0.03481,-0.12951,-0.01597,0.08705,0.07502,-0.01231,-0.1033,-0.02472,-0.07697,-0.01349,0.02946,-0.06033,-0.01408,-0.15576,-0.00951,0.14319,-0.0474,-0.06189,-0.08038,0.06507,0.03208,0.02042,0.05937,-0.05212,-0.01543,-0.00735,-0.11319,-0.11991,0.07956,0.05433,-0.01825,0.08315,0.08303,-0.01866,-0.04676,-0.01164,0.02034,-0.00876,0.0338,0.00343,-0.0177,0.03934,-0.08606,0.00425,-0.10412,-0.06467,-0.03047,-0.01638,-0.01151,0.07092,-0.16608,-0.04797,0.01879,0.01384,-0.15418,-0.0126,-0.15142,-0.09866,-0.06792,0.01042,-0.02993,0.12182,0.04898,0.02613,0.00378,0.0838,0.10047,0.09275,0.09801,-0.05211,0.04072,0.05869,0.01367,-0.05621,-0.05816,-0.08058,-0.09695,0.00403,-0.04253,0.03414,-0.00331,0.07344,0.06161,0.05392,0.05105,0.03259,-0.12427,-0.05452,0.03681,-0.00789,-0.06947,-0.03195,-0.00464,-0.07999,0.01333,-0.01046,0.01674,0.06042,0.08573,0.0653,-0.01404,0.02242,0.01224,-0.06895,0.08823,-0.02468,0.05164,0.07613,-0.11186,-0.02172,0.06814,-0.06378,-0.0337,-0.10966,0.00451,0.03205,0.00684,-0.03346,0.04938,0.02215,0.00892,0.00996,0.03796,0.05612,-0.04223,0.06761,0.00592,0.07582,-0.0685,0.04871,0.04273,0.03895,-0.13208,0.05494,0.04273,0.01401,-0.00927,-0.06663,0.05655,-0.09681,-0.00231,-0.00141,-0.04208]},{"domain":"thermofluids","key":"reynolds_number","name":"Reynolds number from density, velocity, diameter and viscosity","package":"thermofluids-ai999x","example":"Water with density 998 kg/m^3 and dynamic viscosity 0.001 Pa*s flows at an average velocity of 1.5 m/s in a pipe of diameter 0.05 m. What is the Reynolds number?","v":[0.05291,-0.13411,-0.00339,0.09992,0.01461,-0.09142,0.08955,0.05701,0.00168,-0.02067,-0.00791,-0.02415,0.04071,-0.04021,0.01045,-0.09931,-0.10558,-0.06488,0.03938,0.03924,0.00868,-0.01046,-0.03374,-0.02723,-0.02009,0.00538,0.00757,-0.0064,-0.08021,-0.02955,0.04561,-0.06486,-0.00968,-0.11922,-0.01935,-0.00055,0.04575,-0.0145,0.10122,0.11007,0.09453,0.11882,0.00304,-0.06043,-0.08415,0.11177,0.02828,-0.00096,0.0565,-0.08094,-0.05823,-0.03653,0.03588,-0.01207,-0.00655,0.08077,-0.00146,0.0289,-0.1339,-0.01998,0.06677,0.01059,0.02669,-0.00075,0.0354,-0.00099,0.045,-0.0874,0.06584,0.06249,-0.0582,0.06306,-0.09441,-0.03444,0.18176,-0.03923,0.10155,0.01805,-0.07243,-0.06539,-0.00135,-0.0006,-0.08184,-0.04021,0.11782,0.02546,-0.07891,-0.04314,-0.07918,-0.02764,-0.06634,-0.0994,-0.00303,-0.00985,0.00844,0.01833,-0.06428,-0.02199,-0.02853,0.06652,0.02149,-0.03709,-0.05696,0.03249,0.17041,0.02976,0.12057,0.08017,0.02436,-2e-05,-0.02117,-0.11172,-0.08707,-0.07212,-0.11721,0.04543,0.12154,0.03406,-0.0073,-0.05659,0.08265,-0.08036,-0.05861,0.06328,0.04668,-0.0313,-0.10862,-0.02235,0.05661,-0.01148,-0.13212,0.0318,0.01167,0.0209,0.06507,0.12666,-0.05098,-0.03039,-0.07377,-0.06979,-0.03364,0.14948,0.08817,-0.01759,0.013,0.0349,-0.048,-0.00778,-0.01632,-0.09491,0.06097,0.03953,0.00294,-0.01629,-0.0452,-0.02661,0.00268,-0.04344,-0.04226,-0.03429,0.03077,-0.02056,0.01501,-0.10389,0.10838,-0.02037,-0.0077,-0.15698,-0.0478,-0.0372,-0.07578,-0.00255,-0.05139,-0.00866,-0.0026,0.00152,-0.0249,0.01802,0.0677,0.02594,0.17368,-0.04788,-0.02869,0.12224,0.0844,-0.04276,-0.10464,0.05858,-0.03083,-0.10007,-0.04803,-0.05685,-0.01745,-0.05776,0.08112,0.02726,0.04973,0.0634,0.02972,-0.04027,-0.1219,-0.00255,0.05824,-0.06238,-0.07499,0.02472,0.0184,-0.00592,0.01062,-0.00999,0.07792,0.10911,0.02865,0.01797,0.00176,-0.02338,-0.03423,0.16499,0.08144,0.08506,0.01274,-0.03847,0.09719,-0.0337,-0.01105,0.03111,-0.02992,0.01289,0.019,0.00104,-0.05607,0.05627,0.06257,0.06476,-0.07921,-0.02393,0.0027,0.00175,0.10475,-0.03139,0.08478,0.00058,-0.02174,0.02113,0.08291,0.01529,0.04484,0.04815,-0.00296,0.02023,-0.02657,-0.05144,-0.0631,-0.02539,0.01405,-0.04147]},{"domain":"thermofluids","key":"reynolds_number_kinematic","name":"Reynolds number from velocity, diameter and kinematic viscosity","package":"thermofluids-ai999x","example":"Air with a kinematic viscosity of 0.000015 m^2/s flows at 10 m/s past a cylinder of diameter 0.03 m. What is the Reynolds number?","v":[0.05293,-0.13895,0.04675,0.08617,0.05924,-0.11981,-0.01135,0.03782,-0.02975,-0.09775,0.02458,-0.1109,0.00952,-0.10918,0.0373,-0.09174,-0.12925,0.01331,0.00425,0.04248,-0.04115,-0.00491,-0.01718,-0.06404,-0.08586,-0.03439,0.09018,-0.08249,0.00531,0.02142,-0.00448,-0.01851,-0.01864,-0.04916,-0.04014,-0.13306,0.02461,-0.02566,0.07376,0.06167,0.08624,0.01345,-0.02121,-0.03341,-0.09457,0.0844,0.0045,0.00262,0.04904,-0.03643,-0.00874,-0.05242,-0.00215,-0.00776,0.04137,-0.0041,0.05887,0.00128,-0.11408,-0.07021,0.00084,0.0106,-0.08349,-0.0283,-0.00459,0.04955,0.06199,-0.02481,0.03303,0.12955,-0.05525,0.06117,-0.12363,-0.0143,0.09031,-0.00296,0.00898,0.07626,-0.00545,-0.15462,-0.04785,0.05442,-0.06553,0.04807,0.06388,0.09848,-0.07953,-0.04723,-0.02355,-0.03327,-0.04522,-0.08381,-0.03721,0.01474,0.05281,0.00032,-0.09634,-0.09289,-0.03095,0.07569,0.01762,0.05442,-0.01884,-0.00189,0.13858,0.07369,0.09829,0.02251,-0.01802,0.00128,0.0474,-0.16306,-0.01991,-0.04383,-0.12951,0.03722,0.07987,-0.01584,-0.00044,-0.02793,0.10174,-0.03418,-0.04661,0.01562,0.10704,-0.0231,0.04305,0.01107,0.03967,-0.01502,-0.10799,-0.00815,-0.02333,0.06779,0.04836,0.01854,-0.03941,0.08156,-0.02342,0.03969,-0.04605,0.1831,0.04576,-0.01503,-0.07073,0.01006,-0.06445,0.02975,-0.0329,-0.09547,0.00765,0.09345,-0.043,-0.01111,-0.01489,0.0118,0.04221,-0.0111,-0.00473,-0.10081,0.06444,-0.0752,-0.04209,-0.07044,0.04819,-0.03634,-0.03843,-0.17646,-0.01884,0.02038,-0.05753,-0.0031,0.05124,0.03251,-0.02234,-0.09124,-0.01048,0.01483,0.07561,-0.03457,0.06611,-0.08631,-0.04213,0.08589,0.05634,0.01211,-0.10619,0.01276,0.01591,0.0066,-0.04386,-0.04053,-0.07056,-0.04315,0.03433,0.04644,0.05202,0.11924,0.08033,0.06969,-0.02141,0.00042,0.04151,-0.10627,-0.06013,0.03694,0.05327,-0.02406,0.052,-0.03172,0.01769,0.13074,-0.01902,0.02959,0.01539,-0.0455,0.00244,0.16195,0.06639,0.03017,-0.0099,-0.06793,0.11587,-0.00151,-0.03638,-0.0002,-0.02367,0.01763,0.0852,-0.01722,-0.02315,0.08178,0.04153,0.12671,0.00219,0.01271,0.00874,0.08584,0.07512,-0.09061,0.11787,0.02919,-0.01928,0.00675,0.11032,0.05063,0.02271,-0.07658,0.04697,-0.04307,-0.04818,0.01241,-0.09198,-0.05302,0.01638,-0.04484]},{"domain":"thermofluids","key":"kinematic_viscosity","name":"Kinematic viscosity from dynamic viscosity and density","package":"thermofluids-ai999x","example":"A liquid has a dynamic viscosity of 0.002 Pa*s and a density of 800 kg/m^3. What is its kinematic viscosity?","v":[0.1448,-0.06974,-0.0533,0.00493,0.00977,-0.08124,0.10093,0.05489,0.02847,-0.07556,0.02682,-0.04862,-0.02683,-0.01791,0.08479,-0.10887,-0.07031,-0.07337,-0.05851,0.01457,-0.03607,0.0514,-0.07151,-0.05303,-0.01038,-0.03323,0.07184,0.01073,-0.05801,-0.01351,0.01642,0.05187,-0.14986,-0.01364,-0.04666,0.00478,-0.00586,0.02578,0.046,-0.0312,0.00722,0.09872,0.01589,-0.05684,-0.1545,0.08794,-0.0166,0.01378,-0.01535,-0.00841,0.00928,-0.01104,-0.03236,0.04561,-0.06928,0.13006,0.03076,-0.03554,-0.02,0.05026,0.05837,0.00297,0.00065,-0.0109,-0.04149,0.01283,0.10056,-0.01812,-0.01076,0.11476,-0.0497,-0.05146,-0.08091,0.01057,0.18269,-0.02982,0.0887,0.00767,-0.05435,-0.18376,-0.06544,0.09538,-0.11715,0.00041,0.05784,0.05663,-0.01745,-0.075,-0.01321,0.0163,-0.08122,-0.13207,-0.00912,-0.11687,0.05347,0.03426,-0.0371,-0.01782,0.02418,-0.02456,-0.01923,0.07472,-0.03378,0.08835,0.08989,-0.02897,0.17517,0.09739,-0.00951,-0.0616,0.07714,-0.12271,-0.04769,0.006,-0.16499,0.00164,0.13162,0.01012,-0.01895,-0.01127,-0.03213,-0.06989,0.01541,0.06155,-0.02664,0.05071,-0.08731,0.02794,0.05409,-0.0178,-0.03651,-0.00736,0.01928,0.04047,-0.0412,0.03833,-0.00481,0.15532,-0.01196,-0.08422,0.0311,0.12352,0.07563,-0.01294,-0.06644,-0.06867,-0.09856,0.03918,-0.0188,-0.06779,0.02421,0.01103,-0.0736,-0.01103,-0.00149,-0.04111,0.03481,-0.07082,-0.00999,-0.12553,-0.03036,-0.07905,0.02291,-0.01369,0.12124,-0.03569,-0.11659,-0.15249,0.00772,-0.0983,-0.02193,-0.02384,0.00421,0.02216,0.07492,-0.03609,0.04719,0.04014,0.04312,0.02855,0.05537,-0.07496,-0.0696,0.02866,0.06825,0.02957,-0.08296,0.01583,-0.04216,0.03853,0.03964,-0.02868,0.02721,-0.03011,0.01445,0.01336,0.08185,0.06446,0.06886,0.03546,-0.07309,0.07485,0.02901,-0.08053,-0.02321,-0.04969,0.02491,0.0365,0.01916,-0.00801,0.01416,0.02663,-0.03301,-0.03345,-0.03588,0.02533,0.03049,0.10971,0.06365,-0.0234,0.04005,-0.13084,0.10219,0.0663,-0.05163,0.02668,-0.01364,-0.05002,0.06973,-0.04184,-0.0054,0.061,0.07437,-0.02038,-0.04238,0.04633,0.02174,0.01846,0.0258,0.03658,0.07178,0.0473,0.07295,0.06397,0.0692,0.011,0.08024,0.01038,0.10177,-0.0435,-0.03642,-0.0047,-0.06601,-0.06083,0.01616,-0.03363]},{"domain":"thermofluids","key":"laminar_friction_factor","name":"Darcy friction factor in laminar pipe flow","package":"thermofluids-ai999x","example":"Oil flows in a pipe with a Reynolds number of 1200. The flow is laminar. What is the Darcy friction factor?","v":[0.05021,-0.05903,-0.06052,0.00038,0.08499,-0.06999,0.06434,-0.02395,-0.06022,-0.09324,0.05291,-0.13783,0.01642,-0.02232,0.02096,-0.0175,-0.12478,-0.0132,0.01198,0.0842,-0.08993,0.06439,-0.06942,-0.1244,-0.0852,-0.13106,0.05624,-0.1212,-0.01083,0.05943,-0.00144,-0.00486,-0.00083,0.01896,-0.05741,0.01347,0.13661,-0.13101,-0.06747,0.07617,0.1176,-0.02386,-0.00496,-0.0936,-0.02174,0.07015,-0.02728,0.03763,0.04365,0.01117,-0.06462,0.00428,-0.0908,-0.12793,0.01318,0.06229,-0.02174,-0.06622,-0.14472,-0.06346,0.00666,-0.06066,-0.05548,0.0004,-0.03,0.04774,-0.07656,0.00082,0.01917,-0.00834,0.01848,0.01519,-0.05871,0.01987,0.08884,0.00755,0.02664,-0.03643,-0.07557,-0.12971,0.04798,0.03164,0.00906,0.04192,0.15652,-0.02992,-0.08048,-0.04903,0.05232,0.00777,-0.10984,-0.09006,-0.01763,-0.0639,-0.02644,0.06162,-0.04823,-0.09118,-0.00672,-0.05105,-0.01674,0.07313,-0.07474,-0.00044,0.10192,0.07873,0.08295,-0.04582,0.10571,0.02583,0.01541,-0.09374,0.03161,-0.18647,-0.0183,0.01717,0.11647,0.00699,-0.0601,-0.04362,-0.04793,0.10187,-0.01275,-0.05519,0.04483,-0.03655,-0.08974,0.11951,0.03409,0.04674,-0.06469,-0.00951,0.01542,0.08582,0.02057,0.15494,-0.03417,0.00261,0.0069,0.10589,-0.02159,0.06403,-0.02078,-0.0398,-0.00908,0.09585,0.05208,0.02548,-0.07208,-0.02771,-0.03314,0.05562,-0.00143,0.03789,-0.00155,0.01212,0.03747,0.00646,0.04249,-0.019,-0.0116,0.02159,0.01531,-0.04407,0.16136,-0.09196,0.06136,-0.03856,-0.02947,0.01521,0.0072,0.04206,0.05967,0.09527,-0.02689,0.07507,-0.02519,-0.00066,0.06525,0.02142,0.00881,-0.04878,0.02012,0.1645,-0.00795,-0.0135,0.01179,0.08837,-0.05183,0.01198,-0.00807,-0.00804,-0.05815,-0.05083,0.01247,0.01184,0.00437,-0.00231,0.07417,0.05897,0.01811,-0.02373,0.05316,0.01156,-0.00627,-0.01121,0.01913,0.02915,0.10458,-0.03841,0.05639,0.10827,-0.05202,0.05424,-0.06667,-0.06564,0.02409,0.12952,-0.06627,0.03524,-0.00189,-0.00418,0.11731,0.00785,-0.05748,0.0243,0.01529,0.05195,-0.01074,-0.02791,-0.12808,-0.03034,-0.02044,0.09676,0.01934,0.0347,0.00282,0.02992,0.0231,-0.04298,-0.07238,-0.01614,0.03056,-0.11848,0.08615,0.01468,0.02,-0.10703,-0.02372,-0.09592,0.04536,-0.04693,0.02141,0.0731,0.00812,-0.0477]},{"domain":"thermofluids","key":"blasius_friction_factor","name":"Blasius friction factor for turbulent flow in a smooth pipe","package":"thermofluids-ai999x","example":"Water flows turbulently through a smooth pipe at a Reynolds number of 50000. Using the Blasius correlation, what is the Darcy friction factor?","v":[0.03254,-0.01932,0.02622,0.03621,0.04753,-0.11877,0.05879,-0.02819,-0.08892,-0.09538,0.0207,-0.07617,-0.0581,-0.05202,0.01371,0.00856,-0.09057,-0.05047,0.09332,0.08164,-0.0307,0.10628,-0.01823,-0.08472,-0.04978,-0.06587,0.01228,-0.13217,-0.06794,0.04723,-0.01387,-0.05474,0.06197,0.00801,0.03801,0.02221,0.07872,-0.11441,-0.00562,0.05481,0.0671,0.01951,-0.07106,-0.12134,-0.06591,0.02228,0.05499,0.01757,-0.00876,-0.04772,-0.05111,-0.04526,-0.09893,-0.15291,0.00356,-0.00013,0.04408,-0.01672,-0.10545,-0.04106,0.00984,-0.02343,-0.05465,0.0204,-0.08081,0.03329,-0.09007,0.01867,0.03933,-0.04503,0.00643,-0.05627,-0.05362,0.02313,0.04461,0.03187,0.03967,0.05408,-0.09442,-0.10954,0.07611,0.05684,0.02124,0.0184,0.18145,-0.02347,-0.11007,-0.03346,0.0764,0.02421,-0.04921,-0.09863,0.06744,-0.04051,0.01914,0.05249,0.01852,-0.11958,0.07255,0.01539,0.02615,0.07714,-0.03199,0.0062,0.0435,-0.03388,0.00172,0.01476,0.1251,0.04591,-0.00601,-0.07776,0.08996,-0.22119,-0.0262,0.1018,0.08938,-0.00831,-0.07016,-0.06503,-0.05676,0.0488,0.01403,0.01041,-0.0547,-0.02116,-0.07629,0.01932,0.04119,0.03722,-0.0365,-0.05217,-0.10598,0.00066,-0.04408,0.11936,-0.04433,0.00516,-0.0559,0.08919,0.04174,0.00387,0.03957,-0.05923,0.03523,0.05502,0.06772,0.08271,-0.123,0.06277,-0.01884,-0.04797,0.00672,0.05194,-0.04027,0.00127,0.05859,-0.05146,0.06273,0.04747,0.04109,0.05641,0.07779,-0.05816,0.13873,-0.06057,0.05661,-0.05516,-0.03647,0.04704,-0.00641,0.04605,0.01751,0.06127,-0.01117,0.0848,-0.04416,0.10959,0.05014,-0.01388,0.00706,-0.00159,0.03921,0.18422,0.06811,-0.06259,-0.00011,0.08772,-0.08353,0.09586,0.06652,-0.04512,0.03442,-0.07405,0.03539,-0.04357,-0.03525,-0.08022,0.07862,0.01665,0.03175,-0.05218,-0.04049,-0.08122,0.01581,-0.01158,0.03943,0.02294,0.10988,0.00265,-0.03496,0.04235,-0.00714,-0.01546,-0.03662,-0.07482,-0.00795,0.07543,-0.06209,0.07925,0.02616,-0.06358,0.14353,-0.0294,-0.04075,0.06369,-0.0099,0.12243,-0.00962,-0.0072,-0.02181,0.05003,0.02193,-0.00561,0.04894,-0.07283,-0.03819,0.04319,0.11397,-0.00514,-0.011,-0.03211,-0.01746,-0.03772,0.1097,0.00135,-0.00252,-0.09361,-0.11196,0.00151,0.01289,-0.00216,0.03345,-0.00163,0.03877,0.02151]},{"domain":"thermofluids","key":"swamee_jain_friction_factor","name":"Swamee-Jain explicit friction factor for turbulent pipe flow","package":"thermofluids-ai999x","example":"Water flows in a commercial steel pipe of diameter 0.1 m with an absolute roughness of 0.000045 m at a Reynolds number of 100000. Use the Swamee-Jain equation to find the Darcy friction factor.","v":[0.11287,-0.00086,-0.03498,-0.00403,0.08425,0.05378,0.03453,-0.04286,-0.03387,-0.06419,-0.03838,-0.08241,0.00251,0.06579,-0.05893,-0.01971,0.04833,-0.02889,0.12918,0.05612,0.06427,-0.04552,0.00298,-0.04252,-0.09119,-0.00944,0.06196,-0.09414,-0.03047,0.01907,0.04385,-0.06328,0.03643,-0.04629,-0.09427,0.04962,0.03609,0.00656,0.01414,0.04876,0.04844,-0.12877,-0.06341,0.02585,-0.00378,0.07218,0.0321,-0.00069,0.1044,-0.0688,0.00095,-0.00673,0.03807,0.11588,-0.05086,-0.09227,0.01294,-0.03313,-0.03188,0.01615,-0.06044,-0.09918,-0.00951,0.055,-0.00891,-0.05293,-0.02492,0.00479,-0.05026,-0.01406,0.03626,0.02047,0.05592,-0.0307,0.04234,-0.05287,0.12119,-0.10385,-0.12924,0.02954,0.09067,0.05144,0.0098,0.00984,0.17392,-0.02029,0.08459,-0.05916,-0.04439,-0.02308,-0.06175,0.00187,-0.05147,-0.02605,-0.04838,0.03003,-0.05918,-0.09721,0.0768,-0.09602,0.04844,-0.09128,-0.12126,-0.11374,-0.01164,0.02506,-0.07073,-0.0681,0.1113,0.0396,0.04584,-0.00127,0.05749,-0.11653,0.01165,-0.05609,0.03221,0.08333,-0.02698,-0.03323,-0.0005,0.06843,-0.03637,-0.00876,0.08893,-0.05554,-0.10626,0.02456,0.04524,-0.01995,-0.13674,0.0153,-0.0864,-0.04897,0.01906,0.09266,-0.07294,-0.09829,0.10323,0.05635,-0.02707,-0.07932,0.02201,-0.00973,0.04686,0.02981,0.04019,-0.10135,-0.07055,-0.00323,-0.02079,0.1155,-0.08304,0.06145,-0.02822,0.17182,0.04036,0.06098,0.07352,-0.07394,-0.03324,0.01212,0.02128,0.00438,0.04304,-0.04297,0.14911,-0.07167,0.05417,-0.00448,-0.02851,-0.04369,0.02434,0.0565,-0.01676,0.06216,0.02075,-0.02289,0.03242,-0.02008,0.09609,0.00723,-0.02094,0.12531,0.00248,0.01834,-0.02044,0.05824,-0.0744,-0.03073,0.03241,0.00037,-0.02588,-0.10186,-0.02984,-0.02357,-0.01673,0.02209,-0.03206,0.05552,0.01624,-0.00234,0.05216,0.19838,0.05604,-0.06865,0.07626,0.02382,0.07802,0.02528,-0.0589,0.03142,0.00354,0.0601,-0.08811,-0.0356,-0.10267,-0.07319,-0.10564,0.04461,0.07148,-0.01819,0.07453,-0.03499,-0.03317,-0.02504,0.0483,-0.00756,-0.04086,-0.10728,0.04906,0.06562,0.05657,0.02571,0.04163,-0.00047,0.03998,0.05631,0.0431,0.0532,-0.1207,0.04576,0.00098,0.06464,0.11797,-0.03754,-0.05728,-0.07485,-0.0218,-0.05736,0.08192,0.01194,0.13114,0.03124,0.00681,0.01679]},{"domain":"thermofluids","key":"haaland_friction_factor","name":"Haaland explicit friction factor for turbulent pipe flow","package":"thermofluids-ai999x","example":"Use the Haaland equation to find the Darcy friction factor for turbulent flow in a pipe of diameter 0.05 m with an absolute roughness of 0.00015 m at a Reynolds number of 80000.","v":[0.11616,-0.00572,-0.03786,0.01684,0.0787,0.03893,0.05651,-0.02372,-0.04799,-0.05288,-0.00979,-0.04267,-0.02782,0.09574,-0.04976,0.00583,0.02006,-0.03287,0.16815,0.06343,0.08714,-0.00089,-0.00368,-0.0758,-0.04049,0.00014,0.0172,-0.11716,-0.02128,0.0081,0.0101,-0.05189,0.06621,-0.04646,-0.11772,0.05377,0.02281,0.01487,0.02449,0.05798,0.06655,-0.12376,-0.0865,-0.01873,-0.03247,0.06334,0.07506,-0.00613,0.07977,-0.10358,-0.01046,-0.02748,-0.01036,0.03322,-0.05654,-0.09552,0.0398,-0.01661,-0.0427,-0.00074,-0.04169,-0.07997,-0.01537,0.06073,-0.02222,-0.02383,-0.04866,0.00414,-0.0289,-0.02859,0.0178,0.01754,0.04805,0.01956,0.0705,-0.05678,0.08006,-0.08675,-0.14873,-0.00469,0.08772,0.07359,0.03039,-0.00681,0.17774,-0.02214,0.0395,-0.03509,-0.04365,-0.02856,-0.08052,-0.04277,-0.03046,-0.07536,-0.05706,0.05779,-0.06847,-0.10687,0.05653,-0.07018,0.03775,-0.09105,-0.11185,-0.09937,0.00305,0.06878,-0.06726,-0.07051,0.11592,0.02927,0.03805,-0.00548,0.07952,-0.10816,0.01273,-0.02887,0.05943,0.08454,-0.03832,-0.05724,-0.00465,0.03033,-0.00051,0.04429,0.03445,-0.07994,-0.13605,0.05364,0.03819,-0.01059,-0.16791,0.00725,-0.08474,-0.07502,0.00069,0.10743,-0.04965,-0.08433,0.0956,0.05906,0.01474,-0.07793,0.02307,0.00197,0.08573,0.01031,0.05487,-0.06764,-0.08682,0.02871,-0.00663,0.06837,-0.09917,0.09662,0.00355,0.13501,0.03354,0.03456,0.05204,-0.04473,-0.04994,0.00144,0.03779,0.01568,0.07093,-0.02375,0.12167,-0.09144,0.06005,0.00861,-0.01338,-0.05466,0.05287,0.06292,-0.02333,0.0733,0.02222,0.02962,0.01071,-0.0128,0.05624,0.01429,-0.02493,0.14584,0.02617,-0.03282,-0.00811,0.05895,-0.06682,0.00563,0.03486,-0.03075,-0.01037,-0.12424,0.00186,-0.03256,-0.02663,0.01356,-0.01891,0.02332,0.00828,-0.02112,0.01452,0.1499,0.07456,-0.07008,0.09882,0.04086,0.10452,0.01803,-0.02977,0.04755,0.02941,0.06097,-0.11006,-0.05338,-0.10102,-0.02833,-0.09085,0.03431,0.03459,-0.02711,0.10378,-0.04201,-0.03784,-0.05343,0.06348,0.04247,-0.03877,-0.13169,0.05171,0.0347,0.04874,0.01482,0.06836,-0.01017,0.0618,0.04917,0.06034,0.06183,-0.11093,0.01999,0.02281,0.05204,0.12192,-0.00715,-0.05334,-0.07245,-0.02148,-0.0415,0.0766,0.00226,0.10454,-0.00405,0.05477,0.03691]},{"domain":"thermofluids","key":"darcy_weisbach_head_loss","name":"Darcy-Weisbach head loss in a pipe","package":"thermofluids-ai999x","example":"Water flows at an average velocity of 2 m/s through a 100 m long pipe of diameter 0.1 m. The Darcy friction factor is 0.02. What is the head loss?","v":[0.04262,-0.06796,-0.02292,-0.01807,0.09586,-0.0111,0.093,-0.00275,-0.04655,0.02894,0.00601,-0.07308,0.04665,0.06952,-0.1065,0.01448,-0.10159,0.02471,0.03813,0.03226,0.00889,0.09973,-0.03073,-0.09899,-0.02376,-0.04831,0.01578,-0.0874,-0.04988,0.02583,-0.04071,-0.03979,0.04107,-0.07672,-0.07276,-0.05879,0.06672,-0.0752,0.04503,0.05629,0.07418,-0.07728,-0.1138,-0.00471,0.01956,0.10596,0.09164,0.02923,0.10668,-0.11472,-0.07168,-0.00018,0.01383,-0.05999,-0.0141,-0.04119,-0.01818,0.00227,-0.13745,-0.0296,0.05864,-0.10705,-0.09276,-0.05066,-0.0625,-0.00643,-0.06095,-0.00727,0.00272,-0.00493,0.04213,0.06551,-0.02945,-0.0208,0.02784,-0.02632,0.03095,-0.03589,-0.09413,-0.0078,0.09558,0.12405,0.08133,0.03134,0.10256,-0.03411,-0.00336,-0.0896,-0.0388,-0.01101,-0.03125,-0.07521,0.00156,-0.05247,0.03652,0.0468,-0.05534,-0.08949,0.10292,-0.08867,0.04636,-0.03952,-0.02554,-0.02948,-0.01752,0.0079,-0.04975,-0.00479,0.05287,-0.01053,0.05324,0.04314,0.16076,-0.10119,-0.05113,0.03267,0.08884,0.05563,-0.01369,-0.15581,-0.01348,0.06893,-0.01021,-0.04949,0.02372,-0.11348,-0.19332,0.03596,-0.013,0.0096,0.004,-0.01133,0.03034,0.00592,0.08761,0.10408,-0.07113,0.05281,0.04272,-0.01704,-0.0176,-0.03457,0.01778,-0.0268,0.08848,0.09404,0.05332,-0.01827,-0.07176,-0.00165,-0.00638,0.07704,-0.07073,-0.00654,0.06103,-0.00713,0.06409,-0.05169,-0.01217,-0.04829,0.06727,-0.00228,0.11965,-0.11657,-0.02694,0.03581,0.15162,-0.12417,0.04501,-0.03538,-0.0008,0.00335,0.04861,0.03814,-0.06429,0.00786,0.03322,-0.06549,0.07456,-0.02404,0.07279,-0.00683,0.02657,0.06186,-0.03486,-0.03012,0.03534,-0.00381,-0.1621,-0.0285,0.07064,-0.05863,-0.06121,0.00524,0.0559,-0.04826,0.07219,0.04487,0.06487,-0.02622,0.00113,0.00544,-0.00385,0.0711,0.01686,-0.07599,0.04562,0.04683,0.13156,-0.03641,-0.00197,0.13797,0.05857,0.04915,-0.08012,-0.01733,-0.05711,0.06158,-0.01187,0.1004,-0.06532,-0.03437,0.13364,-0.01794,-0.01987,-0.0745,-0.00896,0.09369,0.00645,-0.06623,-0.05993,0.03494,-0.00933,-0.05378,0.07068,-0.05384,0.00416,0.09108,0.07582,0.02152,0.05359,0.08582,0.0149,0.02106,0.08623,-0.04723,0.01866,-0.08863,0.04627,-0.10537,0.04538,-0.02522,0.01342,-0.08942,-0.00228,0.08737]},{"domain":"thermofluids","key":"darcy_weisbach_pressure_drop","name":"Darcy-Weisbach pressure drop in a pipe","package":"thermofluids-ai999x","example":"Oil of density 870 kg/m^3 flows at a mean velocity of 1.5 m/s through a 30 m long pipe of diameter 0.05 m with a friction factor of 0.03. What is the pressure drop?","v":[0.02087,-0.10685,-0.03489,-0.07835,0.04301,0.03501,0.10668,-0.00984,-0.07767,0.02967,0.03888,-0.09087,0.01292,0.04296,-0.04308,-0.0121,-0.09677,-0.01543,0.01223,0.01576,-0.03151,0.03355,0.03665,0.00548,-0.05806,-0.0006,-0.04699,-0.10511,-0.08814,0.01159,0.00285,-0.0265,-0.02039,-0.04989,-0.03808,0.10666,0.08736,-0.05304,0.04334,0.12992,0.09365,0.01573,-0.01031,-0.04016,-0.02097,0.07936,0.0553,0.0133,0.12606,-0.06144,-0.01636,0.05204,-0.05994,-0.01927,-0.03849,0.01905,0.04341,-0.00245,-0.03182,0.02118,0.03598,-0.05698,-0.07232,-0.03368,-0.03534,0.01242,-0.04678,-0.00507,-0.02682,0.00673,-0.05316,0.04061,-0.05462,-0.01825,0.04539,-0.01884,-0.00144,-0.12137,-0.1313,-0.07492,0.06157,0.04592,0.12896,-0.01663,0.11862,-0.08897,-0.01468,-0.06452,-0.07125,0.08122,-0.05348,-0.05726,0.00765,-0.0722,0.02801,0.05916,0.05585,-0.03885,0.06708,-0.04378,0.04722,0.02886,-0.08402,-0.00863,0.02906,0.04655,-0.00162,0.03679,0.12466,-0.06801,-0.0,0.00501,0.03411,-0.15596,-0.07594,-0.02228,0.17864,0.06935,-0.04284,-0.15477,-0.03753,0.02739,0.02065,0.01441,-0.00973,-0.02834,-0.22536,0.06415,0.00695,0.02032,-0.0443,-0.04864,0.14671,-0.02599,0.07278,0.14877,-0.0455,0.01063,0.0793,-0.04014,-0.18249,-0.02803,0.04648,-0.07056,0.04998,0.1083,0.05053,-0.08431,-0.07095,0.00834,0.03665,0.03058,0.01495,0.02392,0.06277,-0.01328,0.09926,-0.04827,-0.04055,-0.01304,0.03703,0.12862,0.08334,-0.10106,-0.01415,-0.03279,0.17178,-0.10251,-0.03346,-0.0244,-0.0402,-0.0302,0.04251,0.01203,0.01724,0.036,-0.00149,0.04737,0.01951,0.01543,0.04495,0.09546,-0.02453,0.06677,-0.00573,0.02773,0.04534,0.02265,-0.0719,-0.05475,0.04583,-0.01485,0.02481,-0.08306,0.04323,-0.00592,0.0649,-0.01532,-0.00718,-0.08931,-0.03266,-0.0081,-0.04157,4e-05,0.03262,-0.11498,-0.05287,0.01102,0.05793,-0.00029,0.03151,0.09669,0.02915,0.01094,-0.03448,0.02887,0.01638,0.11825,-0.04503,0.07968,0.0298,-0.08571,0.09401,0.00195,0.00138,-0.05383,0.01088,0.08372,-0.00949,-0.05843,-0.08728,0.03183,-0.03945,-0.00279,0.06724,-0.0778,0.00327,0.06922,0.02381,0.11179,-0.07288,0.03457,0.05501,-0.04643,0.12574,-0.07178,0.01523,-0.06281,-0.00363,-0.04571,0.01588,-0.00778,-0.02086,-0.02391,0.08122,0.02744]},{"domain":"thermofluids","key":"hagen_poiseuille","name":"Hagen-Poiseuille flow rate in laminar pipe flow","package":"thermofluids-ai999x","example":"Oil with a viscosity of 0.05 Pa*s flows in laminar flow through a 10 m long tube of diameter 0.01 m under a pressure drop of 20000 Pa. What is the volume flow rate?","v":[-0.09158,-0.10403,-0.00142,-0.05722,0.03381,0.02035,0.1309,-0.00098,-0.08209,0.03045,0.03726,-0.08945,0.03616,-0.04198,-0.10993,0.0562,-0.02769,0.0625,-0.05024,0.01507,-0.03803,0.02747,-0.03983,-0.05073,-0.03538,-0.06601,0.02631,0.002,-0.07108,0.05846,-0.00969,-0.02342,-0.08335,0.03713,-0.04085,0.0772,-0.00973,-0.09157,0.02921,0.16135,0.11518,0.04445,-0.05168,-0.05989,-0.04414,0.08643,0.07352,0.00999,0.07553,-0.07554,0.05371,0.0235,-0.06858,-0.05846,-0.03662,0.06585,0.07039,-0.00718,-0.01448,-0.02432,0.06743,-0.02289,-0.06115,0.06678,-0.04356,-0.00603,0.04578,-0.06513,-0.00055,-0.02551,-0.01708,-0.03809,-0.06392,-0.016,0.01244,-0.06847,0.01282,-0.10442,-0.08579,-0.20587,-0.00282,0.05209,0.06358,-0.00753,0.11433,-0.02423,-0.03146,-0.08482,-0.02536,0.01251,-0.02366,-0.0772,-0.05559,0.00857,0.04059,0.09101,0.07541,-0.05936,0.09675,-0.00866,0.03963,0.03272,-0.02239,-0.04406,0.05011,0.02815,0.05328,-0.0279,0.0094,-0.04117,0.04845,-0.07254,0.04284,-0.02884,-0.10311,-0.05202,0.06924,0.06585,-0.07748,-0.14024,-0.00026,0.05852,0.00898,-0.00304,0.03947,-0.01841,-0.11803,0.08898,-0.01423,-0.01349,-0.04487,-0.04411,0.06696,0.00184,0.0187,0.08351,-0.08895,0.13704,-0.03423,-0.02841,-0.12924,0.05517,0.0332,-0.14205,0.02317,0.07644,-0.00945,-0.09095,-0.13052,0.03057,0.01624,0.08577,0.02907,0.04757,0.01871,0.10982,0.09627,0.03812,0.02699,-0.0427,0.08388,-0.0344,0.07358,-0.07624,-0.08377,-0.07194,0.06484,-0.11193,-0.09503,-0.10117,-0.05022,0.04904,0.0058,0.0169,0.0431,-0.01609,0.02643,0.06334,0.04042,-0.0167,0.0299,0.05936,-0.01243,0.02895,0.02226,0.06786,-0.00073,-0.01199,-0.06899,0.00203,0.05488,0.08458,0.02793,-0.05372,0.01351,-0.04381,-0.02796,-0.02695,0.05469,0.01868,0.04988,-0.00814,-0.0441,-0.01689,-0.03699,-0.03314,-0.0535,0.01075,0.02715,0.04008,-0.03267,0.04594,0.05153,-0.01052,0.00563,0.04975,-0.02477,0.12743,0.08608,0.02725,0.09468,-0.11453,0.09012,-0.05951,-0.00601,-0.0513,0.01059,0.11602,0.04326,-0.04381,-0.10381,-0.01805,0.00026,0.05329,0.02599,-0.01456,-0.03307,0.14352,-0.02293,0.0586,-0.15336,0.04104,0.07223,-0.07924,0.11732,0.01115,0.03676,-0.08361,0.03366,0.04456,0.09565,-0.11878,0.06173,-0.00836,0.03585,0.08596]},{"domain":"thermofluids","key":"minor_loss_head","name":"Minor head loss in a fitting","package":"thermofluids-ai999x","example":"Water flows at 3 m/s through a fully open globe valve with a loss coefficient of 10. What is the head loss across the valve?","v":[0.10741,-0.00402,-0.03936,0.04623,0.02157,0.06275,0.04765,0.01331,0.00928,-0.03112,-0.09503,-0.12987,0.03653,-0.01516,-0.08547,-0.04672,0.06904,0.07454,0.02957,-0.05365,0.02189,0.1366,-0.00624,-0.04151,0.0145,-0.03194,0.1426,-0.04244,-0.04687,0.04651,-0.07242,0.01163,-0.00592,-0.08901,-0.03223,-0.12996,0.15616,-0.04445,0.01463,0.06011,-0.02406,-0.03276,-0.18342,0.01304,0.08942,0.08937,0.0305,0.00152,0.07643,-0.07397,-0.0226,-0.08342,0.09183,-0.02398,0.00743,-0.00873,0.01002,-0.06352,-0.11168,-0.05871,0.07343,-0.01686,-0.09334,-0.016,0.00246,0.0203,0.03049,0.01603,0.05995,0.03766,0.08652,0.0482,0.03574,-0.05864,-0.00762,0.0101,0.09595,0.0736,0.01351,-0.02676,0.03762,0.01464,0.02065,0.07427,0.0139,-0.00058,-0.00981,-0.10031,-0.01639,-0.05325,-0.00184,-0.12954,0.01535,-0.07559,0.00224,-0.06462,-0.02526,-0.12432,0.0274,-0.03329,0.03296,-0.00875,0.08981,-0.02699,0.04018,-0.09596,0.00559,0.01516,-0.08193,0.03794,0.12101,0.00029,0.18441,-0.06757,-0.08188,-0.02308,-0.01729,0.02373,0.03507,-0.10541,-0.06893,0.00303,0.03616,0.02406,0.0323,-0.01912,-0.06113,0.01228,0.03804,-0.02626,-0.01159,-0.06597,0.0153,-0.00581,0.01635,-0.06234,-0.06972,0.07538,-0.00319,-0.02608,-0.05043,-0.05726,0.02977,0.0535,0.05943,0.02514,0.0316,0.04396,0.00865,-0.01023,-0.09084,0.05384,0.01793,-0.10437,0.06586,-0.05926,-0.01735,-0.02501,-0.00827,0.00787,0.05095,-0.11924,0.01994,-0.00256,-0.07889,0.04504,0.07642,-0.13309,0.04972,0.02555,-0.03705,0.05043,0.05205,0.02583,-0.01654,-0.05655,0.02513,-0.10306,0.03061,-0.03525,0.03279,-0.04085,-0.08759,-0.06166,0.00989,0.04156,-0.06882,-0.08598,-0.11175,0.06772,-0.00646,-0.03178,-0.03861,0.02473,-0.00183,0.02298,0.08067,0.05505,0.12277,-0.07766,0.02646,0.06324,-0.01405,-0.02134,-0.05798,-0.02704,0.03203,-0.01792,0.13601,-0.02911,0.01298,0.08028,0.04561,0.01153,-0.06674,-0.03348,-0.03853,0.05398,0.10554,0.06809,-0.15285,0.02307,0.08565,-0.01948,-0.10925,-0.01498,-0.05011,0.16149,0.07177,-0.00679,-0.00385,0.02647,-0.0109,0.03168,0.07832,0.03674,-0.07248,0.02891,0.02985,-0.02377,0.2009,0.03339,0.03526,0.05683,0.09779,0.01835,0.01762,-0.08181,0.11304,-0.0215,-0.07611,-0.03695,-0.02082,-0.11434,0.01962,0.02519]},{"domain":"thermofluids","key":"hydraulic_power","name":"Hydraulic power delivered to a fluid","package":"thermofluids-ai999x","example":"A pump delivers water of density 1000 kg/m^3 at a flow rate of 0.05 m^3/s against a total head of 20 m. What is the hydraulic power?","v":[0.04581,-0.09048,-0.12329,-0.12762,0.08005,0.0691,0.0899,-0.01894,-0.02681,0.0208,-0.03032,0.01233,0.02123,-0.01426,-0.03936,-0.02701,0.04757,0.0782,0.06463,0.06167,0.03699,0.07004,-0.0907,-0.003,-0.09055,0.01884,0.0075,0.11158,-0.15348,0.04726,0.00072,-0.0066,-0.0469,-0.03281,0.0009,0.03452,0.04757,0.05622,0.04656,0.03686,0.02369,0.06074,-0.10668,-0.05247,-0.06979,0.07103,-0.00889,-0.09047,0.07697,-0.03869,0.01863,-0.00695,0.00504,0.00118,-0.07694,-0.02275,-0.04877,-0.01584,-0.07399,-0.01006,0.10705,-0.01273,0.01151,0.03172,-0.04218,0.01072,0.05877,-0.05347,0.02257,0.00508,0.05159,-0.03775,-0.04576,-0.01334,0.12815,0.06754,0.09794,-0.04059,-0.05816,-0.02369,-0.03998,-0.03389,0.02543,-0.02276,-0.05551,-0.06566,0.0618,-0.08342,0.00082,-0.07752,-0.02548,-0.1104,-0.02991,0.0384,-0.1199,-0.01712,0.04827,0.08334,0.11351,-0.02643,0.00071,-0.018,0.00978,0.04434,0.02323,-0.05825,0.09614,0.00121,-0.01201,0.12356,0.02508,-0.02648,-0.01005,0.1044,-0.05211,0.0078,0.02831,0.06363,-0.05428,-0.05536,-0.08728,-0.04768,-0.00119,-0.02537,-0.05826,-0.05348,-0.09283,-0.05191,0.0805,-0.06129,0.00432,-0.06198,-0.00995,0.01685,0.00999,0.08933,-0.03936,0.02513,-0.1481,-0.10032,0.0028,0.02113,-0.06514,0.01379,0.08965,0.00625,-0.08544,-0.02151,-0.00687,-0.06259,-0.05579,0.0449,-0.07431,0.03435,0.00976,0.05769,-0.03814,-0.10977,-0.02846,-0.07511,0.0005,-0.04077,0.0786,0.04383,0.01661,-0.01672,0.08082,0.02107,0.00393,-0.11094,-0.01909,-0.03999,-0.04075,-0.06596,-0.03491,0.13028,0.03614,-0.00331,0.01911,0.1371,0.02439,0.06505,0.00608,0.03037,0.10059,-0.03269,-0.09217,-0.08369,-0.17062,-0.0339,0.00718,-0.07937,-0.07254,0.09085,0.0532,0.12181,0.02973,0.04005,-0.00755,-0.13033,-0.02936,0.08516,0.01372,0.05632,-0.01336,-0.01197,-0.05277,-0.07981,0.0302,0.01769,-0.03346,0.009,0.07316,-0.03924,0.11928,0.02565,-0.05282,-0.07345,0.07861,-0.04211,0.21395,-0.09589,0.02305,-0.00167,0.00415,-0.06492,-0.02235,0.05221,0.07328,0.03663,-0.02321,0.05532,0.10282,-0.01868,-0.04567,0.13905,-0.03378,-0.08465,0.02895,-0.00532,-0.00345,-0.02086,-0.01973,0.04748,0.01775,-0.0251,0.10459,0.07642,0.13618,-0.00528,-0.02946,0.01813,0.07515,-0.03094,0.0183,0.13045]},{"domain":"thermofluids","key":"pump_shaft_power","name":"Shaft power required by a pump","package":"thermofluids-ai999x","example":"A pump with an efficiency of 0.8 lifts water of density 1000 kg/m^3 at a flow rate of 0.03 m^3/s through a total head of 25 m. What shaft power is required?","v":[-0.01125,-0.07054,-0.09729,-0.07527,0.15652,0.02601,0.09561,0.03748,-0.04305,-0.04139,-0.06124,-0.02854,0.00516,0.04331,-0.10452,0.05484,0.00819,0.07503,0.01144,0.03262,-0.01437,0.01235,-0.06571,-0.02964,-0.08544,-0.00271,0.01276,-0.00296,-0.10313,0.09584,-0.05979,-0.03626,-0.02924,-0.02767,-0.06846,0.07608,0.11928,0.00989,0.0354,0.08105,0.02003,0.10796,-0.05875,0.02466,-0.00395,0.09084,0.00776,-0.05654,0.10859,-0.0167,0.00904,-0.01064,-0.01564,0.03501,-0.05906,0.01732,-0.03017,-0.02532,-0.0973,-0.00224,0.02315,0.00578,-0.03877,0.06652,-0.03441,-0.01369,-0.03372,-0.02985,-0.03147,0.03732,0.00723,0.0278,-0.07157,-0.04074,0.04953,0.06969,0.02883,-0.00482,-0.08756,0.03999,-0.02743,0.01838,0.07257,0.09377,0.00506,-0.11182,0.09452,-0.03755,0.08042,-0.07073,-0.01742,-0.09608,-0.04555,-0.04309,-0.14855,0.09309,-0.01824,0.0833,0.12606,-0.02213,-0.02257,0.02032,0.02785,0.03293,0.00015,-0.04857,0.03937,0.00469,0.02287,0.08916,0.06856,-0.00123,-0.02838,0.0755,-0.05657,-0.07216,0.02285,0.1243,-0.01955,0.00089,-0.05233,-0.00688,-0.02419,-0.06488,0.03541,-0.0282,-0.0534,-0.01869,0.12169,-0.10489,0.0,-0.02446,-0.01322,-0.05463,0.02554,0.08158,-0.01688,0.04939,-0.11466,0.07169,0.07122,-0.03527,-0.0091,-0.01639,0.10846,0.01085,-0.076,-0.02911,-0.00955,-0.0318,-0.01493,0.07684,-0.07093,0.04338,0.06529,0.09683,-0.00327,-0.04721,-0.05107,-0.16439,-0.03249,-0.01562,0.00048,-0.00408,-0.00874,-0.06538,0.14128,0.04228,0.02588,-0.01816,-0.05813,-0.03698,-0.08566,-0.04093,-0.06212,0.10718,0.0252,-0.02261,0.00271,0.09716,0.02378,-0.00067,0.10814,0.00082,0.01962,0.01083,-0.05542,0.02397,-0.19237,0.03689,0.01456,-0.05379,-0.00109,0.0443,0.00638,0.03872,0.11456,-0.0139,-0.00141,-0.05023,-0.05151,0.0495,0.01888,0.12505,0.00384,-0.05255,0.02526,-0.11923,-0.01344,0.05432,-0.1673,-0.01582,0.01374,-0.06282,0.116,0.01202,-0.08046,-0.06873,0.16467,-0.0112,0.12121,-0.03906,0.05864,-0.06657,0.00962,-0.07144,-0.00023,0.04354,0.07036,-0.03329,-0.02654,0.03677,0.09264,-0.05797,-0.03637,0.13796,-0.02098,-0.04752,-0.03846,-0.02792,-0.11534,-0.037,0.00305,0.05053,0.04447,-0.0018,0.13213,0.04889,0.05952,-0.04366,-0.04899,0.04528,0.07569,-0.10675,0.00499,0.09682]},{"domain":"thermofluids","key":"hydrostatic_force_plane","name":"Hydrostatic force on a submerged plane surface","package":"thermofluids-ai999x","example":"A vertical rectangular gate of area 2 m^2 is submerged in water of density 1000 kg/m^3 with the depth of the centroid at 3 m. What is the hydrostatic force on the gate?","v":[0.1025,-0.05583,0.00503,-0.03962,0.11122,0.10432,0.0785,-0.0399,-0.03206,0.08809,0.04811,0.05509,-0.02237,0.0393,-0.01845,-0.04031,0.00729,0.04825,0.05356,0.00319,0.04083,-0.08661,0.04747,0.05189,-0.04204,0.01071,-0.02394,0.11622,-0.05915,-0.11759,0.02169,0.09302,0.07199,-0.07726,0.01294,0.13909,0.00853,0.04865,-0.04275,0.12594,0.02435,-0.02665,-0.06053,-0.05071,-0.0456,0.04626,0.01576,-0.06443,-0.01409,0.06839,0.01502,-0.08556,0.03701,0.04069,-0.03596,-0.0443,-0.10271,0.02245,0.05345,0.09034,0.10292,0.01633,-0.0643,0.02324,-0.01824,-0.05755,0.03244,-0.01654,0.10395,-0.03537,0.03019,-0.07724,-0.02174,0.06124,-0.02235,-0.00201,0.03101,-0.02625,-0.08781,-0.03788,0.01319,-0.03314,-0.00921,-0.10933,0.03261,-0.02043,0.00482,-0.02388,-0.09009,0.03618,-0.13098,-0.00916,-0.05586,-0.02883,-0.08964,-0.09173,0.04803,-0.05498,0.10175,-0.05786,-0.07987,-0.06115,-0.02107,-0.01475,0.02283,0.0565,0.10809,0.04858,0.01931,-0.04003,0.00315,-0.02315,0.1216,0.0888,-0.01946,-0.05922,0.04681,0.04325,-0.02771,0.03469,-0.14327,0.03713,0.02766,-0.07376,-0.09412,0.00523,-0.09519,0.01052,0.07259,-0.05807,-0.03499,0.00659,0.08186,-0.05052,-0.12982,-0.03253,-0.02456,-0.02441,0.00358,-0.22379,-0.00456,0.02803,0.01251,0.02453,0.03488,-0.05861,0.01928,-0.03352,0.03526,-0.07963,0.05522,0.04262,-0.1319,0.11222,0.00459,0.02074,0.01787,-0.05338,-0.02934,-0.02326,0.00053,0.1195,0.09667,-0.0164,-0.09635,0.05643,0.00029,0.02596,0.05517,-0.06499,-0.08806,-0.03295,-0.03227,0.09509,0.01943,-0.02877,0.04322,-0.01387,0.05237,0.14954,0.11155,-0.00344,0.00313,-0.05571,0.09141,-0.03139,0.00398,-0.10275,-0.08184,-0.16138,0.02582,0.03424,-0.03953,-0.06754,-0.0011,0.10874,-0.01391,0.13048,-0.02641,-0.07327,-0.0019,0.0433,-0.0811,-0.0836,-0.00166,0.00055,-0.11323,0.03471,-0.1115,0.07725,0.01973,-0.00688,0.08635,-0.03793,0.03896,-0.00316,-0.04836,-0.01213,-0.00579,-0.01462,0.12822,-0.0228,-0.02876,-0.07267,-0.01476,0.04967,-0.0167,-0.0212,0.0891,0.0323,0.05253,0.08136,0.034,0.04766,-0.06355,0.05388,-0.04296,-0.01712,0.05033,-0.0254,-0.0336,-0.01843,-0.01177,0.02682,0.08883,-0.05094,0.09201,0.09063,-0.00868,0.01974,0.00921,0.07458,-0.02565,0.10819,-0.0224,0.0543]},{"domain":"thermofluids","key":"drag_force","name":"Drag force from the drag coefficient","package":"thermofluids-ai999x","example":"A car with a drag coefficient of 0.3 and a frontal area of 2.2 m^2 travels at 30 m/s through air of density 1.2 kg/m^3. What is the drag force?","v":[0.16033,-0.08049,0.06105,0.11178,0.07109,-0.05749,0.02707,-0.01289,0.00622,0.04131,0.02017,-0.05566,0.03973,-0.02489,0.0014,-0.10095,-0.05171,-0.05527,0.0188,0.01344,0.00574,0.03923,0.15728,-0.02014,-0.0593,-0.01674,0.03991,-0.02648,-0.08133,-0.0736,0.05413,-0.01876,-0.00777,-0.0293,-0.04511,0.107,0.09819,-0.06476,0.02509,0.03398,0.03292,0.099,0.00665,-0.07519,-0.06592,0.06741,0.05506,0.00174,0.07003,-0.03224,-0.00665,-0.03483,0.07253,-0.00811,0.06405,-0.03351,-0.0625,0.09181,-0.05196,0.00475,0.04975,-0.05787,-0.12809,-0.01443,-0.04814,-0.04532,0.04658,0.0707,0.00182,0.05138,0.00275,-0.01454,-0.1068,-0.15633,0.06699,-0.01643,0.10006,-0.07202,-0.01781,-0.02621,0.02771,-0.01209,0.01144,-0.10834,0.10979,0.03491,0.02333,-0.00214,-0.05111,-0.01995,-0.12268,-0.08606,0.02824,-0.04532,-0.0608,-0.06434,0.03488,-0.03245,0.01719,-0.09793,-0.01379,-0.06897,-0.06851,-0.00306,0.07895,-0.0127,0.0744,0.07174,0.09911,-0.04745,0.04042,-0.044,0.03516,-0.07651,-0.12079,-0.06242,0.08693,-0.02294,-0.08882,-0.06097,-0.01959,-0.05365,0.05597,0.05347,0.01939,-0.07976,-0.20664,0.04439,-0.00379,-0.00361,0.00516,-0.00632,0.06629,-0.01282,-0.15712,0.01273,0.08225,-0.01655,-0.03225,-0.05698,-0.07254,-0.07149,0.08564,0.10962,0.01485,0.0286,0.01611,-0.04545,-0.0377,-0.06134,0.10616,0.0101,-0.05791,-0.04175,-0.0124,-0.08693,0.00698,-0.04645,-0.00827,0.00868,-0.00485,0.0372,-0.00673,0.01403,-0.02319,0.07234,0.06788,-0.09037,-0.09417,-0.04245,-0.1003,-0.00656,0.00261,0.00383,0.09475,-0.0461,-0.02494,-0.01645,0.03432,0.0491,0.14104,0.05429,-0.02711,0.03656,0.10155,-0.02606,-0.05249,-0.00174,-0.02025,-0.00043,0.03369,-0.04099,-0.00415,-0.09557,-0.03867,0.10914,0.03375,0.07753,-0.0953,-0.09345,0.04091,0.09001,0.056,-0.0315,-0.00332,0.12411,-0.12002,-0.04525,0.11083,0.03149,0.08203,0.04135,0.03693,0.04937,0.01156,-0.0085,-0.04359,0.13976,-0.02224,0.06879,0.00696,-0.06316,-0.00368,-0.04293,-0.06023,0.08002,0.05376,0.06438,0.07121,-0.04813,-0.06878,0.09348,0.00199,0.05367,-0.04223,-0.0162,0.02955,-0.07795,-0.03419,0.08266,0.0057,0.0377,-0.01494,0.03697,0.09484,-0.00651,0.11516,-0.01183,0.05428,0.08689,-0.04268,0.04473,-0.0828,0.01289,0.04255,-0.00437]},{"domain":"thermofluids","key":"lift_force","name":"Lift force from the lift coefficient","package":"thermofluids-ai999x","example":"An aircraft wing with a wing area of 20 m^2 has a lift coefficient of 1.2 and moves at 70 m/s through air of density 1.1 kg/m^3. What is the lift force?","v":[0.13244,-0.09798,0.07819,0.05341,-0.01954,0.01923,-0.03038,-0.0072,0.05646,0.05726,-0.03686,-0.03181,-0.02163,0.03342,0.00891,-0.05484,-0.02313,0.00212,0.03856,-0.02127,-0.04053,0.07394,0.09508,0.00317,0.01059,-0.0325,0.06912,0.03515,-0.10666,-0.00984,-0.01308,-0.00852,-0.04051,-0.00961,0.02293,0.076,0.05356,-0.05051,-0.02873,0.0599,0.0632,0.10272,0.04928,-0.00324,-0.0084,0.05964,0.05828,-0.01057,0.01015,-0.02735,-0.00717,-0.07139,0.05702,-0.00527,0.07202,0.02131,-0.06466,0.0086,-0.02438,0.09277,0.0907,0.02189,-0.10382,-0.13618,-0.04985,-0.03657,0.06313,0.00931,0.06885,0.05472,0.0708,-0.03226,-0.10815,-0.12899,0.07054,0.05424,0.0407,-0.03461,-0.04796,-0.01963,-0.02627,-0.0311,-0.00646,-0.05925,-0.02159,-0.07178,-0.0214,-0.02847,-0.04788,-0.02881,-0.14065,-0.11969,0.00603,-0.02757,-0.06897,-0.056,0.03666,0.00632,0.06148,-0.10024,-0.09171,0.04592,0.03766,0.06373,0.13303,-0.06464,0.04422,0.02784,0.06367,-0.06842,0.13527,-0.12337,0.01263,-0.04924,-0.06901,-0.01525,0.11916,-0.01063,-0.07654,-0.00076,-0.09335,-0.0469,0.09836,-0.0316,-0.0845,0.0161,-0.16473,0.05157,0.09133,0.02876,0.00886,0.01863,0.09465,-0.00476,-0.10303,-0.10998,-0.00561,-0.00216,-0.02363,-0.19097,0.00586,-0.01672,0.07477,-0.00711,-0.0743,0.01235,0.05485,-0.00628,0.02092,-0.04041,0.07347,0.02897,-0.02877,-0.00816,-0.0432,-0.03591,0.03179,-0.01873,-0.02872,0.00708,-0.0078,-0.00265,-0.05708,0.06635,-0.04388,-0.01632,0.03854,-0.03119,-0.12423,-0.01201,-0.02114,0.04756,-0.00441,0.02139,0.08792,-0.01646,-0.04408,-0.087,0.07962,0.0811,0.07531,-0.01492,-0.09566,-0.05227,0.10155,0.00428,-0.03996,-0.09258,-0.03987,-0.02498,0.09376,-0.05247,0.02723,-0.0784,-0.03058,0.10191,0.02248,0.05518,0.02979,-0.02363,0.09447,0.03244,-0.07579,-0.04089,0.0302,0.11943,-0.03467,-0.05684,-0.01623,0.03018,0.04961,0.01187,0.09252,0.06438,0.09684,-0.00886,0.04962,0.08587,0.05479,0.02551,-0.029,0.01448,-0.01549,-0.05767,-0.09123,0.0664,0.03855,0.10834,0.1242,-0.03603,-0.0696,0.14403,-0.08268,0.05502,-0.07073,0.04573,0.00681,-0.13626,0.03213,-0.06184,0.00198,-0.04312,0.03832,0.00994,0.04107,-0.01437,0.12405,0.09002,-0.04799,-0.0011,-0.06811,0.08822,-0.10136,0.06918,-0.06203,-0.00551]},{"domain":"thermofluids","key":"stokes_drag","name":"Stokes drag on a small sphere","package":"thermofluids-ai999x","example":"Using Stokes' law, what is the drag force on a sphere of diameter 0.0001 m moving at 0.002 m/s through water with viscosity 0.001 Pa*s?","v":[-0.00032,-0.09883,0.00674,0.13823,0.034,0.02723,0.04241,0.00268,0.04269,-0.06196,0.01043,-0.10186,0.022,-0.0649,-0.07116,-0.11831,-0.04921,-0.06382,0.03006,-0.01144,0.03814,-0.00518,0.05068,-0.01612,-0.07572,-0.04825,0.05044,-0.07902,-0.02785,-0.01213,0.01079,-0.09289,0.00597,0.03791,-0.09315,-0.05717,0.02407,-0.05176,0.06746,0.00781,-0.03394,0.13833,-0.06275,-0.02988,-0.01111,0.10787,0.13385,0.0526,0.08248,-0.06117,0.01825,-0.02386,0.01551,0.04634,0.02495,0.08213,-0.05149,0.07049,-0.01622,0.00579,0.06583,0.00173,-0.14291,0.03936,-0.10874,-0.01713,0.00352,-0.04816,0.00833,0.04657,0.02995,0.00736,-0.12202,-0.07283,0.01741,0.02933,-0.11899,0.02989,-0.04084,-0.14745,-0.02186,0.06901,-0.0272,-0.01591,0.09898,0.0604,-0.06868,0.0436,-0.00823,-0.04677,-0.04419,-0.017,0.04767,-0.03132,0.04485,-0.08499,0.01517,-0.04576,0.02482,-0.02099,0.00304,-0.02215,0.00979,0.01842,0.08354,0.08083,0.06184,0.02404,0.09267,0.04734,0.05442,-0.08562,0.1043,-0.05249,-0.13083,-0.08818,0.08078,0.00434,-0.08265,-0.05803,-0.01824,-0.07179,-0.08139,0.01713,0.05206,-0.11177,-0.08993,0.06095,0.00738,0.01972,-0.01785,-0.09203,0.01515,-0.00866,-0.10673,0.06666,0.07234,0.04944,-0.01181,-0.07911,-0.04853,0.03024,0.06743,0.00548,0.01203,-0.04247,0.04891,-0.04335,-0.09122,0.01783,0.10315,-0.03308,-0.01661,-0.06071,-0.08972,0.00184,-0.01165,-0.04894,0.05763,-0.02807,0.01099,0.00045,0.02031,0.03719,-0.04386,0.06726,0.03145,-0.09604,-0.08158,-0.03913,-0.0567,0.09017,-0.0313,0.01401,0.07659,-0.06787,-0.04321,0.16203,0.08225,-0.0235,0.13929,-0.01162,0.13624,0.10826,0.08479,-0.0277,-0.03001,0.01961,-0.02914,0.11122,0.03643,-0.02569,-0.06482,-0.01494,-0.04179,0.07158,-0.01978,0.00074,-0.05568,-0.06035,-0.06069,0.06116,-0.0515,-0.05802,-0.03368,0.13885,-0.04377,-0.01068,0.12001,0.03732,0.05693,0.07974,-0.00692,-0.00052,-0.0572,-0.01588,-0.07127,0.11242,0.04698,0.12101,-0.00847,-0.00706,0.10332,-0.06531,-0.03694,-0.01762,-0.00281,0.01175,0.11134,0.0292,0.00544,0.04903,-0.00064,0.03735,-0.06055,-0.03222,-0.03577,-0.02371,-0.02298,0.08182,-0.02097,0.01723,-0.04972,0.08107,0.1148,0.11407,-0.0139,-0.07423,0.0309,0.13267,-0.04376,-0.08804,0.06101,-0.06431,-0.02548,0.00925]},{"domain":"thermofluids","key":"stokes_terminal_velocity","name":"Terminal settling velocity of a small sphere (Stokes)","package":"thermofluids-ai999x","example":"A sand grain of diameter 0.0001 m and particle density 2650 kg/m^3 settles in water of density 1000 kg/m^3 and viscosity 0.001 Pa*s. Assuming Stokes flow, what is its terminal velocity?","v":[-0.00915,-0.09377,-0.06816,0.04248,0.05465,0.11143,0.12645,-0.0127,0.04639,-0.09284,-0.00639,-0.01398,-0.02851,-0.01164,-0.05744,-0.08772,-0.02805,-0.0943,0.03573,-0.04404,0.07081,-0.02544,-0.05025,0.06123,-0.02136,-0.01417,0.01943,0.00632,-0.0484,-0.02332,-0.04685,-0.10378,0.01124,0.06262,-0.00726,-0.03915,0.00187,0.03466,0.05095,0.11427,-0.02298,0.16815,-0.00462,-0.0054,-0.01279,0.06873,0.15524,-0.01002,0.00216,-0.02055,0.0189,0.00735,0.03096,0.01904,0.01415,0.1349,-0.02354,0.06096,-0.01405,0.10885,0.02981,0.03227,0.06716,0.0376,-0.05166,-0.06184,-0.03498,-0.08573,0.05177,-0.00334,-0.00049,0.01764,-0.04388,-0.04732,0.03173,-0.03653,-0.04471,-0.02753,-0.09653,-0.03508,-0.05435,0.00848,-0.08166,0.09089,0.06181,0.05807,0.03238,0.00924,-0.01289,-0.06144,-0.01385,-0.07331,-0.09058,-0.01955,0.01274,-0.03107,0.02053,-0.08111,0.00999,0.07273,-0.01284,-0.04591,0.11014,0.05099,0.06349,0.02681,0.10166,0.03639,0.03659,0.10055,0.01179,-0.05197,-0.05316,-0.02945,-0.08938,-0.07512,0.12962,0.05391,-0.06122,0.06788,-0.00189,-0.03415,-0.0628,0.06643,-0.02372,-0.00193,-0.09342,0.01665,0.04172,-0.04674,0.02973,-0.01754,-0.00176,-0.12371,-0.11334,0.06251,0.03296,-0.01887,-0.06993,-0.0762,-0.0241,0.06598,0.08163,0.0034,-0.01245,-0.10381,0.05192,0.05867,-0.09323,0.08878,0.12941,-0.006,0.04597,-0.0522,-0.00294,0.09714,-0.0423,-0.04609,-0.10106,-0.0453,-0.04633,0.08089,-0.0042,0.03912,0.06808,0.06149,0.00421,-0.05285,-0.0395,-0.06189,-0.03878,0.05649,-0.11885,-0.11609,0.03825,0.0261,-0.01355,0.10257,0.02859,0.04895,0.15602,-0.04445,0.11783,0.11629,0.1144,0.00135,0.01995,0.08137,0.00353,0.04917,0.03209,-0.02577,-0.03039,0.00556,-0.03134,-0.00326,-0.02452,-0.05118,-0.02179,-0.08654,-0.16438,0.04165,-0.08359,-0.02183,0.05555,0.10142,-0.08262,-0.08662,0.02417,0.02897,0.0435,0.04504,0.01487,-0.0165,-0.11483,0.01624,-0.02732,0.09191,0.05575,0.08154,-0.00067,-0.01482,0.06787,-0.08804,0.00043,-0.01347,-0.06905,-0.04232,0.02566,0.02698,0.04871,0.0105,-0.03658,-0.12827,-0.07122,-0.09118,0.01002,-0.11603,0.04956,0.10123,0.03235,0.02542,0.00706,0.13153,0.03424,0.08581,0.02516,-0.02824,0.04502,0.12278,0.02905,-0.0375,0.0107,-0.11049,0.0325,-0.05129]},{"domain":"thermofluids","key":"thin_airfoil_lift_coefficient","name":"Lift coefficient of a thin symmetric airfoil","package":"thermofluids-ai999x","example":"Using thin airfoil theory, what is the lift coefficient of a symmetric airfoil at an angle of attack of 5 deg?","v":[0.10508,-0.05011,0.09531,0.00808,-0.01654,0.04695,0.04237,0.01351,0.06323,-0.00574,0.00375,0.01412,-0.00795,-0.04199,-0.01059,0.00627,0.03613,0.00659,-0.04089,-0.12543,-0.13115,0.03139,-0.02022,-0.01006,-0.02876,-0.1323,0.09762,0.08376,0.00739,0.00336,-0.02782,0.04007,-0.0089,0.00116,0.01878,-0.06411,0.01677,-0.09538,-0.04607,0.03066,-0.05012,-0.03132,0.01167,0.04327,-0.02526,0.05366,-0.01746,0.0243,0.0267,-0.00295,0.0248,-0.07179,-0.02825,0.04284,0.05931,-0.0206,0.00176,-0.00433,-0.06054,0.02984,-0.0408,0.02741,-0.10446,-0.07193,0.06014,0.02387,-0.00056,-0.0506,-0.06469,-0.01904,0.1188,-0.05321,-0.00294,-0.00452,0.08587,0.02347,0.04912,0.06209,-0.04123,-0.00114,-0.03579,-0.0466,0.02141,0.04854,-0.00955,-0.08029,0.02527,0.04974,0.04882,0.02648,-0.08078,-0.11613,-0.02525,0.00156,-0.05315,0.02862,-0.02919,0.00679,-0.02953,-0.09481,-0.08202,0.09358,0.09774,0.02974,0.15672,-0.06916,0.06043,0.03372,0.0109,-0.01325,0.092,-0.07062,0.0505,-0.10175,-0.10213,0.035,-0.0296,-0.02555,-0.05839,-0.03661,-0.04629,0.06938,0.12382,-0.05066,-0.05249,0.1094,-0.0659,0.10696,0.08238,0.00021,-0.01597,-0.0273,0.08467,0.06355,-0.06663,-0.14317,-0.09837,-0.01234,-0.04509,-0.12168,0.0934,-0.04839,0.00218,-0.0273,0.00102,0.05608,0.1395,0.05368,-0.04415,0.00175,0.05467,0.07145,0.0035,-0.00048,-0.01067,-0.01814,0.01618,0.06147,0.03647,0.0476,-0.04659,-0.09125,-0.10332,0.1297,-0.0285,-0.09916,0.01864,-0.16313,-0.14615,0.04202,0.00757,0.07495,0.09836,0.0727,0.09575,-0.07604,-0.06392,-0.13739,0.10307,-0.00846,-0.01483,0.07607,-0.03156,-0.05653,0.05117,-0.00971,-0.04443,-0.13057,0.05748,-0.01387,0.06352,-0.00236,-0.05299,-0.02398,-0.00018,0.05511,0.05256,0.1145,0.12757,-0.02385,0.04117,-0.02431,-0.08971,-0.01678,-0.034,0.07153,0.04883,-0.06551,-0.05592,-0.07964,0.08579,-0.02379,-0.01447,0.0856,0.04432,-0.02127,0.01344,0.03629,0.01916,-0.05854,-0.01306,-0.03736,-0.01163,-0.04869,-0.03883,0.02663,0.03583,0.11747,0.14496,0.01429,-0.11376,0.06368,-0.04079,0.04606,-0.1237,0.02988,0.00315,-0.037,-0.00772,-0.08286,0.05913,-0.0221,0.10337,-0.02361,-0.00421,0.0644,0.05089,-0.01656,-0.06785,-0.02901,-0.07935,0.10124,-0.03889,0.0198,-0.08488,-0.0235]},{"domain":"thermofluids","key":"mach_number","name":"Mach number","package":"thermofluids-ai999x","example":"An aircraft flies at 250 m/s where the speed of sound is 300 m/s. What is its Mach number?","v":[-0.09207,0.01949,-0.05237,0.0662,0.0079,-0.0072,0.05143,0.06168,0.04118,-0.02899,-0.0193,0.0025,0.09091,-0.05187,-0.0625,0.03793,-0.02691,-0.03788,0.0294,-0.00174,-0.03202,-0.05155,0.12486,-0.02076,-0.14759,-0.00656,0.12563,-0.00924,0.0193,0.0051,0.04711,-0.039,0.00744,-0.04406,-0.04078,-0.02026,-0.01522,-0.0283,0.0802,0.08601,-0.07254,-0.03479,-0.03653,0.03615,0.04995,0.09246,0.04671,-0.0582,0.05858,0.00428,-0.01858,-0.0346,0.01779,-0.03183,0.07631,-0.02903,-0.01808,-0.14913,0.00335,0.03045,-0.02136,-0.0946,0.02336,-0.06018,0.05727,0.11445,0.06965,0.06073,0.01616,0.11305,-0.04535,0.07489,-0.07592,0.00978,0.04549,-0.04374,0.15152,-0.09904,0.10835,0.02055,0.00988,-0.00791,-0.07189,0.01741,-0.0176,-0.03649,-0.05167,-0.04896,-0.00433,-0.05124,0.02045,0.02234,-0.04933,0.03817,-0.06279,-0.05497,0.00177,0.02148,0.07205,0.02638,0.04015,0.02569,0.00521,-0.13093,0.1229,0.04527,0.05616,0.02218,-0.15953,0.07287,0.0367,-0.05599,0.01044,-0.03856,-0.0802,0.0222,-0.08501,0.02923,-0.0874,0.04282,0.14528,-0.07277,0.02526,0.02634,0.06003,-0.07852,-0.04366,0.02403,0.03684,0.00641,-0.06432,0.11991,-0.02205,0.02571,0.1303,0.03693,0.00907,-0.00914,-0.02327,0.00643,-0.06689,0.09077,-0.02184,-0.01645,-0.02624,0.00132,0.02077,0.01012,-0.17071,0.02192,-0.01773,0.03325,-0.06596,-0.09571,-0.07455,-0.00858,-0.09588,0.01403,-0.02115,-0.08116,-0.09963,-0.04141,-0.08553,-0.1542,-0.02695,0.06242,0.03024,-0.17052,0.07975,0.08843,0.04898,-0.07584,0.11441,0.08035,0.00107,0.00078,0.02718,-0.02538,0.05967,0.00406,0.18723,0.03902,0.03816,0.06249,-0.00076,0.02151,-0.02259,0.04699,-0.02427,0.05176,0.01537,-0.11811,-0.07787,0.01922,0.0403,0.0174,0.00172,0.09122,-0.16038,0.06032,0.02926,-0.06193,0.02457,0.07829,-0.04603,-0.02013,-0.05544,-0.04909,-0.07883,0.01556,0.00741,0.07681,-0.00994,-0.02715,-0.0179,0.00206,-0.08962,0.06753,-0.07691,0.01921,-0.04141,-0.07751,0.00217,0.03209,0.01649,-0.05402,-0.00769,0.13438,-0.00291,-0.0343,-0.05075,0.00369,0.03688,0.06172,0.08802,0.05135,-0.01717,0.02577,0.01438,0.05906,0.066,-0.02566,-0.06206,-0.05994,0.04398,0.02815,0.08075,0.03257,0.03446,0.02615,-0.04315,0.06295,-0.14078,-0.0378,-0.10016,-0.04458]},{"domain":"thermofluids","key":"speed_of_sound_ideal_gas","name":"Speed of sound in an ideal gas","package":"thermofluids-ai999x","example":"What is the speed of sound in air at a temperature of 300 K, with a specific heat ratio of 1.4 and a specific gas constant of 287 J/(kg*K)?","v":[0.01317,0.01481,-0.03536,0.03449,-0.00441,0.142,0.02048,0.04041,0.04099,-0.01645,-0.04217,0.06262,0.1018,0.00156,-0.03825,0.06133,-0.03294,-0.09158,0.0593,0.04917,0.06249,-0.07509,0.18047,0.00368,-0.08002,-0.00194,0.11739,0.02218,0.05873,-0.00226,0.03287,-0.05774,0.06417,-0.03673,-0.06936,0.10972,-0.06068,0.05265,0.00612,0.02694,-0.05351,0.00609,-0.04907,0.10408,0.00299,0.08161,0.06045,-0.03535,0.10489,-0.02908,-0.03072,-0.00295,0.06226,0.03969,0.02165,-0.10714,0.01453,-0.06884,0.09077,0.11249,3e-05,-0.16758,0.05891,-0.14699,0.01108,-0.04651,0.06353,0.07545,-0.03176,0.05558,0.00062,0.056,-0.03965,0.00171,0.05049,-0.06149,0.11815,-0.10653,0.08257,0.0339,0.03592,-0.01965,-0.03292,0.06221,-0.00116,-0.00891,-0.02533,0.00254,-0.00201,-0.00407,-0.00557,0.02958,0.00578,0.00901,-0.03047,-0.03241,-0.02529,0.07148,0.11244,-0.04006,0.0295,-0.00488,-0.08301,-0.06046,-0.01078,-0.01001,0.06211,0.00293,-0.08507,0.06962,0.04213,-0.05175,0.07281,-0.04632,-0.06934,0.01437,-0.08148,0.04459,-0.0502,-0.07538,0.0529,-0.06832,0.08098,0.01908,0.0395,-0.08055,-0.04648,-0.0264,-0.01107,-0.03364,-0.08339,0.00267,-0.07398,-0.01861,0.04434,0.00079,-0.0197,-0.01108,-0.01196,-0.05836,-0.09859,0.11094,0.00315,0.06012,0.02853,0.01965,-0.02111,-0.03201,-0.11305,0.02064,-0.03214,-0.0057,-0.09528,-0.12309,-0.04097,-0.0435,-0.04474,-0.04265,0.00681,-0.14998,-0.10354,-0.05258,0.00286,-0.16921,-0.03181,0.0357,0.03483,-0.19406,0.0873,0.12881,0.01701,-0.08712,0.06966,0.0702,-0.01925,-0.00445,0.02073,0.0108,0.10174,0.03988,0.14005,0.01646,0.00777,0.01889,0.02856,-0.01072,-0.05839,-0.01871,-0.09622,0.08108,0.00217,-0.08109,-0.03157,-0.02303,0.08834,0.02119,-0.0219,0.07914,-0.11927,0.01791,0.06105,-0.06735,-0.00099,0.09414,-0.08325,-0.06247,-0.04312,0.02368,-0.02136,-0.00888,0.00465,-0.0041,0.00606,-0.0345,0.02488,0.00881,-0.11369,-0.03039,-0.04697,0.0616,-0.07373,-0.10408,0.07752,0.00018,0.02467,-0.01587,-0.00551,0.11368,-0.01606,-0.01731,0.03375,-0.02955,0.03799,-0.03814,0.05438,0.02815,-0.01714,-0.05739,-0.00094,0.07333,0.04235,0.09964,0.01057,0.02829,-0.01111,0.11033,0.07028,0.00867,0.03202,0.08226,-0.01492,0.1082,-0.14745,-0.04896,-0.08064,0.03274]},{"domain":"thermofluids","key":"stagnation_temperature_mach","name":"Stagnation temperature from the Mach number","package":"thermofluids-ai999x","example":"A gas with a specific heat ratio of 1.4 flows at a Mach number of 2 with a static temperature of 220 K. What is the stagnation temperature?","v":[-0.0201,-0.02129,-0.02832,0.08727,-0.0702,0.05771,0.07043,0.03161,0.06179,-0.03421,-0.00778,0.01309,0.06011,-0.04748,-0.07543,0.01566,-0.02274,-0.06423,0.05985,-0.00497,0.05099,-0.07939,0.01657,-0.04823,-0.02815,-0.01704,0.04033,0.01686,0.04976,-0.01572,0.01419,-0.02218,0.02241,-0.06161,-0.0088,0.03645,-0.03798,0.00603,0.04163,0.01956,-0.03877,0.00807,-0.08557,0.0506,-0.02229,0.07471,0.02116,-0.03757,0.04636,0.11586,-0.07388,0.04074,0.12683,0.00025,0.09779,0.02512,-0.01798,-0.14445,0.02202,0.09603,-0.07609,-0.07352,0.03873,-0.08969,-0.03837,0.03719,0.07453,0.07611,0.03075,0.04467,-0.04889,0.1418,-0.08008,0.04422,0.00044,-0.0428,0.06035,-0.01319,0.07447,0.01915,0.07896,-0.08747,-0.00888,0.06929,0.09446,-0.03364,-0.12914,0.02861,-0.05361,-0.061,-0.00312,0.06951,-0.02866,-0.01273,-0.07088,-0.07214,-0.07669,0.03477,-0.01753,-0.03487,0.082,-0.00721,0.00299,0.00379,0.05174,0.00689,0.0846,0.03572,-0.16748,0.09554,0.0525,-0.07934,0.02935,-0.02683,-0.08981,-0.06427,-0.02617,-0.02876,-0.06067,0.03411,0.03822,-0.04899,0.11641,-0.05748,0.07448,-0.02921,-0.0098,-0.02191,0.03204,-0.02018,-0.0631,0.07333,-0.1321,-0.03839,0.08178,0.02634,0.01076,-0.02277,-0.09815,0.01476,-0.10151,0.02872,-0.08888,0.07242,0.02068,0.00735,-0.04104,-0.02496,-0.10078,0.01614,-0.07405,-0.00717,-0.0617,-0.0919,-0.04896,-0.09899,-0.10002,0.02489,0.02249,-0.15498,-0.09916,-0.00944,-0.07759,-0.08179,-0.05374,0.06959,0.03338,-0.15055,0.07226,0.1136,0.12242,-0.05679,0.0791,0.06685,0.00059,0.06243,-0.0268,0.03883,0.04466,0.10303,0.13306,-0.02479,0.06679,-0.05857,-0.00624,0.04049,-0.03828,0.04493,-0.04983,0.04912,-0.03117,0.00167,-0.05302,0.10221,0.02075,0.04403,-0.05625,0.09141,-0.07838,-0.00985,0.06522,-0.04866,0.01551,0.05116,-0.05094,0.00788,-0.00044,0.05811,-0.08131,-0.06499,0.06379,0.0868,-0.05142,0.00419,0.02369,0.02931,-0.08592,-0.04082,-0.07015,0.05989,-0.02938,-0.01941,0.03835,0.06031,-0.01499,-0.06957,-0.02186,0.08359,0.01495,0.06969,0.04546,-0.09805,0.01518,-0.06582,0.10103,0.07101,0.08351,0.04808,0.00742,0.08116,0.08671,-0.04886,0.04477,0.0643,0.01239,0.089,0.10971,0.00441,0.08338,-0.03182,-0.04084,0.02919,-0.17693,0.00891,-0.0618,-0.03562]},{"domain":"thermofluids","key":"stagnation_pressure_air","name":"Isentropic stagnation pressure of air from the Mach number","package":"thermofluids-ai999x","example":"Air flows isentropically at a Mach number of 1.5 with a static pressure of 50 kPa. What is the stagnation pressure?","v":[-0.01007,-0.01157,-0.05146,-0.06605,0.01675,0.06665,0.07269,-0.01878,-0.04274,-0.0397,-0.07785,0.06719,-0.0149,-0.01458,-0.0692,0.01555,0.07261,-0.00411,0.03348,0.0206,0.00039,-0.04133,0.08042,0.01783,-0.07926,0.03119,0.09217,0.01842,0.02376,0.0106,0.03961,-0.00528,0.00416,-0.03084,-0.07446,0.05793,-0.04107,-0.01988,0.06087,0.14042,-0.01327,-0.05678,-0.08642,0.03746,-0.00098,0.08435,0.01453,-0.04657,0.0726,0.03754,0.01266,-0.10205,0.02553,-0.01508,0.03466,-0.04674,-0.00841,-0.12578,0.05419,0.01915,-0.03956,-0.05494,-0.08367,-0.08327,-0.07494,0.07265,0.04231,0.03176,0.07032,0.04017,-0.11555,0.11282,-0.08276,0.02743,0.03123,-0.05093,0.16757,-0.09121,0.02934,-0.00416,0.01745,-0.09012,0.0098,0.09928,0.04748,-0.08924,-0.0371,-0.05176,-0.02764,-0.09818,-0.0454,-0.02488,-0.10333,-0.00134,0.01378,-0.09078,0.08836,0.05362,0.00744,0.04377,0.05385,-0.05026,0.04674,-0.02227,0.15912,0.04486,0.03361,-0.02864,-0.13705,0.08552,0.03474,-0.03279,0.0108,-0.0003,-0.07644,-0.09475,-0.00027,-0.00387,-0.0481,0.08094,0.07352,-0.04172,0.03727,-0.01167,0.06315,-0.07479,-0.02738,0.10898,0.08066,-0.06444,-0.08444,0.10288,-0.0599,-0.00877,0.08388,0.0407,-0.05017,-0.0184,-0.0012,0.04286,-0.16018,0.02619,-0.05361,-0.01104,0.04002,0.00896,0.05398,-0.06301,-0.15371,0.04762,-0.05178,0.01566,-0.0071,-0.00091,0.01062,0.05411,-0.08576,0.08538,0.04374,-0.05294,-0.07353,0.05309,-0.04639,-0.13216,-0.14191,-0.03687,0.09455,-0.11751,-0.00988,0.06993,-0.00243,-0.13694,0.09356,0.0164,0.11481,0.05926,-0.00387,0.0144,0.07379,0.07544,0.09646,0.10023,0.04121,0.06222,0.03778,0.05908,0.0297,-0.12187,-0.02673,0.02478,0.03384,-0.05243,-0.01526,0.03161,-0.07453,0.0551,-0.03566,0.04865,-0.12862,0.02972,0.03446,0.04193,-0.05854,0.03931,0.04253,0.01505,-0.05902,-0.079,-0.06983,0.03711,0.00757,0.13166,-0.01825,-0.03031,-0.03965,0.02517,-0.13551,0.03266,-0.04573,0.00725,0.03868,-0.03272,0.01453,-0.01165,-0.04986,-0.06257,-0.02995,0.10026,-0.0133,-0.00809,0.04629,-0.0257,-0.01379,0.10862,0.08461,0.04562,-0.007,0.02132,-0.06793,0.02552,0.04387,-0.12897,0.04266,0.04734,0.03723,-0.0105,0.07099,0.01818,-0.01457,0.06181,-0.03622,0.08641,-0.03734,0.03528,-0.08455,-0.01423]},{"domain":"thermofluids","key":"normal_shock_mach_air","name":"Mach number behind a normal shock in air","package":"thermofluids-ai999x","example":"Air with an upstream Mach number of 2 passes through a normal shock. What is the downstream Mach number?","v":[0.11772,-0.04169,0.03425,-0.02553,0.11824,0.00713,-0.03523,0.01234,0.0346,-0.03613,0.04646,0.07717,-0.02952,0.06375,0.01898,-0.09208,0.0505,-0.06917,0.09522,0.01654,0.01593,-0.09532,0.03982,0.05249,-0.09388,-0.03897,-0.01182,0.09102,-0.0766,-0.07048,0.11515,-0.03071,0.02079,0.04542,-0.1532,-0.02797,-0.01711,-0.01307,0.07747,0.0402,-0.06934,-0.05403,0.0538,0.01716,0.11435,0.00614,-0.01211,0.02551,-0.0578,0.04711,-0.03806,-0.00419,-0.01475,0.02441,0.08151,-0.01591,-0.06424,-0.09613,-0.13018,-0.11013,-0.07885,-0.07169,0.05663,-0.10263,0.03823,0.03747,0.01211,0.05569,0.01377,0.07369,-0.09587,-0.03232,-0.09398,0.05542,0.06777,-0.13055,0.051,-0.01664,-0.02982,0.11481,0.01847,-0.01304,-0.08358,0.0514,0.0372,-0.03809,-0.01575,-0.0909,0.0483,-0.09747,0.03855,-0.02883,-0.0666,0.10354,-0.01451,-0.00201,0.05854,-0.05233,-0.11402,-0.05765,0.11665,0.02892,-0.05086,-0.01912,0.01961,-0.05831,-0.03992,0.01733,0.02147,-0.00416,0.0517,-0.04075,-0.14828,0.05351,0.03109,-0.02137,0.01691,0.01706,-0.03648,0.07633,0.02862,-0.02028,0.10506,-0.05059,0.02371,-0.07819,0.00312,0.02259,0.12008,0.01884,-0.01121,0.13547,0.0048,-0.04927,0.15574,0.07949,-0.03194,0.07632,-0.03614,0.05265,-0.10554,-0.00194,0.04068,-0.01702,0.00185,0.07484,0.04882,0.01655,-0.12594,-0.06672,0.04961,0.05448,-0.02829,0.06783,-0.10102,0.07148,-0.07606,-0.00831,0.05901,-0.06115,-0.10717,0.03624,0.0047,-0.0351,-0.01625,-0.04632,0.03344,-0.04859,-0.03327,0.03393,-0.02966,-0.02875,-0.02559,0.05283,-0.00993,0.0012,-0.01368,-0.14798,-0.01558,-0.01345,0.08405,0.04677,0.02214,0.01785,-0.01949,0.03553,0.06276,0.07398,-0.0263,0.01255,0.02622,-0.01496,0.03398,-0.06072,-0.01177,-0.03589,-0.00147,0.04223,-0.04084,0.15603,0.07406,-0.02166,0.09351,0.08739,0.16273,0.033,-0.0186,-0.09711,-0.06934,0.04539,-0.08152,0.08219,-0.10824,-0.02582,-0.08912,-0.02753,-0.01065,0.10167,0.03866,0.00521,0.08788,-0.04088,-0.05355,-0.00998,-0.14416,0.00994,0.03667,-0.01318,0.01289,-0.08771,-0.11116,0.00256,0.06591,0.06396,0.12586,0.05424,-0.0288,-0.00544,0.03159,-0.0231,0.02288,-0.00723,0.00471,0.03385,0.02158,-0.09811,0.01981,0.09341,0.01799,0.04172,-0.02334,0.05959,-0.0421,0.05729,-0.03888,-0.02331]},{"domain":"thermofluids","key":"normal_shock_pressure_air","name":"Static pressure behind a normal shock in air","package":"thermofluids-ai999x","example":"Air with an upstream pressure of 100 kPa and an upstream Mach number of 2 passes through a normal shock. What is the downstream pressure?","v":[0.12529,-0.02759,-0.01716,-0.11643,0.10737,0.11582,-0.00709,0.02718,-0.03372,-0.00359,-0.05629,0.07803,-0.05129,0.07516,0.00698,0.00491,0.0881,-0.03423,0.02418,0.01745,0.01155,-0.10446,0.06566,0.08927,-0.05444,-0.00475,0.05865,0.0548,-0.05116,-0.05432,0.16614,-0.01545,0.06096,-7e-05,-0.1436,0.11083,-0.05218,0.02906,0.05821,0.04932,-0.00206,-0.01519,0.02141,0.09032,0.03231,0.02863,-0.00949,0.03153,-0.00986,0.03835,0.00763,-0.06338,0.00621,0.07834,0.09931,-0.04921,-0.1069,-0.09681,-0.06401,-0.00421,-0.06407,-0.05533,-0.0253,-0.1145,0.02354,-0.00097,-0.00936,0.05045,0.03552,-0.03446,-0.12737,-0.0123,-0.07262,-0.01467,0.01172,-0.10741,0.07386,-0.01684,0.00431,0.07218,0.01995,-0.05538,0.00342,0.10283,0.05986,-0.08439,-0.02374,-0.12543,0.02715,-0.08454,-0.02352,-0.01526,-0.08763,0.04722,0.05534,-0.01324,0.09251,0.01088,-0.06543,-0.07575,0.08403,0.0256,-0.02621,0.06629,0.0989,-0.02179,-0.01211,-0.00313,0.03345,-0.01862,0.08085,-0.0185,-0.07959,0.02403,0.0127,-0.0924,0.04752,0.01855,-0.05288,0.00618,-0.03358,-0.02868,0.0818,-0.09724,-0.02109,-0.07834,-0.01921,0.06543,0.16535,-0.02241,-0.0759,0.11549,0.0135,-0.0232,0.11143,0.06215,-0.06042,0.04187,-0.02569,-0.04614,-0.17859,-0.00106,-0.00923,-0.03324,0.09331,0.1003,0.00062,-0.05999,-0.1116,-0.02248,0.01823,0.08483,0.03379,0.10631,-0.04043,0.05083,-0.04618,0.01687,0.00948,-0.06759,-0.11567,0.0871,0.09413,-0.09535,-0.12271,-0.06794,0.03863,-0.09271,-0.05598,0.01262,0.0056,-0.06614,0.00552,0.04489,0.0333,0.06662,-0.02121,-0.10281,0.0494,0.05756,0.04814,0.06956,0.01487,-0.02761,-0.00181,0.02514,0.07075,-0.06645,-0.04034,-0.01078,0.044,0.01183,-0.00559,-0.06566,-0.01031,0.00833,-0.05497,0.03107,-0.04168,0.08449,0.03487,0.0255,0.07303,0.00604,0.11669,-0.00678,-0.06346,-0.06872,-0.08641,0.04903,-0.0153,0.05648,-0.02549,-0.08118,-0.06679,-0.02844,-0.06249,0.02607,0.04231,0.00532,0.11092,-0.0451,-0.1119,0.02014,-0.1569,0.02218,-0.02433,0.00113,0.03174,-0.04118,-0.03828,-0.06294,0.01425,0.07364,0.09698,0.05361,-0.0059,0.0427,-0.01577,0.02037,-0.04837,0.0224,0.08534,0.09071,0.01604,-0.09047,0.03244,0.071,-0.02726,0.04588,-0.02602,0.04619,-0.07769,0.06922,-0.05001,0.02507]},{"domain":"thermofluids","key":"blasius_displacement_thickness","name":"Displacement thickness of a laminar flat-plate boundary layer","package":"thermofluids-ai999x","example":"Air flows over a flat plate with a laminar boundary layer. At a distance from the leading edge of 0.5 m the local Reynolds number is 200000. What is the displacement thickness?","v":[0.05182,-0.05509,0.09465,0.04435,0.03613,-0.07196,0.06977,-0.02552,-0.0399,-0.0428,0.04727,-0.04911,-0.08652,0.05133,0.0329,0.11073,-0.08236,-0.06851,-0.06414,-0.038,-0.11412,-0.10562,-0.01711,-0.09387,-0.03683,-0.04195,0.10571,-0.08083,-0.03346,-0.04066,0.10137,0.00775,0.09661,0.01075,0.04164,0.09045,-0.00094,-0.00434,-0.12328,0.08402,-0.05396,-0.04653,-0.01564,-0.03992,-0.0977,0.07449,-0.06829,-0.07361,-0.07656,0.00012,-0.01399,-0.06806,0.02602,-0.04288,0.07372,-0.03261,0.05747,0.11652,-0.06585,-0.06029,-0.00182,-0.04506,0.00847,-0.05123,-0.02557,0.0986,-0.01308,0.04606,0.01449,-0.02692,0.11409,-0.03437,-0.01814,-0.01688,0.0224,0.0423,0.10949,0.0586,-0.03268,-0.0622,0.04177,0.03504,-0.06531,0.07029,-0.00467,0.02272,0.00274,0.02342,0.11652,-0.07054,-0.07636,-0.03553,0.01033,0.08352,0.00336,-0.08666,-0.03567,-0.05959,0.00648,0.01666,0.01535,0.08329,0.02312,-0.07542,0.12891,0.09694,0.06728,-0.03063,-0.05727,-0.00092,-0.03054,-0.21144,-0.00254,-0.11846,-0.03991,0.05267,-0.08049,-0.03658,-0.08104,0.10802,0.08196,0.03683,-0.02083,0.01076,0.10631,0.07793,0.11564,0.14819,0.096,0.02301,-0.06863,0.11961,-0.007,0.07062,-0.14735,0.07155,0.00453,0.05384,-0.08523,0.04004,0.07537,0.04483,-0.01635,-0.09801,-0.02443,0.06442,0.05097,-0.07391,-0.02798,0.00342,-0.06073,0.01456,0.03239,0.07585,-0.03247,-0.04863,-0.02768,0.05193,0.03503,0.06055,-0.04599,-0.08621,-0.08118,-0.03265,-0.02193,-0.01789,-0.00739,-0.11748,-0.01017,0.0476,-0.04654,0.01792,0.0222,-0.11392,0.05632,-0.04877,0.00682,-0.02222,0.12914,-0.05196,0.05797,-0.01265,-0.04593,0.04694,-0.01287,-0.01987,0.00619,0.04,0.04843,-0.05526,0.08112,-0.02058,-0.00222,0.01379,-0.00991,-0.04826,-0.07351,-0.02068,0.07811,0.05818,0.07737,-0.01443,-0.00455,-0.12631,-0.05217,0.07802,-0.0051,-0.01094,-0.01663,0.01828,-0.03346,-0.00307,0.01749,-0.06893,0.05072,0.02016,0.04703,0.05646,-0.0612,-0.06563,0.07757,-0.02945,0.00686,-0.03788,-0.05981,0.0612,-0.10603,0.11235,0.07309,0.06014,0.03095,-0.00714,-0.01432,0.08883,0.0077,0.04447,-0.04372,0.1143,0.03232,-0.09176,-0.01885,-0.08034,0.03943,-0.12908,0.03536,-0.02774,0.01375,-0.03516,0.03551,-0.04597,0.01759,-0.08449,-0.00329,0.03866,-0.00084,-0.04358]},{"domain":"thermofluids","key":"blasius_momentum_thickness","name":"Momentum thickness of a laminar flat-plate boundary layer","package":"thermofluids-ai999x","example":"A laminar boundary layer grows on a flat plate. At a distance from the leading edge of 0.5 m the local Reynolds number is 200000. What is the momentum thickness?","v":[-0.10166,-0.03548,0.05174,0.00686,0.09344,-0.14707,0.10672,0.0415,-0.0186,0.03216,0.06168,-0.04026,0.00959,0.00118,-0.00675,0.0289,-0.02998,-0.04612,-0.03146,0.00627,-0.07409,-0.12687,-0.05427,-0.07501,0.03389,-0.05495,0.13025,-0.04047,-0.05943,0.00318,0.05958,0.03941,0.05894,0.02002,-0.02539,0.09392,-0.00104,-0.0482,-0.07531,0.07604,0.03415,-0.05297,-0.00741,-0.01384,-0.05847,0.08944,-0.07326,-0.0706,-0.06629,0.03096,-0.05201,-0.05715,-0.05244,-0.0335,0.02027,0.04137,0.04314,0.02758,-0.03816,-0.0695,-0.05988,-0.04677,-0.02008,-0.01811,-0.02867,0.0761,0.00678,0.01417,0.04994,0.0206,0.02059,-0.04164,-0.06683,-0.05787,0.08176,0.02383,0.16883,0.02126,-0.02276,-0.0777,-0.04209,-0.02917,-0.08961,0.03245,0.07276,-0.01218,-0.04143,0.06519,0.04454,-0.04704,-0.03767,-0.01698,-0.08903,0.05472,-0.05063,-0.05261,0.07569,-0.05657,-0.00784,0.02272,-0.01951,0.12972,0.01115,-0.07702,0.15124,0.08563,0.05516,-0.03473,-0.07451,0.06158,0.00893,-0.17319,-0.02195,-0.09297,-0.0648,0.05443,-0.01287,0.04139,-0.07233,0.08121,0.05404,0.07698,-0.01637,0.1171,0.09657,0.05079,0.12974,0.05457,0.12627,0.03066,-0.06542,0.12401,0.07706,0.05227,-0.08324,0.03093,0.01169,0.04607,-0.03283,0.08611,0.08968,-0.00349,0.04902,-0.09572,-0.06999,0.02037,0.01778,-0.05517,0.03116,0.01049,-0.07972,0.06096,0.01834,0.07391,-0.0405,0.0524,-0.04271,0.09424,0.04243,0.06207,-0.08405,-0.12391,-0.07242,-0.07745,0.03112,-0.02981,-0.04324,-0.14149,-0.02792,0.02824,-0.05276,-0.02148,-0.01548,-0.12579,0.01989,-0.0127,0.0142,-0.01037,0.07723,-0.00103,0.03569,-0.03187,0.02493,0.00447,-0.0304,0.04221,-0.04113,0.05076,0.02065,-0.10515,0.04712,0.06906,-0.12313,0.00429,-0.02575,-0.01822,-0.13905,-0.0511,0.13954,0.04652,0.04112,-0.07503,-0.015,-0.05017,-0.08148,0.07422,0.04185,0.0039,0.00206,0.13341,-0.06326,0.06041,-0.03205,-0.11155,0.00808,0.004,-0.00917,0.11854,0.01012,-0.07236,0.05916,-0.02316,0.01011,0.01997,-0.07685,-0.01033,-0.07763,0.06773,0.0687,-0.03076,0.01909,0.00378,0.02606,0.04786,0.00916,0.00371,-0.09243,0.08167,0.05856,-0.09183,-0.04303,-0.01276,0.01959,-0.05096,0.04364,-0.0425,0.07545,0.01977,0.05978,0.0595,-0.00741,-0.06479,0.04844,0.02594,-0.09361,-0.05618]},{"domain":"thermofluids","key":"blasius_local_skin_friction","name":"Local skin-friction coefficient of a laminar flat plate","package":"thermofluids-ai999x","example":"For laminar flow over a flat plate, what is the local skin friction coefficient where the local Reynolds number is 100000?","v":[0.03154,0.00302,-0.02035,0.04216,-0.01047,-0.09305,-0.01245,0.02184,-0.09838,-0.02515,0.00342,-0.12898,-0.07533,-0.05316,0.00368,0.02653,-0.01663,-0.09886,0.02771,-0.05197,-0.0696,-0.00061,0.04019,-0.07294,-0.04309,-0.11646,0.14316,-0.15317,-0.0401,0.0073,0.09149,0.07095,0.07248,0.00336,0.04555,-0.03505,0.13716,-0.0858,-0.09676,0.03841,0.03648,-0.04058,-0.04095,-0.01507,-0.03398,0.00747,-0.06053,-0.0432,-0.09317,-0.06652,-0.00184,-0.00233,-0.00318,-0.06074,0.0227,-0.01217,0.03911,0.03048,-0.07348,-0.01059,0.02384,-0.01243,0.0115,0.02247,-0.01112,0.06522,-0.09936,0.05369,0.08606,0.02166,0.01629,-0.08584,-0.04515,-0.02018,0.0243,0.06292,0.16512,-0.01632,0.01188,-0.11054,0.01878,0.01803,-0.02817,-0.02973,0.09642,0.02476,-0.00325,-0.06576,0.10308,0.03275,-0.02516,-0.0738,-0.05551,0.00372,-0.05219,0.00316,-0.00042,-0.10143,0.02421,-0.00228,-0.07603,0.09829,-0.0032,0.00555,0.16826,0.0503,0.07646,-0.04884,-0.0023,-0.02413,0.01783,-0.18011,0.03322,-0.09047,0.03706,-0.00496,0.02402,0.00267,-0.07825,0.01064,-0.01083,0.03581,0.00054,0.02545,0.0166,0.08817,0.04505,0.1613,0.11555,0.03106,-0.04603,0.121,-0.0043,0.00706,-0.13563,0.03837,-0.04621,0.03838,-0.00056,0.10713,0.04009,-0.02779,-0.04511,-0.07042,-0.05788,0.02283,0.03329,0.00107,-0.00918,0.02106,-0.04792,0.10606,0.03423,0.15171,-0.10999,-0.02765,-0.04147,0.03826,0.0212,0.12153,-0.04216,-0.01912,-0.06786,0.01244,0.12539,-0.02015,0.00895,-0.04418,-0.03789,0.03228,-0.0354,0.04605,-0.01165,-0.03378,-0.02396,0.03219,0.00847,0.01754,0.09346,-0.06188,-0.07109,0.02117,-0.05076,0.05201,0.00286,0.06639,-0.03988,0.05646,0.02295,0.0686,0.06995,0.04825,-0.0233,0.02809,-0.09227,-0.07591,-0.07898,-0.0254,0.10504,0.03972,0.07301,0.04055,0.02903,-0.06249,-0.11468,0.01959,0.00642,0.03869,0.07713,0.05875,0.03633,0.04272,-0.07834,-0.0579,-0.06506,0.01821,0.03772,0.11163,-0.04423,-0.0707,-0.08867,0.00936,-0.01473,0.02062,-0.08151,0.05994,-0.03082,0.09962,0.07336,0.00433,-0.03638,-0.04063,-0.04004,0.11185,0.10054,0.00497,-0.02589,0.08543,0.06697,-0.00487,-0.06803,-0.07503,0.01399,-0.10636,0.11146,0.02586,0.07878,-0.12823,0.02566,0.00169,-0.00211,-0.10233,-0.0543,0.08759,-0.01152,-0.02488]},{"domain":"thermofluids","key":"blasius_average_skin_friction","name":"Average skin-friction coefficient of a laminar flat plate","package":"thermofluids-ai999x","example":"Air flows over a flat plate with a laminar boundary layer and a Reynolds number of 250000 at the trailing edge. What is the average skin friction coefficient?","v":[-0.00257,-0.03962,0.10289,0.01907,0.0224,-0.12366,0.03208,-0.00463,-0.08891,0.00224,0.04768,-0.08301,-0.03889,-0.02666,0.04487,-0.03003,-0.02454,-0.09795,-0.01879,-0.03537,-0.01906,0.01646,0.00223,-0.05148,0.02108,-0.09834,0.1011,-0.11883,-0.01071,0.01002,0.08919,0.05241,0.06553,0.00406,0.03181,-0.02178,0.15597,-0.08276,-0.03411,0.11582,-0.03088,0.04369,-0.06653,-0.00785,-0.03318,0.02424,-0.02397,-0.01355,-0.08707,-0.04751,-0.07822,-0.02379,0.04227,-0.08069,0.05073,-0.04109,0.06555,0.12298,-0.01179,-0.08147,0.03621,-0.01078,-0.05235,-0.02385,-0.01193,0.09185,-0.10557,0.01708,0.12092,-0.00512,0.05044,-0.03944,-0.09885,-0.02885,0.05442,0.08591,0.11328,0.02458,-0.04844,-0.13455,0.02537,-0.02573,-0.03576,-0.00767,0.10051,0.03963,0.02998,-0.03972,0.12879,0.0103,-0.04524,-0.06617,-0.04926,-0.0592,-0.02356,0.02122,0.05377,-0.04134,0.02025,0.0411,-0.09303,0.06293,-0.01702,0.05701,0.14597,0.01081,0.04627,-0.00484,0.10859,0.00582,-0.00301,-0.18923,0.01972,-0.1428,-0.01685,0.01033,0.02489,-0.01935,-0.07458,-0.01093,0.02832,0.08099,0.02339,-0.00032,0.00022,0.03682,0.00522,0.14485,0.01692,-0.01236,-0.02649,0.09446,-0.02351,0.01775,-0.17043,-0.01253,0.03409,0.05262,-0.03956,0.11253,-0.01257,-0.03466,-0.00472,-0.09473,-0.06002,0.06185,0.0038,0.06267,-0.02897,0.04195,-0.02956,0.06471,0.07005,0.06516,-0.08536,0.00653,-0.01296,-0.01374,0.03263,0.07206,-0.02536,-0.02844,-0.00755,0.01064,0.06863,-0.01195,-0.03835,-0.06935,-0.02199,0.01701,-0.06912,0.02117,-0.04224,0.01832,0.01683,-0.05308,-0.01531,0.02012,0.08757,-0.0069,-0.01917,-0.03431,-0.03766,0.06589,-0.02088,0.11688,-0.08046,0.0037,0.04224,0.0468,0.01829,0.04028,0.03121,-0.0173,-0.09073,-0.0225,-0.06757,-0.03404,0.10544,0.01254,0.1143,0.02269,-0.00106,-0.08392,-0.06565,0.04879,0.06992,0.01771,0.08705,0.0319,0.01438,0.04499,-0.11822,-0.08739,-0.00885,-0.02744,0.02541,0.11303,-0.01569,-0.01798,-0.07338,-0.01451,0.12738,-0.02492,-0.07062,-0.00722,-0.08451,0.09838,0.08318,0.02884,-0.06982,-0.01739,-0.07412,0.15809,0.10067,-0.00661,-0.05976,0.0455,0.10811,-0.08179,-0.0602,-0.07614,-0.01479,-0.08169,0.06189,0.02574,0.09483,-0.10457,0.01121,-0.00507,0.03001,-0.05684,-0.09832,0.04782,-0.07213,-0.07838]},{"domain":"thermofluids","key":"froude_number","name":"Froude number of an open-channel flow","package":"thermofluids-ai999x","example":"Water flows in an open channel at 3 m/s with a depth of 0.5 m. What is the Froude number?","v":[0.03186,0.00452,0.0199,0.02729,-0.04267,-0.06765,-0.01718,-0.00864,-0.04823,-0.0263,-0.0464,-0.05096,0.01273,-0.00769,-0.04993,-0.06229,-0.12567,0.06583,0.0762,0.03862,-0.01787,-0.03228,0.01432,0.00484,0.00935,-0.11686,-0.02272,-0.02256,-0.06431,0.0217,-0.00881,0.09091,0.0093,-0.10977,-0.10373,-0.0907,0.05215,-0.05179,-0.02154,0.07722,-0.01004,-0.11083,0.0025,-0.02881,0.04869,0.13782,-0.02575,0.013,0.10829,-0.01394,0.03295,-0.0563,-0.05782,-0.04875,-0.01011,-0.03723,-0.02823,-0.00379,-0.06361,-0.12273,0.07016,0.03924,-0.00848,-0.08452,0.00316,0.04236,0.12743,-0.06873,0.01723,-0.03793,-0.00602,0.0691,-0.02415,0.01245,0.0562,0.0668,0.07297,0.0519,-0.03198,0.00303,0.02804,-0.06888,-0.05254,-0.03911,0.09924,-0.0082,-0.08597,0.03008,-0.0639,0.06255,-0.07326,0.04234,-0.00928,0.07885,-0.1186,0.05067,-0.103,-0.06058,-0.0236,0.05891,-0.05728,0.00855,-0.06191,-0.01974,0.04482,-0.02521,0.04621,0.07822,0.01266,0.05291,-0.05187,-0.09158,0.0439,-0.0093,0.05586,0.02859,0.0769,0.03023,0.03377,-0.04923,0.06912,0.05875,-0.08762,0.14517,-0.06826,0.04823,-0.0564,-0.01612,0.0066,0.03921,-0.00906,0.03398,0.11195,0.00755,0.09526,-0.0193,0.06931,-0.02599,-0.03374,-0.10084,0.01245,0.10918,0.01706,-0.04662,-0.05666,-0.01851,-0.14542,0.0237,-0.02029,0.01363,-0.03025,-0.02769,-0.08087,0.00404,-0.07147,-0.02261,-0.01202,-0.04748,-0.01947,-0.08318,0.02228,-0.09131,0.03608,-0.04981,-0.00885,0.0866,0.04777,-0.01439,0.09577,0.05807,0.0086,0.16087,-0.00908,0.15938,0.01361,0.0171,-0.02194,-0.01444,0.03791,0.03556,-0.0037,0.03407,-0.07875,-0.04982,0.08905,0.01695,-0.01739,0.11819,0.00712,-0.01216,-0.08744,-0.06989,-0.10248,-0.12945,0.05735,0.10116,0.02878,0.04983,-0.08816,-0.02595,0.00672,0.06266,-0.01349,-0.01668,-0.01036,-0.02265,-0.09409,0.02516,0.05451,0.01742,-0.0774,0.21037,-0.03343,0.00229,-0.01938,-0.09664,-0.0021,0.12504,0.04697,0.06141,0.04516,-0.00714,0.02924,0.08053,-0.12589,-0.02051,0.0071,0.00664,0.10299,-0.04281,-0.11249,0.02126,0.04122,0.06975,0.08765,0.04715,0.01402,-0.03316,0.10147,-0.02869,0.10099,-0.0457,0.0089,-0.00384,0.1546,-0.13128,0.01024,-0.04425,0.09768,-0.03971,0.01541,-0.03635,-0.06487,0.01034,0.06934,-0.0731]},{"domain":"thermofluids","key":"plane_wall_conduction","name":"Fourier's law: heat conduction through a plane wall","package":"thermofluids-ai999x","example":"A brick wall 0.2 m thick has an area of 10 m^2 and a thermal conductivity of 0.7 W/(m*K). The inner surface temperature is 20 °C and the outer surface temperature is 5 °C. What is the rate of heat transfer through the wall?","v":[-0.04137,-0.10875,0.001,-0.01085,0.06108,-0.03139,0.03561,-0.11746,-0.08045,0.09793,-0.02405,-0.05073,0.0644,-0.00217,-0.02995,0.03279,-0.06703,-0.00672,-0.01821,0.13494,0.01243,-0.07544,0.01017,0.02643,-0.03671,-0.01284,-0.00348,0.0486,0.00725,0.04415,0.12931,0.00223,0.04435,0.05166,-0.0075,0.12598,-0.01959,-0.04764,-0.05158,-0.02212,0.12244,-0.16755,-0.08724,0.08107,-0.09623,0.04397,-0.04563,0.03608,0.03349,0.06542,-0.03419,-0.01631,0.13226,-0.00546,-0.03971,-0.13393,0.11571,0.01691,0.0298,-0.01358,-0.04733,-0.12663,-0.07331,0.09093,0.04186,0.14289,-0.02039,-0.01277,-0.05551,0.02409,0.05467,-0.09612,-0.0821,-0.02363,-0.03089,-0.10091,0.05007,-0.0282,-0.10991,-0.0505,0.04971,-0.03696,-0.00833,0.03209,-0.00118,0.05384,-0.02297,-0.00707,-0.09131,0.0404,-0.02946,-0.00745,-0.0705,-0.04662,-0.07482,0.00768,-0.02451,0.00913,0.12162,-0.06815,0.12938,0.05134,0.00024,-0.03449,-0.01629,0.03794,0.15329,0.02848,0.03345,-0.00385,0.04381,-0.02112,0.07121,0.05069,-0.00814,0.02445,0.04124,0.00301,-0.0527,0.06878,-0.00801,0.154,0.08864,-0.00683,-0.00853,0.02343,-0.02803,-0.04784,-0.11356,-0.06269,-0.02135,0.00168,0.02446,-0.01064,-0.08409,-0.10144,0.00113,0.06739,-0.04123,-0.05778,-0.08813,-0.09815,-0.06138,-0.06429,0.03088,0.02078,-0.00296,-0.12807,-0.07028,-0.07556,0.03671,0.04621,-0.05119,0.0436,0.03453,0.04736,0.05744,-0.00571,-0.01802,-0.11431,0.06675,-0.0659,0.03883,-0.03886,-0.04603,0.05288,-0.04889,-0.06398,0.054,-0.08999,-0.019,0.02395,0.03486,0.05116,0.0241,0.01989,0.0271,-0.16237,-0.01351,-0.08071,0.06766,-0.03106,-0.08202,-0.06386,-0.06378,0.01438,-0.02784,-0.00345,-0.09894,-0.04889,0.06374,0.09232,-0.08128,-0.07396,0.03182,0.02593,0.09128,0.10147,0.09557,0.05223,0.06768,-0.0698,0.02314,0.06205,0.07214,0.01854,-0.01643,0.05403,0.00845,0.0719,0.02287,-0.00104,0.09006,0.00903,0.04691,0.11044,0.01088,-0.06362,0.09127,0.0613,0.03716,-0.08636,0.02673,0.0284,-0.01786,-0.13193,-0.00353,-0.00947,0.07037,-0.09614,-0.05189,0.07011,0.00942,0.02258,0.03784,-0.0599,0.07966,-0.00201,-0.07324,0.0283,-0.00756,0.0179,0.00688,0.02846,0.01639,0.0074,0.06675,-0.01609,0.12121,-0.0413,0.09717,0.05002,-0.01922,0.03619,-0.04931,0.06976]},{"domain":"thermofluids","key":"cylinder_conduction","name":"Radial heat conduction through a cylindrical wall","package":"thermofluids-ai999x","example":"A 5 m long pipe made of steel has an inner radius of 0.05 m and an outer radius of 0.06 m, with thermal conductivity 45 W/(m*K). The inner surface temperature is 120 °C and the outer surface temperature is 119 °C. What is the rate of heat conduction through the pipe wall?","v":[-0.06833,-0.05976,-0.02975,-0.09289,0.01703,-0.01833,-0.01574,-0.03614,-0.03496,0.08905,0.03106,-0.10349,0.08088,0.04492,-0.061,0.06321,-0.06566,0.00256,-0.0057,-0.00909,0.06285,-0.07456,-0.06162,-0.07435,0.04003,0.01878,-0.09789,0.04507,-0.04184,0.0194,0.09635,-0.04827,0.00671,-0.01739,0.0187,0.09146,-0.02011,-0.04074,0.02528,0.06174,0.16193,-0.11997,-0.07247,0.06652,-0.05992,0.07006,0.06884,-0.03828,-0.02519,-0.07846,-0.05118,0.00563,0.0675,-0.03523,-0.11738,-0.05456,0.13793,0.04105,-0.03003,0.04302,-0.04997,-0.0871,0.00021,0.09235,0.03833,0.08978,-0.0055,-0.02228,-0.12397,0.10357,0.0063,-0.01541,-0.15462,0.04744,-0.08437,-0.09432,-0.0574,-0.04313,-0.12195,-0.09023,0.04393,0.01103,0.00024,0.04535,0.00251,0.01845,-0.01614,-0.03575,-0.05819,-0.03005,-0.01174,0.05364,-0.02081,0.00177,0.02186,0.10275,-0.09665,-0.0199,0.08945,-0.02107,0.10897,-0.05125,0.05792,-0.02414,-0.06105,0.05992,0.05248,-0.03118,0.06817,-0.01729,-0.02014,-0.04478,0.08216,0.00021,-0.06711,0.07209,0.11179,-0.00377,-0.13582,-0.04924,-0.03439,0.04676,0.04819,0.02788,-0.04696,0.04213,0.00534,-0.0152,-0.09898,-0.07624,-0.03126,-0.11874,-0.00525,0.02268,-0.05764,0.02051,-0.03947,0.08869,-0.02766,-0.04014,-0.08213,-0.03867,0.00956,-0.09443,0.06359,0.0676,0.02188,-0.10619,-0.12829,-0.01895,0.07808,0.0109,-0.01365,0.01282,0.11096,0.0492,0.06192,0.06104,-0.01609,-0.0328,0.00443,0.00851,0.07615,-0.03871,-0.07149,0.01947,-0.00496,-0.09485,0.1005,-0.03483,-0.03387,0.06769,0.01351,0.01724,-0.08777,0.02886,0.05486,-0.03656,-0.03375,-0.02516,-0.02249,-0.00399,0.03402,1e-05,-0.01897,0.02926,-0.0226,0.03056,-0.08922,-0.01391,0.0253,0.09814,0.03127,-0.03776,0.05868,-0.04202,0.02078,0.07014,0.04728,0.00534,0.08683,-0.05725,0.02196,0.07007,0.0922,-0.06852,-0.01895,0.11772,0.01793,0.02618,-0.02738,-0.04926,0.10855,0.05603,0.01563,0.05772,0.08714,-0.10143,0.05572,0.03615,0.06204,-0.12672,0.06878,0.05088,0.00015,-0.08883,0.06445,0.04928,-0.05772,-0.07212,-0.13395,0.07758,0.0238,-0.01839,-0.03989,-0.10499,0.11096,0.01773,-0.07128,0.07781,-0.04741,0.02155,0.0744,-0.02324,0.01977,-0.05092,-0.02315,-0.0301,0.03995,0.01251,0.13148,0.07709,0.10515,0.0236,-0.06576,0.11388]},{"domain":"thermofluids","key":"sphere_conduction","name":"Radial heat conduction through a spherical shell","package":"thermofluids-ai999x","example":"A spherical shell of insulation with thermal conductivity 0.04 W/(m*K) has an inner radius of 0.1 m and an outer radius of 0.15 m. The inner surface temperature is 400 K and the outer surface temperature is 300 K. What is the rate of heat conduction through the shell?","v":[0.01122,-0.10446,-0.05535,0.02353,0.06328,0.03208,0.01604,-0.09612,0.03847,0.0212,-0.02994,-0.09012,0.02932,-0.02304,-0.01176,0.08866,-0.08375,-0.01457,0.10205,-0.00415,0.04526,-0.08477,0.01305,-0.00309,-0.02017,-0.03465,-0.01433,-0.01388,0.07549,-0.02518,0.09193,-0.02265,0.0561,0.03503,-0.08547,0.00062,-0.08201,0.0055,0.00172,-0.05421,-0.00084,-0.01728,-0.15489,0.1427,-0.06425,0.03853,0.09618,0.04171,0.00811,-0.06362,-0.00782,-0.01371,0.08684,-0.02781,-0.03068,-0.1475,0.08671,0.10902,0.04662,0.06341,-0.04231,-0.06396,0.00032,0.02049,0.06398,0.11521,-0.06033,-0.10556,-0.1031,0.01709,0.09879,-0.06746,-0.12979,0.06349,-0.06139,-0.0118,-0.10007,-0.01636,-0.14838,-0.10512,-0.00964,0.03547,-0.00574,0.04967,0.00187,0.00652,-0.07731,0.00224,-0.04389,-0.04129,0.02184,0.08787,0.01115,-0.02633,0.007,0.02891,-0.11927,0.00053,0.08147,-0.0687,0.15005,-0.05519,0.08613,0.03778,-0.09187,0.06621,0.10891,0.06999,0.04969,0.03883,0.03073,0.01471,0.03988,0.0537,-0.00154,0.02725,0.12153,0.03877,-0.09446,-0.0772,-0.05081,0.01845,0.03615,0.03883,-0.05013,-0.01066,0.04882,-0.00639,-0.07607,-0.01766,-0.03263,-0.11423,0.05848,-0.01132,-0.06673,-0.08839,0.01525,0.03939,-0.12594,-0.05717,-0.13388,-0.00164,-0.04995,-0.019,0.08438,0.05485,0.08892,-0.02854,-0.12812,0.01403,0.0447,0.03346,-0.0322,0.01623,0.06529,-0.03872,0.00099,-0.01109,-0.05517,-0.05968,0.0172,-0.04956,0.01119,-0.0508,-0.02242,0.05469,-0.04305,-0.10275,0.09005,0.00721,-0.01099,0.07247,0.02412,-0.05155,-0.03954,0.04419,-0.00679,-0.02859,-0.0461,0.00062,0.04065,0.06454,0.0272,-0.02217,0.03927,0.00647,-0.00696,-0.01383,-0.0412,0.02664,-0.0131,0.09765,0.02669,0.0125,0.08187,0.02371,0.09392,0.04209,0.10703,-0.02178,-0.01962,0.0094,0.00041,0.0611,0.05254,-0.00688,-0.073,0.0733,0.01579,0.04873,0.03337,-0.01648,0.06696,0.02311,-0.0656,0.02241,-0.08068,-0.09014,0.12389,0.06823,0.05232,-0.10547,0.08171,0.03718,0.03504,-0.07814,-0.03601,-0.02509,0.06056,-0.04421,-0.07032,0.0474,0.01055,-0.06634,-0.05207,-0.11093,0.05215,-0.062,-0.15916,0.06167,0.0289,-0.00717,0.04301,0.09778,-0.01357,0.0983,-0.01108,-0.02725,0.05211,0.06981,0.08852,0.09602,0.03124,0.03431,-0.13104,0.08147]},{"domain":"thermofluids","key":"overall_u_plane_wall","name":"Overall heat transfer coefficient of a plane wall with convection on both sides","package":"thermofluids-ai999x","example":"A brick wall 0.2 m thick has a thermal conductivity of 0.7 W/(m*K). The inside heat transfer coefficient is 10 W/(m^2*K) and the outside heat transfer coefficient is 25 W/(m^2*K). What is the overall heat transfer coefficient?","v":[0.04688,0.00746,-0.05423,0.03492,-0.01506,-0.04639,0.02485,-0.10417,-0.05823,-0.04241,-0.00312,-0.03,-0.02118,0.11954,-0.07013,-0.01093,-0.05393,-0.00448,0.0344,0.11129,0.03332,-0.07636,-0.02591,0.05905,0.11923,-0.0306,0.05198,-0.05293,0.00687,0.01791,0.14658,0.04476,-0.00163,0.01478,0.04843,0.08947,-0.04638,0.03284,-0.04184,-0.00496,0.03285,-0.11376,-0.04537,0.08603,-0.07133,0.0548,-0.00105,0.06427,-0.01807,0.05917,0.00565,-0.00408,0.16279,0.02043,0.01791,-0.0906,0.10806,0.02761,-0.03117,0.02409,-0.10744,-0.06244,-0.05397,0.04737,0.03465,0.09203,0.02024,-0.12368,0.0636,-0.06153,0.01878,-0.07907,-0.01749,0.02735,0.01881,-0.04213,0.02553,-0.00328,0.00659,0.10362,0.00981,0.00308,-0.06105,0.06757,0.05278,-0.00083,0.02517,-0.01762,-0.00885,0.01929,-0.0438,0.00672,-0.09532,-0.01553,-0.02389,-0.03523,-0.06904,-0.0361,0.02319,-0.10646,0.15756,-0.08231,-0.00495,-0.0208,0.01423,0.0041,0.13743,0.01408,0.01076,-0.00804,0.0844,-0.06289,0.04111,0.03293,0.03734,0.01422,0.03842,-0.00449,-0.0619,0.02242,-0.11182,0.13164,0.00808,0.05884,0.04094,0.10356,0.04812,-0.04869,-0.02817,-0.03195,-0.0252,-0.01214,0.03231,-0.04631,-0.14954,-0.11833,0.01673,0.03951,-0.03429,-0.03354,-0.03481,-0.18549,0.04845,-0.08035,0.02218,-0.02402,-0.0886,-0.10125,-0.01585,-0.00144,0.04281,0.06831,0.10012,0.06172,-0.02223,0.05141,0.00413,-0.04467,-0.03958,0.02284,0.13747,-0.02014,-0.03117,0.04454,-0.07723,-0.03464,0.04398,-0.12924,0.03692,-0.01746,0.05711,0.08741,-0.0784,0.02519,-0.05931,-0.03702,0.01612,-0.14116,0.03358,-0.14017,0.0978,-0.03085,-0.12436,-0.05283,-0.09119,-0.03773,-0.01677,-0.00482,-0.07711,-0.00497,0.08133,0.08663,-0.0636,-0.08792,-0.08622,-0.00166,0.00725,0.10948,0.08712,0.04502,-0.02205,0.02028,-0.01094,0.05225,0.04951,0.08024,0.06504,0.02517,-0.00203,-0.02745,-0.04814,-0.02383,0.13145,-0.0287,0.05398,0.10006,-0.08103,-0.04983,0.06398,0.04447,-0.00137,-0.05572,0.04555,-0.06746,-0.13773,-0.11128,0.00979,0.11793,0.10776,-0.06166,0.01208,0.08347,-0.01262,-0.04261,0.06631,-0.05786,0.00324,0.025,-0.00653,0.03684,0.02299,-0.06716,-0.01907,-0.00528,0.07429,0.04407,0.01265,-0.02074,0.10646,-0.00481,0.03838,0.00304,0.01792,0.01329,0.01641,0.02719]},{"domain":"thermofluids","key":"overall_heat_rate","name":"Heat transfer rate from the overall heat transfer coefficient","package":"thermofluids-ai999x","example":"A wall of area 20 m^2 has an overall heat transfer coefficient of 0.5 W/(m^2*K). The inside air temperature is 21 °C and the outside air temperature is -5 °C. What is the heat loss through the wall?","v":[0.12296,-0.07393,-0.11413,0.09581,-0.0117,0.0173,-0.0019,-0.06964,-0.05271,-0.07176,0.06663,-0.10716,0.03956,0.12069,-0.0187,0.07696,0.04642,-0.04678,0.02167,0.06283,0.06998,-0.12697,0.01706,0.01254,0.00602,0.01754,0.12177,-0.00999,0.03511,-0.02193,0.10803,0.03271,-0.02959,0.00363,-0.03979,0.09342,-0.00978,0.00181,-0.06364,0.06064,0.07699,0.00361,0.00699,0.12456,-0.07124,0.06947,-0.01767,-0.00417,0.07034,0.04944,0.03384,0.01445,0.17499,-0.01242,0.04132,-0.08264,0.03544,-0.02594,-0.047,-0.01089,-0.07486,-0.1054,-0.03896,0.10204,0.04023,0.02219,0.01103,0.00656,0.01782,-0.02039,0.03794,-0.05024,-0.06434,0.02419,-0.02725,-0.03701,0.08799,-0.02254,0.00685,0.08848,-0.01224,-0.00709,-0.03951,0.02933,0.0217,0.00495,0.01791,-0.02485,0.01757,-0.03163,-0.03836,-0.0335,-0.05062,-0.05035,-0.16423,0.05082,-0.08427,-0.02475,0.09136,-0.08516,0.18645,-0.05138,-0.01123,-0.02292,0.04386,-0.06042,0.08771,-0.04705,-0.01219,-0.02038,0.02996,-0.04601,-0.0077,0.06997,-0.00675,-0.00885,0.01849,-0.02092,-0.02235,-0.00527,-0.0678,0.03045,0.03659,0.06428,0.02238,-0.06025,-0.05447,-0.05854,-0.08601,-0.07198,-0.09216,-0.02066,0.07095,-0.00558,-0.15537,-0.12746,0.08188,0.02995,0.01819,-0.06182,-0.08624,-0.21929,-0.01916,0.04479,-0.02114,-0.05098,-0.09036,-0.05543,0.04002,-0.00722,0.0581,0.0112,0.04265,0.03308,-0.08281,0.04632,-0.09943,-0.10759,0.01518,0.02928,0.12346,-0.03465,0.02575,0.07602,-0.05982,-0.00427,-0.00309,-0.0216,0.02463,-0.10153,0.01825,0.09475,0.06393,0.00106,-0.04551,0.00198,-0.00102,-0.06126,0.00278,0.03161,0.08482,0.04967,-0.12328,-0.02239,-0.10616,-0.03018,-0.08906,-0.03405,-0.11924,0.00157,-0.01106,0.12438,-0.0596,-0.06173,-0.07964,0.0291,0.0343,0.09084,0.01035,0.03308,0.01048,-0.00215,0.07509,0.04449,0.02935,0.10008,-0.08311,-0.00342,0.04678,0.02587,0.06607,-0.01653,0.06789,0.07098,0.01173,0.04221,-0.01895,-0.07402,0.07334,0.05873,0.0282,-0.0657,-0.00878,0.01026,-0.11692,-0.06124,0.00705,0.07738,0.09801,-0.04238,-0.0254,0.09179,0.03668,0.04257,0.06344,0.05999,0.00575,0.01476,-0.0528,0.05067,-0.06115,-0.02886,0.00782,-0.02146,0.04068,0.00393,0.0896,-0.06131,0.1036,-0.13497,0.06841,-0.00413,-0.00816,-0.04407,0.02241,0.05736]},{"domain":"thermofluids","key":"critical_insulation_radius","name":"Critical radius of insulation on a cylinder","package":"thermofluids-ai999x","example":"Insulation with a thermal conductivity of 0.05 W/(m*K) covers a pipe, and the outside heat transfer coefficient is 10 W/(m^2*K). What is the critical radius of insulation?","v":[0.03947,-0.05034,-0.14278,0.08459,0.04622,0.06726,-0.00457,-0.06408,0.03618,0.04103,-0.0236,0.03111,-0.05934,0.0235,0.02074,0.04714,-0.0727,0.00113,0.10951,0.06915,-0.01188,-0.04785,-0.09657,-0.06733,0.08943,-0.02157,0.0069,0.00079,0.09257,-0.0057,0.09443,0.02321,-0.01596,-0.02528,-0.07911,0.00638,0.03741,-0.03388,0.00274,-0.05573,0.03844,-0.09518,-0.16501,0.12212,-0.03008,0.06012,-0.00411,-0.06573,0.02058,-0.06265,0.07681,-0.05968,0.11953,0.00248,-0.04502,-0.07448,0.06914,-0.00515,-0.00513,-0.07597,-0.06701,0.00275,-0.07734,-0.00021,0.10394,0.04749,-0.00342,-0.01335,-0.03596,0.07988,0.04419,-0.01758,-0.15023,0.06458,-0.01332,-0.05859,-0.13393,-0.04661,-0.07579,0.06776,0.06333,0.0969,-0.00176,0.04565,0.05965,0.06745,-0.13827,0.01424,-0.07164,-0.00592,-0.06681,0.09658,-0.01963,0.03384,0.06405,0.05162,-0.08908,-0.00753,-0.02145,0.02368,0.09913,-0.11694,0.03343,0.07172,-0.04262,0.09106,0.05418,-0.03696,0.01135,-0.07311,-0.00404,0.04271,-0.01428,-0.03533,0.01833,0.06801,0.06564,-0.10302,-0.11555,-0.0498,-0.02187,-0.02466,0.02611,0.02463,-0.08327,0.06941,-0.01249,-0.02033,-0.10303,-0.03459,-0.07326,-0.14182,0.04345,0.00268,-0.07146,0.02459,0.01656,0.07704,-0.01135,-0.03241,-0.03605,-0.10049,0.00882,-0.03998,0.05873,0.03296,0.09788,-0.06618,-0.07007,-0.02984,0.1037,0.03896,0.0776,-0.00515,0.06935,0.06678,0.01658,0.02177,-0.07672,0.01183,0.04353,0.10511,0.03471,-0.02001,-0.02565,-0.00681,0.08582,-0.13245,0.04202,0.01386,0.02552,0.01623,-0.03638,0.01612,-0.00476,-0.0678,0.02665,-0.02253,0.01087,-0.04387,-0.08095,0.00079,0.04915,0.00356,-0.0615,-0.07925,-0.04805,0.08269,-0.01563,-0.00421,-0.00499,-0.06526,0.01343,-0.07062,0.03974,-0.03059,-0.01304,0.09328,0.09563,0.06254,0.00591,0.11566,-0.00763,0.0107,0.02046,-0.12178,0.01926,0.0764,-0.05965,0.00699,-0.02756,0.00175,0.17642,0.0232,-0.06973,0.07548,0.03565,-0.11274,0.10415,0.12944,-0.10128,-0.06647,-0.01392,-0.01263,-0.06904,0.00282,-0.00045,0.07405,-0.00976,-0.01077,-0.08203,0.04549,0.03469,-0.01566,-0.08308,-0.07168,0.03833,-0.01861,-0.05268,0.06201,-0.01703,-0.03445,0.0225,-0.01109,0.00833,0.08973,-0.03257,-0.04206,0.01158,-0.02062,-0.03826,0.16449,0.07311,0.07438,0.0068,0.11128]},{"domain":"thermofluids","key":"wall_generation_max_temperature","name":"Maximum temperature of a plane wall with uniform heat generation","package":"thermofluids-ai999x","example":"A plane wall with a half-thickness of 0.01 m and a thermal conductivity of 20 W/(m*K) has a uniform heat generation of 1000000 W/m^3. Both surfaces are held at a surface temperature of 350 K. What is the maximum temperature in the wall?","v":[-0.06904,-0.06601,0.05191,-0.02096,0.05515,0.00143,0.07336,-0.04231,-0.00067,0.05884,0.01309,-0.0237,0.0495,0.00289,-0.02893,0.00431,0.03543,0.01002,0.01468,0.0689,0.11068,-0.08288,-0.03766,0.02561,-0.01566,-0.04234,-0.03412,0.00674,-0.01977,0.06064,0.09012,0.12009,0.00126,0.05532,-0.01582,0.10941,-0.08409,-0.05984,-0.0267,0.02017,-0.04163,-0.11053,0.0415,0.04172,-0.12017,0.01464,0.02941,0.05782,-0.01822,0.08177,-0.03321,-0.00329,0.01614,0.02294,0.05223,0.00391,0.14269,0.04083,-0.0083,0.06013,-0.0491,-0.09724,-0.01155,0.0677,0.08105,-0.03547,0.00233,-0.02537,0.04291,0.0313,-0.04282,-0.01616,-0.0691,0.1268,-0.05355,0.02962,-0.06826,0.01086,0.01558,-0.08804,0.01652,-0.02538,-0.15235,0.00585,-0.03269,0.0876,0.09617,0.03497,-0.0869,0.02353,0.00752,-0.01757,-0.00309,0.00932,-0.14635,-0.00622,0.03741,-0.05109,0.05974,0.0357,-0.0128,0.07198,0.02626,-0.04543,-0.0424,0.10118,0.08661,0.05451,-0.09619,-0.01609,0.01702,-0.0045,0.08427,0.08469,0.00596,-0.05054,0.04932,-0.09598,-0.09848,0.08595,0.01236,0.13394,0.07252,-0.09686,-0.0467,0.09138,0.08588,0.03788,-0.05467,-0.02435,0.00883,-0.00686,0.05834,-0.03294,-0.11959,-0.08964,0.09967,0.00736,-0.02285,-0.00496,-0.02695,-0.0605,0.11393,-0.05268,-0.05977,0.04123,-0.00109,-0.15713,-0.0511,0.01553,0.05151,-0.00281,-0.0038,0.09122,0.002,0.03923,-0.04535,0.02956,-0.06201,0.01606,-0.0007,-0.01274,-0.06137,-0.02945,-0.08912,-0.00231,0.01017,-0.1089,0.05103,-0.04393,-0.02004,-0.05487,-0.07733,-0.04066,-0.12721,-0.03614,0.07509,-0.09903,-0.04133,-0.03289,0.12229,-0.07925,-0.05223,-0.10071,0.01063,-0.02255,0.00624,0.04903,-0.04682,-0.03577,-0.0346,0.06433,-0.0994,-0.04122,0.03344,-0.01469,0.0561,0.12802,-0.03358,0.02742,0.0799,-0.09658,0.04142,0.07734,0.0782,-0.04205,0.10386,0.04322,-0.07141,-0.07403,-0.03689,0.01798,0.05946,-6e-05,0.078,0.19219,-0.07098,-0.03286,0.0068,0.05595,-0.01592,-0.01428,0.05465,-0.18747,-0.06775,-0.10391,-0.03283,0.04468,0.11791,-0.11565,0.0391,0.05766,-0.04119,0.03342,0.11609,0.02206,-0.10323,0.01406,0.04049,0.01399,0.04058,0.03475,-0.0025,0.07907,0.05216,-0.00691,0.03275,0.00929,-0.04681,-0.00573,0.03252,-0.03119,0.0085,0.0118,-0.07709,0.01304]},{"domain":"thermofluids","key":"thermal_diffusivity","name":"Thermal diffusivity","package":"thermofluids-ai999x","example":"Copper has a thermal conductivity of 400 W/(m*K), a density of 8900 kg/m^3 and a specific heat of 385 J/(kg*K). What is its thermal diffusivity?","v":[0.05543,-0.00218,-0.01899,0.08679,0.02068,0.05058,-0.03169,-0.06161,-0.01432,0.03405,-0.11139,0.0316,0.11909,0.08519,-0.02361,0.02255,-0.08339,-0.05073,0.02166,0.00467,0.07245,0.06963,-0.04882,0.02029,0.03576,0.02632,-0.00562,0.08934,-0.0685,0.03369,-0.04342,0.05194,-0.06321,0.03881,0.11141,0.06721,0.01513,-0.05952,0.03915,-0.07144,0.05058,-0.03191,-0.0368,0.00294,-0.15543,0.0091,-0.08522,0.03471,0.02662,-0.03119,-0.04167,0.06034,0.12054,-0.04073,-0.05591,-0.00337,0.12683,-0.00761,0.08474,0.05426,-0.06441,-0.12896,-0.03048,-0.00334,-0.00929,0.03725,0.03447,0.00049,-0.13473,0.0458,-0.05114,-0.02726,-0.10647,-0.0482,0.09756,-0.00648,-0.02654,-0.02566,0.0248,0.00545,-0.06081,0.02557,-0.08136,-0.09026,0.11279,0.0253,-0.04724,-0.01587,-0.00921,0.08848,-0.11035,-0.08424,0.07518,-0.0054,-0.11269,-0.10641,-0.15126,-0.0275,0.04511,-0.07298,0.02316,0.0727,-0.09154,-0.00673,-0.00567,0.01102,0.07083,0.09802,0.06141,-0.02454,0.10466,0.07248,0.00741,0.00909,-0.0796,-0.02911,0.12906,0.01894,-0.03823,0.02041,-0.06217,-0.00615,0.03672,0.08516,-0.01594,0.12479,-0.05267,-0.03054,-0.01543,-0.00874,0.02689,-0.02737,-0.07163,-0.01344,-0.01572,-0.00297,-0.01377,-0.01886,-0.03178,-0.08787,0.06852,0.01728,-0.00066,-0.04646,-0.01473,-0.00868,0.0475,0.00385,-0.1011,-0.00399,0.11505,-0.01098,-0.17105,-0.08603,0.01855,0.00567,-0.01653,-0.04374,-0.1283,-0.05767,-0.00311,-0.09842,-0.04846,0.02504,0.09692,0.05094,0.00677,-0.14333,-0.03198,-0.0648,-0.00954,-0.06972,-0.02424,0.02718,-0.01439,-0.00887,0.03989,-0.00878,0.03866,-0.01133,0.03399,0.06509,-0.0351,0.06809,0.03453,-0.05352,0.01678,0.08671,-0.05403,0.00442,0.06676,-0.08478,0.00332,-0.06023,0.0406,-0.0113,0.12096,0.01529,0.09721,-0.01127,-0.03739,-0.03157,0.10502,0.01645,-0.01992,-0.131,0.04713,0.09427,0.02035,0.07957,-0.01607,-0.01245,0.04295,0.03713,0.05322,0.08313,-0.04721,-0.08156,0.04013,0.08773,-0.05452,-0.1699,0.03828,-0.02148,0.05331,-0.04162,0.06524,0.06558,0.05517,0.00424,-0.05891,0.11317,0.05235,-0.09677,-0.02423,-0.07645,-0.00602,-0.02959,-0.04503,0.1644,0.01686,0.04258,0.07741,0.02335,-0.00331,0.12502,0.06136,0.05427,0.03958,0.02534,-0.02818,0.03501,-0.04874,-0.01085,-0.05436,0.02623]},{"domain":"thermofluids","key":"biot_number","name":"Biot number","package":"thermofluids-ai999x","example":"An aluminium part with a characteristic length of 0.01 m and thermal conductivity 200 W/(m*K) is cooled with a heat transfer coefficient of 50 W/(m^2*K). What is the Biot number?","v":[-0.01437,-0.09089,-0.0432,-0.08535,0.05433,-0.03953,0.04753,-0.0003,-0.05213,0.04151,-0.01555,-0.00815,-0.01768,-0.02569,-0.0097,-0.01146,-0.08172,0.00248,-0.01568,-0.02223,-0.04512,-0.02653,-0.07925,0.00413,0.14806,-0.09882,0.05229,-0.03779,0.10865,0.00909,0.01788,0.11938,0.01845,0.04861,0.04199,-0.03647,0.03083,-0.05947,-0.02204,0.02581,0.00248,-0.02303,0.06256,0.02211,0.05622,-0.1007,0.02873,0.01313,-0.10987,-0.0251,-0.0069,-0.05438,0.13362,-0.1117,0.02623,-0.02474,0.03894,0.13882,-0.00742,0.08819,-0.0254,-0.03991,0.06947,-0.03251,-0.03826,0.13662,-0.059,-0.06618,-0.00289,0.00271,-0.04451,-0.02795,-0.19028,-0.04011,0.01406,-0.01708,-0.02417,-0.0755,0.01961,0.00332,-0.03149,0.12866,-0.07568,-0.005,0.13068,-0.02611,-0.00971,-0.11096,0.03137,0.00611,-0.0192,-0.07096,0.051,0.03191,0.11112,0.00012,-0.08072,-0.02653,-0.0129,-0.05825,0.03424,0.05147,-0.00405,0.08195,-0.02714,0.02899,0.03967,0.02427,0.05085,-0.13494,0.07812,-0.01221,0.0741,-0.01293,0.00132,0.0093,0.13351,0.00492,-0.06035,0.00054,-0.01531,-0.01429,-0.01718,0.02232,0.02539,0.06663,0.05613,0.05882,0.01995,-0.04172,0.0761,0.0026,0.14951,-0.00695,-0.03168,-0.01692,0.04019,0.06554,-0.1977,-0.03802,0.01001,-0.02053,0.12467,-0.12607,-0.11588,-0.03279,-0.01377,0.05264,-0.13099,-0.03997,0.13923,0.05408,0.00289,-0.05216,-0.00234,-0.00031,0.03059,-0.03546,-0.08583,-0.05592,0.06241,-0.0379,-0.01111,-0.01789,-0.0471,-0.01614,0.09582,-0.08041,-0.06399,-0.02052,-0.03492,0.04935,-0.06086,0.10573,-0.06486,-0.05131,0.0214,-0.02277,0.05961,-0.09916,0.01869,0.01929,0.06934,-0.03029,-0.04332,-0.03938,0.05271,0.05553,-0.08744,0.0457,0.07924,-0.02644,0.00223,-0.09639,-0.0823,-0.04441,-0.02094,0.04719,0.11083,0.0696,0.09125,0.07464,0.05335,0.02377,0.08662,-0.02908,0.06647,0.00438,0.03676,0.03517,-0.11241,-0.04789,0.06623,0.03555,0.10656,0.06307,-0.03025,0.02026,0.09516,0.01759,-0.14386,-0.07135,-0.03474,-0.04027,-0.01293,0.03231,0.06747,0.12149,0.03261,0.03796,-0.06876,0.0205,-0.01891,-0.02343,0.01058,-0.07362,-0.00704,0.03356,-0.05068,0.01494,-0.01729,-0.03819,-0.03153,-0.08665,0.01167,0.04512,0.12524,0.01139,0.0142,-0.04257,0.14208,-0.04014,-0.02443,0.02279,-0.0873,-0.05055]},{"domain":"thermofluids","key":"fourier_number","name":"Fourier number","package":"thermofluids-ai999x","example":"A steel plate with thermal diffusivity 0.00001 m^2/s and characteristic length 0.02 m is heated for a time of 60 s. What is the Fourier number?","v":[-0.0324,-0.01758,0.01287,0.01208,0.00387,-0.04941,0.01738,0.03306,-0.06813,0.01002,0.01714,-0.05784,0.09086,0.04011,-0.0978,0.04936,-0.00601,0.06266,0.02839,-0.00787,-0.0145,0.05331,-0.09186,0.01228,0.05473,-0.023,-0.03758,-0.06544,-0.00587,0.0157,0.0143,0.14193,0.04409,0.04252,0.08306,-0.03031,0.15709,-0.07125,-0.03637,0.05853,0.0401,-0.05782,0.02912,-0.01262,-0.05794,0.01374,-0.03826,0.03433,0.00985,-0.01089,-0.11392,0.02811,0.00632,-0.06256,-0.05875,-0.06865,0.06979,0.0839,0.04362,-0.04023,-0.00733,-0.05188,0.00087,0.03857,0.01638,0.12875,-0.04933,0.02085,-0.05252,0.00396,-0.05905,-0.04221,-0.23302,-0.04527,-0.01482,-0.0403,0.01185,0.04259,0.0071,0.01786,-0.01615,0.00354,-0.04434,0.00403,0.13282,-0.04364,-0.05483,0.03959,0.07552,0.01679,0.00833,-0.08076,0.02542,-0.04907,-0.0473,-0.0002,-0.04255,-0.04419,-0.04233,-0.03764,-0.01996,0.13894,-0.11497,-0.09981,0.01148,0.10256,0.01883,0.02204,0.07615,-0.10363,-0.02771,-0.03433,0.06576,0.0114,-0.01063,-0.04886,0.10652,0.09357,0.01942,0.09904,-0.00852,0.01632,0.03188,0.03492,0.0688,0.18778,-0.0621,0.02099,-0.02372,0.00035,0.05111,0.03269,-0.02547,0.0188,-0.02847,-0.01441,-0.00976,0.04613,0.04813,0.04301,0.20229,0.00421,0.10383,-0.13996,-0.14482,-0.02401,0.01098,0.05135,-0.03888,0.06513,0.03691,-0.09128,-0.10195,-0.02996,-0.04289,-0.10766,-0.03014,-0.00738,-0.11791,-0.07329,-0.03119,-0.02018,-0.05463,0.08553,0.08388,0.05962,0.04782,-0.01383,0.03164,-0.00672,-0.0503,0.03389,-0.03018,0.24467,-0.03941,0.04564,-0.04812,-0.02525,0.07565,-0.08361,-0.072,0.06205,0.08142,0.03529,-0.07734,-0.04886,0.01257,0.04817,-0.11577,0.01231,0.04407,-0.06972,-0.05217,0.03521,-0.0037,-0.0058,0.0683,-0.06006,0.00013,-0.00568,0.07556,-0.07356,0.07684,-0.00547,-0.01669,-0.06329,0.03497,0.02576,0.1015,0.07593,-0.03034,-0.04161,0.01874,0.01776,0.01809,0.04844,-0.01934,0.03229,0.04133,0.02819,-0.0937,0.01078,0.00034,0.00057,0.04194,-0.13448,0.08149,0.05227,0.03862,-0.05056,-0.12198,0.03201,-0.01804,-0.03035,-0.02403,-0.00639,-0.02614,-0.00669,-0.03443,0.07962,-0.00409,-0.0418,-0.02573,-0.04545,0.00084,-0.02891,0.08094,-0.08388,0.01607,0.01939,0.12927,-0.0387,-0.12668,-0.04918,-0.06564,-0.02985]},{"domain":"thermofluids","key":"newton_cooling","name":"Newton's law of cooling (convection heat transfer)","package":"thermofluids-ai999x","example":"A hot plate with a surface area of 0.5 m^2 is cooled by convection with a heat transfer coefficient of 25 W/(m^2*K). The surface temperature is 80 °C and the air temperature is 20 °C. What is the rate of heat transfer?","v":[0.09142,-0.05865,-0.01539,0.01554,-0.00629,-0.03347,-0.05673,-0.10169,-0.05585,-0.04241,-0.02425,-0.05198,-0.04851,-0.01363,-0.02254,-0.05502,-0.01593,-0.05572,0.02696,0.01561,-0.05505,0.02904,0.03456,-0.04177,0.03385,-0.066,0.03772,0.03118,0.06286,-0.00176,0.02886,0.04347,0.02714,0.03791,-0.12298,-0.01227,0.00167,0.0257,-0.00016,-0.05551,0.03898,0.01591,-0.04329,0.07546,-0.07591,-0.02831,0.09434,-0.03256,-0.03621,0.04664,0.02543,-0.1044,0.16895,-0.06181,0.02326,-0.13752,0.01475,0.13679,-0.02928,-0.06845,0.01211,-0.05773,-0.01538,-0.0018,-0.03602,0.04017,-0.02747,0.04052,0.02755,0.11136,0.09494,-0.15048,-0.16075,-0.03324,0.07194,0.00377,-0.00684,-0.02036,-0.0481,-0.09024,0.00425,0.10251,-0.06194,0.02303,0.05987,0.06804,-0.01218,-0.07199,0.0059,-0.00316,-0.01428,-0.0873,0.04615,0.05436,-0.01777,-0.07752,-0.02241,0.08466,0.09381,-0.04517,0.10314,-0.02436,-0.00184,0.07992,-0.03061,-0.09684,0.11283,0.06206,0.02582,-0.06771,0.08359,-0.00865,0.0086,0.06995,0.00826,0.06686,0.10037,-0.00701,-0.01052,-0.03804,-0.06757,-0.03612,0.06163,-0.08089,-0.02803,-0.0244,-0.03422,-7e-05,0.03774,-0.0476,0.01298,-0.08521,-0.00863,0.00656,-0.07313,-0.05737,0.07658,0.05398,-0.08889,-0.15909,-0.04207,-0.09178,0.02069,-0.07371,-0.02916,-0.00657,0.00511,0.04173,-0.10078,-0.01372,0.08691,0.00162,-0.04232,0.09992,0.00793,0.04871,0.01778,-0.05787,-0.05484,-0.00794,0.06147,-0.00807,-0.03386,0.04965,-0.06251,-0.04441,0.01633,-0.0245,-0.02235,-0.04313,0.04353,0.09916,-0.01803,-0.00542,0.11228,-0.08275,-0.01941,-0.03891,0.03117,0.03158,0.04457,0.0291,-0.14328,-0.09288,-0.04691,0.06916,-0.04903,-0.08113,-0.05405,0.02507,0.04193,0.00372,-0.08103,-0.08996,-0.02225,0.07873,0.03963,0.08238,0.11176,0.02975,0.05449,0.05838,0.10435,-0.07261,0.03675,0.09023,-0.04757,-0.07677,0.03695,-0.00301,0.05839,-0.09229,0.06814,-0.01214,0.0887,-0.02032,-0.03472,-0.08277,0.13876,0.02671,-0.00295,-0.13725,-0.0048,-0.01321,-0.0618,0.02322,0.0111,0.03316,0.08843,-0.00959,-0.03573,0.10798,0.10095,0.06888,-0.00643,0.10127,-0.02332,-0.03687,-0.02494,-0.10802,0.15874,-0.01192,-0.0886,0.07448,0.00272,0.07781,0.08041,0.00873,0.05773,-0.07528,0.07086,0.12703,-0.00429,0.05409,0.03306,0.04427]},{"domain":"thermofluids","key":"nusselt_heat_transfer_coefficient","name":"Heat transfer coefficient from the Nusselt number","package":"thermofluids-ai999x","example":"Water with thermal conductivity 0.6 W/(m*K) flows in a tube of diameter 0.05 m, and the Nusselt number is 120. What is the heat transfer coefficient?","v":[-0.03217,-0.01624,-0.013,-0.07429,0.02471,-0.05959,0.01617,-0.027,0.00487,-0.02009,0.00967,-0.0725,0.02317,0.08951,-0.02437,0.01795,-0.06311,0.02557,0.03035,0.02393,-0.04292,0.05131,-0.09261,-0.02267,0.146,0.01006,-0.0004,-0.07597,0.08741,0.00805,-0.04605,0.04987,0.08047,0.08537,0.09441,-0.03082,0.04955,0.00055,0.07619,-0.00852,0.07662,-0.01307,-0.07816,0.03777,0.04018,-0.01453,0.11069,-0.0116,-0.04268,-0.01088,-0.02656,-0.04402,0.15694,-0.04896,-0.01094,-0.14064,0.07014,0.08562,-0.02412,-0.03979,-0.03761,-0.00342,-0.04928,0.0304,-0.01879,0.13138,-0.11389,0.00865,0.06891,0.08995,-0.036,-0.04441,-0.2,0.00558,0.04377,0.01213,-0.09204,0.02203,-0.01667,-0.00601,-0.02295,0.11135,-0.04752,0.07545,0.09566,-0.02525,-0.07339,-0.06836,0.00189,-0.04799,-0.06089,-0.08547,0.02201,0.00502,-0.0417,-0.00769,-0.13937,-0.00057,0.04481,-0.02922,0.05623,-0.01061,-0.00893,0.04642,0.03089,0.00458,0.04829,-0.01692,0.08792,-0.1221,0.03544,-0.07224,-0.0235,-0.02489,-0.03774,0.00753,0.17056,-0.00385,-0.05961,-0.02748,-0.04197,-0.03691,-0.01603,0.07352,0.04901,0.03391,0.06117,0.00486,-0.03096,-0.09752,0.01587,-0.02595,0.02672,0.01236,-0.08236,0.00039,0.10532,0.14475,-0.12248,0.03527,0.03805,-0.00836,0.08249,-0.14809,-0.02081,-0.04636,-0.04583,0.04303,-0.05576,-0.08866,0.1613,0.04789,-0.0473,0.0625,-0.06691,0.12511,0.03121,-0.07636,-0.06023,0.00708,-0.00096,0.02526,-0.04081,0.07095,0.04096,0.01274,0.04444,-0.11849,-0.04136,0.00443,0.00283,0.0226,-0.06938,0.09583,-0.03847,-0.03958,-0.03251,-0.03486,0.09915,-0.10042,-0.00029,0.03218,0.00244,-0.05299,-0.05926,0.03597,0.00388,0.01114,-0.07938,0.07062,0.06544,-0.00816,0.01208,-0.06608,-0.12014,-0.07421,0.01389,0.0452,0.08147,-0.01921,-0.02188,0.04943,0.0833,0.01769,0.02658,0.02279,0.13373,0.03821,0.01585,-0.0314,-0.08386,-0.04328,0.01322,0.00217,0.06748,0.01402,-0.03147,0.0083,0.08856,0.02644,-0.10486,-0.08021,0.09369,-0.02931,-0.03457,-0.04915,0.03207,0.08119,0.08202,-0.05449,-0.10918,0.10231,-0.00684,-0.13067,-0.02329,-0.01936,-0.03314,0.03338,0.0627,-0.04908,0.06011,-0.0696,-0.12354,-0.03318,0.07367,0.03979,0.08261,0.01691,0.06577,-0.0767,0.02827,0.06355,-0.03886,-0.03317,0.03468,-0.02576]},{"domain":"thermofluids","key":"prandtl_number","name":"Prandtl number","package":"thermofluids-ai999x","example":"Water has a specific heat of 4180 J/(kg*K), a dynamic viscosity of 0.001 Pa*s and a thermal conductivity of 0.6 W/(m*K). What is its Prandtl number?","v":[0.06876,-0.00344,-0.0768,-0.00509,-0.06272,0.01912,0.14228,0.02679,-0.07972,-0.01768,-0.08083,0.00854,-0.01006,0.07196,0.00255,-0.00213,-0.08437,-0.04201,0.09625,0.12911,0.01899,0.0423,0.00396,6e-05,0.00289,0.0105,0.05331,-0.0302,0.07403,0.0382,-0.05829,0.0307,-0.09618,0.05637,0.02388,0.04598,-0.02097,-0.00527,-0.00572,-0.06052,0.0738,-0.01556,-0.03011,-0.02537,-0.1035,0.02579,0.05296,0.01802,-0.00496,-0.01952,-0.05691,-0.05499,0.08201,-0.01886,-0.10192,-0.02376,0.01469,-0.04241,0.01788,0.01647,-0.04258,-0.06275,-0.03196,0.09065,-0.07688,0.06497,0.02294,-0.05721,-0.06674,0.05614,-0.08271,-0.03658,-0.08983,-0.00882,0.08167,-0.05473,0.12333,-0.03902,0.01415,-0.06893,-0.06922,0.04305,-0.02088,-0.02406,0.06413,0.00158,-0.03225,-0.07037,-0.07346,0.00247,-0.04978,-0.02006,-0.06304,-0.00272,-0.03412,-0.06231,-0.06555,-0.02838,0.0079,-0.042,0.01572,0.00508,-0.00872,0.03942,0.06708,0.03499,0.11886,-0.03968,0.01736,0.01138,0.15452,-0.00319,0.01384,0.01355,-0.0323,-0.05833,0.11792,-0.01968,-0.05441,-0.01795,0.00306,-0.13074,0.01108,0.12487,0.03412,0.07159,-0.06425,0.02775,0.00083,-0.03704,0.02791,-0.03744,0.01576,0.01343,-0.08575,0.06717,0.05379,0.15587,-0.05944,-0.10944,0.03788,0.11711,0.07194,-0.04131,-0.0148,-0.02921,-0.13629,-0.10633,-0.1048,-0.01537,0.05404,0.12287,-0.10438,0.04258,-0.04294,0.05409,0.10609,-0.09829,-0.03823,-0.13338,-0.04474,-0.08557,-0.07445,0.03645,0.00799,0.00657,-0.06452,-0.11119,-0.0617,-0.02877,-0.04386,-0.06086,-0.04752,0.04973,0.07012,0.0546,0.03534,0.02184,0.02812,0.01543,0.09704,-0.00249,0.02569,0.00962,0.07457,-0.02545,-0.08056,0.01497,-0.07624,-0.00744,0.06651,-0.03923,-0.05914,-0.00656,0.00755,-0.02534,0.05471,0.06595,-0.01027,0.01326,-0.03609,0.03178,0.07122,0.15985,-0.02422,-0.06602,0.08389,0.05855,-0.01034,0.01703,-0.06599,0.0631,0.03043,0.02557,0.08924,-0.01152,-0.03049,0.06234,0.14244,0.02762,0.07035,-0.22589,0.11168,-0.06363,-0.12351,-0.01281,-0.00558,-0.02334,0.09442,0.00077,-0.06115,0.02588,0.12907,-0.02065,-0.00345,-0.03093,0.07474,0.0026,-0.11055,0.05891,0.07395,-0.08652,0.04482,0.10678,0.01959,0.06274,0.04552,0.03589,0.06948,0.0411,-0.05791,-0.02085,0.00515,0.03866,-0.00872,-0.03726]},{"domain":"thermofluids","key":"dittus_boelter_heating","name":"Dittus-Boelter correlation, fluid being heated","package":"thermofluids-ai999x","example":"Water is heated in a pipe at a Reynolds number of 50000 and a Prandtl number of 5. Using the Dittus-Boelter correlation, what is the Nusselt number?","v":[0.05758,-0.01488,-0.00447,-0.01718,-0.10867,0.01025,0.05261,-0.02524,-0.03006,-0.0686,-0.04527,-0.06271,-0.01723,0.09092,-0.07607,0.10606,-0.00456,0.08047,0.12174,0.0896,0.05883,-0.09213,-0.12022,-0.00568,-0.00546,0.06361,0.06587,0.00828,0.06453,0.00363,-0.06061,-0.01926,0.0631,0.04939,0.0435,0.11671,0.07685,-0.04376,-0.01111,0.01604,0.12482,0.00807,-0.08911,-0.0243,-0.0617,-0.01988,0.01686,-0.04755,0.00777,0.05305,-0.08624,-0.12202,0.11934,-0.04087,-0.06108,-0.06171,0.04648,0.00557,-0.02633,-0.04681,-0.09045,-0.05075,0.08191,0.04641,-0.06828,0.06513,0.04071,-0.03068,0.02656,-0.0181,-0.11206,-0.02931,-0.0891,-0.02086,-0.04358,-0.08802,0.08477,0.02981,0.00103,0.03615,-0.00168,0.04213,-0.05323,-0.02711,0.03086,-0.06883,-0.13102,-0.05902,0.00727,-0.06126,-0.01218,-0.02342,0.0625,-0.02853,-0.06085,-0.00302,-0.06812,-0.09229,-0.01981,0.00373,0.07759,-0.01044,0.0043,-0.00876,0.05885,-0.04062,0.02705,0.00744,0.00197,-0.03776,0.05684,-0.02359,-0.02306,-0.01599,-0.0308,-0.03823,0.1347,-0.03206,-0.07298,-0.00156,-0.09002,-0.06905,-0.01585,0.0789,0.1443,0.00078,0.06337,-0.00997,0.08382,-0.0895,0.02384,-0.02499,-0.1586,0.0353,-0.05229,0.09231,0.06773,0.15291,-0.05419,0.04761,-0.04594,0.0935,0.03982,0.02651,0.01461,-0.0116,0.00165,0.02305,-0.01391,-0.02461,0.05931,0.09628,-0.09423,0.06919,-0.11494,0.04325,-0.04734,-0.07663,0.00668,-0.03932,-0.05227,-0.07678,-0.09885,0.06616,0.08121,0.03344,-0.07847,-0.02176,0.00597,-0.01082,-0.0732,-0.00174,-0.09455,0.01501,-0.03974,0.07486,-0.07287,-0.03591,-0.00834,0.0843,0.00245,0.02101,0.00916,0.02848,0.022,-0.00135,-0.02011,0.06873,-0.09688,-0.03899,-0.06783,0.01767,-0.07045,0.01167,-0.00513,-0.01105,-0.05672,0.07257,-0.04859,0.00252,-0.07069,-0.03045,0.15585,0.12829,-0.00403,0.09376,0.03167,0.08619,0.02877,0.02912,-0.14088,-0.02016,-0.01895,0.13558,0.1141,-0.02575,-0.05426,0.02721,0.13118,0.08126,0.07412,-0.07599,0.13488,-0.08268,-0.09647,0.01026,0.00142,-0.07322,0.00762,0.05687,-0.05753,0.02389,0.08572,0.0406,-0.02772,0.00588,-0.05205,0.09667,-0.00497,0.00345,0.03474,-0.12235,-0.04801,-0.01449,0.03459,-0.05955,0.04136,0.04631,0.0438,-0.05886,0.02815,-0.03288,0.04372,0.00805,0.08864,0.02945]},{"domain":"thermofluids","key":"dittus_boelter_cooling","name":"Dittus-Boelter correlation, fluid being cooled","package":"thermofluids-ai999x","example":"Water is cooled in a pipe at a Reynolds number of 50000 and a Prandtl number of 5. Using the Dittus-Boelter correlation, what is the Nusselt number?","v":[0.05854,-0.10061,-0.01657,0.01184,-0.13254,0.07456,0.10404,0.07462,-0.06383,-0.02326,-0.03268,-0.08239,-0.02144,-0.10679,-0.1526,-0.02164,0.00607,-0.03398,0.02501,0.0616,0.0193,-0.06182,-0.04343,-0.00801,0.03119,0.02081,0.05124,-0.0088,0.05422,-0.0812,-0.00075,0.0536,0.04307,0.04562,0.00415,0.11825,0.09776,-0.056,0.04541,0.0294,0.08817,0.00318,-0.08779,-0.01808,0.04355,-0.04981,0.07978,-0.06814,-0.07279,0.11486,-0.05654,-0.08433,0.07314,-0.13631,-0.09431,-0.10419,0.02885,0.04075,-0.06179,-0.09514,-0.05369,-0.01745,0.01632,0.03071,-0.04691,0.11671,0.02776,-0.01551,0.02717,0.02572,-0.05178,-0.08201,0.01542,0.00654,-0.0526,-0.06815,0.06326,-0.05376,-0.00248,-0.0197,0.09408,0.10368,0.05734,-0.04888,0.11135,-0.04541,-0.0423,-0.00063,0.02689,-0.00377,-0.02029,-0.04505,0.02302,0.03374,-0.05834,0.01561,0.0387,-0.07485,-0.03238,-0.03384,0.02323,-0.04136,-0.00097,0.02656,0.06585,0.0653,0.08888,0.01908,-0.05736,-0.06418,0.07754,-0.0282,-0.00281,0.04422,-0.03155,0.01933,0.12317,-0.03741,-0.06979,-0.01004,-0.05736,-0.15546,0.04993,0.11361,0.07189,-0.00884,0.02715,0.06225,-0.00822,-0.10092,0.05291,0.00202,-0.09323,0.03949,-0.02507,0.02379,0.06162,0.14256,-0.11034,-0.03856,-0.08462,0.06699,0.00376,0.00595,-0.07313,-0.01894,0.05393,0.04926,-0.06415,-0.03507,0.15905,0.04712,-0.04771,0.1245,-0.04846,0.0506,0.02893,-0.01905,-0.04627,0.04778,-0.02431,0.00818,-0.04009,0.06865,0.08329,-0.08319,0.03819,-0.07103,-0.05143,-0.01686,-0.04945,-0.00802,-0.04631,-0.00505,0.01234,0.04163,-0.06748,-0.04952,-0.02809,0.01209,-0.06016,0.07986,-0.03352,0.03845,0.06155,-0.0089,-0.11566,-0.02256,-0.07464,0.04841,-0.02651,0.0055,-0.03129,-0.07698,-0.02871,0.07551,0.04048,0.0713,-0.01721,-0.02455,-0.04753,0.02846,0.06728,-0.08245,-0.07991,0.05105,-0.04642,0.01904,0.06015,0.02855,-0.03803,-0.08092,0.03826,0.10914,0.11637,-0.01832,-0.05538,0.03889,0.11476,0.02818,0.02867,-0.10348,0.06565,-0.06114,-0.08201,0.1032,0.07003,-0.02771,-0.00449,0.12162,-0.06875,0.0033,0.07755,0.04404,-0.07535,-0.0454,-0.06142,0.0963,-0.08077,-0.0393,0.06875,-0.13478,-0.02297,-0.02679,0.02944,0.02089,0.08832,0.12499,-0.01379,0.0083,-0.04943,0.00918,-0.04906,0.0154,0.09994,-0.0344]},{"domain":"thermofluids","key":"flat_plate_laminar_average_nusselt","name":"Average Nusselt number for laminar flow over a flat plate","package":"thermofluids-ai999x","example":"Air flows over a flat plate with a laminar boundary layer. At the end of the plate the Reynolds number is 100000 and the Prandtl number is 0.7. What is the average Nusselt number?","v":[-0.06465,-0.03922,0.10825,-0.0842,-0.00685,-0.07968,0.07623,-0.01628,-0.04978,0.0032,0.01001,-0.06581,-0.0056,0.04914,-0.00603,0.04032,-0.02233,-0.01879,0.01666,0.08037,0.02509,-0.03519,-0.05052,0.01928,0.05437,0.05867,0.07977,-0.04757,0.04522,0.02229,-0.04,0.02406,0.07209,0.05729,0.07001,0.09921,0.08034,-0.06616,0.01824,0.09285,0.03725,0.04181,-0.09248,-0.04687,0.01101,0.00832,0.00537,-0.00834,-0.07193,0.04843,-0.10193,-0.08786,0.05658,-0.12219,0.01561,-0.10118,0.10059,0.05751,-0.00828,-0.1289,-0.0035,0.03766,-0.07106,-0.0072,-0.02516,0.17786,-0.11502,-0.04464,0.12803,-0.0088,-0.05964,-0.02171,-0.11998,-0.05403,-0.0425,0.05242,0.0763,0.1005,0.00743,-0.06607,0.00337,0.01912,-0.06179,0.01667,0.0256,-0.03742,-0.0198,-0.01429,0.08605,-0.01295,-0.04407,0.02318,-0.00317,-0.01466,-0.0842,0.03939,0.00582,-0.04344,-0.02016,0.04378,-0.0442,0.0167,0.02658,0.0014,0.1417,0.02431,0.06029,-0.10202,0.05472,-0.02894,0.01032,-0.1584,-0.04459,-0.11384,-0.0294,-0.01684,0.07295,-0.02432,-0.11007,0.03487,0.01564,-0.00652,-0.01068,0.09372,0.09799,0.05181,0.07311,0.08663,0.01441,-0.05377,0.02983,0.02906,-0.0475,0.02911,-0.1726,-0.0007,0.08345,0.20814,-0.11828,0.12611,0.02688,0.07932,0.01894,-0.10666,-0.06553,0.02835,-0.03685,0.04467,0.01212,0.0076,0.04616,0.08477,-0.00245,0.04053,-0.04991,0.08097,-0.00862,-0.05799,0.01744,0.01641,-0.0402,-0.02462,-0.03762,0.04997,0.07204,0.02967,-0.05638,-0.05851,-0.01502,-0.012,-0.07785,-0.06017,-0.07918,-0.02301,0.03598,0.01229,-0.03751,0.01337,0.02581,-0.03818,-0.05663,-0.02422,0.0372,0.01555,0.04909,0.09747,-0.12301,0.04665,-0.01458,-0.0262,-0.02227,0.00745,-0.01664,0.01168,-0.05988,-0.01392,-0.03819,-0.07375,0.02546,0.02646,0.03565,-0.02575,-0.01915,0.02012,-0.05024,0.06533,0.11979,0.06159,0.0172,0.05547,-0.05577,0.02789,-0.08921,-0.02624,0.07915,-0.04255,0.0403,0.09177,0.06117,-0.01069,0.02122,-0.08355,0.14426,-0.0888,-0.11215,-0.05497,-0.09416,0.0533,0.11611,0.03545,-0.05622,0.00017,-0.04005,0.04837,0.03851,0.04242,-0.08289,0.02667,0.04765,-0.0937,0.00333,-0.16083,-0.02865,-0.07957,0.03717,-0.01909,0.09564,0.01042,0.03253,0.02824,-0.01953,-0.047,-0.06835,0.05529,0.00671,-0.08554]},{"domain":"thermofluids","key":"flat_plate_laminar_local_nusselt","name":"Local Nusselt number for laminar flow over a flat plate","package":"thermofluids-ai999x","example":"For laminar flow over a flat plate, what is the local Nusselt number where the local Reynolds number is 100000 and the Prandtl number is 0.7?","v":[-0.02805,0.02173,-0.01094,-0.05242,-0.03195,-0.06199,0.03257,0.00543,-0.08398,-0.02495,-0.02868,-0.11113,-0.04551,0.01447,-0.04877,0.09814,-0.00494,-0.01941,0.059,0.04281,-0.04023,-0.07575,-0.02423,0.00272,-0.02556,0.01145,0.09629,-0.06091,0.00941,0.0275,-0.03167,0.05073,0.06234,0.07296,0.10626,0.05625,0.05145,-0.06451,-0.04398,0.01943,0.12212,-0.07479,-0.09883,-0.0504,-0.01233,0.03578,-0.05379,-0.06522,-0.096,0.03036,-0.01076,-0.0798,0.00361,-0.08486,0.0031,-0.06765,0.07294,-0.04794,-0.07476,-0.04835,-0.02919,0.01535,-0.00921,0.04481,-0.02201,0.15021,-0.07362,-0.01986,0.08969,0.0119,-0.06653,-0.04372,-0.05243,-0.04065,-0.07179,0.01412,0.14461,0.05613,0.09762,-0.04269,-0.01192,0.04447,-0.05447,-0.00322,0.01366,-0.01664,-0.04649,-0.03913,0.06264,0.00189,-0.02784,0.00134,-0.0225,0.02384,-0.10465,-2e-05,-0.05288,-0.12117,-0.01909,0.00701,-0.02739,0.05094,0.06202,-0.05297,0.16479,0.04703,0.09037,-0.10369,-0.0774,-0.04888,0.02412,-0.16638,-0.04531,-0.04156,0.00487,-0.03356,0.06121,0.0036,-0.12881,0.07503,-0.0178,-0.03881,-0.01747,0.11057,0.11663,0.10446,0.13359,0.11438,0.11963,-0.01697,0.00466,0.05459,-0.04657,0.03046,-0.14597,0.04152,-0.03291,0.17301,-0.03247,0.13309,0.05995,0.10619,-0.04549,-0.10484,-0.07668,0.00558,0.01312,-0.03507,0.03735,-0.02647,0.03052,0.16391,-0.0414,0.12844,-0.06076,0.03796,-0.06015,0.00386,0.00296,0.05434,-0.05172,-0.03514,-0.08776,0.04612,0.10777,0.00865,-0.01193,-0.0331,-0.05704,0.00467,-0.04529,-0.01853,-0.04292,-0.065,0.0114,0.07257,-0.01989,-0.00662,0.04532,-0.05892,-0.09339,0.0201,0.00579,0.00448,0.05211,0.03878,-0.05195,0.12514,-0.05594,-0.01345,0.02279,0.00757,-0.05937,0.05491,-0.04414,-0.05425,-0.03645,-0.05133,0.00687,0.07636,0.01705,-0.00158,0.01973,0.02719,-0.08643,0.0536,0.08187,0.06744,-0.01233,0.09856,-0.02568,0.01473,-0.04506,0.00278,0.02072,0.01596,0.0585,0.09829,0.04312,-0.06744,-0.00317,-0.09403,-0.01425,-0.032,-0.13053,0.0229,-0.0235,0.03913,0.07276,0.02547,-0.0101,-0.02882,0.00235,0.05167,0.00603,0.03785,-0.04145,0.0743,0.01383,-0.0569,0.01526,-0.14763,-0.00679,-0.09432,0.06117,-0.00238,0.10257,-0.01635,0.07605,0.00882,-0.04229,-0.08399,-0.01008,0.09321,0.04243,-0.00926]},{"domain":"thermofluids","key":"grashof_number","name":"Grashof number","package":"thermofluids-ai999x","example":"A vertical plate of height 0.5 m has a surface temperature of 330 K in still air at an air temperature of 300 K. The air has a coefficient of volume expansion of 0.0033 1/K and a kinematic viscosity of 0.000016 m^2/s. What is the Grashof number for natural convection?","v":[-0.00354,-0.03698,0.04856,-0.00909,-0.04451,-0.00751,0.05765,0.0615,-0.01504,-0.01243,-0.04535,-0.0739,0.0127,0.03286,-0.09009,-0.14608,0.04476,0.00904,0.00204,-0.0424,-0.00853,-0.00153,-0.10684,-0.04547,0.07272,-0.13371,0.08349,-0.03656,-0.10113,-0.00999,-0.10949,0.04791,-0.0561,0.00369,-0.02592,-0.05765,0.05674,0.06255,-0.00823,-0.07382,-0.01328,0.03179,0.00202,0.05954,-0.03088,0.02381,0.09459,0.04282,-0.08567,0.02448,-0.01753,0.04192,0.12709,-0.06388,-0.07907,-0.01939,0.04105,0.09043,-0.01557,0.01297,-0.01125,0.00252,0.03744,-0.04343,-0.01394,0.0796,0.01921,-0.0147,-0.01834,0.1546,0.02603,-0.04714,-0.05036,0.00721,0.0724,0.06647,0.00128,0.01856,0.01571,-0.01793,0.03427,0.20485,-0.13279,-0.01125,0.02202,0.09636,0.03804,-0.08988,0.0626,0.06466,-0.07148,-0.05387,0.0171,0.05173,-0.00689,0.02845,-0.05625,-0.02277,0.02518,-0.10201,-0.0707,-0.01538,-0.0084,0.11522,0.0442,0.01996,0.12847,-0.01762,0.01191,-0.10916,0.07112,-0.05099,0.01492,0.05967,0.02641,-0.05586,0.07487,0.00309,-0.05047,-0.04026,-0.01557,-0.06784,0.06986,-0.06875,0.00796,0.03427,-0.00512,0.01186,-0.03374,0.0053,0.1007,-0.02785,-0.01948,-0.05288,-0.05969,0.09789,0.09303,0.11552,-0.09211,-0.09157,-0.0006,-0.04967,0.03907,-0.03962,-0.10369,-0.10375,0.00887,0.05101,-0.0658,0.05929,0.04341,0.01929,-0.03723,0.11452,-0.13865,0.05759,0.08042,-0.04357,-0.0509,-0.0621,-0.05989,-0.0412,-0.06274,0.02429,0.01139,0.05964,0.01769,0.04444,0.00329,-0.03647,0.00894,0.01336,-0.07908,0.09305,0.00055,-0.04777,-0.10446,0.0137,-0.00198,-0.02665,-0.03614,-0.09616,0.01919,-0.06375,0.06139,0.08103,0.00384,0.02916,-0.11863,0.05033,0.11776,-0.03673,-0.0432,0.01778,-0.00013,0.05508,0.02678,0.04183,0.02615,-0.034,-0.03312,0.04157,0.10946,-0.01391,0.05912,-0.03491,0.06009,-0.02825,0.09034,-0.07114,-0.02668,0.00747,0.03779,-0.0363,0.05292,0.04438,0.00556,-0.05163,0.15352,-0.0579,-0.04344,-0.08166,0.17936,-0.01065,-0.10604,-0.02538,0.00888,0.04042,0.07234,0.06247,-0.06336,0.03528,0.02089,-0.10033,0.05187,0.11587,-0.01241,0.01834,0.00096,-0.02627,0.13397,-0.08932,0.07356,0.02178,0.05755,0.03281,0.05915,-0.05239,0.09432,-0.03472,0.07541,-0.08911,-0.14076,-0.06111,-0.00206,-0.00297]},{"domain":"thermofluids","key":"rayleigh_number","name":"Rayleigh number","package":"thermofluids-ai999x","example":"Natural convection from a heated wall has a Grashof number of 100000000 and a Prandtl number of 0.71. What is the Rayleigh number?","v":[0.04044,-0.0082,-0.00492,0.01583,-0.1714,0.01287,0.05583,-0.03739,-0.04257,-0.05277,-0.02109,0.01791,-0.01025,0.07308,-0.02177,-0.10026,-0.05067,-0.01501,0.00064,0.0646,-0.04583,-0.0494,-0.08567,-0.05301,0.10405,0.02185,-0.00769,-0.01354,-0.02993,0.00567,-0.08188,0.08901,-0.06369,0.00918,-0.03605,0.01059,0.01262,0.04652,-0.038,-0.11525,0.10128,-0.0445,0.07713,-0.0043,-0.01202,0.05728,0.06299,0.02803,-0.09046,0.05148,-0.02808,-0.04058,0.09915,-0.08631,-0.07759,-0.07275,-0.00214,-0.02009,-0.11798,-0.00357,-0.07682,-0.06742,0.10069,0.09244,0.01461,0.07063,-0.06745,-0.02514,-0.04776,0.06343,-0.00648,0.07286,0.0273,-0.04666,0.07358,0.02945,0.06895,0.05916,-0.09768,-0.00624,0.00263,0.15633,-0.07871,0.008,0.05189,0.07704,0.00983,-0.12655,0.07924,-0.03764,-0.08214,-0.00413,-0.00258,0.03488,-0.05348,0.00462,-0.04691,-0.02229,-0.07645,-0.09466,-0.00275,-0.08252,-0.0118,0.08288,0.09259,0.0771,0.16318,-0.01223,-0.00926,-0.04214,-0.01423,-0.05942,0.02168,-0.03841,0.02201,0.00665,0.1019,-0.07666,-0.03017,-0.06176,-0.00471,-0.17231,0.07866,-0.06248,0.03111,0.00506,-0.07481,0.0462,-0.01612,0.029,0.12071,-0.03657,-0.02451,0.04972,-0.04909,0.08223,0.09968,0.1226,-0.05745,-0.00278,0.01233,0.11028,0.06996,-0.0014,0.01124,-0.09218,0.00711,-0.02144,-0.02045,-0.00455,0.01808,0.02427,-0.00952,0.0601,-0.04322,0.04478,0.04364,-0.01347,-0.02304,-0.1258,-0.07439,0.06965,-0.03241,-0.0531,0.03989,0.03907,-0.05223,0.08018,-0.01715,0.03719,-0.01693,0.00545,-0.09298,-0.05841,0.01771,-0.05259,-0.00122,0.00017,-0.0311,-0.14234,-0.08466,-0.03856,-0.02214,0.00513,0.15073,-0.0877,0.01264,0.05903,-0.03306,0.09183,-0.07474,-0.10981,-0.02809,-0.04024,0.0609,0.07091,0.01264,0.06999,-0.08815,0.05208,-0.01696,-0.01393,0.17279,0.13268,0.04989,0.0393,0.0487,0.01642,-0.00327,-0.01171,0.0123,0.06629,0.05632,0.03653,0.05215,-0.04087,0.06047,-0.02107,0.1316,-0.00346,0.00153,-0.09013,0.10285,-0.04974,-0.12455,-0.00113,0.02182,0.01912,0.06103,-0.06131,-0.03103,0.01116,0.01125,0.01888,0.00612,0.09463,-0.0142,-0.04607,-0.13622,-0.02876,0.11571,-0.09728,0.03236,-0.02254,-0.03692,0.03994,0.01939,0.02478,0.02048,-0.03219,-0.06869,-0.01735,-0.01301,0.05905,0.08602,0.01533]},{"domain":"thermofluids","key":"blackbody_emissive_power","name":"Emissive power of a blackbody (Stefan-Boltzmann law)","package":"thermofluids-ai999x","example":"What is the emissive power of a blackbody at 1000 K?","v":[0.08659,-0.13296,-0.0079,-0.01251,0.10189,0.0764,-0.05595,-0.04009,0.04117,-0.02271,0.06306,-0.04429,0.01126,-0.02058,0.01526,0.02136,0.07855,-0.01047,0.15156,-0.04115,0.12219,-0.1411,-0.0372,-0.05163,-0.08568,-0.00045,0.06271,0.03235,-0.00988,0.08398,0.10651,-0.02029,-0.00642,0.06143,-0.07712,0.01093,-0.01877,0.08329,0.06002,-0.09905,-0.0243,-0.02844,-0.16396,0.04884,-0.03531,-0.02973,-0.03971,-0.0273,0.08867,0.08868,-0.01192,-0.01779,0.07137,0.05229,0.01636,-0.16563,0.03776,0.0576,0.06917,0.08832,-0.07958,-0.02298,0.03954,0.02174,0.00392,-0.12288,-0.03298,0.05925,0.12353,0.06564,-0.02099,0.04054,-0.02969,0.03066,-0.0064,0.02248,0.07413,-0.1065,-0.0413,0.01129,0.06203,0.04946,-0.07018,-0.0891,0.06773,0.04425,0.04789,0.00551,-0.08563,0.02414,0.0388,0.05546,-0.04308,-0.04764,0.00195,-0.06127,-0.0429,-0.0753,0.10935,0.03713,0.00277,-0.01519,-0.01704,-0.05343,-0.10331,0.03486,0.04617,-0.0936,-0.04478,-0.02274,-0.0181,0.02753,0.0841,-0.01936,-0.00297,-0.0533,0.01453,-0.0628,-0.04474,0.02986,-0.067,-0.02449,-0.01616,-0.12379,-0.01889,-0.07799,0.03851,-0.03085,-0.06249,0.00087,0.01637,0.08328,-0.09542,-0.04112,-0.12564,-0.04512,0.06165,-0.0638,-0.00858,0.05451,-0.09397,0.029,0.01243,0.04527,-0.04923,-0.00305,-0.00183,-0.0318,-0.08182,-0.13458,0.03402,0.15847,-0.12281,0.03557,-0.05452,0.0719,-0.08171,0.05234,0.09286,-0.01522,-0.08769,0.01039,-0.03233,0.0338,-0.14777,0.0437,-0.01245,0.11387,-0.03336,-0.05086,0.09571,-0.05154,-0.01621,-0.01211,0.04414,-0.03973,0.00541,0.07977,0.02836,0.02221,0.09812,-0.08494,-0.03945,-0.01053,-0.01463,0.08042,-0.04167,0.03965,-0.13276,-0.08772,-0.05801,0.03024,-0.04442,0.0011,-0.01981,0.04777,-0.01294,0.06846,0.0161,-0.0039,0.06904,-0.02073,0.13023,0.03595,0.11084,0.10293,-0.03811,0.01152,-0.00956,0.00914,-0.08698,-0.0029,0.01736,-0.01105,0.11481,0.05713,-0.01192,-0.08348,0.0194,-0.02796,-0.00599,-0.05697,-0.02063,-0.01508,0.008,0.03881,0.01662,-0.09561,0.03252,-0.0131,0.12587,0.05361,0.01793,0.02597,0.02464,0.10232,0.01125,-0.11544,-0.00522,-0.00937,-0.01311,0.05456,-0.027,0.13757,0.03568,0.10109,-0.01444,-0.03899,-0.00691,0.02681,0.05175,0.00119,0.06703,0.06295,0.00406,0.01757]},{"domain":"thermofluids","key":"radiation_net_exchange","name":"Net radiation exchange of a small grey surface with large surroundings","package":"thermofluids-ai999x","example":"A surface of area 0.5 m^2 with an emissivity of 0.8 is at a surface temperature of 500 K in a large room whose surroundings are at 300 K. What is the net radiation heat transfer from the surface?","v":[0.1024,-0.15477,0.00556,0.07573,0.03005,-0.04611,-0.0897,-0.02788,-0.02404,0.01585,0.02279,-0.11325,0.06215,0.01987,-0.08034,-0.00903,0.0995,-0.06857,0.0324,0.02697,0.05384,-0.11718,0.01778,-0.05591,-0.08416,-0.06327,0.06027,-0.00367,-0.00909,0.04479,0.06837,0.01059,0.01273,0.04445,-0.07033,0.02923,0.02497,0.03061,0.03743,-0.03444,0.1032,-0.0137,-0.09947,0.10063,-0.02439,0.07205,0.09039,-0.03029,0.02707,0.1401,0.01046,-0.04617,0.14408,0.01151,-0.00097,-0.09085,0.08955,0.10014,0.03429,0.0751,-0.09643,-0.05659,0.01279,0.10937,-0.04711,0.00216,-0.10606,0.13722,0.06039,0.04641,0.00127,0.00711,-0.07974,0.0523,-0.03218,-0.05147,-0.00928,-0.0829,-0.10393,-0.02999,0.03005,0.08872,-0.07017,0.00301,0.03975,0.02428,-0.01277,0.01616,-0.00135,0.00287,-0.04564,-0.00084,0.0299,-0.0234,-0.06723,-0.02665,-0.09835,-0.06558,0.12975,0.00865,0.06195,0.04912,-0.0133,-0.00221,-0.0619,0.02084,0.1153,-0.09016,-0.00928,-0.08307,0.03959,-0.02757,0.11345,0.0791,-0.01531,-0.07955,-0.00538,-0.00454,-0.0688,0.08744,-0.1562,-0.05027,0.00477,-0.12097,-0.11083,-0.01298,-0.00595,0.00823,-0.07364,-0.03293,0.05736,0.01936,-0.06316,-0.07034,-0.16467,-0.07156,0.07869,0.02082,-0.09968,-0.03008,-0.00578,-0.01567,-0.0619,-0.04839,-0.02264,-0.01163,0.07419,0.03098,-0.1163,-0.04906,0.1062,0.02513,-0.06591,0.10714,0.02914,-0.00696,-0.04594,-0.00163,0.00638,0.03912,-0.02442,0.07972,-0.06891,0.01588,-0.04488,0.07429,-0.01992,0.1141,-0.03669,-0.06353,0.01067,0.03886,-0.03063,0.03552,0.06739,0.01356,0.00657,0.0974,0.02939,0.00349,-0.03385,-0.04551,-0.02414,-0.06507,-0.05641,0.06203,-0.03876,0.02458,-0.10471,-0.05884,-0.01081,0.04923,-0.00923,-0.02897,-0.01253,0.0138,0.02715,0.12224,0.0623,-0.0797,0.02158,-0.00933,0.18725,0.01632,0.05132,0.04258,-0.04221,0.03622,-0.03049,0.03208,-0.0268,-0.03671,0.02546,0.04248,0.01863,0.01436,-0.01127,-0.08899,0.06436,0.00976,0.01267,-0.0287,-0.04029,0.01759,0.04672,0.06318,-0.01489,-0.04269,0.06995,-0.03502,0.05416,0.10893,0.06231,0.06274,-0.00042,-0.00333,0.04369,-0.14998,-0.13515,0.0191,0.04802,0.01796,-0.00862,0.08825,0.03448,0.09987,0.06389,-0.08337,-0.00659,0.00222,0.07727,0.05572,-0.02335,0.00396,-0.06057,0.07583]},{"domain":"thermofluids","key":"radiation_parallel_plates","name":"Net radiation between two large parallel grey plates","package":"thermofluids-ai999x","example":"Two large parallel plates exchange radiation. The first plate is at 800 K and the second plate is at 400 K. The emissivity of the first plate is 0.8 and the emissivity of the second plate is 0.6. What is the net radiation heat flux between them?","v":[0.04096,-0.13423,0.06677,0.01997,-0.05142,-0.01873,-0.06834,-0.08159,-0.00705,0.07373,0.03189,-0.01018,-0.02137,0.03617,-0.0206,-0.09663,0.00466,0.02782,0.10297,0.03691,0.17747,-0.04395,0.02382,-0.04947,-0.05255,0.01175,-0.06402,0.00075,-0.09565,0.00261,0.04654,0.06759,-0.01458,-0.01812,-0.00632,0.12019,0.02691,0.00752,-0.00998,-0.04374,0.07607,4e-05,-0.01776,-0.01159,-0.00776,-0.0335,0.0789,-0.00267,-0.0208,0.13542,-0.14661,0.05399,0.11937,0.00337,0.00468,-0.04919,0.12015,0.13957,0.09346,0.01353,-0.01705,-0.01418,-0.03622,0.00233,-0.10608,0.04829,-0.04437,0.03799,0.07073,0.00332,0.0982,0.01304,-0.05463,0.00476,-0.04664,-0.01025,0.0187,-0.04126,-0.00164,-0.06552,0.00146,-0.04154,0.03645,0.02812,0.01418,-0.02808,0.02848,0.05576,-0.03522,0.01739,-0.0212,0.00825,0.0829,-0.06384,-0.06349,-0.06668,-0.00272,-0.06037,0.00434,-0.04899,-0.0088,-0.00823,-0.06051,0.08741,-0.1015,0.03836,0.10594,-0.1217,0.02937,-0.04131,0.00857,-0.03856,0.04167,0.02481,0.10931,-0.12751,0.11914,0.04625,-0.04025,0.09603,-0.14792,-0.02993,0.03933,-0.0337,0.00241,-0.02314,0.03207,0.01513,-0.06132,0.04783,0.07407,0.09292,-0.04693,-0.04837,-0.2579,-0.09082,0.02913,0.0686,-0.02052,0.07456,-0.00307,-0.00467,-0.03546,-0.05878,0.01443,0.04544,-0.01714,0.01557,-0.00903,0.0499,0.04414,0.08802,-0.02576,0.12207,-0.03594,-0.03811,-0.07923,-0.07329,-0.02683,0.05231,-0.00964,0.0297,-0.09939,-0.04539,-0.01174,0.03521,-0.10961,0.09314,-0.02201,-0.03399,-0.04106,-0.01305,-0.1063,-0.00047,0.06532,0.05517,-0.03711,0.11015,-0.04048,-0.1466,-0.00108,-0.04049,0.00695,-0.06767,-0.03134,0.08979,-0.06915,-0.01888,-0.03213,-0.02731,-0.04362,0.12637,0.00525,0.07599,-0.03009,-0.04099,0.03738,0.06101,0.06938,-0.08253,0.06376,-0.00015,0.0921,0.00995,0.04981,0.01414,-0.05842,0.00458,0.00997,0.0489,-0.05498,0.04752,-0.03439,-0.02497,0.08565,0.03675,-0.06269,0.00643,0.00816,-0.00748,0.03075,-0.07559,0.0501,-0.07236,0.02392,0.02448,-0.0478,-0.06398,0.1355,0.05132,0.00116,0.06009,0.02991,0.00718,0.08749,-0.03265,0.01191,-0.13515,-0.04669,-0.02264,0.04654,-0.09099,-0.05098,0.06884,0.04622,-0.00403,-0.0563,-0.04725,0.08259,0.07369,0.0473,0.04544,-0.1049,0.04585,-0.02966,0.13869]},{"domain":"thermofluids","key":"wien_displacement","name":"Wien's displacement law","package":"thermofluids-ai999x","example":"A star has a surface temperature of 5800 K. At what peak wavelength does it emit most strongly?","v":[0.07966,-0.00587,0.00647,0.05583,-0.03489,0.09853,-0.0344,-0.09657,0.03658,0.03549,0.00376,0.0266,-0.02864,0.0978,0.0372,0.03397,-0.0026,-0.02679,0.06806,-0.09006,0.04427,-0.05527,-0.04783,-0.05105,-0.01829,-0.00341,-0.01579,-0.00607,0.01912,0.13796,0.12918,-0.0473,0.03523,0.05063,-0.05686,-0.01961,-0.04522,-0.00769,-0.03532,-0.1478,-0.0948,-0.05147,-0.00482,0.07084,-0.02808,-0.00714,-0.00768,-0.02141,0.10151,0.13471,0.05297,0.01785,0.04203,0.06663,0.00207,-0.10467,-0.05263,0.03084,-0.01606,0.14484,-0.03426,0.01224,0.06491,0.05116,0.0438,-0.12637,-0.04294,0.04879,0.09172,0.01781,0.00024,0.05261,0.05433,0.00187,-0.0304,0.05364,-0.02495,-0.09589,0.00887,-0.09036,0.11449,0.07479,-0.07019,-0.063,0.06667,0.04145,0.02833,-0.02176,-0.10266,-0.02337,-0.00089,0.09243,-0.05377,-0.00409,0.05326,-0.12921,0.03933,-0.09555,0.04624,0.14378,-0.03259,0.04487,0.02171,-0.0695,-0.07402,0.06363,-0.06852,0.00661,-0.07497,-0.08938,-0.06118,-0.04819,0.12888,-0.04097,-0.0155,0.02347,-0.05887,-0.03948,-0.02451,0.05901,-0.0012,0.02635,-0.00021,-0.16135,-0.09363,0.02974,0.07864,-0.04214,-0.09433,0.02771,-0.03938,0.08296,-0.01175,0.00328,-0.1069,-0.00112,0.04989,0.00486,0.068,0.00456,-0.05466,0.05572,0.05319,-0.04273,-0.01343,0.03404,0.07492,-0.07029,-0.11577,-0.06638,0.01719,0.08825,-0.10271,0.04697,0.00697,0.0536,-0.03037,0.05116,-0.02074,-0.02941,-0.07412,0.02653,-0.04623,-0.01915,-0.18727,0.03197,0.0921,0.00451,0.01155,0.02197,0.09342,0.07089,0.03598,-0.05186,0.0405,-0.02517,0.05594,-0.05097,0.09456,-0.0406,0.06051,-0.04262,-0.07617,0.01598,-0.07608,0.04884,-0.02257,0.07606,-0.04996,-0.01893,-0.08374,0.02164,-0.01229,0.01007,0.00917,0.00282,0.03793,0.09311,-0.03103,-0.08787,0.07963,0.02785,0.10875,0.07009,0.05606,0.00814,-0.07668,0.04751,-0.10932,-0.11001,-0.08646,-0.01702,-0.07722,-0.00914,0.1134,0.15472,-0.05771,0.01517,-0.03472,0.00927,-0.06405,-0.09166,-0.02523,-0.04371,0.03304,0.07867,-0.04265,0.02743,0.07643,-0.09859,0.07578,0.10477,0.00481,0.02974,0.04366,0.07044,-0.04651,0.00849,-0.0254,-0.03611,-0.00484,0.10124,-0.01129,0.04894,-0.04817,0.05289,-0.07292,-0.03174,-0.07151,-0.00712,-0.00847,0.03128,0.03099,0.02113,-0.07846,-0.02469]},{"domain":"thermofluids","key":"radiation_heat_transfer_coefficient","name":"Linearised radiation heat transfer coefficient","package":"thermofluids-ai999x","example":"A surface with an emissivity of 0.9 is at a surface temperature of 400 K and its surroundings are at 300 K. What is the radiation heat transfer coefficient?","v":[0.15735,-0.02298,-0.03185,0.03129,0.01201,-0.02722,-0.10354,-0.03279,0.00575,-0.03113,-0.01264,-0.17272,0.00658,0.06272,-0.0858,0.04315,0.08339,-0.09046,0.10088,-0.04821,0.0605,-0.09113,-0.04023,-0.05216,0.02397,-0.06886,0.09346,-0.07439,0.03844,-0.0226,0.06727,0.07393,-0.0214,0.05476,-0.03875,-0.0044,0.03797,0.04723,-0.02826,-0.0496,-0.02867,-0.0958,-0.05921,0.10307,-0.09136,-0.01222,0.04313,0.02722,-0.02788,0.06237,0.00126,0.0116,0.15054,-0.01591,0.00567,-0.08481,0.11627,0.08251,0.02136,0.12527,-0.09141,-0.04172,0.05495,0.01189,-0.06633,-0.02141,-0.06168,0.04262,0.12263,0.01977,-0.01674,-0.03451,-0.06702,0.0594,0.07267,-0.02707,0.00591,-0.06984,-0.01527,-0.01682,0.03406,0.11751,-0.06735,-0.0003,0.10641,-0.059,-0.04779,-0.02073,-0.04768,-0.00601,-0.05159,-0.01055,-0.01909,-0.02842,-0.01953,-0.07671,-0.13467,-0.12065,0.09983,-0.03672,0.05739,-0.06139,-0.03706,0.01375,-0.02417,0.04831,0.12117,-0.04357,0.02282,-0.08922,0.0846,-0.00244,0.06585,0.04057,0.02554,-0.09497,0.04091,-0.02032,-0.09633,0.01123,-0.19741,-0.07496,-0.0257,-0.11199,-0.09627,0.01376,0.04388,0.04234,-0.04611,0.01313,0.0234,0.01228,-0.00447,-0.05471,-0.13891,-0.05343,0.04029,-0.06217,-0.0773,-0.03061,0.00921,-0.08864,0.0447,-0.02427,0.01449,0.0644,0.01462,0.08305,-0.14953,-0.05318,0.05763,0.07074,-0.00521,0.05752,-0.02239,-0.03992,-0.02291,-0.02786,-0.03742,0.09036,-0.02275,0.05026,-0.09463,0.07542,-0.03442,-0.01059,-0.00562,-0.01154,-0.04199,0.01478,0.04103,0.03244,-0.09529,0.0427,-0.04108,0.03159,-0.02027,0.05419,0.02996,0.02648,0.0541,-0.05995,-0.0555,-0.02956,-0.07572,0.05468,-0.01226,0.01831,-0.09128,0.00243,0.01816,0.08153,-0.03511,0.007,-0.02018,0.01367,0.03636,0.15641,0.10631,-0.04354,0.0426,0.08663,0.20421,0.0433,0.12085,0.05931,0.00022,0.07577,0.00077,-0.07014,0.00464,0.03763,0.09075,0.02968,0.03709,0.00946,0.0152,-0.04824,0.01335,0.00846,-0.04562,-0.03778,-0.00885,0.01494,-0.03764,0.06329,0.09039,0.04453,0.04286,-0.00119,0.07626,0.05391,0.00727,-0.01138,-0.02153,-0.0061,0.05936,-0.08651,-0.12006,0.04431,0.047,-0.01493,0.03638,0.0501,0.04742,0.12276,0.02248,-0.06187,-0.00412,0.03066,0.06885,0.02758,-0.03422,0.01162,-0.06531,0.03398]},{"domain":"thermofluids","key":"infinite_fin_heat_rate","name":"Heat transfer rate of a very long fin","package":"thermofluids-ai999x","example":"A very long aluminium pin fin has a perimeter of 0.0314 m, a cross-sectional area of 0.0000785 m^2 and a thermal conductivity of 200 W/(m*K). Its base temperature is 100 °C, the air temperature is 25 °C and the heat transfer coefficient is 25 W/(m^2*K). What is the rate of heat transfer from the fin?","v":[0.01756,-0.08365,0.04361,0.0023,0.04709,-0.0775,-0.06328,-0.04636,-0.08712,-0.00177,-0.02546,-0.03017,-0.00215,0.03006,-0.01289,0.05522,0.02619,0.03105,-0.00285,0.00139,-0.03662,0.05067,0.03436,-0.05732,0.12244,-0.08484,-0.03409,0.01129,0.05462,0.0966,-0.06454,0.00198,-0.00672,0.08496,-0.00539,0.05113,0.09437,-0.01282,0.00575,0.07592,0.0832,-0.02206,0.03733,0.1157,-0.01735,-0.00811,0.10736,7e-05,-0.02748,-0.03484,-0.02561,0.05502,0.15671,-0.0573,0.00493,-0.10842,-0.01235,0.07229,0.1212,-0.0005,-0.01045,-0.07048,0.0052,0.07525,-0.02056,0.09632,-0.07608,0.00221,-0.11796,0.02458,0.03571,0.01846,-0.14652,-0.03287,0.07464,-0.02905,-0.00254,-0.06499,0.01344,-0.11485,-0.053,0.022,-0.0422,-0.00964,0.05549,-0.03972,-0.10137,-0.04806,-0.04121,-0.00989,-0.0355,-0.11772,-0.01604,0.05365,-0.04275,-0.01286,-0.09546,0.07061,0.03677,-0.07885,0.15972,0.13588,-0.04096,0.13881,0.00273,-0.05612,0.10318,0.02286,0.01497,-0.05953,0.00534,-0.00793,-0.01972,0.14107,-0.05681,-0.0403,0.05392,0.01229,-0.05013,-0.05922,-0.04037,-0.0193,0.06259,-0.00298,0.02239,0.08377,-0.00869,-0.00839,-0.02359,-0.05539,0.03706,4e-05,0.0442,-0.10108,-0.02748,-0.03387,0.0822,-0.0134,-0.01939,-0.11438,-0.01039,-0.07239,0.00392,-0.07736,-0.01144,0.02946,-0.11544,0.0541,-0.07709,0.02351,0.05018,0.09365,-0.17292,-0.00957,0.02916,0.11757,0.0102,0.01396,-0.05252,-0.04417,0.04266,-0.0314,-0.0171,0.0287,0.0242,-0.02449,-0.03159,-0.00876,0.00277,-0.06981,0.01304,0.03796,0.08647,0.11001,-0.02348,0.00536,-0.00278,-0.0046,0.00207,0.04376,-0.06015,0.0156,-0.0415,-0.07743,-0.11314,0.09572,0.0047,-0.04138,-0.03178,-0.00336,0.02433,0.01719,-0.04859,-0.03345,-0.0058,-0.01413,0.03623,0.01357,0.16725,-0.08866,0.09207,0.01549,0.149,0.04661,0.02197,-0.02625,-0.03351,-0.03181,-0.0138,0.03092,-0.08689,-0.01739,0.08295,0.00789,0.03851,-0.06938,-0.14211,-0.02226,0.111,-0.04127,-0.04408,-0.07988,-0.03181,0.02177,0.07378,0.00654,-0.035,0.12018,0.04489,-0.05712,-0.10292,0.02287,0.02722,0.02061,-0.04653,-0.02574,0.14715,0.03635,-0.02533,0.06132,0.07412,0.08516,-0.06787,-0.06924,-0.039,0.12911,0.04978,-0.02304,0.06698,-0.03307,0.16215,0.06267,-0.00626,-0.05092,0.01963,-0.01312]},{"domain":"thermofluids","key":"lumped_capacitance_temperature","name":"Temperature of a lumped body cooling or heating in a fluid","package":"thermofluids-ai999x","example":"A small steel part with a volume of 0.000005 m^3, a surface area of 0.002 m^2, a density of 7800 kg/m^3 and a specific heat of 450 J/(kg*K) is initially at 300 °C. Treated as a lumped system, it cools in air at an ambient temperature of 25 °C with a heat transfer coefficient of 40 W/(m^2*K). What is its temperature after 120 s?","v":[0.05062,-0.04719,-0.04089,0.01137,-0.04828,-0.0305,-0.0019,-0.04558,0.03516,-0.05217,-0.02463,-0.04824,-0.065,-0.07744,-0.0316,-0.02834,0.0004,-0.02525,0.03453,-0.01209,0.04295,0.01103,-0.02848,-0.04343,0.06474,-0.03564,0.02085,0.03397,0.00553,-0.02357,0.02992,0.08969,0.02364,0.02283,-0.0277,0.04153,0.04901,0.00493,0.00463,-0.03515,-0.00916,-0.03065,-0.09974,0.03123,-0.09653,-0.03504,0.12909,0.04302,-0.03693,-0.03003,-0.09844,-0.12616,0.16365,-0.11993,-0.00373,-0.08243,0.08661,0.18088,0.01418,0.01313,-0.03194,0.00906,0.08074,-0.00808,-0.04228,0.00664,-0.0237,-0.01453,0.07145,0.0767,0.00823,-0.12061,-0.12532,-0.10702,0.08819,-0.00167,0.00234,0.00202,0.00583,-0.03514,-0.00588,0.09334,-0.0722,-0.0556,0.09831,0.02598,-0.06039,-0.06911,-0.04232,0.05572,0.0189,0.00526,0.01839,0.0192,0.03714,-0.02421,-0.02772,0.01722,0.04908,-0.02813,0.10285,0.01509,-0.05382,0.04426,-0.06093,0.00665,0.058,0.16028,0.03223,-0.0842,0.03081,-0.00492,0.03931,0.13029,-0.00059,0.00908,0.1264,0.08253,-0.01785,0.00124,-0.0719,-0.05388,0.03579,-0.04938,0.00413,0.01208,-0.01149,0.01972,0.06253,0.01536,0.11634,-0.00423,0.00373,-0.06337,-0.05614,-0.06537,0.10509,-0.00873,-0.09187,-0.16862,-0.02499,-0.06506,0.13206,-0.09321,-0.14371,0.0227,0.00868,0.08318,-0.17058,0.04465,0.10228,-0.01177,0.00713,0.04985,-0.07951,-0.04371,-0.02886,-0.01328,-0.06937,0.01555,-0.05966,-0.01298,-0.08121,0.15099,-0.01947,0.00601,0.06227,-0.08891,-0.00211,0.02889,0.05725,0.11083,-0.11943,-0.00507,0.0266,0.00453,-0.06876,-0.02128,-0.02795,0.00755,0.081,0.00052,-0.00687,-0.07327,-0.00906,-0.00325,-0.03574,-0.00241,-0.11489,-0.00419,0.07033,-0.0277,-0.06174,-0.01208,0.02807,0.07994,0.11108,0.0616,0.11334,-0.0697,-0.00876,-0.00423,0.05874,-0.04087,0.00822,0.04668,-0.02734,-0.04948,0.01593,-0.05659,0.06861,-0.12949,0.13101,-0.03909,0.12562,-0.00547,-0.01774,-0.07735,0.06298,0.05034,0.02766,-0.0611,0.00115,-0.06037,-0.08628,0.07114,0.09283,0.00159,0.00817,0.03454,-0.05131,0.05686,0.03419,-0.01127,-0.005,0.0237,-0.02369,-0.04763,0.03958,-0.00858,0.17161,-0.05507,-0.07784,0.08827,0.04014,0.03029,0.08766,0.01063,0.02284,0.05575,0.08128,0.02457,-0.00264,-0.01801,-0.0293,0.01301]},{"domain":"thermofluids","key":"lumped_time_constant","name":"Thermal time constant of a lumped body","package":"thermofluids-ai999x","example":"A lumped steel part has a volume of 0.000005 m^3, a surface area of 0.002 m^2, a density of 7800 kg/m^3, a specific heat of 450 J/(kg*K) and a heat transfer coefficient of 40 W/(m^2*K). What is its time constant?","v":[0.06279,-0.02802,-0.05494,0.00835,0.00909,-0.03767,0.0664,-0.05544,0.08292,-0.00776,0.02378,0.05131,0.00415,-0.02602,0.03102,0.00448,-0.01979,0.00722,0.03939,0.02603,0.04074,-0.01491,-0.05888,-0.0441,0.14297,-0.00923,0.01152,0.03574,-0.00345,-0.04299,0.0293,0.02468,-0.00889,0.02675,0.03241,-0.02105,0.07255,0.04869,0.0232,-0.02358,0.03256,0.02431,-0.1165,-0.02442,-0.07123,-0.05308,0.10394,0.02125,0.02843,-0.08143,-0.0763,-0.09954,0.0974,-0.0784,0.03438,-0.09557,0.09282,0.16146,0.06732,0.14406,-0.00788,-0.00637,0.05136,0.06026,0.01351,-0.06531,-0.03155,0.01977,0.05177,0.06476,-0.01468,-0.08921,-0.12818,-0.10592,0.10683,-0.01438,-0.02684,-0.04716,-0.0084,0.03804,-0.06146,0.04693,-0.04908,-0.04305,0.06246,0.05587,-0.04925,-0.08402,-0.01949,0.04285,-0.05873,-0.06085,0.0005,0.00197,-0.01938,-0.00222,-0.10479,0.01877,0.06342,0.02814,0.07668,0.03215,-0.03453,0.03302,-0.10598,0.01684,0.04644,0.13181,-0.02125,-0.07927,-0.0252,-0.02204,-0.01671,0.06617,-0.04869,-0.01015,0.16988,0.08209,-0.05606,0.06421,-0.10583,-0.03384,0.02767,-0.02634,-0.03908,0.00211,-0.01388,-0.0017,0.05788,0.02488,0.09628,-0.00985,0.02827,-0.04442,0.02552,-0.05309,0.04315,-0.08768,-0.04032,-0.07806,-0.00451,-0.04285,0.16086,-0.10082,-0.16423,-0.02646,-0.07047,0.01319,-0.11772,-0.01175,0.10802,-0.02732,0.02763,-0.03882,-0.10281,0.01741,-0.02227,-0.02447,-0.12162,-0.04463,-0.04043,0.06061,-0.04984,0.14684,0.03804,0.03128,0.03548,-0.05798,0.01903,-0.01774,0.00548,0.05375,-0.1232,-0.04885,-0.00977,0.0246,-0.05472,0.06608,-0.02014,-0.04781,0.09872,0.02574,0.06149,-0.06992,0.04201,-0.0705,0.04783,0.00253,-0.14796,-0.04582,0.0528,-0.04481,-0.05512,0.0242,0.02005,0.04202,0.14133,0.05388,0.08528,-0.05536,-0.02102,-0.03693,0.0028,0.02627,0.06309,-0.01391,0.00107,0.0191,0.01082,-0.01334,0.01101,-0.1148,0.13065,-0.09686,0.13309,0.05899,-0.03984,-0.08732,0.00205,0.03987,-0.05155,0.00353,-0.06044,-0.10582,0.00652,0.0649,0.11598,0.02988,-0.00167,-0.03307,0.00216,0.06049,0.03177,-0.12852,-0.0221,-0.00063,-0.05939,-0.0641,-0.00301,0.0198,0.0608,-0.03147,-0.06141,0.08562,0.1187,0.03117,0.10383,-0.01291,0.05032,0.08448,0.08823,0.05524,-0.06126,0.00889,-0.0326,-0.03745]},{"domain":"thermofluids","key":"ntu_definition","name":"Number of transfer units of a heat exchanger","package":"thermofluids-ai999x","example":"A heat exchanger has an overall heat transfer coefficient of 500 W/(m^2*K), an area of 10 m^2 and a minimum heat capacity rate of 2000 W/K. What is the number of transfer units?","v":[0.00633,-0.06073,-0.11083,0.1015,-0.08019,0.02339,-0.04651,-0.05558,0.02312,-0.06918,0.02431,-0.09338,0.03785,0.08495,-0.02457,0.03174,0.06925,-0.02722,0.10736,0.02745,-0.04066,0.01537,-0.00542,-0.07217,-0.02298,0.03296,0.10078,0.0548,-0.01124,0.08515,-0.09626,0.08007,0.00569,0.05199,-0.09456,0.01108,-0.02132,0.00628,-0.05118,0.04305,0.07215,0.07857,0.13908,0.07177,0.01073,0.01139,-0.04503,-0.01841,-0.00129,0.06834,0.07264,0.00302,0.09606,0.04199,0.0167,-0.03138,0.03755,-0.05632,-0.10182,0.03582,-0.09177,-0.11075,-0.02577,0.14482,-0.01583,0.01286,-0.08822,0.09648,0.00166,0.07381,-0.01577,0.00483,-0.00661,0.01257,-0.08881,0.02608,0.02519,0.01233,0.03836,0.09875,-0.03525,0.03976,-0.07761,0.01298,-0.00147,0.02703,-0.04013,0.00187,0.076,0.05402,-0.03592,-0.10945,0.09047,-0.00661,-0.14286,-0.01053,-0.12032,-0.0275,0.02773,-0.02346,0.19567,0.13979,0.05024,0.02374,0.01322,-0.01323,0.0189,-0.05729,-0.02693,-0.01476,0.01214,-0.01544,-0.01522,-0.0107,-0.09628,-0.0423,0.03926,-0.00887,-0.01784,0.02146,-0.08881,-0.04487,0.06664,0.14623,-0.03466,-0.04138,-0.01349,-0.03189,-0.00591,-0.13954,-0.09432,-0.07749,0.02709,-0.00683,-0.04822,-0.10816,0.04613,0.06272,0.03887,0.09055,0.02413,-0.14011,0.01911,-0.01941,-0.08618,-0.0579,-0.05443,0.03934,0.02738,-0.00486,0.02358,0.03208,-0.00481,0.04893,-0.08839,0.03463,-0.09484,-0.04583,-0.02412,0.10595,0.1144,0.11559,-0.03979,0.13948,0.03992,-0.00162,-0.0112,0.02837,-0.04809,-0.02524,-0.05253,0.05292,0.08451,0.01171,-0.06352,0.00645,-0.00439,-0.00671,-0.03101,0.08963,-0.03185,0.0451,-0.04074,-0.02296,-0.10991,0.0071,-0.0368,0.00514,-0.08971,0.04514,-0.02408,0.00904,-0.08737,-0.00117,-0.14139,-0.02426,0.01588,0.05434,-0.00905,0.00086,0.00459,-0.08188,0.0214,-0.07573,0.09557,0.01193,-0.07652,-0.06098,-0.03004,0.00489,-0.02975,-0.02472,0.0301,0.08916,0.01046,-0.04245,0.0543,-0.05723,0.10889,0.06504,-0.06294,0.00115,-0.06985,-0.05251,0.01501,-0.01799,0.01655,0.06882,0.07809,-0.04097,-0.06041,0.06596,-0.00593,0.08336,0.04871,0.1204,0.01088,-0.03748,-0.03383,-0.01136,-0.00988,-0.04891,-0.06359,-0.05611,0.07664,0.06419,0.12098,-0.11242,-0.01021,-0.10862,0.00501,0.10785,-0.02115,-0.02308,0.12115,-0.06626]},{"domain":"thermofluids","key":"effectiveness_parallel_flow","name":"Effectiveness of a parallel-flow heat exchanger","package":"thermofluids-ai999x","example":"A parallel flow heat exchanger has a number of transfer units of 1 and a capacity rate ratio of 0.5. What is its effectiveness?","v":[0.02973,-0.04963,-0.06384,0.08839,-0.07465,0.0506,-0.05404,-0.01231,0.05621,0.02401,-0.04253,-0.09622,0.08709,0.07375,-0.03135,0.05772,-0.06177,0.0349,0.10631,0.06444,0.14227,0.04329,0.03115,-0.10309,0.01575,0.00752,-0.00966,0.10241,0.01124,-0.01047,-0.07783,0.00061,0.0519,0.04052,-0.09945,0.1203,-0.02859,-0.05842,-0.07119,-0.01014,0.13175,0.04608,0.11995,-0.01731,0.01999,-0.04522,0.02265,0.01002,-0.04006,0.04944,0.03973,-0.01963,0.00807,-0.04889,-0.03833,-0.00298,0.03564,-0.04675,-0.13818,-0.06741,-0.04302,-0.18426,0.03532,0.03704,-0.13302,0.00724,-0.00443,0.01417,-0.10341,0.02419,0.11063,0.06496,0.11053,-0.07828,-0.12238,0.05583,0.04018,-0.03072,0.06024,0.00292,-0.02805,0.04209,-0.04192,0.01748,-0.01332,-0.04127,0.01239,0.05377,0.06536,-0.08203,-0.08696,0.07365,0.13003,0.01527,-0.11115,0.05295,-0.14297,-0.03338,-0.00647,-0.08495,0.07294,0.07327,-0.03904,0.09849,0.01444,-0.04873,0.05484,-0.11097,0.00957,0.03017,0.08059,0.01518,0.05168,-0.00901,-0.01529,-0.0426,0.11106,0.00963,-0.02954,0.01773,-0.07671,-0.0055,0.05687,0.12708,0.02416,-0.04815,0.05643,-0.01788,-0.03457,-0.12269,-0.01968,-0.06266,-0.00988,-0.00969,-0.07219,-0.0812,-0.01948,0.142,-0.01909,0.07082,0.06088,-0.10241,0.00229,-0.02832,0.05331,0.07891,-0.0555,-0.0088,0.05782,0.02413,-0.02842,0.00924,-0.04168,0.06221,-0.02496,-0.07851,-0.0658,-0.0963,-0.02973,-0.00294,0.11094,-0.00519,0.01096,0.00014,0.04227,0.00056,-0.00691,0.03278,-0.00666,-0.04662,-0.04566,0.02368,0.04548,0.01041,-0.085,0.06046,-0.02443,0.00837,-0.03433,0.10989,-0.06745,-0.05151,-0.04113,-0.05282,0.00071,0.03131,-0.11083,0.04532,-0.07539,0.04184,0.04873,-0.0397,-0.08274,-0.08679,-0.05054,0.00838,0.04453,0.04379,0.01892,-0.07071,0.00264,-0.00607,0.00589,0.0848,0.02432,-0.06393,-0.02675,-0.00921,0.00214,0.04148,-0.18511,0.03938,-0.05286,0.0754,-0.00306,-0.03339,0.05469,0.05005,0.05818,0.11063,-0.00943,-0.12295,0.0654,-0.03057,0.03473,-0.06726,-0.03227,-0.01882,0.06463,0.02822,-0.09491,-0.00867,0.02151,0.11415,0.10955,0.08039,0.02278,-0.05357,-0.07543,0.00182,0.00371,-0.04229,0.00306,-0.03097,0.05046,-0.01137,0.02793,-0.08623,0.04625,-0.01435,0.06983,0.1303,0.01978,-0.0124,0.08361,-0.01681]},{"domain":"thermofluids","key":"effectiveness_phase_change","name":"Effectiveness of a heat exchanger with one stream changing phase","package":"thermofluids-ai999x","example":"Steam condenses in a condenser whose heat exchanger has a number of transfer units of 2. What is the effectiveness?","v":[0.09767,-0.0276,-0.08695,0.05304,0.02401,-0.01452,-0.00514,-0.05895,0.00533,-0.03335,-0.01712,-0.14696,-0.02561,0.06724,-0.04651,0.08051,0.01098,-0.05228,0.115,0.02362,0.0615,0.06003,-0.104,-0.05653,0.01632,0.06311,-0.04695,0.06322,0.01745,0.01519,-0.0611,0.05833,-0.0234,-0.01014,-0.12223,0.08639,-0.01162,-0.02698,-0.08135,0.03873,0.06568,0.12436,0.10594,0.08613,0.05237,0.01018,0.07313,-0.00405,-0.08446,0.02907,0.00818,0.02395,-0.01341,-0.03408,-0.02867,-0.00167,-0.00142,-0.08026,-0.12516,-0.10495,-0.10885,-0.1777,-0.01216,-0.02085,-0.05774,0.06969,-0.03283,0.01101,0.00145,-0.01381,0.01646,0.11259,0.03429,0.01336,-0.03734,0.04755,0.05873,-0.0201,0.0436,-0.01739,-0.09468,0.10459,-0.05629,0.05419,-0.05191,-0.06375,0.01203,0.04388,0.11559,0.02454,-0.05763,0.03804,0.12611,-0.01714,-0.03382,0.04415,-0.06108,-0.00442,-0.00376,-0.06013,0.18769,0.11929,-0.0311,0.061,0.06586,0.0818,0.05698,-0.06665,0.00524,-0.08217,0.08054,0.06906,0.00732,0.0324,-0.06845,-0.00481,0.08655,-0.00697,-0.05628,-0.00246,-0.05404,0.0211,-0.06139,0.06511,-0.05187,-0.00633,0.0649,-0.0178,-0.02457,-0.1218,-0.01531,-0.08117,0.00197,0.02,-0.00542,0.0057,0.07846,0.09491,0.00685,0.03253,0.0648,-0.07703,-0.01197,0.01732,0.02652,0.02459,0.01718,0.09958,0.05309,0.07668,0.00884,0.01937,0.02481,0.00756,-0.00778,0.03516,-0.09756,-0.01114,-0.04279,0.05485,-0.04318,0.0259,0.00465,0.08981,0.05237,-0.08284,-0.02745,0.00286,-0.00385,0.003,-0.06988,0.08949,0.05712,0.02473,0.01264,0.03199,-0.02411,-0.04843,-0.06085,0.14527,-0.10795,-0.02041,-0.0536,-0.05709,-0.05206,0.01905,-0.06538,0.00937,-0.08604,0.03551,-0.112,-0.04644,-0.04312,-0.04915,-0.05712,0.04551,0.087,0.01382,0.01892,-0.01262,-0.11569,-0.01784,0.07543,-0.05901,0.0328,-0.04581,0.00229,-0.01346,-0.02236,-0.03427,-0.14214,-0.03206,-0.07498,0.10785,-0.04275,-0.11904,-0.01019,-0.05279,0.0991,-0.0249,-0.0205,-0.02968,0.0669,0.01338,0.03902,0.01213,0.04501,0.03254,0.01385,-0.03804,-0.04167,-0.04292,-0.05402,0.15035,0.05884,0.10023,-0.01587,-0.0596,-0.09373,0.05599,-0.03586,-0.03888,0.02791,-0.07678,0.1107,-0.03199,0.07252,-0.05974,0.08667,-0.10366,0.04617,0.06311,-0.03326,-0.06386,0.09933,-0.13366]},{"domain":"thermofluids","key":"heat_rate_effectiveness","name":"Heat transfer rate from the effectiveness","package":"thermofluids-ai999x","example":"A heat exchanger has an effectiveness of 0.6 and a minimum heat capacity rate of 2000 W/K. The hot fluid inlet temperature is 150 °C and the cold fluid inlet temperature is 30 °C. What is the rate of heat transfer?","v":[0.04697,-0.02473,-0.08105,0.01916,-0.05179,0.02409,-0.02994,-0.0719,0.05074,-0.02388,-0.03793,-0.10961,0.00762,0.0809,-0.01517,0.04429,0.00032,0.00395,0.07598,-0.02226,0.08525,0.01366,-0.06176,-0.06471,-0.09098,0.0034,0.04883,0.07989,-0.01055,0.01788,-0.09198,0.01947,0.04992,0.00824,-0.0759,0.14284,-0.02143,-0.06229,-0.08696,0.03054,0.09238,0.01879,0.05764,0.09621,-0.03564,0.05625,0.04031,-0.05846,0.00631,0.08168,0.05936,-0.00653,0.10036,0.06974,-0.00489,0.02242,0.00247,-0.01764,-0.13861,0.00683,-0.08931,-0.23088,0.05381,0.07868,-0.00765,0.06022,-0.01705,0.00973,-0.01454,0.02997,0.04195,0.06942,0.07912,-0.07722,-0.09718,0.00998,0.07797,0.01651,0.09074,-0.02164,-0.05707,0.06065,-0.06718,0.02227,-0.07511,-0.05433,-0.06218,-0.00401,-0.00795,-0.01171,-0.0139,-0.01857,0.085,0.0183,-0.05746,-0.01936,-0.12799,-0.02581,0.02265,-0.02872,0.18168,0.12362,0.04775,0.02871,0.01726,-0.05682,0.09199,-0.0629,0.0121,-0.04861,0.01957,0.00534,0.01772,0.05713,-0.05788,-0.02566,0.05814,0.04019,0.02902,0.02188,-0.07094,-0.03295,0.02753,0.05731,0.03933,0.03863,0.06383,-0.06924,-0.07231,-0.16409,-0.05972,-0.11489,-0.01795,-0.02548,-0.00833,-0.10112,0.04331,0.10299,-0.07861,-0.04564,0.00913,-0.04679,-0.03603,-0.04047,0.01863,0.00668,-0.03397,0.02195,-0.03131,-0.02407,0.01962,0.08147,-0.04768,0.01246,-0.01443,0.06981,-0.02066,0.011,-0.05506,0.0439,0.0329,-0.04092,-0.10537,0.09989,-0.02447,0.05209,-0.01804,-0.01294,0.02806,0.00844,-0.07785,-0.0047,0.0182,-0.01475,-0.07433,0.06235,0.00368,-0.01121,-0.04161,0.11085,-0.01848,0.02238,-0.04323,-0.08198,-0.07705,0.07145,-0.05464,0.09874,-0.08695,-0.01451,0.05829,0.0203,-0.04774,0.03855,-0.04386,0.04,-0.00344,0.09124,0.09063,-0.05009,-0.02629,-0.04354,0.06831,0.01514,0.02934,-0.04854,-0.08113,0.03653,-0.11642,-0.00691,-0.18787,-0.0341,-0.00837,0.14597,-0.00846,-0.0358,-0.02222,-0.05542,0.14733,0.02462,0.01515,-0.03624,0.03361,-0.04852,0.07742,0.01941,0.05354,0.05536,0.06788,0.0945,-0.06312,0.02641,5e-05,0.09309,0.05351,0.02948,0.08377,0.01362,-0.07436,0.08872,-0.02141,-0.08507,-0.02321,-0.07879,0.11379,0.07345,0.04197,-0.10395,0.10638,-0.04269,0.02585,0.08522,-0.0166,-0.05657,0.03291,-0.11514]},{"domain":"thermofluids","key":"sensible_heat_rate","name":"Heat added to a flowing stream (steady-flow energy balance)","package":"thermofluids-ai999x","example":"Water with a mass flow rate of 0.5 kg/s and a specific heat of 4180 J/(kg*K) is heated from an inlet temperature of 20 °C to an outlet temperature of 60 °C. What is the rate of heat transfer?","v":[0.06158,-0.01185,-0.06966,-0.01404,-0.01626,0.01466,0.03957,-0.03025,-0.0137,0.02173,-0.01054,-0.05448,-0.04803,0.00617,-0.01585,-0.01568,-0.05111,0.02695,-0.04433,0.00539,0.06781,0.01827,-0.06743,-0.03835,-0.11991,-0.00315,-0.00376,0.0524,-0.05898,-0.00723,0.02172,-0.04027,-0.0024,0.03081,-0.00976,0.13513,-0.03115,-0.05835,-0.03428,-0.02962,0.05634,0.08979,-0.01412,0.0776,0.04294,0.0269,0.02687,-0.01978,0.06216,0.06805,-0.10777,0.02196,0.07269,-0.08357,0.02282,-0.07716,0.02127,0.00109,0.02977,-0.04692,-0.01386,-0.16851,0.0855,0.0501,0.07331,0.0922,-0.02962,-0.00324,0.05983,-0.03653,0.06,0.00432,-0.01469,0.01031,-0.01081,-0.00378,0.1229,-0.00807,0.04432,-0.08822,-0.06373,-0.11528,0.03137,0.05075,-0.06205,-0.05689,-0.03257,0.04629,-0.06028,0.04576,-0.01553,-0.14381,0.04834,0.11167,-0.10274,0.02548,-0.05757,-0.01432,0.05149,-0.02747,0.16245,-0.00816,-0.0854,0.0169,0.0116,-0.00525,0.14148,-0.00013,-0.07508,-0.01562,0.02514,0.00493,0.02745,0.02171,0.05255,0.02951,0.19251,0.0148,-0.00741,0.03423,-0.09872,-0.03251,0.07745,0.01458,0.0252,0.08023,0.0419,-0.10324,-0.04788,-0.01966,-0.01214,-0.08271,0.05695,-0.02847,-0.00028,-0.08162,-0.00317,0.09422,-0.12978,-0.11551,-0.05671,-0.02488,-0.00598,-0.09334,0.0311,0.09973,-0.04894,0.06845,-0.02339,-0.01482,0.05841,-0.00681,-0.04078,0.03633,-0.0641,0.07947,-0.04742,-0.10793,0.00093,-0.03278,-0.0138,0.02444,0.01596,0.08661,-0.07778,-0.02699,-0.00422,-0.06501,0.05726,-0.01375,0.02244,0.04832,0.00213,-0.07282,-0.08409,0.06398,-0.05734,-0.0413,-0.11892,0.04859,0.04379,0.12582,-0.02941,-0.03202,0.0236,0.08634,-0.07016,0.00903,-0.02137,-0.04009,-0.05681,0.04141,0.02659,0.12522,0.04305,0.06808,-0.01832,0.10923,0.02959,-0.12115,0.04462,0.0232,0.02124,-0.0499,-0.06439,-0.04357,-0.07146,0.03375,0.01386,0.01965,-0.03318,-0.07823,0.01765,0.02634,0.13124,0.00829,-0.09924,-0.05356,0.12302,0.04081,0.14249,-0.0371,-0.05698,0.0816,-0.02782,-0.00798,-0.04874,0.06642,0.03821,0.09974,-0.13703,-0.04066,0.06976,0.05959,0.08461,-0.11262,0.05029,0.005,-0.13118,-0.02964,-0.02839,-0.10817,-0.01891,-0.01733,-0.03893,0.01639,0.1388,0.00684,0.13595,0.047,0.00155,0.05523,-0.02212,0.02374,-0.00529,0.07034]},{"domain":"thermofluids","key":"carnot_efficiency","name":"Carnot efficiency of a reversible heat engine","package":"thermofluids-ai999x","example":"A Carnot engine operates between a hot reservoir temperature of 600 K and a cold reservoir temperature of 300 K. What is its efficiency?","v":[0.08307,-0.16796,-0.08954,0.0124,0.04183,-0.01007,0.00542,-0.00836,0.03241,0.02699,-0.11735,-0.03022,-0.01461,-0.05983,0.00335,-0.01685,-0.04298,-0.05211,0.00907,-0.00762,-0.07121,0.01196,-0.10411,-0.08256,-0.05701,-0.00128,-0.06074,-0.01054,0.09919,0.03292,-0.0133,0.06658,0.07873,-0.03993,-0.09573,0.10594,-0.02587,-0.10581,-0.05944,-0.09241,0.06173,0.04696,0.03753,0.05168,-0.0215,-0.00829,0.11301,-0.03846,-0.04088,0.06818,0.06368,0.06712,-0.03529,-0.11444,-0.08519,0.06144,0.0272,-0.01385,0.01686,-0.04953,-0.04804,-0.18165,0.02125,-0.00947,0.01214,0.08525,-0.00318,0.02959,-0.09402,0.09081,-0.05136,0.10204,-0.01692,-0.02577,0.0134,0.06057,-0.02607,0.01822,-0.02777,-0.01246,-0.00903,0.08552,-0.05736,0.02845,-0.04198,-0.07351,0.03322,0.01658,0.07441,-0.03044,0.07555,0.13616,0.08327,0.09722,-0.0383,0.02349,0.08225,-0.01591,-0.09644,-0.0512,-0.00583,0.04566,-0.00546,0.04181,-0.04617,-0.05324,0.13805,0.01424,-0.06848,-0.03437,0.00966,-0.00767,0.03601,0.04853,0.04335,0.04556,0.00036,-0.03092,0.02318,0.04459,-0.03022,-0.05575,0.04571,-0.05314,-0.07894,-0.00526,-0.00522,0.02055,-0.00106,0.01796,0.04262,-0.03037,-0.0952,0.00514,0.05643,-0.01988,0.07384,0.08277,-0.08884,0.00536,0.1463,-0.00389,-0.10025,0.02273,0.0932,0.0477,0.00337,-0.00159,0.0161,-0.06377,-0.02591,0.012,-0.0894,-0.02482,0.06917,0.12806,-0.04765,0.01276,-0.12649,-0.06008,-0.01097,-0.00108,-0.08604,-0.04956,0.04359,-0.08074,-0.0222,0.06721,0.04422,0.09229,-0.01164,-0.04155,-0.02593,0.05277,-0.11661,-0.00592,0.00781,-0.00282,0.13023,0.02791,0.02095,-0.02541,0.00221,-0.07318,-0.07516,0.04985,-0.13653,0.02413,-0.1055,0.10216,-0.00605,0.02739,0.03688,0.05179,0.06791,0.08713,0.0383,0.05651,0.07452,0.03726,-0.03771,0.00223,0.14653,0.03264,-0.01555,-0.0706,-0.02762,0.07339,-0.03673,-0.09972,0.01317,-0.08904,-0.1119,0.09727,0.12681,0.08529,0.00324,0.07922,0.06643,-0.10354,-0.08707,0.03955,0.09629,-0.11141,0.00053,0.14848,0.03938,-0.00066,-0.02367,0.01482,0.06125,-0.0163,-0.02603,0.00681,0.06126,0.0194,-0.00069,-0.00763,-0.12968,0.04172,0.01865,-0.0003,0.02755,-0.03592,-0.0174,0.01396,0.00769,0.01877,-0.02929,-0.07194,-0.00761,0.05802,0.00432,0.04002,-0.13448,-0.07725]},{"domain":"thermofluids","key":"carnot_cop_refrigerator","name":"Coefficient of performance of a Carnot refrigerator","package":"thermofluids-ai999x","example":"A Carnot refrigerator keeps a cold reservoir temperature of 270 K and rejects heat at a hot reservoir temperature of 300 K. What is its coefficient of performance?","v":[0.09747,-0.16533,-0.11047,0.01692,-0.1188,0.04288,-0.04731,0.00382,0.02893,-0.00233,-0.05821,-0.00726,-0.01428,-0.09931,0.0092,-0.12162,-0.03845,-0.0747,-0.03595,0.03847,-0.05886,0.02657,-0.07232,-0.03776,0.05721,-0.04047,-0.03413,-0.05373,0.07256,-0.08287,0.06236,0.09182,0.01721,-0.01655,-0.13965,0.07806,-0.02869,-0.07339,-0.06798,0.01603,-0.06175,0.02256,-0.0142,0.10347,0.02896,-0.06492,0.09123,-0.01115,-0.03839,0.01581,0.02197,0.11343,0.0627,-0.09008,-0.0788,-0.0336,-0.00545,0.03058,0.05921,-0.0596,-0.01301,-0.10795,0.00578,-0.06099,0.02632,0.08292,0.06061,0.01968,-0.04209,0.04569,0.02579,0.04414,-0.03569,0.03108,0.03087,0.00964,-0.03335,-0.05413,0.08212,0.04901,0.0575,0.05192,0.04267,-0.01972,0.00413,0.03535,0.01238,0.01348,0.05343,-0.02114,0.05187,0.03134,0.06004,0.05821,-0.05654,0.0172,0.06613,-0.00579,-0.101,-0.08291,-0.00711,-0.00307,-0.06159,0.08822,0.00139,-0.04471,0.11736,0.09872,0.01496,-0.08243,0.01341,0.03204,0.065,0.00918,0.08855,0.00724,0.0645,0.00411,-0.0106,0.08276,0.01444,-0.10136,0.02895,0.0612,-0.08765,0.02564,-0.03794,0.00786,-0.03966,0.0632,-0.02674,-0.09768,-0.03058,-0.03053,0.09396,-0.0939,0.09073,-0.0031,-0.12263,-0.07052,0.14554,-0.09756,-0.03586,0.03236,0.03638,-0.0198,0.06762,0.02519,-0.01618,-0.06003,0.01625,-0.01643,-0.01785,0.03413,-0.00302,0.12059,-0.00471,0.02588,-0.11886,0.00683,-0.02277,0.01145,-0.01483,0.00436,0.01889,-0.0999,0.05211,-0.00315,0.08821,0.1025,0.07069,-0.0218,-0.09464,0.05291,-0.07357,-0.0261,-0.06448,0.05805,0.13659,0.02259,-0.01481,0.10039,-0.05967,-0.04527,-0.04737,0.05179,-0.14949,-0.06352,-0.02477,0.14481,0.04595,0.05226,0.09867,-0.05021,-0.00197,0.07702,0.02604,0.06528,0.0032,0.02496,0.07133,0.12859,0.10052,-0.05286,-0.00879,0.00914,-0.14411,0.00811,-0.00617,-0.10021,0.05659,-0.0925,-0.04063,-0.00049,0.0853,0.06403,-0.00523,0.04695,0.05228,-0.07322,-0.09527,0.01183,0.03614,-0.04702,-0.0553,0.15455,0.06078,0.00984,-0.07597,0.06231,-0.02203,-0.07023,-0.03201,0.01658,-0.00673,0.05676,0.06337,-0.01359,-0.10066,0.05925,0.0075,0.00329,-0.01519,-0.06125,-0.01516,0.06289,0.06155,-0.00207,-0.07361,-0.00387,-0.07284,0.08759,-0.02792,0.05832,-0.08668,-0.0767]},{"domain":"thermofluids","key":"carnot_cop_heat_pump","name":"Coefficient of performance of a Carnot heat pump","package":"thermofluids-ai999x","example":"A Carnot heat pump delivers heat at a hot reservoir temperature of 295 K while extracting heat from a cold reservoir temperature of 275 K. What is its coefficient of performance?","v":[0.05823,-0.12005,-0.14714,0.03749,-0.05712,-0.03431,-0.0363,-0.02112,-0.01532,-0.00652,-0.12101,-0.06861,-0.01724,0.02074,0.03459,-0.01341,-0.05198,0.0172,-0.0007,0.0476,-0.07036,0.00024,-0.12016,-0.06813,-0.00168,-0.03417,-0.02498,-0.05108,0.08829,0.00177,0.0119,0.12535,0.03272,0.02144,-0.13382,0.08829,-0.05741,-0.04015,-0.06102,-0.01639,0.03038,0.06465,0.05752,0.13147,-0.04584,-0.07181,0.10345,-0.02189,0.03792,-0.02409,0.03703,0.11675,0.06037,0.01195,0.00245,-0.00033,-0.00056,0.03949,0.06356,-0.03588,-0.07629,-0.15021,0.04977,0.0059,0.03329,0.01756,-0.03583,0.05305,-0.05864,0.04824,-0.01566,0.05438,-0.04157,-0.01124,0.09271,0.07412,-0.07852,-0.0311,0.09618,-0.0101,-0.01547,0.04763,-0.02204,-0.00012,-0.03843,0.00618,-0.01943,-0.03967,0.0213,-0.03348,0.08509,-0.01882,0.09804,0.07058,-0.08483,-0.00145,0.02942,-0.01968,-0.00993,-0.05282,0.01641,0.0093,-0.01789,0.08194,-0.0315,-0.08512,0.08069,0.08223,0.01893,0.00494,0.03515,0.0164,0.0067,0.04324,0.04929,0.04229,0.06858,0.01148,-0.06191,0.06154,-0.0369,-0.11387,0.02128,-0.01878,-0.10215,0.05448,0.00813,0.01041,0.06465,0.0039,-0.06695,-0.12905,-0.00142,-0.01892,0.05102,-0.08531,0.04696,0.00871,-0.05469,-0.04748,0.14734,-0.11715,-0.01266,0.01595,0.13046,-0.03741,-0.04479,-0.06349,-0.04622,-0.04411,-0.0,-0.0218,-0.0236,0.04267,-0.03831,0.16766,-0.04998,0.00126,-0.16393,0.02325,-0.01874,-0.02276,-0.05212,0.02224,-0.02149,-0.10368,0.04122,-0.0457,0.05266,0.12098,0.0485,-0.02312,-0.10858,0.0244,-0.12135,-0.00266,-0.04351,0.10592,0.15257,0.0837,0.04327,0.05942,-0.07459,-0.07461,-0.06043,0.0044,-0.14355,-0.05777,-0.09761,0.10081,0.04865,0.04486,0.07255,0.02106,-0.008,0.07602,-0.00331,0.11987,-0.00778,-0.00566,0.05379,0.03704,0.17924,0.02497,-0.00012,0.00086,-0.08834,-0.01405,0.00284,-0.08303,-0.04263,-0.08817,-0.07537,0.03817,0.14477,0.07594,0.0031,0.05576,0.10194,-0.01139,-0.04736,-0.01143,0.03504,-0.09711,-0.04555,0.08893,0.09403,0.02224,-0.01768,0.00152,-0.03607,0.01676,0.04839,0.0477,0.00304,0.07784,-0.02068,0.02253,-0.04515,0.04556,0.0081,0.05047,-0.07727,-0.02669,-0.04903,-0.01701,0.05721,-0.00066,-0.01142,-0.0725,-0.00912,0.05428,0.00618,-0.01952,-0.09398,0.05053]},{"domain":"thermofluids","key":"otto_efficiency_air","name":"Thermal efficiency of the air-standard Otto cycle","package":"thermofluids-ai999x","example":"An air-standard Otto cycle has a compression ratio of 8. What is its thermal efficiency?","v":[0.1442,0.02098,-0.11277,-0.03585,-0.00285,0.02081,-0.01707,0.04408,-0.022,0.06316,-0.02968,-0.04774,-0.03443,0.07034,0.00393,0.12696,0.00613,0.10526,0.04756,-0.08042,-0.04986,-0.07281,-0.10634,-0.04469,0.01329,-0.00237,-0.02936,-0.01264,-0.08141,0.00573,0.02403,0.02399,0.128,0.08085,-0.0438,-0.04577,0.07965,0.05288,0.01314,-0.03913,0.08308,0.02298,-0.08737,0.05323,-0.02415,0.02186,0.03588,-0.03058,-0.09099,-0.01853,0.05266,-0.10897,-0.0122,-0.0421,0.02129,0.02019,0.00885,-0.02634,-0.04388,-0.04649,-0.00907,-0.15846,0.06549,0.10596,0.03923,0.02201,-0.03355,-0.0284,-0.03135,0.15051,-0.07665,0.1215,-0.02773,-0.09266,0.0284,0.00505,0.07087,-0.00668,-0.06089,0.04742,-0.04227,0.0673,-0.03509,0.05336,-0.07836,0.00441,0.10676,-0.02648,0.01914,-0.09602,-0.03576,0.07259,-0.02808,0.09207,-0.05767,0.01801,0.01593,-0.02598,0.01039,0.12259,-0.01673,0.04908,0.10092,-0.13723,-0.03043,-0.14188,0.03089,0.0602,-5e-05,-0.06434,0.01494,-0.02187,0.08573,-0.0241,-0.07636,0.01246,-0.06588,-0.05697,0.03,-0.03733,-0.01277,0.01287,0.06855,0.02589,-0.11048,0.01661,-0.01313,0.00601,-0.06349,-0.03979,-0.04256,0.15923,-0.07261,0.04582,0.03719,0.0597,-0.06384,0.04541,-0.01547,0.02682,0.03474,0.00866,-0.03696,0.04188,0.05385,0.06411,0.05223,-0.09185,0.11418,0.02914,-0.01938,0.0154,-0.04817,-0.08483,0.01239,0.13196,-0.06326,0.06974,-0.0687,-0.04902,-0.12188,-0.00097,-0.05521,-0.0698,0.05486,-0.03215,0.04629,-0.05009,0.0871,-0.04124,-0.07987,0.0014,-0.0857,0.03404,0.10984,-0.01063,0.0468,0.0683,0.04737,-0.10549,-0.03073,0.00674,0.0498,0.00382,-0.07743,-0.04824,-0.11352,0.08219,-0.12921,0.02771,0.04085,-0.10817,0.03505,-0.07107,0.00658,0.00555,0.08333,0.06955,-0.03873,0.0055,-0.05764,-0.03544,0.07981,0.07806,0.00435,-0.0619,-0.00166,0.05292,-0.10291,0.01325,-0.11321,-0.03127,0.027,0.14482,0.00762,-0.0193,-0.07416,-0.04549,0.09921,0.01041,0.02191,-0.03358,0.04183,-0.04929,0.03503,-0.0213,0.11793,0.04371,0.00534,0.00437,-0.01688,0.04912,-0.06189,0.00297,0.0474,-0.09403,0.02472,-0.01607,0.00577,-0.05577,0.09447,-0.00771,0.1173,0.0187,0.01815,0.00686,0.06676,-0.02786,0.00778,0.02331,0.01308,0.0301,-0.00237,-0.07046,-0.16967,-0.06873]},{"domain":"thermofluids","key":"diesel_efficiency_air","name":"Thermal efficiency of the air-standard Diesel cycle","package":"thermofluids-ai999x","example":"An air-standard Diesel cycle has a compression ratio of 18 and a cutoff ratio of 2. What is its thermal efficiency?","v":[0.11875,-0.05812,0.01617,0.00231,-0.05519,0.04294,-0.03117,0.03705,-0.02747,0.0359,-0.02318,0.02959,-0.07366,0.0079,-0.01265,0.06478,-0.03349,0.05503,0.0259,-0.11714,-0.03697,-0.02117,-0.01615,-0.09851,0.07128,-0.00092,-0.04698,0.01413,-0.00771,-0.06333,-0.05633,-0.00812,0.10164,-0.00485,0.00319,0.03613,0.12556,0.05641,0.04131,-0.05295,0.03934,0.02764,-0.0525,0.01427,0.05354,-0.05425,0.11644,-0.04024,-0.12408,-0.03939,0.06972,0.00887,-0.01436,-0.05354,-0.0266,0.03383,0.04324,0.00058,-0.05471,0.02716,-0.01515,-0.16034,0.04016,-0.03628,0.01312,0.00459,-0.10559,0.0053,-0.14232,0.18236,0.00072,0.12,0.0081,-0.03364,0.02071,-0.0258,-0.03529,-0.01285,-0.04318,0.0421,-0.07226,0.05609,-0.04098,-0.00364,-0.04805,-0.04244,0.07771,0.0115,-0.0703,-0.07784,-0.07063,0.09739,0.07769,0.05339,0.062,0.0182,-0.00576,-0.03767,0.01149,0.01033,0.0002,0.05301,0.06426,-0.01423,-0.04396,-0.04918,0.0865,0.06644,0.01849,0.00789,0.03427,-0.04306,0.04363,0.05059,-0.0836,0.09073,-0.0599,-0.11346,0.03377,-0.03654,-0.03269,-0.05596,0.04318,0.07484,-0.08733,-0.00575,0.0115,0.01923,-0.07374,-0.06803,0.00809,0.11017,-0.09586,-0.08237,-0.01992,0.07009,-0.10394,0.01971,-0.07197,0.00533,0.02303,-0.00153,0.02063,-0.01003,0.06009,0.07633,0.09129,-0.02001,0.08488,0.02448,0.03436,-0.04857,-0.01854,-0.06352,-0.00037,0.02164,-0.00274,-0.05865,-0.04025,-0.0467,-0.08284,-0.02982,-0.03065,-0.13284,0.13816,0.00744,0.08193,-0.0404,0.09376,0.01405,-0.03225,0.04021,-0.00889,-0.05181,0.04791,0.0349,0.0525,0.04938,0.03399,-0.05469,0.03713,-0.02276,0.11985,-0.0443,0.02513,-0.01169,-0.02157,0.02023,-0.06566,0.05584,0.01728,-0.16942,0.05543,-0.05206,0.0232,0.04328,0.06845,0.08511,0.09394,-0.08585,-0.11052,0.01337,0.03165,0.08059,-0.05161,-0.08293,-0.04564,0.0453,-0.02707,-0.05903,-0.09243,0.00545,0.0196,0.13703,0.02767,-0.02239,-0.07878,-0.0108,0.02006,0.01246,0.00432,-0.01259,0.17732,-0.07659,0.12441,0.0215,0.11293,0.04126,0.03201,0.03198,-0.03596,0.04232,-0.00104,-0.01115,0.04395,-0.11133,0.09439,-0.02984,0.08436,0.00011,0.12845,0.02016,0.09606,-0.05264,-0.02222,0.07564,0.00453,-0.01933,0.00991,0.05037,0.03606,0.09838,-0.06767,0.01213,-0.17045,-0.15554]},{"domain":"thermofluids","key":"brayton_efficiency_air","name":"Thermal efficiency of the air-standard Brayton cycle","package":"thermofluids-ai999x","example":"An air-standard Brayton cycle operates with a pressure ratio of 10. What is its thermal efficiency?","v":[0.0614,-0.00748,-0.07732,-0.10089,0.01355,0.07764,-0.00552,-0.00349,-0.05263,0.10694,-0.07737,-0.00655,0.03315,0.0476,-0.00834,0.03798,-0.03363,0.05098,0.02205,-0.00539,-0.052,-0.05117,-0.04164,0.00615,0.0275,-0.01549,-0.0496,-0.03342,-0.00904,0.0149,0.03572,0.00535,0.0157,0.02497,-0.067,0.06992,0.04525,0.00886,-0.13653,-0.102,0.06693,0.04084,-0.09232,0.01429,0.06701,-0.03,0.09392,-0.04834,-0.02212,0.02219,0.04416,-0.06775,-0.01173,-0.0967,-0.06245,0.07404,0.07122,-0.09895,-0.03662,0.01331,-0.09759,-0.1786,-0.04177,0.00153,0.01421,-0.00954,-0.11162,0.00491,-0.1663,0.04743,-0.0442,0.09341,0.08134,-0.12627,-0.04169,-0.02637,0.04472,-0.01081,-0.07078,0.07383,-0.06216,0.061,0.06343,0.07987,-0.15523,-0.10801,0.16492,-0.03873,0.0093,-0.04864,-0.06267,0.07112,0.01406,0.14016,0.07564,0.02113,0.07529,0.00918,0.0004,0.00563,0.06314,0.06333,0.04145,-0.00454,0.01355,-0.03994,0.11146,0.06421,-0.00278,-0.05173,0.05834,0.02738,0.03221,-0.06406,-0.02295,-0.06904,-0.01338,-0.03613,-0.00475,-0.02421,-0.04284,-0.00801,0.07478,-0.00665,-0.04761,0.01324,-0.00296,0.00497,-0.05133,-0.1126,-0.09517,0.07538,-0.03094,0.01957,0.03078,0.01224,-0.02626,0.03577,-0.01621,0.02507,0.03271,-0.0337,-0.10657,0.00924,0.11512,0.06192,0.08683,-0.10691,0.08614,0.03614,-0.0153,0.08359,0.02635,-0.03082,0.07081,0.04482,0.03537,0.11919,-0.00642,-0.07239,-0.0451,0.04944,-0.02054,-0.06819,0.04543,-0.12503,0.07621,0.0245,0.07201,-0.0029,0.0208,-0.00539,-0.07909,-0.00959,0.07392,0.01635,0.05942,0.04765,-0.03001,-0.05343,-0.03172,-0.02807,0.0098,-0.05957,-0.0885,0.06915,0.00896,0.00288,-0.16755,0.00107,-0.0352,-0.04756,0.01095,-0.01179,0.03355,0.03306,-0.00718,0.05845,-0.0038,0.05972,-0.04735,0.10127,0.05646,0.07925,0.10347,-0.09518,0.02193,0.09769,-0.04705,-0.01696,-0.13135,-0.01439,-0.01119,0.10489,0.0763,-0.01146,-0.04645,-0.06858,0.17573,0.04138,-0.01818,-0.06708,0.05632,-0.04383,0.02594,-0.02945,0.0929,0.02946,0.01639,0.01536,0.00149,-0.0696,-0.10431,0.09189,0.06724,-0.03885,-0.01386,-0.01132,0.01878,0.01943,0.03354,-0.01216,0.13418,-0.00344,0.00769,0.03041,0.00955,-0.02839,0.04321,-0.07308,-0.03575,0.05026,-0.08136,0.05771,-0.1353,-0.07936]},{"domain":"thermofluids","key":"isentropic_temperature_pressure_air","name":"Temperature after an isentropic pressure change of air","package":"thermofluids-ai999x","example":"Air at an initial temperature of 300 K and an initial pressure of 100 kPa is compressed isentropically to a final pressure of 800 kPa. What is the final temperature?","v":[-0.00539,-0.04668,-0.02729,-0.12211,0.03568,0.06767,-0.03119,-0.01738,-0.06182,0.00257,-0.09766,0.01713,-0.06966,0.07874,0.05646,-0.0015,0.09761,-0.00663,0.09674,0.03167,0.01131,-0.07839,0.05556,0.05945,-0.07161,0.01243,0.01532,-0.04206,-0.04376,-0.03229,0.04077,0.00138,-0.04418,0.01068,-0.00723,0.18489,-0.0519,-0.03249,-0.00086,0.07813,0.0386,-0.11134,-0.02481,0.08772,-0.04243,0.08289,0.02728,-0.01394,-0.00366,-0.06273,0.00721,-0.05403,0.04341,-0.08957,0.04214,-0.06562,0.0082,-0.00066,0.0853,0.03867,-0.05951,-0.03472,0.0229,-0.10217,-0.09321,0.00992,0.04154,0.08152,-0.00941,0.08535,-0.04468,0.09286,-0.04173,-0.00829,-0.05212,-0.03716,0.11358,0.02967,-0.01076,0.00955,-0.01758,-0.11226,0.06834,0.12062,0.03075,-0.0755,0.01698,-0.0373,0.00913,-0.04875,0.09077,-0.03146,-0.01355,0.00627,-0.03823,-0.11544,0.17505,-0.05763,0.05359,-0.10027,0.14153,-0.00225,0.03426,0.02175,0.00848,-0.05348,-0.06711,-0.01841,0.02574,0.02879,0.05182,0.03793,-0.0298,-0.0201,-0.06877,-0.03341,0.00649,0.0132,-0.03662,-0.04209,-0.01976,0.07518,0.04198,0.04144,0.0053,0.01684,0.02349,-0.01232,0.07457,0.02182,0.04844,-0.02512,-0.09315,-0.02506,0.00507,-0.0007,-0.01413,0.01769,0.00912,-0.08165,-0.09145,-0.02817,0.05756,-0.03115,0.10349,0.10554,0.0141,0.04297,-0.09932,0.0038,-0.0102,-0.05307,-0.09325,-0.03371,0.08583,0.08859,-0.11024,0.06676,0.05855,-0.03591,-0.07168,-0.02271,0.02034,-0.05172,-0.17403,-0.07613,0.09085,-0.1225,-0.02198,0.10589,-0.00381,-0.03792,0.07414,0.09462,0.03016,0.07848,-0.0721,0.028,0.04982,0.05898,0.03175,0.06359,0.01937,0.0948,-0.05697,0.0208,0.0129,-0.02764,-0.00846,-0.0396,0.09004,0.02755,-0.027,0.00834,-0.01029,0.0706,0.03425,-0.07339,-0.09509,-0.01876,0.01206,0.07985,0.07005,-0.04132,0.10125,-0.02552,-0.03387,-0.01867,-0.03621,-0.03851,0.04832,-0.03248,-0.0824,0.00279,0.02597,-0.01524,-0.07181,-0.00701,-0.11814,-0.01316,0.08105,-0.07997,0.13833,-0.01605,0.01049,0.00247,-0.0139,0.03909,-0.12933,0.0037,0.03485,-0.06486,-0.10751,0.07712,0.06303,-0.04738,0.07463,-0.07906,-0.04861,0.13197,0.10846,-0.13689,0.14547,0.08558,-0.03739,-0.02039,0.01583,-0.04281,-0.05031,0.00151,-0.04081,0.14229,-0.02117,-0.02371,-0.06165,0.03212]},{"domain":"thermofluids","key":"isentropic_temperature_volume_air","name":"Temperature after an isentropic volume change of air","package":"thermofluids-ai999x","example":"Air at an initial temperature of 300 K is compressed isentropically from an initial volume of 0.001 m^3 to a final volume of 0.000125 m^3. What is the final temperature?","v":[-0.00244,-0.0855,-0.03329,-0.05299,0.03474,-0.00361,-0.0543,-0.00179,-0.0176,0.02314,-0.00466,-0.0024,-0.08736,0.00838,0.0561,-0.06131,0.08809,0.02539,0.08222,0.0104,0.02531,-0.01328,-0.02722,0.03725,-0.08767,-0.07231,0.02005,0.01081,-0.10107,-0.08807,-0.03452,-0.04674,-0.08034,0.01276,0.05489,0.0571,-0.05676,-0.09433,0.06918,0.08413,0.02631,-0.08369,-0.0313,0.01812,-0.03396,0.02952,0.05154,-0.0288,-0.05914,-0.09759,0.01096,-0.06948,0.02762,-0.12824,0.01912,-0.06537,0.01956,0.03846,0.08389,0.01378,-0.01386,0.04583,0.0661,0.01823,-0.06719,0.0249,0.12606,0.01922,-0.01082,0.17993,0.02816,0.0906,-0.05313,0.04636,-0.00838,-0.0219,0.04632,-0.00494,0.03069,0.03062,-0.04548,-0.12188,-0.0475,0.04709,0.03366,0.09365,0.01337,-0.01272,0.02673,-0.07715,0.11204,-0.08575,-0.01868,0.04511,-0.11492,-0.05324,0.11394,-0.08605,0.11653,-0.07258,0.10964,-0.02264,0.07756,-0.04215,-0.06587,-0.09508,-0.05359,-0.01329,-0.01243,0.06922,0.09008,0.02059,-0.02284,0.05942,-0.10679,0.02806,0.00304,-0.01069,-0.0316,-0.02169,0.03525,0.06936,0.06452,0.02267,0.01105,0.02262,0.0516,-0.09179,0.07142,0.0155,0.09944,-0.0069,-0.12212,-0.0461,0.00856,0.00617,0.03153,0.02286,0.0004,-0.09328,0.01141,0.01136,0.03417,-0.02149,0.01549,0.06052,0.00779,0.03045,-0.08363,-0.02834,0.01405,-0.06924,-0.04398,-0.11698,0.01544,0.13856,-0.13657,0.05212,0.08919,-0.04993,-0.06536,-0.07192,-0.01223,-0.03898,-0.0674,-0.00147,0.04336,-0.12747,0.01116,0.06526,-0.03779,0.03233,-0.00827,0.08815,0.02585,0.02273,-0.08971,-0.00099,0.05484,-0.03553,0.0537,0.06183,0.05157,0.10862,-0.02129,0.01582,0.01391,0.017,0.02311,-0.03473,0.08749,0.01437,-0.00613,0.06483,0.02134,0.08496,0.07273,-0.04391,-0.1063,0.0176,0.00127,-0.00026,0.12914,-0.05085,0.09547,-0.00266,-0.06224,-0.06204,0.00033,-0.07538,0.02493,-0.08753,-0.08463,0.0472,0.02707,-0.01659,-0.06389,-0.0032,-0.06187,-0.03145,0.05723,-0.01961,0.16289,-0.06952,0.06772,0.053,0.01116,0.09756,-0.12856,0.01642,0.02388,-0.04287,-0.11573,0.01137,0.07612,-0.06277,0.08592,-0.13716,-0.01806,0.06406,0.1633,-0.11146,0.11237,0.04438,0.0264,-0.00939,0.05093,0.02988,0.03259,0.06333,0.00564,0.05081,-0.04992,-0.08109,-0.07804,0.02946]},{"domain":"thermofluids","key":"compressor_outlet_temperature_air","name":"Actual outlet temperature of an adiabatic air compressor","package":"thermofluids-ai999x","example":"An adiabatic compressor takes in air at an initial temperature of 300 K and an initial pressure of 100 kPa and delivers it at a final pressure of 600 kPa. Its isentropic efficiency is 0.85. What is the final temperature?","v":[0.04448,-0.07015,-0.07797,-0.09143,0.03363,0.05179,-0.03305,-0.0465,-0.07038,0.03562,-0.15185,-0.00736,0.05272,0.0527,0.02874,0.03802,0.03207,0.04942,0.06992,0.03382,0.03142,-0.00908,0.06072,0.08112,0.00317,0.02404,-0.03623,-0.05076,-0.04577,-0.0194,0.06932,-0.04541,-0.03357,-0.03485,0.00619,0.13252,-0.00502,0.0139,-0.07148,6e-05,-0.03386,-0.04313,-0.11604,0.12205,-0.00958,0.03706,0.02741,-0.03137,0.05744,-0.0626,0.03903,-0.04611,0.0707,-0.018,-0.01742,0.01111,0.07351,-0.01367,0.02079,0.05183,-0.05119,-0.18147,-0.07263,-0.02578,-0.07629,0.01681,-0.04261,0.04749,-0.06878,0.04648,-0.02261,0.06957,0.04779,-0.04263,-0.05078,-0.06075,0.1238,0.00665,0.05082,0.05821,0.02261,-0.021,0.10715,0.11691,-0.13142,-0.12501,0.07609,-0.08559,0.02726,-0.06952,0.12271,0.02922,0.01571,0.04046,-0.0493,-0.08743,0.14762,-0.0677,0.03903,-0.09534,0.15497,0.03298,-0.00584,-0.03273,-0.02042,-0.08333,-0.04635,0.02785,0.08572,-0.04018,0.03782,0.09908,0.03856,-0.00565,-0.03725,-0.09657,-0.0195,-0.01103,-0.033,-0.02286,-0.05819,0.05502,0.00085,0.00703,-0.02076,0.08889,-0.02832,-0.01254,0.026,-0.0058,-0.04154,0.03047,-0.10352,-0.06841,0.03101,0.02333,-0.0172,0.0461,0.03211,-0.10924,-0.06859,-0.07849,0.00455,-0.01997,0.16345,0.10783,0.06344,-0.02272,0.0419,-0.02449,-0.03302,0.05752,-0.03284,0.00411,0.07621,0.11362,-0.04564,0.06195,-0.03713,0.00485,-0.0453,-0.03917,-0.03717,0.02559,-0.11287,-0.05925,0.14412,-0.06173,0.05003,0.02238,0.01288,-0.04773,-0.03032,0.11975,-0.02475,0.08968,-0.02794,0.07256,-0.00085,-0.06825,0.02184,0.02548,0.01656,0.06432,-0.12671,0.05524,0.02316,0.01489,-0.12522,-0.01421,0.07298,-0.03132,-0.02938,0.00591,-0.00305,0.02157,0.03299,0.02694,-0.06093,-0.03263,0.02531,0.14164,0.02823,0.04329,0.11579,-0.08266,0.00151,0.03192,-0.03819,-0.01936,-0.04538,-0.13266,-0.03669,0.00505,0.04339,-0.07337,0.02538,-0.04154,0.02793,0.02156,0.10995,-0.05853,0.10303,-0.06632,0.0092,0.02185,0.01158,0.05092,-0.07753,0.00567,-0.01557,-0.04274,-0.11041,0.07379,0.02844,-0.0613,0.08385,-0.004,-0.02347,0.12361,0.07482,-0.09328,0.12198,0.05586,-0.0322,0.01615,0.03661,-0.05479,-0.00829,-0.06584,-0.05168,0.06424,0.0212,-0.00361,-0.08965,0.02876]},{"domain":"thermofluids","key":"ideal_gas_law","name":"Ideal gas law","package":"thermofluids-ai999x","example":"An ideal gas of 2 mol is held in a volume of 0.05 m^3 at a temperature of 300 K. What is its pressure?","v":[-0.00524,-0.03747,-0.10851,0.00846,0.00904,0.0737,0.02794,-0.02072,0.07797,0.06926,-0.04004,0.04304,0.03663,0.02793,-0.038,-0.00018,0.09737,0.0173,0.09424,0.13002,0.08426,-0.03381,-0.03945,0.01488,-0.02062,0.04158,0.09125,0.06387,0.08764,0.02392,0.0376,-0.01088,0.0816,0.02759,-0.11061,0.04865,-0.04401,0.0742,0.04563,0.02579,-0.04336,-0.0662,0.01054,0.07138,0.0367,-0.04723,0.03682,-0.08788,0.14291,-0.04951,0.10745,-0.10247,-0.06023,0.077,-0.04006,-0.13667,-0.03221,0.0097,0.09007,0.03711,-0.02867,-0.08354,-0.08349,-0.01908,0.04611,-0.20794,0.02114,-0.06799,-0.0849,0.109,-0.08123,0.00502,0.0384,-0.05179,0.06083,0.02399,0.04656,-0.06324,0.02173,0.01109,0.09538,0.00294,0.03389,0.04104,0.0777,0.13263,0.04535,-0.0513,-0.06744,-0.01569,0.04671,0.00504,-0.11039,0.05008,-0.02646,0.04306,-0.02555,0.05096,0.0468,0.01551,-0.03109,-0.08158,-0.00575,-0.01694,-0.08306,0.00983,0.00926,-0.07136,0.07019,0.01182,0.00688,-0.09076,0.0228,0.01871,-0.08857,-0.04535,-0.02483,-0.00869,-0.04752,0.03793,0.05407,-0.08947,0.00728,-0.13886,0.06669,-0.11071,0.10304,-0.0402,0.03898,0.01621,-0.09569,-0.0767,-0.03055,-0.01126,-0.05704,-0.05393,-0.07078,0.05995,0.0798,0.04189,0.01162,-0.02062,-0.02003,0.04491,0.07504,0.0228,0.01006,-0.12274,-0.02449,-0.11674,-0.01256,0.11522,-0.043,-0.00216,-0.04058,0.16739,-0.03943,0.02381,0.10909,-0.10186,-0.07325,-0.02506,-0.00026,-0.075,-0.10912,0.05885,0.0495,-0.00515,0.00679,-0.05142,-0.04691,-0.04434,-0.0261,0.0755,0.02422,-0.04442,-0.00048,-0.08298,0.11726,0.0342,0.11726,0.04876,-0.00391,0.00678,0.02852,-0.02175,0.03176,-0.04716,-0.12866,-0.06239,-0.00541,0.02022,-0.0137,0.04377,0.06044,0.01645,-0.00611,0.11653,-0.07175,0.09343,0.03223,-0.02513,0.05585,0.03701,-0.01625,0.01853,-0.00942,0.01823,0.12682,-0.01842,0.03415,-0.06199,0.03217,0.0022,0.04644,-0.01453,-0.00416,-0.15285,-0.00993,-0.07059,-0.0483,0.04601,0.01324,-0.10362,-0.12893,-0.06224,0.04423,-0.02058,-0.07365,-0.08446,0.10689,-0.0257,0.08886,0.0428,0.01948,0.08997,-0.04673,0.00658,-0.01042,-0.04215,0.02856,0.0527,0.06848,0.0484,0.04627,0.00864,0.01483,-0.01916,-0.03803,-0.01295,0.06626,-0.05031,-0.06339,-0.02276,-0.04756,-0.02591]},{"domain":"thermofluids","key":"isothermal_work_ideal_gas","name":"Work done by an ideal gas in a reversible isothermal process","package":"thermofluids-ai999x","example":"An ideal gas of 1 mol expands isothermally at a temperature of 300 K from an initial volume of 0.01 m^3 to a final volume of 0.02 m^3. How much work is done by the gas?","v":[0.09337,-0.11364,-0.05615,0.05724,-0.037,0.07847,-0.04726,-0.04182,-0.04039,0.04692,-0.05432,6e-05,0.02105,-0.02585,0.00114,-0.04954,0.02862,-0.05321,0.12619,0.12489,0.05946,0.04639,-0.02971,0.08294,-0.07783,-0.00021,0.02287,0.08192,0.01534,0.05176,0.05569,-0.02556,0.03287,0.04927,-0.02624,0.08412,-0.15953,0.03085,0.05117,-0.07463,-0.02158,-0.05057,-0.01507,-0.00535,0.04169,-0.06218,0.06633,-0.06454,0.04032,-0.0536,0.04968,-0.06294,0.0202,0.01358,-0.0351,-0.09128,-0.00746,0.1175,0.04486,0.07298,0.03584,0.00261,-0.07995,0.0426,0.05772,-0.10036,0.10449,-0.08722,-0.08302,0.08412,0.01163,0.04955,-0.01423,-0.04861,0.00106,0.00045,-0.0328,0.01395,0.03374,0.01614,0.00024,0.01481,-0.02236,0.047,-0.02395,0.07786,0.04526,-0.01231,0.06752,0.05055,0.0664,-0.05028,-0.025,0.0371,-0.08161,-0.00251,0.01272,0.06878,0.03518,-0.03359,0.06166,-0.06476,-0.01627,0.00656,-0.11817,-0.02456,-0.06369,-0.14137,0.02444,0.01249,-0.02639,-0.0638,0.0476,-0.0133,-0.05625,0.06174,-0.09136,-0.11788,0.00927,0.07829,-0.04476,-0.09991,0.07539,-0.10604,0.03902,-0.11606,0.05576,-0.10186,-0.01759,0.12933,0.01161,-0.04126,-0.09202,-0.0014,-0.08038,-0.0277,-0.00917,0.03245,0.02055,-0.0494,0.03918,-0.04368,-0.0878,0.04108,0.01539,0.01741,-0.03669,-0.09551,0.04123,-0.14574,0.03279,0.00581,-0.07446,0.02113,-0.0039,0.15519,0.00627,-0.0451,0.14998,-0.09193,0.01653,-0.07602,0.04032,-0.03477,-0.08882,0.00186,0.0587,-0.02487,-0.01613,0.06052,0.00319,0.06198,-0.02878,0.14321,-0.05778,-0.11339,0.02523,0.0209,0.10772,-0.05662,0.05416,-0.02283,-0.01331,-0.06051,0.01863,-0.0195,-0.06673,-0.03702,-0.02046,-0.06374,-0.10871,0.0136,-0.01934,0.12646,0.05515,0.05024,-0.04956,0.05557,-0.08487,0.00618,-0.0089,0.05491,0.05918,-0.09715,0.05866,-0.03557,-0.00997,-0.02964,0.0482,-0.09888,0.08094,-0.10117,-0.06462,0.08436,0.13938,0.05955,0.06236,-0.16522,-0.03898,-0.04567,0.03436,0.01904,0.08022,-0.09142,0.0438,0.03001,0.03313,0.05373,-0.09587,-0.04514,0.08665,-0.04024,0.0144,0.00082,0.03351,0.01773,-0.02899,-0.03935,-0.04173,-0.07542,0.03664,0.00341,0.09364,0.12707,0.06478,0.04573,0.04495,0.02932,0.0034,0.01786,0.08696,0.02814,-0.01926,0.05674,0.00797,0.06471]},{"domain":"thermofluids","key":"entropy_change_ideal_gas","name":"Specific entropy change of an ideal gas","package":"thermofluids-ai999x","example":"An ideal gas with a specific heat at constant pressure of 1005 J/(kg*K) and a gas constant of 287 J/(kg*K) goes from an initial temperature of 300 K and an initial pressure of 100 kPa to a final temperature of 600 K and a final pressure of 500 kPa. What is the specific entropy change?","v":[0.04906,-0.0281,-0.02759,-0.02155,-0.02101,0.11209,0.04997,0.01524,-0.03336,-0.00125,-0.0583,0.0324,-0.03064,0.09313,0.08522,0.03683,-0.0029,-0.0409,0.05095,0.18037,0.07217,-0.01254,0.03899,0.05556,-0.04574,0.03562,-0.00217,-0.04008,0.01316,0.0397,-0.03399,0.0144,0.02663,-0.00837,-0.00083,0.2184,-0.17503,0.00914,-0.00761,0.04429,0.01921,0.01109,0.07161,0.07859,-0.0113,0.04369,0.12703,0.01613,0.01689,-0.04665,0.0162,0.01163,0.0253,0.00239,-0.02071,0.00249,0.04926,0.10365,0.07054,0.03185,-0.06449,-0.06575,0.00834,0.00106,-0.01338,-0.05343,0.02007,0.07884,-0.0496,0.07596,-0.07119,0.06585,-0.06255,0.08436,0.06723,-0.00796,0.0232,-0.02642,-0.10147,-0.00625,-0.04643,-0.03986,0.12807,0.09532,0.0671,-0.07018,0.00536,-0.02297,-0.0445,0.0226,-0.01154,-0.10686,-0.00297,-0.03643,-0.06411,-0.04164,0.00042,0.02253,0.07075,-0.11569,0.08182,0.06256,-0.09285,0.01493,-0.05916,0.03825,-0.00895,-0.02524,0.01726,0.03867,0.03575,0.06345,0.03982,-0.04336,-0.05099,-0.06026,0.01535,0.04766,0.01542,-0.05421,-0.08787,-0.02288,0.05421,0.07891,-0.03706,-0.03866,-0.01908,-0.1061,0.0142,0.09483,0.03643,-0.04509,-0.0941,-0.03847,0.03472,0.02036,0.03025,0.03566,-0.03331,-0.0395,-0.02493,0.01452,0.0121,0.05787,0.08677,0.03373,-0.05345,-0.07515,-0.05306,0.0381,-0.01051,-0.20774,-0.11068,-0.04801,0.06671,0.05267,-0.01567,-0.03556,0.09659,-0.06523,-0.03828,0.0297,0.07958,-0.06171,-0.07641,-0.07329,0.05252,-0.04391,0.00521,0.14019,0.02646,-0.02501,-0.0274,0.03086,-0.02524,0.02309,-0.04866,0.12428,0.0481,-0.00153,0.00475,0.03712,-0.08192,0.02052,0.01925,0.00061,-0.0218,-0.05473,-0.017,-0.04577,-0.04434,0.09343,0.01467,-0.00527,0.03105,0.01207,-0.09579,-0.09222,-0.09235,-0.09657,-0.09021,0.0187,0.08719,-0.04961,-0.00934,-0.05882,-0.00326,-0.01679,-0.01343,-0.04619,-0.01925,-0.00792,-0.00684,-0.03817,0.10954,0.01959,-0.02214,-0.017,-0.03812,0.00743,-0.03517,-0.01435,0.1213,-0.0272,-0.09863,-0.06955,-0.02373,0.06377,-0.11856,-0.02294,0.08841,-0.10222,-0.01439,-0.1029,0.0523,-0.00441,0.01461,-0.12661,-0.08221,0.16423,0.02246,-0.03476,0.13494,0.18321,0.02376,-0.01727,-0.00191,-0.07881,-0.03762,0.00032,-0.06617,0.14384,-0.02357,0.02316,-0.02472,0.11067]},{"domain":"thermofluids","key":"entropy_change_incompressible","name":"Entropy change of an incompressible substance","package":"thermofluids-ai999x","example":"A mass of 2 kg of liquid water with specific heat 4180 J/(kg*K) is heated from an initial temperature of 20 °C to a final temperature of 80 °C. What is its entropy change?","v":[0.04372,0.02288,-0.04037,0.00312,0.00846,0.06614,0.05075,-0.05047,-0.00536,-0.01115,0.02091,0.06918,-0.02343,-0.00319,0.1012,-0.08105,-0.04594,-0.04986,0.02243,0.09096,0.07623,0.01211,-0.06405,0.04237,-0.09607,0.02843,-0.02363,-0.0218,-0.02421,0.05374,-0.11223,-0.01796,-0.04934,-0.04392,0.05855,0.15231,-0.12546,-0.09651,0.01745,0.02122,0.00575,-0.01295,0.09361,0.05636,-0.02781,0.02961,0.0542,-0.00033,-0.00059,0.00873,-0.05192,0.00758,0.03583,-0.03975,-0.01187,0.02347,0.0815,0.10361,0.09146,-0.0147,-0.06437,-0.01156,0.05509,0.10084,0.08224,0.02721,0.05667,0.04173,0.03733,0.08321,-0.0215,0.02453,-0.08005,0.10745,0.03379,0.04392,-0.00078,-0.05905,-0.08819,-0.03457,-0.06364,-0.09564,0.04751,-0.01613,0.03622,0.01557,-0.06342,0.01175,-0.02951,-0.02344,-0.01403,-0.13071,0.04268,-0.06772,-0.08964,-0.0493,-0.08665,-0.02489,0.1001,-0.06292,0.08482,0.03051,-0.15633,-0.07505,-0.06778,0.05498,0.03673,0.02865,-0.06195,0.05352,0.03611,0.12378,0.03644,0.00375,-0.03713,-0.04689,0.07188,0.01553,0.01657,0.08506,-0.04192,0.03256,0.04511,0.10735,0.05355,0.00874,-0.01528,-0.12527,0.04155,0.06662,0.06918,0.03995,-0.0838,-0.02166,0.01471,0.02599,0.12907,0.02284,-0.05341,-0.06352,-0.00779,0.00393,-0.01691,0.02453,-0.02422,-0.01689,0.01228,-0.00689,-0.04273,0.02216,0.01679,-0.16862,-0.1705,-0.17512,-0.0099,0.09765,-0.12929,-0.09618,0.10093,-0.01916,-0.01671,0.0438,0.03332,0.01881,-0.02148,-0.01288,0.02392,-0.07182,0.0494,0.06578,0.06933,-0.06717,-0.0656,0.01726,-0.05354,-0.00206,-0.0406,0.09385,-0.05075,-0.01363,0.04307,0.05232,-0.06323,0.04438,0.00651,0.03652,0.0203,0.01718,0.00412,-0.07092,-0.08949,0.0821,0.0658,-0.0149,-0.00764,0.0185,-0.05629,-0.04937,-0.08177,-0.01153,-0.09594,-0.02513,0.08891,-0.05749,-0.00638,0.01331,0.03824,-0.04755,-0.07864,-0.0356,0.01308,-0.03622,-0.0062,0.02356,0.0822,-0.03182,0.0028,-0.03599,0.03826,0.01436,-0.03434,0.00135,0.04615,-0.03195,-0.04253,0.01143,-0.06566,0.06459,-0.11402,0.04538,0.07294,-0.05797,-0.03339,-0.09377,0.09871,0.02363,0.03927,-0.14379,-0.09609,0.09583,-0.0263,-0.09886,0.05579,0.16279,0.04413,-0.01221,0.09204,0.0261,0.05903,0.01615,-0.07529,0.08199,0.09282,0.0029,-0.06144,0.154]},{"domain":"thermofluids","key":"humidity_ratio_vapour_pressure","name":"Humidity ratio from the partial pressure of water vapour","package":"thermofluids-ai999x","example":"Moist air at a barometric pressure of 101325 Pa has a partial pressure of water vapour of 2000 Pa. What is the humidity ratio?","v":[0.01424,-0.02726,-0.06403,0.00126,0.13737,0.07038,-0.00245,0.07879,-0.07346,0.02693,-0.03394,0.09895,0.04601,-0.06409,-0.00048,0.0059,-0.0148,0.01865,-0.04928,0.07605,-0.05959,-0.1224,0.0259,-0.01365,-0.06369,0.02552,0.08413,-0.03228,0.01956,-4e-05,0.08362,0.05435,-0.04642,0.02185,-0.00885,-0.04664,0.02437,0.02885,0.02896,0.12678,0.17344,-0.06307,-0.04982,-0.02088,-0.0561,-0.06085,-0.04378,-0.08629,-0.14732,0.00202,0.02838,-0.12895,-0.02614,0.02792,-0.07648,0.01385,-0.02507,-0.06777,0.03459,-0.05985,0.00229,-0.06872,-0.00768,0.01346,0.01833,-0.00285,-0.03568,-0.03018,-0.00139,-0.04328,0.06606,0.01452,0.07738,-0.05832,0.03989,-0.01698,0.06706,-0.1006,0.0524,-0.06865,-0.06236,0.05048,-0.01341,0.09091,0.0271,-0.06767,0.02396,0.02579,0.12178,-0.02413,-0.008,0.05746,-0.06781,-0.04841,-0.04549,-0.03611,0.032,0.00623,-0.10171,0.01478,0.00729,0.09257,0.09986,-0.05491,-0.04536,-0.12775,0.10178,0.01397,0.11775,-0.06257,0.06202,-0.19565,0.02329,0.01963,-0.19122,-0.03119,0.04976,0.06029,0.03054,-0.02569,-0.02288,-0.00189,-0.0637,-0.04518,-0.00577,0.06607,0.03365,0.00193,0.0045,-0.07486,0.05507,0.10348,0.11818,0.06828,-0.03111,0.02082,-0.06124,0.01699,-0.03189,0.06362,0.03285,0.01885,0.08801,-0.11293,0.02058,0.01658,0.07851,-0.05052,-0.04437,0.00019,-0.08081,-0.01368,0.05391,-0.00272,0.09524,0.06335,-0.04303,-0.02622,0.07005,0.04808,0.01105,-0.12864,0.08158,-0.05556,0.01553,-0.09284,0.02353,0.01417,0.01797,-0.06728,-0.04022,-0.0164,0.01018,-0.03583,0.07047,-0.07586,0.06555,-0.09901,0.09975,0.05222,-0.05425,0.11361,0.01609,0.0589,-0.01876,-0.00843,-0.04075,-0.06066,-0.06843,-0.0251,-0.02536,0.06658,-0.13836,-0.05805,-0.02713,-0.04176,0.04132,0.14394,0.03185,0.04469,0.06136,0.03888,0.03801,0.0486,-0.08916,-0.01602,-0.05285,-0.00204,0.01703,-0.01314,-0.07893,0.04729,-0.0689,0.07817,0.0554,-0.09089,0.06017,-0.05162,-0.05066,-0.02436,0.08153,-0.12022,-0.09072,0.0436,-0.01568,-0.04401,0.07273,0.02718,0.10214,-0.08382,-0.05427,-0.0018,0.00478,0.04689,0.0835,-0.0128,-0.10562,0.03745,-0.011,-0.02274,-0.02677,-0.07992,0.0275,0.07234,0.04174,0.00525,0.15633,0.0438,-0.01649,-0.02667,-0.08532,-0.02989,0.02304,-0.01591,-0.02265,0.04663]},{"domain":"thermofluids","key":"moist_air_enthalpy","name":"Specific enthalpy of moist air","package":"thermofluids-ai999x","example":"Moist air has a dry-bulb temperature of 25 °C and a humidity ratio of 0.01. What is its specific enthalpy?","v":[0.10473,-0.01252,-0.00461,0.05893,0.0118,-0.04697,0.08785,0.07943,-0.04882,0.06098,-0.01653,0.10186,-0.02484,0.04961,0.01792,-0.01744,-0.09249,-0.01488,-0.04189,0.03425,0.03309,0.00308,-0.03957,-0.06535,-0.02151,-0.02358,0.07873,-0.04122,-0.07182,0.01626,0.00883,0.01082,-0.0066,0.03079,0.06306,-0.00407,-0.11918,0.05841,0.05552,0.07955,0.05764,0.03104,-0.05029,0.09981,0.00022,-0.06361,0.01983,0.00372,-0.0318,-0.04723,-0.04984,-0.07447,0.01843,-0.00576,-0.05339,-0.05513,0.01588,0.04464,0.08908,0.03846,-0.00612,-0.07726,0.10065,0.1,-0.0289,-0.0025,-0.15003,0.03122,0.04689,0.01388,0.01265,0.09496,0.00351,-0.03001,0.21761,0.00353,0.00758,-0.07418,0.00798,-0.06642,-0.13615,0.00604,-0.03542,0.08139,0.0169,-0.04982,-0.07499,-0.03965,0.02231,0.03258,-0.06353,-0.03595,-0.00625,-0.02567,-0.09615,-0.07842,-0.08422,-0.07115,-0.03011,-0.00116,0.08167,0.0066,-0.03452,-0.02928,-0.10373,-0.04154,0.03517,0.02776,0.08347,-0.05731,0.09535,-0.10879,0.05807,-0.01057,-0.09524,0.03696,0.06982,0.01311,0.01609,0.05502,-0.05171,-0.12104,-0.00666,-0.01396,-0.00337,-0.0102,0.05182,-0.09172,-0.0766,-0.00915,0.04966,0.08871,0.07731,-0.08957,0.10612,-0.00191,0.01886,-0.06266,-0.05173,-0.0108,0.18721,-0.07941,0.08809,-0.02257,0.08384,0.05516,-0.07087,-0.11069,-0.01549,-0.03288,0.04063,-0.10894,-0.04242,-0.02437,-0.05115,0.09773,-0.05757,-0.06916,0.09456,0.01629,0.06306,-0.01088,0.08541,-0.04178,-0.04054,-0.00231,-0.01635,-0.03825,0.09506,0.00681,0.03405,-0.05887,-0.0414,0.03265,-0.0891,0.00644,-0.01189,0.02702,0.07425,-0.0426,0.03385,0.09632,-0.0353,0.06275,0.06847,-0.07982,-0.00755,0.00391,-0.02894,-0.00393,0.02314,0.07096,0.01005,0.02949,0.02104,-0.00694,-0.04508,0.13652,0.00211,-0.04308,-0.01487,0.037,0.09992,-0.06448,-0.05359,-0.08689,0.02349,0.01033,-0.02861,-0.1084,-0.09519,0.04117,-0.00618,0.04846,0.08888,-0.0174,-0.07249,-0.06686,0.05832,0.04606,0.02468,-0.03424,0.06788,0.05492,-0.07213,0.00033,0.07691,0.14124,-0.04151,-0.02592,-0.02484,-0.01496,-0.00733,-0.06579,0.10812,-0.08175,0.01503,-0.11098,-0.07834,0.14068,-0.01466,-0.01967,0.06054,0.1082,-0.01872,-0.00267,0.1728,0.02205,0.02227,0.01737,-0.0538,0.04647,0.10101,-0.02888,-0.06543,0.08537]},{"domain":"thermofluids","key":"moist_air_specific_volume","name":"Specific volume of moist air per kilogram of dry air","package":"thermofluids-ai999x","example":"Moist air at a dry-bulb temperature of 25 °C, a humidity ratio of 0.01 and a barometric pressure of 101325 Pa. What is its specific volume?","v":[0.02864,-0.07374,-0.02592,0.01494,0.03629,0.02758,0.03472,0.11045,-0.00479,0.0737,0.01071,0.13554,0.10183,-0.03234,0.01053,-0.06588,-0.03771,0.01514,-0.03218,0.03296,0.03178,-0.0756,0.02564,-0.02419,-0.0094,-0.0565,0.09847,-0.06012,-0.05987,-0.0499,0.09318,-0.02089,-0.00066,-0.01362,0.05125,-0.10368,-0.04671,0.06472,0.0675,0.10272,0.10667,0.02557,-0.0727,0.05048,-0.0511,-0.1037,-0.07765,-0.06463,-0.02166,-0.09833,-0.01372,-0.05955,0.01239,-0.03756,-0.02835,-0.0916,0.03566,0.03125,0.11603,0.09794,-0.00657,-0.04351,-0.04519,0.0195,-0.0472,-0.01299,-0.03508,-0.01989,0.00149,0.1136,0.08108,0.07638,0.03402,-0.05885,0.19908,0.02664,0.07387,-0.12496,0.04243,0.00925,-0.07433,0.07918,-0.00209,0.09342,-0.00702,0.01788,0.01944,0.02459,0.14665,0.04929,-0.0542,0.00927,-0.09345,0.01462,-0.09258,-0.04979,-0.02472,-0.01968,-0.04921,-0.03214,0.04691,0.01583,0.01032,-0.02568,-0.08615,-0.06907,0.02774,0.00021,0.13541,-0.03415,0.06893,-0.20793,0.05203,0.05715,-0.15955,-0.01989,0.03758,0.02075,0.00746,-0.0635,-0.0673,-0.05878,0.00906,-0.08845,0.04554,-0.07553,0.08723,-0.07272,-0.03535,-0.00624,0.0205,0.09067,0.05534,-0.02889,0.06565,-0.03372,-0.04196,-0.05594,-0.00967,0.05614,0.07247,0.03081,0.02511,-0.01937,0.00528,0.10308,-0.00173,-0.10919,0.03528,-0.03055,-0.02562,0.01538,-0.00612,-0.03931,0.0557,-0.02533,-0.05738,-0.04809,0.09006,-0.01417,0.02122,-0.06334,0.08944,-0.10451,0.04717,0.01735,0.0169,-0.07432,0.02344,-0.03241,-0.00932,-0.04546,-0.0222,0.01316,0.02164,-0.01175,0.01878,-0.16872,0.05741,-0.02711,-0.05242,0.10269,0.04954,0.09471,0.01465,-0.06358,0.06377,-0.06164,-0.04335,-0.05693,-0.01294,0.07229,-0.11896,0.01735,-0.00248,0.03079,-0.01919,0.17377,-0.01708,-0.06528,-0.01003,0.07319,-0.00708,0.0138,-0.02455,-0.08044,-0.01789,-0.00027,0.06804,-0.09682,-0.0843,0.02111,-0.0331,0.02535,0.04376,-0.04907,-0.01628,-0.07384,-0.03362,0.02046,-0.03975,0.01229,0.03807,0.09143,-0.05627,-0.00405,0.02856,0.07629,-0.00131,-0.02554,0.01621,-0.02088,-0.0039,-0.0587,0.09772,-0.00252,-0.00337,-0.08339,-0.06575,0.07238,-0.04654,-0.04374,0.09275,0.1001,0.08525,0.08754,0.17453,-0.00809,-0.03159,0.07763,-1e-05,0.03498,-0.02325,0.00915,-0.08379,-0.03825]},{"domain":"thermofluids","key":"adiabatic_flame_temperature_simple","name":"Adiabatic flame temperature with constant product specific heat","package":"thermofluids-ai999x","example":"Methane with a lower heating value of 50000000 J/kg burns at an air-fuel ratio of 17.2 with a reactant temperature of 298 K. Taking the specific heat of the products as 1200 J/(kg*K), what is the adiabatic flame temperature?","v":[-0.02626,0.01277,0.06314,-0.05433,0.01134,-0.11458,0.00721,0.03937,-0.03381,0.0978,-0.03835,-0.05422,0.08401,-0.02966,0.02944,0.06988,-0.06236,0.11177,0.01506,-0.0193,0.03831,-0.13705,-0.01609,-0.10337,0.02098,-0.00923,-0.01005,-0.09396,-0.06088,-0.01602,-0.00987,-0.0213,0.00758,0.0118,0.1877,0.05851,0.1442,0.02233,-0.08178,-0.00015,0.02786,-0.00595,-0.06075,-0.00717,0.0029,-0.02764,-0.05043,-0.09658,0.00787,0.00321,-0.06574,-0.03367,0.02902,0.08092,-0.03662,-0.08285,0.07938,0.07468,0.04093,0.09242,-0.04925,-0.09132,0.05225,0.01404,-0.03972,0.01979,-0.0341,0.06967,0.01784,0.07858,0.00073,0.043,-0.02375,-0.08762,0.01104,0.07919,0.06705,0.03983,0.03623,0.01973,-0.08028,-0.11333,0.01007,0.02385,0.03781,-0.06186,0.09469,-0.05048,-0.02754,0.06224,0.12193,0.04731,0.06793,0.05575,-0.05819,-0.02624,-0.06111,-0.07714,0.04945,-0.03891,0.0379,0.02397,-0.03691,-0.15236,-0.03926,-0.10534,-0.0155,-0.00807,-0.05943,-0.11379,0.03108,-0.02741,0.11132,0.0312,-0.07253,0.01247,0.01068,0.01621,-0.03795,-0.02031,-0.09401,0.00161,0.04537,-0.06952,-0.01386,0.17635,0.01983,-0.06243,-0.02194,0.06805,0.02765,0.09225,0.01743,-0.05703,-0.04269,-0.00916,-0.03189,-0.03193,0.00683,-0.03492,0.01631,0.04343,0.2246,-0.08116,0.01519,0.10752,-0.0735,-0.03366,0.05012,-0.06206,-0.00169,-0.01445,-0.03622,-0.06833,-0.07676,-0.06669,-0.04584,-0.09755,0.02163,-0.02366,-0.07601,0.00784,-0.06373,-0.08886,-0.06692,0.064,0.05078,-0.07486,0.07247,0.03973,-0.0813,0.1444,-0.04867,0.09588,-0.01521,0.08014,0.01203,0.01035,0.08775,-0.0288,-0.04594,0.00742,-0.09372,0.09967,0.00731,-0.06135,-0.05442,0.09642,0.00457,0.02438,0.01426,0.06228,-0.05378,0.06919,0.0187,-0.03774,0.01326,0.09942,-0.04379,-0.05756,0.07031,-0.07054,0.0804,0.01267,-0.04328,-0.09851,0.02677,0.14446,-0.02656,-0.03636,-0.0453,-0.04495,-0.04987,0.00723,0.09485,0.08745,0.0015,0.03281,0.04182,0.07393,0.00605,0.00578,0.03869,0.06262,-0.02437,0.03383,-0.02747,0.06454,0.03037,-0.00131,0.01567,-0.00915,-0.00906,-0.0997,0.11316,-0.09709,0.12436,0.00956,-0.05791,0.07381,-0.00268,0.03787,0.02604,0.01765,-0.03114,-0.01025,0.02917,-0.15136,0.03041,-0.00541,-0.008,0.08835,-0.04657,0.04524,-0.02243,-0.0143]},{"domain":"thermofluids","key":"churchill_bernstein_cylinder","name":"Churchill-Bernstein 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epidemic model: peak prevalence and the time of the peak","package":"biomedical-science-ai999x","example":"SEIR peak: beta = 0.5 1/day, sigma = 0.2 1/day, gamma = 0.1 1/day, s0 = 0.99, e0 = 0.008, i0 = 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epidemic model: final size (final susceptible fraction and attack fraction)","package":"biomedical-science-ai999x","example":"SIR final size: R0 = 2.5, s0 = 0.99, i0 = 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epidemic model: peak prevalence and the time of the peak","package":"biomedical-science-ai999x","example":"SIR peak: beta = 0.3 1/day, gamma = 0.1 1/day, s0 = 0.999, i0 = 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epidemic model: prevalence at a time and the endemic level","package":"biomedical-science-ai999x","example":"SIS prevalence: beta = 0.4 1/day, gamma = 0.1 1/day, i0 = 0.01, t = 10 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clearance: well-stirred liver model (a model calculation, not medical advice)","package":"biomedical-science-ai999x","example":"Well-stirred hepatic clearance: Q = 90 L/h, fu = 0.1, CL_int = 500 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IV bolus doses: concentration after the nth dose (a model calculation, not medical advice)","package":"biomedical-science-ai999x","example":"Concentration after the nth IV dose: D = 500 mg, V = 40 L, k = 0.1 1/h, tau = 8 h, n = 3, t = 2 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dose, first-order absorption: concentration at a time (Bateman function) (a model calculation, not medical advice)","package":"biomedical-science-ai999x","example":"Oral dose concentration: F = 0.8, D = 250 mg, V = 35 L, ka = 1.2 1/h, k = 0.15 1/h, t = 3 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Windkessel: diastolic pressure decay","package":"biomedical-science-ai999x","example":"Windkessel diastolic decay: P0 = 120 mmHg, Pv = 5 mmHg, R = 1 mmHg*s/mL, C = 1.5 mL/mmHg, t = 0.5 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models (two- and three-element): input impedance at a frequency","package":"biomedical-science-ai999x","example":"Windkessel impedance: model = two_element, R = 1 mmHg*s/mL, C = 1.5 mL/mmHg, f = 1.2 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attenuation through tissue layers (narrow monoenergetic beam)","package":"biomedical-science-ai999x","example":"X-ray attenuation through layers: I0 = 1000 W/m^2, mu_rho = [0.2, 0.5, 0.2], rho = [1, 1.85, 1], x = [2, 1, 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3]","v":[0.05947,-0.04112,0.07839,0.06427,-0.05378,-0.03727,0.03846,0.01874,-0.00529,0.00873,-0.04752,0.08324,-0.03542,0.00203,-0.03179,-0.05599,-0.05042,-0.06335,-0.04625,-0.01145,0.03849,0.05249,0.07924,0.01714,0.00993,0.08,0.12469,-0.12504,-0.08709,-0.02421,0.00555,0.06074,-0.04859,0.01853,-0.03873,0.02555,-0.04054,-0.07071,-0.0309,-0.04681,0.03492,0.04498,-0.07037,-0.01425,0.03058,-0.09816,0.01206,0.01434,-0.13755,-0.05159,-0.03479,0.10697,-0.04546,-0.03407,-0.05609,0.10723,0.09394,-0.01486,-0.00614,0.04292,-0.01282,-0.09582,-0.01038,-0.0778,-0.12856,0.04336,0.02112,0.04642,-0.11989,0.09576,0.10478,-0.0195,0.16309,-0.02477,-0.09955,0.05302,-0.00399,-0.10733,0.03003,0.07246,0.05891,0.04426,0.04008,0.01897,0.08716,-0.05058,0.10547,-0.06564,0.02058,0.02449,-0.09486,-0.08714,0.04139,0.04122,0.04403,0.03828,-0.00849,-0.03163,0.01024,-0.0872,0.05465,-0.02673,-0.02797,-0.10214,-0.03438,0.02623,-0.09076,-0.01793,0.01465,-0.10137,0.05121,-0.0701,0.0491,0.02566,0.00616,-0.10206,0.01994,0.05566,0.07897,-0.05603,-0.03298,-0.01052,-0.03567,0.0859,0.02627,0.10909,0.0012,-0.10748,-0.10349,0.04001,0.05336,0.04543,-0.02668,-0.03635,-0.05344,-0.04592,-0.06339,-0.00198,-0.04486,-0.06349,-0.024,0.06606,0.01961,-0.05308,0.10084,0.15469,0.01294,-0.00776,0.05893,0.02632,0.01094,-0.01105,-0.07151,-0.0088,0.07747,-0.11518,0.07709,-0.06157,-0.02451,0.02624,0.11566,0.01336,-0.00871,-0.04798,0.03099,-0.06685,0.03263,-0.05194,0.04591,0.03995,0.06578,-0.02092,0.08265,-0.0327,-0.04553,-0.06903,-0.00303,0.09178,-0.00114,-0.19376,0.01346,0.04737,0.00023,0.00581,-0.02209,0.02463,0.10996,0.10165,-0.04151,0.13557,0.14063,0.06792,-0.10022,0.06176,-0.02254,-0.08231,0.02985,-0.01617,-0.05622,-0.03792,-0.05234,0.09876,0.04994,-0.01818,-0.07759,-0.00784,-0.02778,-0.02024,0.05212,0.08374,-0.09193,-0.13965,0.02984,0.12471,-0.03853,0.01712,0.02406,-0.02709,-0.0382,-0.03047,0.1004,-0.01956,0.0197,-0.00105,-0.03757,0.03159,-0.01978,-0.02382,0.02331,0.03485,0.00802,0.14078,0.04291,0.01,0.0251,-0.08596,0.0294,-0.0027,0.09242,0.02313,0.02886,-0.03835,0.06768,0.03953,-0.03775,-0.02103,-0.09227,0.01675,0.1122,-0.03372,-0.03689,0.00965,-0.04671,0.03126,-0.08984,0.08191]},{"domain":"computational_biology","key":"bio_brillouin_diversity","name":"Brillouin 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2]","v":[-0.12606,-0.03879,0.01941,-0.02843,-0.03735,-0.02103,-0.00497,0.01561,-0.1021,-0.02414,0.05112,0.06656,-0.18247,-0.01597,0.00911,0.00979,-0.1071,0.02279,-0.02741,-0.03787,-0.01563,-0.12787,-0.03068,0.01662,-0.03669,0.04518,0.08971,-0.05666,0.04445,-0.05017,-0.04692,-0.0162,0.02662,-0.10557,0.05884,0.05434,-0.09592,-0.04987,-0.00139,-0.15111,-0.06186,0.01476,-0.05813,-0.06975,0.10262,-0.01935,0.0281,-0.04256,-0.175,-0.04131,-0.02863,-0.06955,-0.08094,-0.04308,-0.15695,0.11222,0.0403,-0.04358,0.08277,0.02064,0.08707,0.2372,-0.05681,-0.00925,-0.01682,-0.00539,0.01226,-0.0034,0.01102,0.06453,-0.00835,-0.06291,0.07783,0.02793,-0.06917,-0.04577,-0.03179,-0.06287,0.02046,0.01373,-0.03903,0.01866,0.05167,-0.03915,0.06579,-0.0857,0.02877,-0.05421,0.0392,0.02851,-0.07111,-0.05341,0.04568,0.05066,0.02764,0.10718,0.00308,0.01081,0.01237,-0.03291,0.00613,-0.05716,-0.00109,0.0204,0.11608,-0.04696,-0.04851,0.01654,0.10301,-0.0808,0.01786,-0.06998,0.0505,0.02387,0.00281,-0.03148,0.09476,-0.02518,0.00936,-0.04593,-0.13844,0.05008,0.03714,0.0718,0.0709,0.02833,0.02207,-0.02161,-0.02315,-0.01762,-0.01291,0.04832,0.02451,-0.01084,-0.01628,0.0029,-0.00279,0.00616,-0.02604,-0.01456,-0.0243,0.14974,0.04271,-0.04838,0.07999,-0.03863,0.06854,-0.03021,0.05246,0.04966,-0.04706,0.03718,0.02898,-0.0823,0.10906,-0.05527,0.04525,0.00482,-0.02741,0.02482,0.11101,0.01883,0.05606,-0.01598,0.14223,-0.15569,0.02223,-0.09333,-0.00995,0.00823,0.05872,0.00338,0.00384,0.02581,-0.06567,-0.12709,-0.04343,0.00211,-0.03234,-0.01688,-0.01263,0.04653,-0.08716,-0.0116,0.08163,0.04711,0.0985,0.08706,0.01162,0.1863,-0.03497,0.07152,-0.11273,0.03554,-0.00714,-0.03291,-0.03723,0.02577,-0.05473,0.00879,-0.0258,0.05492,-0.01203,-0.02685,-0.0519,-0.00423,0.11013,0.05323,-0.06113,0.06432,0.00346,-0.03946,0.00776,0.1153,0.06433,-0.08606,0.00195,-0.0024,0.12063,0.00851,-0.03977,-0.01818,-0.04124,0.01808,0.06539,0.07816,-0.06237,-0.03165,0.00385,-0.01799,-0.02337,0.04201,0.0159,0.06375,0.08806,-0.08998,-0.01091,0.11975,-0.02484,0.04911,0.03156,-0.07265,0.04573,0.0368,0.00019,0.07358,-0.04038,0.01443,0.0994,-0.04781,-0.03873,0.01431,-0.06882,0.13059,-0.02042,0.02122]},{"domain":"computational_biology","key":"bio_chao1","name":"Chao1 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7.27272727273]","v":[-0.08863,0.00673,-0.0065,0.0485,-0.10429,0.07332,-0.02089,0.07219,0.02564,-0.04266,-0.10881,-0.06081,-0.00422,-0.08456,0.00179,-0.00109,-0.05031,0.025,-0.02413,0.00352,0.01208,-0.11079,0.03103,-0.03042,0.02122,-0.01937,0.06838,-0.05678,0.07022,0.02934,-0.02755,-0.04141,0.03951,-0.0188,0.08677,-0.04884,-0.02558,0.0626,0.04128,0.08541,0.07028,-0.02767,-0.09834,-0.04073,-0.04125,-0.00762,-0.01657,0.00284,0.04025,-0.07218,0.11555,0.02316,0.02022,0.00243,-0.04171,0.0065,0.08293,0.08218,0.00083,0.11715,0.04836,0.06238,-0.08679,0.02753,-0.05777,0.0263,-0.05062,-0.01107,-0.06171,0.095,0.08032,-0.04003,0.01902,-0.07741,0.05343,0.08864,-0.02605,0.00307,0.00032,0.01081,0.04746,0.085,-0.05299,-0.01592,-0.09963,-0.03332,0.04524,0.01409,-0.00171,-0.11226,-0.0003,0.09329,0.07442,0.02321,-0.01711,-0.00928,-0.04758,-0.01395,0.08418,-0.05734,0.0177,0.0712,0.00847,0.02978,0.06415,-0.08698,-0.08046,-0.01681,-0.14303,-0.0016,0.03302,0.10003,0.06965,0.06974,-0.01584,-0.08528,-0.0709,0.04728,0.00582,0.12106,0.06488,0.07106,0.05656,-0.0182,-0.02157,0.09847,0.08341,0.03777,-0.07189,-0.0238,-0.10866,-0.0665,-0.14026,-0.04277,0.03616,-0.04549,-0.10577,-0.01104,0.0463,-0.04765,0.0612,0.12945,0.07784,0.04446,0.04393,0.08021,0.00342,-0.0302,0.11598,-0.06998,-0.10393,0.12793,-0.09732,0.10089,-0.05945,-0.0162,-0.02873,-0.06159,-0.02161,0.05277,0.08245,-0.09977,-0.09202,-0.07203,0.05905,0.12057,0.04467,-0.02999,0.00811,-0.04803,-0.04077,-0.06611,0.05787,-0.00525,-0.04785,0.01232,0.08646,0.04632,0.0272,-0.07971,-0.10844,-0.0358,-0.03345,-0.07059,-0.05849,0.11541,0.033,-0.07485,0.00914,0.06565,0.00309,0.07023,0.01064,-0.0866,-0.03236,-0.00565,0.0021,-0.04769,0.03326,-0.01695,0.01508,0.05105,-0.04317,-0.0596,-0.15406,-0.05809,-0.02985,0.09054,-0.06549,-0.0196,-0.03165,-0.05102,-0.03721,0.05681,-0.10023,0.1124,-0.05768,0.08082,0.04258,0.01782,-0.06963,-0.05459,-0.05494,0.06581,-0.01443,0.05889,-0.17489,0.02217,0.01362,-0.05535,0.06604,0.06887,0.02141,-0.01308,0.09641,0.06189,0.10525,0.06722,-0.05143,0.0183,0.00371,0.01627,0.01079,0.03756,-0.09646,-0.04213,-0.02206,-0.03432,-0.0552,0.02036,-0.04611,0.01316,0.09511,0.0737,-0.01695,0.11871]},{"domain":"computational_biology","key":"bio_cross_genotype_probability","name":"Probability 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score of a tree (Fitch)","package":"computational-biology-ai999x","example":"Parsimony score: tree = ((A,B),(C,D));, states = A:AACG B:AATG C:GACT 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0.8]","v":[-0.09362,0.0339,-0.07048,-0.05971,0.00044,-0.02293,0.01685,-0.04292,-0.07646,-0.05195,-0.00715,-0.02397,-0.05812,-0.0449,-0.03118,-0.03369,0.00097,-0.00845,0.01231,0.00508,-0.03312,0.00427,-0.02102,0.0041,-0.01748,0.01658,0.00886,-0.14349,0.02603,-0.00624,-0.06258,-0.03529,-0.01886,-0.00896,0.10577,0.06635,0.02173,-0.06633,-0.00481,0.04073,-0.0289,-0.11459,-0.11424,0.00302,0.05295,-0.04258,-0.01249,-0.05149,-0.05683,-0.09792,-0.00326,0.04583,0.02742,-0.00826,-0.03996,0.05282,-0.05984,0.0137,0.00089,0.00471,0.07127,0.0647,0.02699,-0.17685,-0.05611,-0.03792,0.04967,0.002,-0.01685,0.02644,-0.06096,0.00988,-0.00463,0.03365,0.00844,0.05478,-0.11235,0.03795,0.04452,0.06589,0.02087,-0.06093,0.02545,0.06357,0.00509,-0.12347,-0.04102,-0.04462,-0.0536,0.0627,-0.10603,-0.04413,0.03054,0.00913,0.09365,-0.1329,-0.09249,0.0111,-0.07266,-0.05406,0.05055,-0.07644,0.16539,0.01308,0.05237,-0.03652,0.08249,0.02581,0.00954,0.05432,0.05535,0.07104,0.02736,0.13126,0.00635,-0.01436,0.12875,0.06289,0.0913,-0.07411,-0.06982,-0.04369,-0.06974,0.01798,0.1077,-0.00765,0.01279,-0.10536,0.03489,0.02565,0.07874,0.01534,-0.14589,-0.03533,-0.04489,-0.01615,0.01379,0.01557,0.03842,-0.06344,0.06928,0.04979,0.02499,-0.01959,0.15183,0.10294,-0.03718,0.06571,0.05858,0.03044,-0.06905,0.02956,-0.10676,0.05651,0.05095,-0.07843,0.00333,-0.01788,-0.08753,0.01374,0.08884,-0.10355,0.01609,-0.03373,-0.00767,-0.01679,-0.06083,-0.01793,0.07309,0.11152,0.08867,-0.04887,0.17034,0.06992,-0.04636,0.0191,-0.00103,0.10583,0.00486,0.04338,-0.03833,0.08761,-0.10435,-0.00568,-0.0116,0.03385,0.05228,0.0164,0.00028,0.03536,-0.03564,0.11537,-0.02725,0.0277,0.06199,0.05736,-0.04344,-0.06022,-0.02053,-0.08925,0.04931,-0.01724,-0.01172,-0.03583,-0.12519,-0.05766,0.08439,0.03772,-0.04858,0.13744,0.05526,-0.02262,0.00629,0.05986,-0.03775,0.04552,-0.03874,0.05728,0.06007,-0.04423,0.00166,0.05553,-0.11955,-0.08825,-0.02783,0.03326,-0.06533,0.02823,0.06089,-0.02379,0.09037,0.01378,-0.0166,0.0816,0.08084,-0.078,0.15606,-0.10205,-0.0526,0.12753,0.05236,-0.04492,0.03678,0.08339,-0.00111,-0.02452,-0.00644,-0.06566,0.14282,-0.06127,0.01767,-0.06161,-0.03867,0.0039,-0.04074,0.04484]},{"domain":"computational_biology","key":"bio_gc_content","name":"GC 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alignment score with affine gaps (Gotoh)","package":"computational-biology-ai999x","example":"Global alignment score with affine gaps: seq1 = ACGTTTACG, seq2 = ACGACG, match = 2, mismatch = -1, open = -5, extend = -1","v":[-0.00898,-0.05439,0.01052,0.01363,-0.10624,0.03246,0.02596,0.02842,-0.02768,0.05006,-0.01746,0.04434,-0.09669,0.11136,0.06701,-0.08083,0.00558,0.00943,-0.04787,0.01334,0.01133,0.01267,0.11379,0.06022,0.08843,-0.05328,0.01317,0.11121,-0.1205,0.06421,0.01938,0.07252,-0.07422,0.00884,-0.136,0.08594,-0.08097,-0.10043,-0.04202,0.06453,-0.11429,0.06587,-0.06459,0.05964,0.0045,-0.00409,0.09132,0.07562,0.00722,0.08246,0.00094,0.08686,0.09855,0.11672,-0.05334,0.15139,0.0338,0.01678,0.00461,0.09845,-0.06755,-0.03994,0.00713,-0.09092,-0.04922,-0.05331,0.07992,-0.00872,0.02603,-0.08102,-0.05664,0.00071,0.05112,-0.04319,0.05817,-0.03312,-0.00278,0.00471,0.08342,0.01341,0.03787,0.04021,-0.02767,0.00021,0.00463,-0.00495,0.02865,0.02394,-0.01043,0.05043,-0.08478,-0.0755,-0.04461,0.08445,-0.01359,-0.10043,-0.03233,-0.00979,-0.05214,-0.03613,-0.06345,-0.04684,-0.19477,0.01587,-0.00228,-0.09399,-0.09252,-0.01393,-0.04263,0.00497,-0.06412,0.01731,0.08492,0.03391,0.12657,0.06115,-0.02777,-0.0604,0.02387,-0.0519,-0.0083,0.00694,0.04237,0.12091,-0.05778,-0.0149,-0.11451,0.0245,-0.12373,0.00997,-0.01044,-0.00847,0.02108,-0.07105,0.10387,-0.03935,0.06505,0.01495,0.09608,-0.15277,-0.01052,0.00365,-0.07614,0.06108,0.04029,0.10625,0.03751,-0.02886,0.05837,0.04408,-0.05303,0.00944,0.02367,0.02246,-0.139,-0.03071,0.17042,-0.0618,0.01939,0.00664,0.0017,-0.1142,0.01226,-0.00631,-0.04035,0.02838,-0.02442,-0.02534,-0.01488,-0.05675,-0.06265,-0.00145,0.00389,-0.04117,0.16709,0.0219,0.00181,0.01769,-0.01107,-0.05959,0.00621,-0.04081,0.06984,0.00168,-0.0371,-0.01248,0.04713,0.01827,0.04938,-0.03883,-0.06097,0.09638,0.05638,0.01945,0.04536,0.10036,-0.00211,0.00335,0.05133,-0.03804,0.03657,-0.00869,-0.06791,-0.01249,0.05261,0.07356,-0.01386,-0.03734,-0.0132,0.01249,-0.02455,-0.09539,-0.07222,0.10004,-0.08211,-0.00076,0.01522,-0.08324,-0.09012,0.0425,-0.01215,-0.11454,0.02505,0.01564,-0.07785,0.01062,-0.03381,0.00749,0.11904,-0.0551,0.00121,0.01341,0.01729,-0.11542,0.10776,0.05336,0.01049,0.06263,-0.10921,0.02844,0.03372,0.11077,0.02591,-0.05333,-0.01067,0.06145,-0.07872,0.08774,-0.00859,0.01917,0.05193,0.02967,-0.06372,0.0256,0.13193,0.01338]},{"domain":"computational_biology","key":"bio_global_alignment_score","name":"Global alignment score (Needleman-Wunsch, linear gaps)","package":"computational-biology-ai999x","example":"Global alignment score: seq1 = GATTACA, seq2 = GCATGCU, match = 1, mismatch = -1, gap = 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6]","v":[0.15411,0.01936,0.00636,-0.00892,-0.09948,0.00123,0.10665,0.03513,-0.00796,-0.06702,0.05215,0.10013,-0.10121,-0.0897,-0.03085,0.00234,-0.02282,-0.0011,0.03789,0.02683,-0.0408,-0.00312,0.14668,-0.00721,0.05944,0.14606,0.02306,-0.1414,-0.02072,-0.01064,0.01363,0.06512,0.03749,0.00746,-0.05702,-0.10632,-0.00139,0.03063,-0.07865,0.06036,-0.0748,0.05865,0.09209,0.00323,0.04693,-0.07766,-0.04627,0.12321,-0.06818,-0.03495,0.06899,0.03403,0.07883,-0.06491,-0.00238,0.15758,0.05747,-0.03633,0.02966,-0.06395,0.00956,0.10154,-0.09472,-0.05091,-0.19871,0.08253,-0.07379,0.06695,0.09421,-0.0037,-0.0101,-0.05834,0.01481,0.09923,0.05838,0.054,-0.04305,0.03005,-0.07885,0.0324,0.18813,-0.01297,0.01449,-0.00192,0.1003,0.05136,0.02641,0.01093,0.08339,0.04941,0.00557,-0.0183,-0.05755,-0.06998,-0.11336,0.07756,-0.05261,0.10428,0.01295,0.05131,-0.01895,-0.03745,0.01089,-0.0173,-0.02957,-0.00542,0.01872,-0.02702,0.04046,0.0312,-0.02366,-0.05839,-0.04035,0.03031,-0.04645,0.07326,0.06214,-0.02485,0.06473,0.01464,-0.07597,-0.00355,0.03642,0.00236,-0.00104,0.00636,-0.02442,-0.0101,-0.05036,0.01624,0.03245,0.01754,-0.08871,-0.03445,-0.0576,-0.00255,0.00148,0.04147,-0.07234,-0.03341,-0.00977,0.08783,-0.09621,-0.04682,0.03226,-0.00682,-0.02709,0.04749,0.02152,0.00562,0.06546,-0.08724,0.07001,0.01712,0.02467,-0.0299,-0.09503,-0.07827,-0.01039,0.00781,0.04036,-0.05258,0.05502,-0.03293,0.14151,-0.11698,-0.04071,0.02468,-0.04512,0.01977,0.08023,-0.02085,0.02597,0.03104,0.02546,-0.00386,-0.04097,0.02887,0.05523,-0.07949,-0.1305,-0.02578,0.01248,0.0202,-0.06758,-0.03507,-0.03339,0.02812,0.02455,0.13564,-0.03896,-0.00084,0.00356,-0.05621,-0.12361,0.06754,-0.00191,-0.06045,0.01345,-0.02878,0.05695,0.00405,-0.05147,-0.11327,-0.11333,0.00132,-0.07495,0.0161,0.0042,0.02141,0.11293,-0.07997,-0.05543,0.09763,-0.03631,0.01276,0.06682,-0.01257,-0.03428,-0.05358,-0.0195,0.03155,-0.09297,0.03423,-0.0919,-0.03744,-0.00172,-0.07461,-0.02031,-0.04583,0.05412,0.13205,0.01072,-0.06128,-0.0302,0.0501,0.00156,-0.11743,-0.03984,0.00075,0.06817,-0.09337,0.07317,0.065,0.07713,0.02503,0.01747,0.02728,0.11405,0.00812,-0.0545,-0.05233,-0.12545,0.08278,0.02663,0.08751]},{"domain":"computational_biology","key":"bio_gravy","name":"Grand average of hydropathy (GRAVY)","package":"computational-biology-ai999x","example":"GRAVY: seq = MKTLLIL","v":[-0.08506,0.04465,0.03334,0.02057,0.02515,0.0515,0.07051,0.09843,-0.163,-0.0482,-0.0624,-0.02794,-0.0062,-0.0076,0.04438,0.03146,-0.04056,0.07821,-0.14016,0.05369,-0.00236,-0.12265,-0.09475,0.04837,0.05247,-0.01904,0.00023,-0.0047,0.00538,-0.00839,-0.09956,0.04832,0.07998,-0.07824,-0.00181,-0.04683,0.01551,-0.07429,-0.01395,0.07915,0.04054,-0.04135,-0.05703,-0.01054,0.05231,0.00222,0.09217,0.01364,0.02767,0.0686,0.08356,-0.05362,0.08041,-0.05761,-0.01257,-0.0828,-0.01576,0.02548,-0.00641,-0.03402,0.01488,-0.02478,0.01551,0.04285,0.08612,-0.03135,-0.03185,0.08757,0.06099,0.02584,0.06514,0.00776,-0.01602,-0.0832,0.07928,0.1518,-0.02459,0.07406,-0.00676,-0.08186,-0.06481,0.10067,0.03502,-0.03899,-0.00442,-0.01368,0.08901,-0.02087,0.0803,0.05338,-0.0104,0.03097,0.03322,0.0414,0.00512,0.05761,-0.07502,0.01491,-0.00272,-0.03473,0.0155,-0.06968,-0.00689,0.0896,-0.0216,0.04772,-0.06729,-0.05284,0.07703,0.07333,-0.00654,0.01562,0.10901,-0.04389,0.08688,-0.09249,0.00513,-0.03528,0.05309,-0.15194,0.07202,0.00185,-0.14253,-0.01298,-0.02663,0.01251,-0.0421,-0.01502,-0.03941,-0.04806,0.03346,-0.05173,0.11052,-0.0743,0.02472,0.01186,-0.0254,0.05194,-0.00562,-0.07591,-0.0029,0.00911,-0.03955,-0.03926,0.09682,0.00112,0.01488,-0.02005,0.10454,-0.00964,0.01078,0.0778,0.00015,0.12875,-0.14682,0.13787,0.11485,-0.10398,0.00812,-0.03559,0.02447,0.03353,-0.02615,0.00647,-0.05881,0.00477,-0.00768,0.04853,-0.03392,-0.103,-0.03764,-0.12971,0.01464,-0.0292,0.12067,0.0255,-0.09951,-0.05213,0.08131,0.0085,0.03806,0.01014,0.04904,0.0635,0.10119,0.06985,-0.00581,-0.07033,0.01156,-0.04112,-0.07191,-0.01443,-0.01786,-0.01299,0.03515,0.01757,-0.06144,0.03714,0.02985,-0.04958,0.00354,-0.02483,0.01753,0.0883,-0.10846,-0.16822,0.18482,0.00932,0.0579,-0.00559,0.06423,0.03378,-0.0066,0.06292,-0.05438,-0.09625,0.04422,-0.05618,-0.05639,-0.01206,-0.04826,-0.01641,-0.02173,0.1376,-0.01534,-0.09732,0.02852,-0.03452,-0.05227,-0.01104,-0.01645,0.12763,0.08626,-0.05798,0.0861,0.04107,-0.02995,0.04389,-0.05925,-0.00413,0.00375,0.00592,-0.02471,-0.07033,-0.06785,-0.01111,0.02437,0.01376,0.10734,-0.053,0.00654,0.05504,-0.16348,0.0802,-0.03499,-0.09477]},{"domain":"computational_biology","key":"bio_hamming_distance","name":"p-distance (Hamming) between aligned sequences","package":"computational-biology-ai999x","example":"p-distance: seq1 = GAGCCTACTAACGGGAT, seq2 = 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8.8888888889]","v":[-0.09713,0.06514,0.04698,0.0657,-0.0238,0.04311,-0.06701,-0.03671,-0.01365,-0.12516,-0.11528,-0.02776,-0.01809,-0.08394,0.03962,0.04248,0.00987,-0.03825,0.04176,-0.00626,0.01197,0.01843,-0.02091,-0.07476,-0.0268,0.08041,0.02101,-0.09723,-0.02389,0.06832,-0.00627,0.00247,0.03178,-0.03759,0.04766,-0.09772,0.01296,0.10547,0.06947,0.03624,0.00153,-0.0524,-0.11915,-0.10291,-0.02088,0.02283,-0.07859,0.05736,0.02008,0.04235,0.05945,0.04997,-0.0497,-0.06553,-0.00916,0.00894,0.11576,0.09008,-0.01471,0.08486,0.09774,0.07145,-0.05722,0.07492,0.01347,-0.02662,-0.00572,0.04097,-0.08447,0.0433,0.05167,-0.01373,0.00047,-0.09033,0.10527,0.09724,-0.0099,0.01865,0.02207,-0.07537,-0.0009,0.05027,-0.05195,-0.02792,-0.01114,-0.0201,0.01042,0.11035,0.00541,-0.05261,0.06694,0.05371,0.0802,-0.11195,-0.08783,-0.04669,0.02493,-0.06235,0.0563,0.02469,0.01836,0.03446,0.10154,0.04655,0.0441,-0.00402,-0.05068,-0.00236,-0.06624,0.03368,-0.03831,0.08885,0.00952,0.08299,-0.04557,-0.02408,-0.12075,0.03087,0.06153,0.02042,0.06921,-0.01399,-0.02174,0.04611,-0.09408,0.00622,0.07006,0.06838,-0.09077,0.00286,-0.10631,-0.06585,-0.11727,-0.0582,0.04511,-0.11482,-0.10256,-0.00804,0.0865,-0.05296,0.05443,0.09756,0.10229,0.09218,0.02831,0.09066,-0.08504,-0.0103,0.13838,-0.01393,-0.04911,0.04259,-0.02884,0.03636,-0.08222,-0.00739,-0.00441,0.04203,0.02439,0.07366,0.09432,-0.1127,-0.04208,-0.0641,-0.02355,0.00077,-0.05643,-0.0662,0.00623,0.02448,-0.01002,0.01868,0.04465,0.04384,-0.04537,0.0249,0.06429,-0.03401,0.03873,-0.08478,-0.07724,-0.01488,-0.03066,-0.04738,-0.05338,0.11925,-0.0236,-0.13206,0.03264,0.05679,-0.06521,0.11709,-0.01756,-0.07975,0.04015,-0.01433,0.02129,0.00307,0.01416,0.00834,-0.00653,-0.01532,-0.12672,-0.11224,-0.0403,-0.04003,0.02706,0.04988,-0.06056,-0.0576,0.07526,0.03193,-0.01032,0.05277,-0.05605,0.06778,0.0013,0.08061,-0.01074,0.07084,-0.13572,0.01813,0.00143,0.08088,-0.01736,0.01254,-0.10799,0.16601,0.00268,-0.13499,0.01231,0.08385,-0.03245,0.08231,0.03342,0.04471,0.07242,-0.00568,-0.06404,0.06582,-0.06083,-0.01608,-0.02717,0.09196,-0.15736,-0.02249,0.0379,-0.00475,-0.04126,0.01681,-0.06073,-0.03276,0.05686,0.11945,0.06397,0.06045]},{"domain":"computational_biology","key":"bio_haploid_selection","name":"Allele 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1","v":[0.0133,-0.05577,-0.12886,-0.10925,0.11538,-0.01879,-0.0145,-0.01676,-0.06057,-0.05819,-0.04554,-0.08499,-0.09153,0.05856,0.0004,-0.01727,0.05591,-0.02527,0.07727,0.02754,0.01952,-0.00347,-0.02303,0.15312,-0.09782,-0.00746,-0.00892,0.01588,0.03564,0.09345,-0.04199,0.0174,-0.08353,-0.00598,-0.12305,0.10204,-0.01336,0.00924,-0.04206,0.00203,-0.07759,-0.00581,-0.08019,0.07459,-0.02317,-0.06357,-0.00364,0.01321,0.05121,-0.01538,0.03348,0.04705,0.07763,-0.04541,0.01475,0.05523,-0.05257,0.0061,0.02895,-0.11002,-0.00431,0.00466,0.00551,-0.03195,-0.03044,-0.07885,-0.03178,-0.00461,-0.05239,-0.02088,0.08566,0.0385,-0.08725,0.10414,0.03736,0.15455,-0.05602,-0.03753,-0.14797,0.02966,-0.00562,-0.05749,0.04415,0.09555,-0.01558,-0.07737,-0.01413,-0.01629,0.0041,-0.13649,-0.05807,-0.13986,0.02768,-0.1311,0.05979,-0.01654,-0.00801,0.17034,0.02119,-0.0012,-0.00322,-0.07316,-0.01131,0.06349,0.05672,-0.10162,-0.00637,0.02838,0.10218,0.05172,-0.01203,0.13448,-0.09756,0.01764,0.0555,-0.00601,-0.07798,0.05856,0.03068,0.01946,-0.00787,0.02585,0.07417,0.03951,0.02169,-0.09691,-0.03017,0.07869,0.05671,-0.00016,0.02879,0.02398,-0.059,-0.07091,-0.05574,0.04681,0.03313,-0.0511,0.04989,0.00127,0.01101,0.06802,0.00325,-0.02279,0.08461,-0.01998,-0.04321,0.13205,0.05381,0.09096,-0.02642,-0.08722,-0.06756,0.04677,0.00877,0.06464,-0.04051,0.01915,0.00029,-0.0611,-0.05026,-0.03267,-0.04842,0.13245,-0.06622,-0.08757,-0.00187,0.01793,0.00671,0.04074,0.11012,-0.08767,0.16855,0.03544,0.03731,-0.01623,-0.02029,-0.06626,-0.02819,0.16505,0.05596,0.02005,-0.02216,0.02437,0.0417,0.07115,-0.03971,-0.08517,-0.03722,-0.0185,-0.03007,0.0987,-0.01128,-0.08658,0.02153,0.07977,0.04599,0.04089,-0.0038,-0.05595,0.06857,0.01045,-0.07843,-0.01798,0.04123,0.06454,0.01819,-0.09819,0.00713,-0.00853,0.03493,-0.0643,0.03591,0.06099,0.00531,-0.09906,-0.03627,0.01228,-0.02487,-0.00857,0.04049,-0.02777,0.0594,-0.11425,0.04641,0.04841,-0.04586,0.05097,0.07775,-0.01482,0.03052,0.01974,-0.05367,0.23993,0.07418,0.09801,0.02504,-0.14156,-0.00515,0.03444,0.01177,-0.01505,-0.03301,0.0748,0.00836,0.03526,-0.02629,-0.05892,0.02224,-0.03174,0.01399,-0.00401,-0.02703,-0.01102,0.02783,-0.02449]},{"domain":"computational_biology","key":"bio_hardy_weinberg_exact_test","name":"Hardy-Weinberg 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213","v":[-0.00124,0.07075,-0.10687,-0.10253,0.10414,-0.02344,0.05413,-0.05507,-0.03852,-0.07825,-0.06357,-0.07248,-0.00805,-0.00918,-0.04689,-0.03281,-0.00302,-0.04378,0.02305,0.01676,-0.0095,-0.07451,-0.07194,0.07721,-0.04761,-0.04868,-0.02724,-0.11818,-0.00873,0.03038,-0.10014,0.0435,0.00241,0.0811,0.07128,0.02468,0.13608,0.00719,-0.01763,0.01995,-0.0734,-0.168,-0.01556,-0.00604,0.05287,-0.05031,-0.09335,-0.00381,-0.02654,0.0319,0.07527,0.00575,0.02914,-0.02678,-0.03486,0.06556,-0.12396,-0.00905,-0.01864,-0.09141,0.04487,0.05432,0.02329,-0.03634,-0.0798,-0.0154,-0.02115,0.07235,-0.09278,0.10532,-0.07032,0.05296,-0.07691,0.12512,0.04632,0.03749,-0.05436,-0.0391,-0.07109,0.07306,-0.00702,-0.02038,-0.01092,0.00276,-0.00606,-0.05276,-0.02913,-0.00461,-0.00529,-0.06502,-0.04568,-0.11113,0.00674,-0.04056,-0.05021,-0.08055,-0.14728,-0.01479,-0.04717,0.02394,0.07466,-0.00871,0.09857,0.01517,0.09867,-0.00057,-0.01315,0.02676,0.1064,0.0045,-0.00895,0.03699,-0.02076,0.06275,-0.01203,-0.05009,0.17776,0.02964,0.02573,-0.00428,0.01794,-0.05623,0.03444,-0.11183,0.12326,-0.03732,0.00938,-0.04897,-0.00474,-0.06393,0.14045,0.10185,-0.07894,-0.05929,-0.10635,0.07006,0.01156,0.02158,0.12581,0.05339,0.0138,0.06458,0.0353,-0.10508,0.02728,0.0476,-0.04445,0.15693,-0.00017,0.02397,-0.00685,-0.04673,-0.09268,0.03427,0.09633,0.09877,-0.03243,-0.01605,-0.00332,0.01024,-0.06298,-0.05206,-0.04249,0.11019,0.07068,0.02754,-0.03575,0.02949,0.06522,0.0424,0.03864,-0.01566,0.10439,0.07177,-0.00253,0.03336,-0.05032,0.03762,-0.02372,0.03186,-0.05786,0.10814,-0.06463,0.06483,0.02118,0.05172,0.01865,0.03189,-0.03433,0.08352,-0.01717,0.02199,-0.01705,-0.00428,-0.06011,-0.04912,-0.00535,-0.048,-0.07609,-0.12788,0.13457,0.01215,0.05992,0.04828,-0.13912,-0.06758,0.06426,0.02997,0.01172,0.17267,0.09359,-0.0342,-0.05255,0.05142,-0.02166,0.01503,0.02178,0.09704,-0.00737,-0.00346,-0.07661,0.09374,-0.0701,0.02906,0.04457,-0.02342,-0.01212,-0.00408,0.05516,-0.05401,0.01416,0.00751,0.01369,0.11004,0.07861,-0.06919,0.05756,-0.0796,-0.03172,0.03721,0.0187,-0.08705,0.05447,-0.00101,0.02359,-0.00784,0.02888,-0.06534,0.12722,-0.03507,-0.00767,-0.04062,-0.09765,0.00695,0.00656,0.02435]},{"domain":"computational_biology","key":"bio_heterozygote_advantage","name":"Equilibrium under heterozygote advantage","package":"computational-biology-ai999x","example":"Heterozygote advantage equilibrium: w_AA = 0.8, w_Aa = 1, w_aa = 0.6","v":[0.11675,-0.02224,-0.1179,0.0451,0.08962,0.07496,-0.02201,-0.06895,-0.00979,-0.00876,-0.04997,-0.00888,-0.13596,-0.00561,-0.11168,-0.02543,0.04324,-0.05121,-0.01754,-0.08092,-0.00049,-0.03542,-0.04598,0.14806,-0.03031,0.01635,-0.01256,-0.08681,-0.01265,0.04469,0.05159,-0.01679,-0.00797,-0.00817,0.04165,0.09108,0.02845,-0.01502,0.01908,-0.03928,0.01113,-0.08463,-0.10122,0.0402,-0.02351,0.02792,-0.04548,-0.09625,0.07195,0.02542,0.0804,0.02379,0.04959,0.06539,0.013,0.06422,-0.09572,-0.04202,-0.03511,-0.05485,-0.00704,0.0164,-0.01973,0.04076,0.01997,-0.02691,0.01837,-0.10503,-0.02358,-0.04769,0.02133,0.07674,-0.00882,0.0163,0.01887,0.03381,-0.03665,-0.04131,0.08176,0.11473,0.01224,0.00301,-0.09824,0.01677,-0.05549,-0.02717,-0.0088,-0.02934,-0.00272,-0.0751,-0.03139,0.02868,-0.01591,0.06666,0.01168,-0.09118,-0.07873,0.06717,-0.10561,0.1272,0.02987,-0.00358,0.1277,-0.00644,0.10957,-0.15977,0.06069,0.05315,-0.00439,0.01397,0.04038,0.0159,-0.05366,0.02809,0.06371,-0.02445,-0.01044,0.06144,-0.05622,0.07528,-0.02775,0.04715,0.00571,-0.08064,0.07829,0.05046,0.10589,-0.00831,-0.00727,-0.05461,0.06076,0.05683,-0.15175,-0.12265,-0.15267,0.01835,-0.01735,-0.00384,0.02851,-0.00821,0.0787,0.03803,-0.04492,-0.07384,0.06355,0.13091,-0.01387,0.06698,0.1202,-0.00581,0.0143,0.12758,-0.04759,0.04274,0.06753,0.05706,-0.03615,-0.00572,-0.0047,-0.02608,0.03722,-0.17568,-0.05808,0.11796,-0.0428,0.09027,0.05039,0.0917,0.09403,0.00896,0.07873,0.00673,0.09321,-0.01711,-0.0095,-0.03837,0.0233,-0.0607,0.10284,0.02941,0.04428,0.00938,-0.0777,0.071,-0.03607,0.0521,-0.07187,0.10811,0.01483,-0.03638,-0.051,0.1058,0.03668,-0.03376,-0.06754,0.01351,0.00983,0.02687,-0.00739,-0.04776,0.10564,-0.08199,0.02268,0.0,-0.1399,-0.0349,0.07219,0.0163,-0.05321,0.04997,0.0182,-0.11941,-0.02613,0.1001,0.0132,0.01125,-0.07023,-0.03756,-0.10951,-0.03772,0.06475,0.02908,-0.12859,-0.00875,0.04337,0.06993,-0.11581,-0.02786,0.1095,0.05879,0.01572,0.08303,-0.00123,0.12871,0.00459,0.02494,-0.0489,-0.00689,0.03096,-0.00808,0.03851,-0.06298,-0.00284,-0.03073,0.00198,0.01145,-0.07414,-0.07752,0.03692,-0.0097,-0.03214,-0.08149,-0.04429,-0.0059,0.06585,0.02964]},{"domain":"computational_biology","key":"bio_hill_fit","name":"Hill equation nonlinear least-squares fit","package":"computational-biology-ai999x","example":"Hill fit: S = [1, 2, 4, 8, 16], v = [0.588235294118, 2, 5, 8, 9.41176470588]","v":[-0.16574,0.07731,-0.05153,0.0235,-0.02078,0.09332,-0.01587,0.00252,0.02295,-0.09154,-0.08945,-0.0966,-0.03752,-0.01402,-0.01561,0.04689,0.02409,0.04705,0.04107,-0.01987,0.01913,-0.08053,-0.02199,-0.07603,0.01009,0.00883,0.0545,-0.07588,0.01249,-0.01544,-0.06449,0.03185,0.09193,-0.03375,0.05517,-0.01631,0.04938,0.07664,0.06306,0.07523,0.04208,0.08002,-0.08768,-0.03412,-0.08497,0.05934,0.02798,-0.02513,0.01378,-0.03767,0.09184,0.02192,-0.00926,-0.09119,0.03443,-0.06994,0.02859,0.09425,0.0193,0.04201,0.03678,0.10944,0.01961,0.03822,0.03464,0.05543,-0.10215,0.02002,0.02308,0.08049,0.10212,-0.0011,0.00572,-0.06557,0.07167,0.13124,-0.07817,-0.01865,-0.0158,-0.05311,-0.06411,0.0375,-0.12985,-0.01875,0.02191,-0.04226,0.0965,0.02202,-0.00906,-0.11686,0.05617,0.03591,0.12575,-0.10931,-0.05904,0.02702,-0.05086,-0.01387,0.10256,-0.03009,0.03131,0.03401,0.07769,0.05618,0.02527,-0.06166,-0.04329,-0.05311,-0.09154,0.03072,-0.00536,0.08308,0.13386,0.09199,0.02303,0.01591,0.00912,0.10658,0.00922,0.06432,0.05095,0.06026,0.03302,-0.00134,-0.12223,0.0179,0.00752,0.03224,-0.05494,-0.11687,-0.09402,-0.06309,-0.09903,-0.05205,0.00201,-0.04202,-0.12951,0.00274,-0.00349,0.02891,-0.00985,0.05143,0.10847,0.08857,0.03627,0.06761,-0.03707,-0.03023,0.14806,-0.03383,-0.11782,0.03288,-0.0325,0.02632,-0.01013,-0.0171,-0.07056,-0.0258,-0.00048,0.08122,0.0847,-0.08707,-0.09553,-0.115,0.02945,0.0007,-0.02321,-0.04665,0.01573,-0.05759,-0.05845,-0.00257,0.07479,-0.06882,-0.05276,0.02988,0.02279,-0.04817,0.09941,0.01151,-0.04544,0.01865,-0.10751,-0.05291,0.02152,0.05344,0.01711,-0.07,-0.0112,0.08199,-0.09463,0.06451,0.05889,-0.01496,-0.0094,0.0464,0.03701,-0.08445,0.01237,-0.04318,0.07126,0.02811,-0.05448,0.00341,-0.05246,-0.04351,0.04706,0.06548,-0.0164,0.02034,0.03084,-0.08234,0.0381,0.06709,-0.09239,0.1102,-0.00918,0.14709,0.00958,-0.04274,-0.10477,-0.02783,0.0542,0.06925,-0.07713,0.06234,-0.11127,0.07972,-0.04641,-0.05509,-0.01061,0.03567,-0.04199,0.02256,0.06239,0.09425,0.06123,0.05426,-0.03551,-0.06419,-0.02079,0.00883,0.02995,0.04525,-0.13954,-0.14854,0.01183,-0.00456,-0.09625,-0.01342,-0.05573,0.02121,0.04612,0.06984,0.00697,0.04212]},{"domain":"computational_biology","key":"bio_hill_plot","name":"Hill coefficient from a Hill plot","package":"computational-biology-ai999x","example":"Hill plot: S = [1, 2, 4, 8], Y = [0.0588235294118, 0.2, 0.5, 0.8]","v":[-0.09409,0.0928,-0.05067,-0.01759,0.02206,0.09665,-0.09014,-0.01684,0.00584,-0.12276,-0.09967,-0.1337,-0.05342,-0.05134,-0.03793,0.0571,-0.00781,-0.02351,0.07131,-0.00114,0.01086,0.01608,-0.04777,-0.06942,0.05114,0.05798,0.01129,-0.13124,0.0044,0.02488,-0.13405,0.05386,0.06699,-0.0834,0.06047,0.03047,0.00355,0.06922,0.02337,0.03111,0.05053,0.03904,-0.09172,-0.03601,-0.0101,0.01118,0.01273,0.03189,0.00096,0.05855,0.10743,0.02962,-0.02677,-0.14347,0.09394,-0.01375,-0.01492,0.11458,0.03296,0.03017,0.0057,0.13254,-0.01783,-0.0313,0.02935,0.02448,-0.12169,0.04586,0.07807,0.04479,0.08931,-0.01167,0.0165,-0.07669,0.12852,0.11784,-0.12794,-0.01691,-0.01335,-0.0947,-0.09428,0.04823,-0.05202,0.06543,0.09417,-0.02055,0.07887,0.054,0.0251,-0.06378,0.07032,-0.05268,0.12384,-0.12443,-0.00798,0.00212,0.01854,-0.0055,0.0999,-0.08959,-0.00912,-0.01031,0.05932,0.10555,-0.00199,0.03789,0.00938,-0.01517,-0.02586,0.05691,0.0012,0.07093,0.07363,0.08586,0.05501,0.00105,-0.02703,0.11385,-0.02314,0.01803,0.00528,0.02498,0.04381,-0.01109,-0.12181,0.03559,-0.02963,0.0379,-0.08689,-0.06204,-0.03443,-0.05956,-0.02653,-0.03632,-0.02973,0.01706,-0.07744,-0.01812,-0.00632,0.03594,-0.04887,-0.00248,0.08501,0.12298,-0.03088,-0.00719,-0.05428,-0.04302,0.12725,-0.00116,-0.07202,-0.04781,-0.00288,0.04945,0.03385,-0.07313,-0.00116,0.0319,-0.01992,0.06216,0.06196,-0.02387,-0.04912,-0.08466,0.04596,-0.13426,-0.07164,-0.04212,-0.05749,0.05328,-0.00678,-0.00482,0.04488,-0.08924,-0.01996,-0.01529,0.00961,0.02121,0.08919,-0.00717,-0.11448,0.04723,-0.06054,-0.00906,0.05745,0.05249,0.03584,-0.11024,0.00026,0.11474,-0.08073,0.07164,0.00133,-0.03556,-0.03752,0.02693,0.0194,-0.02932,-0.04839,0.00526,0.03835,0.08838,-0.07373,-0.07799,0.00171,-0.09182,0.0446,0.04763,-0.02907,0.07109,0.0342,-0.02888,0.01756,0.08579,-0.06411,0.05859,-0.01122,0.1205,-0.03762,0.0035,-0.16111,-0.0043,0.04494,0.04621,-0.151,0.0711,-0.05999,0.15393,-0.04043,-0.04253,0.03736,0.02837,-0.08025,-0.01927,0.06399,0.04904,0.06035,-0.00587,-0.03552,-0.01468,-0.08568,-0.03336,0.07209,0.01989,-0.08408,-0.05543,0.03613,-0.03086,-0.02075,0.0295,-0.09584,0.05389,-0.01854,0.0491,-0.00244,0.05633]},{"domain":"computational_biology","key":"bio_instability_index","name":"Protein 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MAEGEITTFTALTEKFNLPPGNYKKPKLLYCSNGGHFLRILPDGTVDGTRDRSDQHIQLQLSAESVGEVYIKSTETGQYLAMDTSGLLYGSQTPSEECLFLERLEENHYNTYTSKKHAEKNWFVGLKKNGSCKRGPRTHYGQKAILFLPLPV","v":[-0.03073,0.0802,-0.00121,0.09457,-0.15998,0.08741,0.1316,0.02936,-0.10929,-0.07458,-0.02052,0.00228,-0.06213,-0.04152,-0.01353,0.02493,-0.03409,0.12089,-0.01983,-0.04346,0.03974,-0.00301,-0.02035,0.04644,0.07302,-0.04773,0.04961,-0.04711,-0.05847,-0.03234,-0.14568,0.00171,0.06402,-0.02243,0.03238,-0.01758,-0.01219,-0.0671,-0.02124,-0.04006,0.05263,-0.00197,-0.00297,0.04182,0.0593,0.07023,0.01193,0.02234,0.07857,-0.00794,0.04909,0.01497,0.0431,0.05812,0.02479,0.03326,-0.04731,-0.00189,-0.0777,0.08247,0.04325,0.03335,-0.08632,0.05372,0.00592,0.05065,-0.0328,0.10785,0.13918,-0.06405,0.03561,-0.05221,-0.01043,-0.01668,-0.03232,0.01747,0.02487,0.0255,0.14276,-0.02519,-0.00556,-0.05337,0.07419,-0.0877,-0.06861,-0.06704,0.00055,-0.04172,0.08987,0.0605,-0.02497,0.08578,-0.01573,-0.0348,0.10951,0.0698,-0.05431,0.03312,0.03857,-0.02199,-0.01024,-0.03171,0.00416,0.08123,-0.01032,0.03108,-0.02719,-0.06539,-0.00698,0.0139,0.03047,0.03566,0.14182,-0.02893,-0.03522,-0.14721,0.02939,-0.11331,0.00406,-0.08065,0.09049,-0.0093,-0.11164,0.0838,-0.0605,0.11614,-0.01427,0.02839,-0.05681,-0.01909,0.01291,-0.15624,0.04617,-0.11551,0.10235,-0.0189,0.02242,0.10377,0.04692,-0.05583,-0.03274,0.10341,0.005,-0.07177,0.13017,-0.04195,0.0504,-0.13959,0.10271,-0.02866,0.02828,0.0578,-0.00551,0.05114,-0.02108,-0.03441,0.04678,-0.03991,-0.0835,-0.05046,-0.05714,0.04573,-0.0215,-0.03601,-0.04491,0.01032,-0.01943,-0.06559,-0.00811,-0.01022,-0.03734,-0.07069,0.0147,0.02258,0.13698,-0.01835,0.02282,0.04084,0.01861,0.01127,0.07783,0.03063,-0.02393,-0.02451,0.07221,0.034,0.04461,-0.03554,0.0051,-0.04897,-0.11885,-0.01689,-0.02913,-0.106,-0.0288,-0.06004,-0.12352,0.1053,0.0168,-0.02096,0.0175,0.06461,-0.03787,-0.04536,-0.14602,-0.11003,0.10696,0.04162,-0.09843,0.051,-0.01645,0.09273,0.00873,0.1348,-0.0305,0.03248,-0.01709,-0.10703,0.02226,0.03815,0.05571,0.01899,-0.09849,0.04095,-0.02544,0.06992,-0.05508,-0.11798,-0.03241,-0.00797,0.0126,-0.04722,-0.02222,-0.03392,0.10533,0.05279,0.05307,0.07397,-0.07941,0.12321,0.07762,-0.01255,-0.01009,-0.04557,0.02635,0.02313,-0.00057,0.02196,0.05843,-0.04933,0.01438,0.07712,-0.0697,0.07309,0.01741,-0.04143]},{"domain":"computational_biology","key":"bio_isoelectric_point","name":"Isoelectric point of a protein","package":"computational-biology-ai999x","example":"Isoelectric point: seq = INGAR","v":[-0.01468,-0.01858,-0.01617,-0.13777,0.00026,-0.00302,0.04888,0.10786,-0.19706,-0.01179,-0.08889,-0.08476,-0.02971,-0.05981,0.04809,0.06435,-0.04093,0.01484,-0.03397,0.00216,0.11368,-0.19433,-0.07182,-0.02719,-0.04675,0.06072,-0.07083,0.09032,0.0263,-0.02043,-0.04907,-0.04434,0.00501,-0.07989,-0.006,0.01413,0.08529,-0.0974,0.02824,-0.02495,0.05594,0.01826,-0.01801,-0.05299,0.12587,0.01921,0.04788,0.02701,0.06275,0.02545,0.03616,-0.00836,0.14658,0.01862,-0.03,-0.01046,-0.12284,0.08193,-0.00554,-0.00042,0.01953,-0.08633,0.0196,0.00198,0.07482,0.04224,-0.04481,-0.00429,-0.04093,-0.06307,0.05516,0.03483,0.03682,-0.09683,0.00908,-0.01494,0.10357,-0.04864,0.04414,-0.14752,-0.04247,-0.07599,0.03972,0.05644,-0.09114,-0.09187,0.06638,-0.04954,0.04919,-0.0024,-0.01497,0.02082,-0.04213,0.03162,0.08069,-0.03543,0.03815,-0.07104,0.07761,0.02365,0.02703,-0.17579,0.08573,0.01562,-0.03691,0.06392,-0.03239,-0.0329,0.0053,0.0322,0.00198,-0.01479,0.1334,-0.07456,0.05227,-0.11827,-0.00042,0.03423,0.01696,0.03479,0.0267,0.03164,-0.10329,-0.03981,-0.01877,-0.04773,0.00394,0.03539,0.02388,-0.05562,0.04853,-0.03165,0.04166,-0.046,-0.0245,-0.02823,-0.04684,0.03996,-0.01547,-0.05104,-0.00459,0.09966,0.00917,-0.07637,0.04602,-0.00729,-0.00774,-0.04966,0.04155,0.02884,0.06614,0.14232,0.08522,0.13147,-0.07055,0.13351,0.07876,0.04064,0.04124,-0.05802,0.02144,-0.09033,0.06027,-0.0425,-0.07172,0.0287,-0.0091,-0.01444,0.00183,-0.0829,-0.08506,-0.05875,0.07009,0.05586,0.12461,0.04587,0.00718,0.04869,-0.039,0.08076,0.04561,-0.02442,0.06246,-0.03585,0.06753,0.06372,-0.05812,-0.0666,0.09586,-0.07803,0.02747,0.04659,-0.00385,0.0272,0.00492,-0.0726,-0.17421,0.01998,0.08708,-0.00976,-0.03717,-0.01081,0.09698,0.06655,0.0533,-0.12296,-0.01666,-0.03612,0.02708,0.0113,-0.00336,-0.00902,-0.02251,-0.04651,0.0316,0.10208,-0.00645,-0.00591,-0.05995,-0.03531,-0.01725,-0.00497,-0.05205,0.023,0.14036,0.07315,0.0303,-0.14988,-0.01653,-0.05274,0.06307,0.02003,0.00383,0.01691,0.02324,-0.02952,-0.01893,0.02481,-0.0292,0.07861,-0.02637,0.0532,0.04693,0.00096,-0.0207,-0.06492,0.10317,-0.06086,-0.01278,0.0949,0.10823,0.04626,0.03472,-0.04048,-0.05236,-0.06132]},{"domain":"computational_biology","key":"bio_jukes_cantor_distance","name":"Jukes-Cantor distance","package":"computational-biology-ai999x","example":"Jukes-Cantor distance: seq1 = AAAAAAAAAA, seq2 = AAAAAAAACC","v":[-0.01601,-0.01358,0.02984,-0.06132,-0.03086,-0.1285,0.06056,-0.04933,-0.02734,0.01427,0.03018,-0.05189,0.02373,-0.04399,-0.02873,-0.03624,0.00966,-0.07128,-0.05617,0.10773,-0.00949,0.02287,0.0422,-0.07567,0.04399,0.01446,-0.00915,-0.11395,-0.10912,-0.00579,-0.02963,0.04641,-0.07363,0.02356,0.10696,0.00267,0.06229,-0.07631,-0.01762,0.08464,-0.03035,-0.08367,-0.00094,-0.05699,-0.00756,-0.0328,0.06347,0.03501,-0.12932,0.0251,-0.01594,0.03754,-0.00805,0.02483,-0.02913,0.10169,0.01909,0.03074,-0.07279,-0.11189,-0.01188,-0.1182,0.00076,-0.04835,-0.0776,-0.03992,0.16804,0.10991,-0.16301,0.18096,-0.05432,-0.07065,0.04988,0.07568,0.01809,0.02089,-0.0535,-0.01081,0.02636,-0.02159,0.09517,-0.01357,-0.00065,0.11901,0.0265,-0.07405,-0.01727,-0.10338,-0.05993,0.00041,-0.08973,-0.0349,0.09083,0.11443,0.04419,-0.01784,-0.01255,-0.0286,0.10922,0.02657,0.03174,-0.04958,0.0153,-0.00789,-0.0546,0.01706,-0.06279,-0.03013,0.01045,0.02376,-0.03339,-0.02896,0.08444,-0.02103,-0.00919,0.01913,0.10589,-0.00496,0.04213,-0.09909,0.02734,-0.04373,-0.01299,0.00133,0.02758,-0.04055,0.05103,-0.07407,-0.04264,0.0225,0.07671,-0.04354,-0.02271,-0.0309,0.06248,0.0051,0.01192,0.05955,0.03087,-0.05428,0.04297,0.08238,0.05085,0.00338,0.06838,0.20531,-0.03522,0.008,0.10577,-0.02364,0.01073,-0.15756,-0.05345,-0.02737,0.01189,-0.00947,0.0682,-0.08769,0.09023,-0.01434,0.07568,-0.02955,-0.01873,-0.0545,-0.01589,0.02223,-0.02437,-0.13115,0.02798,0.06056,0.07099,-0.12143,0.05436,-0.08537,0.04902,0.07492,0.01566,0.09119,0.03256,-0.02107,0.06642,-0.01603,0.07496,0.00497,0.04632,-0.01434,0.0146,0.05878,-0.03242,0.05847,0.10729,0.06341,0.04716,0.01731,-0.04392,0.00678,0.03118,-0.04312,0.01575,-0.09223,0.01637,-0.01726,-0.01794,-0.03937,-0.038,-0.00621,-0.01312,-0.13341,0.03996,0.10496,-0.11586,-0.14378,-0.00647,0.03859,0.06775,-0.0028,0.14516,0.02078,-0.05858,-0.07136,0.05593,-0.00413,0.07349,-0.00747,-0.01465,-0.00361,-0.03428,-0.07362,-0.01602,-0.06435,0.14517,0.12674,0.05162,-0.01828,-0.05285,-0.0321,0.05773,0.00332,0.06866,-0.01094,-0.01439,-0.01783,-0.00415,0.01585,0.00113,-0.06553,-0.15311,-0.07214,0.03899,0.02866,0.06254,0.09926,0.00635,-0.00521,-0.05065,0.0363]},{"domain":"computational_biology","key":"bio_kimura_distance","name":"Kimura two-parameter distance","package":"computational-biology-ai999x","example":"Kimura distance: seq1 = AAAAAAAAAA, seq2 = 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2","v":[-0.02756,0.02439,0.01708,-0.03484,-0.01333,-0.14743,0.12213,0.09569,0.03992,-0.03645,-0.02901,-0.01657,-0.02556,0.00811,0.07269,0.05617,-0.00062,-0.06581,0.00762,0.12869,-0.05346,0.03863,0.03719,-0.05985,-0.00726,0.00961,0.03846,0.02868,-0.09933,-0.06638,-0.02913,-0.0373,0.05804,-0.00207,0.05047,-0.12959,-0.06645,-0.03291,-0.03559,0.13439,-0.09428,0.0732,0.06859,-0.05234,-0.01934,0.05862,-0.0564,0.19872,-0.0889,-0.01749,-0.08419,0.19844,0.06516,-0.06067,-0.00086,0.12263,-0.06179,0.07037,0.1327,-0.06778,-0.00855,0.02913,-0.01374,-0.02278,-0.00154,-0.02136,0.05625,0.12143,0.06248,0.06164,-0.02424,0.0194,-0.06259,0.07756,-0.0041,0.1248,0.01213,-0.00536,0.00941,-0.00249,0.01161,-0.02181,-0.08196,-0.0581,0.0236,-0.10221,0.04115,-0.02503,-0.03559,-0.00035,-0.04922,-0.02449,0.045,0.00094,-0.05899,-0.08468,-0.02372,-0.0411,0.02924,0.1031,0.06558,-0.0022,0.03374,0.12091,-0.02406,0.01328,-0.0665,-0.08645,-0.04683,0.01482,-0.01064,-0.11924,0.09773,-0.01407,-0.07987,0.05491,0.03966,0.01297,0.02032,0.09001,-0.08246,0.00455,0.02826,0.12637,0.0267,0.0578,0.07903,-0.0557,0.0286,-0.08484,0.03005,-0.04027,-0.01171,-0.01122,-0.01169,-0.05211,-0.08508,-0.09603,-0.01998,0.05493,-0.07251,0.0506,0.02868,-0.01134,0.03747,0.10393,-0.06302,0.1219,0.01691,-0.0586,0.00893,0.03954,-0.07928,-0.02002,0.01783,-0.06177,-0.06918,0.02203,-0.02309,-0.04539,0.0032,-0.02539,-0.0222,0.03583,0.01874,0.07389,-0.04962,-0.05404,0.08474,0.00768,0.02962,-0.02107,0.06597,0.03663,-0.00117,0.06257,-0.06775,0.03873,0.04141,0.08681,-0.04642,0.02912,0.09222,0.07917,-0.05244,-0.00625,0.01387,0.09385,-0.05297,0.04087,0.03031,0.10386,-0.00554,0.02118,-0.01368,-0.01294,-0.02404,-0.02071,0.04225,-0.13593,0.00981,-0.10355,0.01462,0.05453,-0.00777,0.06371,-0.04591,-0.09374,0.00195,-0.0513,0.01902,-0.14533,-0.08099,0.07042,-0.07111,0.13289,-0.08898,0.02941,-0.05372,-0.00179,0.01872,-0.00177,0.02451,0.04289,-0.06893,-0.03454,0.00211,-0.05799,-0.05496,-0.051,-0.09789,0.13224,-0.00264,-0.17783,-0.04903,-0.02108,0.03123,-0.07068,-0.02806,0.06771,-0.05708,-0.00261,0.0053,-0.00248,0.02773,0.04785,-0.05505,-0.0147,0.06297,0.0426,-0.06571,0.09994,-0.04065,0.01724,-0.03757,-0.06533]},{"domain":"computational_biology","key":"bio_leslie_growth_rate","name":"Leslie matrix growth rate and stable age distribution","package":"computational-biology-ai999x","example":"Leslie growth rate: F = [0, 2], S = [0.5]","v":[-0.12844,-0.15476,-0.05638,-0.03005,-0.01171,-0.04534,0.0258,-0.02798,-0.00759,0.02824,0.03359,0.00791,-0.02112,0.0281,-0.01472,0.05933,-0.03255,0.03779,-0.03314,-0.02352,-0.14489,-0.02778,0.02307,0.10309,0.03787,-0.07306,0.03437,-0.03566,-0.03646,-0.00535,-0.02324,-0.13336,0.00445,-0.02171,0.03719,-0.09329,0.02595,-0.00401,-0.04639,0.03741,0.06572,-0.03913,0.05991,0.07763,0.04461,-0.00162,-0.05081,0.03684,0.00097,-0.00695,-0.00371,0.06427,-0.05426,0.01116,0.0624,0.03961,-0.01366,-0.02524,0.01914,0.05491,0.03912,0.05558,0.00026,0.01147,-0.03696,0.03288,-0.05102,0.01671,0.15721,-0.0193,0.02954,0.08901,0.0216,-0.00847,0.05904,-0.05158,-0.01859,-0.0842,-0.04769,0.03306,0.01561,0.026,-0.02566,0.01193,0.02166,-0.11797,-0.0067,-0.00115,-0.03322,0.0322,-0.19243,0.04889,0.02965,-0.07247,0.01399,0.08684,-0.13338,0.054,0.05262,0.0064,0.01597,0.03692,0.03132,-0.14957,0.04478,-0.03824,0.11322,-0.00485,0.11089,-0.10697,0.00756,-0.0641,0.06415,-0.0172,0.02836,0.00419,0.01475,0.08931,0.00907,-0.10877,0.04131,0.00063,0.10715,0.03834,-0.07163,-0.03645,0.02496,-0.0241,-0.08818,0.04138,-0.09943,0.02302,0.04687,-0.03074,0.02445,-0.06982,-0.01431,-0.04203,0.06055,-0.11301,0.20826,0.10457,0.0443,-0.01356,-0.05341,0.15078,-0.08254,0.00084,0.07774,0.02761,0.00383,-0.07587,-0.07663,-0.03254,0.18545,-0.15932,-0.02763,-0.01874,-0.04517,-0.00992,-0.02642,-0.05401,-0.00409,-0.03911,0.03139,0.06266,0.04361,0.07732,-0.01791,0.05139,0.0348,0.0007,0.02687,0.02978,0.0154,0.10324,0.02457,-0.02751,0.05747,-0.02343,-0.0633,-0.01641,0.00924,-0.05891,0.0737,-0.05945,0.02861,0.03925,0.0041,0.05075,0.14797,0.17033,0.14531,0.00403,-0.05181,-0.04442,-0.05375,0.03282,0.05323,-0.09499,0.09163,-0.03501,-0.00647,0.01533,-0.06607,-0.05259,0.06532,0.02123,0.0005,-0.01528,-0.00581,0.06402,0.01589,0.0075,-0.03908,-0.00337,-0.02852,-0.0505,-0.01901,-0.01428,-0.02597,-0.01335,-0.0752,0.10932,-0.05621,0.04359,-0.1367,0.01686,0.00287,-0.04795,0.0351,0.06364,0.05338,-0.02108,-0.07904,-0.01366,0.10791,-0.0001,-0.17573,0.00803,0.03492,-0.04647,0.05427,0.05205,-8e-05,0.069,0.08067,-0.12709,-0.03125,-0.0173,0.01663,-0.04945,0.00621,0.03476,-0.04051,-0.04733]},{"domain":"computational_biology","key":"bio_leslie_projection","name":"Leslie matrix population projection","package":"computational-biology-ai999x","example":"Leslie projection: F = [0, 1.5, 1], S = [0.5, 0.8], n0 = [100, 50, 20], t = 1","v":[-0.10549,-0.00457,-0.04956,-0.09999,0.07675,-0.07671,0.00803,-0.0512,0.03614,0.03934,-0.01359,-0.08414,-0.04518,0.02168,-0.01711,0.0253,-0.00328,0.12913,0.09169,-0.05371,-0.14412,-0.09907,-0.0172,0.10244,-0.07709,-0.06162,0.03298,-0.02587,0.00271,0.01463,-0.03452,-0.10802,-0.02095,0.02011,0.02407,-0.10595,0.0316,-0.00228,-0.07272,0.02237,0.02187,-0.10851,0.04443,0.02398,-0.01219,-0.03975,-0.0686,0.0303,-0.07918,-0.01002,-0.03734,0.04232,-0.06996,-0.06292,-0.03643,0.07517,0.04031,-0.1224,0.02333,-0.00584,0.06981,0.11392,0.0721,-0.04379,-0.07984,-0.00975,0.02535,0.00275,0.1312,0.09664,-0.09433,0.00483,-0.04227,0.0834,-0.00553,-0.07278,-0.00253,0.04273,-0.06787,0.09126,-0.01301,-0.03509,0.08726,0.08013,0.01276,-0.04937,-0.0565,-0.09163,-0.01148,0.02829,-0.12798,0.01631,0.01991,-0.08675,-0.04999,0.07742,-0.10895,0.02116,0.04614,0.02904,0.03383,0.02407,0.0209,-0.12408,-0.00745,-0.01262,0.05169,-0.01497,0.08919,-0.08561,0.0344,-0.04975,0.00848,-0.06021,0.01706,0.0131,0.09599,0.03673,0.03254,-0.04564,0.01105,0.03848,0.1609,0.03902,-0.02988,-0.06533,-0.01277,-0.0142,-0.00049,-0.0097,-0.00416,0.03633,-0.00727,-0.02865,0.06056,-0.06397,0.05253,-0.04567,0.11743,-0.06151,0.10857,0.06086,0.02921,-0.07443,0.01898,0.11708,-0.12543,0.1574,-0.04015,-0.04585,-0.05918,-0.10351,-0.17014,-0.05612,0.12463,-0.09339,-0.10246,-0.04727,-0.01748,0.04482,-0.04441,-0.01965,0.02478,0.09052,0.06145,-0.00617,0.02559,0.02061,-0.05551,0.0598,0.04077,-0.06137,-0.01474,-0.01022,0.0696,0.09968,-0.04173,-0.05518,0.00747,0.05012,0.07182,-0.04336,0.03397,0.01506,-0.02322,-0.03218,0.01102,0.03201,-0.03074,-0.01182,0.19107,0.16796,0.02746,0.09696,-0.07399,0.00413,0.05434,0.00878,-0.02248,-0.0173,0.01951,-0.08732,-0.08503,-0.00489,-0.02033,-0.00276,0.10727,0.04564,0.05865,0.01516,0.07605,0.0193,0.03881,0.01685,-0.02601,-0.09588,0.1106,0.01264,-0.02105,-0.01002,0.06637,0.03399,-0.00829,0.02202,-0.00562,0.03863,-0.0592,-0.0155,0.00216,-0.04551,0.06309,0.03851,0.04031,0.06499,0.00381,0.00328,0.11853,-0.02884,-0.08277,-0.00714,0.00622,-0.03603,-0.0065,0.13526,-0.03199,0.00045,0.10665,-0.05719,0.00174,-0.07401,0.00421,-0.01606,-0.00746,0.06223,0.02278,-0.04299]},{"domain":"computational_biology","key":"bio_lineweaver_burk","name":"Lineweaver-Burk fit of Michaelis-Menten data","package":"computational-biology-ai999x","example":"Lineweaver-Burk fit: S = [1, 2, 4, 8], v = [5, 6.6666666667, 8, 8.8888888889]","v":[-0.12225,0.01037,0.07099,0.09702,-0.02933,0.05901,-0.06685,-0.01127,-0.00799,-0.09742,-0.11124,-0.00359,-0.00073,-0.09023,0.03952,0.00153,-0.00794,-0.01018,0.03763,0.04451,0.00828,-0.01371,0.01242,-0.03406,-0.00815,0.06947,0.05615,-0.0789,0.00757,0.09528,-0.00992,0.00885,-0.00725,0.00283,0.02493,-0.09714,0.00094,0.05423,0.01366,-0.00284,0.00705,-0.02689,0.01657,-0.12497,-0.03448,-0.0114,-0.06736,0.0267,0.06158,0.00538,0.11673,0.0398,-0.05527,-0.03908,0.02405,0.03613,0.11637,0.08723,-0.01587,0.05879,0.05687,-0.00682,-0.05316,0.07128,-0.07253,0.03301,-0.0296,0.0397,-0.11256,0.08751,0.04872,-0.00602,-0.00755,-0.08183,0.10958,0.08347,-0.08707,-0.01867,-0.00761,-0.12218,0.03773,0.07709,-0.05116,-0.05022,-0.04279,-0.00266,0.04956,0.06673,0.01096,-0.06004,0.08717,0.10482,0.11553,-0.05121,-0.05195,-0.01407,0.01132,-0.05472,0.08766,-0.01307,0.02452,0.07321,0.01235,0.03339,0.04626,0.00342,-0.05175,0.02576,-0.12332,-0.00088,0.00429,0.07844,0.0148,0.05428,-0.04213,-0.08875,-0.09914,0.00292,-0.02246,0.0741,0.07165,-8e-05,-0.01087,-0.02047,-0.10954,0.04057,0.04108,0.0872,-0.0844,0.04588,-0.05083,-0.01165,-0.10803,-0.01165,0.05149,-0.13828,-0.09555,0.01072,0.07408,-0.007,0.08958,0.14434,0.14052,0.06554,-0.01059,0.10165,-0.03641,-0.03998,0.12878,0.05012,-0.10185,0.03063,-0.07234,0.04484,-0.04153,-0.02717,-0.01147,0.04517,-0.00054,0.02821,0.09928,-0.06521,-0.0365,-0.11569,0.03721,-0.04678,-0.04258,-0.04743,-0.01578,0.02845,-0.0352,0.01013,0.09202,0.01889,-0.02909,-0.04266,0.10017,0.01108,0.00089,-0.07095,-0.12938,-0.04635,-0.02122,-0.06179,-0.08007,0.13708,-0.04832,-0.13176,-0.00997,0.05461,-0.0769,0.12145,-0.04184,-0.12009,0.0035,-0.0275,0.02602,-0.00169,0.03227,-0.0255,-0.01916,-0.0021,-0.08095,-0.0436,-0.04717,-0.05706,0.03139,0.03648,-0.01919,0.01452,0.00866,0.05416,-0.07776,0.02047,-0.04949,0.07307,-0.05133,0.11815,-0.03068,0.05371,-0.10523,-0.02956,0.00382,0.07195,-0.01696,0.03648,-0.13056,0.10824,0.02556,-0.12899,0.04982,0.08605,-0.04007,0.05761,0.03758,0.05288,0.01149,0.06317,-0.04365,0.05029,-0.0828,0.05003,-0.03026,0.04046,-0.10948,-0.04095,0.0129,-0.0836,-0.06031,-0.02449,-0.03803,0.06094,0.07483,0.10996,0.04691,0.05101]},{"domain":"computational_biology","key":"bio_linkage_disequilibrium","name":"Linkage disequilibrium D, D' and r^2","package":"computational-biology-ai999x","example":"Linkage disequilibrium: n_AB = 40, n_Ab = 10, n_aB = 10, n_ab = 40","v":[-0.01364,-0.07345,-0.08994,-0.0378,0.03429,-0.04982,0.06378,-0.01968,0.04757,0.00815,0.0409,-0.07823,-0.02324,-0.01121,0.00831,0.03777,0.01381,-0.11715,-0.07995,-0.00214,-0.03881,-0.09911,0.02454,-0.0243,-0.0513,0.09497,0.08118,-0.07512,-0.07013,-0.00208,-0.07491,0.02471,-0.00462,0.03797,-0.01525,0.10328,0.0738,0.03253,-0.04085,-0.00697,0.02128,-0.02989,0.10458,-0.08769,-0.01352,-0.09541,0.01132,-0.03023,-0.0676,-0.0675,-0.02947,0.08176,0.07237,0.08062,-0.01987,0.03178,-0.1035,0.04316,0.04809,0.04586,0.06353,-0.01965,0.03734,-0.17684,-0.18053,-0.01463,-0.0812,0.1281,-0.06022,-0.02792,0.01883,-0.07803,0.02607,0.02569,0.09573,0.01217,-0.07677,-0.07283,0.04789,0.03745,-0.07358,-0.03252,-0.14671,-0.00664,0.03684,-0.05618,-0.03252,-0.05277,-0.06027,0.03383,-0.08014,-0.07251,0.06157,0.02812,0.02435,-0.1118,-0.0029,0.07143,-0.00378,-0.00902,0.06329,-0.0355,0.08115,-0.02371,-0.08703,0.07283,-0.0408,0.01722,0.01545,0.01235,-0.01696,-0.0684,-0.07057,0.00092,-0.08874,0.0196,0.09856,0.00603,0.04409,-0.02242,0.00979,-0.09649,-0.01957,0.04417,0.04124,0.00667,-0.00125,0.00806,0.05908,0.04626,0.18848,0.14148,-0.0485,-0.03343,-0.04337,0.08856,0.06007,-0.06264,0.00566,0.0028,-0.04197,0.08296,0.11442,-0.06212,0.01654,0.04287,0.00342,0.12877,0.03989,-0.03231,-0.01693,-0.02815,0.03448,0.03946,0.02937,-0.00689,0.03248,0.08732,-0.02592,0.00222,0.05278,-0.02268,-0.04747,-0.00164,0.06905,-0.01558,-0.04738,-0.04603,0.01598,0.04601,-0.01176,-0.03957,0.06827,-0.18093,0.02347,-0.06946,-0.03907,0.10406,0.02656,0.01917,0.01704,0.11527,-0.01849,0.10535,0.06118,0.00339,-0.02156,0.11156,-0.06966,0.01286,0.01339,0.11964,0.07995,0.03085,-0.05253,-0.01843,-0.06816,0.00283,0.0267,-0.06805,0.15507,-0.06236,0.07326,0.04503,-0.12269,0.08161,-0.0646,0.00018,0.07089,0.05798,0.00186,-0.15832,-0.11828,0.08802,-0.03135,-0.01253,-0.07698,0.00583,-0.08488,0.00953,0.13105,0.0376,-0.1019,0.02094,0.02981,0.02774,0.10968,0.08456,0.00668,-0.01339,-0.02333,0.0161,-0.02403,0.00111,0.05083,-0.02741,0.03844,0.00166,0.05878,0.03689,-0.00475,0.03279,0.09166,-0.06394,-0.06585,-0.01605,0.01374,0.01466,0.04126,0.01918,0.03192,-0.07111,-0.02091,-0.04181,-0.01052,-0.03462]},{"domain":"computational_biology","key":"bio_local_alignment_affine","name":"Local alignment score with affine gaps","package":"computational-biology-ai999x","example":"Local alignment score with affine gaps: seq1 = TTACGTACGTTT, seq2 = GGACGTTACGTGG, match = 2, mismatch = -1, open = -3, extend = 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alignment score (Smith-Waterman, linear gaps)","package":"computational-biology-ai999x","example":"Local alignment score: seq1 = TGTTACGG, seq2 = GGTTGACTA, match = 3, mismatch = -3, gap = 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CCATGAAATTTGGGTAACC","v":[-0.07565,0.00051,0.05926,-0.03879,0.0585,-0.05337,0.13538,-0.03335,-0.00443,-0.02029,0.01264,0.05196,0.02831,0.08625,0.05125,0.10642,0.02413,0.06705,0.0078,0.07235,0.03354,-0.02245,-0.0826,0.01465,0.11377,-0.02415,-0.03499,-0.01341,-0.00874,0.09015,0.00533,0.01831,-0.00241,-0.05511,-0.01522,-0.01103,0.05362,-0.01243,0.0229,0.05893,0.03145,-0.01723,-0.05191,0.0406,0.012,0.08477,0.05688,0.00463,0.01773,0.0503,-0.07891,0.05828,0.04247,-0.03941,0.01759,-0.04693,-0.04396,0.09998,0.04268,-0.12173,0.00238,0.07892,-0.00227,0.01074,-0.03538,0.03296,0.05439,0.08628,0.02708,0.0102,-0.09672,-0.05925,-0.1575,0.06056,-0.07501,-0.00029,0.00309,-0.03435,-0.00797,0.08059,0.13612,-0.00753,0.00592,-0.01883,0.05155,0.08714,0.01567,0.0155,0.08074,-0.08353,0.03007,0.00872,0.06192,-0.00291,-0.03623,0.04153,0.04216,0.09878,-0.01604,0.10296,-0.05941,-0.08559,-0.04788,0.00162,-0.03356,-0.09389,-0.19044,-0.07491,-0.0414,-0.02719,-0.16884,0.07578,0.09845,-0.01076,-0.0176,-0.1,-0.05141,0.01371,0.08946,-0.07367,0.06239,0.05043,-0.11736,0.06296,-0.01189,0.01035,0.04152,0.06498,-0.03513,-0.05752,-0.03507,-0.02034,0.10443,-0.09312,0.03809,0.01216,0.01739,-0.06492,0.0462,0.01929,-0.06622,0.04217,0.02013,-0.06525,0.0175,0.07161,-0.09525,0.01351,0.0755,-0.06064,-0.02875,-0.05093,-0.09471,0.01135,-0.17164,0.09513,-0.01318,0.05572,0.00407,0.03751,-0.02849,0.06222,0.04186,0.08804,0.05545,0.1294,0.14301,-0.08784,0.05249,-0.05287,-0.04034,-0.10243,-0.04854,0.15584,0.07359,0.01077,-0.10525,-0.04987,0.07782,0.10433,0.00288,0.06491,0.01104,0.03799,-0.08811,0.05825,0.00774,-0.00095,0.02852,-0.06453,-0.01952,-0.04072,0.02193,-0.04047,-0.04236,-0.05591,-0.00043,-0.00484,-0.01026,-0.05056,0.04336,-0.02232,0.04306,0.06768,-0.06137,-0.02277,0.06542,-0.01166,-0.05485,0.01541,-0.00416,-0.14439,-0.0614,-0.03103,-0.04839,0.0828,0.01891,0.06495,-0.05432,-0.03191,-0.01032,0.02979,-0.0113,0.00999,0.00163,-0.06176,0.06759,-0.02445,-0.06438,-0.16715,-0.05285,0.02651,-0.0667,-0.05038,0.03617,0.04594,0.0294,0.02522,-0.02018,-0.037,-0.08962,0.02656,-0.13166,-0.05469,0.09367,-0.01705,0.00706,-0.00057,-0.00169,0.02208,0.1428,0.08342,0.00305,0.0125,0.04043,-0.11311]},{"domain":"computational_biology","key":"bio_map_distance","name":"Map 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5","v":[-0.07327,0.05627,0.08324,0.04028,-0.13505,0.04181,0.03533,0.03895,0.03288,0.01701,-0.03391,0.04749,0.03892,-0.0454,0.06648,0.027,-0.03618,-0.02147,0.08271,0.04874,-0.01263,-0.06312,-0.02335,-0.00276,-0.02021,0.05606,0.01319,-0.02556,0.0566,0.03393,0.06029,-0.01383,0.01353,-0.05074,-0.01964,-0.02879,-0.03308,0.03688,-0.00278,-0.01887,0.04851,-0.08158,-0.07282,-0.07781,0.00285,0.01383,0.00348,0.01187,0.04522,-0.04072,0.04064,0.0433,-0.04765,-0.08808,0.03878,0.128,0.00275,0.10153,-0.04101,0.02176,0.062,-0.03031,-0.03913,0.00999,-0.08957,-0.06128,-0.03293,0.03244,-0.00682,0.01314,0.02714,-0.03746,-0.03324,0.03455,0.01825,0.04677,-0.00494,-0.01908,-0.10372,-0.10313,0.07421,0.02164,-0.04145,-0.047,-0.02413,0.00762,0.09987,0.01069,-0.01317,-0.11059,0.00782,0.15401,-0.01863,0.03207,-0.03525,0.04563,0.11476,-0.0978,0.10177,0.00543,0.06887,-0.01977,0.04967,0.04041,-0.0167,0.03857,-0.23355,0.0224,-0.15854,-0.04002,-0.01651,0.18383,0.05029,0.06245,-0.00733,-0.03951,-0.13661,0.00399,-0.0044,0.16939,0.06274,0.04374,0.05254,-0.0329,-0.04315,0.02962,0.05323,0.02445,-0.01877,0.10131,-0.05784,-0.0562,-0.09686,-0.01714,0.02604,-0.10245,-0.03479,-0.09615,-0.00064,-0.00835,0.01571,0.14445,0.1085,0.02051,-0.03818,0.04597,0.00654,0.03395,-0.01931,0.02748,-0.05195,0.03585,-0.17754,0.024,-0.05763,0.02034,-0.01824,0.06072,-0.02626,-0.04054,0.10121,0.00496,-0.01701,-0.07296,-0.05127,-0.00861,0.02547,-0.06142,0.00747,0.05512,-0.04559,-0.00467,0.04833,0.02007,-0.01858,0.01344,0.01571,-0.02419,0.08044,0.02153,-0.02591,-0.06163,-0.10033,-0.09178,-0.1095,0.06715,-0.02355,-0.11698,0.00576,-0.05376,0.02659,0.04914,-0.02528,-0.10977,0.01835,-0.0222,0.02249,-0.0317,0.01206,-0.00017,-0.03317,0.03814,-0.02414,0.00296,-0.02622,-0.05816,0.00808,0.0739,-0.03888,-0.06074,0.02213,-0.0428,-0.01809,0.0653,-0.0613,0.13673,-0.11803,0.12014,-0.04839,0.02927,-0.01973,-0.09814,-0.03663,0.00215,0.03752,0.01151,-0.09205,0.041,0.0484,-0.14234,0.06808,0.02142,0.00152,0.04153,0.06017,0.04211,-0.01246,0.02035,-0.05874,0.08497,-0.0092,0.07647,-0.08342,0.11189,-0.08487,0.02323,0.01179,-0.01329,-0.10698,0.0786,-0.00468,0.04162,0.15739,0.1108,-0.04315,0.11615]},{"domain":"computational_biology","key":"bio_michaelis_menten_time","name":"Time 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diversity","package":"computational-biology-ai999x","example":"Nucleotide diversity: seqs = AAAA AAAT AATT","v":[-0.13714,-0.01671,-0.04509,-0.04861,0.11233,-0.08063,0.01889,-0.03087,-0.06283,-0.00144,0.03099,0.01498,-0.04652,0.05898,-0.00979,0.03454,-0.06196,0.00655,-0.04888,0.07108,0.00804,-0.13992,-0.00831,-0.03154,0.01373,0.02681,0.08046,-0.11916,0.04906,-0.03158,-0.08278,-0.00749,-0.05333,-0.0495,0.08065,0.05782,0.01934,-0.08012,0.01618,-0.01367,0.03685,-0.12362,-0.06412,-0.02381,-0.00088,0.12825,0.00317,0.00338,-0.09692,0.01518,0.02501,0.0948,0.03872,0.04544,-0.0326,-0.02055,-0.04723,0.105,-0.06106,-0.09703,-0.00079,0.07528,-0.01885,-0.08031,0.06349,0.1379,0.08203,0.0215,-0.08526,0.10018,-0.07086,0.06587,-0.00841,0.19221,-0.05302,0.0793,-0.17435,-0.02702,-0.05084,0.02623,0.0015,0.03544,-0.02533,0.06627,0.01433,-0.08085,0.00122,-0.10627,-0.01505,-0.08962,0.0294,-0.10124,0.09029,0.0099,-0.01684,-0.01231,-0.105,0.05764,0.00579,-0.02504,-0.01801,-0.03435,0.0863,-0.0486,0.06553,-0.03085,-0.02969,-0.0478,0.08655,-0.03385,0.00767,-0.03132,-0.07549,0.01762,-0.00338,-0.05753,0.06638,0.04372,0.06703,-0.03868,0.00926,0.04908,-0.0626,-0.00332,0.1317,-0.06716,0.02142,-0.03276,0.02339,-0.01807,0.01953,0.0119,0.00695,-0.04131,-0.05523,0.02843,0.07403,-0.01312,0.02636,-0.00071,-0.1325,0.12681,-0.0385,-0.02374,0.0973,0.11957,-0.0629,0.00668,0.03215,-0.05047,0.01714,0.04565,-0.12181,0.09088,-0.00214,0.13051,0.02526,-0.02115,0.02534,0.07033,0.04431,-0.06309,0.02176,0.0422,0.03778,0.02728,0.1214,-0.10821,0.04928,-0.0723,0.0184,-0.14638,-0.04942,0.00824,0.0949,0.0065,-0.05871,0.06689,-0.01244,0.01556,-0.01001,0.08037,-0.11329,0.02047,0.06577,0.0873,-0.00808,0.09603,-0.04257,-0.02598,0.04106,0.10285,-0.02446,0.0117,-0.04489,0.02257,0.0736,-0.02243,-0.0406,0.03188,-0.01792,-0.02635,0.04649,0.00077,-0.04025,0.01837,0.02099,-0.1204,-0.06402,0.11635,0.03547,-0.05364,-0.06599,0.06127,0.00146,-0.06792,0.08746,-0.01071,-0.03341,-0.14132,0.01539,-0.08106,-0.02583,0.02051,0.05702,-0.0848,0.02908,-0.09297,0.02621,0.01721,0.00739,0.1069,0.01024,0.03479,-0.0171,-0.02565,0.05937,-0.01997,0.0834,0.04705,0.08735,-0.00458,0.01063,0.01174,0.09968,0.00148,-0.02518,-0.05732,0.06491,-0.0417,0.03905,-0.04217,-0.1281,0.02067,0.00974,0.02755]},{"domain":"computational_biology","key":"bio_pedigree_inbreeding","name":"Inbreeding coefficient from a pedigree","package":"computational-biology-ai999x","example":"Pedigree inbreeding coefficient: pedigree = [P-S, Q-S, P-D, Q-D, S-X, D-X], individual = X","v":[0.0233,0.05645,-0.03355,-0.05286,0.11257,-0.02724,-0.00374,0.01917,-0.0539,-0.13097,-0.07834,-0.01032,-0.06533,-0.00047,0.00225,-0.08561,-0.01717,-0.04429,-0.13184,0.03518,-0.06781,-0.064,-0.02249,0.06106,-0.04885,-0.03449,-0.00303,-0.16136,0.04177,0.01897,0.02104,-0.04609,-0.03883,0.02815,0.01616,0.02204,0.06394,-0.08655,-0.00613,0.02303,-0.02607,-0.10788,-0.12257,0.03478,0.03079,-0.051,0.02242,0.04099,-0.06684,-0.08034,0.02171,0.13756,0.04486,-0.07137,-0.00628,0.04978,-0.0934,0.1033,-0.00106,-0.01556,0.04575,0.11874,-0.07605,-0.03281,-0.06046,-0.05743,0.02298,-0.08913,0.00439,0.09037,-0.04316,-0.01837,-0.02203,-0.08822,0.0578,0.01962,-0.01158,-0.08786,0.0156,0.04984,-0.01737,-0.02765,0.11984,-0.12498,0.02406,-0.02163,-0.0483,0.01373,-0.04118,-0.02944,-0.01484,-0.03405,0.06088,-0.00372,0.05744,-0.06309,-0.06914,0.03615,-0.05669,-0.08332,0.01993,-0.02314,0.02925,0.05369,-0.02163,-0.08655,0.09086,-0.01994,0.11036,-0.09581,-0.0369,0.05016,-0.05621,0.12011,0.11549,-0.11473,0.03363,-0.01938,0.05664,-0.18164,-0.02444,-0.00967,0.02101,0.02231,0.08114,-0.04569,0.0328,-0.00985,0.05741,-0.0087,0.00182,-0.00446,-0.01048,-0.06917,-0.06543,0.10836,0.03913,-0.04589,0.06108,-0.06252,0.0908,0.0246,0.01734,-0.04026,0.08981,0.06537,0.03705,0.02415,0.05057,0.13126,-0.0821,0.01592,-0.07933,0.03399,0.16872,-0.04176,0.04531,-0.08504,-0.01544,0.10287,0.00562,-0.15406,-0.04651,0.0819,0.06596,0.04016,0.1099,0.05817,-0.02206,0.05484,0.02701,0.04281,0.02652,-0.05041,-0.00891,-0.00798,0.04766,-0.01716,0.02666,0.07911,0.00412,0.10566,-0.09973,0.02525,-0.0498,0.0158,-0.00545,0.00823,0.00704,-0.02755,0.15879,0.04052,-0.00293,-0.00514,-0.12504,0.06387,0.02872,0.09001,0.03831,-0.01901,-0.01344,-0.0062,0.08628,0.01426,-0.09402,-0.02919,0.04504,-0.09755,0.05406,0.06486,0.07918,-0.0185,0.04877,0.04804,0.01221,0.0108,-0.00729,0.04816,0.05205,0.08462,-0.04052,0.07564,-0.07437,0.0159,-0.0395,0.02179,-0.00607,0.02091,0.09959,0.01602,-0.08072,0.02267,-0.04976,0.08259,0.07071,-0.06065,0.07697,0.03786,-0.00224,0.07432,0.1155,-0.00997,0.03773,-0.02581,-0.02415,-0.0047,-0.0376,-0.04204,0.09896,-0.08291,-0.01731,-0.05638,-0.10446,0.08609,-0.05489,-0.03023]},{"domain":"computational_biology","key":"bio_petersen_estimate","name":"Mark-recapture population estimate (Petersen MLE)","package":"computational-biology-ai999x","example":"Petersen estimate: M = 100, C = 80, R = 12","v":[-0.06215,0.05753,0.00956,0.06114,0.03104,-0.08462,0.0971,0.02652,0.02214,0.01575,0.00297,0.08257,0.07118,0.02546,-0.04299,0.08539,-0.01917,0.06069,0.02578,-0.07031,-0.03279,0.02405,0.06887,0.01394,-0.14515,0.0685,-0.00599,-0.05093,0.10257,-0.0146,0.11907,-0.01278,0.01934,0.01089,-0.0703,-0.09973,0.03127,0.03847,-0.07672,-0.1488,-0.00887,-0.08062,0.08215,0.00019,-0.01184,-0.03735,0.02844,-0.08317,-0.01979,0.02744,0.02155,0.04776,0.02965,0.01864,-0.11563,0.04969,-0.08374,0.04271,-0.04727,-0.02097,0.02719,-0.04357,-0.01544,-0.08562,-0.17269,-0.00385,-0.16808,0.02705,-0.02479,0.04966,0.04093,-0.02078,0.03718,0.06001,0.01079,0.01637,0.00666,-0.05102,-0.08093,0.08089,0.03411,0.02904,-0.05451,0.00935,0.00111,0.00246,0.05409,-0.00663,0.02604,-0.08293,0.00848,0.1544,-0.0147,0.13784,0.01595,0.07947,-0.03219,0.01468,-0.06185,-0.02445,0.02833,0.02565,0.01462,-0.06435,-0.03935,0.06224,-0.1283,0.03081,-0.03226,-0.05881,-0.10568,0.01268,0.03077,0.05993,0.01293,-0.00087,0.02901,0.07094,0.08793,-0.02499,0.06643,-0.0871,0.04977,0.05392,-0.01749,-0.04912,0.08479,-0.04217,-0.00372,-0.06237,0.03724,0.08955,-0.05096,-0.00686,0.00282,-0.02318,0.05503,0.00879,-0.09539,-0.06838,0.01178,0.1239,0.09113,0.01645,0.0769,0.10537,-0.07605,0.07695,0.01783,-0.03408,-0.06074,-0.07335,-0.03903,-0.06432,0.01622,-0.04296,-0.14057,-0.02694,-0.02905,0.02622,-0.06164,0.05432,-0.05852,-0.11858,0.10005,-0.02508,0.0499,-0.07044,0.04065,-0.05203,-0.10356,-0.05233,0.06099,-0.03003,0.03279,0.03875,0.00941,-0.03375,0.03607,-0.02225,0.03121,0.01964,0.06436,0.07837,-0.01943,-0.09213,-0.11933,0.09046,-0.04169,-0.03475,0.08611,0.04481,0.07063,0.03299,0.01409,0.07181,-0.00914,0.06072,0.00696,-0.11289,0.09618,-0.01409,0.01121,0.05764,-0.05343,-0.03083,0.00769,0.10814,0.05929,-0.06982,0.02722,-0.10947,0.10458,0.0502,-0.06055,0.08521,0.02703,0.18975,-0.01744,-0.08026,0.0751,0.05649,-0.06808,-0.01934,-0.10896,-0.00531,-0.02316,-0.04732,-0.00074,-0.08422,0.02696,0.07459,0.05576,0.06158,-0.11168,-0.02925,-0.00624,0.01697,-0.13422,-0.07284,0.03881,-0.01028,-0.06066,0.09429,-0.00663,-0.03184,0.04813,0.03966,-0.0011,-0.03782,-0.00098,0.01776,0.01223,0.09227,-0.04535,-0.06267]},{"domain":"computational_biology","key":"bio_protein_extinction","name":"Protein extinction coefficient at 280 nm","package":"computational-biology-ai999x","example":"Protein extinction coefficient: seq = MAEGEITTFTALTEKFNLPPGNYKKPKLLYCSNGGHFLRILPDGTVDGTRDRSDQHIQLQLSAESVGEVYIKSTETGQYLAMDTSGLLYGSQTPSEECLFLERLEENHYNTYTSKKHAEKNWFVGLKKNGSCKRGPRTHYGQKAILFLPLPV","v":[0.07545,0.14964,0.028,0.08939,0.00907,0.18284,0.0235,0.07928,-0.00734,-0.03851,-0.04091,-0.05564,-0.01476,-0.01552,0.06328,0.04929,0.02575,0.07505,0.08638,-0.06886,-0.01766,-0.13101,-0.11606,0.03227,0.01569,0.0548,0.06039,0.00878,-0.07611,0.10689,-0.02773,-0.0571,-0.0047,0.0484,0.0148,-0.02978,0.07111,-0.09354,0.05838,0.01862,0.04364,-0.06386,-0.0154,0.00298,0.00105,0.03549,0.00141,0.01478,-0.02613,0.01068,0.03569,-0.02231,0.06515,-0.09805,0.02436,-0.0512,-0.03721,0.10613,-0.02653,0.06154,0.01402,0.03652,0.02766,0.07813,-0.01051,-0.10656,-0.01944,0.02003,0.07186,-0.01376,0.03087,0.0297,0.02299,-0.07993,0.01447,0.00817,-0.0043,-0.08124,0.0809,0.00831,0.04438,0.0496,0.03343,-0.02152,0.01723,0.04818,-0.00923,-0.0149,0.10107,0.02652,0.02121,0.12205,0.00204,-0.02195,0.08544,0.00414,-0.07643,0.00363,-0.03099,0.05034,0.06673,-0.09015,0.03196,0.00285,-0.02396,0.07596,-0.09677,-0.12557,0.05053,-0.00489,-0.01282,0.02959,0.03313,-0.10463,-0.12046,-0.0997,-0.12878,-0.03513,0.02276,0.01058,0.05269,-0.09279,-0.11752,0.03199,-0.02574,0.04769,0.06909,0.03448,-0.08132,-0.07007,-0.04801,-0.07837,-0.06962,-0.07274,-0.02529,-0.09559,-0.04172,-0.09481,0.07002,0.03467,-0.05613,0.05188,0.0321,0.03225,0.03246,-0.04552,0.03132,-0.11643,0.05277,-0.10155,0.03152,0.07375,-0.02197,-0.014,-0.0714,0.01825,0.08685,0.00447,0.01804,-0.0098,-0.02867,-0.01794,-0.10835,0.03456,0.02788,0.04055,-0.04783,0.00757,-0.14498,-0.04314,0.02562,-0.12101,0.02189,0.00891,0.14746,-0.0606,-0.03122,0.02195,0.07472,0.01031,0.02188,0.01636,-0.02014,-0.01785,-0.00186,0.18266,-0.01105,-0.04098,-0.01141,-0.05274,-0.02811,0.11391,0.00663,-0.08052,0.01756,-0.08456,-0.03829,0.03287,0.01034,0.01354,0.11882,0.04844,-0.01023,0.00732,-0.06076,-0.03394,0.04897,-0.06823,-0.12564,-0.00563,-0.06385,0.03159,-0.02169,0.08713,-0.0586,0.01366,0.10618,0.04059,0.02056,0.06938,-0.10854,0.02177,-0.07385,-0.01043,-0.0997,0.02459,-0.00431,-0.03963,0.00263,0.06166,0.0901,0.09857,0.01492,-0.01443,0.08092,0.01487,0.1341,-0.08362,0.06611,-0.0072,-0.00609,0.03663,-0.08899,-0.01756,-0.02222,0.05941,0.082,-0.06121,0.06934,-0.01661,-0.06475,0.09097,0.08496,0.05528,-0.02921,-0.1719]},{"domain":"computational_biology","key":"bio_protein_global_blosum62","name":"Global protein alignment score (BLOSUM62, affine gaps)","package":"computational-biology-ai999x","example":"Global protein alignment score: seq1 = HEAGAWGHEE, seq2 = PAWHEAE, open = -10, extend = -1","v":[0.03811,-0.0495,0.00184,-0.02387,-0.09189,0.03871,0.02334,0.06407,-0.06402,-0.03551,-0.07956,-0.00972,-0.09619,0.04772,0.11882,-0.03855,-0.021,0.09018,-0.06165,0.04536,-0.02408,-0.06837,0.0995,0.02838,0.06457,-0.06784,-0.03017,0.12526,-0.05331,0.06168,-0.03611,0.02224,-0.04685,-0.03243,-0.11243,0.0745,0.02428,-0.15605,-0.04199,0.00863,-0.03247,0.10775,-0.07019,0.02675,-0.00756,-0.03818,0.08956,0.07275,-0.0359,0.06826,-0.00389,0.00251,0.0691,-0.00195,-0.02243,0.06851,0.03906,0.07066,-0.022,0.03815,-0.01446,0.00606,-0.04086,-0.08947,0.00536,0.00839,0.0574,-0.0181,0.03921,-0.05894,0.00342,-0.06846,0.02353,-0.10928,-0.01342,0.04463,-0.00398,0.03155,0.0477,-0.0134,0.01348,0.05878,-0.00279,0.01673,-0.00695,-0.05121,0.07047,0.04544,0.08999,0.05756,-0.06895,0.01762,0.02672,0.06086,0.05204,-0.08527,-0.00526,-0.00783,-0.03234,-0.03636,-0.03956,-0.03557,-0.13282,0.05853,-0.05701,-0.06826,-0.1002,-0.09684,-0.00445,0.01593,-0.08713,0.0129,0.12073,-0.01631,0.02536,-0.02174,-0.03757,-0.05371,0.01859,-0.1363,-0.09044,0.02125,-0.00609,0.04883,-0.03337,0.06943,-0.07211,0.02333,-0.12377,-0.0144,-0.02423,-0.05844,0.0114,0.02088,0.08352,-0.10872,0.07426,0.09837,0.01132,-0.12067,0.03911,0.13157,-0.06339,0.08558,0.08056,0.08167,-0.00398,0.02332,0.08235,0.05686,-0.07531,0.07818,-0.01597,0.04355,-0.08766,-0.01972,0.14815,-0.056,0.01875,0.07394,0.02247,-0.08208,0.03716,-0.0006,-0.06628,0.02788,-0.02506,-0.00349,-0.03253,-0.07409,0.03364,-0.0338,0.00631,-0.10167,0.19488,0.03206,-0.03216,-0.0428,-0.07418,-0.06232,-0.01405,0.03947,0.10607,0.05634,0.03499,0.00239,0.02507,-0.05971,0.12927,-0.02354,-0.16204,0.06748,0.04011,0.01518,0.06476,0.01976,-0.00845,-0.03533,0.09856,0.01156,0.0377,-0.03222,-0.05032,-0.04001,0.00228,-0.04518,-0.02739,-0.03677,0.04243,-0.00631,0.01121,-0.13205,-0.09173,0.10912,-0.09581,0.02254,0.01028,-0.06628,-0.02536,0.07095,-0.0735,-0.10046,-0.06732,0.06468,-0.06278,0.07789,-0.07488,-0.04324,0.09978,0.03282,0.06656,0.0578,-0.02409,-0.13269,0.06547,0.05948,0.04628,0.06312,-0.11098,0.01266,-0.02657,0.04494,0.01945,-0.05749,-0.00903,0.02513,-0.07257,0.0625,0.03211,0.04324,0.04043,0.06241,-0.05284,0.09062,0.0589,-0.00672]},{"domain":"computational_biology","key":"bio_protein_local_blosum62","name":"Local protein alignment score (BLOSUM62, affine gaps)","package":"computational-biology-ai999x","example":"Local protein alignment score: seq1 = HEAGAWGHEE, seq2 = PAWHEAE, open = -8, extend = -8","v":[-0.03435,-0.01291,-0.10367,-0.01923,-0.07604,0.02007,-0.01567,0.08203,-0.09624,-0.02107,-0.09115,-0.03514,-0.08954,0.03602,0.10801,0.06824,-0.02169,0.12949,-0.07234,-0.02636,-0.08856,-0.11012,0.0604,0.02026,-0.03238,-0.04871,-0.01546,0.05009,-0.05765,0.09036,0.00382,0.07135,-0.00367,-0.0553,-0.03397,0.01128,0.03851,-0.15338,-0.05114,-0.00429,0.05631,-0.00536,-0.1066,-0.00507,-0.0481,-0.0191,0.03195,-0.03236,-0.06388,0.01047,0.04823,0.03229,0.03396,0.02326,0.02728,0.0312,0.04755,0.08171,-0.0032,0.05968,-0.02698,0.08371,0.01683,0.04129,0.02446,0.03732,-0.01018,0.00929,0.01564,-0.00418,-0.04051,-0.08458,0.03388,-0.1332,-0.05959,0.03482,0.05653,0.01266,0.07613,-0.00296,-0.00821,0.10517,0.02894,-0.04301,0.00504,-0.04873,0.08744,-0.03684,0.05129,0.07039,0.00437,0.03946,-0.04364,0.09089,0.04141,-0.07978,-0.03179,-0.02453,-0.03457,0.01439,-0.06261,0.03433,-0.06391,-0.01746,-0.03894,-0.0369,-0.11962,-0.13056,-0.08576,0.00285,-0.0678,-0.02294,0.11263,-0.01754,0.05769,-0.05825,-0.0428,-0.00042,-0.00091,-0.04573,-0.07263,-0.02899,-0.00155,0.07503,-0.06498,0.15656,-0.03517,0.03204,-0.03486,-0.00781,-0.02762,0.05383,0.05416,-0.03173,0.09354,-0.03085,-0.04177,0.04386,0.00446,-0.07647,0.09835,0.13941,-0.0781,0.01842,0.08609,0.08407,-0.0066,0.01416,0.09895,0.00241,-0.06479,0.14084,-0.00889,0.05872,-0.06697,0.00847,0.12439,-0.01315,-0.02676,0.11236,0.01286,-0.04853,-0.06815,-0.00899,0.01043,0.05954,0.02825,0.04015,0.0049,-0.10384,-0.00947,-0.02324,-0.00991,-0.08505,0.19632,0.07004,-0.02571,-0.06603,-0.0143,-0.07879,-0.03412,0.10659,0.09907,0.02357,0.02396,0.00809,0.03756,0.03744,0.10073,-0.04383,-0.10595,0.04819,0.04821,0.08068,0.06161,-0.04066,-0.03322,-0.05381,0.1179,-0.0085,0.02484,-0.02719,-0.0233,-0.00824,-0.05268,-0.05693,-0.01986,0.0187,-0.01715,0.027,0.04392,-0.14329,-0.05001,0.12286,-0.10982,0.08597,0.05897,-0.03197,-0.05026,0.00941,-0.10234,-0.026,-0.19217,0.10174,-0.06689,0.06988,-0.03423,-0.01708,0.03562,-0.01001,0.05743,0.00939,0.00772,-0.13523,0.05857,0.02323,0.09345,0.09637,-0.02927,0.05356,-0.0371,0.01531,-0.03582,-0.13417,0.00411,0.02123,-0.01728,0.01479,0.007,0.02629,-0.01142,0.02817,-0.02819,0.11114,0.02703,-0.01951]},{"domain":"computational_biology","key":"bio_protein_mass","name":"Molecular mass of a protein","package":"computational-biology-ai999x","example":"Protein mass: seq = MAEGEITTFTALTEKFNLPPGNYKKPKLLYCSNGGHFLRILPDGTVDGTRDRSDQHIQLQLSAESVGEVYIKSTETGQYLAMDTSGLLYGSQTPSEECLFLERLEENHYNTYTSKKHAEKNWFVGLKKNGSCKRGPRTHYGQKAILFLPLPV","v":[-0.10257,0.05976,0.0899,-0.05282,-0.00014,-0.04231,0.08729,0.01211,-0.08807,-0.05049,0.08045,0.00514,0.06638,-0.02025,0.14744,0.02172,-0.00572,0.03157,-0.07427,0.07792,0.05309,-0.0756,-0.07028,0.04657,0.00588,0.00185,-0.06348,-0.00315,-0.00184,0.02926,-0.05489,-0.0423,0.00716,-0.04534,-0.05861,-0.05279,0.03039,-0.05332,0.05117,0.00182,-0.03178,0.03591,-0.00686,-0.05623,0.07078,0.08695,0.05434,0.03906,0.08433,-0.00339,-0.07041,0.03384,0.0901,-0.07327,0.07112,0.01244,-0.08166,0.03408,0.02654,-0.07346,0.02589,-0.08694,-0.02941,0.02031,0.08417,0.05883,-0.0256,0.07649,0.06923,-0.01349,0.01081,-0.04341,-0.06872,-0.01151,0.0569,0.06218,0.02751,-0.04915,-0.06403,-0.02774,-0.02642,-0.05589,0.07623,-0.027,-0.02323,-0.01029,0.06212,0.03168,0.12899,-0.05585,0.01127,0.0198,0.00093,0.02116,0.09442,0.00422,-0.03079,0.09748,0.06601,0.06289,0.06212,-0.11378,-0.06532,0.01342,-0.01858,0.03752,-0.01389,0.03918,-0.00715,0.07513,-0.06516,0.03805,0.07386,-0.11977,-0.09083,-0.08988,-0.06356,-0.07372,0.02936,-0.0606,0.0499,-0.02681,-0.11784,0.01118,-0.03676,-0.04523,0.02441,-0.026,-0.07943,-0.0343,-0.0114,0.04633,0.10568,-0.01303,0.12142,-0.08364,0.00354,-0.00817,0.03934,-0.06981,0.01905,0.03616,0.07102,-0.04699,0.1078,0.05643,0.02065,0.02669,0.00593,-0.04216,0.00137,0.02037,-0.05642,0.0161,-0.10607,0.01796,0.05619,-0.01509,-0.0062,-0.01688,0.02923,0.01064,0.07311,0.0459,-0.0167,0.09094,-0.06101,-0.02651,-0.03142,-0.1267,-0.06476,-0.08951,0.07047,0.01006,0.08347,-0.00699,-0.01716,-0.09223,-0.07915,0.09557,0.11986,0.1741,0.0742,0.06838,0.00957,0.12694,-0.10597,-0.06692,0.01748,-0.17126,-0.0397,0.09641,-0.00184,-0.02095,0.04488,-0.10743,-0.10224,0.04026,0.02221,0.00598,0.00766,-0.03595,-0.05239,0.00842,-0.02263,-0.11254,0.09457,-0.03957,-0.01236,-0.07089,-0.02137,0.00177,-0.04164,-0.06123,-0.01643,-0.03644,0.0904,0.00345,0.00796,0.05455,-0.07983,0.03371,-0.11016,0.04917,0.0381,-0.13791,0.01635,-0.05931,-0.05933,-0.09753,0.08822,0.11996,-0.00738,-0.01777,0.13084,-0.02969,0.07405,0.01742,-0.04646,-0.04299,-0.00246,0.06124,-0.09062,-0.05268,-0.034,0.06578,0.1197,0.04807,0.04329,0.05922,0.02328,0.07297,-0.03524,0.05307,-0.08633,-0.1322]},{"domain":"computational_biology","key":"bio_protein_net_charge","name":"Net charge of a protein at a pH","package":"computational-biology-ai999x","example":"Protein net charge: seq = INGAR, pH = 7","v":[-0.04497,0.06705,-0.00152,-0.06688,0.01539,-0.02127,0.04511,0.12279,-0.13517,-0.06798,-0.06329,-0.06065,-0.03217,-0.00242,0.03635,0.05343,-0.04309,0.02863,0.03112,-0.00055,0.11033,-0.15109,-0.05798,0.00457,-0.08995,0.04196,-0.02598,0.06099,0.04631,-0.02158,-0.12247,-0.015,0.11196,-0.08467,-0.04063,0.0063,0.14764,-0.12007,0.00681,0.00891,0.03305,0.01734,-0.05465,-0.01072,0.05102,0.05074,0.04269,0.04276,0.0444,0.06783,-0.03877,-0.04479,0.13086,-0.00549,0.01837,-0.07783,-0.11169,0.01074,0.03357,-0.07993,-0.00678,-0.03342,-0.02771,-0.00057,0.05349,0.05287,-0.04096,-0.0015,-0.02623,-0.04615,0.0121,0.03815,-0.02547,-0.08919,-0.00747,-0.00413,0.07484,0.03344,0.00473,-0.04623,-0.04373,-0.13122,0.05993,0.04852,-0.09529,-0.0141,0.09235,0.00143,0.07307,-0.02607,0.0335,0.01661,0.01702,0.01882,-0.03012,-0.06825,-0.05289,-0.0293,0.08781,0.00262,0.01108,-0.17769,0.06701,0.05906,-0.05395,0.01746,-0.06098,-0.0517,0.12995,0.09207,0.01517,-0.05933,0.07942,0.00369,0.02589,-0.13134,0.03629,0.0707,0.07992,-0.00259,-0.01401,0.04862,-0.05626,-0.01282,0.01081,-0.10013,0.08571,0.03385,0.02588,-0.08274,0.0641,-0.07289,-0.0107,-0.0336,-0.07368,-0.08622,0.00074,0.10047,-0.05132,-0.09862,-0.01023,0.06491,-0.08183,-0.06596,0.00777,-0.00608,-0.0067,0.04347,0.07965,0.01859,-0.02604,0.0963,-0.02592,0.06037,-0.1224,0.13109,0.04264,-0.05395,0.02545,0.02048,-0.01205,-0.09355,-0.00157,0.04119,-0.03287,0.07239,-0.04868,0.03566,-0.04401,-0.08406,0.03487,-0.11353,0.05036,0.03377,0.091,0.0663,0.00928,-0.06637,-0.05763,0.08296,0.01214,0.0011,0.1227,-0.02964,0.07799,0.09802,-0.04665,-0.08997,-0.00256,-0.07478,-0.02627,0.03584,0.01512,0.0568,0.01059,-0.09238,-0.14293,0.03828,0.09813,-0.05017,-0.03116,0.00213,0.09509,0.0782,-0.00585,-0.03517,0.04794,-0.05699,0.13463,0.07222,0.04051,-0.06701,-0.05361,0.00762,-0.00699,-0.05137,-0.03919,-0.00987,-0.02649,-0.04625,0.03801,0.04839,0.01649,0.04845,0.03189,0.04163,-0.00862,-0.17028,0.04955,-0.0007,0.09252,0.09383,0.07004,-0.04172,0.02397,-0.05049,0.02495,-0.00805,0.01249,-0.04594,0.07641,-0.00264,-0.02403,0.04897,-0.04376,-0.09422,0.06822,-0.06069,0.0208,0.02954,0.0583,0.14841,0.01366,0.02177,-0.07595,0.05312]},{"domain":"computational_biology","key":"bio_rarefaction","name":"Rarefied species richness","package":"computational-biology-ai999x","example":"Rarefaction: counts = [2, 1, 1], n = 2","v":[-0.02099,0.00011,-0.03556,-0.126,0.03574,0.02502,0.10668,0.02183,0.00856,-0.00145,0.06653,0.04811,-0.05735,0.04045,0.03978,-0.09524,-0.03255,0.01581,0.01696,0.01297,-0.02287,-0.01438,0.08014,-0.07537,0.00014,0.05589,0.06307,-0.10872,0.07302,0.00513,-0.0733,0.03114,0.00024,-0.036,-0.08654,-0.06913,-0.0485,-0.01509,-0.09748,0.01957,0.00985,-0.05898,-0.02258,-0.0031,0.04948,-0.05267,0.00123,0.02346,-0.13109,-0.09645,0.02787,0.08412,0.00794,-0.02989,0.01076,0.05739,-0.0267,-0.01388,0.09539,-0.08633,-0.00449,0.12843,-0.00811,-0.14554,-0.13312,0.03455,-0.12658,0.0198,0.02056,0.06626,0.01076,0.00017,0.07103,0.24603,-0.00377,0.05992,-0.00977,-0.06168,-0.14948,0.0657,0.07434,-0.01852,-0.02751,0.01189,0.10947,-0.05437,0.03905,-0.07253,-0.0354,-0.05972,-0.06251,-0.02804,-0.01572,0.0075,0.0153,0.14072,-0.06955,-0.00863,0.00358,-0.05141,0.02134,-0.05625,0.0773,-0.01723,-0.03586,0.00781,0.0025,0.02332,0.14013,-0.01899,-0.06398,0.0266,-0.11222,0.06417,-0.03026,-0.0206,0.03214,0.03576,0.09004,-0.06788,-0.02412,0.003,0.02376,0.03878,0.10198,-0.04547,0.06949,0.00887,-0.08642,-0.01763,0.00857,-0.02586,-0.00579,0.01716,-0.01037,-0.01987,0.0261,-0.07315,-0.12107,-0.01097,-0.03068,0.14758,-0.02134,0.02854,0.02463,0.14695,-0.04185,0.09888,-0.11326,0.06537,0.04741,-0.03056,0.01652,0.0381,-0.01222,0.00453,-0.01206,-0.09302,-0.01281,-0.02623,-0.05757,-0.00168,-0.06146,-0.03953,0.01529,-0.10806,0.04337,-0.05725,0.01488,0.03772,0.05224,-0.03181,0.07864,0.09886,0.01778,0.0417,-0.07263,0.07116,-0.07117,0.01691,-0.03138,-0.0089,0.05102,-0.03747,0.09172,0.07395,0.04215,0.09708,0.05167,0.09735,0.03676,0.04069,-0.01887,-0.09858,-0.02337,-0.01703,0.06913,-0.0539,-0.06376,-0.08653,-0.04007,-0.0087,-0.03287,-0.00543,-0.05536,-0.03744,-0.00184,-0.04139,-0.02793,0.0396,0.00848,-0.02331,0.06852,0.15092,0.0363,-0.1007,-0.04113,0.0799,0.00467,-0.08771,0.04741,0.00803,-0.02375,-0.00484,0.02015,-0.02814,-0.04192,-0.02994,-0.03519,-0.10897,0.0357,0.03764,0.07521,0.17569,-0.05502,0.00081,-0.03592,-0.0697,-0.08527,0.01891,-0.00395,-0.05721,-0.02993,0.10398,0.10646,0.03815,0.03562,0.03588,0.07489,0.05702,-0.08802,0.01855,0.01049,0.12628,-0.09412,-0.0296]},{"domain":"computational_biology","key":"bio_recessive_lethal","name":"Decline of a recessive lethal allele","package":"computational-biology-ai999x","example":"Recessive lethal allele frequency: q0 = 0.5, t = 1","v":[0.02689,-0.02586,-0.0799,-0.11291,0.07818,-0.11828,-0.0206,-0.017,-0.03044,0.08015,-0.02809,-0.05995,0.00644,-0.08997,0.0504,-0.02183,0.00834,-0.07447,-0.0385,-0.00526,-0.07408,-0.03465,-0.10378,0.15634,-0.0313,-0.0714,-0.03665,-0.08311,-0.06173,0.05024,-0.02947,0.02318,-0.0554,-0.00395,0.02021,0.10202,0.0566,0.01553,-0.03158,0.07183,0.03508,-0.06231,-0.02929,-0.02663,0.01524,-0.01871,-0.12038,0.07005,-0.03435,0.00781,-0.03419,0.03125,0.00289,-0.20485,0.09248,0.08153,-0.05255,-0.0252,-0.08356,-0.06469,0.05036,0.05588,0.01518,-0.00782,-0.08523,-0.00205,-0.06109,0.03511,-0.0246,0.07102,0.03722,0.07593,-0.041,0.04355,-0.01238,-0.02513,0.01653,0.01451,-0.16047,0.07067,0.04698,0.021,-0.00427,-0.03426,-0.08946,-0.03895,-0.10218,-0.01869,0.05201,-0.02349,-0.03955,-0.02438,0.05727,-0.02685,0.03796,0.03288,-0.03814,0.10345,0.03086,0.01907,0.00394,-0.06256,0.05684,0.01721,-0.02005,0.04876,0.10364,0.07218,0.04434,-0.06396,0.01299,0.01013,-0.14441,0.00249,0.06447,0.09755,-0.04021,-0.00477,0.0677,-0.03435,-0.01794,-0.05798,0.14534,-0.03438,0.07425,-0.00699,0.06381,-0.0121,0.0112,0.0629,0.0745,0.06025,-0.10412,-0.06371,0.00599,-0.03667,0.08507,-0.06727,0.08392,-0.05083,0.02606,0.13886,-0.0013,-0.03387,-0.03206,0.05211,0.06779,0.13864,0.07583,-0.0028,0.07667,-0.13193,-0.15598,-0.07899,0.09664,-0.09709,-0.10322,0.04039,-0.03821,-0.01083,-0.03376,-0.00975,0.09054,0.08624,-0.01675,0.02725,0.04942,0.0207,0.04336,-0.02004,0.12976,0.03311,0.09881,-0.05118,0.03879,-0.01396,-0.00234,-0.07417,-0.01705,0.02763,-0.10678,0.06179,0.01217,0.00189,0.12161,-0.03726,-0.09483,0.02962,0.00733,0.02397,-0.01568,0.0879,0.07264,-0.03303,0.00564,0.05375,-0.02764,0.00804,0.01871,-0.01589,0.07014,-0.09574,0.00587,-0.12098,-0.01255,0.01032,0.02908,-0.04417,-0.00889,0.04875,0.08364,-0.0709,0.05281,0.05699,0.00922,-0.0694,0.01268,0.14049,-0.02138,-0.05058,-0.02913,-0.00656,0.04199,-0.0555,0.05024,0.04242,0.02592,-0.0236,0.05323,-0.02083,0.0515,-0.01387,-0.10333,0.07632,0.05872,0.00866,0.02158,-0.08283,-0.02119,0.06364,0.03827,-0.03516,0.07177,-0.00387,-0.03802,0.14446,0.04448,-0.07324,0.06583,0.01786,-0.08401,-0.10023,0.01683,0.03734,0.06111,-0.069]},{"domain":"computational_biology","key":"bio_recombination_fraction","name":"Recombination fraction from a map distance","package":"computational-biology-ai999x","example":"Recombination fraction: d_cM = 50, map = haldane","v":[-0.05174,-0.01187,0.01793,0.01007,0.08343,-0.08127,0.12278,-0.03161,-0.00854,-0.03994,-0.01776,-0.04382,0.02845,-0.09118,0.04507,0.02613,0.01232,-0.06486,-0.02898,0.03194,-0.0279,0.02023,0.01752,-0.06057,-0.01578,0.01895,-0.07696,-0.08956,-0.07028,-0.04168,-0.0126,0.11414,0.01305,0.0024,-0.02526,0.04625,0.05262,-0.0337,-0.11668,0.07419,-0.00189,-0.03394,0.05762,-0.0527,-0.09991,-0.11899,-0.11025,0.07753,-0.08138,-0.01012,-0.12725,0.05292,-0.10219,-0.06689,0.05995,0.1258,-0.0302,0.03816,0.03247,-0.04078,0.10584,-0.04868,-0.04817,-0.12708,-0.14738,-0.01994,0.07483,0.13274,0.00876,0.04543,0.05642,0.00439,-0.06624,-0.04877,0.05666,0.07124,-0.09071,-0.01057,0.01629,0.00259,0.07776,-0.0361,-0.02806,-0.04198,0.04899,-0.09743,0.05384,0.08183,0.07086,0.1152,-0.07881,0.06773,0.08841,0.01075,0.05909,-0.02607,0.0432,0.01763,-0.04932,-0.01822,0.01433,0.00448,0.0699,0.06574,-0.08799,-0.00102,0.02214,0.10348,-0.06517,0.05005,-0.00405,0.01668,-0.05842,0.06328,0.0185,0.02025,0.02174,0.02854,-0.00247,-0.00789,-0.02336,-0.02706,0.02057,0.07306,-0.03965,-0.07272,0.02122,-0.09435,-0.0077,0.12384,0.06227,0.07233,-0.0046,-0.1095,-0.02716,0.0544,0.06309,0.00836,-0.02857,0.06474,0.09966,-0.03295,0.074,-0.02935,0.02233,0.12869,0.02564,0.05566,0.03275,0.05047,-0.03751,-0.11678,0.05052,-0.04856,0.17461,-0.12516,0.11167,0.00436,-0.04074,0.0744,0.02503,-0.0289,-0.03528,-0.07276,0.087,-0.04787,0.00327,-0.06642,0.04127,0.00931,-0.03266,0.01481,0.16143,-0.06683,-0.01088,0.00936,0.05741,0.0035,0.05012,0.03817,-0.07962,0.0348,0.06104,0.00789,0.00673,-0.0216,0.00832,0.04944,0.00764,-0.01348,0.04915,0.10985,0.0203,-0.02684,0.03729,0.01931,-0.09495,0.03419,-0.01561,0.02129,0.04939,0.00534,0.04398,-0.17992,-0.1243,0.00678,-0.00182,-0.00463,0.07436,0.08381,-0.02434,-0.08999,-0.09682,0.07823,-0.02663,0.02063,-0.02221,0.17098,0.03218,0.08995,0.03769,-0.00618,0.06301,0.02842,-0.09576,-0.05173,0.09951,0.02536,0.06973,0.03607,-0.0231,0.06458,-0.12158,-0.07149,0.04593,-0.05589,0.02097,-0.08513,-0.03015,-0.02965,0.00232,-0.10187,0.00241,-0.00479,-0.01635,0.0014,-0.01409,-0.03048,0.00073,-0.04545,-0.03583,0.04301,-0.07988,0.01233,-0.05333,-0.01428]},{"domain":"computational_biology","key":"bio_restriction_sites","name":"Restriction sites and fragments","package":"computational-biology-ai999x","example":"Restriction sites: seq = AAGAATTCTTGAATTCGGATCC, enzyme = EcoRI","v":[-0.06949,0.09607,0.08671,-0.09233,-0.0799,-0.11161,0.00618,-0.08319,-0.04084,0.04273,-0.04476,0.03598,-0.03236,-0.03106,0.05051,-0.01801,0.01592,-0.02018,0.0557,-0.0737,0.00337,0.04051,-0.0125,-0.01258,-0.02002,-0.04279,0.00243,-0.02235,0.05167,-0.03246,-0.011,0.01617,0.00271,-0.08456,0.04479,0.0401,0.08824,-0.0367,-0.02635,0.08022,-0.09128,-0.03746,0.01075,-0.02806,0.02559,0.06381,-0.02295,0.12474,-0.12721,0.0032,-0.16323,0.13437,0.02802,-0.08199,0.09375,0.11943,-0.03744,0.12032,-0.0116,-0.00559,-0.03499,0.01482,-0.00311,-0.09815,-0.07688,-0.06401,0.06759,0.10449,0.06384,0.06902,-0.03251,0.00292,-0.04619,0.06914,-0.02271,-0.02695,-0.07868,0.07149,0.1286,-0.02333,0.0585,-0.11298,0.0362,-0.08324,0.03832,-0.00244,0.02224,0.06075,-0.04873,0.05916,0.0011,-0.02863,0.04404,0.05316,0.02815,-0.08691,0.06943,0.01131,-0.00764,0.02192,0.03735,-0.04917,0.05795,0.09236,-0.03401,0.01478,-0.11832,-0.03276,-0.01881,0.03062,-0.02803,0.01288,0.0144,0.01793,-0.02071,0.08543,-0.03509,-0.0081,0.08636,-0.0871,-0.0295,-0.0109,-0.07063,0.11393,0.03797,0.04085,0.05603,0.12001,0.01875,0.06163,0.04457,-0.02037,0.06254,-0.17843,0.08492,-0.04547,0.01036,-0.0758,-0.03082,0.00764,-0.13016,-0.03092,0.05592,-0.00594,0.05019,0.11492,0.00899,0.00171,-0.01375,-0.06804,-0.0737,-0.01584,-0.03586,-0.02043,-0.03422,-0.02276,0.00626,-0.03443,0.01053,0.01694,0.03455,0.12274,0.02667,0.00905,-0.00942,0.06242,0.04957,-0.16388,0.06119,0.06745,-0.04436,-0.0627,0.04261,0.04147,4e-05,0.08513,-0.02952,-0.11483,0.00157,0.00159,0.05114,0.00341,0.0269,-0.03461,-0.07645,0.04344,0.08923,0.05845,-0.02282,-0.07775,0.06,0.0875,0.0617,0.02271,0.01311,-0.05989,-0.07321,0.01329,0.06883,0.00266,0.01028,0.06074,-0.02513,-0.0074,0.01425,0.05875,-0.02782,-0.04151,-0.04223,0.02895,0.03977,-0.04941,-0.1604,0.16099,-0.04779,0.00991,0.11555,0.07287,0.00947,0.02286,-0.02774,0.08899,0.1563,0.03441,-0.05521,0.01124,0.06763,-0.01513,0.00463,-0.00137,-0.08818,-0.0081,-0.0493,-0.02836,0.08677,-0.08356,0.07997,-0.1356,-0.04886,0.02657,0.0186,-0.00371,0.00613,-0.05079,-0.05925,0.0372,0.00335,0.04397,0.0773,0.13462,-0.00773,-0.03199,-0.09815,0.02378,0.03264,-0.13696]},{"domain":"computational_biology","key":"bio_reverse_complement","name":"Reverse complement of a DNA sequence","package":"computational-biology-ai999x","example":"Reverse complement: seq = ATGCCGTA","v":[0.00873,0.05244,-0.05369,0.08399,0.0589,0.00561,0.00402,-0.02371,-0.1015,-0.00562,-0.0339,0.06169,0.00399,-0.01614,0.08844,0.01849,-0.01862,-0.0297,7e-05,0.1079,-0.10194,0.01368,-0.04559,-0.00324,-0.02171,-0.08035,0.01289,-0.01938,0.05324,0.11626,-0.01729,0.02681,-0.02729,-0.07345,0.07751,-0.01178,-0.08045,-0.09877,-0.05929,0.09345,-0.01963,-0.03434,-0.01837,-0.05347,0.0853,0.10462,0.03865,0.09824,-0.09736,-0.00721,-0.00173,-0.03169,-0.01218,-0.05857,0.02406,0.12033,-0.05937,0.00268,0.04073,-0.00517,-0.03446,0.01221,0.01074,-0.04464,-0.09423,-0.04925,-0.00404,-0.02673,0.05941,0.11716,-0.016,0.02085,-0.01907,-0.02575,0.01209,-0.10149,-0.11929,0.00892,0.10089,0.06472,0.10187,0.11482,0.03472,-0.00964,-0.00029,0.07113,-0.04405,-0.0696,0.04589,-0.01019,0.01727,-0.01494,0.14071,0.13143,-0.01074,-0.04848,-0.00224,-0.00223,0.01817,0.11087,0.01956,-0.1192,0.04167,0.1315,0.02036,-0.16169,-0.05265,0.02362,-0.12023,0.08038,-0.00683,0.04174,-0.05214,-0.0407,0.10042,-0.05714,-0.0317,-0.12831,-0.06441,-0.06541,-0.03307,-0.04759,-0.08564,-0.03427,-0.00915,0.09473,0.12047,0.02104,0.0332,0.00281,-0.05514,-0.07882,0.00183,-0.13398,0.09464,0.00227,-0.04536,-0.02746,-0.05482,-0.10994,0.02637,-0.05373,-0.06041,-0.05842,0.08924,0.12669,0.02683,0.02963,0.11439,-0.07816,-0.05522,0.03595,0.053,0.06708,-0.05122,0.08767,0.02918,-0.03733,0.00962,-0.00348,0.02211,-0.04525,-0.05878,-0.01634,-0.01709,0.08001,0.01584,0.00047,-0.01504,0.05717,-0.01106,0.09358,0.0977,0.0151,0.00445,0.04852,0.02942,-0.03854,0.06738,-0.00915,0.01519,-0.05648,0.01081,-0.00772,0.02445,0.01884,0.08217,0.04453,-0.042,-0.05473,0.09392,0.06284,0.01744,-0.12878,0.05915,0.03066,-0.11878,0.074,0.11027,0.0418,-0.00237,-0.12862,0.15997,-0.02976,-0.11164,0.07396,0.05456,-0.02843,-0.00615,-0.00175,0.10199,-0.09937,-0.10857,0.03463,0.02721,-0.07699,0.08432,0.01543,0.04669,-0.01637,0.09445,0.02625,0.07842,-0.08217,-0.00051,-0.02693,0.09021,0.04247,0.04231,-0.0618,0.03201,0.01467,0.04691,0.04053,-0.06621,-0.05994,-0.08854,-0.0122,0.04309,-0.06093,-0.01998,-0.008,-0.03313,0.00265,0.01239,0.05904,-0.044,-0.0062,0.00415,-0.01585,-0.06523,0.06702,-0.02084,0.02045,-0.06217,-0.05257]},{"domain":"computational_biology","key":"bio_richness_indices","name":"Margalef and Menhinick richness indices","package":"computational-biology-ai999x","example":"Richness indices: counts = [10, 20, 30, 40]","v":[-0.03432,0.04159,0.02746,-0.02124,-0.00867,-0.00656,0.09037,0.10778,-0.01529,-0.10831,0.03323,-0.02496,-0.02294,-0.01312,-0.08061,0.0577,-0.00784,0.04361,0.05245,-0.05304,0.01386,-0.06919,0.01607,-0.01138,-0.02476,0.11897,0.09191,-0.19319,-0.11839,-0.06037,-0.11177,0.01194,0.04613,0.00372,0.00506,-0.09804,-0.01502,0.01463,0.01492,-0.0899,-0.05906,-0.01326,0.01854,0.02442,0.11277,0.08158,0.00565,0.01967,-0.04722,-0.07809,-0.01902,0.12728,0.00272,0.01482,-0.05942,0.05152,-0.05232,0.00649,0.05399,-0.0324,0.02766,0.07489,-0.10607,-0.00857,-0.08399,0.02033,-0.06897,0.07163,-0.00178,0.1589,0.05804,-0.02741,0.02668,0.09089,0.04902,0.00558,0.09785,-0.05258,0.03687,-0.01084,-0.00717,-0.01997,0.0122,0.00575,0.06217,-0.04964,0.0039,-0.06634,0.03886,-0.04911,-0.01117,-0.10668,-0.04373,-0.02739,-0.04705,0.07163,-0.04573,0.00181,0.07911,-0.03198,0.06402,-0.00466,0.04401,-0.03983,0.01384,-0.01707,-0.03811,-0.00376,0.0504,0.00107,-0.05911,-0.07411,0.03823,0.0111,-0.00782,-0.02559,0.10507,0.09671,0.05088,-0.02011,-0.03713,0.03932,0.13004,0.02597,0.06354,0.01074,0.00413,-0.06801,-0.09062,0.0584,-0.01833,0.16515,-0.0414,-0.04346,0.03953,0.10766,-0.05573,-0.02167,-0.0429,0.05304,-0.01793,0.02651,0.10643,-0.03281,0.08461,-0.04743,-0.05909,-0.03534,0.04002,-0.06446,-0.06018,-0.02431,-0.16277,0.03904,0.02348,-0.01225,-0.06854,0.00729,-0.07668,0.00995,-0.0201,0.00632,-0.03919,-0.07122,0.07798,-0.10251,-0.04992,-0.08284,0.13509,0.08561,-0.01678,-0.08386,0.0664,0.08661,0.03463,-0.01238,-0.01563,0.01095,0.02298,0.03319,0.00879,0.01186,-0.01442,0.01775,0.03345,0.03363,0.08574,0.0608,-0.03814,0.11639,0.0736,0.01652,-0.09936,0.08841,-0.06987,0.01646,-0.04458,0.0096,-0.14811,-0.10181,0.03537,-0.07291,-0.02583,0.10678,-0.07896,-0.04954,0.10431,-0.01559,-0.02002,0.07296,-0.03336,-0.01432,-0.06086,0.06762,-0.02696,-0.10616,-0.07631,-0.04012,-0.03447,-0.04268,0.09443,0.06787,0.0093,0.07911,0.02919,-0.01375,-0.11882,-0.06549,-0.10683,-0.0333,0.02159,0.08604,0.12937,0.0194,0.02651,-0.03937,0.02432,-0.01317,-0.03438,0.06351,-0.0293,-0.07318,-0.05237,0.12573,0.05297,-0.02438,0.05003,-0.01103,0.04549,0.03498,0.06108,0.10536,-0.05543,0.10589,-0.11641,-0.02853]},{"domain":"computational_biology","key":"bio_robinson_foulds","name":"Robinson-Foulds distance between trees","package":"computational-biology-ai999x","example":"Robinson-Foulds distance: tree1 = ((A,B),(C,D),(E,F));, tree2 = ((A,C),(B,D),(E,F));","v":[0.03963,-0.07757,0.06916,-0.00843,-0.10824,-0.01184,0.01433,0.04123,-0.03714,-0.03834,-0.00358,0.05277,-0.12472,-0.00852,0.05982,-0.03291,0.04267,-0.03503,-0.03998,-0.09792,-0.04745,0.01502,0.10404,-0.11369,0.05455,-0.03908,0.01292,-0.07971,-0.01541,-0.08916,0.01406,0.04168,-0.04254,-0.05451,-0.0587,0.06611,0.02345,0.04816,-0.03253,0.08568,-0.03299,0.036,0.08717,0.00056,-0.00663,-0.12508,0.16657,0.04645,-0.07295,-0.05387,-0.09308,0.14218,-0.07307,-0.07163,5e-05,0.06035,0.03384,0.094,0.05506,0.00434,-0.04409,-0.02325,-0.03757,-0.13881,-0.01439,0.02661,0.0258,-0.01028,-0.00266,0.0913,-0.04303,-0.12008,0.04486,0.05021,0.02277,-0.03128,-0.07838,-0.09468,-0.04572,-0.01246,0.01213,-0.10017,0.05167,-0.01706,0.09936,-0.00176,0.09865,-0.08156,-0.06686,0.06149,-0.10905,0.01126,0.06593,0.01796,0.05346,0.02322,0.00153,0.05358,-0.09197,-0.06416,0.00728,0.02211,0.06856,0.04041,-0.1574,-0.14222,0.07261,-0.00769,-0.04133,-0.08926,-0.05175,-0.04005,0.01432,0.13194,-0.05437,0.01628,0.06231,0.01995,0.0321,-0.111,0.01383,0.1072,-0.02434,0.14019,0.02467,0.06579,-0.02966,-0.01915,0.00109,0.03145,-0.04553,0.06567,0.01806,-0.04998,-0.03618,-0.06039,-0.05294,-0.03157,-0.00592,-0.03407,0.13796,0.07946,0.06612,-0.05281,0.05043,0.08127,0.02177,0.02659,-0.002,-0.00583,0.08722,-0.1188,0.08887,-0.04657,0.05782,-0.08421,0.10376,-0.08514,0.05153,-0.02016,0.0125,0.06233,-0.03716,0.01447,-0.08626,-0.02738,0.06597,-0.0418,0.01688,0.09896,0.04458,0.03404,0.05405,0.06908,0.01547,-0.05227,0.02199,0.08536,-0.07272,-0.05534,-0.002,-0.03046,0.00271,-0.00768,0.03915,-0.04542,0.05778,0.01928,0.0503,0.12091,0.06525,0.06636,-0.0383,0.02026,-0.06521,-0.03094,-0.01152,0.0668,-0.04406,0.00029,-0.01502,0.0911,-0.04516,-0.02307,0.01024,0.02384,-0.06446,-0.07411,0.0081,0.09857,-0.00258,-0.12086,-0.07926,0.10794,0.05211,-0.05949,-0.01252,-0.00309,0.05411,0.02181,0.07953,-0.10661,0.02922,-0.08402,-0.06212,0.00065,-0.03815,-0.00958,0.03333,-0.02237,-0.01301,0.0579,0.02954,0.0497,-0.01127,-0.05673,-0.00209,-0.08552,-0.08117,0.07525,0.07641,-0.08556,0.01517,-0.03146,0.02528,-0.03837,-0.04999,0.03689,0.11842,0.11589,0.08184,0.02335,-0.04167,0.0731,-0.01277,0.0808]},{"domain":"computational_biology","key":"bio_schumacher_eschmeyer","name":"Schumacher-Eschmeyer multiple-census estimate","package":"computational-biology-ai999x","example":"Schumacher-Eschmeyer estimate: C = [10, 10, 10], R = [0, 2, 3], M = [0, 10, 18]","v":[-0.02114,0.08627,0.00023,-0.01473,-0.02075,-0.00571,0.13604,0.01599,0.05189,-0.07579,0.02761,0.01209,0.09541,-0.02162,-0.03639,0.03108,-0.01601,0.07479,0.0573,-0.11776,-0.02114,-0.02117,-0.00209,0.04759,-0.08466,0.07258,0.09439,-0.08452,-0.01469,-0.02972,0.09953,-0.10924,0.01064,-0.0073,0.01424,-0.06579,0.05042,0.08145,-0.04274,-0.1367,-0.02843,-0.00466,-0.03841,0.01498,0.01596,-0.02079,-0.06759,-0.00603,-0.01447,0.07637,-0.00132,-0.00564,0.07054,-0.01415,-0.03764,0.07237,-0.07358,0.05013,-0.06801,0.00523,-0.03856,0.00516,-0.05621,-0.08016,-0.19219,-0.02811,-0.12419,0.0018,0.04303,0.02823,0.09726,0.00565,0.10658,0.0585,-0.0238,0.00288,0.02295,0.04869,-0.12091,0.08616,0.05904,0.0126,0.0167,0.00306,0.06823,-0.02911,-0.00457,-0.02451,0.0828,-0.07538,-0.0681,0.08322,0.02397,0.11399,-0.01819,0.04394,0.00901,-0.0125,0.00589,0.00068,0.10935,0.00243,-0.05079,-0.07589,-0.06599,0.04795,-0.107,0.03298,0.01347,-0.00428,-0.0801,-0.09592,0.01864,0.02166,-0.05458,0.0513,0.10942,0.06947,0.09621,-0.04259,-0.02273,-0.13099,0.02861,0.04278,0.01427,0.02045,0.0234,-0.0694,-0.00987,-0.01542,0.02144,0.03065,-0.08434,-0.02302,0.00036,-0.04531,0.06814,0.05103,-0.11798,-0.11233,-0.02352,0.03413,0.05188,-0.01644,0.08115,0.06072,-0.05316,0.12764,-0.01934,0.00732,0.00235,-0.13974,0.03989,-0.0799,0.05666,-0.05784,-0.06123,-0.01643,0.02036,-0.06417,-0.08073,0.00525,-0.09475,-0.05506,0.10202,-0.06156,0.04252,-0.08659,-0.01807,-0.03541,0.01255,-0.06799,0.04435,-0.06311,0.01075,0.06246,-0.01414,-0.06516,0.01594,0.00934,0.00395,-0.05068,0.078,0.00373,0.01614,-0.02602,-0.10033,0.07378,-0.01148,-0.01668,0.09706,0.02221,0.11504,-0.00084,0.06368,0.14981,0.03934,0.08867,0.00593,-0.11261,-0.00319,-0.10315,-0.0036,-0.02851,-0.04724,0.02042,-0.05268,0.03854,0.03906,0.00785,-0.08238,-0.09139,0.09245,0.10843,-0.03662,0.00695,0.04835,0.15113,0.08177,0.00705,0.12203,0.12237,-0.01838,-0.05044,-0.08443,0.0254,-0.03588,-0.07347,-0.02228,-0.02772,0.13376,0.05232,0.01507,0.02351,-0.08889,-0.06375,0.02965,-0.00767,-0.11887,-0.05497,0.04584,-0.00878,-0.04704,0.07819,0.04651,-0.01,0.05309,0.06723,0.05045,0.00697,-0.02429,0.01688,-0.02446,0.13159,-0.01588,-0.07142]},{"domain":"computational_biology","key":"bio_secondary_structure_fraction","name":"Secondary-structure propensity fractions","package":"computational-biology-ai999x","example":"Secondary structure fraction: seq = EMALKNPGSD","v":[0.02167,0.0818,6e-05,-0.0153,-0.02036,0.07828,0.00477,0.00553,-0.04081,-0.06441,-0.09411,-0.08102,-0.13163,0.04284,0.00684,0.06517,-0.13517,0.07768,-0.08061,0.02782,-0.04997,-0.01614,0.00354,0.06476,0.08347,-0.10371,-0.02971,-0.03562,0.014,0.09776,-0.12495,-0.01606,0.0697,-0.02206,0.03128,-0.09431,0.03082,-0.12211,-0.02909,0.15324,0.06258,0.04034,0.0247,0.02592,-0.01597,0.04442,0.0067,0.04017,-0.03582,-0.01429,0.0085,-0.02948,-0.04586,-0.11951,0.0461,0.02005,0.02203,0.06954,-0.01373,-0.05573,0.04762,0.07861,-0.01457,-0.05622,-0.00337,0.028,0.0707,0.02979,0.11131,-0.04973,0.02428,-0.0888,-0.06095,-0.03836,-0.00169,0.08213,0.02393,0.0858,0.05255,-0.09763,-0.01976,0.04348,0.00341,-0.0462,0.04466,-0.04072,0.02734,0.05325,0.06713,-0.01048,-0.00381,0.01374,0.09367,-0.08568,0.06228,0.01168,-0.11191,0.00975,0.01629,0.08352,0.04594,-0.02354,0.0611,0.0107,-0.05775,-0.0891,0.01773,0.01175,0.05725,0.18187,0.0112,-0.06194,0.09943,-0.14487,-0.06777,-0.0871,0.02652,0.00152,0.097,0.00172,-0.07541,0.0307,-0.03371,0.16477,-0.08318,0.12279,-0.03957,0.01862,-0.11979,-0.01275,-0.02458,-0.06673,0.07447,-0.10085,0.04079,-0.09262,-0.03928,0.04285,-0.03264,-0.0363,0.14045,0.0269,0.00791,-0.06787,0.09739,0.06211,-0.01646,0.03416,0.06003,0.0177,-0.05265,0.00655,0.04845,0.08993,0.04064,-0.06343,0.05391,-0.06543,0.04677,0.00975,0.04046,-0.1578,-0.03622,0.07201,0.00295,-0.04184,-0.05403,0.02371,-0.05929,-0.00365,0.0411,0.00182,0.02501,-0.00977,0.15995,0.07097,-0.03317,-0.03542,0.04628,0.07198,-0.05881,0.01191,0.03089,0.03511,1e-05,0.10229,0.0052,-0.02956,0.01774,-0.04507,-0.01856,0.00596,0.02384,-0.04874,0.05405,-0.10403,0.00393,-0.01508,0.00499,0.01775,0.00464,-0.0637,-0.06901,0.03494,-0.01896,-0.13039,0.09482,-0.00622,-0.03987,-0.05401,-0.0226,0.01706,-0.08921,0.11401,-0.01166,0.0656,0.10384,0.03071,-0.01462,0.01,-0.13285,0.02454,-4e-05,0.09423,0.00863,-0.06976,0.01965,-0.04158,0.00634,-0.09769,0.00729,0.08141,-0.01134,-0.06109,-0.00873,0.03445,0.07529,-0.09089,0.02726,-0.0177,0.0301,0.00235,0.02855,0.0268,-0.01159,-0.02794,-0.02405,-0.04201,0.07684,-0.07274,-0.1457,0.08344,-0.02421,0.1213,0.06219,-0.03152]},{"domain":"computational_biology","key":"bio_semiglobal_alignment_score","name":"Semi-global (end-gap-free) alignment score","package":"computational-biology-ai999x","example":"Semi-global alignment score: seq1 = TTTTACGTACGGGG, seq2 = ACGTAC, match = 1, mismatch = -1, gap = 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infinite","v":[0.04826,0.05083,-0.02878,0.02308,0.00475,-0.0091,0.03215,-0.01043,-0.09668,-0.17839,-0.09787,0.04495,-0.12404,-0.02168,-0.08715,0.03775,-0.11192,0.13909,-0.01353,-0.00055,-0.02392,-0.0404,0.02407,-0.02708,-0.00218,0.04688,0.08245,-0.11557,-0.0044,-0.03364,-0.13377,-0.02306,0.08564,-0.01073,0.02703,-0.00201,-0.15449,-0.06557,-0.0297,-0.02632,-0.07772,-0.01808,-0.03864,0.03733,0.06314,-0.0726,-0.01456,0.03178,-0.0707,-0.07177,0.03086,0.02907,0.03255,0.10043,-0.05571,0.05441,-0.05398,0.0462,0.04024,-0.03629,0.04328,0.16976,-0.01782,-0.06748,-0.19421,-0.06837,-0.03782,-0.05965,0.05003,0.11187,0.04769,0.03269,0.05106,0.09184,0.01268,0.06463,-0.02589,0.00511,-0.03275,-0.01395,0.0053,0.05775,0.01475,0.00576,0.15244,-0.03264,-0.03771,-0.11211,0.01304,-0.04682,-0.01979,-0.02439,0.0582,-0.02504,0.01756,-0.04651,-0.01768,0.02301,0.09099,-0.0126,0.06345,0.08122,-0.02999,-0.0259,-0.02123,0.02291,-0.00749,0.01562,0.04332,-0.09068,-0.04009,-0.04678,-0.03161,0.1255,-0.03598,-0.06394,0.08486,-0.01709,-0.03865,-0.06125,-0.0776,0.00996,-0.0132,-0.02773,0.137,0.12424,0.01318,-0.08539,0.01027,0.02683,0.02638,0.06807,-0.0731,-0.02419,0.04572,0.04489,0.02876,-0.00947,-0.0917,0.01099,-0.05463,0.10697,0.02089,-0.02463,0.11818,0.10915,-0.10196,0.05279,-0.00482,0.02908,0.00606,-0.00854,-0.07511,0.03629,0.0966,0.01033,-0.03417,-0.04757,-0.02862,0.01916,-0.02046,-0.0491,-0.06808,0.01251,0.06894,-0.13621,0.04073,-0.07059,-0.03051,0.03525,0.04622,-0.09107,0.07877,-0.02263,0.00247,-0.02082,-0.03215,0.15668,0.00552,0.06299,-0.04049,-0.03392,-0.04734,0.07587,0.02893,0.05079,-0.00627,0.05575,0.00551,0.08279,0.07513,0.00569,-0.03461,-0.05908,-0.06474,0.04067,-0.05634,0.01515,0.00979,-0.05003,-0.08541,-0.01496,-0.01306,-0.07649,-0.08168,0.10144,0.03629,-0.05231,-0.09008,0.02986,-0.03149,-0.06836,0.09089,0.04298,-0.00664,-0.00803,-0.01018,0.0465,-0.08471,-0.0618,0.1363,0.07935,-0.01042,-0.04337,0.0166,0.06277,-0.12724,-0.08453,-0.00093,0.10796,0.11458,0.08833,0.02115,-0.04482,0.02254,-0.06336,-0.02252,0.0687,0.00071,0.04591,0.04508,0.0294,0.04957,0.07855,0.11055,-0.0036,0.02089,0.00427,0.01493,-0.05993,0.02049,0.03839,-0.00779,0.10187,-0.02702,0.03564]},{"domain":"computational_biology","key":"bio_species_area","name":"Species-area relationship fit","package":"computational-biology-ai999x","example":"Species-area relationship: A = [1, 10, 100, 1000], S = [10, 20, 40, 80]","v":[-0.04162,-0.11956,-0.05355,-0.01483,-0.03229,0.02945,-0.08741,0.04654,-0.01537,-0.0545,0.04223,-0.06869,-0.04732,-0.06171,0.03694,0.06736,0.08329,0.04207,0.10117,0.04681,0.04411,-0.05859,0.15047,-0.0262,-0.06749,0.1115,0.05944,-0.02033,-0.01504,0.11736,-0.06493,-0.06521,-0.00149,-0.02937,0.01679,-0.07014,0.07268,0.07245,-0.0599,0.04581,0.03235,0.0626,-0.09724,-0.06936,-0.07166,-0.04841,0.06216,-0.01077,-0.06683,-0.11823,0.04245,0.06403,0.05117,0.05416,-0.05392,0.0215,0.10504,0.03453,0.02824,0.10104,0.111,0.1075,-0.16106,0.10202,-0.03359,-0.03764,-0.02774,0.12963,0.02488,0.14018,0.09533,-0.02434,-0.00927,-0.00762,-0.02473,-0.01928,0.00056,-0.09722,0.01671,0.03346,0.00016,-0.02051,0.00231,-0.00625,0.01335,0.02594,0.05588,-0.02072,0.04425,-0.11712,-0.05482,-0.10295,0.01811,-0.08492,-0.05963,0.01983,-0.02595,0.06559,0.06851,-0.0475,0.06105,0.12069,-0.01354,-0.02396,0.0165,-0.02565,-0.01045,-0.02815,0.02228,-0.00039,-0.03251,0.0576,0.01098,-0.02743,0.02631,-0.02263,-0.07369,0.10095,-0.02747,-0.02963,-0.05043,0.00361,0.1674,0.1093,-0.09738,0.06169,-0.11335,0.03256,-0.10749,-0.03701,-0.06973,0.03208,0.02113,-0.0965,-0.01827,0.02991,-0.03297,-0.09902,0.03771,-0.00549,0.0685,0.12636,0.05278,0.1042,0.00639,0.00161,-0.02061,-0.01875,0.06181,0.03513,-0.04413,0.05258,-0.0259,-0.02504,0.03032,-0.09227,-0.12035,-0.06505,0.09034,0.02308,-0.01894,0.07589,0.01129,0.06335,0.02361,0.06727,0.00916,0.06537,-0.00109,0.03132,0.00751,-0.00332,0.08879,0.06561,0.03649,-0.08154,-0.01001,0.13247,-0.05813,0.02117,-0.09036,-0.02234,-0.07175,-0.00962,0.05708,0.00687,-0.07763,0.00967,0.00024,0.10028,-0.01671,0.02523,0.0114,-0.03646,-0.09179,-0.03398,0.00586,-0.0036,-0.03398,-0.03733,0.06119,-0.04701,-0.0446,-0.15134,0.00045,0.02197,-0.0128,0.016,0.05238,0.09125,0.00272,-0.12372,0.05444,0.02915,0.08702,-0.0007,0.07704,-0.07445,-0.03185,0.06066,-0.07255,-0.0198,-0.04522,-0.03407,-0.01743,0.0383,-0.05883,-0.0154,-0.05197,-0.13314,0.02536,0.02673,0.08042,-0.02153,-0.0167,0.07009,0.09706,0.00399,-0.01876,-0.0379,-0.08947,0.03414,0.03909,0.08839,-0.09128,-0.0574,-0.01953,-0.04771,-0.02417,0.0336,-0.10699,0.10568,-0.08249,0.04609,0.0445,0.03837]},{"domain":"computational_biology","key":"bio_tajima_d","name":"Tajima's 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25","v":[-0.16853,0.04146,0.01033,-0.05312,0.01066,-0.07456,0.06673,0.10576,-0.02223,-0.0583,-0.01792,0.0043,0.03849,-0.04748,0.00554,0.05391,-0.06817,-0.03728,0.01596,0.11366,0.02977,0.04054,-0.07645,-0.02617,0.06147,0.01424,-0.0435,-0.02645,-0.02545,0.09353,-0.01649,0.01673,0.04565,-0.04192,0.05137,0.03336,-0.01099,-0.13909,0.016,-0.00705,-0.02517,-0.00794,-0.05248,-0.04865,0.05859,0.07922,0.10167,0.02336,-0.06146,-0.01499,-0.06884,0.08763,0.07485,-0.01288,0.03478,0.11342,-0.06849,0.1181,0.02039,-0.02452,0.00372,0.01859,0.1057,-0.06411,-0.05128,0.03679,0.00346,0.08526,-0.13729,0.14077,-0.02951,-0.04011,-0.06938,0.08073,0.00173,0.00017,-0.18477,-0.10419,0.0053,-0.06984,-0.04216,0.10033,-0.08657,0.06117,-0.01751,-0.01486,-0.00098,0.00781,0.03503,-0.06838,0.01184,0.01098,0.09323,0.1032,-0.03714,0.01703,-0.06453,0.11294,0.00283,0.09488,0.04134,-0.05642,0.12408,0.07484,-0.02785,-0.05782,-0.06893,0.02391,0.01866,-0.01037,0.01181,-0.06361,-0.00168,-0.03727,0.05065,-0.08948,0.05391,-0.02587,-0.0573,0.07075,0.05375,-0.01292,0.02627,0.03248,-0.01565,0.02357,0.1081,-0.01238,-0.03711,-0.03773,0.01413,-0.0463,-0.09744,-0.03438,-0.00532,0.21565,0.00731,0.05298,-0.0245,-0.01366,-0.00809,-0.01261,-0.01175,-0.0285,0.08973,0.05343,0.00645,0.06628,0.02366,-0.03956,0.0713,0.0238,-0.09818,0.1799,-0.07139,-0.08825,0.011,-0.076,-0.08143,0.02007,-0.0154,-0.06418,-0.06652,-0.04309,0.08822,0.10848,-0.05388,-0.10891,0.03803,0.00173,0.05993,-0.05033,0.04221,-0.09051,-0.01189,0.02254,0.04335,0.00798,0.05389,0.12585,0.07546,0.07143,-0.10863,0.00222,0.02115,0.06658,0.04352,0.10144,-0.09724,-0.00549,0.05395,0.00959,0.00747,0.01581,0.05787,-0.02245,-0.026,-0.00056,0.06037,-0.07019,-0.01349,-0.06759,0.03916,-0.00167,-0.06215,0.05215,0.00576,0.01091,-0.00513,-0.00947,0.04639,-0.17861,-0.07993,0.007,-0.06103,0.0872,0.04526,-0.00571,0.01752,-0.0223,0.05909,-0.01672,0.06366,0.01125,0.069,-0.10046,0.03308,-0.01814,0.02187,0.03987,0.07836,0.0439,0.08858,-0.0576,-0.03638,-0.04714,-0.07267,-0.04389,0.03623,0.03687,0.0413,0.05276,-0.03203,-0.04467,-0.11248,-0.10658,-0.05292,-0.02703,-0.0348,-0.07143,-0.02217,0.02403,-0.04457,-0.06641,-0.01574,-0.09784]},{"domain":"computational_biology","key":"bio_tm_wallace","name":"Melting 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of a bond","package":"economics-finance-ai999x","example":"Find the convexity with face = 1000, coupon rate = 5%, years = 10, ytm = 6%, frequency = 2.","v":[-0.07238,0.05698,0.04473,-0.05013,-0.02447,-0.15227,-0.08921,0.03206,0.0437,-0.00564,-0.03566,-0.03876,-0.01316,-0.01284,-0.10692,0.04177,-0.01919,-0.04432,0.0776,0.11697,-0.04954,0.04269,0.06013,-0.0106,0.06736,-0.0246,0.01926,0.04695,0.02453,0.08612,-0.00525,0.03061,0.05691,-0.01782,0.02158,-0.03851,0.02017,-0.06514,0.05406,-0.05259,0.04438,-0.0335,0.03441,-0.03035,0.01753,-0.06368,0.07074,-0.06133,0.06009,0.0245,-0.08836,-0.03738,-0.02754,-0.03866,0.01447,-0.02523,-0.06602,0.09591,-0.04734,0.03577,0.04722,-0.07159,-0.01956,0.01757,-0.19849,-0.00972,-0.10759,0.06508,-0.03488,0.04357,0.09219,-0.04816,0.01029,-0.06867,0.13306,0.07224,-0.09504,0.01178,0.06827,-0.08416,0.00753,-0.03054,0.08306,0.01349,0.06639,0.01821,0.00468,0.00718,0.08224,0.0015,-0.06888,-0.02634,0.11186,0.05199,0.00478,-0.10447,-0.05904,0.00176,0.07746,0.01929,-0.04163,0.00556,-0.02221,0.13669,0.00956,-0.09009,0.07381,0.01501,-0.00738,0.11654,0.0868,-0.08923,-0.01823,0.10468,-0.00279,0.16436,0.04465,-0.09379,0.01076,-0.00467,-0.12034,-0.03388,-0.03539,-0.06589,0.06697,-0.00466,0.0022,0.03464,0.02678,0.02632,0.08205,-0.01958,-0.07338,-0.05487,-0.04976,-0.01692,-0.05195,0.08285,0.02847,0.08284,0.04018,-0.00657,0.00925,-0.01364,0.10118,0.0472,-0.12135,-0.05806,0.01395,0.0699,0.04451,-0.07085,-0.07414,-0.01401,0.12013,-0.13821,0.13003,-0.05562,0.05004,0.01995,0.16793,-0.0265,-0.03328,-0.0473,0.03346,0.03252,0.01922,0.0266,-0.04269,-0.07149,0.03612,0.05204,0.02218,-0.07522,-0.09755,0.02138,0.06374,0.02242,0.08376,-0.08056,-0.00801,0.06322,-0.06125,-0.0081,0.03682,0.02664,0.04119,-0.13198,-0.00524,0.0524,0.12009,-0.14885,-0.09062,-0.05029,-0.04202,-0.00538,-0.04623,-0.07292,0.04494,-0.02576,-0.10901,0.0022,0.10915,0.07138,-0.01616,-0.04141,0.04695,0.0575,-0.11189,0.06433,0.02017,-0.08139,0.0331,-0.10697,0.06247,0.00101,0.04434,0.00219,0.10037,0.05627,-0.08017,-0.03206,-0.06147,0.00169,0.03419,-0.03492,-0.03863,-0.01486,-0.05838,-0.01527,0.05027,0.02343,0.00263,0.07196,0.01157,-0.01468,0.03052,0.02705,0.03514,-0.0146,0.05899,0.05079,0.0247,0.01195,-0.06557,0.03491,-0.0997,-0.05569,-0.02924,-0.12972,0.01494,0.00353,0.03675,0.07842,-0.0271,0.07081]},{"domain":"economics_finance","key":"bond_duration","name":"Macaulay and modified duration of a bond","package":"economics-finance-ai999x","example":"Find the Macaulay duration with face = 1000, coupon rate = 5%, years = 10, ytm = 6%, frequency = 2.","v":[-0.14374,0.11144,-0.00584,0.04202,0.0293,-0.07826,0.02866,0.07047,0.0797,0.03953,0.08754,0.03746,0.0459,0.04201,-0.13716,0.11125,0.01728,-0.07705,0.08138,0.13441,0.03344,-0.0181,4e-05,0.09903,0.08433,0.03595,-0.01743,0.03782,0.07037,0.03293,0.10291,0.0606,-0.00997,0.02831,-0.04839,-0.02525,0.01838,0.01516,0.1393,-0.02016,-0.01445,0.01186,0.06859,-0.0296,-0.04242,0.02557,0.04126,-0.08961,0.1818,-0.09562,-0.15303,0.02176,-0.06928,-0.03908,0.07248,-0.03954,-0.11111,0.07894,-0.03111,0.00045,0.03169,-0.02032,-0.0218,0.05017,-0.03993,-0.06972,-0.01212,0.08277,0.02501,0.05704,0.02292,-0.02641,0.01091,-0.04594,0.08356,0.00624,-0.06343,0.05071,-0.05495,-0.10917,-0.00875,-0.02956,-0.01773,0.0191,0.13867,0.04765,0.05398,0.02326,0.00056,-0.08566,-0.00864,-0.02046,-0.02059,0.02072,0.02848,-0.00189,-0.01244,0.01472,-0.09506,0.08415,0.06023,-0.08551,-0.00455,0.08647,-0.05598,-0.04682,-0.11008,0.05223,-0.00638,0.13057,0.04766,-0.04309,-0.0254,0.06056,-0.06035,0.07938,0.03735,-0.08853,0.00784,0.04487,-0.03064,-0.02632,-0.02396,-0.00289,-0.03827,-0.03779,-0.00389,-0.01862,-0.04134,0.01386,0.05322,0.05721,-0.06879,-0.03065,-0.018,-0.06453,0.00688,0.09496,-0.01502,0.10611,0.06116,-0.10507,0.01685,0.06078,0.01862,0.10757,-0.0536,0.00589,-0.07623,0.07113,0.02478,-0.13665,-0.03513,-0.08048,0.02722,-0.05534,0.10304,-0.00603,-0.02317,-0.04254,0.01736,-0.05432,-0.01893,-0.0489,0.04436,0.07391,0.04077,0.00811,0.01322,-0.10686,0.06145,-0.06363,0.09908,-0.07663,-0.11068,0.03272,0.02915,-0.03812,0.09179,-0.00601,0.06893,0.06237,-0.0404,-0.09285,-0.00561,0.02846,-0.0667,0.03547,-0.00677,-0.10541,0.07855,-0.11096,-0.03175,0.01754,-0.03012,0.00052,-0.02619,-0.13432,0.02162,-0.02614,-0.05505,-0.05169,0.08442,0.13166,0.06688,-0.03672,0.04247,0.00772,-0.15317,-0.01938,0.03609,0.00657,-0.10486,-0.01148,0.01318,0.0533,0.01892,-0.01059,0.07075,0.04221,0.06349,-0.05232,-0.06469,-0.03297,-0.07533,-0.19174,0.00717,0.01811,-0.045,-0.1095,-0.02172,-0.03071,-0.04264,0.01,0.01839,-0.01646,-0.0258,0.0224,0.05338,0.02815,0.10987,0.00583,-0.00615,0.01469,0.00384,0.03216,-0.0072,0.07948,0.00519,-0.09521,0.00657,-0.03382,0.07217,-0.00141,-0.11633,0.00186]},{"domain":"economics_finance","key":"bond_price","name":"Bond price from its yield","package":"economics-finance-ai999x","example":"Find the bond price with face = 1000, coupon rate = 5%, years = 10, ytm = 6%, frequency = 2.","v":[-0.05248,0.04325,0.04209,-0.06953,0.01505,-0.12925,-0.03068,0.05668,0.04427,0.03516,-0.04815,-0.04606,0.07281,-0.01947,-0.12131,0.06314,-0.03122,-0.12095,0.04384,0.10554,-0.03465,0.0245,0.07552,0.04042,0.05046,-0.02596,0.00066,0.08353,0.07051,0.07316,0.06624,0.02251,0.00022,-0.01598,-0.01647,-0.03185,0.09568,-0.06637,-0.02015,-0.05077,0.04339,-0.01321,0.03864,0.00426,-0.01146,-0.08491,-0.01225,-0.06509,0.03769,0.05154,-0.15486,-0.04782,-0.04843,-0.11116,0.03642,0.00357,-0.05065,0.09028,0.00159,0.06842,0.01561,-0.05074,-0.00265,-0.00905,-0.11517,-0.02873,-0.09228,0.05447,-0.02073,-0.00012,0.11464,-0.04356,0.06433,-0.06601,0.04902,0.03436,-0.0502,0.00624,0.03695,-0.085,0.01877,-0.07697,0.07653,0.03533,0.07748,0.03857,0.07198,0.05775,0.0858,-0.00045,-0.03326,-0.00559,0.06078,0.05537,-0.00624,-0.02984,-0.04809,0.0086,0.03569,0.02141,-0.023,-0.0408,-0.00676,0.16427,-0.0046,-0.0565,0.03868,0.02027,-0.00627,0.12219,0.05643,-0.09054,-0.04178,0.09401,0.03954,0.17351,0.01471,-0.07297,0.01139,-0.0047,-0.07722,-0.0137,-0.0037,-0.0661,0.01824,-0.03658,-0.02194,0.06151,0.03896,-0.02863,0.11724,0.00582,-0.05769,-0.04159,-0.06728,-0.09646,0.01179,0.102,0.02604,0.04516,-0.01127,-0.02022,-0.01751,0.08932,0.0859,0.0985,-0.10506,0.01595,0.03772,0.08979,0.06785,-0.02943,-0.05474,0.0064,0.10691,-0.18179,0.11846,-0.04369,0.0627,-0.01352,0.11035,-0.05568,0.00892,-0.02078,0.02009,0.08295,-0.02145,0.03452,-0.05,-0.10174,0.04248,-0.00162,0.03414,-0.08442,-0.12348,0.06078,0.07623,-0.08059,0.05801,-0.00586,-0.01575,0.08727,-0.03044,-0.01611,-0.04061,0.02368,0.01971,-0.13485,-0.02166,-0.0101,0.07805,-0.09862,-0.08993,-0.00923,-0.05052,-0.0015,-0.07131,-0.04801,0.00404,-0.02851,-0.06142,0.02973,0.08233,0.12467,0.01633,-0.07322,0.00043,0.13427,-0.10941,-0.01017,-0.01386,-0.09236,-0.05179,-0.04402,0.01684,-0.00123,0.063,0.05018,0.12165,0.12457,-0.08432,-0.05678,-0.07775,-0.02041,-0.02005,-0.06478,-0.03505,-0.04166,-0.06615,0.00553,0.02662,-0.05545,-0.02593,0.08275,-0.00429,-0.0372,0.05099,0.01499,0.04654,-0.04772,0.04326,0.05852,0.04744,-0.01131,-0.12194,0.02885,-0.02278,-0.01399,0.01824,-0.08384,0.04957,-0.0349,0.03227,0.08483,-0.11301,0.04255]},{"domain":"economics_finance","key":"bond_price_change","name":"Bond price change from duration and convexity","package":"economics-finance-ai999x","example":"Find the bond price change with face = 1000, coupon rate = 5%, years = 10, ytm = 6%, yield change = 1%, frequency = 2.","v":[-0.10149,0.15721,0.02217,0.02485,-0.00828,-0.10027,-0.03598,0.02408,0.06137,-0.00133,0.03775,0.02177,-0.0627,0.00406,-0.08376,-0.00403,0.08232,-0.04638,0.1181,0.07593,-0.00957,0.02374,0.00776,0.00145,0.09004,0.05362,0.02292,0.0081,0.04129,0.04515,-0.03743,0.07769,-0.07065,-0.06148,0.00856,-0.00501,0.03748,-0.04428,0.0757,-0.06633,0.04001,0.03506,0.09105,-0.01091,0.09703,-0.02163,0.06332,-0.08442,0.12629,-0.03977,-0.11733,0.01371,-0.05702,-0.00989,0.06508,-0.02581,-0.08872,0.07078,-0.0174,-0.06582,-0.02822,0.00471,-0.06366,0.01255,-0.10519,-0.02079,-0.08103,0.16769,0.01969,0.07068,0.03696,-0.00626,-0.00032,-0.05662,0.11058,0.01951,-0.02373,0.05544,-0.03823,-0.04925,-0.03461,-0.06827,-0.02037,0.0485,0.14719,0.05514,-0.00629,-0.0051,0.03709,-0.03332,0.00442,-0.01052,0.04111,0.13661,0.03687,-0.11166,-0.02117,0.02207,0.03045,0.04874,0.014,-0.02799,-0.01925,0.1105,-0.04636,-0.03723,0.02457,0.06572,0.01526,0.1767,0.07053,-0.00732,-0.05564,0.11503,-0.05358,0.15035,0.05984,-0.01928,0.08026,-0.01683,0.03296,0.05045,-0.04191,0.0425,0.02381,-0.02795,0.00552,-0.0125,0.07172,-0.00822,0.01993,-0.08023,-0.07035,-0.04523,-0.02614,-0.08616,0.09138,0.09142,0.04299,-0.00169,0.01923,-0.01864,-0.09383,0.03216,0.02337,0.04335,-0.07811,-0.00015,-0.03748,0.09873,0.09109,-0.20056,0.00182,-0.13532,0.05773,-0.06277,0.14555,-0.03549,0.03357,-0.04338,0.04442,-0.07272,-0.006,0.01244,-0.00093,0.05074,0.02923,-0.04544,-0.06423,-0.02376,0.04929,-0.00919,0.07259,-0.04306,-0.06768,-0.00033,0.02465,-0.04829,0.03644,-0.08179,-0.07304,0.00991,-0.04122,-0.08063,0.07502,-0.00902,0.03286,-0.07852,0.01581,-0.01282,0.03199,-0.06594,-0.01211,-0.00521,-0.01889,0.04186,-0.03185,-0.11386,0.03648,0.00587,-0.1182,0.05764,0.20895,0.0305,0.0172,-0.01307,0.08949,0.01351,-0.18811,0.06428,0.04268,-0.09119,-0.08487,-0.03894,-0.01268,-0.06286,-0.0384,-0.00011,0.10553,-0.0045,-0.03546,0.01771,-0.01432,-0.02724,-0.00279,-0.09882,-0.06135,0.0594,-0.06572,-0.02986,-0.00119,-0.09678,-0.06066,0.01929,0.02696,-0.00947,0.00431,0.01449,0.04105,-0.03395,0.07266,-0.04374,0.01638,-0.00491,-0.06194,0.01411,-0.11572,0.02738,-0.0398,-0.07879,-0.03177,-0.02026,-0.00802,0.0282,-0.02163,0.05901]},{"domain":"economics_finance","key":"bond_ytm","name":"Yield to maturity of a bond","package":"economics-finance-ai999x","example":"Find the yield to maturity with price = 925.61, face = 1000, coupon rate = 5%, years = 10, frequency = 2.","v":[-0.08006,0.03219,0.04587,-0.09941,0.09373,-0.17077,-0.00206,0.12833,0.05805,0.01131,-0.0965,-0.04679,0.0464,0.01119,-0.1462,0.11349,-0.03161,-0.10238,0.03465,0.02256,-0.09182,-0.01849,0.015,0.03272,0.04764,-0.02716,0.02919,0.01634,0.08453,-0.02996,0.08407,0.03575,0.03396,-0.04135,0.02463,-0.09285,0.1382,-0.02718,0.04025,-0.05225,0.03055,-0.0634,0.02663,-0.01094,0.03681,-0.01565,0.00048,-0.06285,-0.00766,0.062,-0.08564,-0.06912,-0.02958,-0.10877,0.02213,-0.04397,-0.04673,0.09369,-0.0057,0.09917,0.03451,-0.08409,0.01784,0.01695,-0.03082,-0.0715,-0.10198,0.06512,0.0137,0.06843,0.07931,-0.02634,0.06329,-0.0309,0.04082,0.06809,-0.03335,-0.01964,0.05752,-0.03251,0.0035,-0.06705,0.02055,0.0381,0.07778,-0.00707,0.09139,0.0177,0.04927,-0.01488,0.06943,-0.00806,-0.01898,0.06745,0.00605,-0.02898,-0.06153,-0.04205,0.0934,0.03149,0.02133,-0.07503,0.1005,0.0087,-0.07035,-0.05858,0.05431,0.05697,-0.05924,0.04908,0.00929,-0.08491,-0.02914,0.10319,0.01189,0.19183,-0.03043,-0.03376,0.02848,-0.02645,-0.06077,-0.03617,0.00869,-0.1334,0.01797,-0.03544,0.02964,0.05291,0.04318,-0.06792,0.10266,0.09568,-0.06593,-0.02874,-0.09818,-0.02195,-0.01651,0.11888,0.00365,0.10858,0.00697,-0.0176,0.0065,0.04226,0.04774,0.03106,-0.09483,0.03273,-0.00116,0.02199,0.09478,-0.02445,-0.01327,-0.00429,0.12116,-0.05991,0.1162,0.04875,0.06282,-0.01101,0.08697,-0.04889,0.00291,0.00025,-0.0255,0.08225,0.02238,0.04658,-0.07309,-0.1072,-0.01362,-0.00955,-0.01722,-0.06134,-0.10281,0.01617,0.0648,-0.08418,0.08997,-0.08285,-0.00899,0.13906,0.00247,-0.00109,-0.03818,-0.03267,-0.01576,-0.07112,-0.04473,0.00289,0.15344,-0.11227,-0.0693,-0.01427,-0.03409,0.04247,-0.04188,-0.00419,0.02598,0.05211,-0.06527,-0.04349,0.07174,0.08134,-0.09953,-0.09533,-0.04904,0.10385,-0.07023,-0.00333,0.03312,-0.12422,-0.09182,-0.04448,0.04697,0.0438,0.07816,0.0315,0.08345,0.04278,-0.13194,0.00616,-0.09359,-0.0037,-0.01269,0.01359,-0.06608,-0.01259,-0.03658,0.05719,0.0515,0.04968,-0.03329,0.04839,-0.0713,-0.06429,-0.00451,0.02983,0.04059,-0.01147,0.02727,-0.00405,0.03935,-0.07048,-0.04106,-0.0107,-0.00121,-0.08668,0.02642,-0.01112,0.05192,-0.02943,0.00547,0.11017,-0.11879,0.06974]},{"domain":"economics_finance","key":"break_even","name":"Break-even and target-profit volume","package":"economics-finance-ai999x","example":"Find the break-even quantity with fixed costs = 10000, price = 50, variable cost = 30.","v":[-0.00444,0.01664,-0.02389,-0.15354,0.07262,-0.01319,0.01656,-0.04939,-0.05659,-0.06534,0.03281,0.09999,0.03847,-0.08229,0.00845,0.02892,0.01234,-0.03811,-0.02553,0.0157,-0.14073,0.00105,0.01752,-0.05847,-0.0643,0.0508,-0.01942,-0.11107,-0.00422,-0.00152,-0.04084,-0.03891,-0.14172,-0.00762,-0.14806,0.03669,0.11688,-0.00117,0.00303,0.0069,0.07369,0.00233,-0.05051,0.04192,0.01626,0.07395,-0.00791,0.07696,0.03932,0.04947,0.02099,-0.08794,-0.0108,0.0203,0.04031,0.05303,-0.08257,-0.00743,0.02566,0.09265,0.00496,0.05357,-0.05932,0.00204,0.00661,0.01558,-0.07935,-0.12234,-0.04134,-0.01845,0.04071,0.06289,-0.00965,0.05143,-0.01625,-0.03438,0.0177,0.00466,0.06609,0.16094,0.11402,0.03995,0.10322,0.04298,0.00822,0.02509,0.0468,-0.0281,-0.04546,0.128,0.06855,0.00555,0.04368,-0.06232,0.07543,-0.07206,-0.04177,-0.01034,-0.05777,-0.10712,-0.01964,-0.00966,-0.00172,-0.07093,-0.10243,-0.00687,-0.00109,-0.05581,0.09614,-0.00843,0.05494,0.01261,-0.0335,0.00624,-0.01085,-0.00628,0.10873,-0.04036,0.00375,0.01846,0.07668,0.04908,-0.07286,-0.07588,0.04235,0.09266,-0.08633,0.04295,0.09096,0.04404,-0.02767,0.00117,-0.01003,-0.00313,0.02154,-0.04567,-0.01973,-0.06172,0.02991,0.00765,-0.10546,0.00647,0.04268,-0.06825,-0.04174,0.00932,-0.03413,-0.10523,0.05569,0.14843,0.08257,0.05927,0.06228,0.06913,-0.01733,0.00714,0.04608,0.10819,0.00235,-0.07109,-0.06601,-0.01245,-0.02256,0.00129,-0.11688,0.04117,0.0736,-0.05401,-0.07141,0.0903,0.07037,0.05684,-0.139,0.04229,-0.00979,0.00787,-0.05944,0.01058,-0.07138,-0.02013,0.07736,0.04534,0.06257,-0.0922,-0.04491,0.02245,0.04119,0.03767,-0.07667,-0.06115,-0.05262,0.07442,-0.08439,0.05352,-0.06959,0.00179,-0.02995,-0.01088,-0.04412,0.00429,0.02851,0.06812,0.04816,0.09483,-0.03843,-0.10519,0.103,0.05722,0.00479,0.07171,-0.12848,-0.02817,-0.083,-0.08404,0.00586,0.09093,-0.02376,0.01319,0.11861,0.03818,0.04006,-0.02169,-0.11615,-0.10804,0.04889,-0.04237,-0.02511,0.13091,-0.06893,-0.00545,0.0696,-0.13773,-0.06275,-0.10006,-0.09016,-0.07489,0.06566,-0.00854,0.0392,0.03415,-0.01021,-0.02442,-0.02069,-0.00325,0.00599,0.05838,0.20855,0.1014,0.02334,0.00137,0.01125,0.01523,0.01131,0.01106,-0.00686,-0.05579]},{"domain":"economics_finance","key":"bs_greeks","name":"Black-Scholes Greeks","package":"economics-finance-ai999x","example":"Find the option greeks with spot = 100, strike = 100, time = 1, rate = 5%, volatility = 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crossover rate of two projects","package":"economics-finance-ai999x","example":"Find the crossover rate with cash flows a = [-1000, 100, 1200], cash flows b = [-1000, 700, 500].","v":[-0.11936,-0.04743,-0.05917,0.15639,-0.01531,-0.02439,-0.07981,-0.03837,0.02751,-0.00208,-0.05959,0.1092,-0.04704,-0.07088,-0.02444,-0.11,-0.0428,-0.00282,0.0008,0.04568,-0.01593,0.01761,0.1221,-0.02036,-0.05275,-0.08183,0.00011,0.10831,-0.03286,0.01272,-0.0559,0.05054,-0.10021,-0.00876,0.03178,0.03666,0.00248,-0.00611,-0.00747,0.01047,0.02648,-0.02364,0.02801,-0.02145,0.02047,-0.07234,-0.00083,-0.0136,-0.00011,0.14257,0.03422,0.00152,0.0128,0.02274,0.04119,0.01174,0.03193,0.00476,0.02703,0.00172,-0.02172,-0.04276,0.00895,-0.06351,-0.08635,0.02816,0.17294,0.05602,-0.08381,-0.1074,0.05013,0.03648,0.03249,-0.11939,-0.15141,0.06929,-0.07553,-0.03219,0.09054,-0.06433,0.00717,-0.06174,0.10222,-0.06753,-0.01379,-0.03973,0.06176,-0.02372,-9e-05,-0.03761,-0.01689,-0.00578,0.05326,-0.05992,0.03263,-0.09882,0.00365,-0.02755,-0.03924,0.04942,0.09908,0.00051,-0.0768,-0.04009,0.00522,-0.034,-0.04524,-0.05788,-0.01366,0.07173,0.07951,-0.08911,0.02275,0.02789,0.00996,-0.06809,0.04598,-0.02688,0.00453,0.09444,0.01364,0.00569,-0.06537,0.05994,0.07495,0.0654,0.00675,0.07783,0.01046,0.07497,-0.00418,0.00308,-0.0519,-0.03674,-0.12909,-0.13187,-0.10105,0.04007,-0.00928,-0.02075,-0.11768,0.02285,-0.02594,-0.0965,0.03696,0.05704,-0.01268,-0.00941,-0.04434,0.03912,0.02207,-0.03163,0.01574,0.09094,0.08533,0.01311,0.09056,0.02937,0.04281,-0.00451,0.10253,-0.09632,0.00427,-0.02125,-0.01722,-0.02564,0.00993,-0.00755,0.01394,-0.05918,-0.01111,0.00891,-0.00682,-0.08069,0.03137,0.09389,-0.04908,-0.04074,0.05499,-0.15404,0.00433,0.06111,-0.08077,-0.0099,0.01676,0.1251,-0.01874,0.091,0.01838,0.06164,0.01968,0.14534,0.04961,0.11182,0.03679,-0.01469,0.01258,-0.11552,0.10002,-0.02187,0.06981,0.1162,0.02145,0.0544,-0.07097,-0.02518,-0.10845,-0.05094,-0.00878,0.01788,-0.01834,-0.01518,-0.22067,0.03584,0.01711,0.04642,0.06439,0.03663,0.09427,-0.00391,0.14235,-0.08626,0.02973,-0.02301,0.02615,-0.05316,-0.12185,0.14018,0.04321,0.05598,-0.08168,0.03894,0.11085,0.12676,0.03325,-0.00713,0.03281,-0.03181,-0.06668,0.01238,-0.03959,0.0189,0.03953,-0.05765,-0.03649,-0.04841,0.03088,-0.02856,0.09191,-0.02234,-0.02365,0.03353,0.05461,0.0434,-0.02802,-0.06383]},{"domain":"economics_finance","key":"discounted_payback","name":"Discounted payback period","package":"economics-finance-ai999x","example":"Find the discounted payback period with rate = 10%, cash flows = [-1000, 300, 400, 500, 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500].","v":[-0.14021,0.01115,-0.06796,0.02534,0.07675,-0.04496,-0.05622,-0.01296,0.00865,-0.02706,0.00544,-0.02994,-0.09916,-0.05823,-0.06975,0.00448,0.05354,-0.02778,-0.07246,-0.03936,-0.08284,-0.07088,-0.0399,-0.02653,-0.08167,-0.05934,0.00879,-0.02331,-0.02004,-0.04224,-0.06712,0.0017,-0.01165,-0.1132,0.06511,-0.02811,0.09539,0.01358,0.03592,0.05115,0.02884,-0.05675,-0.02172,0.02418,0.06136,0.01224,0.08387,-0.04718,-0.01052,0.05716,0.04669,-0.05112,-0.03703,0.06158,0.1007,-0.06875,-0.07153,-0.00671,0.05787,-0.0334,0.03598,-0.01431,0.02919,-0.0378,-0.01017,0.02778,0.04926,-0.01321,-0.11183,0.03128,0.05407,0.06227,0.0457,-0.09395,-0.10737,0.09528,-0.05857,-0.04552,0.05405,-0.09832,-0.04811,0.0304,0.17251,-0.00559,0.0065,-0.05659,0.07395,-0.09415,0.00206,-0.11501,-0.03667,0.01622,-0.03058,-0.0762,-0.03833,0.00352,-0.10838,-0.09375,0.13022,0.04813,0.06153,-0.06025,-0.0589,-0.05244,0.00179,0.01727,0.00876,-0.06122,0.03427,-0.01067,0.09005,-0.13835,-0.00051,0.12133,0.00818,-0.01095,0.0409,-0.04734,0.04378,0.08391,-0.03264,-0.0257,0.00945,-0.06958,0.08123,0.02521,0.04854,0.1041,-0.01868,0.0452,-0.0109,0.09068,-0.04152,-0.00575,-0.14088,-0.04505,-0.08786,0.07132,-0.00013,0.10026,-0.06606,-0.00023,-0.05255,-0.05527,0.0529,0.0429,-0.08772,0.03034,-0.05349,-0.00546,0.05026,0.0153,0.00886,0.06132,0.04906,0.06237,0.03277,0.06878,0.04318,-0.01053,0.01128,0.00412,-0.04751,0.02399,-0.04158,-0.0002,0.01854,0.06885,0.05304,-0.08588,-0.01188,-0.04275,-0.06871,-0.09498,-0.06114,0.16473,-0.06976,0.02794,0.15134,-0.15649,0.05264,0.06307,-0.04298,0.02077,0.10463,0.07778,-0.01728,0.06661,0.05271,0.0545,0.08698,0.01825,0.09063,0.10775,-0.01244,0.04279,0.02488,-0.05943,0.07932,-0.0673,-0.02277,0.02218,0.02222,0.06251,-0.08538,-0.08444,-0.0439,-0.08476,-0.00432,0.02726,0.0253,-0.06038,-0.13007,0.00674,0.04289,-0.02302,0.08403,-0.01876,0.02434,-0.10673,0.12762,-0.0216,0.00187,0.00599,0.05443,-0.00757,-0.03411,0.12503,0.00404,0.08004,0.03841,0.04876,0.1563,0.12404,-0.02237,-0.06081,0.00727,0.00937,-0.0625,-0.01189,-0.02921,0.05269,0.02287,-0.11561,0.00061,-0.05133,0.0351,-0.04262,0.07049,-0.01629,0.08484,0.04557,0.02878,0.0555,-0.09061,-0.00396]},{"domain":"economics_finance","key":"fisher_real_rate","name":"Real interest rate (Fisher equation)","package":"economics-finance-ai999x","example":"Find the real interest rate with nominal rate = 8%, inflation = 3%.","v":[0.06148,-0.02435,-0.02887,0.01403,0.01893,0.02771,-0.00269,0.02,-0.00793,-0.04377,-0.03737,0.11781,0.07573,-0.06954,-0.12664,0.02119,0.0713,-0.00892,0.05462,-0.0383,0.03135,-0.05722,-0.02341,-0.01891,-0.02175,-0.02477,-0.04388,0.00355,0.04984,-0.09375,-0.09082,0.01691,0.01399,-0.05484,-0.03903,-0.06032,-0.0116,0.06111,0.08232,-0.04307,0.04734,-0.16118,-0.07058,-0.0174,0.03542,0.0059,-0.01044,-0.14828,0.07244,-0.03636,0.05554,-0.04342,-0.05216,0.07562,-0.11668,-0.06637,0.01967,0.00248,-0.04517,-0.10229,0.08679,-0.04654,-0.00672,0.09436,-0.03572,0.01785,0.00556,0.02919,0.03259,0.08836,-0.00346,-0.03861,0.022,-0.10664,-0.05078,-0.02367,0.06879,0.05331,-0.04451,0.04096,0.07366,0.07011,0.0365,0.13606,0.02689,-0.01579,0.09474,-0.12111,-0.04,-0.00494,0.08764,-0.0199,-0.09828,0.15816,0.01152,0.04737,-0.17193,-0.0222,0.0428,0.03162,-0.06841,-0.07387,0.01985,-0.08414,-0.029,-0.09579,0.14804,-0.0416,-0.11557,0.06556,0.11402,-0.02999,-0.08645,0.11872,0.0394,-0.10778,-0.02147,0.06635,0.12324,-0.06813,0.06159,-0.01029,0.06702,-0.02318,0.05439,-0.00317,0.05746,0.02202,-0.09762,0.01035,-0.009,-0.01896,-0.09654,0.00276,0.00692,-0.01827,-0.00546,0.05558,-0.08522,-0.01687,0.04434,0.01579,-0.10191,0.00435,0.07785,0.0443,0.02416,0.00677,-0.04885,-0.03287,0.07048,0.04719,0.00537,0.11545,0.10946,0.04887,0.10468,0.0614,0.06511,0.01616,0.01263,-0.19372,0.05549,-0.01502,0.01851,0.09067,0.02272,0.08792,0.00514,-0.05555,0.02464,-0.05712,0.05095,0.05873,-0.02208,-0.03097,0.09658,-0.04123,0.07115,-0.08291,-0.06324,-0.00276,-0.04219,-0.09153,0.09802,-0.00995,-0.07004,0.00617,0.02018,-0.02012,0.0628,-0.01779,0.00266,-0.07572,0.02789,0.06344,-0.05311,0.00544,0.04331,0.00186,-0.0249,0.0493,-0.01051,-0.03024,-0.0955,-0.06098,0.02203,0.06731,-0.02362,0.07229,0.08047,-0.0012,-0.03221,0.0706,-0.08058,-0.00436,-0.04337,-0.04625,0.0941,-0.11575,0.06278,-0.02124,-0.02048,0.00841,-0.01803,-0.05812,-0.03278,-0.02608,0.03496,0.0193,0.05878,-0.03179,0.03994,-0.07749,-0.0433,-0.04991,0.02995,0.11085,-0.04276,0.00283,0.10313,-0.04548,-0.031,0.0341,-0.02918,0.05422,-0.00201,-0.06518,-0.01681,-0.06914,0.06548,0.07202,-0.07753,-0.02853,-0.06844,0.11556]},{"domain":"economics_finance","key":"forward_price","name":"Forward price with cost of carry","package":"economics-finance-ai999x","example":"Find the forward price with spot = 100, rate = 5%, time = 0.5, dividend yield = 2%.","v":[0.13003,-0.01254,-0.03126,-0.07538,-0.01747,0.0662,0.04694,0.05857,-0.02138,0.05108,-0.04109,0.02023,-0.0111,-0.03855,-0.02812,0.09314,0.00432,-0.11717,-0.01324,0.00965,-0.03827,-0.02502,-0.0991,0.10231,0.03464,0.03215,0.07937,-0.02929,0.05566,-0.03404,0.00762,0.03115,0.01631,0.05075,-0.02273,0.04327,-0.02069,0.02352,0.0349,-0.06153,0.0163,-0.00508,-0.03561,0.0358,0.02157,-0.02673,0.00172,-0.16527,0.00838,-0.1176,0.00655,-0.06081,-0.07825,0.01814,-0.03501,-0.0495,-0.01617,0.10083,-0.02856,0.06604,-0.00151,-0.0311,-0.06076,-0.0888,-0.06982,0.04978,-0.05358,-0.03687,0.02172,-0.11665,-0.04465,-0.08956,-0.00876,0.06787,0.05653,-0.05,-0.01413,-0.0501,-0.09992,0.12432,0.15023,0.03018,0.02961,0.07669,0.07236,0.00255,-0.01615,0.0732,0.07927,0.02478,0.01488,0.02147,0.11356,0.12857,-0.0105,0.01244,-0.04298,0.06567,-0.02845,-0.09647,-0.02563,-0.02826,-0.02346,0.08777,-0.09988,-0.03109,0.08202,0.13504,-0.10354,0.01234,0.07368,0.00109,0.00561,0.07095,0.19716,0.03213,-0.01667,-0.02781,0.03908,0.05916,-0.03489,0.00786,0.16995,0.03981,0.03141,-0.04155,-0.01864,0.08138,0.00337,-0.04481,0.01001,0.01249,0.04564,-0.0326,0.06322,-0.06633,0.03144,-0.0856,-0.01296,-0.14347,0.01463,-0.03633,-0.02127,-0.10619,0.02822,0.03124,-0.07774,0.01187,-0.04927,-0.03718,0.03874,-0.06095,0.02151,0.01038,-0.01704,-0.04573,0.09302,0.05742,0.04762,-0.06901,-0.0484,-0.04009,0.16024,0.03336,0.0772,0.12487,-0.03141,0.07833,-0.1281,-0.03906,0.07366,-0.01218,0.00164,-0.04825,-0.0005,-0.02888,0.00853,0.00304,0.09735,-0.0286,-0.03621,0.10267,-0.00545,0.0064,0.09789,-0.02195,0.03866,-0.06688,-0.00421,0.02456,0.06107,-0.18206,0.0169,-0.05407,0.04972,0.04193,-0.09996,0.09514,-0.0173,-0.01979,-0.06714,0.01049,0.00506,-0.05002,0.00658,-0.0454,-0.0414,0.1504,-0.05149,0.00755,0.10334,-0.03711,0.03965,-0.037,0.01459,-0.09484,0.03288,-0.07684,0.07078,0.01141,-0.07734,0.02066,-0.1339,0.04657,-0.01803,0.00956,-0.06238,0.00486,-0.03925,-0.02198,0.04899,-0.07543,-0.00656,-0.05331,-0.02787,-0.08247,0.06341,0.01652,0.05402,0.00058,-0.05104,0.06292,-0.01177,-0.02735,-0.03929,0.06287,0.04734,0.05605,-0.00472,0.08583,0.06201,-0.10835,-0.05826,-0.10852,-0.06997,-0.01233]},{"domain":"economics_finance","key":"forward_price_dividends","name":"Forward price with known dividends","package":"economics-finance-ai999x","example":"Find the forward price with dividends with spot = 50, rate = 5%, time = 1, dividends = [0.75, 0.75], dividend times = [0.25, 0.75].","v":[0.07206,0.01717,0.04562,-0.0877,0.00773,0.02571,-0.0205,0.0952,-0.02943,-0.07249,-0.07754,0.03464,-0.10815,0.01229,-0.00411,0.02652,-0.07189,-0.04951,-0.03323,0.03371,-0.09176,-0.02728,-0.05348,0.0549,0.04445,0.00277,0.01501,-0.09179,0.09385,-0.00177,-0.03458,0.00523,-0.01023,0.01951,0.07784,0.04035,-0.01833,0.03658,-0.0099,-0.03516,-0.01616,-0.04501,0.02038,-0.02574,0.02781,0.01869,0.04675,-0.14884,-0.07622,-0.08997,-0.03878,0.00785,-0.11459,-0.03198,-0.03805,0.03973,0.07691,0.06317,0.03376,0.00661,-0.01783,0.00412,-0.00676,0.01142,0.00764,-0.01639,0.09565,-0.00584,-0.00598,-0.0593,-0.07922,-0.08818,-0.04414,0.03959,-0.0262,-0.00908,-0.1143,0.00231,-0.07736,0.0775,0.10699,0.04175,0.04984,0.01243,0.06511,-0.00477,-0.05577,0.0149,0.07709,-0.07016,-0.01339,-0.02882,0.12284,0.00538,-0.03059,0.0209,-0.06929,-0.03189,0.02849,-0.10529,0.0477,0.02639,-0.03511,0.0224,-0.02728,0.04502,0.04748,0.04095,0.01334,0.05001,0.1041,-0.03118,-0.03915,0.0765,0.11509,0.11733,-0.05217,0.03539,-0.0044,0.00881,-0.12015,0.0618,0.01931,-0.00223,0.10474,-0.0136,0.04276,0.112,0.02309,-0.01824,-0.04431,0.00321,0.05586,-0.11141,0.00926,-0.00277,0.03633,-0.0211,0.06705,-0.12016,0.03748,0.07605,0.01574,-0.1451,0.0829,-0.0166,-0.10143,0.01115,-0.04411,0.06539,0.01619,-0.08597,-0.01921,0.06453,-0.00063,-0.05523,0.10698,0.06921,0.10715,-0.11971,-0.00133,-0.01006,0.10503,-0.00983,0.01464,0.09402,0.0135,0.0861,-0.10979,-0.10705,0.03752,0.03005,-0.0439,0.09398,-0.00011,0.0625,-0.09204,0.03324,0.04849,-0.03308,0.04213,0.08087,-0.02866,-0.0105,0.14395,-0.00197,0.10962,-0.04535,0.09157,0.01738,0.15432,-0.11003,-0.08818,-0.08325,0.04818,0.08304,0.00236,0.09332,-0.03112,0.01139,-0.11398,-0.08534,0.04994,-0.0164,0.02902,0.07398,-0.06974,0.06931,-0.08573,-0.00422,0.0541,-0.05849,-0.0379,-0.02124,0.08746,-0.09579,0.121,0.00071,0.14605,0.02512,-0.02547,0.05461,-0.09621,-0.00559,-0.00591,-0.03342,-0.0024,0.03327,0.01492,0.07583,0.0313,-0.04953,-0.02995,0.03738,0.02953,-0.13875,0.05132,-0.05279,0.10741,0.00754,-0.0435,0.09698,-0.04043,-0.06069,-0.01527,0.022,-0.07954,-0.01451,0.01595,0.05153,-0.00599,-0.16416,-0.02257,-0.06558,-0.02995,0.01685]},{"domain":"economics_finance","key":"forward_rate","name":"Implied forward rate from spot rates","package":"economics-finance-ai999x","example":"Find the forward rate with s1 = 4%, t1 = 1, s2 = 5%, t2 = 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4%.","v":[-0.06534,-0.05332,0.05581,-0.12932,0.05987,-0.03957,0.08944,0.02473,-0.04278,-0.06363,-0.06636,0.00451,-0.03914,0.06596,-0.17835,0.02596,-0.02438,-0.16595,-0.01268,-0.00962,-0.06765,-0.05424,-0.07062,-0.00248,0.03168,-0.05271,-0.06677,-0.04089,0.09356,-0.07727,-0.00934,-0.0416,0.06842,-0.06416,-0.03875,-0.01302,-0.02813,0.07091,0.0611,-0.01224,-0.02283,-0.03048,-0.01735,0.02744,0.01987,0.09765,0.04387,-0.02802,0.01495,0.05784,-0.00724,0.05475,0.01975,0.0092,-0.01087,0.09516,0.04712,0.07823,-0.02598,-0.00016,-0.05711,-0.07819,0.04918,-0.00525,0.0033,-0.03046,0.05635,-0.04594,-0.01619,-0.02489,0.06505,-0.00837,-0.05222,-0.00328,-0.06114,0.00418,-0.06073,-0.01973,-0.12755,0.09044,0.04415,0.15744,0.04987,0.09285,0.00057,-0.05803,0.09094,-0.02296,-0.03804,-0.04362,0.04354,0.04588,0.01448,-0.00508,0.03594,0.09469,-0.15992,0.01753,0.0473,-0.14162,-0.01221,-0.07056,0.00796,-0.02642,-0.03013,0.05831,0.12837,-0.00538,0.14721,0.01772,0.06227,-0.05653,-0.13335,0.08024,0.07262,-0.0063,0.06385,0.02387,-0.00075,-0.11664,0.04209,-0.0261,-0.01287,-0.07624,0.10515,-0.07804,0.0197,0.0681,-0.01751,-0.01321,-0.05554,0.03888,0.03194,0.01315,0.05014,0.0799,0.05129,0.05293,-0.07134,0.06948,0.02658,0.02146,0.06269,-0.09457,0.09325,0.0049,-0.05115,-0.11628,0.01334,0.06845,0.00158,-0.07557,0.03382,0.06991,0.05211,-0.09678,0.111,0.00463,0.03809,-0.17183,0.01323,-0.0541,0.00321,-0.04647,-0.08688,-0.00342,0.07311,0.02735,0.00224,-0.08135,-0.02565,-0.0476,-0.06716,0.02742,-0.04293,0.0865,-0.08702,-0.05434,0.09116,-0.02124,0.11836,-0.01102,-0.02636,-0.03665,0.0895,-0.10069,0.08333,0.07674,0.04045,-0.1192,0.10719,0.05622,9e-05,0.03282,-0.05654,0.00709,0.07661,0.09468,0.04765,-0.08683,-0.04832,-0.04568,0.03691,0.05375,0.04818,-0.03276,-0.00953,-0.05043,0.05561,-0.02847,-0.02353,0.01588,-0.0101,0.02886,0.11476,0.0611,0.0067,0.02556,0.02649,-0.00836,0.04449,0.0771,-0.03919,0.05553,-0.05589,0.0045,0.04637,0.02333,0.00963,0.10175,0.07079,-0.01417,0.07977,-0.07103,-0.05482,-0.10526,0.00802,0.06531,-0.02256,-0.00741,0.01585,-0.01124,-0.02176,-0.02181,0.09718,0.01462,-0.03818,0.03295,-0.07462,-0.05347,0.02182,-0.10027,-0.1341,-0.08332,-0.05317,-0.02184]},{"domain":"economics_finance","key":"gordon_implied_return","name":"Required 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10.","v":[-0.08106,-0.00348,0.01112,0.02133,-0.02322,-0.08603,0.083,0.09088,0.01871,0.05776,-0.03203,0.04561,-0.03712,0.02689,0.0173,-0.01947,-0.02222,-0.08263,-0.00077,0.01511,0.02654,0.03539,-0.02747,0.03069,0.02488,-0.09213,0.00106,-0.00167,-0.04146,0.02579,0.01,-0.04819,-0.05633,-0.06835,0.08705,-0.10274,-0.02177,0.05636,0.03757,0.04116,0.00737,0.09556,-0.00645,0.01455,-0.00969,0.09288,-0.01662,0.02152,0.01355,-0.02443,-0.05677,0.15873,-0.00063,0.06874,0.09028,0.15709,0.04055,0.01963,0.04481,0.00839,-0.11677,-0.0667,0.01394,-0.08156,0.08774,-0.03185,0.0481,-0.0174,-0.02166,-0.03522,0.044,0.02722,-0.05483,-0.09866,-0.10486,-0.01967,-0.02952,0.03027,0.08912,-0.10304,0.02588,0.04901,0.03146,-0.03755,0.0097,0.02132,-0.06317,-0.06626,0.00957,-0.02295,0.02105,-0.05982,-0.00071,-0.0701,0.01503,0.02715,-0.07979,0.0338,0.08839,-0.01443,0.06971,-0.00401,-0.07246,-0.07737,0.02245,-0.01444,0.09589,-0.03362,0.12384,-0.03995,0.02908,-0.13019,-0.1529,0.09744,0.05841,0.04514,-0.04763,-0.12514,-0.02393,-0.01692,0.00029,-0.06589,0.03804,0.01441,0.03843,-0.00276,-0.01657,0.0396,0.00878,0.09937,-0.01163,0.04127,0.0353,-0.10391,0.01194,0.08818,0.09248,0.00435,0.09638,-0.00631,0.03379,-0.0015,0.02931,-0.08074,0.04992,-0.04514,-0.10854,-0.01393,-0.01205,0.08934,0.01895,-0.1846,0.0628,-0.08508,0.07925,-0.00069,0.06721,0.033,0.16187,-0.10195,0.00411,-0.00706,0.09202,-0.00723,-0.10967,0.05982,-0.01055,0.14442,0.00511,-0.09902,-0.09324,0.02153,-0.06288,0.05224,-0.10707,0.13982,-0.13782,-0.06562,-0.03451,-0.02184,0.02462,-0.01231,-0.02767,-0.05067,0.04497,-0.03832,0.06691,-0.00536,0.05441,-0.03767,0.07544,0.07578,-0.02852,-0.00406,0.02363,0.11276,0.05415,0.00558,0.04453,-0.08339,-0.04016,-0.03546,0.03649,0.02907,0.11081,0.03514,-0.10607,-0.09851,-0.05465,-0.02848,0.01263,0.01131,-0.08148,0.03167,-0.00869,-0.03191,0.13771,0.02426,0.01992,-0.0311,0.03681,-0.01045,0.0395,0.00118,-0.10402,0.07351,-0.08267,0.1412,0.00111,0.09085,-0.0247,-0.03815,0.08015,0.01505,0.06164,-0.02497,0.13934,0.00739,0.0379,0.04729,-0.0294,0.09488,-0.03407,-0.04323,0.00974,-0.01811,-0.05784,-0.01527,-0.02075,-0.07652,0.05173,-0.07546,-0.05634,-0.03388,-0.00462,-0.03685]},{"domain":"economics_finance","key":"growing_perpetuity","name":"Present 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10].","v":[-0.04237,0.02163,0.01147,-0.02835,0.02899,-0.01265,-0.0097,0.14188,0.05431,-0.23957,0.08513,0.08816,-0.00798,-0.03244,-0.09915,-0.04233,-0.11689,-0.02868,0.00677,-0.00357,-0.02405,-0.00813,0.09467,-0.03212,0.04609,-0.03243,-0.04465,-0.0466,-0.03482,-0.06585,-0.1189,0.02959,0.09178,-0.03642,0.02498,-0.03881,-0.01251,0.03777,0.13083,-0.00085,-0.01373,0.08251,-0.07276,0.05099,0.11684,-0.02783,-0.07016,0.00624,-0.03225,-0.00992,-0.01108,0.05026,0.00221,-0.06863,-0.00276,0.03592,0.09815,0.07156,-0.01595,0.04329,0.01325,-0.05951,0.00065,0.03533,-0.04533,-0.04838,0.02285,-0.01497,-0.01147,-0.00245,-0.01541,-0.07333,-0.04551,-0.01958,-0.0938,0.0654,-0.15358,0.03898,-0.04938,-0.02155,-0.06079,-0.02053,0.04445,-0.02973,0.04946,-0.08083,-0.01202,0.01087,0.03769,-0.01547,0.02538,0.0288,0.02415,-0.01138,0.03784,0.00873,-0.063,0.05211,0.05853,-0.03245,0.02163,0.06758,0.06975,-0.00041,-0.03935,-0.03692,0.10094,-0.02687,0.10252,0.04518,0.01063,-0.05531,0.02912,0.03588,-0.06757,0.0622,0.08836,0.04546,0.05135,0.06766,-0.08425,0.06124,0.12455,-0.04956,0.04226,0.06888,0.00824,-0.04439,-0.03269,-0.0157,-0.0139,0.10939,-0.13496,-0.01053,-0.10099,0.02178,-0.10021,0.04066,-0.08869,0.04076,0.11902,-0.07194,0.06729,-0.02293,0.11284,-0.0292,-0.02362,0.04971,-0.00885,0.03487,-0.04582,-0.01872,-0.03079,0.07264,0.02316,-0.08339,0.00989,0.03194,-0.00302,-0.02931,0.11087,-0.0345,-0.00691,-0.06413,0.06464,-0.02517,-0.03661,-0.05082,0.17537,-0.0486,0.01637,-0.07296,-0.03551,0.03442,-0.0114,-0.01511,0.05069,0.09004,0.08513,-0.05221,-0.01514,0.06744,-0.04573,0.01254,-0.01094,-0.06934,0.01123,0.10466,-0.12615,-0.01917,0.05843,-0.03327,0.02351,-0.05308,-0.1193,-0.01205,-0.03478,-0.06401,-0.02153,-0.07565,0.0659,-0.07879,0.06295,0.14016,-0.07437,0.02732,-0.02898,-0.06311,-0.01569,0.04444,-0.13238,0.02626,-0.14396,-0.00996,-0.02859,0.07219,-0.04478,0.06301,0.06884,-0.11008,-0.07658,-0.05383,0.05377,0.07482,0.13562,-0.10475,-0.06789,-0.0462,0.02881,-0.02462,-0.00636,0.02882,0.04359,-0.01958,0.04893,0.01299,0.12569,-0.07859,0.07117,0.05496,0.0177,0.03025,-0.05431,0.0308,0.04825,0.01342,0.10248,0.01186,0.05827,-0.02609,0.04671,-0.01963,-0.11519,-0.00396,-0.05206,0.1166]},{"domain":"economics_finance","key":"historical_var","name":"Historical 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90%.","v":[-0.00518,0.02833,0.01915,0.01117,0.05075,0.05987,0.02553,0.04834,0.02231,-0.10388,-0.01465,-0.05631,0.05041,0.03733,-0.05689,-0.07806,0.05823,0.03364,-0.10545,-0.04415,0.04728,-0.02808,-0.05547,-0.0682,0.0704,0.04348,-0.04549,-0.04565,0.01303,0.00685,-0.0659,0.07937,0.05243,-0.03884,0.08546,-0.08722,0.00358,0.04062,-0.00504,0.01348,-0.0028,-0.04491,0.00316,0.05454,0.10066,0.00039,-0.01525,-0.05304,0.02567,-0.05035,-0.07751,-0.00117,-0.02385,-0.08555,0.00947,-0.06185,0.08993,-0.05644,0.03515,-0.03672,-0.04407,-0.01016,-0.05738,0.1176,-0.07407,-0.03168,0.05089,-0.01863,-0.06288,-0.02029,-0.07653,0.06111,-0.0475,-0.05849,0.00816,0.10539,-0.03334,0.07256,-0.02628,0.04886,-0.01774,0.04501,-0.07118,0.00809,0.00544,-0.02093,-0.00313,0.14535,0.08345,0.05938,-0.0339,-0.00377,0.03274,-0.07048,0.02343,-0.00173,-0.05795,-0.07252,-0.12092,0.03077,0.0159,0.04226,-0.03791,0.1009,0.02871,-0.015,-0.0492,-0.01909,0.11668,0.06562,0.15847,-0.00678,-0.00841,0.10553,0.00353,0.04219,0.0555,-0.163,0.0882,-0.02273,0.05107,0.0332,0.03669,-0.04927,0.005,0.02635,0.01185,0.05811,0.03804,0.01249,-0.04066,-0.04083,-0.02342,-0.07122,-0.01253,-0.11362,-0.14722,-0.05489,0.08887,0.01117,0.07116,-0.03966,0.04846,0.0469,-0.01795,-0.04771,-0.05592,0.11065,-0.06923,0.01683,0.00972,-0.04558,-0.03154,-0.0222,0.00046,0.02928,0.16247,0.00395,-0.04258,0.01829,0.01848,0.068,-0.02524,0.0061,0.01162,0.01927,-0.11307,0.114,0.00158,-0.12951,-0.13268,0.0285,0.07845,0.02341,0.01546,-0.05014,-0.01089,-0.04576,0.1201,-0.00103,-0.00546,-0.04399,0.08086,0.00884,0.18741,0.03608,-0.01842,0.07037,0.12645,0.04553,-0.00757,-0.20145,-0.03651,-0.00493,0.14817,0.00651,0.03403,0.00159,0.07096,-0.062,0.05948,-0.03103,0.09219,0.09382,-0.06882,-0.07638,0.04402,-0.0378,-0.06383,0.00933,0.06585,0.04154,-0.00053,-0.04526,0.05552,-0.01915,-0.01397,0.03656,0.03776,-0.03927,-0.1983,0.09678,-0.00771,0.04294,0.01756,0.00552,-0.01079,0.05907,0.0251,-0.00121,-0.01299,-0.06549,0.02693,0.06142,-0.12374,-0.07742,-0.01633,0.06159,-0.04108,0.02078,0.04771,0.04909,-0.05763,0.06236,0.01566,-0.09153,0.02658,-0.00758,-0.00851,-0.06485,0.00236,0.06616,0.01034,-0.13936,-0.12923,-0.02727]},{"domain":"economics_finance","key":"implied_volatility","name":"Implied volatility","package":"economics-finance-ai999x","example":"Find the implied volatility with option price = 10.45, spot = 100, strike = 100, time = 1, rate = 5%.","v":[0.04095,-0.01246,-0.0182,-0.0363,-0.07803,-0.0003,0.04343,-0.03436,-0.02705,-0.08818,-0.05193,0.02468,-0.07778,0.06264,-0.03967,-0.04008,-0.05502,0.07397,0.01192,0.03042,0.03393,-0.03793,-0.06442,0.04426,0.09784,0.06466,0.11425,-0.09149,0.07742,0.02993,-0.03207,0.11349,-0.0188,-0.03892,0.09053,-0.06176,0.01036,-0.02228,0.06461,-0.08508,0.00358,-0.08866,0.01059,0.03644,0.07525,-0.03503,-6e-05,-0.20258,0.03526,0.02973,-0.02006,-0.08561,-0.09201,0.01736,-0.08972,0.05364,0.05586,0.06987,0.03329,0.07055,0.01351,0.06711,0.01526,0.02589,-0.09114,-0.04259,-0.00561,-0.04288,-0.01099,-0.01987,-0.08445,-0.00303,-0.00074,-0.01477,0.15921,0.01983,-0.05414,-0.01483,-0.14348,0.01369,0.05833,0.07673,0.02184,0.04328,0.00582,0.02362,-0.00999,-0.00767,0.01498,0.0416,0.02789,0.02993,0.04645,0.0435,-0.01154,0.02178,-0.1556,-0.06475,0.05852,-0.08407,0.02739,0.06518,-0.00558,-0.05071,-0.02949,-0.03432,0.08097,0.06406,-0.07602,-0.00999,0.05379,0.00511,-0.04408,0.09262,0.05714,0.06433,-0.07638,-0.01852,0.04627,0.0143,0.01657,0.02319,-0.02851,0.06029,-0.00371,-0.00839,0.01076,0.05202,0.01597,-0.05448,-0.03,0.03852,0.02964,0.00676,0.01361,-0.00786,0.10983,0.00128,-0.00229,0.07194,0.05193,0.07017,-0.0383,-0.07624,0.00613,-0.08101,-0.13375,-0.04245,0.04954,0.03852,0.02329,-0.0556,0.01555,0.06115,-0.02944,0.03957,0.10619,0.07992,0.09893,-0.01193,0.00726,-0.14708,0.03374,0.01621,-0.06077,0.12807,-0.05465,0.07764,-0.05582,-0.05945,0.01255,0.03327,-0.06733,0.0891,0.04608,-0.1233,0.00618,0.08271,0.09822,-0.14213,-0.07392,0.00441,0.04778,-0.01677,0.09865,-0.02802,0.04888,-0.07634,0.05292,0.02721,0.01304,-0.09574,-0.02352,-0.11732,-0.01121,0.02742,-0.1281,0.02452,0.0059,0.14052,-0.13517,-0.04546,0.04596,0.01452,-0.06678,0.05562,-0.05368,0.09061,-0.14617,0.04832,-0.04174,0.02447,-0.10656,-0.05332,0.05162,-0.06591,0.02169,-0.07983,0.12517,0.06726,-0.11939,0.067,-0.05925,0.04669,-0.02139,-0.06777,-0.07251,-0.04062,0.03798,0.07367,0.08791,-0.02002,-0.08432,-0.05332,0.06397,-0.11092,0.01771,0.06776,0.03983,0.00192,0.02627,-0.00885,-0.00087,-0.04173,0.04914,0.01152,-0.02323,0.00326,0.1208,-0.04015,0.05736,-0.10486,-0.02867,0.01063,-0.01625,0.02778]},{"domain":"economics_finance","key":"income_elasticity","name":"Income elasticity of demand (midpoint)","package":"economics-finance-ai999x","example":"Find the income elasticity with income 1 = 40000, q1 = 10, income 2 = 50000, q2 = 13.","v":[0.10087,0.11614,0.05155,-0.01819,0.02661,-0.01277,-0.07345,-0.04167,0.00155,0.03773,0.05011,0.02508,-0.00789,0.0272,0.01446,-0.0011,-0.1085,0.01255,0.02822,-0.01845,0.07577,0.06088,0.01811,0.10624,-0.04584,0.06909,0.06329,-0.08163,-0.01405,0.05312,-0.0563,0.03955,-0.15318,-0.06542,-0.09974,0.03697,-0.01715,-0.00862,0.07408,-0.05856,0.00598,0.04736,-0.09893,0.06553,-0.03303,0.09612,0.04315,-0.03747,0.06212,-0.09653,-0.01039,-0.02841,-0.0796,0.09505,-0.0371,0.09218,-0.018,-0.006,-0.09545,0.01097,-0.03849,-0.04791,-0.0903,-0.053,0.02755,-0.06103,0.08357,-0.00133,0.19758,-0.01568,0.0285,-0.0019,0.01216,-0.05656,0.10243,0.01098,0.05345,0.01799,0.03558,-0.1,-0.04045,0.02515,0.03543,0.15074,-0.05413,-0.0191,-0.04413,-0.0298,-0.12173,0.08009,0.13613,0.01979,0.09088,0.028,0.05692,0.05152,-0.04701,-0.0223,-0.03095,0.01721,0.07717,0.02751,0.04877,-0.11142,-0.06305,-0.0433,0.09633,-0.01598,0.06737,-0.04011,0.09483,0.00834,-0.1214,-0.04144,0.01932,-0.15295,0.05695,0.01908,0.01093,-0.05272,0.08532,0.05208,0.01423,0.06309,0.04025,-0.04963,0.00508,-0.06601,-0.09336,0.12632,0.00541,-0.05613,0.10056,-0.05646,-0.06447,-0.05681,0.13296,0.05217,-0.17968,-0.00953,-0.02316,-0.02801,0.02361,-0.01408,0.07343,0.11763,0.00948,-0.03754,0.06485,-0.03476,0.04877,0.05618,-0.02679,-0.04811,0.14232,-0.00148,0.08196,-0.03242,0.13468,-0.00136,-0.08441,-0.15466,-0.05239,-0.00702,-0.01398,0.0548,0.00355,0.00507,0.01949,0.08868,-0.04214,-0.04442,0.01161,-0.04301,0.00794,-0.07407,0.05798,0.00077,-0.01804,-0.06599,0.06659,-0.08036,-0.02298,0.0159,-0.02846,0.05246,-0.01466,0.01925,0.038,-0.04768,-0.01332,0.07438,0.02065,-0.01916,-0.04244,-0.07618,-0.00455,0.02784,0.04919,-0.01154,-0.05026,-0.00336,0.10324,-0.05198,0.00982,-0.05344,0.1234,0.02485,-0.08606,0.05362,-0.01636,0.04688,0.02018,0.06187,-0.06423,-0.0174,-0.11779,0.11234,0.02704,-0.06726,-0.00438,-0.03116,-0.05143,-0.05712,0.05516,-0.11017,-0.0643,-0.03265,-0.0399,0.0171,-0.11537,-0.05763,0.04729,-0.10782,0.04449,-0.01695,-0.00352,0.00594,0.08343,-0.00614,0.02444,-0.01781,0.02191,-0.03976,0.07507,-0.00805,0.00552,0.01825,0.01452,-0.0667,0.03995,-0.02551,-0.01238,-0.04262,-0.01897,0.06701]},{"domain":"economics_finance","key":"inflation_adjustment","name":"Inflation 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ratio and tracking error","package":"economics-finance-ai999x","example":"Find the information ratio with portfolio returns = [0.03, 0.01, 0.04, 0.02], benchmark returns = [0.02, 0.015, 0.03, 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500].","v":[-0.08577,-0.02292,-0.06825,0.05915,0.05518,0.03141,-0.00217,-0.00153,0.02845,-0.03977,0.01697,-0.00905,-0.09192,-0.06829,-0.00484,0.0466,-0.03703,-0.03864,-0.06595,0.03196,-0.07838,-0.12569,-0.06574,-0.02572,-0.02077,0.022,-0.02066,0.05138,0.03475,-0.05828,0.00515,-0.02296,-0.06195,-0.13576,-0.02853,-0.00647,-0.02325,-0.01364,0.03867,-0.0429,0.05033,-0.08881,-0.04229,0.01681,0.05009,0.02989,0.02554,-0.07649,0.01709,-0.00126,-0.03092,0.00859,-0.01376,0.0074,-0.0361,-0.01761,-0.10548,0.04108,0.00353,-0.0245,-0.03322,-0.00784,0.05988,-0.01515,0.05562,0.06276,0.11857,0.04679,-0.15573,-0.07776,0.02864,0.00433,0.02711,-0.00138,-0.08359,0.04442,-0.01038,0.02233,-0.08761,-0.0979,-0.00059,0.07652,0.14599,-0.00481,0.0002,0.00789,0.03575,-0.03249,-0.0693,-0.08554,0.05217,0.06094,-0.04933,-0.06813,0.08665,0.10647,0.01203,-0.04599,0.04926,0.08536,0.09373,-0.04525,-0.0208,-0.02973,-0.02714,0.02627,0.06711,0.01372,-0.00607,0.05708,-0.08459,-0.06383,-0.01824,0.10979,0.06277,0.07163,0.03612,-0.06116,0.03214,0.04238,0.05971,0.01057,-0.00128,-0.0095,0.00555,0.03458,0.00842,0.05024,-0.10107,0.05568,-0.02167,0.04879,-0.02055,-0.03028,0.05474,-0.04404,-0.08575,0.06434,0.04927,0.02917,-0.08136,0.04508,-0.10126,-0.0983,-0.03833,-0.00483,-0.07383,-0.01026,-0.0152,0.02234,0.02661,-0.09715,0.0941,0.01304,0.03142,0.04859,0.0728,0.05335,0.06953,0.00407,0.04277,-0.02004,-0.00034,0.00704,0.01722,0.03418,0.09077,0.02638,0.02057,-0.07058,-0.00366,-0.02747,-0.0278,0.00174,-0.10293,0.10139,-0.00934,-0.0366,-0.0047,-0.12265,0.0294,0.13644,-0.08345,-0.02727,0.11186,0.10518,-0.03816,0.11919,0.01947,-0.0162,0.02879,0.04337,0.07688,0.06209,0.04269,0.04164,-0.02172,-0.08754,0.04492,-0.04239,-0.09383,0.11334,0.03508,0.00747,-0.00705,-0.04526,-0.18118,-0.0141,-0.04894,0.05031,0.08556,0.06198,-0.06504,0.05159,-0.01063,0.08126,0.10002,-0.03461,0.09186,-0.04674,0.14722,-0.07285,-0.06079,0.06223,0.06144,-0.15514,0.01075,0.11122,-0.06398,-0.02952,-0.05023,-0.13917,-0.02727,0.08539,0.01983,-0.05652,0.04861,0.06956,0.0041,0.14634,-0.06618,-0.01724,0.06396,-0.12263,0.06635,-0.06033,0.06237,-0.04867,0.10328,-0.05517,0.10743,-0.05537,0.03213,0.09341,-0.10142,-0.09747]},{"domain":"economics_finance","key":"life_annuity_due","name":"Whole life annuity-due","package":"economics-finance-ai999x","example":"Find the life annuity-due value with mortality rates = [0.1, 0.3, 0.6, 1], interest rate = 5%, payment = 1000.","v":[-0.10917,-0.03384,-0.05258,0.01985,0.10252,-0.16983,-0.07267,0.03392,0.0223,-0.07054,0.02251,0.04503,-0.02934,-0.07351,-0.01457,-0.07887,0.09953,-0.02948,-0.04401,0.0118,-0.0053,-0.01457,-0.05491,0.01057,0.01451,0.01172,0.04687,0.0803,0.03682,-0.02432,-0.07252,0.05831,-0.00272,0.01551,0.0412,-0.07532,0.05805,-0.05396,0.03266,0.08691,-0.01317,-0.12116,0.04196,0.06927,0.02875,-0.06628,0.00019,-0.0004,0.08493,-0.00425,-0.02567,-0.0195,-0.03913,-0.06902,0.0651,0.00312,-0.02802,-0.02788,0.05023,0.03239,0.04337,-0.07283,0.02506,0.02375,-0.06402,-0.08118,-0.00435,0.04459,-0.06635,0.06884,0.0066,0.0559,0.02795,-0.15011,-0.1042,0.06452,0.08424,-0.00628,0.12221,-0.02553,-0.04647,-0.0422,0.08083,-0.05178,-0.05111,-0.07044,0.02283,-0.04674,0.07155,-0.00044,0.01987,-0.06272,-0.02691,-0.06079,-0.08697,-0.04333,-0.07082,-0.06514,0.19529,0.01285,0.02542,-0.04618,0.03286,-0.07131,0.00998,-0.01407,-0.05294,-0.07667,0.10118,-0.03409,0.13636,-0.08575,0.06976,0.08685,0.01891,-0.08994,-0.02292,-0.09747,-0.00835,0.00961,-0.09155,0.00792,-0.03158,0.02398,0.10783,-0.01738,0.00409,-0.05888,0.04261,0.08338,0.05596,0.09591,0.03183,-0.08224,-0.10144,0.06287,-0.03001,-0.04703,0.08039,0.03291,0.04526,-0.00754,0.02747,0.00641,0.07037,0.08751,-0.06791,0.05439,-0.01432,0.0427,0.00935,-0.00401,-0.10472,0.00687,0.09536,0.06004,-0.04573,0.062,0.00737,-0.03741,-0.00768,-0.08422,0.08151,-0.03903,0.03207,-0.07138,-0.01606,-0.00625,-0.01034,-0.08627,-0.02332,0.02147,-0.01069,-0.05792,-0.13365,0.16308,-0.05999,-0.1395,0.11284,0.04212,0.03429,0.09439,-0.01002,0.05312,0.09587,-0.0025,-0.04551,-0.10709,0.01655,0.02155,0.15006,-0.00834,-0.03315,0.00225,0.00738,0.05591,0.06902,0.00013,0.07514,0.0138,-0.11695,-0.10165,0.01491,0.10457,-0.02469,-0.03502,-0.05012,0.04012,0.0065,0.06174,0.01052,0.00723,-0.02681,-0.03177,-0.01685,-0.00399,0.10911,0.02398,-0.02838,-0.02271,0.1135,0.06065,-0.0076,-0.04182,0.05104,0.0136,-0.08979,0.09132,0.01855,0.04436,0.03946,0.06066,0.12035,0.03636,0.04533,-0.05712,0.09048,-0.02302,-0.07966,0.03762,-0.03477,0.09989,0.07349,-0.03643,-0.06512,0.00799,-0.01077,-0.11819,0.08573,-0.05417,0.00177,-0.02005,0.11415,0.00338,-0.06324,-0.01841]},{"domain":"economics_finance","key":"life_expectancy","name":"Life expectancy from a life table","package":"economics-finance-ai999x","example":"Find the life expectancy with mortality rates = [0.1, 0.3, 0.6, 1].","v":[-0.07041,-0.1216,0.02682,-0.00392,0.16273,-0.08113,0.00631,0.0118,0.00439,-0.02608,0.07481,0.14766,-0.01677,-0.03849,0.02468,-0.081,0.01101,-0.01003,0.00922,-0.06516,-0.05224,0.01354,-0.05033,-0.03429,0.00986,0.01799,-0.01608,0.01005,0.03149,-0.03772,-0.1082,0.1032,0.0042,-0.0072,0.00121,-0.10372,0.06874,-0.00514,0.05446,0.12825,-0.02338,-0.11056,0.07269,0.1146,-0.00154,-0.05869,-0.06209,0.04687,0.0052,-0.01772,-0.09716,-0.00035,-0.02271,-0.13615,0.01501,-0.01074,0.07198,-0.08009,-0.02426,-0.00769,0.08115,0.0153,0.00144,-0.02314,-0.12227,-0.1084,-0.03267,0.08813,0.04368,0.11832,0.04638,0.0339,-0.08608,-0.03555,-0.00775,0.02308,0.08053,-0.03705,0.0141,0.04741,-0.06415,-0.02228,0.00137,-0.00232,-0.044,-0.06301,0.00509,0.06774,0.08205,0.00111,0.02166,-0.01952,0.00395,-0.0197,-0.01424,0.02442,-0.07288,-0.09386,0.04784,0.0074,0.02362,-0.04595,0.09267,0.01382,-0.03514,0.02162,-0.02859,-0.07263,0.11687,-0.03432,0.08142,-0.04934,0.09814,0.01493,0.03388,-0.07209,0.01481,-0.03261,0.02875,-0.01769,-0.09154,0.01986,0.00342,0.07133,0.09705,-0.09159,0.0542,-0.12787,0.00206,0.02278,0.13365,0.03461,0.05052,-0.0717,-0.05323,0.00986,-0.02513,0.03615,0.02737,0.05974,0.0878,-0.02708,-0.03283,0.01671,-0.03421,0.14923,0.01692,0.01873,0.03682,0.04395,0.02503,-0.12093,-0.15623,-0.03206,0.08298,-0.02549,-0.06706,-0.04666,-0.01341,0.01776,-0.08329,-0.04749,0.1092,-0.04965,0.13283,-0.04881,-0.08609,-0.02237,0.02615,0.03793,0.02383,0.00947,-0.0241,-0.02518,-0.1031,0.15199,-0.00888,-0.05367,0.04871,0.09768,-0.02032,-0.04115,0.05284,0.01684,0.07297,0.04322,0.02664,-0.06268,-0.04142,0.03386,0.13262,0.02532,-0.01135,-0.06466,-0.00851,-0.00038,0.05487,0.01384,0.07883,-0.01376,-0.03791,-0.07989,0.02411,0.07331,-0.1005,-0.06726,0.04721,0.01076,0.0101,0.07624,0.01161,0.0633,0.02082,-0.11311,0.04735,-0.01478,0.03705,0.0773,-0.08261,0.04196,-0.05056,0.11367,-0.00608,-0.02668,0.0583,-0.03802,-0.0783,0.00515,-0.01742,-0.00056,-0.0008,-0.00621,0.12289,0.02234,0.13544,-0.08991,0.13399,-0.05559,-0.12491,-0.02015,-0.01451,0.07144,0.04015,0.01384,-0.02972,-0.02517,0.03344,-0.09423,0.07591,-0.06284,0.01291,0.0354,0.06281,0.03165,-0.11061,-0.09686]},{"domain":"economics_finance","key":"loan_balance","name":"Remaining balance of a loan","package":"economics-finance-ai999x","example":"Find the remaining balance with principal = 200000, annual rate = 6%, years = 30, payments made = 60.","v":[-0.03524,0.1225,-0.01706,0.02827,0.03954,-0.11357,-0.02434,0.02264,0.11202,0.12906,-0.02191,0.02692,-0.05627,-0.016,-0.0227,-0.06285,0.06543,-0.00312,0.02284,0.03591,-0.09937,-0.01432,-0.05184,0.12085,-0.06522,0.01413,0.00281,0.05915,0.04934,-0.09282,0.04268,-0.03044,0.07678,0.04102,-0.06803,0.08086,0.02589,-0.02829,-0.01949,-0.01918,0.12186,-0.02136,0.00223,-0.0519,0.00377,-0.03169,-0.04769,-0.05983,0.02674,-0.05357,-0.13395,0.00768,-0.04318,-0.14589,0.01494,0.01286,-0.10804,-0.0944,0.07192,-0.05509,0.00972,-0.09656,0.08048,0.02598,0.06349,-0.05839,-0.02506,0.02681,0.01512,-0.00581,-0.02598,-0.00571,0.0249,-0.05918,-0.0763,-0.02378,0.00821,0.09939,0.01563,-0.08709,0.02649,-0.0254,0.00977,0.04467,0.00098,0.07544,0.11004,-0.02552,-0.01633,0.05282,0.05255,-0.07093,-0.06715,0.04486,-0.06417,-0.00896,-0.05217,-0.0488,0.01345,-0.05803,0.04722,-0.03599,0.12779,-0.04211,-0.02154,-0.05365,-0.05813,0.04223,-0.02303,-0.05134,0.12998,-0.1302,-0.00567,-0.05503,0.02794,0.06368,0.0776,-0.05316,-0.02318,0.02233,-0.06562,0.04066,-0.00059,0.03347,0.08302,0.01912,0.09204,-0.03207,-0.05502,-0.03313,0.08217,0.04733,-0.0119,-0.05021,-0.04826,0.01621,0.04149,0.053,0.02312,0.13017,-0.028,-0.05101,-0.04852,0.02324,0.02121,0.10738,0.00559,0.19827,-0.05895,0.02845,0.15714,0.10111,-0.00684,-0.00073,0.00686,0.00793,0.0532,0.03338,0.05884,-0.01002,-0.05311,0.05087,0.08136,0.08355,-0.06325,-0.03583,0.03325,-0.01728,-0.0388,-0.05477,0.09504,-0.03542,-0.02129,-0.10629,-0.12001,0.02598,-0.12782,-0.16888,-0.0385,-0.06772,0.04489,0.05892,0.06765,-0.02362,0.02004,-0.01503,-0.0503,-0.03152,-0.00559,-0.06077,0.08226,0.00778,0.00529,-0.01859,-0.05688,0.01222,-0.07364,0.02168,-0.00583,-0.02347,-0.06487,0.0035,-0.0834,-0.11728,0.05668,0.06691,-0.03484,0.14278,0.01691,0.00133,0.02831,-0.01411,0.01009,0.06821,-0.00477,-0.07507,0.08017,0.06152,-0.02416,-0.01413,0.20867,-0.10002,-0.03584,0.03428,-0.02811,0.05624,-0.04615,-0.07552,-0.01387,0.17376,-0.01107,-0.01893,0.05749,-0.02863,0.03639,-0.04038,-0.06015,-0.00733,-0.05343,-0.05574,-0.00513,-0.09785,-0.01632,0.01556,-0.01926,0.02658,0.09717,0.05238,0.10191,0.0413,0.04743,-0.06496,0.01343,0.04981,0.01483,0.05065]},{"domain":"economics_finance","key":"loan_cumulative_interest","name":"Cumulative interest of a loan","package":"economics-finance-ai999x","example":"Find the cumulative interest with principal = 200000, annual rate = 6%, years = 30, payments made = 12.","v":[-0.05472,0.09879,-0.04463,0.07899,-0.03688,-0.09463,-0.03865,0.06075,0.11866,-0.00821,-0.04463,0.03151,0.05491,0.03055,-1e-05,-0.06671,0.05656,-0.01323,0.08744,0.04835,0.0047,0.00096,-0.02622,0.08627,-0.0536,0.05675,-0.00672,0.09848,-0.02907,-0.05793,-0.04013,-0.00956,0.04374,0.063,0.04642,-0.03233,0.05275,-0.0053,0.04755,0.02779,0.02933,-0.0043,-0.09602,-0.01626,-0.06273,-0.0276,-0.11258,0.04199,0.04554,-0.056,-0.20118,-0.00986,-0.06618,-0.0608,0.01231,0.07539,-0.06173,-0.05997,0.10092,-0.09612,-0.02387,0.00192,0.01838,0.04309,0.01426,-0.14099,0.06907,0.06211,0.02287,0.08261,-0.10763,0.05523,-0.01789,-0.16456,-0.13476,0.0512,0.03234,0.07089,0.03828,-0.0877,0.07283,-0.05076,0.05411,-0.00537,0.04945,0.05718,0.00218,0.0332,-0.07334,0.0739,0.02319,-0.09817,-0.08588,0.0093,-0.03027,-0.13217,-0.03885,-0.04338,0.07073,0.01272,0.04979,-0.01347,0.07605,-0.00794,0.04066,-0.03717,-0.06046,0.03232,-0.019,0.00607,0.08076,-0.13461,-0.0231,0.05358,0.01342,0.0056,0.03371,-0.09434,-0.00977,0.09098,-0.11426,0.01926,0.00323,0.05878,0.09679,0.00039,0.08771,-0.02346,0.00023,0.0108,0.12177,0.01506,-0.13178,-0.05666,0.05152,0.05342,0.01283,0.02295,0.0993,0.08839,0.00255,-0.02841,-0.08915,0.05337,0.0334,0.03467,-0.00391,0.14984,0.01801,0.02733,0.04774,0.0825,-0.03487,-0.02631,0.0088,0.06742,0.00773,0.07546,0.03983,-0.01644,-0.06948,-0.02875,0.02255,0.07913,0.04012,0.04544,-0.06168,-0.02259,-0.04035,-0.04329,0.06992,-0.00012,0.00404,-0.06057,-0.13836,0.04415,-0.0603,-0.20368,-0.0469,0.0317,-0.01923,0.04446,0.00978,-0.07492,-0.02282,0.05945,-0.02549,-0.07774,-0.01955,-0.06547,0.03843,0.04998,-0.06824,0.09987,-0.05399,0.03201,-0.05953,-0.01816,0.07191,-0.08026,-0.06145,0.0147,0.00668,0.01331,0.06211,0.05108,-0.02127,0.11767,-0.06504,-0.02082,0.0666,-0.00059,-0.03184,0.06681,-0.11625,-0.02157,0.07256,0.02177,0.03725,0.0054,0.11824,-0.04874,0.00907,-0.02215,-0.08595,0.00326,-0.06358,-0.01525,-0.03624,0.05538,-0.00857,0.00628,-0.01283,-0.01446,0.11337,-0.00383,0.10191,-0.02153,0.01663,-0.01518,-0.00742,-0.10861,-0.00756,0.00191,-0.12716,0.05522,0.02923,0.01156,0.15642,0.0159,-0.05771,-0.0124,0.06978,0.02256,-0.08799,0.02194]},{"domain":"economics_finance","key":"loan_payment","name":"Loan payment (amortizing loan)","package":"economics-finance-ai999x","example":"Find the monthly payment on a loan with principal = 200000, annual rate = 6%, years = 30.","v":[-0.11509,0.12933,-0.05185,0.01076,0.03709,-0.09271,-0.03845,0.0282,0.076,0.04899,-0.04027,-0.03582,0.14337,-0.00354,-0.03273,0.00385,0.07098,0.02233,-0.02469,0.02956,-0.06748,-0.06741,-0.05484,0.02156,-0.01197,-0.0135,-0.00168,0.0762,0.04355,-0.01983,0.04938,0.00447,0.0638,0.05208,0.02062,-0.00985,0.0848,-0.02955,-0.00106,0.09019,0.03482,-0.07342,-0.03681,0.00735,0.0146,-0.05046,-0.06436,0.03694,0.0035,-0.06748,-0.09643,-0.07062,-0.13159,-0.07334,0.04687,0.03468,-0.05814,-0.0815,0.06419,-0.05349,0.00647,0.00052,0.08067,0.03572,0.06075,-0.11565,-0.03993,0.0414,-0.02521,0.07336,-0.06288,0.02925,0.01166,-0.15901,-0.07943,0.03751,-0.05568,0.04963,0.05596,-0.121,0.08821,-0.01353,0.08846,0.00122,0.0265,-0.00155,0.00884,-0.09185,-0.05182,0.03466,0.04652,-0.03008,-0.13476,-0.00837,0.02104,-0.06599,-0.10015,-0.03502,0.0588,-0.09862,0.00413,-0.01105,0.0887,-0.05509,0.01716,-0.00825,0.03154,0.04029,0.02133,-0.0375,0.14361,-0.12328,-0.02964,0.0538,0.07399,-0.05372,0.02531,-0.05865,-0.06621,-0.00298,-0.06101,0.03931,-0.04984,-0.02916,0.123,0.01516,0.08724,0.0126,-0.00882,-0.01881,0.03939,0.08856,-0.03338,-0.04655,0.03479,0.07562,0.00919,-0.00117,0.10675,0.1033,-0.03708,-0.0054,-0.06909,0.00467,0.07294,0.06908,-0.07963,0.09668,-0.02933,0.03331,0.06494,0.16283,0.00084,-0.01353,-0.00807,0.08,0.0563,0.12287,0.08734,0.0195,-0.0372,-0.00075,0.07367,0.06808,-0.03252,-0.02804,0.02092,0.00404,-0.04046,-0.10565,0.0438,-0.01628,-0.05181,-0.00497,-0.15484,0.04743,-0.06409,-0.14933,0.02264,0.00026,0.03358,0.07524,-0.01696,-0.07595,0.02528,-0.0051,0.0067,-0.08034,-0.05253,-0.0895,0.01711,0.02779,-0.09827,0.05081,-0.06301,0.01142,-0.10788,0.03179,0.08156,0.0654,-0.06279,0.02887,-0.05528,-0.02851,0.02625,-0.01631,0.06622,0.1785,-0.04987,-0.04809,0.03985,0.03103,-0.05809,0.00832,-0.06882,-0.04313,0.08148,0.03865,0.07425,-0.05761,0.10202,-0.02904,-0.06124,-0.00296,-0.05763,0.02213,-0.03229,-0.03982,-0.05268,0.10528,-0.01383,-0.01134,0.03278,0.02214,0.0702,0.01229,0.11481,0.01797,-0.05208,-0.02132,-0.05764,-0.00694,0.03682,-0.05266,-0.1084,0.04853,0.12887,-0.02383,0.0926,-0.05815,0.0367,-0.07856,0.03114,0.10525,-0.06512,0.03515]},{"domain":"economics_finance","key":"loan_payment_split","name":"Interest 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12.","v":[-0.00437,0.02341,0.0051,0.02504,0.09502,-0.01258,-0.04855,-0.02171,0.0834,-0.00659,-0.01226,0.01175,0.12259,-0.00339,-0.08066,0.07577,0.18241,0.0199,0.0269,0.05129,-0.039,-0.1024,-0.10417,0.02711,0.03248,-0.00881,0.01123,-0.00096,0.00134,-0.01578,-0.07494,-0.02439,0.0563,0.00668,-0.0315,0.00951,-0.00546,0.01925,0.03884,-0.0349,0.06049,-0.08961,-0.01982,-0.00218,0.03457,0.03754,-0.0186,-0.11868,0.07664,0.00572,0.05469,-0.03549,-0.05244,0.09239,0.03547,0.00473,-0.06538,0.02852,-0.06988,-0.05935,0.02163,-0.11338,-0.01008,0.07599,-0.0327,0.02037,0.04067,0.03158,-0.00146,0.09723,-0.00458,0.0059,0.0799,-0.15666,-0.09953,0.08118,-0.057,-0.0052,0.00898,0.04842,-0.05584,0.04859,0.01157,-0.02917,-0.05235,-0.06746,0.03342,-0.09558,-0.03705,-0.12729,0.05833,-0.02732,-0.09935,0.05581,-0.08156,-0.00273,-0.15387,-0.06346,0.13034,0.07272,0.03747,-0.05248,0.1019,-0.03916,0.03808,-0.05838,0.11006,-0.00869,-0.0821,-0.02732,0.07154,-0.0434,0.04955,0.11855,-0.06336,0.00034,-0.07859,0.01331,0.01094,0.01465,-0.02664,0.05886,0.0256,-0.05373,-0.01097,-0.02486,0.03485,-0.00665,-0.09994,-0.03845,0.02838,0.0688,-0.13978,0.04022,0.02061,-0.0093,0.01934,0.03399,0.03542,0.05364,-0.01736,0.00668,-0.05603,0.06003,0.05825,-0.00188,-0.04764,-0.04573,-0.05273,0.01002,0.02958,0.09432,-0.02405,0.03415,0.04703,0.06145,0.02786,0.16325,0.03804,-0.02595,0.0624,-0.11181,-0.04073,0.02967,-0.00673,0.0497,0.03805,0.12359,0.06858,-0.13155,0.03758,-0.13309,0.02038,-0.03555,-0.06716,0.05573,0.00748,0.00129,0.09288,-0.02979,-0.14587,0.02945,-0.02885,-0.08292,0.07064,0.08221,-0.04863,0.01892,-0.06765,-0.03431,0.06492,-0.04046,-0.03382,-0.08962,-0.06739,0.03518,-0.05367,-0.0357,0.06641,0.03427,-0.05612,-0.00868,-0.01731,0.07868,-0.02895,0.02447,-0.02467,0.1156,-0.1506,0.05746,-0.03737,-0.05156,-0.13859,0.07775,-0.08063,-0.05017,-0.01622,-0.12705,0.06544,-0.09696,-0.00044,-0.03536,0.00765,0.01078,0.08182,0.01299,-0.0314,0.02024,-0.01133,0.06469,0.07733,0.00156,0.03528,0.06794,-0.05876,0.00014,0.03187,0.05527,-0.04351,0.09003,-0.00028,0.04908,0.02808,-0.06522,0.08764,0.07791,0.01721,-0.14895,0.07541,-0.02644,0.04587,0.0659,0.01385,-0.07955,-0.1067,-0.00307]},{"domain":"economics_finance","key":"npv","name":"Net 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linear regression (OLS)","package":"economics-finance-ai999x","example":"Fit a linear regression with x = [1, 2, 3, 4, 5], y = [2.1, 3.9, 6.2, 7.8, 10.1].","v":[0.00585,-0.00336,-0.00561,0.04473,-0.01974,-0.00215,-0.06258,-0.06388,0.09725,-0.13194,0.05764,-0.08412,0.04077,-0.00019,-0.07334,0.06584,0.06269,-0.05564,0.00391,-0.06667,-0.03867,-0.05063,-0.00013,0.03058,-0.06421,0.04763,0.03462,-0.17955,-0.06765,0.00485,0.00209,-0.129,0.11648,-0.00529,0.06019,-0.01038,0.0231,0.06058,-0.0881,0.08793,-0.03787,0.06127,-0.05798,0.06616,-0.09092,0.0397,0.04285,0.07057,0.02537,0.03358,-0.02732,0.08458,0.00369,0.03679,0.1489,-0.03137,0.09961,-0.01016,-0.00378,0.09245,-0.0003,0.04739,0.01288,-0.02176,0.07142,-0.03264,0.02195,0.01698,0.02529,0.0193,0.08669,0.02202,-0.054,-0.11824,0.04295,0.09755,0.08504,-0.03231,0.03092,-0.04328,-0.04844,-0.0067,-0.0704,-0.02014,0.07535,-0.01801,-0.11083,0.06519,-0.02331,0.00263,0.01375,-0.04615,0.11233,-0.02878,-0.0345,-0.10706,-0.03683,-0.03414,-0.11022,0.07576,-0.00253,-0.01909,-0.01417,-0.0101,-0.09138,0.02547,0.09333,0.02399,0.18839,0.07146,-0.10099,0.02594,-0.05716,-0.0318,-0.0329,0.08478,-0.01621,0.03447,0.04699,-0.06229,0.05571,0.06565,-0.10078,0.01258,-0.03196,-0.00258,0.02441,0.03146,0.02389,0.015,-0.03391,0.01489,-0.01055,-0.04087,0.04548,0.0303,-0.0213,-0.07903,0.00754,0.02177,-0.12707,-0.00424,0.03953,0.10865,0.01712,0.00043,-0.09694,0.03359,0.11905,-0.04909,-0.07306,0.00934,-0.04107,-0.04754,-0.01798,0.01371,0.04648,0.06653,0.03813,0.1268,0.06706,0.10124,-0.06174,-0.00371,-0.03658,0.03801,-0.07776,-0.05224,-0.05568,0.08113,0.00103,0.02095,0.01372,0.02985,0.02292,-0.0804,-0.00979,-0.09784,-0.06157,-0.0457,-0.07573,0.0542,-0.05317,-0.0837,0.09089,0.04038,-0.07835,0.0728,3e-05,-0.02903,0.01454,0.03888,0.02803,0.01415,0.08323,0.00314,0.04442,0.09977,0.03897,0.01676,0.1089,0.06497,-0.0205,-0.06734,0.00224,0.02783,-0.02885,0.08877,-0.02184,0.12896,-0.07478,-0.03417,0.05264,-0.04346,-0.10923,0.0168,0.08541,-0.03832,-0.03981,0.11711,0.01856,0.0618,0.0453,0.10134,0.00376,0.02418,0.10608,0.03862,-0.08153,-0.02847,-0.0542,-0.10574,-0.11356,-0.07374,-0.01162,-0.07499,0.03123,0.08111,-0.06146,-0.0118,-0.01672,-0.02466,0.05091,-0.03532,-0.06688,-0.11576,0.14306,0.02449,-0.09323,-0.05921,-0.03694,-0.08407,-0.08543,-0.06439,-0.05743,-0.02954]},{"domain":"economics_finance","key":"parametric_var","name":"Parametric 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tax incidence (linear curves)","package":"economics-finance-ai999x","example":"Find the tax incidence with demand intercept = 100, demand slope = 2, supply intercept = -20, supply slope = 4, tax = 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20.","v":[-0.03127,0.05796,-0.0079,-0.17284,-0.10834,-0.00778,-0.06876,-0.03174,-0.0475,0.01255,-0.08432,0.02141,-0.05388,0.06337,0.04058,-0.01497,-0.01573,-0.00266,0.17249,-0.04035,0.05915,-0.06226,0.04386,0.00289,-0.09534,0.06377,0.08462,-0.0215,0.08933,0.04716,-0.04116,0.14035,0.03265,0.00963,-0.04691,-0.02862,0.04978,-0.01319,-0.01616,-0.0503,-0.03839,-0.01828,0.02182,-0.00757,-0.01807,0.02132,0.08399,-0.05773,0.00179,-0.05196,0.07285,-0.03119,-0.08465,-0.01376,-0.08103,0.11661,-0.04909,-0.02881,0.01147,0.01826,-0.01789,-0.05086,0.00241,0.04532,-0.13395,-0.12041,-0.01943,-0.01285,0.05858,-0.0566,-0.03714,0.03719,0.09655,-0.10457,0.13834,-0.06552,0.17485,-0.09052,0.05145,-0.05492,-0.04421,-0.0177,-0.06342,-0.03136,-0.033,-0.06789,-0.0061,-0.06179,-0.07868,-0.01776,0.11238,0.04682,0.14041,0.01126,-0.01475,-0.08748,0.12935,-0.09674,0.07641,0.02212,-0.00084,-0.05106,0.02771,-0.0741,-0.04596,0.08842,0.01276,-0.04911,-0.05459,0.0003,-0.01944,0.06605,0.00481,0.0237,0.06173,-0.00034,-0.03023,0.00129,0.00292,0.03151,0.09648,0.07246,0.04261,-0.00621,-0.0568,-0.05365,0.01134,0.03466,0.04106,0.02778,-0.0752,0.08381,0.07658,-0.01896,-0.05665,-0.02114,0.13031,-0.00883,-0.21999,0.03446,-0.04714,0.04162,0.05972,-0.01934,0.0427,0.09369,0.07386,-0.03954,-0.06247,0.0577,-0.04028,0.02508,0.02365,-0.03377,0.08295,0.03573,0.02998,0.05689,0.08075,-0.05891,-0.05464,-0.03387,-0.01216,-0.00454,0.01381,0.01913,-0.02525,-0.04139,-0.10189,0.02621,-0.07015,-0.04258,0.01428,-0.06876,0.0543,-0.05121,-0.03982,-0.07798,-0.00597,0.06916,-0.06058,-0.04068,-0.01208,0.08686,0.07269,0.00323,-0.04971,-0.04878,-0.00183,-0.00818,-0.00866,0.14793,0.00961,-0.01475,-0.0298,-0.01365,0.00677,0.01085,0.15036,0.0225,0.0369,0.00778,0.14913,0.02101,0.05553,0.04375,0.0936,0.02707,0.06156,0.02401,-0.0069,0.02022,-0.01338,-0.00775,-0.04696,0.03886,-0.12551,0.12344,0.03656,0.04167,-0.01899,-0.09319,0.048,0.01351,0.15485,-0.08573,-0.12165,0.02919,-0.05275,0.03367,-0.0038,-0.0737,0.03355,-0.08968,-0.01967,0.04747,0.0142,-0.02337,0.01924,-0.03592,-0.08893,0.05281,0.02684,-0.01949,-0.0249,-0.03611,0.03008,0.07431,-0.04947,-0.09575,-0.01089,-0.08025,0.08443,0.00851,0.02192,0.04185]},{"domain":"economics_finance","key":"portfolio_return_risk","name":"Portfolio expected return and risk","package":"economics-finance-ai999x","example":"Find the portfolio variance with weights = [0.6, 0.4], expected returns = [0.1, 0.15], covariance = [[0.04, 0.006], [0.006, 0.09]].","v":[0.00088,-0.00089,-0.0354,0.03615,0.03432,0.15159,0.04691,-0.02933,0.03201,-0.12501,0.06348,0.09944,0.08671,0.04801,-0.06637,-0.13541,-0.0751,-0.03022,0.01359,0.01504,0.00111,0.01544,-0.03638,0.0424,0.01923,-0.01672,-0.0341,-0.09001,0.04895,0.11476,0.03634,0.11469,0.04468,-0.01344,0.04539,-0.06281,0.00574,-0.00191,-0.00385,0.09151,-0.01244,-0.01471,0.04287,0.06094,0.05516,-0.05684,-0.04897,-0.06517,-0.08225,0.03312,-0.05458,-0.00815,0.04214,0.03562,0.06053,0.05192,-0.06214,-0.05097,-0.02516,0.00836,0.01237,-0.00121,-0.03054,-0.04774,-0.14785,-0.04113,-0.01005,-0.02311,0.04206,-0.05995,-0.08992,-0.02105,-0.04438,0.00175,0.01778,0.03984,-0.12471,0.00601,-0.05688,-0.01757,-0.00512,-0.01026,-0.03884,0.03303,0.0236,-0.04878,0.01492,0.106,0.02169,0.0565,-0.07583,-0.01829,-0.06281,-0.01344,0.02099,-0.01924,-0.01378,-0.05962,-0.15478,0.02458,0.00146,0.02082,-0.06402,0.09352,0.09502,-0.0158,0.03496,0.01848,0.00357,0.08353,0.13417,0.01801,-0.05556,0.02416,0.0099,0.04799,0.00521,-0.17931,0.13165,-0.05978,0.02261,0.03969,-0.03084,-0.0522,0.01504,-0.04946,0.00769,0.03943,-0.04499,0.09197,-0.04276,0.00279,-0.02325,-0.06837,0.02769,-0.12034,-0.07277,-0.0517,0.02137,-0.05348,0.03276,-0.04238,-0.04964,0.06254,-0.01797,0.05841,-0.08184,0.10474,-0.05053,0.03378,0.03468,-0.00921,0.00124,0.0112,-0.03692,-0.05214,0.14288,-0.04605,-0.01583,0.07414,0.02844,-0.01008,-0.02035,0.04928,0.09211,0.04726,-0.10988,0.09322,-0.06354,-0.06658,0.05657,0.02381,-0.01887,0.04378,-0.04806,-0.00785,0.09021,-0.09425,0.04667,0.00881,0.00976,-0.04829,0.01212,0.01863,0.09347,0.12547,0.05289,0.11214,0.09614,0.02645,0.01928,0.03461,6e-05,-0.08105,0.07505,-0.01021,0.00976,-0.04241,0.07411,-0.10141,-0.0351,0.03668,0.11018,0.10191,-0.02217,-0.06039,-0.03844,0.07695,-0.12605,0.01503,0.0622,0.07377,-0.0466,-0.05826,0.10022,-0.04901,-0.04659,-0.07835,0.07481,-0.01234,-0.16782,0.10732,-0.07308,0.10491,0.07356,0.00575,-0.06376,0.0137,0.07396,-0.03464,-0.05059,-0.025,0.03695,0.09202,-0.07586,-0.02512,0.10641,0.03063,-0.05208,-0.00749,0.07444,0.04096,-0.01904,0.04073,-0.06133,-0.09579,0.03555,0.05806,0.0636,-0.06136,0.05008,0.02148,-0.11533,-0.11458,-0.13078,0.0272]},{"domain":"economics_finance","key":"portfolio_var","name":"Portfolio value at risk (variance-covariance)","package":"economics-finance-ai999x","example":"Find the portfolio VaR with weights = [0.6, 0.4], covariance = [[0.0004, 0.00006], [0.00006, 0.0009]], confidence = 99%, portfolio value = 1000000.","v":[-0.06115,0.01285,-0.05866,0.04246,0.02519,0.06439,-0.03056,0.09046,0.0596,-0.09073,0.01127,-0.03611,0.09828,-0.08216,-0.05667,-0.04757,-0.05633,-0.00805,-0.11148,0.02895,-0.03679,-0.09693,-0.08702,0.06032,0.0047,-0.01849,0.02647,0.00536,0.00911,-0.03709,0.03089,0.01157,0.04456,0.00516,0.04783,-0.09926,0.03899,0.00598,0.03047,0.07004,0.0724,-0.04931,-0.02523,0.01852,0.10155,-0.03888,-0.06544,0.00881,-0.0654,-0.01477,-0.06668,-0.04295,0.0128,-0.09098,0.01382,-0.03441,0.06142,-0.03515,-0.01691,0.0431,-0.00675,6e-05,-0.04037,0.02902,-0.08426,-0.02868,0.01694,-0.06258,0.00494,-0.03238,-0.00423,0.0017,0.11527,-0.07289,-0.03678,0.07602,-0.11155,0.03259,0.12609,0.01031,-0.01591,0.00511,-0.05343,-0.06101,0.07513,-0.06153,-0.00197,0.06966,0.07861,0.08824,-0.00469,-0.02505,-0.05195,-0.04037,0.05702,-0.01563,0.05364,-0.02807,-0.07755,-0.00896,0.0109,0.00496,-0.10885,0.03891,0.00327,-0.07038,-0.05596,-0.0157,0.07909,0.06276,0.08897,-0.04469,-0.03966,0.08731,-0.03251,0.01528,0.02782,-0.21582,0.08833,0.02424,-0.05646,0.02362,-0.06727,-0.09472,0.06033,0.03321,-0.02823,0.04052,0.046,0.12336,-0.01031,0.08543,-0.03549,-0.05564,-0.02378,-0.11973,-0.15856,-0.07205,0.08161,0.05539,0.07536,-0.01953,0.00433,0.04381,-0.00687,-0.07189,-0.06925,-0.0037,-0.0597,0.05508,0.00124,0.03738,0.0338,0.00878,0.03872,-0.01802,0.20106,0.01039,0.01675,0.05625,0.06139,-0.02449,0.0049,-0.01359,0.11189,0.00293,-0.02217,0.09252,-0.03781,-0.22814,-0.05603,-0.00434,-0.07217,-0.03612,-0.07209,0.00264,0.02953,-0.10378,0.15859,-0.07159,0.08374,-0.00311,0.00482,0.04091,0.12065,-0.00683,-0.06347,0.0753,0.04551,0.01698,0.03963,-0.06004,-0.06693,0.01292,0.07605,0.04603,-0.01024,0.00677,0.11458,0.01079,-0.00928,-0.09133,0.04712,0.0643,-0.06187,-0.01113,-0.01809,-0.01429,-0.05304,-0.02779,0.11611,-0.00367,-0.06903,-0.05003,0.0914,0.03972,0.02025,-0.06514,0.01458,-0.0519,-0.12078,0.06142,-0.05809,0.08599,-0.00547,0.12439,-0.04572,0.04504,0.02019,0.09977,-0.01777,0.12439,0.03679,0.03824,-0.07891,-0.00502,-0.00555,0.06036,-0.07613,0.03158,0.03261,0.0952,0.05177,0.03019,0.0335,-0.07837,0.05434,0.08218,0.05841,-0.07027,0.07169,-0.02324,-0.04625,-0.03514,-0.06312,0.03252]},{"domain":"economics_finance","key":"present_value","name":"Present value of a single sum","package":"economics-finance-ai999x","example":"Find the present value with future value = 1000, rate = 5%, periods = 10.","v":[-0.03463,-0.00868,-0.10412,0.03376,0.12277,-0.12853,0.01358,0.082,-0.01316,0.02865,-0.06028,-0.0148,0.02167,-0.05613,-0.04628,0.02858,-0.07307,-0.0705,0.00744,0.02769,-0.0495,-0.09095,0.03338,0.04939,-0.01219,-0.07214,-0.03909,-0.03656,0.09553,-0.06337,0.01501,-0.009,-0.02277,-0.04935,0.08226,-0.10898,0.07165,0.01667,-0.00754,0.01009,-0.01384,-0.06256,0.02886,-0.02466,-0.01384,0.01824,-0.01604,-0.06573,-0.04399,-0.12385,-0.07002,0.07191,-0.08859,-0.01194,0.1493,-0.05572,-0.04551,0.03239,0.03859,-0.00598,0.00692,-0.10808,0.03545,-0.06958,0.01034,0.03765,-0.00867,0.02664,-0.12006,0.02508,0.14504,-0.01916,0.00134,0.03764,-0.03879,-0.00066,0.10111,-0.0427,0.03216,-0.04644,-0.03657,0.05177,0.0623,-0.05773,0.07943,-0.061,0.01152,-0.01046,0.08478,-0.08778,0.04736,-0.05165,0.0077,-0.01398,-0.02361,0.05092,-0.10079,0.01082,0.06543,-0.06512,0.09713,-0.06666,-0.00388,-0.03353,-0.1155,0.06157,0.0913,-0.03162,0.0388,-0.0204,0.06844,-0.05912,-0.0879,0.11473,0.08584,-4e-05,-0.00065,-0.07551,-0.02653,0.02812,-0.01209,-0.09073,0.09739,-0.06467,0.09073,-0.10685,-0.07554,0.08777,-0.02664,0.06851,-0.0171,0.10052,0.05451,-0.02742,-0.03383,0.07534,0.00542,-0.01174,0.06161,0.0385,0.08122,-0.03239,0.03404,-0.03852,0.01506,0.03833,-0.07607,0.07588,-0.06727,0.01406,-0.00403,-0.05811,0.01288,-0.01036,0.07718,-0.0497,0.02325,-0.00293,0.08226,-0.10258,0.06309,-0.04086,0.04312,-0.02634,0.00601,0.0686,-0.03385,0.13037,0.02813,-0.17829,-0.12948,0.00932,0.03382,0.10462,-0.08115,0.09824,-0.03215,-0.07022,0.06488,0.02825,0.04294,0.10463,0.03337,0.0337,0.05,-0.03379,-0.04161,-0.01772,-0.0538,-0.04906,0.12017,-0.06993,-0.01339,-0.00046,0.09669,0.11436,0.11173,0.02728,0.05182,-0.03179,-0.09056,-0.03287,0.08268,0.06893,-0.00016,-0.01815,-0.14901,-0.01927,0.00732,-0.03082,0.07,-0.01173,0.00233,0.02244,-0.0259,-0.06105,0.09683,0.03185,0.01906,-0.06514,0.07882,-0.03608,-0.01091,0.0483,-0.03644,0.06422,0.00336,0.08271,0.00955,0.13451,0.00538,-0.01111,0.09515,0.02749,-0.06397,-0.00415,0.07754,-0.02233,0.06768,0.06064,-0.00765,0.05515,-0.02863,-0.0589,-0.0388,-0.03207,0.03747,-0.05394,-0.03967,-0.05441,0.15471,-0.09593,-0.05296,0.01633,-0.11253,-0.0694]},{"domain":"economics_finance","key":"present_value_annuity","name":"Present value of an annuity","package":"economics-finance-ai999x","example":"Find the present value of an annuity with payment = 100, rate = 5%, periods = 10.","v":[-0.08833,0.06122,-0.07648,0.00217,0.06925,-0.16037,0.0252,0.10783,0.06953,0.04267,-0.04908,-0.00482,0.01333,0.05461,-0.01175,0.01976,-0.0284,-0.03212,-0.03227,0.02486,0.00347,-0.08137,-0.03727,0.00286,0.05165,-0.03763,0.07123,0.0186,0.01849,0.05197,0.05977,0.00327,-0.04251,-0.00871,0.08997,-0.12156,0.06596,0.02154,0.02891,0.0211,0.04323,-0.02565,0.02997,-0.0139,0.01082,0.03759,-0.01714,-0.00537,0.04051,-0.03312,-0.03649,0.02033,-0.11145,-0.01288,0.13001,-0.00547,-0.01419,0.02354,0.05906,0.00239,-0.05021,-0.04505,0.05679,-0.00811,0.07089,-0.00954,0.02969,-0.04702,-0.0824,0.07447,0.00283,0.05284,0.02077,-0.11703,-0.09458,-0.02745,0.02241,0.01434,0.08062,-0.11449,0.02253,0.07371,0.05634,-0.04685,0.07673,-0.00806,0.01528,-0.10732,0.07364,-0.05677,0.03791,-0.07713,-0.08127,-0.03028,-0.09744,0.03249,-0.06699,-0.08715,0.0602,0.00328,0.06784,-0.02384,-0.00202,-0.09826,-0.06189,-0.05066,0.02729,-0.0395,0.07912,-0.07923,0.04532,-0.09853,-0.09749,0.0805,0.06167,-0.05759,0.03016,-0.08224,-0.07748,0.07493,-0.03402,-0.05708,-0.01953,-0.01627,0.08211,-0.00478,0.02214,0.01567,0.00406,0.11814,0.06481,0.12534,0.04685,-0.09458,-0.01493,0.08193,0.03681,0.02054,0.1116,0.16638,0.04669,-0.00939,0.09683,-0.02433,0.03963,0.02765,-0.14051,0.06471,-0.05713,0.02976,0.06463,-0.04746,-0.01636,0.00381,0.06271,0.09759,0.06771,0.07184,0.13985,-0.07507,-0.00192,-0.04446,0.06958,-0.01641,-0.05734,0.03262,-0.0123,0.09939,0.00229,-0.17596,-0.11473,0.01762,-0.05399,0.03911,-0.15182,0.09926,-0.07893,-0.07007,0.03488,-0.0613,0.04658,0.09028,0.01832,-0.00886,0.06833,-0.02785,-0.0487,0.01091,0.03951,-0.02508,0.10024,-0.00221,-0.03193,0.00401,0.00699,0.06089,0.03275,-0.00926,0.01882,0.00978,-0.09581,-0.02769,0.07816,0.03982,0.02935,-0.02541,-0.09433,-0.01956,-0.04762,0.04728,0.02173,-0.04304,-0.07158,-0.01074,-0.02537,-0.00626,0.15379,0.05369,0.01391,-0.12733,0.12424,-0.03509,0.00723,-0.04553,-0.08444,0.02601,0.00739,-0.00802,-0.02294,0.05563,-0.0026,-0.01531,0.06656,-0.01713,-0.01325,-0.0434,0.00119,-0.00632,0.04094,0.09346,-0.05662,0.09229,0.06623,-0.01728,-0.01416,-0.05149,-0.0212,-0.17593,0.04217,-0.06193,0.11642,-0.10739,0.06236,-0.0261,-0.04058,-0.00615]},{"domain":"economics_finance","key":"price_indices","name":"Laspeyres, Paasche and Fisher price indices","package":"economics-finance-ai999x","example":"Find the Laspeyres and Paasche price index with base prices = [2, 5], base quantities = [100, 50], current prices = [3, 6], current quantities = [150, 40].","v":[0.0192,0.10872,0.01253,-0.03281,-0.01675,-0.01439,-0.03648,-0.00062,-0.13568,0.01977,-0.09295,-0.04319,0.02934,-0.05908,-0.08956,0.03249,-0.07686,0.07739,-0.01629,0.01655,-0.01348,0.04098,-0.01139,0.09662,-0.03577,0.00344,0.02403,-0.1162,0.02025,0.00724,-0.11188,0.01291,-0.03432,0.00405,0.02184,-0.04206,0.03827,-0.00533,-0.0149,-0.03071,-0.07167,-0.0266,-0.02964,0.02596,0.05972,-0.01725,-0.02704,-0.02792,-0.00468,-0.10835,0.00502,-0.07265,0.00176,-0.08597,0.00985,-0.07223,0.05909,-0.06277,-0.00838,0.02318,0.04518,-0.03244,-0.08875,-0.03661,-0.07209,-0.0911,-0.02711,-0.01107,0.14996,0.09995,-0.04738,-0.02396,-0.01251,-0.1569,-0.01837,0.00117,0.07696,0.03399,0.02856,0.01728,0.01821,-0.02206,0.16187,0.13155,0.01422,-0.07872,-0.02243,-0.12584,0.062,0.11017,0.02419,-0.02227,0.0643,0.09801,0.03746,0.003,-0.05418,0.0232,0.12488,-0.1797,-0.02886,0.00726,-0.01754,-0.02979,-0.04549,0.05049,0.00164,-0.07544,0.0753,-0.02937,0.15311,-0.02688,0.06623,0.03212,-0.03477,0.01334,0.05598,0.01972,0.04539,-0.05876,-0.03452,0.0321,0.09265,-0.00886,-0.00839,-0.0028,0.00156,-0.00293,-0.01519,0.05641,0.04174,-0.02082,-0.0278,0.03749,0.0213,-0.03255,-0.01157,0.07947,-0.08775,-0.02608,0.08819,-0.10072,0.11889,-0.0352,0.15812,0.01369,0.04287,-0.04619,-0.07058,0.02832,-0.06688,0.07728,-0.10296,-0.0034,0.12031,-0.04892,0.10299,0.0215,0.01232,-0.06974,0.04973,-0.02061,0.15814,-0.08611,-0.00569,0.03551,-0.04131,0.00016,-0.0225,0.08459,0.03192,-0.03135,0.03104,-0.02549,0.03152,0.00832,-0.06852,0.02419,0.03812,-0.02353,-0.09706,-0.04561,0.04488,0.10337,0.04685,-0.07803,-0.03811,-0.05794,-0.12574,0.01308,0.11391,0.00056,0.03195,0.00569,-0.02419,0.01122,-0.02504,-0.01548,-0.08148,0.07004,0.02105,-0.05808,0.05834,0.02586,-0.20952,-0.02563,0.08684,0.13156,0.04105,0.09966,-0.00415,-0.01681,-0.01203,0.01485,0.0721,-0.1236,-0.04029,-0.03799,0.09311,-0.01882,0.00148,0.00339,-0.09146,-0.02652,-0.00359,-0.00318,-0.08691,0.02698,0.00093,0.06743,0.04317,0.00608,0.07984,-0.1195,0.06333,-0.04069,0.08945,-0.03195,0.0471,-0.07883,0.08882,-0.01155,0.01467,0.04843,-0.09553,-0.02368,0.0729,-0.01715,0.01873,-0.01134,0.06416,-0.02434,0.00901,-0.03527,-0.09262,0.04236]},{"domain":"economics_finance","key":"profitability_index","name":"Profitability index","package":"economics-finance-ai999x","example":"Find the profitability index with rate = 10%, cash flows = [-1000, 300, 400, 500].","v":[-0.04181,-0.0013,-0.04517,0.06175,0.03394,-0.0366,-0.03959,0.00491,0.02635,-0.05947,-0.02841,0.01465,-0.09991,-0.14743,-0.02473,0.05496,-0.04426,-0.02591,-0.06314,-0.01643,-0.057,-0.05422,0.02028,-0.00221,-0.08423,-0.07216,-0.00872,-0.03477,-0.01163,-0.06783,-0.05982,0.00254,-0.0716,-0.10172,0.04058,0.0266,0.10244,0.02434,-0.02013,-0.01227,0.04617,-0.06619,0.00405,-0.03639,0.03994,0.01204,0.05163,-0.0467,-0.05899,0.00081,-0.01527,-0.03273,0.02636,0.02822,0.10164,0.03018,0.02713,-0.06316,0.01687,-0.05394,0.02995,-0.04916,0.04233,-0.0941,0.01581,0.01744,0.11616,0.01196,-0.17552,-0.03453,0.08822,-0.00796,-0.03215,-0.02779,-0.18257,0.09892,-0.02853,0.0267,0.11687,-0.09966,-0.02689,0.03103,0.27802,-0.04434,0.01392,-0.07617,0.04556,-0.01486,0.06091,-0.07178,0.03136,0.02512,0.06748,-0.10369,0.07189,-0.00256,-0.07751,-0.03363,0.1167,0.04821,0.00619,-0.01784,-0.02718,0.01132,-0.06066,0.04405,0.0301,-0.06294,0.04751,0.09957,0.12082,-0.08071,0.00565,0.08398,0.02466,0.01345,0.01427,-0.09342,0.07959,0.07382,-0.00046,-0.05021,-0.02277,0.02181,0.06549,0.08176,-0.00583,0.12701,0.0167,0.10075,-0.00797,0.01473,0.05327,-0.05236,-0.07552,-0.09639,-0.08523,0.08395,0.05102,-0.0421,-0.0444,0.02411,-0.04,-0.17025,0.05878,0.01647,-0.06126,-0.03912,-0.0233,0.02732,-0.03653,-0.09293,0.01622,0.02467,0.04028,-0.05818,0.06921,-0.0201,0.03036,-0.01986,0.00407,-0.00411,-0.01096,-0.00871,0.01551,0.00419,0.04518,0.04441,0.02515,-0.08764,-0.03528,-0.00794,-0.1249,0.01852,0.00604,0.11552,-0.09172,-0.001,0.04482,-0.1196,0.0659,0.04675,-0.08022,-0.02988,0.07072,0.00942,-0.00706,0.03713,0.03264,0.05821,0.03984,-0.05648,0.06724,0.03025,0.03666,0.06095,0.02486,-0.03399,0.04517,-0.05813,0.00723,0.05447,0.02666,0.00785,-0.08147,-0.11289,-0.04751,-0.01485,-0.01923,0.04359,0.01391,0.00142,-0.10207,0.04318,0.07235,-0.04897,0.09285,0.00187,0.08264,-0.04329,0.07664,-0.01213,-0.0575,0.05852,0.02115,-0.0007,-0.09555,0.14737,0.00993,0.04902,-0.02853,-0.02819,0.05153,0.17325,0.05379,-0.12431,0.10707,0.01057,0.00114,0.13029,0.02333,-0.04572,-0.01121,-0.06449,-0.02562,0.00938,0.10167,0.01721,0.04459,-0.00873,0.07678,-0.04174,-0.0098,0.05141,-0.04745,-0.01038]},{"domain":"economics_finance","key":"put_call_parity","name":"Put-call 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return and risk from scenarios","package":"economics-finance-ai999x","example":"Find the expected return from scenarios with probabilities = [0.3, 0.5, 0.2], returns = [0.2, 0.1, -0.15].","v":[-0.04142,-0.0581,-0.03019,0.01803,0.12095,0.1082,0.03776,-0.03325,-0.00642,-0.12091,0.12953,0.07281,-0.00239,0.03317,-0.00262,-0.10328,0.02412,-0.01955,-0.03442,0.0099,0.02939,-0.00586,-0.02381,0.04196,0.03719,0.05631,-0.09019,-0.0345,0.09452,-0.01529,-0.07713,0.1331,0.00203,-0.04253,-0.00374,0.00023,-0.00197,-0.07639,-0.04607,0.03257,0.01237,0.03603,0.05186,0.08226,0.04569,-0.01415,0.00494,-0.0666,0.00326,-0.01974,-0.12956,-0.06522,0.02138,0.01693,0.01461,0.04065,-0.05434,-0.07368,-0.0035,-0.05899,0.02839,-0.02279,0.00492,-0.14637,-0.15504,-0.00274,-0.02312,0.0131,0.10096,-0.04238,-0.04878,0.0423,-0.07731,0.02527,0.02455,0.04803,-0.07234,0.0029,-0.09249,0.00226,-0.06772,0.06437,0.01567,0.04247,-0.04338,-0.0433,0.04738,0.14278,0.01278,-0.05101,-0.05337,-0.00486,-0.07777,0.03578,0.03055,0.0138,-0.02027,0.00642,-0.08276,0.00788,0.04281,0.05539,-0.06502,0.02827,0.05697,0.039,-0.02549,0.08022,0.05764,0.1144,0.07753,0.01787,-0.03922,0.05423,0.06258,0.03709,0.04746,-0.15462,0.15527,-0.03196,0.05887,0.10589,-0.00775,-0.03566,0.02192,-0.0788,0.01128,0.03092,-0.08795,0.06291,-0.00985,-0.03189,0.05124,-0.0316,-0.01254,-0.02769,-0.07112,-0.05544,-0.06652,-0.02419,0.01561,0.01542,-0.05091,0.08487,-0.02056,0.0136,-0.05259,0.0905,-0.01719,0.02084,-0.09225,-0.00572,0.0129,-0.01718,-0.01844,0.0307,0.02993,-0.05998,-0.04969,-0.03638,-0.08001,0.00252,-0.00689,-0.01712,0.18628,-0.02885,-0.11315,0.06521,-0.01363,-0.03562,0.02841,-0.0006,-0.0064,-0.02321,0.07022,0.01622,0.01471,-0.0524,0.02729,0.03753,-0.09606,-0.07176,0.07508,0.07275,0.09481,0.09426,0.04321,0.06257,0.0656,-0.02184,-0.09829,0.00846,0.01053,0.00702,0.10659,-0.02071,0.00598,-0.03843,0.00359,-0.12666,-0.0163,0.04348,0.08428,0.15973,-0.00465,-0.05191,-0.05797,0.05634,-0.07229,0.08961,0.05432,0.13635,-0.07777,-0.06115,0.00689,-0.07624,0.00614,-0.03546,0.01476,-0.00539,-0.13714,0.13903,-0.04831,0.11253,0.03984,-0.07299,-0.0356,0.07819,0.04819,-0.02668,-0.03496,-0.06842,0.02901,0.12931,-0.09374,0.00314,0.08899,0.0176,-0.03496,0.01329,0.10056,0.02321,0.01011,0.05075,-0.01669,-0.05989,0.02586,0.03587,0.06136,-0.0977,0.02329,-0.04646,-0.10708,-0.14204,-0.10693,-0.03108]},{"domain":"economics_finance","key":"sharpe_ratio","name":"Sharpe ratio","package":"economics-finance-ai999x","example":"Find the Sharpe ratio with returns = [0.05, 0.02, -0.01, 0.04], risk-free rate = 0.5%.","v":[0.03362,-0.00503,-0.02106,0.16746,-0.04885,0.01993,-0.09717,0.02649,0.01631,-0.03442,-0.07213,-0.00808,0.06246,-0.02655,-0.08096,0.0023,0.06813,0.00338,-0.04159,0.04718,0.00972,-0.01769,-0.02934,0.05951,0.07941,0.0727,-0.03109,-0.05423,0.0011,0.00043,-0.08337,0.05792,0.06852,0.00749,0.02511,-0.07546,0.00947,0.04672,0.00309,-0.00197,-0.0343,0.04916,0.02633,0.04366,0.12919,-0.01553,-0.06463,-0.03107,0.03562,0.05412,-0.05951,0.0251,-0.02062,-0.02003,0.02919,-0.02011,-0.00892,-0.05666,0.01757,-0.07107,0.01546,-0.0041,-0.05078,0.01008,-0.01437,-0.01622,-0.03471,-0.01001,-0.01352,-0.03695,-0.06883,0.04128,-0.03846,-0.15925,0.01864,0.09968,-0.05558,0.07155,-0.04885,-0.01809,-0.02215,0.03413,-0.03613,0.04677,0.01895,0.00758,-0.09913,0.08588,0.03444,-0.00154,-0.00207,-0.01687,0.00966,-0.03001,-0.00996,0.04737,-0.03316,-0.00328,0.00292,0.04877,0.00778,0.04235,-0.03383,0.123,0.03505,0.00658,0.05127,0.04793,0.05732,0.12992,0.05905,-0.05996,-0.02239,-0.01826,-0.01559,0.15811,-0.04364,-0.08633,0.05501,-0.02677,-0.02033,0.07944,0.0399,-0.00214,-0.07743,0.03029,0.03057,0.01801,-0.02231,0.07304,-0.00297,0.0056,-0.11328,-0.03567,0.06635,-0.06433,-0.0446,-0.09723,0.03044,0.06952,0.03092,0.00457,-0.07969,0.10907,0.06276,0.02392,-0.07527,0.02703,0.01825,0.04862,-0.01641,-0.08797,0.00415,-0.05542,-0.06513,-0.04539,0.05048,0.04358,0.01439,0.02859,0.10371,-0.0011,0.00922,0.03687,-0.00521,0.03351,-0.06819,0.04121,0.0935,-0.10836,0.0682,-0.03596,0.00527,-0.03206,0.01116,-0.04017,0.01565,-0.04507,0.02167,-0.02008,-0.17561,0.04169,0.02122,0.02499,0.19108,0.11905,-0.03131,0.05417,0.07595,-0.00856,-0.109,-0.0887,0.01297,-0.10037,0.09884,0.05266,-0.03097,-0.06593,0.04479,-0.11695,-0.04637,-0.02874,0.05272,0.04115,0.07674,0.03478,-0.04089,-0.0125,-0.20206,0.02896,0.07176,0.0763,-0.14849,-0.06267,-0.0188,-0.15156,-0.00367,-0.0903,0.12902,-0.0237,-0.15312,0.06547,-0.01483,0.10575,0.08513,-0.01617,-0.07543,0.07456,0.06019,0.0045,-0.05804,-0.09769,-0.04879,0.11534,-0.0603,0.0605,0.05872,0.06887,0.03371,0.07104,0.0563,0.11922,0.00812,-0.02267,-0.01887,-0.04964,0.07217,-0.00304,0.0254,-0.12603,0.02056,-0.02496,-0.03879,-0.09898,-0.08844,-0.10601]},{"domain":"economics_finance","key":"simple_interest","name":"Simple interest","package":"economics-finance-ai999x","example":"Find the simple interest with principal = 1000, rate = 5%, years = 3.","v":[-0.02807,0.04607,-0.03385,0.04882,0.03168,-0.02145,0.03244,-0.02412,0.02216,-0.0543,-0.09121,0.07931,0.07916,0.03341,-0.11198,-0.02599,0.06739,0.0081,0.01108,0.04103,-0.01752,0.0325,-0.0111,0.04743,-0.07679,0.09203,-0.00851,0.0858,0.063,0.05152,-0.07534,0.06036,0.07407,0.00179,-0.09505,-0.03514,-0.04506,-0.08823,-0.12774,-0.06363,-0.06878,-0.10451,-0.16931,0.03942,-0.01645,-0.05811,-0.03691,-0.0457,0.09,0.00499,-0.09393,-0.08934,-0.06138,0.00016,0.0095,0.0394,-0.02542,-0.02638,0.0275,-0.10567,-0.01209,-0.06351,-0.01043,0.06526,0.03432,0.0191,0.00079,-0.03697,0.00271,0.10592,0.01911,-0.04727,-0.05273,-0.06008,-0.09679,-0.01581,0.14865,0.05836,-0.20029,-0.11996,0.03026,-0.0024,0.11098,0.04221,0.05939,0.02996,0.13289,-0.03833,0.03662,0.03025,0.04678,-0.10839,-0.08182,-0.09205,-0.00011,0.04275,0.0338,0.02579,0.01751,0.01851,0.02479,-0.04533,0.06331,-0.03732,-0.00492,-0.02001,0.09887,0.02918,0.02732,0.0047,0.00374,0.02622,0.01539,0.03854,0.07929,-0.11556,0.00406,-0.09207,0.03679,0.06422,0.00424,-0.0155,0.00137,0.0361,0.02637,-0.03157,0.08279,-0.00092,-0.06933,0.03758,-0.02104,0.02923,-0.00404,0.03356,0.13578,-0.07389,0.02998,0.09267,0.00337,0.00407,0.00522,0.05679,-0.11293,0.08641,0.0305,0.07288,-0.03703,0.11808,0.00416,0.04373,-0.05053,0.08294,-0.02725,-0.03624,0.05367,0.06151,0.06652,0.05545,0.05466,-0.14064,-0.05785,-0.05077,-0.07975,0.05708,-0.05854,0.03337,-0.02905,0.01131,-0.05092,-0.0125,-0.01303,-0.07504,0.04335,0.01093,-0.02135,-0.00965,-0.00129,-0.17309,-0.04566,0.03512,0.02872,0.11955,0.08304,-0.11016,-0.06521,0.04559,-0.04593,-0.07521,-0.03058,-0.06169,0.04353,-0.07524,-0.00887,0.00495,0.08265,0.01155,0.04423,0.06611,0.03101,-0.02003,-0.12436,0.1031,-0.0252,0.13367,0.05787,-0.03982,-0.0451,0.05404,-0.07334,-0.01987,0.05542,-0.01832,0.01127,0.00145,-0.03821,-0.01955,0.09565,0.03181,0.08504,-0.04533,0.02225,-0.02397,-0.01179,-0.11725,0.01847,-0.01204,-0.02781,0.03301,0.08089,0.08468,-0.02363,0.01265,-0.0172,0.02456,0.01568,0.00533,0.03341,0.03326,-0.07894,0.01459,0.04719,-0.05938,-0.01938,0.01513,-0.05193,0.05643,0.18248,-0.00395,-0.00831,-0.06942,0.03653,-0.07754,0.00401,0.00228,-0.19186,0.02012]},{"domain":"economics_finance","key":"sinking_fund","name":"Sinking fund payment","package":"economics-finance-ai999x","example":"Find the sinking fund payment with future value = 10000, rate = 4%, periods = 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ratio","package":"economics-finance-ai999x","example":"Find the Sortino ratio with returns = [0.05, 0.02, -0.01, 0.04, -0.03], target = 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spending multiplier","package":"economics-finance-ai999x","example":"Find the spending multiplier with mpc = 0.8, tax rate = 25%, mpi = 0.1, spending change = 100.","v":[-0.05481,0.07704,-0.09698,0.05602,0.1088,0.02105,-0.02048,-0.05113,0.03164,-0.0472,0.09306,0.10842,-0.05388,-0.00157,-0.01895,0.03048,-0.05908,0.01562,0.19352,0.07325,0.0313,0.064,0.02378,0.03739,0.04471,0.01227,-0.00248,0.03411,0.00818,0.01364,-0.08063,-0.05047,-0.10749,-0.06004,-0.08147,0.03644,-0.0772,0.0163,-0.03011,0.03046,-0.08656,0.02593,0.00673,0.00706,0.04674,0.0238,0.03562,0.00491,0.06875,-0.15007,0.00254,0.01419,-0.03337,0.01097,0.09535,0.11531,-0.07447,-0.05452,-0.01227,-0.07803,-0.02127,-0.02694,-0.01542,-0.00141,-0.12426,-0.02497,0.06347,0.01989,0.11726,0.06889,0.03473,-0.00298,-0.04711,0.00488,-0.01069,-0.05833,0.01262,0.0073,-0.07659,-0.07899,-0.07874,-0.02398,0.01103,0.08124,0.08942,-0.03335,-0.10367,-0.07829,-0.0201,0.01959,0.08198,0.06388,0.06304,-0.00784,-0.02949,-0.00199,-0.08849,-0.04246,0.12261,-0.00083,0.04061,0.03878,0.05498,-0.09073,-0.05595,0.01692,0.08935,0.00423,0.0397,0.09996,0.15466,0.02566,-0.11853,-0.01338,0.01534,-0.02781,-0.00038,-0.02563,0.06203,-0.02457,0.02589,0.15268,0.07617,0.13546,0.063,0.08028,-0.05951,-0.19974,-0.1061,0.07579,-0.07694,0.03531,0.06007,-0.09984,-0.02164,-0.09389,0.05811,-0.00954,-0.10522,-0.00853,0.02822,-0.07972,-0.09269,0.0296,0.06586,0.09915,-0.10558,-0.01217,0.02118,0.04432,0.0073,-0.03032,-0.10752,-0.01688,0.00367,0.09205,0.07254,-0.02289,0.02897,-0.03482,-0.06471,-0.18908,0.01868,0.06878,0.04303,-0.0151,0.03365,-0.04705,0.02937,0.09053,0.08328,0.02825,0.07504,0.03863,0.034,0.0355,0.01155,-0.07308,0.00555,0.04718,0.06356,-0.06898,-0.02518,-0.07775,-0.02796,-0.04212,-0.01478,0.0096,-0.06606,0.01226,0.08102,0.08256,-0.05145,0.02491,-0.09468,-0.01656,-0.01865,-0.03444,-0.0252,0.02946,-0.05706,-0.00202,0.08788,0.06738,0.04822,0.00951,0.02801,-0.00899,-0.07852,0.06753,-0.08855,0.10702,-0.11256,-0.04536,-0.02009,-0.07126,-0.03851,0.06981,0.0547,-0.02305,0.03706,-0.07656,0.00991,0.01529,-0.03298,-0.12613,0.00785,0.02371,0.01831,-0.05996,-0.05151,-0.03863,0.08158,-0.09873,-0.00158,0.02289,0.00817,0.05512,0.04196,0.00712,0.04446,0.09551,0.03054,0.02718,0.01834,0.07869,0.03074,0.04175,-0.00502,-0.03103,0.02041,0.00497,-0.02776,-0.01016,-0.05421,0.04876]},{"domain":"economics_finance","key":"stackelberg","name":"Stackelberg duopoly equilibrium","package":"economics-finance-ai999x","example":"Find the Stackelberg equilibrium with price intercept = 100, price slope = 1, cost leader = 10, cost follower = 10.","v":[0.03993,-0.00155,-0.02902,-0.05542,-0.06372,0.04601,0.00684,-0.00238,0.03964,-0.01303,-0.07654,0.03029,-0.08088,0.04609,-0.00669,-0.05777,-0.06314,0.01239,0.0211,-0.0419,0.02392,0.05918,0.06378,0.03078,-0.00148,-0.01068,0.07378,-0.04273,0.02068,-0.00581,-0.02161,0.13608,0.02645,-0.05172,0.02642,0.04672,-0.12574,0.02878,0.07035,-0.03136,-0.00431,0.04948,-0.03666,0.00853,0.03885,0.07573,0.01438,0.05937,0.03125,-0.04815,-0.01595,0.03792,-0.11071,0.01415,-0.04996,0.10614,-0.02206,-0.00691,0.077,0.08115,-0.11106,0.0475,-0.05137,0.02282,-0.05735,-0.06416,0.03651,-0.09205,0.13768,-0.05286,0.05604,0.03856,0.00345,-0.02359,0.06119,-0.07944,0.07435,-0.04673,-0.02449,0.05576,-0.00459,-0.00935,0.03507,-0.05403,-0.07771,-0.09179,-0.07474,-0.01196,-0.03385,0.0711,0.08735,-0.00952,0.15417,0.04605,0.05376,-0.11299,-0.05893,0.00788,0.0119,0.01798,0.0393,0.06756,0.0566,-0.01285,0.03107,-0.0038,0.04181,-0.03719,0.03107,-0.0367,0.09471,-0.03069,0.0284,-0.01422,0.03703,-0.01151,0.03705,-0.05287,-0.14234,0.09288,0.00316,-0.00341,0.16034,0.00657,-0.03918,0.09614,-0.01027,0.13641,-0.002,0.01536,-0.14184,0.00756,0.00268,-0.0764,-0.07966,-0.04221,-0.0039,0.01402,-0.13821,-0.14713,0.07339,-0.05254,0.05558,-0.06301,0.09374,0.09366,0.01834,0.03555,-0.04705,0.05145,0.04532,-0.02259,-0.01822,0.04442,0.18413,-0.05781,0.0492,0.01056,0.02961,-0.01143,-0.08841,-0.02713,-0.02985,0.00284,-0.0613,0.02537,-0.04572,0.00431,-0.09338,0.03184,-0.0135,0.157,0.02914,-0.09037,0.07477,-0.0269,0.03842,-0.08843,-0.04367,0.06759,-0.13861,0.01089,-0.09727,0.04813,0.07244,-0.10412,0.00191,-0.09641,-0.00124,0.07648,0.02927,0.10284,0.09353,0.00924,-0.02458,0.06797,-0.03906,0.06666,0.05366,-0.06547,0.03987,-0.03093,0.03528,0.02374,-0.06744,0.03976,0.03835,0.03162,0.05539,0.00591,-0.07597,-0.00515,-0.08549,0.06675,-0.04195,0.07422,-0.10009,0.07979,0.05025,0.0539,-0.02627,-0.05173,-0.03506,-0.00176,0.04371,-0.05602,-0.20019,0.04522,-0.0092,-0.01408,0.01335,-0.06562,0.02474,-0.14275,-0.07368,0.02515,0.01926,-0.09057,0.02372,0.01783,-0.04957,0.02527,0.02988,-0.01153,0.01409,-0.06169,0.03548,0.01073,-0.10681,0.09768,-0.05899,0.00834,0.0795,-0.05458,0.08157,0.07087]},{"domain":"economics_finance","key":"survival_probability","name":"Survival and death probabilities from a life table","package":"economics-finance-ai999x","example":"Find the survival probability with mortality rates = [0.01, 0.02, 0.03, 0.05], years = 3.","v":[-0.07232,-0.08757,0.01019,0.02336,0.11421,-0.10602,-0.03091,0.00839,0.03512,-0.10419,0.04319,0.12188,-0.02086,-0.03796,-0.00458,-0.07291,0.05172,-0.0307,0.00937,-0.02713,-0.08247,0.01239,-0.03415,-0.02267,-0.04159,-0.03481,0.00583,0.01399,-0.01686,-0.07625,-0.0656,0.09236,-0.02199,0.01287,-0.01294,-0.11713,0.03932,-0.04632,0.03781,0.07403,-0.02467,-0.11295,0.12671,0.03963,-0.05186,-0.07906,-0.05393,0.06876,0.03091,0.02857,-0.06824,0.03304,-0.02744,-0.19236,0.01699,-0.01098,0.07114,-0.03235,-0.05615,-0.00137,0.07534,-0.02969,0.04293,0.01618,-0.04788,-0.05638,0.00237,0.08709,0.03266,0.13816,0.01169,-0.04857,-0.06934,0.00226,-0.04291,-0.0339,0.07319,-0.04462,0.03214,0.09976,-0.04886,-0.04404,0.02735,0.00807,-0.03892,-0.03782,0.01329,-0.00467,0.09253,0.00558,0.00831,-0.05307,0.02761,-0.02735,-0.00128,0.02282,-0.06306,-0.05777,0.08114,0.00832,0.03918,-0.08903,0.11765,-0.0235,-0.03171,0.0021,-0.06341,-0.01636,0.10331,-0.03325,0.0491,-0.06733,0.08387,0.00391,0.00969,-0.07657,-0.03485,-0.02239,0.01105,-0.00119,-0.14888,-0.03163,-0.00518,0.08598,0.07642,-0.04636,0.02417,-0.12057,0.03456,0.02516,0.10773,0.05013,0.01633,-0.05985,-0.0434,0.00966,-0.02645,-0.00611,0.05006,0.01352,0.06972,-0.02491,-0.03338,-0.03061,0.01572,0.13724,0.00332,0.02012,0.00463,0.0426,0.00273,-0.17946,-0.16477,0.002,0.08655,-0.03276,-0.08039,-0.02886,-0.03263,-0.00036,-0.03102,-0.06804,0.10751,-0.07596,0.16157,-0.04333,-0.05712,-0.03471,0.01791,0.00494,0.04113,0.02029,0.014,-0.05427,-0.0693,0.15495,0.00843,-0.0882,0.10224,0.08426,0.01319,0.04171,0.04101,0.06261,0.05167,-0.01272,0.06029,-0.05964,-0.03302,0.08364,0.17957,0.02836,-0.01068,-0.02889,0.01381,-0.01389,0.06689,0.04407,0.05818,0.06372,-0.03271,-0.13337,0.02505,0.04219,-0.05986,-0.01244,0.02053,0.02936,0.06036,0.02239,0.0502,0.00902,0.01619,-0.1158,0.02092,-0.03194,0.03498,0.10418,-0.10597,0.02341,0.00951,0.10743,0.03038,-0.07035,0.0405,0.03037,-0.03982,0.01687,-0.02104,0.01608,0.05563,0.06613,0.11069,0.05981,0.10452,-0.06469,0.11536,-0.03607,-0.1282,-0.01685,0.00754,0.04466,0.07267,0.01157,-0.0564,-0.01987,0.0342,-0.11341,0.07693,-0.08965,0.01371,0.01657,0.07161,0.03372,-0.0589,-0.08116]},{"domain":"economics_finance","key":"tangency_portfolio","name":"Tangency (maximum Sharpe ratio) portfolio","package":"economics-finance-ai999x","example":"Find the tangency portfolio with expected returns = [0.1, 0.15], covariance = [[0.04, 0.006], [0.006, 0.09]], risk-free rate = 3%.","v":[-0.00548,0.01881,-0.03833,0.04694,-0.07791,0.11682,0.00283,0.01672,0.07581,-0.1528,-0.01862,0.07526,0.06826,0.03933,-0.06769,-0.11505,-0.06396,-0.05446,0.06309,0.03913,-0.00618,0.06616,0.02128,-0.03451,0.07996,-0.01538,-0.05025,-0.08146,0.02668,0.11148,-0.01662,0.14363,0.03572,-0.00853,0.03784,-0.04342,0.00519,-0.00831,-0.0291,0.11312,-0.01199,0.0148,0.07488,0.01539,0.03528,-0.06298,-0.05709,-0.06525,-0.10508,0.01148,0.00788,-0.01335,-0.03429,0.00324,0.03041,0.07378,-0.01754,-0.07595,-0.04466,0.00507,4e-05,0.02101,-0.00447,0.02816,-0.19231,-0.07251,0.00577,-0.03463,0.0225,-0.07425,-0.08352,-0.01741,-0.04614,0.04826,0.0279,0.03568,-0.10603,0.00919,-0.10056,-0.02829,0.01428,-0.03929,-0.0857,0.05674,0.01773,-0.04442,-0.00732,0.09869,0.04618,0.02951,-0.00364,0.06599,-0.00363,-0.07171,0.0193,0.01584,-0.08932,-0.06097,-0.07267,-0.00563,-0.04136,0.04266,-0.0842,0.09771,0.07853,-0.01464,0.1016,0.04363,-0.00263,0.08144,0.09106,-0.00419,-0.00498,0.02888,0.04006,0.05554,-0.00355,-0.15521,0.10538,-0.04358,-0.04405,0.05758,0.05552,0.02504,0.00353,0.02711,-0.00035,0.0251,-0.00992,0.10185,-0.08215,-0.0017,-0.06965,-0.0461,-0.00188,-0.1264,-0.00751,-0.03879,0.03315,-0.03953,0.1015,-0.03265,-0.0248,0.04391,0.04464,0.09298,-0.08016,0.087,-0.03001,0.06845,0.01097,-0.1039,-0.06862,0.03049,-0.01205,-0.11548,0.10503,-0.01215,0.00059,0.08433,0.08848,-0.04053,0.00816,0.04337,0.02837,0.07631,-0.10947,0.106,-0.02441,-0.05105,0.07794,0.03823,0.0068,0.00834,-0.01167,-0.03584,0.10376,0.01657,0.02363,0.00214,-0.09065,-0.03513,0.01685,-0.01216,0.09928,0.06605,-0.02065,0.10564,0.13409,0.08743,-0.01413,-0.01399,0.01458,-0.14039,0.08441,0.00647,0.01499,-0.05704,0.10316,-0.05724,-0.05099,-0.03968,0.11119,0.08296,0.01123,-0.06481,-0.02919,0.09351,-0.13977,-0.01324,0.01492,0.05349,-0.07199,-0.06263,0.0442,-0.06858,-0.08556,-0.04088,0.07511,-0.03556,-0.22766,0.08273,-0.03484,0.1003,0.07065,0.0326,-0.07966,0.02744,0.05847,-0.03623,-0.03875,-0.02528,-0.00253,-0.00113,-0.0756,0.04403,0.05313,0.02244,-0.07476,0.01313,0.03203,0.05722,0.03942,0.01309,-0.04321,-0.00268,-0.0007,0.0237,0.03085,-0.06848,-0.0036,0.04313,-0.01222,-0.09142,-0.05832,0.036]},{"domain":"economics_finance","key":"temporary_annuity_due","name":"Temporary life annuity-due","package":"economics-finance-ai999x","example":"Find the temporary annuity value with mortality rates = [0.01, 0.02, 0.03], interest rate = 4%, term = 3, payment = 1000.","v":[-0.12767,-0.0377,-0.04873,0.00775,0.10243,-0.15844,-0.07189,0.04175,0.03907,-0.05708,0.01709,0.05863,-0.01624,-0.04622,-0.04444,-0.03809,0.12963,0.0,-0.00879,-0.00061,0.00268,0.00076,-0.083,0.0064,0.03247,0.00149,0.03294,0.07529,0.03357,-0.04015,-0.08878,0.06332,0.01828,0.01668,0.05664,-0.04391,0.03858,-0.05309,0.01569,0.08665,-0.02141,-0.08919,0.07032,0.06354,0.00948,-0.05667,0.01344,-0.0335,0.09604,0.02288,-0.03616,-0.00112,-0.04279,-0.06831,0.0898,0.01911,-0.05964,-0.01336,0.0357,-0.00587,0.03623,-0.0886,0.02135,-0.01314,-0.07408,-0.07732,-0.00174,0.06079,-0.05474,0.07173,0.00503,0.05473,0.03646,-0.14543,-0.10022,0.05526,0.06682,0.00048,0.10314,-0.03722,-0.08726,-0.06171,0.07918,-0.03078,-0.0292,-0.06674,0.02529,-0.05838,0.06173,-0.03038,0.01652,-0.05651,-0.03356,-0.05886,-0.08111,-0.01903,-0.05944,-0.07443,0.19735,0.01316,0.05541,-0.04862,0.06573,-0.05548,-0.00324,-0.00841,-0.05144,-0.0609,0.09974,-0.02987,0.12808,-0.07892,0.07684,0.08439,0.01469,-0.08963,-0.02131,-0.09231,-0.00255,0.00602,-0.09824,0.01988,0.01608,0.03384,0.0751,-0.03935,0.00736,-0.06244,0.01718,0.05355,0.07052,0.07719,0.01926,-0.06619,-0.09005,0.07238,-0.01225,-0.02958,0.05627,0.03729,0.04055,-0.01452,0.02161,0.01529,0.083,0.07568,-0.07711,0.03932,-0.03803,0.04673,0.02975,-0.02695,-0.10245,-0.01545,0.08356,0.05242,-0.06023,0.05018,0.00588,-0.03995,-0.01782,-0.0923,0.08168,-0.03857,0.03864,-0.06823,-0.03229,0.01127,-0.00247,-0.1028,-0.01786,0.00288,-0.01568,-0.0755,-0.12469,0.20289,-0.05886,-0.13795,0.12025,0.05161,0.00741,0.06607,-0.00542,0.02521,0.08985,0.03193,-0.0533,-0.08292,0.00013,0.03877,0.1681,-0.00575,-0.03996,-0.00885,0.00316,0.05333,0.07098,0.00414,0.0683,-0.02207,-0.12498,-0.12167,0.01782,0.09078,-0.00927,-0.02027,-0.03288,0.06574,-0.01512,0.05893,0.04209,-0.00654,-0.06019,-0.02857,-0.01584,-0.03644,0.11696,0.00314,-0.03002,-0.04321,0.09743,0.06814,0.02239,-0.02171,0.04882,0.01249,-0.07657,0.07361,-0.00736,0.05186,0.05802,0.03482,0.1076,0.04774,0.03302,-0.04098,0.10095,-0.01856,-0.06105,0.05632,-0.02752,0.10061,0.07763,-0.03394,-0.06341,-0.01924,0.01354,-0.11603,0.1219,-0.05891,0.0068,-0.00736,0.08427,-0.00862,-0.10002,-0.03795]},{"domain":"economics_finance","key":"term_insurance","name":"Term life insurance (net single premium)","package":"economics-finance-ai999x","example":"Find the term insurance value with mortality rates = [0.01, 0.02, 0.03], interest rate = 4%, term = 3, benefit = 100000.","v":[-0.1004,-0.09988,-0.01112,0.01683,0.13802,-0.13135,-0.04069,0.07182,0.07638,-0.03571,0.03617,0.10573,0.00088,-0.10702,-0.06655,0.00632,0.06345,0.0005,-0.04929,0.05259,-0.02253,-0.01622,-0.05714,0.01753,0.02923,0.01598,0.02167,0.1001,0.04285,-0.07726,-0.12218,0.10479,-0.02424,-0.01394,0.02579,-0.05367,0.0513,-0.04423,0.01206,0.04891,-0.02566,-0.10226,0.07419,0.07794,0.03242,-0.09013,-0.00517,-0.0412,0.06164,0.04185,-0.07472,-0.00947,-0.02865,-0.10276,0.0883,-0.0158,-0.0467,0.01854,0.0188,0.01704,0.02614,-0.07114,0.0027,-0.00667,-0.06586,-0.05288,-0.02312,0.08287,-0.05383,0.03358,0.07594,0.06016,0.01234,-0.08494,-0.0928,-0.00409,0.07981,-0.05448,0.08453,-0.00119,-0.10749,-0.05725,0.05072,-0.03077,-0.06893,-0.06206,0.00935,-0.01409,0.14238,0.03256,0.01327,-0.05187,-0.00176,-0.05184,0.00122,-0.01154,-0.02339,-0.08507,0.12526,0.05873,0.07104,-0.08223,0.09923,-0.01364,-0.03047,-0.00509,-0.06753,-0.08704,0.0803,-0.01558,0.10727,-0.04366,0.06241,0.07869,0.02662,-0.11828,-0.03691,-0.10474,0.00609,0.0353,-0.12847,-0.00341,-0.00897,0.05257,0.09964,-0.0479,0.03405,-0.05053,0.02596,0.03553,0.0752,0.11259,0.06004,-0.08272,-0.13663,0.03551,-0.04763,-0.02356,0.02259,0.03529,-0.00657,-0.00234,0.02594,0.01783,0.03124,0.0891,-0.04357,0.04672,-0.02979,0.03076,0.05453,-0.04841,-0.09903,-0.00909,0.0801,0.02014,-0.00367,0.03825,-0.01902,-0.04826,-0.00498,-0.07332,0.08477,-0.04837,0.05758,-0.05718,-0.01012,-0.06428,0.00473,-0.09958,-0.07902,0.01184,-0.01252,-0.05848,-0.08998,0.18304,-0.00776,-0.1315,0.08999,0.07471,0.00939,0.04789,-0.04069,-0.01199,0.11819,0.01799,-0.04122,-0.09619,-0.0601,0.05078,0.17489,-0.01851,-0.01798,-0.04798,0.01771,0.04424,0.04302,0.03666,0.10599,0.00198,-0.09253,-0.07852,0.05825,0.04348,0.01108,-0.03015,-0.03892,0.07345,0.02154,-0.00707,-0.00388,0.00428,-0.04272,-0.03497,0.00476,-0.01855,0.09569,0.08812,-0.0246,-0.03106,0.0382,0.06525,-0.0279,-0.03517,0.0905,0.02161,-0.07256,0.0312,-0.01219,0.04506,0.04484,0.03041,0.10344,0.07161,0.06196,-0.03297,0.06659,-0.03878,-0.10275,0.05174,-0.04726,0.09583,0.0483,-0.06621,-0.03712,-0.02314,0.03254,-0.08124,0.14424,-0.01469,0.05175,0.02733,0.05278,0.01994,-0.09009,-0.06372]},{"domain":"economics_finance","key":"treynor_jensen","name":"Treynor ratio and Jensen's alpha","package":"economics-finance-ai999x","example":"Find the Treynor ratio and Jensen's alpha with portfolio returns = [0.03, -0.01, 0.04, 0.02], market returns = [0.02, -0.02, 0.03, 0.01], risk-free rate = 0.2%.","v":[0.06404,-0.03805,-0.00488,0.15585,-0.06183,0.02713,-0.02048,0.07671,0.06326,0.02063,-0.08528,-0.02387,0.14062,-0.02338,-0.13666,-0.02365,0.06712,-0.06984,0.00229,0.03972,0.03655,0.0388,0.00102,0.01712,0.0729,-0.00416,-0.03044,0.03503,0.00582,-0.00773,-0.01889,0.08116,0.0545,0.02339,0.00452,-0.00375,-0.03493,0.03398,0.00087,0.00421,-0.02762,0.06367,0.00535,0.01856,0.03246,-0.01545,-0.08359,0.00641,0.01551,0.0391,-0.08287,0.09321,-0.05161,0.04252,0.01588,-0.00234,0.02696,-0.03626,-0.05627,-0.01107,-0.00434,-0.1196,-0.04206,-0.00481,-0.07018,-0.05729,0.0504,-0.03681,-0.09603,-0.08855,-0.04053,0.01886,0.045,-0.2095,-0.01684,0.06915,0.0157,0.07676,0.07592,0.03726,-0.02317,-0.00086,-0.06615,0.02367,-0.01904,-0.02827,0.0283,0.13476,0.08966,0.02425,-0.05053,0.01482,0.01836,-0.02126,0.02529,0.01307,-0.04042,-0.01334,-0.06357,-0.01848,0.0026,0.01019,-0.05031,0.11501,0.01738,0.0112,0.04007,0.01714,0.02267,0.11037,0.07284,-0.02352,-0.04194,-0.01621,0.01347,0.06577,0.01441,-0.09417,0.01328,-0.01347,-0.04675,0.02539,0.01736,-0.00911,-0.02996,0.10816,-0.00119,0.0216,-0.05557,0.04246,-0.03974,-0.0913,-0.13895,-0.03758,-0.03737,-0.16619,-0.08053,-0.13032,0.01282,-0.01934,0.07525,-0.01642,-0.02094,0.03466,0.0822,0.03697,0.03154,0.05862,0.02787,0.01518,-0.03985,-0.01401,-0.05287,-0.01658,-0.02939,-0.11581,0.0981,0.00397,0.03307,0.01408,0.19648,-0.11541,0.01517,0.07817,0.04355,0.0589,-0.11668,0.02276,0.07681,-0.08895,-0.00953,-0.01987,0.03019,-0.04543,0.054,0.00355,0.10573,-0.04018,0.09841,-0.0088,-0.11642,-0.00406,0.00044,0.01537,0.14654,0.05356,0.01941,0.03978,0.01266,-0.01112,0.00378,-0.05206,0.01934,-0.04635,0.11569,0.07314,-0.0559,-0.0421,0.09598,-0.10457,0.02217,-0.05828,0.11255,0.06868,0.06919,0.01142,-0.03587,0.09222,-0.12774,0.0477,0.02759,0.02806,-0.15753,0.00686,0.02238,-0.00966,0.01885,-0.05459,0.14871,-0.0251,-0.1358,0.07381,-0.0339,0.08983,-0.00071,0.01956,-0.11347,-0.02248,0.05338,0.04512,-0.13642,-0.06768,-0.0308,-0.0053,-0.14526,0.01297,0.02808,0.02773,-0.01776,0.07946,0.0122,0.10714,0.07068,0.01226,-0.05161,-0.04624,0.02911,-0.06537,0.0356,-0.05606,-0.01186,0.00325,-0.037,-0.07115,-0.05122,-0.06017]},{"domain":"economics_finance","key":"two_asset_portfolio","name":"Two-asset portfolio return and risk","package":"economics-finance-ai999x","example":"Find the two-asset portfolio return and risk with w1 = 0.6, r1 = 10%, r2 = 15%, sd1 = 20%, sd2 = 30%, correlation = 0.1.","v":[0.00826,-0.02312,-0.05653,-0.00886,-0.00687,0.13919,0.03208,-0.03231,0.00434,-0.08483,0.04348,0.088,0.08402,0.05589,-0.09841,-0.05494,-0.05455,-0.09669,0.00477,-0.01397,0.05582,0.01718,0.01981,0.07881,-0.03421,0.06992,-0.03188,-0.0151,0.02585,-0.00746,-0.03641,0.12077,0.02852,-0.02455,-0.00098,0.02503,-0.03024,0.04525,-0.03312,0.01288,-0.01739,0.01354,0.01773,0.03787,-0.00846,-0.01588,-0.00547,-0.07466,-0.02854,-0.03403,-0.09118,0.0057,0.04486,0.03728,0.04385,-0.03042,-0.09678,0.01313,-0.02839,0.04949,-0.01183,-0.04947,-0.00343,-0.13272,-0.13743,0.02629,-0.01056,0.02261,0.06468,-0.08377,-0.08342,-0.1072,-0.03831,-0.01639,0.05166,-0.03921,-0.08201,0.0035,-0.03153,0.05412,-0.04914,0.02441,-0.05194,0.11415,0.02828,-0.00222,0.03915,0.11453,0.04762,0.01538,-0.04027,-0.01208,-0.04169,0.03658,0.09699,-0.00014,-0.02221,0.03104,-0.21238,-0.05339,0.00504,-0.00809,-0.03986,0.12419,0.06665,-0.03474,0.09572,0.06707,0.00554,0.07264,0.03412,-0.003,-0.10584,-0.02251,0.01176,0.05565,0.11947,-0.09852,0.13037,-0.11825,0.09472,0.09262,0.04604,0.00137,-0.07128,-0.08384,-0.0122,0.0408,-0.03984,-0.02042,-0.0188,0.00993,0.03479,-0.05582,0.04763,-0.07936,-0.02873,-0.09643,-0.03476,-0.03054,0.03468,-0.02138,-0.0935,0.06252,0.01306,0.02416,-0.04674,0.06394,-0.02242,-0.01993,-0.01019,0.01005,0.00397,0.05119,-0.03268,-0.05254,0.14327,-0.04095,-0.00612,0.02356,0.04656,-0.00812,-0.01163,0.05326,0.06871,0.0955,-0.09353,0.05266,-0.01578,-0.05921,0.0709,0.03549,0.02334,-0.02868,0.01615,-0.03738,0.05926,-0.15241,-0.0079,-0.04852,0.0825,3e-05,-0.01668,0.01086,0.08619,0.13997,0.00919,0.14915,0.046,-0.05077,-0.0248,0.04912,0.03771,-0.01036,0.0841,-0.01669,-0.01282,0.00343,0.04016,-0.14676,-0.03891,0.08647,0.06593,0.07206,0.04811,-0.00037,-0.06966,0.0274,-0.14205,0.0338,0.05768,0.05772,-0.00622,-0.06038,0.06952,-0.01323,-0.05033,-0.04205,0.0583,0.05726,-0.05147,0.0663,-0.04425,0.04203,0.08736,0.02484,0.07052,-0.00649,0.02625,-0.00439,-0.0959,-0.05608,0.01032,0.02335,-0.04063,-0.01917,0.07854,0.07542,0.01608,0.01483,0.08773,0.0263,-0.00525,0.01084,-0.08079,-0.07884,0.00335,0.10365,0.03637,-0.11517,0.06718,0.02911,-0.16874,-0.20092,-0.12368,-0.01714]},{"domain":"economics_finance","key":"two_stage_ddm","name":"Two-stage dividend discount model","package":"economics-finance-ai999x","example":"Value the share with the two-stage dividend discount model with dividend = 2, high growth = 15%, high growth years = 5, stable growth = 4%, required return = 10%.","v":[-0.06734,-0.05136,0.0547,-0.04286,0.05225,-0.02853,0.01236,0.03841,0.00603,-0.03339,-0.04767,0.05778,-0.04465,0.0464,-0.13289,-0.02876,-0.02424,-0.1556,-0.02875,-0.049,-0.08069,0.0135,-0.03111,0.03906,0.01306,-0.04262,-0.05261,0.01145,-0.02288,-0.03993,-0.05844,-0.05112,0.06539,-0.06541,-0.0202,-0.01888,-0.04634,0.00101,0.05208,0.00575,0.0129,0.08904,0.03221,0.07555,-0.00231,0.06435,-0.04749,0.00821,0.02103,0.10441,-0.06062,0.13253,-0.00285,0.03943,0.03542,0.21145,0.07232,0.06438,-0.0045,-0.00161,-0.16196,-0.07069,0.02127,-0.01738,0.02638,-0.02165,0.05049,-0.04691,0.04796,-0.13202,0.06119,0.00653,-0.12808,-0.01843,-0.09038,-0.00492,-0.07637,-0.0002,-0.02088,0.07147,0.02166,0.04211,0.01307,0.01897,0.00341,-0.06502,0.01425,-0.01517,-0.04414,0.04014,0.02053,0.05768,0.02154,-0.07633,0.0822,0.09936,-0.123,0.04519,0.04409,-0.12679,-0.00491,-0.04577,0.00475,0.03126,-0.01281,0.04343,0.12245,-0.0081,0.15077,0.0429,0.06257,-0.04552,-0.15317,0.07635,0.02722,-0.04152,0.02587,0.01051,0.01032,-0.11633,0.01163,0.007,0.01868,-0.04564,0.10035,0.00367,-0.02426,0.06581,-0.02154,0.02841,-0.06534,0.06253,0.00139,-0.01204,0.02821,0.01342,0.03933,0.04182,0.02325,0.03876,0.03757,0.00116,0.00765,-0.06159,0.14746,-0.01555,-0.0462,-0.02276,0.01958,0.08493,-0.03246,-0.0878,0.04821,0.00823,0.05619,-0.13776,0.06584,0.02132,0.03734,-0.14165,0.00104,-0.02348,0.00137,-0.05934,-0.13543,-0.01817,0.03459,0.03745,0.07058,-0.08385,0.01658,-0.03591,-0.0888,-0.0505,0.01323,0.14294,-0.11955,-0.04054,0.07593,-0.00979,0.06489,0.03403,-0.01689,-0.12642,0.03977,-0.06144,0.11353,0.05927,0.09731,-0.09146,0.00949,0.09398,0.02011,0.02705,-0.02482,0.01479,0.07531,0.06708,0.1091,-0.13782,-0.02486,-0.05476,0.08396,0.08389,0.06391,0.03726,-0.01856,-0.10624,0.0163,-0.06831,-0.05515,0.06382,-0.07236,0.04717,0.07134,0.06507,-0.03039,0.02995,-0.00161,0.05824,-0.00543,0.05393,-0.01078,0.08259,-0.04371,-0.00344,-0.04596,0.08556,-0.01324,0.10038,0.00211,-0.0743,0.00966,0.01906,-0.00594,-0.01517,0.0555,0.05466,0.01988,-0.05363,-0.03398,0.04378,-0.04292,-0.04925,0.08247,0.01507,-0.03455,0.04015,-0.04361,-0.1288,-0.0058,-0.06026,-0.09565,-0.0925,-0.00463,-0.04593]},{"domain":"economics_finance","key":"wacc","name":"Weighted average cost of capital","package":"economics-finance-ai999x","example":"Find the WACC with equity value = 600, debt value = 400, cost of equity = 12%, cost of debt = 6%, tax rate = 25%.","v":[-0.01736,-0.03398,-0.05876,-0.02733,0.10138,-0.01116,-0.01598,0.01543,0.02549,-0.11768,0.0092,0.03791,-0.04402,-0.02138,-0.09873,0.05374,-0.0812,-0.14504,-0.06976,-0.08922,-0.00717,-0.03245,0.02494,0.11403,-0.01724,-0.00014,-0.00708,-0.0919,-0.02762,-0.06019,0.01138,0.01794,0.0444,-0.07323,0.02854,-0.0101,0.06986,-0.0572,0.11582,0.01608,-0.0368,-0.00802,-0.01062,0.0469,-0.03022,-0.03946,-0.04465,-0.0466,-0.05433,-0.02324,0.03746,0.0151,0.01808,-0.03154,0.13017,-0.01975,-0.01522,0.09001,-0.11015,0.10987,0.01979,-0.07664,-0.01773,0.07044,-0.07517,-0.00682,-0.02787,-0.08414,-0.11723,-0.01337,-0.0308,0.0463,-0.01187,-0.03972,-0.08536,0.00752,-0.06062,-0.03203,-0.0604,0.02239,-0.02898,0.02382,0.04399,-0.02088,0.04617,-0.05904,0.0649,-0.0883,0.08459,-0.00266,0.07558,0.01681,0.02064,0.01933,-0.03924,-0.04855,-0.13092,-0.03281,0.00934,0.00803,-0.02494,-0.00757,0.0143,0.02228,-0.04941,-0.0544,0.10687,-0.00367,0.10109,0.0412,0.14296,-0.05736,-0.13157,0.0602,-0.02222,0.03444,0.02766,-0.03241,0.08703,0.02877,-0.01685,-0.01208,0.00335,-0.10583,0.10795,0.025,-0.00014,-0.07623,-0.07648,0.00461,0.03271,0.21714,0.03069,-0.04404,-0.05785,-0.05609,-0.0665,-0.02991,-0.04116,0.0584,0.08289,-0.07817,0.00503,-0.01032,0.0084,0.03244,-0.11027,0.03943,-0.02759,-0.03853,0.08891,0.04002,0.05433,-0.03274,-0.02285,0.05311,0.0941,0.01677,0.03194,-0.02222,0.05918,-0.10755,-0.00941,0.02898,-0.02926,0.07348,0.03907,0.05051,0.02486,-0.11545,0.08463,0.0591,-0.05697,-0.01444,-0.01381,0.04403,-0.01557,-0.06947,0.09729,-0.08233,0.13185,0.07875,-0.01,-0.08758,-0.001,-0.09216,-0.04948,0.11036,-0.01398,0.02521,0.03516,0.01835,-0.05224,0.06952,-0.04535,0.12333,0.08121,0.0627,0.17488,-0.04194,-0.07403,-0.11223,0.01737,0.08509,-0.09145,-0.01246,-0.03063,-0.11082,0.05406,-0.083,-0.02043,0.10174,-0.10531,0.00233,0.09962,0.01049,0.02342,0.03432,-0.00806,0.00557,0.0292,0.00215,0.03379,0.05571,0.04419,-0.06757,-0.0229,0.07543,0.03559,0.08637,0.03045,0.01384,0.02993,-0.01644,-0.08122,0.02076,0.00552,0.10507,0.10542,-0.03093,0.08334,0.0469,0.02444,-0.05865,0.03073,0.01801,0.101,0.01978,0.04543,-0.01383,0.09349,-0.01456,-0.06635,0.05672,-0.15748,0.01313]},{"domain":"economics_finance","key":"whole_life_insurance","name":"Whole life insurance (net single premium)","package":"economics-finance-ai999x","example":"Find the whole life insurance value with mortality rates = [0.1, 0.3, 0.6, 1], interest rate = 5%, benefit = 1000.","v":[-0.08819,-0.11698,-0.00148,0.03828,0.14329,-0.12821,-0.04679,0.06108,0.05856,-0.03898,0.03931,0.11208,-0.0165,-0.10554,-0.04535,0.00292,0.06734,-0.03473,-0.05518,0.05788,-0.01344,-0.04042,-0.04274,0.02358,0.02469,-0.00758,0.03129,0.11405,0.07707,-0.04522,-0.11257,0.10164,-0.02429,-0.02727,0.00155,-0.05612,0.0521,-0.05852,0.03556,0.02841,-0.01346,-0.1212,0.05413,0.08934,0.06578,-0.08083,-0.00044,-0.0258,0.06872,0.04634,-0.06098,-0.02103,-0.01194,-0.08743,0.07678,-0.04073,-0.02363,0.02659,0.03339,0.03726,0.015,-0.07361,-0.00734,0.0249,-0.08372,-0.05844,-0.00928,0.05193,-0.05544,-0.00722,0.10634,0.07891,0.01615,-0.13381,-0.0821,0.02202,0.07051,-0.05716,0.09843,0.00721,-0.09507,-0.03006,0.05634,-0.06786,-0.05395,-0.08004,-0.00141,-0.00983,0.13279,0.00513,0.01555,-0.05583,-0.00486,-0.05591,0.00604,-0.00918,-0.03062,-0.06842,0.11231,0.0731,0.07251,-0.07292,0.07275,-0.01567,-0.01664,-0.02741,-0.04202,-0.08841,0.07349,-0.00407,0.08713,-0.03835,0.06474,0.10098,0.02446,-0.1325,-0.03585,-0.0942,0.0007,0.03123,-0.08831,-0.01753,-0.03336,0.0359,0.10809,-0.01927,0.03504,-0.04295,0.03948,0.05461,0.06235,0.13653,0.0605,-0.09382,-0.14267,-0.0103,-0.0538,-0.01165,0.01044,0.03379,0.00362,-0.0089,0.02803,0.00851,0.04543,0.11924,-0.04446,0.00016,-0.00523,0.02596,0.02395,-0.00349,-0.07015,0.01182,0.07799,0.0511,-0.00078,0.04069,-0.02704,-0.07331,-6e-05,-0.1281,0.08016,-0.06285,0.01954,-0.06188,0.0044,-0.0431,0.02696,-0.11027,-0.05176,0.02167,-0.0137,-0.05379,-0.09168,0.16654,0.00933,-0.12768,0.1029,0.05669,0.00789,0.07571,-0.03054,-0.01682,0.10471,0.01572,-0.0722,-0.07416,-0.02189,0.006,0.13051,-0.01636,-0.00932,-0.04333,0.01855,0.03639,0.03422,0.03654,0.1349,0.01105,-0.08721,-0.0849,0.04644,0.07465,0.01428,-0.0524,-0.02412,0.04826,0.01843,0.00509,-0.04345,0.02453,-0.08131,-0.0314,0.0,0.02239,0.05864,0.06226,-0.01867,-0.03281,0.04533,0.06994,-0.03974,-0.03386,0.08736,0.01806,-0.10218,0.03069,0.00423,0.04098,0.05628,0.03101,0.11929,0.0712,0.05389,-0.03313,0.0555,-0.03208,-0.12397,0.05213,-0.05838,0.11799,0.03794,-0.07348,-0.00441,-0.00565,0.0212,-0.08049,0.13365,-0.05211,0.04139,0.02051,0.07456,0.02383,-0.06816,-0.0397]},{"domain":"economics_finance","key":"zero_coupon_bond","name":"Price of a zero-coupon bond","package":"economics-finance-ai999x","example":"Find the price of a zero-coupon bond with face = 1000, ytm = 5%, years = 10, compounding = semiannual.","v":[-0.05706,0.03608,-0.00857,-0.09611,0.02621,-0.12131,-0.02353,0.07652,-0.07305,-0.04597,-0.06923,-0.07045,-0.03135,0.01291,-0.07345,0.06503,0.02076,-0.11731,-0.05542,0.13352,-0.13451,-0.0435,0.04662,0.08405,-0.03236,0.03657,0.05202,0.06867,0.01876,0.00432,-0.01937,0.06371,-0.04856,-0.05685,0.00487,-0.03562,0.07734,-0.05711,-0.05595,-0.06576,0.00722,0.0335,0.00612,-0.05826,0.04657,-0.03661,0.02433,-0.11688,0.01407,0.03888,-0.07846,-0.03925,0.00145,-0.09654,-0.00844,0.06972,0.00617,0.0834,0.09921,0.11943,0.02735,-0.06518,-0.00118,0.02307,-0.0375,0.05498,-0.09488,0.0712,-0.0584,-0.02014,0.06855,-0.03124,0.05368,0.01559,0.02138,0.04234,-0.01528,-0.0233,0.06724,-0.06747,0.02942,0.04936,0.08582,0.00804,0.01507,-0.01381,0.05192,0.06864,0.106,-0.01052,0.00282,-0.03747,0.05997,0.01319,0.03146,-0.02997,0.02325,-0.0123,0.10812,0.01761,0.05106,-0.04475,0.01612,-0.01593,-0.03796,0.05698,0.04631,0.04159,-0.01963,0.03208,-0.01075,-0.03082,0.04685,0.07381,-0.00175,0.16044,-0.073,-0.09984,0.07266,0.04436,-0.04333,-0.01294,0.00284,-0.02193,0.03913,-0.03328,-0.01864,0.08072,0.01896,-0.04744,-0.02665,0.07501,-0.00915,-0.05287,-0.01892,-0.04221,0.05868,-0.00031,0.07983,-0.01898,0.06703,-0.00995,-0.02292,0.04878,-0.00056,0.05278,0.02082,0.03484,0.01042,0.08566,0.01985,-0.01162,0.00118,0.02444,0.13955,-0.13758,0.10183,0.0872,0.01659,-0.03042,0.01214,-0.04235,0.01498,-0.06752,-0.00363,0.11709,0.06056,0.07013,-0.04241,-0.14994,0.03256,-0.03461,-0.00197,-0.08894,-0.03686,0.02325,-0.06044,0.01118,0.06221,-0.07226,0.05034,0.13266,0.00538,-0.01348,-0.01969,-0.07283,-0.01871,-0.10356,-0.05692,0.03416,0.17764,-0.17432,-0.08572,-0.05994,-0.00571,0.02966,-0.06565,-0.0793,-0.09596,0.01239,-0.16625,-0.05659,0.06569,0.07074,-0.03305,0.00101,-0.06369,0.13,-0.0624,-0.02381,0.03571,-0.06669,0.00667,-0.03674,0.04402,-0.03403,0.13123,-0.01825,0.00275,0.08842,-0.0795,0.01556,-0.08806,-0.0255,0.06939,-0.02229,-0.03468,0.07422,-0.02645,0.10868,0.03354,0.0732,0.00527,0.07119,-0.04768,-0.05422,0.04587,0.04442,0.07647,-0.00523,0.03348,0.09261,0.04968,-0.13001,-0.11123,0.03503,-0.00173,0.01553,0.00504,-0.08653,0.00337,-0.09126,0.04867,0.0741,-0.11372,-0.1017]},{"domain":"geospatial_analytics","key":"geo_albers_equal_area_forward","name":"Albers equal-area conic projection: coordinates and scale factors","package":"geospatial-analytics-ai999x","example":"Albers equal-area forward: lat = 40, lon = -100, lat1 = 29.5, lat2 = 45.5, lat0 = 23, lon0 = -96, ellipsoid = GRS80","v":[0.07696,-0.0272,-0.01792,0.00458,-0.0064,0.01384,-0.07275,0.01086,-0.04156,0.07391,0.08344,-0.03666,-0.02589,-0.0306,0.04123,-0.02883,0.1393,0.0913,0.02051,0.05732,-0.05681,0.12662,0.11713,0.06891,-0.02724,0.07192,0.01277,0.08852,-0.08538,-0.00486,-0.09578,-0.08528,0.06202,0.14333,-0.00492,-0.03826,-0.00494,0.05455,-0.07314,0.03117,-0.03341,0.03656,-0.03257,-0.03404,-0.03695,-0.09066,-0.06975,-0.00569,-0.00213,0.01616,-0.02217,-0.08713,0.04423,0.09253,0.03062,0.01061,0.01033,-0.01812,0.10989,-0.01562,-0.05566,-0.064,-0.00315,-0.05438,0.01756,-0.04682,0.03697,-0.03547,0.08117,0.00983,0.00876,-0.00751,0.03205,-0.03789,0.00347,-0.06268,0.10432,-0.09242,0.14406,0.05957,-0.03371,-0.11673,0.02635,-0.02189,0.05013,0.01704,0.01766,0.00324,-0.02191,0.11441,-0.02524,-0.09353,0.00157,-0.07454,-0.13662,-0.11527,-0.00061,-0.06252,0.01051,-0.04581,-0.0212,0.02381,-0.01772,0.00509,0.00118,0.00704,-0.01812,-0.06162,-0.04511,0.07104,0.09637,0.05395,-0.09086,-0.17825,-0.13003,-0.00209,0.09154,0.05361,-0.00258,0.07402,-0.04493,-0.08145,0.06624,0.0489,-0.05132,-0.02584,-0.10562,-0.02383,-0.02224,0.00212,0.01192,-0.07911,-0.0648,-0.03198,-0.0926,-0.08865,-0.03866,0.02586,-0.07773,-0.0134,0.06242,-0.04504,-0.06097,-0.00711,0.00683,-0.02519,-0.09321,0.0161,0.03096,0.11309,0.0238,-0.02567,-0.04944,0.03871,0.10176,-0.10227,0.03705,-0.00955,-0.02755,-0.05763,0.08106,-0.01769,0.03545,0.05231,-0.00942,0.03303,-0.16512,0.06425,-0.01883,0.02267,0.01027,0.06497,0.09719,-0.02309,0.06177,0.00769,-0.05533,0.08027,-0.08408,-0.12905,-0.02015,-0.01849,0.06298,0.0098,0.09501,0.05196,0.00779,0.01633,0.02932,0.1074,-0.01111,0.09687,0.01362,-0.01786,0.08317,0.0246,0.01181,-0.10469,0.0745,-0.011,0.03103,-0.09804,0.04169,0.02849,0.10832,-0.00241,-0.04408,-0.02147,-0.07602,0.02397,0.00291,0.01995,-0.0394,0.20449,0.00718,-0.01974,0.02347,-0.04987,-0.11947,0.03811,-0.04777,-0.14324,0.00451,-0.01452,0.02374,-0.00347,0.02808,0.01549,0.06975,-0.01659,-0.01923,-0.01111,0.0233,-0.052,-0.0164,-0.01401,0.09508,-0.03982,-0.01074,-0.05609,0.06631,0.1555,-0.02792,0.00377,-0.02775,0.02997,0.03598,-0.06907,0.05456,-0.02371,-0.01566,0.18795,0.03619,0.02119,0.06095,0.00661]},{"domain":"geospatial_analytics","key":"geo_albers_equal_area_inverse","name":"Inverse Albers equal-area conic projection","package":"geospatial-analytics-ai999x","example":"Albers equal-area inverse: x = -338796.0 m, y = 1952260.0 m, lat1 = 29.5, lat2 = 45.5, lat0 = 23, lon0 = -96, ellipsoid = GRS80","v":[0.09567,0.00438,-0.02186,-0.00523,0.034,0.04747,-0.10909,-0.01554,-0.05837,0.05958,0.04146,-0.00905,-0.0398,-0.07057,0.01515,-0.01656,0.1607,0.05372,-0.01069,0.03285,-0.15549,0.09571,0.0381,0.09977,-0.05645,0.0726,0.0141,0.08664,-0.06556,-3e-05,-0.10221,-0.12298,0.03697,0.12521,0.02766,-0.03662,-0.02355,0.01315,-0.06019,-0.00345,-0.01159,0.03452,-0.02387,-0.04058,-0.00458,-0.08529,-0.11792,-0.01837,-0.02133,0.07745,0.00986,-0.12283,0.01945,0.08066,0.01953,0.01631,0.05105,-0.04697,0.06327,-0.0448,-0.05784,0.00031,-0.0349,-0.05914,0.0198,-0.09398,0.03448,-0.07837,0.08691,0.03672,-0.04932,-0.05501,0.0776,-0.07126,-0.02698,-0.10089,0.07179,-0.01578,0.13451,0.09104,-0.01196,-0.05028,0.05349,0.01598,0.06562,0.03318,-0.00958,-0.02215,-0.00762,0.1221,0.01571,-0.09701,0.03696,-0.05132,-0.13409,-0.09637,-0.05538,-0.04488,-0.01047,-0.07954,-0.02874,0.0124,0.05997,-0.01116,0.02236,-0.03423,-0.02156,-0.02876,-0.09414,0.03726,0.09635,0.07339,-0.17102,-0.16988,-0.11483,-0.04554,0.12617,0.01703,-0.00539,0.07878,-0.06873,-0.08772,0.06606,-0.00761,0.01619,0.0453,-0.0541,0.01727,-0.00745,-0.00204,0.01634,-0.07432,-0.10721,0.01569,-0.08459,-0.03872,-0.06163,0.04926,-0.07392,-0.03676,0.04016,-0.047,-0.09425,-0.04824,-0.00094,-0.06329,-0.05094,0.03006,0.03651,0.06894,0.0258,0.01662,-0.03762,0.07965,0.09481,-0.0715,0.01423,0.01453,0.03184,0.01826,0.10093,-0.05541,0.00806,0.08291,-0.05328,0.0251,-0.11577,0.06829,-0.05957,0.0722,0.02691,0.0347,0.12818,-0.04381,0.0347,-0.03529,-0.05756,0.04314,-0.09246,-0.13187,-0.01219,-0.01069,0.03941,-0.01082,0.11763,0.07166,0.04755,0.01615,0.05083,0.10661,-0.02848,0.07263,-0.00906,0.00075,0.06519,0.0276,0.03159,-0.09859,0.03408,0.01674,-0.00299,-0.05914,0.04231,0.0091,0.06425,-0.01227,0.01636,0.00996,-0.08063,0.01997,0.02566,-0.00675,-0.04247,0.17227,0.03704,-0.07279,0.06139,-0.06368,-0.06709,0.04225,-0.04001,-0.06735,-0.06389,0.01318,0.05665,0.00319,0.03888,0.04948,0.08216,-0.0074,0.00847,-0.02108,0.02558,0.00447,-0.05709,-0.02654,0.06807,0.03301,-0.03719,-0.02433,0.05253,0.11922,-0.01782,-0.00911,0.002,0.03272,0.05266,-0.04295,0.07279,-0.05195,-0.07928,0.14456,0.03951,0.01564,0.04656,0.01018]},{"domain":"geospatial_analytics","key":"geo_auxiliary_latitudes","name":"Auxiliary latitudes: geocentric, reduced, conformal, authalic and rectifying","package":"geospatial-analytics-ai999x","example":"Auxiliary latitudes: lat = 45, ellipsoid = WGS84","v":[0.01152,-0.03328,0.05209,0.04474,0.09133,0.03674,0.04151,-0.05314,-0.02879,0.09345,-0.00549,-0.10594,-0.03727,-0.05187,-0.0447,0.0643,0.11875,0.07143,0.01218,0.03817,-0.07875,-0.03356,-0.00531,0.12853,0.02888,-0.04314,0.01307,-0.10956,0.05319,0.02799,-0.11961,-0.08315,-0.04119,0.05292,0.0682,-0.0476,0.02071,-0.0172,-0.00691,-0.16275,0.05332,-0.04614,-0.02036,0.03568,0.05222,-0.03616,-0.01339,0.0208,0.03659,-0.0498,0.01717,-0.13466,0.05883,-0.10201,-0.08742,-0.00335,-0.07657,-0.04453,0.00998,-0.0468,0.08344,0.00991,0.01671,-0.03109,0.01858,0.02331,0.07173,-0.07204,0.05175,0.05286,-0.00084,-0.04222,0.01249,-0.00196,0.0364,-0.09443,-0.05151,0.00927,-0.15284,-0.01415,0.01032,0.09219,0.05152,0.14699,-0.03768,-0.03343,-0.12559,-0.07932,0.11645,0.02775,0.07084,-0.0596,-0.0221,0.00566,-0.03959,0.05395,-0.05652,0.02335,0.03286,-0.08229,0.04626,-0.02533,0.18461,0.0398,0.05358,-0.0903,0.00912,0.06909,-0.09843,-0.03489,0.14977,0.08806,-0.0841,-0.06317,-0.00995,0.08864,0.045,0.05211,-0.00477,-0.00632,-0.06589,0.02205,0.0408,-0.07811,0.0017,0.05215,0.04748,0.08217,0.0166,-0.01594,0.01547,-0.10649,0.04203,0.02149,0.01724,0.13334,0.05608,0.04094,-0.07928,0.0277,0.05789,-0.04992,0.0674,-0.06708,0.02538,0.00677,0.07044,-0.0229,-0.05579,0.02121,-0.00187,0.00413,-0.00138,0.02275,-0.01781,0.03643,0.04688,-0.05984,-0.04735,0.05334,0.0356,-0.1102,0.06152,-0.01337,-0.06243,0.03918,0.02892,0.03263,-0.05741,0.12016,0.00779,0.08167,0.07723,-0.0214,-0.07757,-0.06009,-0.10206,0.05322,0.0093,-0.06929,-0.04869,-0.0067,-0.01839,-0.03359,0.10539,-0.06066,-0.12636,-0.04698,0.0049,0.01438,-0.01324,0.11067,-0.00638,-0.02875,-0.02175,0.00925,0.05758,0.02419,0.05419,0.08518,-0.02557,-0.01733,-0.01573,-0.06995,-0.13115,-0.11322,0.03395,-0.03834,-0.06908,-0.00156,0.05263,-0.02524,-0.0348,0.10337,0.06588,-0.09509,-0.02475,0.00788,-0.04823,-0.08931,-0.03156,-0.09761,-0.00625,0.0555,0.10132,-0.06776,-0.00833,-0.08912,0.06232,-0.01318,0.02438,0.08418,-0.05129,-0.01215,-0.00913,-0.02876,0.08328,0.05963,0.02222,-0.17262,0.06435,0.07198,-0.04855,-0.0228,0.03701,0.03282,0.03895,0.00374,0.02456,-0.11832,0.01318,0.06935,0.09699,-0.01911,-0.04085,0.05533]},{"domain":"geospatial_analytics","key":"geo_azimuthal_equidistant_forward","name":"Azimuthal equidistant projection (ellipsoidal, geodesic)","package":"geospatial-analytics-ai999x","example":"Azimuthal equidistant forward: lat = 40.71, lon = -74.01, lat0 = 51.5, lon0 = -0.13, ellipsoid = 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facility for every node of a network","package":"geospatial-analytics-ai999x","example":"Closest facility: edges = [0-1 2; 1-2 3; 0-2 6; 2-3 1; 3-4 4], facilities = [0, 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cylindrical equal-area projection (sphere)","package":"geospatial-analytics-ai999x","example":"Cylindrical equal-area forward: lat = 45, lon = 10, lat_ts = 45, lon0 = 0, R = 6371000 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degrees to degrees, minutes and seconds","package":"geospatial-analytics-ai999x","example":"Decimal degrees to DMS: decimal = 51.477222, axis = 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population density gradient (Clark's negative exponential model)","package":"geospatial-analytics-ai999x","example":"Density gradient: r = [1, 2, 4, 6, 8, 10], D = [9000, 7600, 5300, 3900, 2800, 2000]","v":[-0.0278,-0.06804,-0.05235,-0.03228,0.02095,-0.009,-0.05586,-0.03641,0.03634,-0.09259,-0.02445,-0.08036,0.02233,0.09655,-0.01052,0.01028,0.03497,-0.00445,0.00986,-0.0494,0.01265,-0.1013,0.12644,-0.07213,-0.02303,0.00606,0.06009,-0.07162,-0.09906,-0.08179,0.01698,-0.00963,0.02937,-0.10595,0.04965,0.05203,0.05954,0.12157,-0.04638,0.03712,-0.02668,0.06672,0.03001,-0.01012,-0.11019,0.08729,-0.0299,-0.04791,0.01077,-0.10148,-0.00981,0.08577,0.00485,0.01452,-0.16339,-0.06718,0.12763,-0.00996,0.00868,0.00709,0.07094,-0.01555,0.0576,0.02312,0.09484,-0.0502,0.06634,0.07455,-0.14081,0.18941,0.11668,-0.02877,-0.09457,0.00577,0.03197,0.11217,0.03737,-0.08688,0.01149,0.03511,0.02553,0.0578,-0.00509,-0.02872,-0.04365,0.01581,0.04235,0.00858,-0.07867,-0.03589,-0.0817,0.0508,0.15649,-0.06948,-0.09424,0.07653,-0.00403,0.04987,0.07647,-0.0107,0.04332,0.0117,0.0134,-0.06196,-0.00519,-0.03612,0.0135,-0.10729,0.09075,-0.01813,-0.03897,0.01369,0.00261,0.02333,0.04884,-0.00427,0.01415,0.15447,-0.01782,-0.04772,0.08035,-0.10922,-0.06364,0.10573,-0.09321,-0.09154,-0.02457,-0.001,-0.03761,-0.05715,-0.01944,0.00217,0.04552,-0.03595,-0.04051,0.13807,0.04119,-0.01408,0.07968,-0.06401,0.0613,-0.01304,0.04168,0.00313,0.04151,0.10834,-0.01474,-0.02675,0.07593,0.0094,-0.02595,-0.03397,0.02919,-0.04212,0.12992,-0.0948,-0.02073,-0.02662,0.04507,0.10011,0.01911,-0.00667,-0.03647,-0.04057,0.07289,0.01991,0.07699,-0.10392,0.01882,-0.01639,-0.13909,-0.07076,0.05888,-0.01921,-0.02669,-0.04233,-0.04574,0.0233,-0.01915,0.1092,-0.00571,0.04518,-0.0053,0.00432,0.08953,-0.04215,0.02539,0.04119,-0.02582,-0.06189,0.08289,0.00747,0.02209,-0.0311,0.04451,-0.00483,0.02315,-0.0029,0.01684,-0.16358,-0.05917,-0.02359,0.00281,-0.13552,-0.04428,-0.04103,0.11789,-0.07731,0.07372,0.09276,0.0119,-0.01355,0.12882,-0.00696,-0.04601,0.00858,0.0432,0.05973,-0.0351,0.08452,0.00434,-0.00573,0.17637,0.04391,-0.02444,-0.00523,-0.09649,0.02229,-0.03329,-0.0084,0.06294,0.0241,0.06521,-0.0288,-0.07675,0.01151,-0.02544,-0.06874,-0.02502,0.05099,0.02244,-0.05205,0.06271,-0.02026,-0.12875,-0.07123,-0.06241,0.01756,-0.06916,-0.01788,-0.01735,-0.00115,0.00568,-0.00026,0.02801,-0.00405]},{"domain":"geospatial_analytics","key":"geo_detour_index","name":"Network detour index (circuity) between two nodes","package":"geospatial-analytics-ai999x","example":"Detour index: coords = [[0, 0], [3, 0], [3, 4], [0, 4]], edges = [0-1; 1-2; 2-3], origin = 0, destination = 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Frechet distance between two polylines","package":"geospatial-analytics-ai999x","example":"Frechet distance: x1 = [0, 1, 2], y1 = [0, 0, 0], x2 = [0, 2], y2 = [1, 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2.5","v":[-0.10181,-0.06561,0.05127,-0.04046,-0.05199,-0.01138,-0.05506,-0.00205,0.08958,-0.10148,-0.07776,0.02957,-0.00705,-0.02903,-0.04275,-0.03917,-0.02215,0.00666,-0.09004,0.00326,-0.04743,-0.20574,-0.01762,-0.01345,-0.03402,0.07802,-0.0224,-0.0685,-0.06489,0.00226,0.13207,-0.01137,-0.03594,-0.02314,0.02082,-0.08571,0.02638,0.05571,0.00509,0.05276,0.02826,0.0536,-0.01011,0.06079,-0.17795,-0.00858,-0.03072,-0.02446,-0.08329,-0.00632,0.03623,0.0352,0.042,0.01252,0.01874,0.0018,0.03564,0.01688,0.04898,0.12077,-0.00841,-0.02393,-0.10741,-0.11818,-0.05026,0.01248,-0.01569,0.15922,0.00643,0.1066,-0.03711,-0.09703,0.06222,-0.09414,-0.1051,-0.01066,-0.11776,-0.06793,0.05301,0.00013,-0.01588,-0.02097,0.01808,-0.03746,0.00464,0.00743,0.02979,0.00286,-0.0205,-0.00569,-0.057,0.02368,0.04297,0.02393,0.02499,-0.00463,0.03334,0.16134,-0.16446,0.06966,0.02058,-0.00229,-0.09724,-0.03915,-0.02453,-0.07056,-0.03138,-0.11713,-0.09768,-0.01445,-0.00426,-0.11955,-0.05582,0.02666,0.02905,0.05699,0.06473,0.07627,0.04504,0.0997,-0.01076,-0.03497,0.00412,-0.06449,-0.00117,0.06956,-0.06429,-0.05603,0.05518,-0.13494,0.03774,0.09474,0.02376,0.01386,0.05542,0.06851,-0.02631,-0.06969,0.03421,-0.00933,0.00106,-0.00104,-0.032,-0.01217,-0.01007,-0.03884,-0.03237,0.01469,-0.02397,-0.10492,0.06016,0.06103,0.10987,0.03651,0.06957,-0.10498,0.08798,-0.03453,-0.03295,0.15214,-0.02409,0.02176,-0.06651,0.0222,0.23104,0.04051,0.09331,-0.04864,-0.01245,-0.05095,0.0446,-0.04163,-0.04443,-0.02554,0.01843,-0.04465,0.02458,-0.01721,0.02787,0.10553,0.06517,0.08125,-0.04823,-0.01089,-0.0832,0.00832,0.04328,0.12336,-0.00362,-0.01166,0.05154,0.00755,0.0432,0.12,-0.03986,0.05539,0.01747,-0.03961,0.05566,-0.02627,-0.08572,0.03472,0.04213,-0.04837,-0.00149,-0.02582,-0.04441,0.01665,-0.02077,0.07166,0.0605,-0.03659,0.07328,-0.01471,-0.02013,0.03808,0.11126,-0.03726,0.01734,0.12707,0.00143,0.02401,-0.03353,0.05737,0.08288,0.0502,-0.02955,-0.02528,0.03985,0.02998,-0.01612,0.06456,-0.04385,-0.00712,0.01925,0.00457,0.03591,0.0927,0.0073,-0.06345,0.05564,0.03343,-0.01054,-0.01298,-0.13447,-0.03609,0.00144,0.08899,0.02349,0.00385,0.09733,0.01787,-0.17319,-0.04169,-0.04398,-0.03599]},{"domain":"geospatial_analytics","key":"geo_dms_to_decimal","name":"Degrees, minutes and seconds to decimal degrees","package":"geospatial-analytics-ai999x","example":"DMS to decimal degrees: degrees = 51, minutes = 28, seconds = 38, hemisphere = N","v":[-0.00915,0.02526,-0.11754,0.02197,0.13257,0.04377,0.01425,-0.13498,0.00467,-0.0424,-0.0273,0.04342,0.04993,0.05278,0.04574,-0.0048,-0.00024,0.00584,-0.10536,-0.03719,-0.21844,-0.00407,-0.07138,0.0185,0.02374,-0.05439,-0.05802,0.07889,0.03298,0.05843,-0.08467,0.05214,-0.09904,-0.01903,0.0393,-0.09149,-0.02141,-0.06838,0.01748,-0.05464,-0.08484,-0.04982,0.00768,0.02231,0.10601,0.01613,-0.0163,0.01108,-0.01671,-0.028,0.04368,-0.07069,0.02568,-0.03791,-0.00947,-0.06664,0.01677,-0.00645,0.01215,-0.02785,0.00737,0.07307,-0.00995,0.0426,0.06516,0.05277,-0.00723,-0.07446,-0.07895,0.03089,-0.06808,-0.07956,-0.06647,0.07429,0.11782,-0.09872,0.08021,0.00082,0.00416,-0.03455,-0.00339,0.10534,0.15255,0.02217,0.06288,0.03796,0.00247,0.03762,0.05785,0.05802,-0.02397,-0.07882,0.00573,-0.0656,0.00365,-0.00751,-0.02196,0.01272,-0.05499,0.02257,-0.00934,-0.02229,0.1019,-0.00175,0.07657,-0.09066,0.00694,0.12683,-0.15075,-0.02277,0.15058,0.00884,-0.09016,-0.01493,-0.00291,-0.00695,0.00867,0.0381,-0.07193,0.03681,-0.0616,0.0156,-0.0183,-0.10453,0.04315,0.0308,0.07188,0.10829,0.06414,-0.07811,-0.03459,-0.00694,0.0702,-0.02985,0.03259,0.04115,-0.00327,-0.02158,-0.0376,0.08748,-0.00674,0.01753,-0.14035,-0.09179,0.03321,-0.04417,0.04432,0.20328,-0.0166,-0.02663,0.03165,0.01146,-0.02445,-0.01081,-0.02986,0.02798,0.04022,-0.00439,0.05173,0.06506,0.06782,-0.01491,-0.0538,0.07721,0.04083,-0.03468,-0.00481,0.09316,-0.05827,0.03216,0.00534,0.04647,0.15049,0.11793,-0.1083,-0.03783,0.03791,-0.08433,0.00246,-0.04646,-0.0275,0.02675,0.01423,-0.07064,0.11469,0.04342,0.05574,-0.02588,0.06647,-0.01497,-0.09764,-0.02079,-0.02113,0.00952,-0.01924,0.05338,-0.00284,0.11734,0.10897,0.07905,-0.1163,0.02862,-0.00202,-0.06471,-0.04787,0.01613,0.01192,-0.04924,-0.04766,-0.14386,0.07235,0.04744,0.04514,0.07272,-0.01506,-0.03408,-0.09509,-0.0501,-0.04616,-0.05901,-0.07922,0.01563,-0.05543,-0.01811,0.11717,-0.06018,0.09381,-0.10489,0.04836,0.03928,0.05305,-0.08377,0.05587,0.11335,-0.08728,0.03789,-0.03626,0.05335,0.00849,-0.01073,0.02663,0.05943,-0.07622,0.00583,-0.01475,0.09137,-0.01544,-6e-05,-0.04011,-0.05825,0.03143,0.07008,-0.00387,-0.05403,-0.04911,-0.05545]},{"domain":"geospatial_analytics","key":"geo_douglas_peucker_simplification","name":"Douglas-Peucker line simplification","package":"geospatial-analytics-ai999x","example":"Douglas-Peucker simplification: x = [0, 1, 2, 3, 4, 5, 6, 7], y = [0, 0.1, -0.1, 5, 6, 7, 8.1, 9], tolerance = 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(ECEF) to geodetic coordinates","package":"geospatial-analytics-ai999x","example":"ECEF to geodetic: X = 4517590.879 m, Y = 796576.168 m, Z = 4487348.409 m, ellipsoid = WGS84","v":[0.0234,-0.03621,0.02175,-0.01644,0.07669,0.03227,-0.10043,-0.01644,-0.00425,-0.00064,-0.00842,-0.13909,-0.10365,-0.04126,-0.06438,0.02789,0.13143,0.08819,-0.03816,0.05473,-0.08292,-0.06612,-0.04112,0.11384,-0.00985,-0.0017,0.0279,-0.04147,-0.00697,0.06002,-0.05265,-0.09362,-0.11386,-0.01249,0.02821,-0.01375,0.04204,-0.00978,0.0194,-0.22387,0.01757,0.02836,-0.08664,0.14075,-0.05486,-0.01908,-0.02695,-0.0216,0.01278,-0.04744,0.04137,-0.05201,0.10089,0.00771,-0.12656,0.06756,-0.05129,-0.0125,-0.12723,0.00498,-0.00674,-0.06403,0.02252,0.00451,0.00801,-0.03216,0.00567,-0.04305,0.10351,0.081,0.02098,-0.0709,0.03882,0.01423,0.02077,-0.02726,-0.01488,-0.01835,0.00237,-0.05944,0.03745,0.14268,-0.02257,0.07729,-0.07989,0.02579,-0.15215,-0.0825,0.04107,-0.05354,0.05978,-0.11652,-0.08081,0.05084,0.05349,0.09106,-0.07205,0.04082,0.01314,-0.12075,0.05164,-0.01534,0.12734,-0.00358,0.03609,-0.04591,-0.01813,0.06023,-0.09285,-0.07284,0.07332,0.08995,-0.00715,-0.03905,0.06169,0.05922,0.09415,0.08693,-0.02965,-0.00028,0.02826,-0.0262,0.02445,-0.08844,0.03858,-0.01538,0.06533,0.01525,0.106,-0.0738,-0.02521,-0.06258,-0.00041,0.04546,0.09672,0.11502,0.04615,0.00886,0.00129,-0.04001,-0.04238,0.01032,-0.01126,0.01628,0.00342,0.01084,0.00536,-0.08102,0.07135,-0.00592,0.02483,0.0781,0.03403,0.05171,-0.00278,0.06621,0.09226,0.05336,-0.00574,0.05341,0.02189,-0.07843,0.04936,0.00551,-0.14004,0.04055,0.01987,0.05202,-0.03636,0.16337,0.13206,-0.06089,0.06598,0.01921,-0.01837,-0.05451,-0.08907,0.05964,0.01275,0.08173,0.06581,-0.06424,-0.06055,-0.0852,0.03024,0.01036,-0.04469,-0.02787,0.02629,-0.02541,0.07976,0.01359,-0.00194,0.01636,-0.05162,-0.02566,0.01611,0.06038,0.03689,0.03744,-0.13209,-0.00374,0.05417,0.02008,-0.06178,-0.1094,0.00353,0.0269,-0.04385,-0.04943,0.0232,0.03113,0.03475,-0.03505,-0.01035,-0.05997,-0.02267,-0.01492,-0.05905,-0.07373,-0.01249,0.01194,-0.07933,0.03664,0.10624,-0.04968,0.00792,-0.02956,-0.02447,-0.02162,0.05053,-0.01204,-0.07258,0.02099,0.03808,-0.05778,0.0668,0.13607,-0.0286,-0.09654,-0.05159,0.13478,0.03785,-0.06579,0.04834,0.00916,-0.01065,0.08521,0.1036,-0.11266,0.0365,-0.02066,0.0569,-0.09742,-0.06219,-0.03338]},{"domain":"geospatial_analytics","key":"geo_empirical_semivariogram","name":"Empirical 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4.5]","v":[-0.0705,-0.05921,0.08091,0.01282,0.05933,0.00924,0.00524,-0.01451,0.00383,-0.11212,0.08822,-0.06247,-0.09358,-0.08712,0.01138,0.11489,0.05885,0.01586,-0.0962,-0.00429,0.00273,-0.08082,0.07748,-0.0635,0.05674,0.11387,-0.01202,-0.06828,-0.10769,0.03415,0.06344,0.00679,-0.08466,0.01967,0.04102,-0.02906,-0.00479,0.04154,-0.02035,0.01667,-0.046,0.07528,-0.02307,0.01093,-0.11549,-0.06709,0.03698,0.00627,-0.1025,-0.05583,0.02076,0.06437,0.06438,0.08892,-0.05316,0.11501,0.11751,0.10246,0.12052,0.0237,-0.00379,-0.03324,-0.1176,-0.0149,-0.08717,0.05624,0.03282,0.06676,-0.03832,0.06049,0.00781,-0.07284,0.11067,0.00699,-0.00511,0.12804,-0.0908,0.01608,-0.01094,-0.08477,0.05074,0.05325,-0.04714,0.06391,0.06139,0.0191,-0.06587,0.07454,0.00719,0.01338,-0.02777,-0.02925,0.02686,0.00455,-0.0039,-0.00719,0.034,0.05112,-0.03066,0.03621,0.01399,0.10817,-0.02328,-0.05926,-0.00749,-0.05106,-0.13982,-0.07203,-0.0439,-0.05809,-0.08646,-0.09056,-0.01631,0.10439,-0.00603,0.07119,0.08529,0.02412,-0.03899,0.00891,0.04469,0.06063,0.01905,-0.00812,-0.0938,0.12461,-0.03058,0.04367,-0.01208,-0.0292,0.0162,0.0761,0.04346,-0.05863,-0.01936,0.11785,-0.06583,-0.00661,-0.03734,0.04593,-0.04568,0.01735,0.11928,0.03298,-0.04599,-0.07187,-0.08753,0.01299,0.02962,0.07596,0.10102,-0.00641,0.11775,-0.08651,0.10751,-0.0299,0.09783,0.01279,-0.02853,0.13898,-0.09953,0.04539,0.02124,-0.08632,0.04231,-0.06235,-0.01349,0.07186,-0.04885,0.04131,-0.05432,-0.04007,0.03735,0.03706,0.0163,-0.13742,0.03398,0.13376,-0.0798,0.08937,-0.05737,-0.00289,0.00254,-0.00854,0.08061,-0.03286,-0.00884,-0.02908,0.03217,0.03273,-0.0678,-0.07533,0.00934,0.07569,0.05191,-0.0664,-0.06417,-0.08719,-0.03991,-0.00525,-0.01158,0.00642,-0.04371,-0.02812,0.01363,-0.05634,-0.04323,-0.09269,0.03449,0.02397,-0.0779,-0.08572,0.06053,0.03913,0.0391,0.07131,0.05839,-0.03134,-0.02216,0.06441,0.01864,0.05062,-0.05827,0.03971,-0.05291,-0.05006,0.04268,0.07929,-0.05615,0.0475,0.05787,-0.00036,-0.07721,0.02424,0.01108,-0.08253,0.01099,0.08992,0.11607,-0.07949,0.04655,-0.01258,0.02256,0.02184,-0.04246,-0.10074,-0.04658,0.06297,0.06432,-0.02054,0.08084,-0.06339,-0.11377,-0.09665,-0.11363,-0.01606]},{"domain":"geospatial_analytics","key":"geo_enu_to_geodetic","name":"Local east-north-up (ENU) to geodetic coordinates","package":"geospatial-analytics-ai999x","example":"ENU to geodetic: lat0 = 46.017, lon0 = 7.75, h0 = 1673 m, e = -7123.1 m, n = -4557.3 m, u = 2848.2 m, ellipsoid = WGS84","v":[-0.02447,0.08003,-0.07818,0.03818,0.03998,-0.0173,-0.07471,-0.00242,-0.06142,-0.06653,-0.04117,0.0298,-0.071,0.09161,-0.01215,0.07876,0.16305,-0.00176,0.0114,-0.03848,-0.13431,-0.01784,-0.01499,0.06254,-0.0617,0.03721,-0.01863,-0.0702,-0.05538,0.07194,-0.01563,-0.08505,0.05152,0.02526,0.05241,-0.07805,0.08546,0.04935,0.02988,-0.09879,0.07416,0.023,-0.03772,0.00303,-0.08683,0.02451,-0.0798,-0.04659,-0.11248,-0.0996,0.04698,-0.05245,0.08742,0.01629,-0.09389,-0.02801,0.00798,-0.02968,-0.0175,0.0276,-0.05391,0.0194,0.07822,-0.09672,-0.00138,0.07876,0.00672,-0.07887,-0.02158,0.09942,-0.15506,-0.1802,0.01514,0.00749,-0.01457,-0.10758,0.04078,0.03804,-0.01833,0.04916,0.10991,0.03331,0.04605,0.02034,-0.02681,0.00054,-0.0906,-0.06057,0.0513,-0.01226,0.09214,-0.02735,-0.10401,0.04985,-0.06466,0.0376,-0.05633,0.06405,-0.01813,0.01063,-0.03916,-0.03989,0.10116,-0.07657,0.03286,-0.10786,-0.01309,0.01533,-0.20295,-0.05562,0.05807,-0.00369,-0.06319,0.01784,0.05478,0.01535,0.0576,0.02919,-0.03555,0.02466,0.02318,-0.07228,-0.00565,-0.10629,0.09242,0.05997,0.08185,0.02223,0.12408,0.03543,0.02839,-0.01817,-0.02777,-0.00992,0.0415,0.07968,0.0344,0.0441,-0.06614,0.00724,0.10003,-0.01082,-0.04458,-0.05182,0.04672,0.01084,-0.02793,-0.05383,0.08422,-0.00666,-0.06367,0.02176,0.0254,0.08271,-0.08048,0.0678,-0.03451,0.03953,-0.03909,0.0983,0.06325,-0.05787,0.02887,0.07601,0.06008,0.13855,-0.01572,0.06623,-0.05829,0.08169,0.01189,0.00051,0.0501,0.0178,-0.09227,-0.00676,-0.04525,0.08656,0.03838,-0.09005,-0.01318,-0.02412,-0.01298,-0.08042,0.03198,-0.01883,0.02639,0.07847,0.00931,0.01815,0.03383,0.03085,0.0882,0.12988,-0.02785,-0.03261,-0.02164,-0.00403,-0.00342,0.04703,-0.12438,-0.01669,0.14973,-0.02198,-0.06495,-0.0619,0.08623,0.03137,0.00346,-0.02842,0.07057,-0.00846,0.02826,0.05664,0.00927,-0.02436,-0.00342,-0.02116,-0.05658,-0.108,-0.09316,0.05465,-0.08939,0.10279,0.00137,-0.01265,0.03864,0.06488,-0.02679,-0.07313,0.05462,0.01459,-0.02254,0.03765,-0.03363,0.01316,0.06875,0.06068,0.04803,-0.00063,0.06591,-0.04391,-0.10424,-0.10671,-0.00065,0.01137,0.10418,0.07743,0.05874,-0.00829,-0.01204,-0.14622,0.05863,-0.10218,0.01505,-0.01228]},{"domain":"geospatial_analytics","key":"geo_equirectangular_forward","name":"Equirectangular (equidistant cylindrical / plate carree) projection","package":"geospatial-analytics-ai999x","example":"Equirectangular forward: lat = 45, lon = 10, lat_ts = 0, lat0 = 0, lon0 = 0, R = 6371000 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C spatial autocorrelation with normal and randomization inference","package":"geospatial-analytics-ai999x","example":"Geary's C: y = [8, 6, 6, 3, 2, 1], W = [[0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0]], transform = row","v":[-0.03404,-0.03001,0.00154,0.00572,-0.07587,0.04282,-0.06613,0.0032,0.0897,-0.07047,0.08432,-0.01057,-0.07967,0.01589,0.05198,0.00724,-0.04187,-0.03292,-0.11298,-0.03988,0.00256,-0.14756,-0.03667,0.07277,-0.02847,0.10929,-0.05003,-0.084,-0.04342,-0.00393,0.05352,-0.00708,0.07055,0.06172,0.05004,-0.00984,-0.03836,0.01676,0.01502,0.01802,0.10531,-0.07444,-0.07031,0.05678,-0.04244,-0.05331,0.08389,-0.03954,-0.03703,0.02715,0.03171,0.01108,0.13521,0.05404,-0.05775,0.01642,0.01146,0.00505,0.01236,0.16428,0.07274,0.02949,0.02409,-0.12453,-0.07591,-0.05479,-0.02279,0.1213,0.02654,-0.02391,-0.07742,-0.0292,0.1046,0.01949,-0.04909,-0.00879,-0.14049,-0.01807,0.07325,-0.04992,-0.00196,0.07622,-0.03011,-0.05275,-0.02834,0.03579,-0.03582,0.05941,-0.06396,-0.06347,-0.08986,-0.02486,-0.04284,-0.0293,0.03969,0.01945,0.02055,0.09481,-0.10937,0.0853,0.03067,-0.02545,-0.11921,-0.0385,0.0647,-0.09898,-0.00948,0.03155,0.03871,0.06729,-0.08307,-0.0282,-0.14445,-0.01518,0.04648,0.07151,0.0835,0.00488,0.05244,0.04869,-0.01168,-0.0198,0.03224,-0.00357,-0.0638,0.10931,-0.07006,-0.06297,-0.04869,-0.05011,-5e-05,0.1069,0.05388,-0.06404,0.10115,0.06965,-0.01361,-0.02961,0.00516,0.06109,0.06066,-0.00093,-0.06403,-0.01736,0.01749,-0.11222,-0.05987,-0.02638,-0.01061,-0.07592,0.04955,-0.03781,0.10294,0.05443,0.03653,-0.01573,0.11976,-0.10841,0.01457,0.11577,-0.05739,0.0427,-0.00482,-0.0896,0.18276,0.00361,0.05606,0.12867,0.02887,0.01325,0.07309,-0.00428,-0.09359,-0.04231,-0.0119,0.09876,0.03646,0.05354,0.00673,-0.01964,-0.01671,0.00862,-0.06326,-0.08918,-0.01856,-0.01039,-0.03019,0.12735,-0.01578,-0.01212,0.07229,-0.01747,0.06194,0.06291,-0.01403,-0.03205,-0.07026,-0.01639,0.00321,-0.02407,-0.04431,-0.07236,0.00963,0.00142,0.02538,-0.05682,-0.00995,0.02365,-0.01138,0.0713,0.03296,-0.04334,-0.05936,0.01515,0.03596,-0.02703,0.1116,-0.16454,-0.07972,0.11547,-0.03727,-0.03861,-0.0636,0.08882,0.09593,-0.01872,-0.00284,-0.03828,-0.02024,-0.01903,-0.02369,0.05004,0.00341,-0.05252,0.08869,0.00193,0.0022,0.14723,0.03713,-0.01478,0.03969,0.04647,0.05651,-0.00656,-0.05147,0.02657,0.00941,0.11263,0.01956,0.07553,0.09222,-0.06129,-0.15013,-0.05213,-0.05902,-0.02564]},{"domain":"geospatial_analytics","key":"geo_geodesic_destination","name":"Geodesic destination point on the ellipsoid (direct problem)","package":"geospatial-analytics-ai999x","example":"Geodesic destination: lat1 = 52.2, lon1 = 0.12, azimuth = 45, distance = 100 km, ellipsoid = WGS84","v":[0.06525,0.01406,0.04194,-0.00783,-0.00112,0.0101,0.01294,-0.04909,0.01811,-0.04586,-0.02196,-0.02257,0.06774,0.03979,0.057,0.05949,0.1075,0.02951,-0.01666,0.10231,0.02555,-0.01922,-0.00438,0.14031,0.01056,0.00258,-0.06775,0.05387,0.04657,0.08457,0.03285,-0.04237,-0.0486,0.05413,0.0148,0.04913,-0.03596,0.12628,-0.00717,-0.13331,0.06332,-0.00813,-0.05347,0.00621,-0.09602,0.06414,-0.00404,0.05067,0.05693,-0.13804,0.0408,-0.06056,0.15348,0.01993,-0.09389,0.08838,-0.0226,0.01639,0.02953,-0.02126,0.06167,-0.01431,0.00307,-0.10101,0.01194,-0.01039,0.06003,-0.07048,-0.02332,-0.05343,-0.06388,-0.06605,0.05018,0.02947,0.04295,-0.01317,-0.053,0.04358,-0.17256,-0.04921,0.1191,0.03135,0.07607,0.10419,-0.05243,0.03292,-0.15868,-0.03257,0.08734,0.0337,-0.03974,-0.10236,-0.01261,-0.06684,-0.04471,-0.0174,0.02184,0.14449,-0.01143,-0.10721,0.08454,0.00474,0.07036,-0.02624,0.05014,-0.10139,-0.07291,0.02129,-0.11114,0.02756,0.09009,0.0977,-0.05338,-0.03954,0.04507,0.09247,-0.08904,-0.0444,-0.02616,-0.01596,0.02025,0.05087,-0.01426,-0.04189,-0.06432,-0.02435,-0.02695,0.03675,0.10945,0.00691,0.00507,-0.04628,-0.00897,-0.04975,0.07461,0.03358,0.08893,-0.00178,-0.02706,-0.1244,-0.026,0.07336,-0.0784,-0.03878,0.11348,-0.01205,0.04576,-0.04052,0.01899,0.03204,-0.03563,-0.0035,3e-05,0.01052,-0.04202,0.05954,-0.04826,-0.04767,0.10184,-0.07001,-0.04369,-0.09788,0.04966,0.02837,-0.07981,0.04564,-0.01017,-0.03,-0.04375,0.07294,0.00997,0.00398,0.01025,0.00516,-0.01921,-0.10281,-0.11193,-0.01388,-0.09858,0.04426,0.02885,-0.12297,-0.00188,-0.02287,-0.04748,-0.00871,-0.13089,-0.02035,0.09013,-0.06217,-0.08219,0.0103,-0.04522,0.03128,0.07439,0.03291,-0.06374,-0.00534,0.04031,0.01789,-0.07501,-0.01667,0.046,-0.1029,0.03758,-0.04508,0.07265,-0.00981,-0.02171,-0.01351,0.0667,0.05122,-0.00087,0.07964,0.03678,-0.16366,0.11999,-0.06118,-0.03086,0.10095,0.00898,-0.08499,-0.00669,0.04965,0.06049,-0.02683,-0.0484,0.00733,0.00243,-0.02523,0.05963,-0.00661,-0.07867,0.0192,-0.02501,0.0434,0.06915,0.02846,0.10135,-0.09486,0.07265,0.09333,0.00459,0.01745,-0.03814,0.04579,-0.00321,0.07785,0.05226,-0.05477,0.09533,-0.10646,0.09258,-0.11214,0.06339,0.04877]},{"domain":"geospatial_analytics","key":"geo_geodesic_midpoint","name":"Midpoint of a geodesic on the ellipsoid","package":"geospatial-analytics-ai999x","example":"Geodesic midpoint: lat1 = 51.5, lon1 = -0.13, lat2 = 40.71, lon2 = -74.01, ellipsoid = WGS84","v":[-0.05157,-0.03168,0.1161,0.03531,0.05504,0.01125,0.05239,0.0741,0.02553,0.04865,-0.00397,-0.00793,0.08841,0.00675,0.00864,0.01642,0.11857,0.04884,-0.00163,0.04004,0.01968,0.01774,0.04555,0.15901,0.02678,-0.00156,-0.09818,-0.00561,-0.04736,0.12392,0.00362,0.06243,-0.12782,0.07129,0.03696,-0.03149,-0.05108,0.0368,0.04145,-0.06154,-0.01134,0.09073,0.03476,0.05158,-0.07153,0.03194,0.03049,0.03429,-0.03051,-0.11635,-0.00016,-0.01686,0.04778,0.03186,-0.07244,0.04468,-0.05223,0.08286,0.03581,-0.06491,0.07246,-0.10854,0.00485,-0.05176,-0.01029,0.0289,0.10178,0.00685,0.07373,-0.00186,-0.06875,-0.08949,-0.01809,0.00341,0.00634,-0.05002,-0.045,-0.03345,-0.08208,-0.07774,0.06751,0.03724,0.0344,0.1295,0.01055,-0.04333,-0.05922,0.00333,0.04238,0.08731,0.00068,-0.09646,-0.01527,-0.01851,-0.02183,-0.01872,0.08292,0.14248,-0.11066,-0.01802,0.01146,0.04195,0.19185,-0.00557,-0.01869,-0.15092,-0.06639,-0.00425,-0.18094,-0.09851,0.07768,0.02687,0.00511,-0.02943,-0.00728,-0.03925,0.02083,0.06921,-0.05578,0.00485,0.02988,0.0549,-0.00426,-0.00406,-0.08161,-0.0218,0.03242,0.06211,-0.01279,0.01981,0.0645,-0.05238,0.06702,-0.03426,0.05341,0.09991,0.0881,0.04865,-0.13583,-0.02977,0.01922,-0.01114,0.12262,-0.07099,0.03515,0.05482,0.01291,-0.02276,-0.0886,0.03311,-0.03942,0.0272,0.06416,0.00112,0.03003,0.01141,0.06743,-0.08717,0.00332,0.0414,0.01287,-0.1193,-0.01625,-0.02401,-0.01103,0.10779,0.03008,-0.01041,0.01094,0.00825,-0.16391,0.0395,0.02257,0.02629,-0.08847,-0.17279,-0.05656,0.04492,-0.06591,-0.05027,0.05857,-0.03336,0.00916,-0.03195,0.01006,0.03133,-0.08034,-0.03328,0.08087,0.01409,-0.08509,0.0969,-0.03205,0.06102,0.02516,-0.01598,-0.03771,-0.01888,0.11768,-0.02142,-0.01469,-0.00588,0.06339,-0.05127,-0.0002,-0.08548,0.07869,-0.02493,-0.12057,0.01402,-0.02338,0.06471,0.03714,0.07538,0.03164,-0.02123,-0.05073,0.03057,-0.15635,-0.00604,-0.01556,-0.07999,0.03166,-0.04142,0.11391,-0.02244,0.00951,-0.00888,0.06377,-0.05046,-0.06652,0.01631,-0.04136,0.03342,-0.03131,-0.0125,0.00802,0.0264,0.04225,-0.1112,0.11719,0.03886,-0.10147,-0.10154,0.04361,-0.01016,-0.05213,0.02252,-0.02358,-0.05855,0.09688,-0.06248,0.04183,-0.12572,-0.05099,-0.01801]},{"domain":"geospatial_analytics","key":"geo_geodesic_polygon_area","name":"Area and perimeter of a geodesic polygon on the ellipsoid","package":"geospatial-analytics-ai999x","example":"Geodesic polygon area: lats = [0, 0, 1, 1], lons = [0, 1, 1, 0], ellipsoid = WGS84","v":[0.00404,-0.11595,0.11083,0.03771,0.0473,-0.0504,0.02869,0.027,0.04412,0.05634,0.09368,-0.01609,0.02987,0.01587,-0.0583,0.06522,0.13114,-0.01084,-0.03756,0.1422,-0.01419,-0.04626,0.01762,0.08042,-0.00577,0.06224,0.05409,0.00091,0.04198,0.07487,0.04292,0.0067,-0.00783,-0.02551,-0.06105,-0.06258,-0.02384,-0.02076,0.00102,-0.07519,0.07776,0.07015,-0.08056,0.04101,0.0364,0.05189,0.03167,0.03321,0.0406,-0.05162,0.05682,-0.09551,0.17726,0.00859,-0.10006,0.08084,-0.09073,0.01121,0.07311,-0.02046,0.08512,-0.0091,-0.08164,0.03581,-0.01107,-0.05489,0.0785,0.0127,0.10468,-0.01568,-0.03013,0.02773,-0.03289,-0.09,0.02453,-0.08944,0.00571,-0.04435,-0.15822,0.03509,0.00786,0.04711,0.0955,-0.00094,-0.00838,0.06263,-0.07943,-0.01486,0.0506,-0.03296,0.00983,-0.07801,-0.06023,0.00623,-0.08559,0.03244,0.09747,0.12161,-0.00761,-0.03057,0.05023,0.10775,0.10029,-0.04427,0.08001,-0.12746,-0.02473,-0.06462,-0.1441,0.00884,0.02476,-0.02103,-0.06632,-0.03454,-0.04204,0.04328,0.02112,0.07327,-0.04428,0.04401,-0.05349,0.06007,-0.04894,-0.01824,0.01067,-0.00969,-0.06047,0.05842,-0.06145,0.01529,0.0443,-0.05087,0.09582,-0.04659,0.04488,0.10604,0.08387,0.01985,-0.02475,-0.04388,0.03229,-0.08991,-0.04399,-0.01486,0.11223,-0.03503,-0.06625,-0.09789,-0.02467,0.05287,0.00902,0.06427,0.01883,-0.04646,-0.05734,0.04771,-0.04976,-0.05307,0.04648,-0.02497,0.00662,-0.07485,0.00643,0.06204,0.00658,0.1523,-0.00123,0.05057,-0.00758,-0.01642,-0.05526,0.03977,0.04792,0.05533,-0.02116,-0.04476,-0.05423,0.03829,-0.05499,-0.0153,-0.00364,-0.03265,-0.11884,-0.02854,0.05105,0.02268,-0.13175,-0.04381,0.04925,-0.01749,-0.10023,0.07488,0.00887,0.02889,0.02736,0.00692,0.00534,0.00842,0.1203,0.01331,-0.03453,-0.0581,0.15291,-0.00976,-0.03017,-0.05654,0.03309,-0.04162,-0.111,0.03101,0.05309,-0.09066,0.16808,0.11834,-0.0064,-0.00477,0.00184,-0.1026,-0.0997,-0.11997,-0.07312,-0.0066,-0.11352,-0.02067,0.0979,-0.02445,-0.07105,-0.09128,0.01113,-0.05558,0.01972,-0.0037,-0.05909,0.01133,-0.00664,-0.04099,0.02029,0.03007,0.01966,-0.1197,0.05426,0.11999,-0.01419,0.00675,0.04908,-0.06267,-0.00051,-0.0012,0.05492,-0.07656,0.05857,-0.12404,-0.02531,0.01944,0.06022,0.04059]},{"domain":"geospatial_analytics","key":"geo_geodetic_to_ecef","name":"Geodetic to geocentric (ECEF) coordinates","package":"geospatial-analytics-ai999x","example":"Geodetic to ECEF: lat = 45, lon = 10, h = 100 m, ellipsoid = WGS84","v":[-0.01191,0.00562,0.04964,-0.06062,0.08901,0.02833,-0.08116,-0.00411,-0.04164,-0.0579,-0.01695,-0.11919,-0.05846,-0.01441,-0.02139,0.00266,0.11956,0.04747,-0.02958,-0.0012,-0.11614,-1e-05,-0.00501,0.08317,-0.01854,0.01039,-0.03527,-0.04394,-0.04113,0.06247,-0.02808,-0.09716,-0.07483,-0.00013,0.07128,-0.01737,0.05144,0.00763,0.02972,-0.13236,0.00752,0.01969,-0.04135,0.092,-0.11512,-0.05385,-0.04805,-0.01003,-0.0432,-0.08889,0.00308,-0.03781,0.08205,-0.06976,-0.13094,0.04421,-0.03865,0.01722,-0.07302,-0.05412,-0.02321,-0.11157,0.05083,-0.08093,-0.01103,-0.03141,0.04927,-0.02294,0.08157,0.08454,-0.02996,-0.07497,-0.00573,-0.0187,0.02296,-0.07071,-0.00968,0.00109,-0.01846,-0.06111,0.08035,0.09352,0.0216,0.09516,-0.02231,0.01506,-0.11082,-0.06932,0.08945,-0.00448,0.07463,-0.1029,-0.04999,0.02701,0.0197,0.07367,-0.04865,0.03773,-0.02505,-0.08926,0.0182,-0.01426,0.11583,-0.0189,0.05724,-0.06777,-0.0482,0.06359,-0.10732,-0.10428,0.10514,0.08139,-0.04353,0.00338,0.06824,0.04294,0.10135,0.10725,-0.01796,0.0062,0.00623,-0.02665,0.00997,-0.10783,0.11306,-0.00533,0.07245,0.01937,0.11895,-0.02506,-0.012,-0.06826,0.05465,0.05267,0.05466,0.14629,0.05904,0.01574,-0.04865,-0.00368,-0.03735,0.02873,0.01802,-0.07205,-0.00961,0.04547,-5e-05,-0.01959,0.0354,-0.01398,0.00279,0.04499,0.06956,0.08753,0.01318,0.04533,0.07732,0.06039,-0.03772,0.04996,0.05546,-0.11063,0.10393,0.04164,-0.1267,0.04712,-0.04432,-0.00896,-0.01885,0.19894,0.0636,-0.02129,0.06715,0.02277,-0.09243,-0.085,-0.0747,0.06445,0.03534,0.06807,0.00589,-0.074,-0.05626,-0.06474,0.01638,0.01099,-0.00104,-0.03104,0.05134,0.01258,0.07271,0.02874,0.04909,0.08714,-0.06448,-0.01329,-0.00219,-0.00643,0.0512,0.06535,-0.11332,0.00132,0.12093,-0.01817,-0.07607,-0.1139,0.02789,0.06719,0.01019,-0.02145,0.02814,-0.00178,-0.01191,0.01387,0.00089,-0.07733,0.0349,0.01176,-0.04976,-0.06674,-0.05549,0.00954,-0.06315,0.08373,0.11525,-0.04525,0.04585,0.01004,-0.03673,-0.0495,0.03208,-0.01542,-0.06928,0.06534,0.04523,-0.09203,0.03357,0.09182,-0.09086,-0.1203,-0.05972,0.12473,0.00844,-0.12939,0.02409,-0.00688,0.02401,0.0919,0.07334,-0.0736,0.0392,-0.04499,0.03943,-0.13318,-0.04887,0.00277]},{"domain":"geospatial_analytics","key":"geo_geodetic_to_enu","name":"Geodetic to local east-north-up (ENU) coordinates","package":"geospatial-analytics-ai999x","example":"Geodetic to ENU: lat0 = 46.017, lon0 = 7.75, h0 = 1673 m, lat = 45.976, lon = 7.658, h = 4531 m, ellipsoid = WGS84","v":[-0.12325,0.05748,-0.04216,0.02241,-0.00085,-0.05767,-0.08547,0.04845,0.02002,-0.10767,-0.02431,-0.02607,-0.03144,0.08412,-0.00911,0.02067,0.12795,0.01864,0.03849,-0.07963,-0.04776,0.00348,0.02215,-0.02091,-0.03044,-0.04308,-0.01627,-0.071,-0.10374,0.07414,-0.05435,-0.07505,0.10548,-0.0126,0.07621,-0.03069,0.07914,0.03817,0.05806,-0.05156,-0.038,0.05507,-0.01832,0.06237,-0.20086,-0.02669,-0.07175,0.01521,-0.18903,-0.12284,0.00511,-0.0046,0.03286,-0.02972,-0.04363,0.00424,-0.00038,0.01707,-0.02749,-0.01912,-0.02474,0.02767,0.08325,-0.1433,-0.01276,0.10385,0.05159,-0.03084,-0.00928,0.07288,-0.09556,-0.13078,0.00941,0.00409,0.01659,-0.06985,0.10133,0.00443,-0.02128,0.01749,0.09858,-0.04138,0.00937,0.06038,0.07457,-0.04317,-0.05625,-0.08838,0.01746,0.01123,0.03674,0.00316,-0.13603,-0.01242,-0.10542,-0.03106,-0.00236,0.05756,0.01737,0.04309,-0.06782,-0.015,0.05607,-0.03892,-0.00238,-0.08078,-0.04483,0.03693,-0.12909,0.01806,0.01253,-0.00022,0.0544,0.01577,0.08772,-0.00346,0.01503,0.08535,0.01535,0.10702,0.07073,-0.01269,0.01941,-0.02932,0.09104,0.02783,0.02623,-0.01599,0.11554,0.07387,-0.00122,-0.0258,-0.02184,-0.04455,0.03583,0.08899,0.05582,-0.00478,-0.15983,0.04397,0.07766,-0.01409,0.02874,0.00379,0.04364,0.07268,-0.07529,0.02457,0.07013,0.06088,-0.12265,-0.0333,-0.01853,0.05905,-0.07524,0.07845,-0.0288,0.02646,-0.00595,0.03868,0.02064,-0.05958,-0.00629,0.06794,0.03953,0.13428,-0.08432,0.02753,0.00594,0.06912,0.0103,0.0225,0.02631,0.02629,-0.08704,-0.02205,-0.02515,0.00499,0.05481,-0.0672,-0.00701,-0.04791,0.04441,-0.04203,0.12304,0.02921,-0.02746,0.07885,0.04608,-0.01072,0.09266,0.06136,0.07058,0.22503,0.05267,0.01527,0.00555,-0.03295,0.11303,-0.04186,-0.06819,-0.08513,0.12324,-0.06944,0.00913,-0.06653,0.09587,-0.00565,0.05003,-0.02655,0.02639,0.00983,0.05275,-0.02022,-0.0142,-0.02878,-0.04451,0.03701,-0.06208,-0.09832,-0.04042,0.01192,0.09607,0.07508,-0.01095,-0.05391,-0.02752,0.08396,-0.02968,-0.05269,0.03674,0.00407,-0.1083,-0.05781,0.0228,0.01743,0.05483,-0.01315,-0.00138,-0.0109,0.06978,-0.00772,0.0256,-0.07244,-0.0652,-0.01312,0.03933,0.05602,0.04607,-0.04897,-0.01522,-0.10745,0.11601,-0.13743,-0.02539,-0.01351]},{"domain":"geospatial_analytics","key":"geo_geohash_decode","name":"Decode a geohash: cell centre and size","package":"geospatial-analytics-ai999x","example":"Geohash decode: geohash = u4pruydqqvj","v":[0.03272,0.03936,0.07857,-0.03682,0.0706,-0.01575,0.10443,0.13514,-0.04357,0.06172,0.07497,-0.02977,0.10458,-0.03748,-0.03814,0.00221,0.16365,0.021,-0.06605,0.0542,0.0177,-0.01015,-0.04,0.00407,-0.03161,-0.00116,-0.04348,-0.06804,-0.03319,0.03499,-0.03254,0.04819,0.04926,-0.01059,-0.01039,-0.09434,0.0266,0.04251,-0.08387,0.06574,-0.00989,0.04161,0.01502,0.04554,-0.00199,0.02235,-0.09767,-0.02146,-0.07563,-0.17302,0.03773,-0.07482,0.00736,-0.06971,-0.00593,0.04664,0.03111,-0.03121,-0.04386,0.01445,-0.00288,-0.09386,0.03347,0.04876,0.08885,-0.05285,0.09155,0.07701,-0.01461,0.07153,-0.06299,-0.09825,-0.07097,0.00828,-0.01585,-0.01898,-0.11928,-0.00647,-0.16313,-0.07838,0.09635,0.05563,0.02225,0.02446,-0.02083,-0.05992,0.07759,-0.01817,0.09391,0.00087,0.02878,0.03104,0.0142,-0.07688,0.05388,0.11549,0.00893,0.1531,0.01203,0.0106,-0.08656,-0.04019,0.11377,-0.01037,-0.06262,0.05845,-0.02408,-0.06689,-0.14432,-0.12008,0.00779,0.00858,-0.00403,-0.02796,0.03723,0.04681,0.0803,0.05382,-0.06965,0.02278,-0.02534,-0.16582,0.04458,-0.00111,0.00535,0.0264,-0.03605,0.07551,0.00094,-0.08141,0.09924,-0.023,0.17179,0.02043,-0.00973,0.02767,0.05285,0.03566,0.00199,-0.03462,0.1446,-0.03122,0.11316,-0.0839,0.03955,-0.02973,-0.01868,0.05745,-0.03751,0.03492,-0.03321,-0.04775,0.03453,0.04567,0.03225,-0.01905,-0.03172,-0.01516,-0.0059,0.07595,0.08012,-0.04931,0.05002,-0.07014,0.01719,0.02007,0.05105,-0.04557,0.05911,-0.1249,-0.12124,-0.05337,-0.04361,0.10563,-0.09188,-0.07277,-0.069,2e-05,0.03623,-0.09144,-0.03031,0.07381,0.01653,-0.01223,0.04746,-0.13246,0.01417,0.05762,-0.0013,0.01588,-0.04333,0.01529,-0.00559,-0.04955,-0.01187,-0.00772,-0.02645,0.06972,-0.07082,0.03264,-0.05975,-0.02855,0.0346,-0.0364,-0.08567,-0.11812,0.11126,0.09544,0.01818,-0.00833,-0.00765,0.00176,0.06185,0.10247,-0.03733,0.05511,0.03306,0.0625,-0.02359,-0.05859,-0.04657,0.06017,-0.06005,0.02169,-0.01871,-0.08069,0.09061,-0.05247,0.00844,0.09213,0.03852,0.0377,-0.00341,-0.00279,-0.01811,0.01434,-0.09041,0.01378,0.11018,-0.00959,-0.02436,0.01438,-0.14213,-0.06905,-0.0104,-0.11592,0.08199,0.05659,-0.05346,0.01121,-0.02991,-0.08395,-0.04344,-0.03759,0.01542,0.04892]},{"domain":"geospatial_analytics","key":"geo_geohash_encode","name":"Geohash of a point and its cell","package":"geospatial-analytics-ai999x","example":"Geohash encode: lat = 57.64911, lon = 10.40744, precision = 11","v":[0.01033,0.02835,0.0805,-0.03701,0.05391,-0.03452,0.12178,0.11356,-0.05975,0.04676,0.01674,-0.03389,0.10613,-0.06758,-0.02577,-0.0022,0.14193,-0.01642,-0.04163,0.08053,-0.01298,0.00222,-0.02821,-0.01033,-0.03542,0.02004,-0.07137,-0.06145,-0.01528,0.03505,-0.02227,0.0299,0.02068,-0.01423,-0.00709,-0.13081,0.01271,0.0667,-0.08505,0.05034,0.02403,0.07412,-0.00712,0.04297,0.02061,0.04081,-0.11181,0.02816,-0.04783,-0.14433,0.06399,-0.06166,-0.00944,-0.09466,-0.01353,0.01677,0.02437,-0.06156,-0.01818,0.0077,0.01261,-0.085,0.02227,0.03306,0.07596,-0.04165,0.0354,0.04878,-0.014,0.09641,-0.10902,-0.13591,-0.08044,0.01304,-0.01931,-0.02417,-0.10208,0.00412,-0.16052,-0.037,0.08313,0.04656,0.04599,0.02925,-0.01277,-0.05862,0.0327,-0.03273,0.13345,-0.02832,0.0222,0.0017,0.0231,-0.0927,0.04008,0.10926,-0.01735,0.18092,0.00846,-0.02988,-0.08127,-0.00935,0.11979,-0.01995,-0.02219,0.04887,-0.00474,-0.06309,-0.14779,-0.09986,0.02399,0.0168,-0.02266,-0.02137,0.05079,0.06011,0.09521,0.05918,-0.05408,0.03494,-0.01525,-0.17137,0.03754,-0.03341,0.00171,0.02087,-0.01676,0.09966,0.01562,-0.07871,0.1222,-0.03688,0.151,0.0513,0.00845,0.02365,0.02031,0.03826,-0.0133,-0.04467,0.1402,-0.02517,0.07109,-0.11435,0.0519,-0.04312,-0.03102,0.05812,-0.0286,0.00384,-0.01004,-0.04418,0.03922,0.04779,0.0125,0.00815,-0.04955,-0.01312,0.00391,0.09027,0.08296,-0.04566,0.02267,-0.05243,0.03836,0.02009,0.04976,-0.04729,0.04568,-0.12173,-0.12566,-0.07593,-0.06315,0.11647,-0.08777,-0.07785,-0.05343,-0.01077,0.02003,-0.0962,-0.0095,0.10051,0.01216,-0.02393,0.04276,-0.1304,0.01056,0.05707,-0.00021,0.04697,-0.05228,0.0084,-0.00903,-0.01411,-0.0103,0.01021,-0.01292,0.07046,-0.04583,0.0461,-0.08532,-0.03607,0.06589,-0.04338,-0.07873,-0.09824,0.11451,0.06689,0.01876,0.01493,0.02333,0.03312,0.05262,0.08025,-0.02933,-0.00478,0.01833,0.07785,-0.01849,-0.06448,-0.07283,0.06079,-0.0379,0.03656,0.01093,-0.05479,0.11305,-0.06867,-0.00261,0.09989,0.01679,0.03206,0.01177,-0.0121,-0.04129,0.01702,-0.07873,0.01995,0.10595,-0.01857,0.00795,-0.00463,-0.14621,-0.07796,-0.00843,-0.08968,0.10328,0.04478,-0.01697,0.01253,-0.01454,-0.07575,-0.08291,-0.02811,-0.00967,0.01868]},{"domain":"geospatial_analytics","key":"geo_getis_ord_general_g","name":"Getis-Ord general G (global high/low clustering)","package":"geospatial-analytics-ai999x","example":"Getis-Ord general G: y = [10, 12, 11, 2, 3, 2], W = [[0, 1, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0], [1, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 1], [0, 0, 0, 1, 0, 1], [0, 0, 0, 1, 1, 0]]","v":[0.00558,-0.03905,0.03939,-0.08208,-0.0301,0.04586,0.02716,-0.08327,0.05616,-0.04762,0.06371,-0.01387,-0.05348,0.02688,0.06062,-0.05733,0.00163,0.02113,-0.12032,0.0325,0.02559,-0.10908,0.01114,0.04708,0.01262,0.08028,0.02899,-0.04371,0.0176,0.04865,-0.04637,-0.04435,0.02383,0.00755,-0.05318,0.03386,-0.13332,-0.0487,0.02136,0.05317,-0.01685,0.05645,-0.08556,0.13111,-0.0036,-0.05781,0.06793,-0.0019,0.0174,-0.05088,-0.0197,-0.04147,0.16892,0.05666,-0.10422,0.14076,-0.064,-0.02529,0.00886,0.0989,0.08529,-0.01941,0.03515,-0.19418,-0.08411,-0.03778,0.04625,0.0915,0.08857,-0.01871,-0.02202,-0.01836,0.03009,0.05411,0.00597,0.03366,-0.13408,-0.00799,0.06253,-0.06795,-0.04348,0.12364,-0.00635,0.07848,-0.09129,-0.01794,-0.02296,0.04816,-0.04309,-0.00905,-0.19166,-0.01632,-0.04469,-0.00449,0.06598,0.04369,-0.03003,0.05444,-0.08835,-0.02858,0.06137,-0.01448,-0.0829,0.0086,0.14493,-0.01219,0.08576,-0.04944,0.04641,0.02872,0.02141,-0.00907,-0.09959,0.08447,0.044,0.03141,0.06005,-0.06352,0.05623,-0.01502,0.04484,0.00888,-0.08312,-0.01601,-0.05946,-0.03493,-0.05538,-0.07065,-0.07662,-0.03844,0.04733,0.06938,0.06016,-0.00518,0.06897,0.05387,0.06132,-0.00153,-0.01404,-0.04294,0.10894,0.00615,-0.05605,0.0582,0.01386,-0.08464,-0.0864,-0.00382,0.06294,-0.01269,0.0297,-0.02079,0.07637,0.06234,-0.03808,-0.03147,0.10602,-0.07792,0.02377,0.07197,-0.06901,-0.02437,0.05991,-0.03973,0.07453,-0.00513,-0.01503,0.13004,0.01409,0.02576,0.1219,0.01253,-0.0274,0.06282,-0.05068,-0.00478,-0.01546,0.07848,-0.02074,0.01567,-0.01079,-0.05358,-0.0257,-0.06916,0.04006,-0.09686,0.00689,0.06576,0.03249,-0.03759,-0.04806,0.0039,-0.01144,0.00113,0.03603,0.0068,-0.07409,-0.01516,0.03767,-0.09382,-0.10834,-0.04272,0.05551,-0.04286,0.02743,-0.08186,0.02313,-0.03101,-0.02913,0.06013,0.02949,0.09183,-0.00316,-0.00813,0.04266,-0.08748,-0.02086,-0.138,0.01064,0.05335,-0.07607,-0.00288,-0.0272,0.12422,0.01019,-0.05143,-0.07839,-0.01578,-0.01051,-0.01076,0.02544,-0.0162,-0.02872,-0.07327,0.05726,0.00471,0.04816,0.1518,-0.00047,0.04701,0.02784,0.05955,0.09442,0.02074,-0.04711,-0.01639,-0.02198,0.10058,0.12089,-0.02274,0.11814,-0.11897,-0.14125,-0.12608,-0.05524,-0.02604]},{"domain":"geospatial_analytics","key":"geo_gnomonic_forward","name":"Gnomonic projection (sphere)","package":"geospatial-analytics-ai999x","example":"Gnomonic forward: lat = 40, lon = 10, lat0 = 45, lon0 = 0, R = 6371000 m","v":[-0.06645,0.05295,0.02049,-0.02967,0.07073,0.10693,0.02564,-0.04021,0.06986,-0.07694,0.05245,-0.08695,0.04182,-0.0657,-0.02115,-0.00389,0.05326,-0.04955,0.06464,-0.04148,-0.13518,-0.07361,0.04459,-0.06368,-0.04839,-0.02304,-0.08813,-0.05582,-0.03924,-0.05134,-0.07454,-0.08816,0.0173,0.02631,0.01076,-0.07252,-0.02285,0.08694,-0.05103,0.08009,-0.06433,0.04014,-0.05438,0.11039,0.00337,0.06545,-0.03955,0.09645,-0.0181,0.10655,0.01624,-0.1107,-0.00823,-0.00094,-0.02352,-0.00952,0.00135,-0.04814,0.01834,0.05092,0.0493,-0.00816,-0.02032,-0.09508,-0.00497,-0.03852,0.01787,-0.04295,0.05182,0.13958,-0.05717,-0.09845,-0.0615,-0.00871,-0.11263,0.01739,-0.12259,0.03636,-0.00074,0.00938,0.00431,0.02108,0.07579,-0.01564,0.07767,-0.04025,-0.06185,0.03889,0.12779,-0.02706,0.03916,0.03696,0.07857,-0.07348,-0.03678,-0.02897,-0.01398,-0.00194,0.00719,-0.10581,-0.02797,-0.07889,0.06611,-0.08065,-0.02158,0.02167,-0.05354,0.03108,-0.05618,0.01913,-0.01076,0.03669,0.03591,-0.02345,-0.03621,0.02982,0.09481,0.02251,0.02908,-0.04449,-0.10909,-0.1094,-0.01118,-0.12543,0.11803,-0.02909,0.06041,0.02603,-0.01045,0.04178,-0.03928,-0.12747,0.08186,0.02546,-0.10909,0.05508,0.04658,0.04262,-0.08411,-0.06033,-0.08725,0.0822,0.02527,-0.0614,-0.03089,-0.02326,0.07475,-0.05362,-0.06852,0.08216,0.09527,-0.01372,0.12848,0.09286,0.03634,-0.02515,-0.0126,0.09367,-0.00576,0.06808,0.07618,-0.02315,0.03398,-0.05981,-0.04351,-0.03751,0.01156,-0.14043,0.02486,0.06844,-0.04925,-0.01235,-0.02772,-0.03635,-0.02618,-0.06655,-0.09248,0.05172,0.07829,-0.01455,-0.02373,0.1008,0.11902,-0.09342,0.11127,-0.07323,0.0687,0.02931,0.0092,0.02481,0.06972,0.06943,-0.00568,0.04431,-0.02916,0.0552,0.07579,-0.05119,-0.06462,0.06566,-0.0781,-0.0077,-0.02252,-0.0034,-0.00663,-0.09529,-0.00518,0.01841,-0.01709,0.07316,0.02083,0.02441,-0.02514,0.05679,0.0149,-0.01513,-0.01283,0.08423,-0.00345,0.09133,-0.04902,-0.01549,0.04666,0.06121,0.08298,-0.02832,0.05269,0.08506,0.10068,0.08142,0.0663,0.08508,-0.05375,-0.01271,-0.14471,-0.1191,-0.00215,-0.06553,-0.15241,-0.04278,0.04828,0.04948,-0.09223,-0.05507,-0.00315,0.02515,0.03586,0.10257,-0.0021,0.07275,-0.09941,0.10987,0.04307,0.06012,-0.0344,0.02116]},{"domain":"geospatial_analytics","key":"geo_graticule_cell_area","name":"Area of a latitude-longitude cell on the ellipsoid","package":"geospatial-analytics-ai999x","example":"Graticule cell area: lat1 = 0, lat2 = 1, lon1 = 0, lon2 = 1, ellipsoid = WGS84","v":[-0.02869,-0.09087,0.12891,0.06733,-0.00523,0.01662,0.08265,0.0617,0.03997,0.07718,0.14056,0.03476,0.1288,-0.03742,-0.01966,-0.01152,0.11485,-0.02032,0.05026,0.12654,0.06032,0.02799,0.09538,0.05559,-0.05487,0.05562,-0.07569,0.04838,-0.03592,0.00112,-0.03348,-0.1191,0.01862,0.03876,-0.11098,-0.05878,0.01696,0.00175,0.01418,0.00445,0.14881,0.01077,-0.01094,0.02457,0.00837,-0.09675,0.00357,-0.01051,-0.04637,-0.04782,-0.0576,-0.02509,0.0971,-0.09772,-0.05837,0.04059,0.08472,0.03816,0.05801,0.00876,0.0206,-0.03537,-0.03429,0.01079,0.06838,-0.06423,0.11886,0.01862,-0.00299,0.01966,0.01922,-0.0893,-0.03167,0.0122,-0.09201,-0.03825,0.01644,-0.07469,-0.14836,0.02814,0.09152,-0.01998,-0.00689,-0.01662,-0.04303,0.00149,0.08732,0.04361,0.04692,-0.01616,-0.07234,0.02523,-0.01717,0.00808,-0.13359,-0.01961,0.04174,0.10245,-0.00058,0.00924,-0.10553,0.03223,0.06191,0.0372,-0.02366,-0.0621,-0.02489,-0.10225,-0.12094,-0.01546,0.03883,-0.03196,-0.11853,-0.03293,0.0106,0.00283,0.02536,0.12645,-0.00067,0.07574,-0.08496,-0.0385,0.0231,0.0427,-0.02297,-0.08058,-0.13322,0.07804,-0.04097,-0.02299,0.1364,0.00091,0.13792,-0.01523,-0.13063,0.0623,0.14025,0.01553,-0.0501,0.04614,0.05809,-0.08956,-0.01941,-0.01496,-0.01303,-0.07529,0.00351,-0.04868,0.03103,0.10768,0.05256,-0.01338,-0.01938,0.01591,-0.06954,-0.00915,0.02038,-0.04442,0.02737,0.02485,0.08462,0.011,0.03388,-0.02416,0.01764,0.10564,0.0038,0.1038,0.03762,-0.11642,-0.05173,0.01358,0.08946,0.04877,-0.01789,0.01751,-0.02056,0.00453,-0.04581,-0.13588,-0.01336,-0.00352,-0.1054,-0.09067,0.09038,0.07285,-0.07463,0.03939,-0.01233,-0.07405,-0.03899,0.12582,-0.00347,0.02018,0.00545,0.04569,-0.00407,-0.04953,0.06844,0.00652,0.04325,-0.0266,0.04604,-0.02828,0.00252,-0.03278,-0.01919,-0.0181,-0.00361,-0.02087,0.02862,-0.05149,0.00579,0.12973,0.01207,0.07405,0.02608,-0.02125,-0.07792,-0.09122,-0.04549,-0.08576,-0.00282,-0.02276,0.09161,-0.07774,-0.00145,-0.17607,0.06661,0.00844,-0.06895,-0.00822,0.00322,-0.03748,0.04564,0.03996,-0.02236,-0.05951,0.0203,-0.08413,0.10793,-0.01927,-0.0433,-0.00287,0.00447,-0.02154,0.03632,-0.09946,0.07726,-0.06239,-0.0257,-0.055,-0.05727,0.02836,-0.04307,0.11265]},{"domain":"geospatial_analytics","key":"geo_gravity_accessibility","name":"Gravity-based (Hansen) accessibility on a road network","package":"geospatial-analytics-ai999x","example":"Gravity accessibility: edges = [0-1 2; 1-2 3; 0-2 6; 2-3 1], opportunities = [100, 50, 80, 20], beta = 1, impedance = 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distance weighted (IDW) interpolation at a point","package":"geospatial-analytics-ai999x","example":"IDW interpolation: x = [0, 10, 0, 10], y = [0, 0, 10, 10], z = [1, 2, 3, 4], px = 2, py = 3, power = 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count statistics of a binary map (BB, BW, WW)","package":"geospatial-analytics-ai999x","example":"Join count statistics: y = [1, 1, 0, 0, 1, 0], W = [[0, 1, 1, 0, 0, 0], [1, 0, 1, 1, 0, 0], [1, 1, 0, 0, 1, 0], [0, 1, 0, 0, 1, 1], [0, 0, 1, 1, 0, 1], [0, 0, 0, 1, 1, 0]]","v":[0.00167,-0.09084,0.07594,0.02757,-0.02172,-0.05328,0.12683,-0.00642,0.08696,-0.03264,0.00842,-0.06479,-0.03405,-0.15584,-0.01576,-0.03796,-0.03521,-0.08408,-0.01759,0.05159,-0.04807,-0.10833,0.09331,0.00341,-0.0388,0.06846,0.05197,-0.02583,-0.09784,0.04113,0.02846,-0.03054,-0.06816,0.02144,0.06029,-0.09558,-0.03359,0.0433,0.06768,-0.0432,0.0988,0.06255,0.03823,-0.1145,-0.00922,-0.14141,-0.04403,0.06788,-0.06598,0.11255,-0.07071,0.01608,0.06679,-0.06701,-0.01807,0.09385,0.02148,0.06146,0.13556,0.09271,-0.00336,0.04353,-0.02097,-0.11019,-0.04191,-0.00627,0.10277,0.14135,0.01666,0.00952,-0.0455,-0.05055,0.13867,0.00504,-0.0841,-0.14031,-0.1469,0.01633,0.03084,-0.05108,0.0263,-0.08675,0.00888,-0.05256,-0.05538,0.00554,0.06104,0.01333,-0.061,0.12173,-0.01465,-0.02989,0.00732,0.02794,-0.00332,-0.03049,0.08827,0.05404,-0.06413,0.11068,0.0497,0.06079,-0.04806,0.01668,0.00292,-0.01545,0.01247,-0.04256,-0.16417,-0.0154,-0.13354,-0.08503,0.00156,-0.04649,-0.03419,0.02202,0.11406,-0.01643,-0.03463,0.05684,-0.04375,-0.0666,0.01256,0.02817,-5e-05,0.16492,-0.02672,-0.02077,0.03056,3e-05,0.10301,0.1026,0.01388,-0.00533,0.02247,-0.04798,-0.01424,-0.07092,0.01598,0.02858,-0.0446,0.01662,0.04611,-0.03771,-0.07536,-0.0414,-0.04582,0.02949,-0.00151,-0.03323,0.02712,-0.0538,0.09,-0.01918,0.13261,-0.0616,0.02346,-0.04865,-0.0193,0.10756,0.05474,-0.01714,0.02563,-0.04457,0.12035,0.01789,-0.01913,0.04468,0.03227,-0.03242,0.05971,-0.01054,0.00071,-0.03144,0.03319,0.00644,0.04094,0.07929,-0.0178,-0.0445,-0.09255,0.07936,0.00875,-0.0001,-0.11602,0.04485,0.00856,0.08405,-0.0785,-0.02205,0.00501,0.10818,0.03424,0.04109,-0.08607,-0.03779,-0.02457,-0.05681,-0.07763,0.03961,0.03609,-0.01145,0.03215,0.00367,0.11529,0.00443,-0.11767,0.06167,-0.04092,0.14599,0.00056,-0.12284,-0.08701,0.03187,0.01665,0.06839,0.09842,0.00097,-0.00757,0.04458,0.01046,0.00928,-0.06892,0.01295,0.0428,0.09183,-0.00663,-0.06925,-0.0171,-0.00715,-0.0765,0.05973,-0.03621,-0.01754,0.11527,-0.02589,0.02892,0.0518,0.00853,0.04902,-0.0774,-0.02218,0.0122,0.0059,-0.02946,0.00145,0.01871,-0.0409,0.06706,-0.04133,-0.0509,-0.04704,-0.13089,0.03336,-0.00573,-0.02542]},{"domain":"geospatial_analytics","key":"geo_kernel_density","name":"Kernel 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spatial weights","package":"geospatial-analytics-ai999x","example":"k nearest neighbour weights: x = [0, 1, 3.5, 6, 10], y = [0, 0, 0, 0, 0.5], k = 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azimuthal equal-area projection (ellipsoidal)","package":"geospatial-analytics-ai999x","example":"Lambert azimuthal equal-area forward: lat = 50, lon = 5, lat0 = 52, lon0 = 10, ellipsoid = GRS80, FE = 4321000 m, FN = 3210000 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conformal conic projection (two standard parallels): coordinates, scale factor and convergence","package":"geospatial-analytics-ai999x","example":"Lambert conformal conic forward: lat = 40, lon = -100, lat1 = 33, lat2 = 45, lat0 = 23, lon0 = -96, ellipsoid = 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Lambert conformal conic projection (two standard parallels)","package":"geospatial-analytics-ai999x","example":"Lambert conformal conic inverse: x = -339545.0 m, y = 1937380.0 m, lat1 = 33, lat2 = 45, lat0 = 23, lon0 = -96, ellipsoid = 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visibility along a terrain profile (with Earth curvature and refraction)","package":"geospatial-analytics-ai999x","example":"Line of sight: d = [0, 100, 200, 300, 400, 500], z = [100, 104, 112, 103, 101, 109], observer_height = 2 m, target_height = 2 m, curvature = 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angles: azimuth, elevation and range from an observer to a target","package":"geospatial-analytics-ai999x","example":"Look angles: lat0 = 40, lon0 = -105, h0 = 1600 m, lat = 0, lon = -100, h = 35786000 m, ellipsoid = 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scale (representative fraction) from a map and a ground distance","package":"geospatial-analytics-ai999x","example":"Map scale from distances: map_distance = 5 cm, ground_distance = 2.5 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projection (ellipsoidal): coordinates and scale factor","package":"geospatial-analytics-ai999x","example":"Mercator forward: lat = 51.5, lon = -0.13, lon0 = 0, lat_ts = 0, ellipsoid = WGS84","v":[-0.0146,-0.01626,-0.00089,-0.05552,0.07199,0.14106,0.01449,0.07497,0.01557,-0.03366,0.14595,-0.05398,0.06391,0.00179,-0.05514,0.04584,0.0797,0.096,0.04535,0.07556,-0.07123,0.04008,0.02741,0.04097,-0.02238,-0.01808,0.06457,0.05555,-0.0093,-0.00564,-0.04675,-0.10676,0.09634,0.05001,0.01072,-0.06629,-0.06318,0.01817,-0.06392,-0.01969,-0.06731,-0.0234,0.02044,-0.0286,0.03796,-0.08738,-0.01053,-0.01962,0.0512,-0.02,-0.0596,-0.14947,0.01535,0.01048,-0.01715,0.00348,-0.03799,0.03014,0.10458,-0.02592,-0.01115,-0.10455,-0.01921,0.00598,-0.0538,0.00417,-0.02579,-0.07972,0.09016,0.03639,0.04058,-0.07638,0.04434,0.01525,-0.00072,-0.13471,0.11137,-0.1436,-0.11451,0.03507,0.02078,-0.04211,0.06901,-0.01767,0.10635,-0.05842,-0.03631,0.03903,0.05403,-0.06056,-0.03519,0.05181,-0.016,0.00968,-0.10201,0.01924,-0.00944,-0.0175,-0.08169,-0.04644,-0.0172,-0.04199,-0.04431,-0.003,-0.02008,-0.10498,-0.05868,-0.00644,-0.04547,0.06263,0.07018,0.00821,-0.02968,-0.11729,-0.06614,-0.04594,0.06084,0.13653,0.03518,0.12301,-0.03767,0.0539,0.07494,-0.041,0.01693,-0.11542,-0.002,0.00707,-0.09798,0.00317,-0.04482,-0.00971,0.02899,0.00346,-0.04892,-0.00291,0.03246,-0.0187,-0.15993,0.03739,0.09876,-0.0434,0.00567,0.00286,0.02355,0.04411,-0.09328,-0.1167,-0.02583,0.07118,0.03691,0.08021,0.02266,0.11719,-0.01447,-0.11619,0.06179,-0.03945,-0.04657,0.02975,-0.00182,-0.07636,0.01485,0.01752,-0.02581,-0.02419,-0.04793,0.06903,-0.04685,0.05542,-0.02186,0.05498,0.03408,0.06073,-0.03031,0.04985,-0.04246,0.00046,-0.04795,0.09643,0.06752,-0.03015,0.08249,-0.09434,0.11943,0.05051,-0.03392,0.0114,-0.03978,0.04107,0.09709,0.07639,-0.09501,-0.03993,0.02486,0.00104,0.00729,-0.02542,-0.063,-0.02649,-0.00448,0.00322,0.04087,0.16322,0.08326,-0.09068,0.00546,0.03382,-0.05885,-0.01481,-0.03758,0.15139,-0.05258,0.06482,-0.02018,0.03157,-0.10326,-0.0018,-0.11413,0.0343,-0.01267,-0.09904,0.08363,0.04461,0.11937,-0.11384,0.09078,-0.0433,0.00148,-0.00239,0.01473,0.02479,0.00779,-0.0263,-0.05358,0.0018,0.0046,0.02989,-0.08582,-0.02644,0.0209,0.13143,-0.14471,0.02201,0.07447,0.00289,0.02087,0.02699,0.11139,-0.07632,0.03053,0.12703,0.07501,-0.00282,-0.0571,0.01525]},{"domain":"geospatial_analytics","key":"geo_mercator_inverse","name":"Inverse Mercator projection (ellipsoidal)","package":"geospatial-analytics-ai999x","example":"Mercator inverse: x = -14471.5 m, y = 6680752.0 m, lon0 = 0, lat_ts = 0, ellipsoid = WGS84","v":[-0.0175,0.02333,0.00557,-0.07791,0.1407,0.12668,0.01318,0.01846,-0.00183,-0.0514,0.09346,-0.01197,-0.00259,-0.03208,-0.01125,0.04313,0.08642,0.01724,0.01482,0.01851,-0.22489,0.02809,-0.03626,0.05585,-0.08872,-0.00981,0.05962,0.0234,0.05294,-0.02899,-0.04215,-0.11038,0.06668,0.02623,0.02259,-0.07826,-0.05319,-0.00677,-0.03777,-0.03981,-0.01103,-0.06412,-0.00807,0.03338,0.08539,-0.07217,-0.04397,0.01729,0.06462,0.03709,-0.00937,-0.17796,0.00717,0.01084,-0.04233,-0.02138,0.03718,-0.04222,0.0479,-0.03552,-0.01608,-0.01886,-0.06206,-0.0025,-0.03928,-0.06335,-0.03802,-0.12558,0.1108,0.07104,-0.04538,-0.11395,0.08847,-0.02917,-0.05507,-0.14019,0.07271,-0.04948,-0.0948,0.05524,0.0685,-0.00221,0.10021,0.01844,0.07479,0.01571,-0.06312,-0.032,0.04716,-0.02599,-0.00505,0.03262,0.01136,0.04883,-0.06296,0.0406,-0.0366,-0.01511,-0.06135,-0.05669,0.01633,-0.01713,0.02248,-0.00582,-0.01649,-0.13357,-0.02809,0.0448,-0.13938,0.04406,0.0666,0.00687,-0.11707,-0.0795,-0.03056,-0.0226,0.08418,0.07738,0.00401,0.09066,-0.03401,0.03774,0.05255,-0.13261,0.09584,-0.00973,0.07718,0.07358,-0.04189,0.00231,-0.02241,-0.06151,-0.01472,0.03754,0.0119,0.01859,-0.01537,0.02334,-0.17265,-0.0123,0.01613,-0.0129,-0.05828,-0.03395,0.01042,0.00988,-0.04723,-0.06359,0.00343,0.0067,0.01462,0.10867,0.05938,0.15294,-0.01712,-0.00782,0.0358,0.02515,0.04495,0.06319,0.01034,-0.10485,-0.04055,0.04073,-0.11192,-0.02673,-0.0257,0.05349,-0.11657,0.14378,0.0051,-0.01636,0.09255,0.00792,-0.04243,-0.01765,-0.05873,-0.03656,-0.0427,0.02148,0.07124,-0.06586,0.04321,-0.12167,0.14078,0.07335,0.03767,-0.00104,0.00229,0.04082,0.05676,0.09457,-0.0476,-0.01679,-0.01351,0.0308,0.0115,0.02197,-0.08701,0.01598,-0.05349,0.03675,0.06228,0.06912,-0.01071,-0.10637,0.0452,0.04633,-0.03871,-0.02925,0.01005,0.08222,-0.00918,0.05396,0.02934,-0.06228,-0.04483,-0.00719,-0.02051,-0.026,-0.00125,-0.00275,0.00405,0.07689,0.13288,-0.06307,0.10572,-0.00152,0.01294,-0.01191,0.05858,-0.00039,0.0083,-0.01275,-0.06341,-0.0181,-0.03307,0.10888,-0.11184,-0.01502,-0.01002,0.06471,-0.11058,-0.0062,0.103,-0.00777,0.04076,0.05292,0.1614,-0.11701,-0.05549,0.10602,0.05551,0.00547,-0.05009,0.00189]},{"domain":"geospatial_analytics","key":"geo_meridian_arc","name":"Meridian arc length between two latitudes","package":"geospatial-analytics-ai999x","example":"Meridian arc length: lat1 = 0, lat2 = 90, ellipsoid = WGS84","v":[-0.1066,-0.05375,0.06832,0.00987,0.09098,0.02209,0.10347,-0.00378,0.09745,0.06527,0.11235,-0.05981,0.02959,0.08133,0.01108,-0.0,0.09389,0.01485,0.02157,-0.0178,-0.12439,0.01818,0.02696,0.06714,0.05517,0.02429,-0.03663,-0.03842,-0.07365,0.01505,-0.02794,0.03461,-0.10657,0.0371,0.06433,-0.02212,0.05803,0.01146,0.03117,0.01881,-0.07081,-0.03562,0.03921,-0.03129,-0.00488,-0.06808,0.01573,-0.00659,-0.03286,-0.02703,-0.06027,0.05202,0.04887,-0.03578,-0.07095,0.05008,-0.01065,0.0614,0.10455,-0.10469,0.0754,-0.1052,-0.051,-0.00697,0.02414,0.0726,0.13589,-0.01158,-0.0244,-0.04879,0.01743,-0.0026,0.00967,0.05938,0.04806,-0.0625,0.03876,-0.12953,-0.03704,-0.0424,0.01271,-0.0304,0.03873,0.03301,0.06922,-0.062,-0.02415,0.04734,0.00655,0.02899,-0.02304,-0.03782,-0.04998,-0.03272,-0.07416,-0.0334,0.10032,-0.03689,-0.04476,0.03104,0.07447,0.03606,0.05912,0.00089,0.03628,-0.13761,-0.17401,0.0007,-0.0406,0.00387,0.07994,-0.04133,-0.05494,-0.01243,-0.02282,0.02782,0.03445,0.17038,-0.01706,0.06773,-0.12387,0.03206,0.02252,0.03996,0.03057,0.03116,-0.03955,0.04838,-0.07183,0.05375,0.04567,0.04351,0.119,-0.01982,-0.08861,0.16956,0.12698,0.01437,-0.11419,0.05897,-0.00727,0.05677,0.02996,-0.09542,-0.00687,0.02389,0.0701,0.04613,-0.06076,0.09918,0.08568,-0.0166,-0.03011,-0.06391,0.04099,-0.04197,0.04672,0.0079,-0.00165,0.02909,0.02811,-0.12093,0.00959,-0.02394,0.05931,0.02803,-0.07958,-0.00217,0.01409,0.06368,-0.05822,0.08803,0.0904,-0.08788,-0.11316,-0.08036,-0.00772,0.00444,-0.008,0.0398,-0.00451,-0.05803,0.026,-0.01646,0.03432,0.14441,-0.06484,-0.03459,0.05902,-0.05573,-0.06587,0.15787,0.02167,0.04934,-0.00945,-0.01092,-0.01009,-0.09967,0.00488,-0.05007,0.05943,-0.06005,0.02471,-0.087,-0.04478,-0.01706,-0.05047,-0.10434,-0.05003,-0.06023,-0.07841,-0.00468,-0.10851,0.10642,0.03312,0.0083,-0.00975,0.03762,-0.14598,-0.00213,-0.01588,-0.1047,0.08271,0.05127,0.13773,-0.0947,-0.00853,-0.07018,0.02471,-0.01709,-0.00601,-0.01423,-0.0924,0.02686,-0.02676,0.03452,0.01647,-0.03522,-0.02657,-0.12539,0.07014,0.0009,-0.07023,-0.07255,0.01529,-0.02321,-0.0343,-0.03111,0.0746,-0.0106,0.0978,0.05833,0.03875,0.02761,-0.11459,0.06437]},{"domain":"geospatial_analytics","key":"geo_mgrs_encode","name":"MGRS grid reference of a point (1 m)","package":"geospatial-analytics-ai999x","example":"MGRS grid reference: lat = 50, lon = 10","v":[-0.09775,0.09551,0.11598,-0.00716,-0.0038,-0.05827,0.05292,-0.01047,-0.0398,0.02062,-0.02351,0.0829,0.06878,-0.07071,0.01606,-0.02876,0.17583,-0.04122,-0.09303,0.02973,-0.17057,0.03144,-0.0267,0.07304,-0.04877,0.02666,-0.07595,-0.05555,-0.0342,0.04159,-0.01839,-0.0577,-0.00381,-0.00095,-0.06653,-0.10311,0.06661,-0.00637,0.01915,-0.06255,-0.01115,-0.01509,-0.0302,0.00299,0.06673,-0.01174,-0.13529,0.02855,-0.07824,0.00534,-0.08701,0.00126,0.09325,-0.07452,-0.00689,0.01278,-0.00745,-0.05151,0.07029,0.00981,-0.03528,-0.09054,-0.03046,-0.06185,-0.03752,0.01599,0.04488,0.02401,-0.07451,0.13343,-0.07569,-0.10742,-0.04945,0.00584,-0.07248,-0.12979,0.07291,-0.04433,-0.01132,0.08196,0.05265,0.00758,0.04433,-0.08377,-0.00311,-0.00985,0.0266,0.03857,0.11755,-0.05081,-0.01002,0.04271,-0.01966,0.01397,0.05482,-0.00104,0.05038,0.08122,-0.05206,-0.02436,-0.01076,-0.0078,0.04534,-0.02877,0.0534,-0.04502,0.02862,0.04499,-0.19573,-0.00016,0.00936,-0.02624,-0.13866,-0.00703,-0.01629,0.06675,0.01,0.03364,-0.00818,0.0379,-0.04439,-0.13798,-0.04246,-0.02661,0.13346,0.03754,0.10033,0.00892,-0.0521,-0.03699,0.0951,0.06111,-0.02975,0.03383,0.03948,0.02855,0.08514,-0.05454,-0.05307,0.08665,-0.03592,-0.06055,-0.00741,-0.09942,0.0252,-0.07248,0.03705,0.06174,-0.03122,-0.00195,-0.06463,-0.03612,-0.03644,0.08267,0.02609,-0.04079,-0.02073,0.02581,-0.01796,0.14973,0.09218,-0.01232,0.03418,-0.02371,0.07097,0.06198,0.03032,0.02187,0.02209,-0.01482,-0.05318,-0.02263,0.05824,0.07687,-0.04165,-0.01748,0.0479,-0.07254,-0.05086,-0.05129,0.01791,0.06428,-0.07027,-0.07168,0.08963,0.01351,0.1046,0.02548,-0.01055,0.00962,-0.06702,0.04433,0.04337,0.03808,-0.00502,0.05613,-0.09303,0.1107,-0.01409,0.08948,-0.11938,-0.01562,0.09015,-0.03004,0.02551,0.00389,0.02858,0.00185,0.01006,-0.01493,-0.055,0.10722,-0.05726,0.09836,-0.00721,-0.00466,-0.04579,0.03313,-0.07617,-0.02679,-0.05956,0.10173,-0.04864,0.11091,0.06443,-0.0064,0.05291,-0.08177,-0.00887,-0.00867,-0.05451,-0.03447,0.06276,0.05152,-0.03784,-0.03272,0.02619,0.07171,-0.00608,0.04604,0.08021,0.05289,-0.18837,-0.15047,-0.00914,0.0599,0.17032,0.01251,0.0608,0.0046,0.00444,0.07689,-0.06904,0.00152,-0.07873,-0.05404]},{"domain":"geospatial_analytics","key":"geo_mollweide_forward","name":"Mollweide equal-area projection (sphere)","package":"geospatial-analytics-ai999x","example":"Mollweide forward: lat = 45, lon = 90, lon0 = 0, R = 6371000 m","v":[-0.06666,-0.05573,-0.00407,0.02864,0.10009,0.00733,0.04048,0.04721,0.09352,0.01442,0.06634,-0.04239,0.02752,-0.14777,-0.06393,0.02968,0.08526,-0.09637,-0.0172,0.03988,-0.02802,-0.04089,-0.00904,0.04574,-0.03608,0.05742,-0.03925,-0.02592,-0.03684,-0.03986,0.07733,-0.06072,-0.01656,0.00038,-0.0539,-0.13886,-0.00351,0.07239,0.00082,0.02148,-0.04218,0.04257,0.09024,0.00041,0.10995,-0.01803,0.02602,0.00013,-0.05913,0.05115,-0.02581,-0.03474,-0.02117,-0.05899,-0.07319,0.08127,-0.01184,-0.04253,0.00897,-0.05574,0.10322,-0.07278,-0.09411,0.10668,0.09552,0.00099,-0.0123,0.00703,0.05183,0.12755,0.00587,-0.0222,-0.14027,0.05975,-0.05371,0.02346,-0.01424,-0.03767,0.00645,-0.10899,-0.0313,-0.00175,0.07546,-0.01772,0.15924,-0.01454,0.00495,0.11016,0.09036,-0.08355,0.03843,0.01506,-0.02562,0.00943,-0.11449,0.00304,0.04909,-0.01765,-0.07842,0.03196,-0.01324,-0.00171,0.10803,-0.02957,0.02367,0.02535,-0.10235,0.08729,-0.06407,0.10098,0.07238,-0.03484,-0.01469,-0.07306,-0.06597,-0.00045,0.02797,0.04224,0.01049,0.07324,-0.00426,-0.16311,-0.03363,-0.01399,0.04268,-0.0854,0.01658,0.00583,-0.12249,0.02935,-0.0021,0.0861,0.13685,-0.00653,-0.17687,0.03788,0.02481,0.0522,-0.08026,0.01133,-0.02611,-0.0022,0.03217,8e-05,-0.04651,-0.03655,0.07691,-0.03275,-0.09039,0.0537,0.14609,0.02004,0.0236,0.03125,0.02244,0.03034,-0.0553,0.09857,-0.0143,0.06361,-0.01566,-0.14335,0.04983,0.01979,0.00692,0.00448,-0.03879,0.05138,0.06651,-0.01481,-0.00121,0.05438,0.11882,-0.06596,-0.03606,-0.09756,0.04013,-0.00846,0.03926,-0.05385,0.03328,0.11015,0.04542,-0.058,0.12033,-0.00847,-0.04032,0.04754,0.06643,0.01998,-0.03878,0.06668,0.0115,0.07889,-0.01003,0.0324,-0.05112,-0.05921,-0.05842,0.07457,-0.04667,-0.11978,0.00626,-0.0106,0.00329,-0.02083,-0.07993,0.0212,0.01388,0.05136,0.11122,-0.02932,-0.01326,0.07044,-0.0106,-0.04359,0.0577,-0.00604,-0.06365,-0.02652,-0.00909,0.01577,-0.0304,0.08364,0.10686,-0.10062,0.0653,-0.02674,0.09127,-0.0302,-0.03949,0.07168,-0.00233,0.07174,-0.06944,-0.11405,-0.11435,-0.08577,-0.15476,-0.05227,0.01592,0.0346,-0.08341,-0.04504,0.0033,-0.00562,0.00743,0.09848,-0.00028,0.06989,-0.05995,0.01269,0.04485,0.02187,-0.09557,-0.06469]},{"domain":"geospatial_analytics","key":"geo_morans_i","name":"Global Moran's I spatial autocorrelation with normal and randomization inference","package":"geospatial-analytics-ai999x","example":"Moran's I: y = [8, 6, 6, 3, 2, 1], W = [[0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0], [0, 1, 0, 1, 0, 0], [0, 0, 1, 0, 1, 0], [0, 0, 0, 1, 0, 1], [0, 0, 0, 0, 1, 0]], transform = 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projection (sphere)","package":"geospatial-analytics-ai999x","example":"Orthographic forward: lat = 40, lon = 10, lat0 = 45, lon0 = 0, R = 6371000 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compactness indices of a polygon (Polsby-Popper, Schwartzberg, convex hull, Reock)","package":"geospatial-analytics-ai999x","example":"Polygon compactness: x = [0, 4, 4, 0], y = [0, 0, 3, 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analysis: chi-square test of complete spatial randomness","package":"geospatial-analytics-ai999x","example":"Quadrat test: x = [1, 2, 3, 8, 9, 2, 1, 7, 8, 9], y = [1, 1, 2, 8, 9, 8, 9, 1, 2, 1], nx = 2, ny = 2","v":[-0.07579,-0.01446,0.04558,-0.06866,-0.13642,-0.06049,-0.02912,-0.01306,0.02099,-0.1093,-0.03873,-0.03425,-0.09649,-0.03574,0.00347,-0.0058,-0.009,-0.0252,-0.04351,0.00916,0.00143,-0.09401,0.00478,-0.0726,-0.06934,0.10328,-0.06369,-0.12713,-0.04994,-0.0135,0.0003,0.02694,0.05268,-0.01081,0.06179,-0.07583,0.0211,0.06419,-0.00975,0.01539,0.0446,0.01276,0.01932,0.03383,-0.05621,-0.07766,0.02824,0.09132,-0.03788,0.09173,0.05181,0.02909,0.08619,-0.0454,0.001,0.05041,0.05895,0.04119,0.1179,0.0219,0.03967,0.01705,0.02173,-0.06583,-0.08809,-0.10969,-0.08355,0.12203,0.01509,0.16619,-0.14023,0.0515,-0.00228,0.08383,-0.05302,0.11055,0.00918,0.06873,0.06324,-0.08957,-0.0418,-0.01541,-0.03404,-0.02426,-0.00801,-0.00782,-0.03536,0.02902,-0.05384,-0.06839,-0.09288,0.04511,0.01942,-0.01906,-0.02257,-0.03328,0.01484,0.08026,-0.03017,0.05919,-0.00952,0.01302,-0.0354,-0.04456,0.05328,0.06221,-0.0307,0.04051,-0.06098,-0.01105,-0.09551,-0.07753,-0.0006,0.07745,-0.04155,0.12393,0.21272,0.01675,-0.00769,0.10476,0.00134,0.00423,-0.01051,-0.06009,0.00746,0.11768,-0.04138,-0.05701,-0.02301,0.02285,0.03097,0.04419,0.0114,-0.04238,0.01809,0.02814,0.05101,0.03735,-0.01185,0.08151,-0.01628,-0.02662,0.03633,-0.08713,-0.04111,-0.11442,-0.06734,0.04633,0.07972,-0.05365,0.03159,-0.10688,0.10461,-0.02501,0.09284,0.02332,0.07247,-0.02831,-0.0785,0.10785,-0.10183,-0.02637,-0.00466,-0.05611,0.13629,-0.09374,-0.04528,0.04793,0.05568,0.00918,-0.02171,-0.00816,-0.01189,0.01185,0.00121,0.08181,0.0414,0.09701,-0.11643,-0.02775,-0.1556,0.03659,-0.01131,-0.06004,0.12354,-0.01424,-0.01154,0.01179,0.06618,0.10446,-0.04426,-0.11731,0.10277,0.10243,0.06033,-0.02733,-0.0611,-0.05576,-0.0574,-0.09444,0.06556,0.03375,0.06811,-0.01383,-0.00766,-0.00315,-0.076,0.0317,0.01577,0.16244,0.02293,-0.03384,0.03337,0.0309,-0.01853,-0.04843,0.06122,-0.04546,-0.06168,0.04188,-0.08436,0.07324,-0.05501,0.09483,0.06346,-0.0121,-0.03863,-0.09276,-0.03602,0.00833,-0.01632,0.03441,-0.01868,0.01234,0.06543,-0.04629,-0.01133,0.04526,0.05678,-0.00086,0.04246,-0.06787,0.10715,0.05724,-0.06223,-0.01023,0.07847,0.04108,0.02263,0.06076,-0.02524,-0.03227,-0.12377,0.00779,-0.00304,-0.0358]},{"domain":"geospatial_analytics","key":"geo_radii_of_curvature","name":"Radii of curvature of the ellipsoid at a latitude","package":"geospatial-analytics-ai999x","example":"Radii of curvature: lat = 45, ellipsoid = WGS84","v":[-0.03841,-0.00618,0.02908,0.0276,0.02049,0.02202,-0.05442,0.01939,0.10401,0.00957,0.04539,-0.08157,0.01537,-0.03159,-0.02586,0.02661,0.10762,0.05797,0.09046,0.04273,-0.07217,-0.1114,-0.0053,0.10213,-0.00444,0.04812,0.03427,-0.11554,0.0186,-0.01049,0.01596,0.03253,-0.05809,-0.02849,0.13111,-0.13797,0.05493,0.05397,0.06061,-0.01691,0.05277,0.01167,-0.0626,0.00056,0.00152,0.04269,0.00877,-0.04292,-0.02571,-0.13328,-0.0036,-0.09299,0.1219,-0.02471,-0.20577,0.01656,-0.00497,-0.02967,0.05301,-0.04606,0.07413,-0.01669,0.00168,0.02289,0.06848,0.05115,0.0763,-0.04083,-0.00677,-0.01615,-0.03287,0.01762,-0.01191,0.02177,-0.03222,-0.08367,-0.07879,0.02869,-0.07913,0.0197,-0.01606,0.10325,-0.0083,-0.01301,-0.04337,-0.0251,-0.08582,-0.00755,0.01908,-0.03733,0.0666,0.03356,-0.01053,-0.00355,0.00519,0.00066,-0.04757,-0.01613,-0.05089,0.02942,0.0139,-0.09734,0.16865,0.07111,0.03917,-0.0582,-0.05212,-0.00242,-0.05595,-0.04101,0.04516,-0.0606,0.03698,-0.05344,-0.04245,0.05402,0.09686,0.00812,0.03162,-0.03238,-0.01624,0.03139,-0.08431,-0.00636,-0.05095,-0.00893,0.0716,0.00589,-0.00448,0.04094,0.01211,-0.11966,-0.0072,0.05524,0.02125,0.12834,0.08324,0.10047,-0.09284,0.09789,0.09443,0.08049,0.01071,-0.03183,0.04853,0.03547,0.10217,-0.04753,0.0114,0.05978,0.0114,0.12309,-0.04407,0.07378,-0.03704,0.01374,0.06964,0.01705,-0.06322,0.10742,-0.0169,-0.07827,0.04196,-0.04055,-0.03627,0.11972,-0.05266,0.07143,-0.04932,0.08336,-0.02964,0.06377,0.00067,-0.10057,-0.14695,-0.04773,-0.0513,0.09842,-0.02806,-0.04541,-0.11151,0.0003,-0.06005,-0.06265,0.13021,0.04862,-0.08451,0.02214,-0.06074,-0.11301,-0.06454,0.15867,-0.00817,-0.0008,0.10622,0.049,-0.04572,0.03919,0.04312,0.02053,-0.01739,0.02237,0.02129,-0.08454,0.00352,-0.12598,0.03153,0.06836,-0.03965,-0.1458,0.07727,0.05124,0.01527,0.03469,-0.01618,-0.12538,-0.07598,-0.10853,0.00487,0.00273,-0.08371,-0.02718,-0.02825,0.03011,0.05353,-0.11831,-0.00892,-0.0432,0.01086,0.01416,-0.05422,0.06002,-0.00746,0.00495,-0.10511,-0.0302,0.02167,-0.00564,-0.01316,-0.03258,0.11373,-0.00936,-0.04191,-0.08338,0.03567,0.0035,-0.06515,0.06023,-0.00705,-0.05021,0.04387,-0.02751,-0.01928,0.10467,-0.10876,0.05056]},{"domain":"geospatial_analytics","key":"geo_rank_size_rule","name":"Rank-size rule (Zipf) fit of a settlement system","package":"geospatial-analytics-ai999x","example":"Rank-size rule: populations = [8400000, 3900000, 2700000, 2300000, 1600000, 1500000, 1400000, 1300000]","v":[-0.08195,-0.06244,-0.07462,-0.01706,-0.04016,-0.03107,-0.12942,-0.07744,-0.0563,-0.0765,-0.04393,-0.08037,-0.00864,0.01646,0.08645,0.02262,0.07531,0.06725,-0.00373,-0.05168,0.04678,-0.03957,0.1627,0.02744,-0.07841,-0.04374,0.03575,-0.08686,0.00221,0.03003,-0.09948,0.0412,0.08724,-0.13016,0.02731,-0.00732,0.0994,0.10494,-0.03318,0.00733,-0.01019,6e-05,0.02857,-0.07741,0.03633,0.1274,0.05975,-0.10323,-0.0763,-0.04699,-0.05912,0.08552,0.03445,0.09384,-0.09066,-0.04297,0.05122,-0.01665,0.01227,0.04884,0.01242,0.01042,-0.04175,0.0885,0.09044,-0.05868,0.02702,0.05511,-0.06341,0.09562,0.10636,0.01886,-0.10579,0.07206,-0.07837,0.03261,0.05313,-0.04401,0.07424,-0.04329,-0.12314,-0.00606,0.0505,-0.08777,-0.02762,0.08526,0.01687,0.07563,0.06369,-0.07116,-0.07699,0.03578,0.06137,-0.13734,0.02124,0.01585,-0.06042,0.02593,0.06509,0.08307,0.0411,0.07339,0.04525,0.00505,0.0136,-0.01204,0.08451,-0.07309,0.11073,0.01217,-0.10844,0.03439,0.03405,0.03977,0.05893,-0.05394,-0.16056,0.12742,0.08274,0.00067,0.02348,-0.01633,-0.04355,0.0995,-0.01633,0.04652,-0.04251,0.00735,-0.03913,-0.04678,-0.03834,0.0038,-0.02416,-0.09213,-0.08401,-0.01962,0.04877,-0.027,0.02693,-0.06223,0.04881,0.06838,-0.03257,0.02857,0.02785,0.01272,-0.03597,-0.02504,0.04596,0.01316,-0.03872,0.0658,-0.08652,0.05238,0.07358,0.01136,-0.08781,0.06407,-0.01299,0.0472,0.0422,-0.06751,0.00435,0.06624,0.01908,0.06799,0.06585,0.03114,0.06936,0.00379,-0.11943,-0.01501,-0.04591,0.04103,0.06387,-0.02967,0.06134,0.09191,-0.02812,0.06795,0.01261,0.08041,0.08531,-0.02854,0.01562,-0.07011,-0.13265,0.06148,0.04592,0.03941,-0.01263,-0.01271,0.05605,-0.05511,-0.02643,-0.06938,-0.159,0.01508,-0.10659,-0.06721,-0.01898,-0.1833,0.09206,-0.07126,0.00387,0.0216,0.05601,-0.01477,0.04121,0.03163,-0.05392,-0.06926,0.09076,-0.03123,0.06481,0.0023,-0.05715,-9e-05,-0.0144,0.02319,-0.0077,0.02067,0.04962,-0.066,0.10497,-0.0343,-0.09131,-0.02021,-0.06189,-0.00455,-0.00512,0.04099,0.07208,-0.01692,-0.03593,-0.00352,0.12412,0.00378,-0.02797,0.02764,-0.04986,-0.04965,0.00332,-0.06285,-0.07464,0.05289,0.01368,0.00137,-0.05444,0.07187,-0.02591,0.02788,0.08939,0.04768,0.06681,0.05758]},{"domain":"geospatial_analytics","key":"geo_rhumb_line_destination","name":"Destination 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WGS84","v":[0.03923,0.02514,0.03705,-0.05084,0.09428,0.00162,0.06319,-0.03359,0.04263,-0.07007,0.00858,0.02716,0.08062,0.1203,0.09904,0.03908,0.04515,-0.04863,-0.07191,0.05017,-0.0959,-0.0127,-0.03499,0.09274,0.03142,-0.0358,-0.05885,0.00739,0.08386,0.01312,0.07289,-0.02958,-0.01783,0.05566,0.02005,0.06097,-0.0231,0.12187,0.0097,-0.05801,0.06939,-0.09106,-0.03661,-0.10203,-0.03403,0.02438,-0.01261,0.00805,0.05872,-0.09449,0.03196,-0.07522,0.09424,-0.02606,-0.05056,-0.05313,-0.00393,0.00422,0.01991,0.01094,0.06393,0.04447,0.02836,-0.11886,0.00784,0.03727,0.0163,-0.07125,-0.0858,-0.04223,-0.10109,-0.04158,0.01481,0.0113,0.01479,-0.02249,-0.02124,0.03692,-0.08866,0.02517,0.10031,0.05574,0.08016,0.00061,0.02684,-0.01112,-0.1133,0.04341,0.11825,0.07823,-0.07125,-0.06607,-0.00976,-0.07029,-0.03841,-0.05944,0.00458,0.03806,-0.05328,-0.0995,0.04711,-0.05475,0.09118,-0.07837,0.09417,-0.11292,-0.10325,0.02837,-0.12329,-0.0067,0.09969,0.05066,-0.03853,-0.0671,0.00122,0.01662,-0.05106,-0.05963,-0.05263,0.04193,-0.10119,-0.02042,-0.11669,-0.02304,0.03182,0.00723,0.08418,0.06021,0.08047,0.02294,0.00726,-0.0073,0.02645,-0.01811,-0.01913,-0.00024,0.06611,-0.0316,-0.08728,-0.05324,-0.13809,0.15551,-0.11598,-0.11035,-0.00141,-0.06749,0.06295,0.01355,-0.05778,0.00439,0.01446,-0.02092,0.06419,0.00512,0.01273,0.03047,0.01027,0.02426,0.12878,-0.09819,-0.02388,-0.13175,0.0338,0.06193,-0.08626,-0.00067,0.02635,-0.14306,-0.00917,0.07611,-0.04762,-0.01958,-0.04195,-0.04992,-0.08788,-0.03561,-0.03563,-0.03034,-0.03763,0.06242,0.00836,-0.05993,0.07299,-0.07095,0.09078,-0.03474,-0.03402,0.01047,0.04266,-0.04575,-0.04708,0.06235,-0.00556,-0.00321,0.05579,0.07009,-0.06745,-0.02775,0.01145,0.0109,-0.05211,0.05581,0.0299,-0.03585,0.01894,0.01104,0.06223,0.0434,0.01168,-0.01672,-0.00797,0.04312,-0.03379,0.18915,0.0989,-0.0731,0.0384,-0.04416,0.00952,0.10866,-0.0425,-0.02959,-0.02034,0.07534,0.13581,0.02439,0.0544,0.04384,0.0522,0.00109,0.03092,-0.05959,0.06941,0.05999,-0.19761,-0.05425,-0.011,0.02017,-0.10683,-0.00794,0.01592,0.00304,-0.0251,-0.04926,0.0006,0.12904,0.04879,0.12587,0.01369,0.07821,0.01831,-0.08055,0.08617,-0.02312,0.01859,0.07341]},{"domain":"geospatial_analytics","key":"geo_rhumb_line_inverse","name":"Rhumb-line (loxodrome) distance and bearing on the ellipsoid","package":"geospatial-analytics-ai999x","example":"Rhumb line distance and bearing: lat1 = 50, lon1 = -5, lat2 = 58, lon2 = 3, ellipsoid = WGS84","v":[-0.06904,-0.01587,0.09759,-0.05779,0.0779,-0.04679,0.10452,-0.01136,0.08372,-0.01618,-0.01058,-0.01401,0.15407,0.14218,0.04034,-0.00616,0.013,-0.04289,-0.07773,-0.01238,-0.11996,-0.00962,-0.0125,0.05494,0.11868,-0.01854,-0.09048,-0.00862,0.00597,0.02989,0.03408,0.02195,-0.06729,0.0275,0.07295,-0.01442,-0.0241,0.10943,0.02311,0.01698,0.04356,-0.05771,0.01044,-0.04026,-0.00425,0.03851,-0.01937,0.05363,0.01164,-0.07162,0.0015,-0.01757,0.0741,-0.04753,-0.0679,-0.04644,0.01477,0.06388,0.04786,0.0149,0.09113,-0.01079,0.00485,-0.06227,-0.03186,0.06653,0.02483,-0.00617,-0.06783,-0.06349,-0.08811,0.01646,-0.04924,-0.03576,0.02486,-0.01707,0.00465,-0.00849,-0.03284,0.04077,0.07158,0.03502,0.0913,-0.02983,0.09019,-0.06134,-0.06353,0.07562,0.13731,0.06869,-0.07236,-0.08941,-0.00891,-0.05641,-0.00485,-0.08831,0.05676,0.03655,-0.08982,-0.05031,0.03072,-0.01994,0.07558,-0.04253,0.01164,-0.15624,-0.17899,-0.00127,-0.09718,-0.02969,0.09775,0.00236,0.02894,-0.02206,-0.02228,-0.06056,-0.04365,0.03884,0.00315,0.03387,-0.12119,-0.00859,-0.09696,-0.03174,0.02927,0.03054,0.05943,0.06897,0.03378,0.05166,0.05356,0.00835,0.12718,-0.00108,-0.02143,0.02994,0.02777,-0.00914,-0.11627,-0.00642,-0.10442,0.13285,-0.0234,-0.13992,-0.01276,0.01462,0.05811,0.01649,-0.08864,0.00985,0.06224,-0.00929,0.06882,-0.00597,0.02297,-0.04375,0.03627,-0.0165,0.10768,-0.05354,0.00322,-0.09877,0.01675,0.05124,-0.05212,0.01816,0.076,-0.1218,0.01206,-0.00979,-0.1081,0.03171,-0.05125,0.00594,-0.13281,-0.07793,-0.01618,-0.05139,0.05409,0.01295,-0.0251,-0.02678,0.09442,-0.09927,0.05096,0.00501,-0.0158,0.00216,0.0522,0.0078,-0.06491,0.06357,0.00714,0.02095,0.02172,0.00161,-0.0674,-0.10165,0.07935,-0.0393,0.00457,0.02318,0.05352,-0.06515,-0.03749,0.00228,0.03166,0.00455,-0.03895,-0.0181,-0.0214,0.02821,0.0046,0.16398,0.10311,-0.01863,-0.01269,0.01991,-0.06875,0.09066,-0.07743,-5e-05,0.05837,0.05283,0.18565,0.00665,0.05323,0.03364,0.03321,0.00806,-0.05808,-0.03474,0.03009,0.02678,-0.19714,-0.06212,-0.02027,-0.01066,-0.13377,-0.0567,0.03024,0.03174,-0.03844,-0.12217,-0.01836,0.08432,0.01991,0.14381,0.00336,0.07891,0.08089,-0.06539,0.03198,-0.02005,-0.03817,0.05048]},{"domain":"geospatial_analytics","key":"geo_ripley_k","name":"Ripley's 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12]","v":[-0.09381,-0.16304,0.1051,-0.08309,-0.0718,-0.10374,0.01437,0.05297,0.00754,-0.05915,-0.02971,-0.03799,-0.02173,0.00089,0.02275,-0.05426,0.03998,-0.0314,-0.11131,-0.04372,-0.04924,-0.10756,0.00116,-0.08769,0.05039,0.07136,-0.05409,-0.06644,-0.07699,-0.12058,0.08584,0.03371,0.03258,-0.11111,0.08225,-0.04533,0.03219,0.08821,-0.04091,0.06952,0.06199,0.0628,-0.00868,0.04804,-0.06286,-0.01384,0.03015,0.12635,-0.02502,-0.04918,-0.01342,0.02087,0.007,0.03875,-0.03854,-0.03931,0.12094,0.04129,0.15844,0.08193,0.10394,-0.03133,0.01575,-0.05393,-0.09836,0.00167,-0.14108,0.16986,-0.00719,0.11536,-0.04649,-0.0402,-0.0024,-0.03008,0.07519,0.08848,0.07065,-0.0916,0.04247,-0.07579,0.01646,0.0625,0.01051,-0.03217,-0.01525,-0.03643,0.0427,0.07299,-0.03117,-0.01146,-0.04775,0.00204,0.02437,0.07721,-0.00693,-0.01921,0.04259,0.05964,-0.0442,-0.02268,-0.00381,0.05147,-0.06671,-0.0443,-0.08854,0.06614,-0.11072,0.01942,-0.09788,-0.05071,0.00465,-0.09024,0.03195,0.13173,0.07698,0.12268,0.02062,0.03969,0.02456,0.02722,0.01842,-0.02549,-0.01011,0.01142,-0.01148,0.03832,-0.07532,0.03378,0.02055,0.01063,-0.0562,0.03763,0.07628,-0.01722,-0.09598,0.05148,-0.02123,0.00134,-0.00053,0.03473,-0.0719,0.01705,0.01237,-0.01876,0.07008,-0.05025,-0.00611,-0.01269,0.08241,-0.01185,-0.00431,-0.023,0.0459,-0.04238,0.10413,-0.13586,0.13821,-0.01388,-0.06651,0.03429,-0.07484,-0.00641,-0.09207,0.01674,0.07801,-0.04144,0.01079,-0.04967,-0.00283,0.02693,-0.10388,-0.04843,-0.03266,-0.05003,-0.00888,0.02778,0.00461,0.05663,0.01117,0.02621,-0.0154,-0.01949,0.01278,0.01676,0.06004,-0.10214,0.02916,-0.02886,0.06304,0.03412,-0.00203,0.04764,0.12746,0.08972,0.07728,-0.00558,-0.02334,-0.05309,0.0612,-0.16825,0.05191,0.03286,0.02638,-0.13767,0.01434,-0.05262,0.01391,-0.02425,0.00486,0.01261,0.04266,-0.05454,0.13941,0.04273,0.00106,0.02022,0.01162,-0.00256,-0.02894,0.07662,-0.02676,0.06712,-0.00626,0.10582,-0.02487,0.07234,-0.03265,0.00381,0.00449,-0.00643,0.0206,0.03802,-0.02684,-0.09674,-0.11472,-0.05573,0.04661,0.01668,-0.06157,-0.02787,0.10039,-0.06657,0.0528,0.01762,-0.0795,0.00855,-0.01197,0.11946,0.03604,0.07274,0.09804,-0.05965,-0.14357,-0.01596,-0.03016,-0.0733]},{"domain":"geospatial_analytics","key":"geo_segregation_evenness","name":"Residential 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1000]","v":[-0.07076,0.04332,-0.00928,0.00863,-0.06022,-0.0955,0.07945,-0.04351,0.02865,-0.05204,-0.01575,0.00396,0.03771,-0.05543,-0.04774,-0.04217,0.00848,0.0146,-0.04599,0.01677,0.03152,-0.07384,0.09673,-0.01728,0.00096,0.09149,0.07551,-0.13823,-0.06079,-0.07985,-0.08905,0.00042,0.03947,0.03764,0.01197,0.02616,-0.02902,-0.00846,0.01856,0.04171,0.04149,-0.01536,-0.10768,0.07081,-0.03477,-0.05785,0.06727,-0.05138,-0.00718,-0.02743,0.0058,0.07033,0.04224,-0.09087,-0.05951,0.02867,0.02808,0.00716,0.00919,0.04141,0.08416,0.04652,-0.00331,-0.01864,-0.01984,-0.03659,0.14683,0.07985,-0.0577,0.15445,-0.03045,0.02348,0.06838,0.00808,-0.12531,0.03421,0.00282,-0.07852,0.12145,0.02464,0.05579,0.01404,0.0615,0.00023,-0.07005,-0.06621,0.04714,-0.04186,-0.04342,0.03375,-0.15038,-0.04243,-0.01777,-0.03513,-0.00158,0.0089,-0.10384,0.03673,0.0091,-0.0301,0.02086,0.00796,0.08519,-0.06565,0.08304,-0.05972,0.09863,-0.15879,0.0029,0.06917,0.04106,-0.06251,0.06565,0.04277,-0.02011,-0.0548,0.09775,0.03188,0.05755,0.01816,-0.03854,-0.01185,-0.06575,0.1396,0.01474,0.01772,-0.06935,-0.13636,-0.01564,-0.02337,0.08455,-0.01103,-0.02501,-0.08761,-0.03909,0.02476,-0.01134,0.05698,-0.01724,-0.01709,0.02802,-0.03196,0.08253,0.03298,0.19423,-0.00431,-0.02259,-0.01901,0.02192,0.0181,-0.03214,-0.04631,-0.05135,0.049,0.14364,-0.01251,-0.01807,0.03649,0.02325,0.06113,0.03067,-0.07648,0.00277,-0.00884,0.09791,-0.03503,-0.00702,-0.01155,0.10186,0.06427,-0.01663,-0.1067,0.11155,0.01268,-0.00184,-0.03506,0.01863,0.0914,-0.00382,-0.01735,0.05803,0.03269,-0.17527,-0.03701,-0.01636,-0.041,0.04745,0.04169,-0.07036,-0.01112,0.1289,0.07014,0.02141,0.07925,-0.01239,0.04115,-0.08607,0.01913,-0.05882,-0.04239,-0.03203,-0.07027,0.05579,-0.08545,-0.07493,0.02041,0.07849,-0.09177,0.06191,0.11896,0.02327,-0.0788,0.04708,0.02555,-0.08411,0.05617,0.03462,-0.04442,0.01094,-0.06926,0.03353,-0.06901,0.05016,-0.0583,0.02479,-0.07033,-0.09156,-0.141,-0.0481,0.00718,0.04282,0.12053,0.02451,-0.08681,0.14214,-0.03347,0.06234,-0.04929,0.06408,0.01279,0.05754,-0.05874,0.0585,0.04938,0.01577,0.00308,-0.02318,-0.08614,0.10386,-0.05922,0.0451,-0.02996,-0.11402,-0.02364,0.05303,0.09646]},{"domain":"geospatial_analytics","key":"geo_segregation_exposure","name":"Residential 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1000]","v":[-0.12065,-0.01287,-0.07227,0.03497,-0.08731,-0.08488,0.00342,-0.03113,0.03137,-0.06131,0.0426,0.02789,0.02866,-0.10175,-0.0064,-0.05293,-0.0068,0.00175,0.02345,0.03711,0.00607,-0.06002,0.13175,-0.03053,-0.0401,0.14392,0.00512,-0.09878,-0.07366,-0.06046,-0.03316,-0.02049,-0.0045,0.04639,-0.01046,0.00838,-0.00949,0.07114,-0.01353,0.01648,0.07033,0.03116,-0.08966,-0.00245,-0.03677,-0.03669,0.02768,-0.04184,-0.0241,-0.00903,0.0148,0.09315,0.05928,-0.02831,-0.06075,-0.02874,0.08315,-0.04992,0.00888,0.07027,0.06944,0.06646,-0.01139,-0.02787,-0.01676,-0.09188,0.1218,0.14958,-0.00468,0.05936,0.03411,-0.01726,0.07079,-0.05398,-0.1918,0.00583,0.02656,-0.03365,0.1655,0.02021,0.07795,-0.0793,0.04424,-0.03137,-0.12208,-0.08097,-0.01712,0.11652,-0.00861,0.09421,-0.06356,0.0065,-0.00783,-0.0968,0.00582,-0.02501,-0.08851,0.05877,0.02528,0.00957,0.03228,-0.03114,0.14289,-0.03378,0.05557,-0.03346,0.07486,-0.15872,0.02117,0.12461,0.00535,-0.05496,0.00383,0.00397,-0.02686,-0.01696,0.07362,-0.02092,0.05992,-0.05526,-0.08254,0.01399,-0.04282,0.15689,0.02751,0.08397,-0.03791,-0.09748,0.03025,0.02026,0.07345,-0.01124,0.00149,-0.01316,-0.05385,0.04567,-0.02271,0.05392,0.0227,0.05212,0.01451,-0.03774,0.03449,0.0323,0.0968,-0.06659,0.00833,-0.04345,0.02297,0.00989,-0.07093,0.0214,-0.03174,0.10188,0.11491,-0.02429,-0.08783,0.04519,-0.00723,0.13444,0.05741,0.01187,-0.00179,-0.0403,0.11011,0.02333,-0.0017,-0.05876,0.02482,0.09114,-0.04846,-0.03991,0.02468,0.02562,0.04566,-0.03585,0.06912,0.05597,-0.09285,0.06414,-0.04961,0.09785,-0.18338,-0.07177,-0.05697,-0.03379,0.04808,-0.02569,-0.04828,-0.10331,0.0231,0.00428,-0.02172,0.06287,-0.02035,0.02827,-0.06264,-0.02993,-0.07447,0.0208,0.00615,-0.13088,0.07126,-0.01991,-0.01133,-0.01513,0.01098,-0.04348,-0.00336,0.11934,-0.00716,-0.07537,-0.00861,-0.00581,-0.1549,0.11262,0.02858,-0.05835,0.00912,0.06465,0.05105,-0.04917,-0.03118,-0.00399,0.13069,-0.01633,0.01813,-0.10823,-0.00907,-0.03694,-0.08397,0.08855,-0.0048,-0.03963,0.10253,-0.03796,0.06789,-0.06392,0.03579,0.02867,0.05483,-0.08667,0.06485,0.00289,0.00398,-0.00947,0.00277,-0.06106,0.06658,-0.01659,-0.05241,-0.03858,-0.07727,-0.0157,0.04734,0.05678]},{"domain":"geospatial_analytics","key":"geo_service_area","name":"Network service area (isochrone) of a facility","package":"geospatial-analytics-ai999x","example":"Service area: edges = [0-1 2; 1-2 3; 0-2 6; 2-3 1; 3-4 4], source = 0, cutoff = 6","v":[-0.12703,0.02937,0.07533,-0.04038,-0.00912,0.01624,0.04109,-0.05003,0.15668,-0.13528,0.03371,0.00919,0.04096,0.07225,-0.02521,0.06854,0.02943,0.05839,-0.02144,-0.0207,-0.00113,-0.07732,0.07209,-0.01414,0.03214,0.07021,-0.02547,-0.02623,-0.00509,-0.01331,0.02897,0.05178,-0.01287,-0.01647,0.023,0.02063,0.09924,0.10711,-0.03161,0.05568,0.00649,0.04375,-0.04639,-0.06652,-0.04036,0.07306,-0.02191,-0.02142,0.00417,-0.04554,0.03552,-0.00362,-0.04837,-0.06196,0.01275,-0.10564,0.01969,0.00047,0.03837,-0.00232,0.10766,-0.03174,-0.09037,0.03896,0.00052,0.03718,0.06138,0.09063,-0.0387,0.02068,-0.0689,-0.06126,-0.07264,-0.00897,-0.05984,-0.03881,-0.05526,0.00027,-0.06468,0.00168,-0.01528,-0.05518,0.12982,0.02928,0.06304,0.03593,0.01247,-0.0066,0.09189,-0.01066,0.00334,0.05892,0.02646,-0.07167,-0.13976,-0.04674,0.02997,0.07862,-0.0903,0.02938,0.03424,0.01415,0.00566,-0.03501,-0.09235,-0.05622,-0.13921,-0.16127,-0.07347,-0.02116,0.02788,0.01495,0.04122,0.08019,0.09995,-0.04686,0.03153,0.07101,0.03356,0.09433,0.09834,0.02214,-0.03548,0.01593,-0.00686,-0.0508,-0.09309,0.00802,0.05069,-0.04933,-0.07526,0.0661,0.02926,-0.0097,-0.13102,0.06683,-0.04235,-0.05185,0.05541,0.06742,0.03216,0.05018,-0.00463,-0.10069,-0.06255,-0.03615,-0.02332,-0.03318,-0.07026,-0.03683,-0.04067,-0.05153,0.05743,0.05794,0.04224,0.00371,-0.111,-0.01485,-0.04311,0.07955,-0.08771,0.11621,0.01812,0.10174,0.1092,0.0146,0.09177,-0.00898,0.06956,0.00435,-0.05533,-0.01402,0.0383,0.00807,-0.01918,-0.08214,-0.08015,0.03378,0.02323,0.09932,-0.05158,-0.00321,0.04948,0.00065,-0.14464,0.01811,-0.05245,0.111,0.05939,0.09654,-0.09457,-0.13044,0.05019,0.07789,-0.1067,0.00293,0.02791,-0.08619,0.03176,0.04314,0.00941,-0.05897,0.15908,-0.02892,-0.07182,-0.10479,0.09369,0.00572,0.02498,-0.05365,0.09657,-0.07348,-0.06285,0.02521,-0.02201,0.0893,0.11432,0.10201,0.03358,0.05674,-0.01314,0.01267,0.04226,-0.02169,0.02549,-0.04711,-0.07727,0.05207,-0.06532,-0.04476,0.03381,0.05021,0.06038,-0.05466,-0.005,0.04395,-0.04475,0.05844,0.00141,-0.07686,0.0519,-0.03092,0.00284,-0.09469,-0.01381,-0.13515,0.00615,-0.07125,-0.04086,0.10734,0.10547,0.03265,-0.04761,0.02022,-0.13716,-0.00395]},{"domain":"geospatial_analytics","key":"geo_shimbel_index","name":"Shimbel accessibility index of every node","package":"geospatial-analytics-ai999x","example":"Shimbel index: edges = [0-1 2; 1-2 3; 0-2 6; 2-3 1]","v":[-0.11376,-0.02174,0.0556,-0.02878,-0.07213,0.04115,0.08549,-0.04252,0.11901,-0.15715,0.00572,-0.01469,0.04995,0.08604,-0.04545,-0.07886,0.05638,0.00953,-0.00087,-0.09613,0.05757,-0.1192,0.08689,0.0437,0.06793,0.06735,0.02676,-0.06069,-0.03424,-0.1023,-0.05705,0.02102,0.06496,-0.05106,0.00649,0.01078,0.01611,0.05495,0.03012,0.07846,-0.12422,0.02206,-0.08031,0.00482,-0.03597,0.07383,-0.01795,-0.02394,0.04092,-0.08988,-0.03124,-0.03979,-0.07711,-0.01882,0.03207,-0.15165,0.05779,-0.00954,0.01007,0.01771,0.14596,0.05254,-0.09282,0.00859,-0.05049,0.06758,0.01998,0.04006,-0.03016,-0.0502,-0.01512,-0.04107,0.04877,0.03126,-0.04656,0.03799,-0.0533,-0.01471,0.00473,-0.01265,-0.03406,0.02505,0.16167,0.04069,-0.0008,-0.06313,0.07273,-0.01816,0.06345,0.00697,-0.07745,-0.04866,0.02891,-0.10235,-0.06989,-0.00515,-0.05078,0.09093,-0.00546,0.04662,0.06978,-0.00905,-0.03984,-0.06568,-0.02955,-0.03269,-0.01298,-0.18281,-0.01599,0.08508,0.05769,0.02114,0.01744,0.08734,0.05973,-0.07023,0.04384,0.09076,0.08673,0.09296,0.07123,0.09523,0.01796,0.07897,0.01219,-0.04216,-0.12891,-0.09813,-0.01586,-0.04035,-0.02512,0.04448,-0.01176,0.01194,-0.08743,0.07094,-0.09795,-0.05884,-0.06279,0.04014,0.08621,-0.02207,-0.07205,0.02098,0.04994,-0.02679,0.09139,-0.04099,-0.07155,-0.06471,-0.0738,0.00676,0.02627,0.0542,0.07291,-0.09798,-0.05471,-0.04799,-0.0414,0.04771,-0.09671,-0.04214,0.02278,0.08002,0.10547,0.00253,0.10454,0.04071,0.08404,0.02254,0.00729,0.03875,0.08994,-0.03037,-0.06357,-0.05663,-0.09102,-0.01526,0.04103,0.00843,0.00825,-0.07804,-0.03202,0.03943,-0.1254,0.03221,0.00608,0.00253,0.02772,0.06531,-0.04798,-0.05561,0.05834,0.01339,-0.07561,-0.03027,0.00374,-0.0557,0.09198,-0.17585,-0.05494,-0.04782,0.08187,-0.03743,-0.03697,-0.06271,0.08212,-0.06646,0.00943,-0.04511,0.05975,-0.02308,-0.07754,0.05683,0.05312,0.0282,0.06806,-0.01049,0.04677,0.05338,0.03856,-0.04115,0.12255,0.01299,-0.001,-0.05298,-0.17096,0.04808,-0.00547,0.04977,0.07119,0.08766,0.04419,-0.01681,0.05828,0.0526,0.00986,0.03496,-0.03452,0.01598,0.12561,0.02877,0.05265,0.01552,0.00409,-0.08481,0.02644,0.03045,0.01766,0.00398,0.05993,-0.05971,-0.05722,-0.03773,-0.09224,0.03041]},{"domain":"geospatial_analytics","key":"geo_sinusoidal_forward","name":"Sinusoidal equal-area projection (ellipsoidal)","package":"geospatial-analytics-ai999x","example":"Sinusoidal forward: lat = 45, lon = 10, lon0 = 0, ellipsoid = WGS84","v":[-0.03974,0.05237,0.02897,-0.08928,0.08592,0.0217,0.01948,0.04647,-0.01412,-0.0593,0.08112,-0.07454,-0.01778,0.01433,-0.01297,0.10657,0.10859,0.02368,-0.01476,-0.01663,-0.11371,0.02597,0.01265,0.02428,-0.10121,-0.00078,-0.01862,0.00602,-0.05496,-0.08884,-0.08127,-0.11471,0.00706,-0.00748,0.0106,-0.05055,0.04352,0.01442,-0.03511,0.04798,0.0488,-0.06755,-0.05617,0.0813,0.01336,-0.04771,-0.02035,0.00595,-0.0757,0.03647,0.00537,-0.12305,0.03548,0.02657,-0.05939,-0.0046,0.01118,-0.01143,-0.03313,-0.02426,0.0677,-0.04281,-0.04067,-0.01883,0.06062,-0.04182,0.05742,-0.02692,0.08275,0.07139,-0.04821,-0.13067,-0.00294,0.05003,-0.12169,-0.04194,0.15765,-0.14046,-0.05701,-0.04803,0.03028,0.01151,0.10981,-0.00989,0.08721,-0.05981,-0.02136,-0.04048,0.02102,-0.05873,-0.01734,-0.07351,0.03703,-0.03415,-0.1116,0.03153,-0.0201,-0.04087,0.04147,-0.04192,-0.05203,0.06832,0.09867,-0.06377,0.09058,-0.00589,0.00134,0.02987,-0.14312,-0.01279,0.08301,0.03284,-0.02058,-0.05212,0.03496,0.02609,0.01692,0.16082,-0.03535,0.03951,-0.05455,-0.05451,0.00448,-0.07297,0.05478,-0.06719,0.02058,0.01835,-0.05475,-0.02329,0.03913,-0.04827,0.04194,-0.0227,-0.0413,0.11795,-0.01198,0.02389,-0.17282,-0.01493,-0.06469,-0.02265,-0.037,-0.00649,0.04082,-0.05257,-0.00255,0.0294,-0.07549,0.10553,0.05162,-0.01374,0.03956,0.03045,0.04157,0.05342,0.02291,0.12633,0.04412,0.06644,0.04235,-0.11005,0.00594,0.04624,-0.00854,0.03035,-0.08386,0.09611,-0.02421,0.14143,-0.01597,-0.02715,0.14087,0.00192,0.00861,0.00618,-0.00991,-0.00214,-0.01711,-0.04485,0.03854,-0.05178,-0.07673,-0.06928,0.17323,0.05411,-0.03111,0.00431,0.08057,0.02596,0.0428,0.12305,0.05931,0.06179,0.03964,0.13217,0.07041,-0.00397,-0.05947,0.05516,-0.10424,-0.06064,0.07534,-0.01838,-0.00601,-0.04179,-0.10279,0.03326,0.05776,-0.03023,0.01497,-0.04495,0.03923,0.1463,0.04147,-0.01754,0.01366,-0.00416,-0.07328,-0.14346,-0.09953,-0.0125,0.06271,0.09013,0.1119,-0.03572,0.05136,-0.0319,0.09567,-0.02345,0.04288,-0.01615,-0.00442,0.10981,-0.03203,-0.09101,-0.01879,-0.02373,-0.04534,-0.02702,0.04822,0.0288,-0.06639,-0.06372,0.06585,-0.05519,0.05731,-0.03826,0.14195,-0.03733,-0.01359,0.05825,-0.05188,-0.04918,-0.07521,-0.02899]},{"domain":"geospatial_analytics","key":"geo_slope_aspect_horn","name":"Slope and aspect of a 3x3 elevation window (Horn's method)","package":"geospatial-analytics-ai999x","example":"Slope and aspect: window = [[37.2, 42, 47.2], [45.2, 50, 55.2], [53.2, 58, 63.2]], cell_size = 10 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lag of a variable","package":"geospatial-analytics-ai999x","example":"Spatial lag: y = [8, 6, 6, 3], W = [[0, 1, 0, 1], [1, 0, 1, 0], [0, 1, 0, 1], [1, 0, 1, 0]], transform = 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60","v":[0.11269,-0.03095,0.0598,0.04002,-0.00088,0.03668,-0.14658,0.00254,0.01966,-0.02591,0.0047,-0.05359,-0.00503,0.02326,-0.06588,-0.04795,0.0866,0.01617,0.09957,-0.00292,0.06937,-0.17297,-0.07621,-0.07058,0.07542,-0.00872,0.00773,-0.02769,-0.08767,-0.04786,0.03875,0.02724,-0.04155,0.00203,-0.0191,0.04328,0.09479,0.10605,0.05753,-0.05932,0.05499,0.02812,-0.04733,0.00806,0.0209,0.04478,0.06409,-0.06588,-0.0676,-0.0125,-0.00639,0.03731,0.00882,-0.03685,-0.02958,-0.03821,0.04156,0.04957,0.05407,0.04412,-0.04518,0.06721,-0.03298,-0.06962,-0.12725,-0.14503,-0.00471,0.01393,0.07022,-0.00359,0.08891,-0.0964,0.13249,0.0119,-0.00376,0.05793,0.0545,-0.03197,0.0173,-0.00477,0.04352,0.07089,-0.00296,-0.06285,0.00843,0.00882,0.0553,-0.07772,0.01204,0.00954,-0.07932,0.01422,0.0768,-0.00837,-0.11907,-0.00257,0.06421,-0.04569,0.06596,0.02918,0.05106,-0.04321,-0.01467,-0.07054,-0.02732,-0.01711,-0.02457,-0.04917,0.03307,-0.05561,0.07319,0.0411,-0.07773,-0.05669,0.15187,0.06138,-0.00493,0.02354,0.01033,-0.09111,0.0518,-0.07231,-0.11874,0.01678,-0.00317,-0.04639,0.00221,-0.04764,-0.11068,0.08743,-0.02703,0.02886,-0.02641,-0.08805,-0.01478,0.06738,-0.05897,-0.19823,-0.03419,0.16241,0.03814,0.05108,0.04265,0.04033,0.05377,0.00484,0.04593,-0.04377,-0.09415,0.05274,-0.04491,0.04871,0.00906,0.00579,-0.13503,-0.00463,-0.02524,-0.00772,-0.00997,0.05441,-0.02983,-0.00913,0.00841,0.06103,-0.01065,0.10514,-0.13422,0.11114,-0.07057,0.14527,0.05197,0.04907,0.04863,-0.07849,0.07815,-0.03801,-0.00898,0.09082,0.01645,-0.03361,-0.01187,-0.00112,-0.0846,0.01946,-0.04479,0.11436,0.0629,-0.03867,0.01192,-0.01031,-0.02564,-0.04685,0.03372,0.06161,0.0272,-0.01118,-0.00131,0.09776,0.08372,-0.01689,0.02093,0.00842,0.10862,-0.00408,0.08842,-0.02346,-0.05356,0.0882,-0.13731,0.0033,0.0194,0.03561,-0.00393,-0.05577,0.04146,-0.01585,-0.01806,0.04898,-0.00841,0.01048,0.07218,-0.04622,-0.03635,-0.03977,0.02253,-0.00018,-0.01655,-0.09938,0.0417,-0.14578,0.08444,0.06177,-0.10416,0.09146,0.03648,-0.06656,0.10434,-0.14809,-0.04402,0.04618,-0.04,-0.0268,-0.00187,0.0155,-0.04273,0.05705,0.00132,-0.06749,0.115,0.0336,0.03406,0.04115,-0.03158,0.07082,-0.08699,0.10528]},{"domain":"geospatial_analytics","key":"geo_transverse_mercator_forward","name":"Transverse 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and longitude to UTM coordinates (with scale factor and convergence)","package":"geospatial-analytics-ai999x","example":"UTM forward: lat = 51.5, lon = -0.13, ellipsoid = WGS84","v":[0.03687,0.04432,-0.0001,0.02702,0.01649,0.08532,-0.02502,-0.05464,-0.0813,-0.07479,0.0597,0.0134,0.00422,0.13212,0.04182,-0.00783,0.07513,0.0342,0.04022,0.12286,-0.08151,-0.02593,-0.03241,0.03683,-0.02115,-0.04665,0.00866,-0.03256,0.00447,0.00229,-0.00672,-0.07587,0.00492,-0.04523,-0.00655,-0.09443,0.07398,0.03991,-0.05614,-0.01083,0.04091,0.03676,-0.09987,0.0532,-0.07373,0.03011,-0.10299,0.05341,-0.03651,-0.05146,0.01561,-0.12203,0.03792,0.02934,0.02946,-0.01816,-0.01235,-0.05617,-0.04718,-0.03155,-0.10124,-0.04834,-0.00121,-0.07223,-0.03482,0.01945,0.03132,-0.05879,0.03367,0.08123,-0.04329,-0.09594,0.01618,0.06801,-0.0479,-0.05231,0.05884,-0.06033,-0.02736,0.11119,0.00666,0.07072,0.02453,-0.04245,0.05612,0.0013,-0.03269,-0.03547,0.08744,-0.06227,0.03273,0.05038,-0.03051,-0.02501,-0.01158,0.04006,-0.12401,-0.00556,0.01946,-0.14096,0.08251,-0.02288,0.04555,-0.0582,0.01009,-0.08388,0.03534,-0.02763,-0.15785,-0.02869,0.08552,-0.02269,-0.03394,-0.03866,0.04119,0.00838,0.01839,0.07704,-0.08149,-0.03723,-0.08822,-0.04017,0.03041,-0.00514,0.07589,-0.10705,0.05782,0.01463,0.02382,0.0476,-0.01795,-0.15728,-0.08277,0.03595,-0.00087,0.03563,0.10722,0.01433,-0.06295,0.04129,0.10177,-0.00042,-0.06751,0.03412,0.02551,0.04488,-0.10416,0.01196,0.07512,0.0974,0.00643,-0.04419,-0.05879,0.12047,-0.02793,-0.02877,0.03008,-0.02771,-0.0092,0.15316,0.04741,-0.1191,0.06013,0.04819,0.04615,0.07639,0.0178,0.08754,-0.12248,0.04057,0.01372,0.02131,0.09357,0.12911,-0.04145,0.03211,0.03615,-0.00952,-0.01114,0.00487,0.02706,-0.02721,0.03674,-0.10688,0.10379,-0.05954,0.00191,0.05308,-0.01081,0.06968,0.01107,0.05723,0.00366,-0.05729,0.01726,0.05818,-0.07872,0.07401,-0.05091,0.15325,-0.16603,-0.02328,0.12511,-0.07734,0.06216,-0.00364,0.03026,0.00904,0.00948,-0.10021,0.03146,0.12698,0.10057,0.10696,-0.02001,-0.04374,-0.11027,-0.02099,-0.10576,-0.07037,-0.14675,-0.0455,0.0216,0.03916,-0.01303,0.03723,0.06108,-0.05303,-0.01851,0.01886,0.04237,-0.00649,-0.00011,-0.06942,-0.12293,0.02353,0.01709,0.03993,-0.0072,-0.01155,0.0572,0.00552,-0.10323,-0.11759,0.00318,0.07704,0.0581,-0.01221,0.10686,-0.07701,0.08879,0.02248,0.01197,-0.05152,-0.00949,-0.01262]},{"domain":"geospatial_analytics","key":"geo_utm_inverse","name":"UTM coordinates to latitude and longitude","package":"geospatial-analytics-ai999x","example":"UTM inverse: easting = 699316.0 m, northing = 5710164.0 m, zone = 30, hemisphere = N, ellipsoid = WGS84","v":[0.01328,0.01908,-0.0249,0.04854,0.04968,0.09491,0.01085,-0.06288,-0.04663,-0.03793,0.03711,0.03434,0.0025,0.11159,0.06668,0.01274,0.09427,0.00151,0.03674,0.06908,-0.14674,-0.03327,-0.09211,0.04233,-0.03457,-0.05906,-0.0023,-0.01153,0.05109,0.00778,-0.00756,-0.02533,0.00955,-0.00817,-0.01822,-0.10264,0.08463,-0.02142,-0.022,-0.0485,0.04112,-0.01382,-0.09723,0.05767,-0.04005,0.00453,-0.12602,0.00672,-0.05188,-0.04911,0.03276,-0.11821,0.02589,0.01882,0.00142,-0.02661,0.01549,-0.05151,-0.05785,-0.07034,-0.10214,0.01934,-0.02729,-0.03083,-0.02474,-0.00779,0.06045,-0.06707,0.00904,0.10008,-0.08653,-0.11532,0.02346,0.05887,-0.05784,-0.10591,0.02311,-0.01397,0.00306,0.12959,0.01352,0.06714,0.03779,-0.03736,0.02316,0.0351,-0.02482,-0.0383,0.10149,-0.01947,0.03469,-0.01227,-0.04394,-0.02885,0.00408,0.07788,-0.12425,0.0125,-0.02528,-0.1058,0.06069,0.02876,0.10117,-0.02978,0.02454,-0.13758,0.03123,0.00117,-0.18593,-0.0518,0.06445,-0.02614,-0.07788,-0.02438,0.06616,-0.01821,0.02,0.03244,-0.14542,0.0038,-0.07865,-0.01797,0.04654,-0.04192,0.07503,-0.0373,0.14701,0.0348,0.03722,-0.00083,0.00539,-0.12418,-0.05766,0.05375,0.03632,0.01868,0.1026,0.03806,-0.05585,0.04752,0.05483,0.03976,-0.10618,-0.00701,0.0352,-0.01433,-0.05154,0.03259,0.04737,0.04884,0.02602,0.00176,-0.06484,0.13973,-0.05866,0.03856,-1e-05,0.00025,0.01987,0.14372,0.05074,-0.13197,0.01577,0.04103,0.02329,0.09098,-0.00304,0.05588,-0.12701,0.01279,0.01777,-0.02578,0.13999,0.08473,-0.0809,-0.01997,0.05381,-0.01628,-0.02559,-0.00561,0.01921,-0.04602,0.00212,-0.11708,0.11373,-0.03883,0.03178,0.06831,0.00279,0.05089,0.00643,0.0837,-0.01975,-0.06159,-0.02206,0.04245,-0.05469,0.10815,-0.0629,0.14368,-0.15614,0.01643,0.09288,-0.1003,0.01652,-0.01496,0.09929,0.01347,0.01676,-0.09524,0.00887,0.10358,0.0902,0.08167,0.00327,-0.07251,-0.04292,0.02204,-0.03543,-0.09277,-0.11164,0.01495,0.00066,-0.02217,-0.00694,0.01588,0.0456,-0.06923,0.0191,0.00823,0.07573,-0.02567,0.00702,-0.07681,-0.10657,0.05357,0.0149,0.08497,-0.00819,-0.0107,0.01158,-0.02703,-0.0977,-0.051,0.04054,0.03088,0.04061,-0.01624,0.14299,-0.07869,0.0226,0.01012,0.03167,-0.09031,-0.00504,0.02252]},{"domain":"geospatial_analytics","key":"geo_utm_zone","name":"UTM zone, latitude band and central meridian","package":"geospatial-analytics-ai999x","example":"UTM zone: lat = 51.5, lon = 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indices: NDVI, EVI, SAVI, OSAVI, MSAVI and EVI2 from band reflectances","package":"geospatial-analytics-ai999x","example":"Vegetation indices: red = 0.08, nir = 0.45, blue = 0.04, L = 0.5","v":[0.0934,0.0584,0.02484,0.07805,0.03746,0.00598,-0.031,0.07537,-0.04996,-0.11369,0.0631,-0.03251,-0.02725,-0.08656,-0.03545,0.02386,0.02029,-0.00178,0.0092,0.01695,0.05217,-0.01332,-0.08446,-0.02234,-0.00044,-0.02758,0.05762,-0.1774,-0.07453,-0.00452,-0.01252,-0.04928,0.03973,0.13421,0.05576,-0.04461,0.13445,0.12336,0.0597,-0.03045,0.04943,0.04921,-0.02268,-0.03677,0.00991,-0.07675,0.07157,-0.00152,-0.04466,-0.03915,-0.00732,0.08062,-0.05544,-0.036,-0.03018,-0.05479,-0.00858,0.09845,0.08576,0.04014,0.02006,0.06382,0.02589,-0.01732,-0.03583,-0.00924,-0.02827,0.03198,0.12031,0.07852,0.0353,-0.04896,0.0542,0.0091,-0.01689,0.00046,-0.08733,-0.08176,0.01273,0.06283,0.03765,0.12864,-0.03716,-0.05732,0.10767,0.05767,0.03408,-0.12992,-0.03978,0.05137,-0.0578,0.04952,-0.03586,-0.12078,0.00849,-0.00468,-0.00317,-0.06351,-0.01809,-0.10061,-0.04397,-0.04353,-0.02866,-0.0445,-0.00261,-0.04833,-0.01846,-0.04384,0.11839,-0.0563,0.02844,-0.03446,-0.09995,-0.05734,-0.003,0.01946,0.04783,0.00596,0.079,-0.0113,0.01884,-0.15042,-0.04023,-0.04769,-0.05472,-0.00141,0.0377,-0.0055,-0.12513,0.04328,-0.06927,0.04526,-0.06884,-0.03987,-0.01039,0.00454,-0.11008,-0.06209,-0.07023,0.08127,0.01586,-0.00965,0.14968,-0.02549,0.07378,-0.07263,-0.01053,-0.01727,0.00279,-0.01376,0.03448,0.03038,0.10173,-0.08437,-0.06182,-0.09451,0.09391,-0.09312,-0.04406,0.04035,-0.05262,0.03002,0.00196,0.00948,0.09634,-0.03175,-0.06675,0.05411,0.04396,0.12602,0.08394,0.04602,-0.02292,-0.04937,0.14078,0.02957,-0.08985,0.03378,0.01655,-0.08017,0.04,-0.04458,-0.15103,-0.0433,-0.00576,0.08738,0.06527,0.03649,0.01931,0.07907,0.0844,0.04856,0.06759,0.02236,0.00969,0.00831,-0.03622,0.02432,-0.03168,0.07969,0.01792,0.03055,0.08491,0.07243,-0.02816,-0.0139,-0.03788,0.07517,-0.12191,0.08496,0.02992,0.00615,-0.10656,0.04927,0.0697,-0.01958,0.02632,-0.02603,0.06826,-0.01491,0.03745,0.03848,-0.06926,-0.08007,-0.12765,-0.00934,0.00082,-0.00321,-0.01804,-0.114,0.03971,0.01763,0.00645,-0.00982,0.07343,-0.07311,0.08123,-0.06468,-0.02328,0.03078,0.06208,-0.056,0.07285,0.12304,0.0478,0.02753,0.04246,-0.00788,-0.01593,0.10144,-0.01762,0.04361,-0.10942,-0.0181,-0.17951,0.01375]},{"domain":"geospatial_analytics","key":"geo_water_burn_built_indices","name":"Water, moisture, burn and built-up indices: NDWI, MNDWI, NDMI, NBR and NDBI","package":"geospatial-analytics-ai999x","example":"Water indices: green = 0.08, nir = 0.03, swir1 = 0.02, swir2 = 0.01","v":[0.04823,-0.00722,0.12057,0.06307,0.02396,-0.08391,-0.02757,0.09948,-0.02921,-0.01124,-0.08105,0.07237,0.00337,-0.01501,-0.12991,-0.03261,-0.00778,-0.03598,-0.02436,0.04006,0.0844,-0.1693,-0.04259,0.09293,-0.01495,-0.01474,0.0275,-0.03014,-0.05779,-0.02614,0.04679,-0.00854,0.01482,0.0778,0.03972,-0.0152,0.02727,0.02358,0.08814,-0.09832,0.06703,0.01322,0.03677,-0.00923,0.0435,-0.0727,-0.00269,-0.03025,0.04287,0.02388,-0.05306,0.15779,0.01518,0.02808,-0.05446,0.02911,-0.03774,0.07312,0.0715,0.07157,-0.05603,0.03904,-0.01281,-0.11651,-0.05061,0.06628,-0.00992,0.05165,0.07458,-0.02759,-0.02228,-0.07957,0.05262,0.0243,0.00464,-0.03715,-0.12678,-0.03777,0.05677,-0.00323,0.00439,0.09067,0.05102,-0.0907,-0.00293,-0.03044,0.01219,-0.09524,-0.01518,0.10202,-0.09229,0.09998,-0.00452,-0.00722,0.06161,0.02038,0.09283,-0.01161,-0.05995,-0.02785,0.0,0.08724,-0.07337,-0.08174,-0.05346,-0.09758,-0.05534,-0.01798,0.07323,-0.06639,-0.06736,-0.09437,-0.00139,-0.04423,-0.07315,-0.0444,0.07149,-0.06126,0.07942,0.10113,0.05623,-0.06995,-0.12467,-0.03996,-0.04467,-0.03688,0.05092,0.01556,-0.12508,-0.08336,0.05143,0.13289,0.03123,-0.07679,0.06495,0.04105,-0.04615,-0.03936,-0.07402,0.06649,-0.04143,0.02196,0.07572,-0.13157,0.06153,-0.09541,-0.03036,-0.10242,0.00711,-0.11429,0.07044,0.03385,0.06221,-0.00669,-0.07686,-0.06749,0.02146,-0.10298,0.01088,0.04559,-0.00694,0.0565,-0.0148,-0.01967,0.08246,-0.04328,0.04387,0.04144,0.05361,0.05965,-0.02771,-0.05743,-0.0051,0.03782,0.12746,0.01723,-0.01162,-0.01241,0.08366,-0.07546,-0.00619,-0.03348,-0.12733,-0.0968,-0.04399,0.12185,0.05361,0.13422,-0.0733,0.00909,0.07233,0.01394,-0.04137,0.06916,-0.02269,-0.01799,0.02084,0.0579,0.01074,0.00184,0.0204,0.09073,0.12122,0.05213,-0.04864,-0.03103,0.04085,0.09847,-0.08564,0.07084,-0.00311,0.07814,-0.03024,0.06412,0.06426,-0.05386,0.06541,-0.05949,0.04355,-0.04026,0.12179,0.03467,-0.13738,0.00963,-0.02861,0.02137,-0.0257,-0.05473,-0.05816,-0.0672,-0.02613,-0.00776,0.01213,0.05216,0.12682,-0.05735,0.02249,0.10436,-0.02626,0.06564,0.00221,-0.01143,-0.01912,0.00739,-0.05888,0.00449,0.02596,0.10953,0.05185,-0.03025,0.07182,0.03121,-0.04452,0.00455,-0.05761,0.00486]},{"domain":"geospatial_analytics","key":"geo_watershed_delineation","name":"Watershed (catchment) of an outlet cell on a small DEM","package":"geospatial-analytics-ai999x","example":"Watershed delineation: dem = [[78, 72, 69, 71], [74, 67, 56, 49], [69, 53, 44, 37], [64, 58, 55, 22]], cell_size = 10 m, row = 3, col = 3","v":[0.04096,0.06644,0.08547,0.09005,-0.1165,0.02354,-0.02887,-0.0254,0.01348,-0.03956,0.08511,-0.02921,0.00413,-0.01023,0.03813,0.0643,0.04255,0.15524,-0.03242,0.02236,-0.00768,0.04123,-0.05915,-0.03476,-0.22057,0.05221,-0.09377,0.07984,-0.17732,0.03124,-0.06138,-0.16347,0.1992,0.06877,-0.04275,-0.06645,-0.01144,0.05158,0.03435,0.00738,0.13114,0.04066,-0.06068,-0.07388,-0.05591,-0.06802,0.07646,-0.02454,0.01573,0.0284,0.00495,-0.0155,0.01752,-0.14267,-0.00599,0.03591,-0.00098,-0.06095,-0.00436,-0.00631,0.00416,0.0698,0.01576,-0.08624,-0.02757,-0.06938,0.03337,0.08436,0.02669,0.07935,0.01472,0.02568,0.20183,0.01351,-0.04628,0.09777,0.04616,-0.01835,-0.11558,-0.0994,0.06395,-0.00773,0.00343,-0.03937,-0.04987,0.00808,0.07058,0.02198,-0.13345,0.04043,-0.09566,-0.01513,0.00777,0.011,0.00951,0.01674,0.00277,-0.01492,0.07899,0.02455,0.0358,0.01827,-0.02176,-0.08288,-0.04801,0.06157,0.03195,-0.04242,-0.13506,0.07307,-0.03176,-0.03652,-0.02845,-0.03538,0.11178,0.06765,0.05186,0.0281,0.04801,0.00478,-0.02756,-0.11294,0.04426,0.0564,-0.11874,0.01528,-0.11631,-0.00813,0.03826,-0.02688,0.0016,0.01123,0.11307,-0.05509,0.05849,0.09673,-0.0193,-0.02402,-0.06137,-0.08778,-0.04963,-0.0073,0.03088,-0.04837,0.05125,-0.06622,-0.0523,0.03794,0.0009,-0.04791,-0.10369,-0.11053,0.05053,0.02929,0.02747,6e-05,0.03457,-0.07089,0.03097,0.01677,-0.09477,0.06923,-0.00313,0.03811,0.001,0.09048,0.05378,-0.03352,-0.00318,0.02036,0.03538,-0.04067,0.07228,-0.03514,0.06732,0.00814,-0.04356,0.03958,-0.0156,-0.00892,-0.0677,0.01368,-0.03468,0.0173,0.03556,0.08978,0.02004,0.10691,0.02041,-0.03724,0.06261,-0.0785,0.04069,0.10218,-0.02555,0.18731,0.02669,0.05078,0.06299,-0.05705,-0.04037,-0.0951,0.04383,0.05175,-0.02126,-0.05656,0.06308,0.04669,0.08277,0.0129,0.06411,-0.042,0.05687,0.06388,-0.01849,-0.04777,0.01187,-0.10267,0.00501,-0.02946,0.07352,-0.02302,-0.07011,0.04171,0.02312,0.0052,-0.06573,-0.03939,-0.0045,0.01157,-0.11994,0.03709,-0.01656,-0.04661,0.04857,-0.00661,-0.0409,0.02565,0.04833,-0.08687,-0.05573,0.01343,-0.00188,-0.06148,-0.01429,0.00717,0.05409,-0.05299,0.05477,0.00876,-0.04102,-0.00349,-0.07046,0.00965,0.08139,0.02032]},{"domain":"geospatial_analytics","key":"geo_web_map_tile","name":"Web-map tile (slippy map / XYZ) and quadkey containing a point","package":"geospatial-analytics-ai999x","example":"Web map tile: lat = 51.5, lon = -0.13, zoom = 12","v":[-0.0714,0.06401,0.08597,0.00548,-0.0942,-0.05738,-0.00416,-5e-05,0.03637,-0.0565,-0.02081,-0.11831,0.03144,-0.07009,-0.00506,-0.02403,0.02845,-0.04995,-0.09237,-0.02686,-0.05309,-0.02542,-0.053,0.02339,-0.11898,0.01752,-0.05175,-0.05533,-0.10483,0.03724,0.08678,0.02726,0.03392,-0.04259,0.02958,-0.05913,0.08634,-0.0184,0.02514,-0.0553,0.04626,0.03475,-0.04992,-0.04402,-0.0582,0.04901,-0.15496,0.14624,-0.00804,-0.03333,0.00437,-0.01368,0.01938,-0.11225,-0.00506,0.06072,-0.00316,0.01105,0.08038,0.05496,0.01764,-0.09902,-0.08934,-0.02619,0.00718,-0.08306,-0.03985,0.07246,0.09628,0.06693,-0.08175,-0.11416,0.05026,-0.05988,-0.05849,-0.02084,-0.0021,0.03673,0.031,-0.17268,0.0188,-0.13422,0.06616,-0.05884,-0.07154,-0.00687,-0.06929,-0.04681,0.20107,0.02979,-0.0426,-0.0133,0.01373,-0.10963,0.02745,-0.04549,0.13908,0.082,0.00551,0.0579,-0.02621,0.05142,0.04178,-0.00539,-0.0274,0.0585,0.02253,0.02439,-0.12288,0.00479,-0.00326,-0.11347,-0.03327,-0.07718,0.0248,0.13193,0.04478,0.0383,0.0203,0.00216,-0.09546,-0.08653,0.05283,-0.02574,0.12266,0.13002,-0.00812,-0.04519,0.02862,-0.00221,0.07844,-0.01071,0.10542,-0.02518,0.03159,0.00144,0.0338,-0.05804,-0.05983,-0.02784,-0.03815,-0.03148,0.02823,-0.05377,0.0311,0.00611,-0.04366,0.02522,0.04171,0.01051,-0.11403,-0.05797,0.13198,0.04307,-0.00433,-0.0164,-0.05758,0.08355,-0.08216,0.12701,0.10084,0.05926,0.05685,0.01849,0.00891,-0.0467,-0.00792,0.00804,0.00521,-0.03799,0.0597,0.04034,-0.0017,0.06672,0.08419,-0.02639,0.00216,0.00336,0.06012,0.00522,-0.05975,0.08119,-0.06919,-0.11373,-0.00603,-0.12612,-0.01645,0.1123,0.07523,0.03817,0.06372,0.03244,-0.0737,0.0007,-0.01456,0.04453,-0.04201,0.04053,-0.07971,0.08287,-0.01233,-0.07177,0.12356,-0.11875,0.03144,-0.03607,0.01437,0.10075,-0.00783,0.04559,0.02008,0.00767,-0.00687,0.09715,0.06597,0.01112,0.07959,0.02018,-0.07167,-0.01196,-0.04388,0.09216,-0.0262,0.0688,0.0591,-0.02257,0.05174,-0.05874,-0.04889,0.04993,0.01129,0.02129,-0.08695,-0.01849,0.04882,-0.03592,0.04825,0.06701,0.08044,0.04822,-0.03321,0.11203,-0.05171,-0.06394,-0.01969,0.01756,0.01877,0.04052,0.06396,-0.05785,-0.07146,0.06219,-0.04602,0.03663,0.04252,-0.0154]},{"domain":"geospatial_analytics","key":"geo_web_mercator_forward","name":"Latitude and longitude to Web Mercator (EPSG:3857)","package":"geospatial-analytics-ai999x","example":"Web Mercator forward: lat = 51.5, lon = 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Mercator (EPSG:3857) to latitude and longitude","package":"geospatial-analytics-ai999x","example":"Web Mercator inverse: x = -14471.5 m, y = 6710219.1 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1]","v":[0.16777,-0.04283,0.08296,-0.04545,0.06848,-0.07153,0.05115,-0.02669,-0.05524,0.10216,0.0475,0.07522,-0.01859,0.02,-0.05079,0.06748,0.02971,0.01253,0.10134,-0.00629,-0.01678,-0.00473,0.12977,0.03563,0.0478,0.01112,-0.03799,0.02592,0.22901,-0.00296,-0.03537,-0.07073,0.03489,0.00844,-0.0852,-0.08494,-0.02442,-0.03411,0.03044,-0.0798,0.00379,-0.02794,0.12072,-0.00274,0.10661,-0.04162,0.04962,-0.02632,0.11061,-0.03229,-0.03893,-0.0048,-0.01185,0.00278,-0.02582,-0.10428,-0.03219,0.09738,0.02878,-0.03832,0.0258,-0.02232,0.02057,-0.02016,0.01799,0.06575,-0.04316,-0.18113,0.0355,-0.09369,-0.03547,-0.02899,0.02329,0.01953,0.05027,0.04389,-0.07793,0.09028,-0.02432,0.03133,-0.02337,0.00911,0.09784,0.00247,-0.13752,0.13508,0.05116,-0.06965,-0.03723,-0.0336,0.06712,0.0039,-0.00901,0.04798,-0.06876,0.14793,-0.0461,0.00925,-0.13676,0.06838,0.009,-0.02776,-0.00685,-0.08096,-0.02619,-0.04769,-0.00284,0.00451,-0.0464,0.11175,-0.01503,-0.05931,-0.06351,-0.04735,-0.02432,0.05168,0.02377,0.0124,0.02702,0.04737,0.0283,-0.03883,0.02075,-0.01397,-0.03553,0.01226,-0.0444,-0.08602,-0.10378,0.01216,0.10182,-0.02174,-0.02063,-0.02104,-0.05567,-0.09068,0.03262,0.06088,-0.15279,0.09186,0.19786,-0.00279,-0.02474,0.06775,0.01003,0.05432,0.01048,0.11576,0.00583,-0.09174,0.06641,-0.00264,0.05863,0.06345,-0.05705,0.03034,-0.09175,-0.08184,-0.04391,-0.05217,-0.06824,-0.09491,0.06149,0.05126,0.00024,0.01927,0.04398,0.05865,0.05684,0.01534,0.06156,-0.0684,-0.02719,-0.00189,0.0752,0.07189,-0.05672,0.01358,0.06391,0.00397,0.06589,-0.09037,0.05884,0.03586,-0.07088,-0.00121,-0.07111,0.06042,-0.0684,-0.02967,0.04733,-0.03815,-0.0651,-0.08695,-0.08697,0.01153,-0.01679,0.10062,-0.08192,-0.12789,0.00485,0.03676,-0.07668,0.01739,0.07806,-0.03958,0.03316,-0.02086,-0.00249,0.13549,0.01495,0.07611,-0.09317,-0.01017,0.06279,-0.0384,0.01807,-0.00454,-0.04436,-0.0551,0.02019,-0.04973,-0.00061,0.06012,-0.07114,-0.12421,-0.04986,-0.01407,0.0319,-0.03398,-0.01587,-0.03279,-0.04705,-0.0384,-0.018,0.0597,-0.08537,-0.02282,-0.01436,0.04544,0.00725,-0.00468,0.0312,0.11189,0.06034,-0.05243,0.07851,-0.01644,0.09419,-0.05662,-0.01075,-0.04296,-0.04424,-0.01055,0.04665,0.03371]},{"domain":"data_science_ml","key":"ml_balanced_class_weights","name":"Balanced 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1]","v":[0.07862,0.04561,0.01862,-0.03918,0.0278,0.00876,0.0246,-0.04675,-0.04123,0.03434,-0.04733,0.10485,-0.05868,0.03909,-0.00138,-0.01445,-0.09608,-0.02593,-0.04911,-0.02037,-0.11842,-0.11055,0.01041,0.0507,-0.05491,-0.04491,-0.05322,0.00617,0.05771,0.0153,0.03234,-0.05678,-0.02009,0.05226,-0.08701,-0.01399,0.00523,-0.02227,0.00231,-0.13479,0.12306,-0.00606,0.09426,-0.03667,0.02392,0.07251,-0.06694,-0.10099,0.06996,-0.04703,-0.05229,0.07938,-0.03893,-0.02213,0.02215,-0.05096,-0.05106,-0.01766,0.01932,0.04809,-0.068,-0.0209,0.02115,-0.03216,0.00602,0.10443,-0.02305,-0.14934,0.1025,-0.01921,0.01726,-0.03339,-0.05182,0.06737,-0.04165,0.01683,-0.20752,0.10757,0.06327,0.02031,-0.07854,0.01031,0.02578,0.00638,-0.10835,0.20067,-0.05407,-0.07036,-0.0332,-0.03953,0.15575,-0.02852,0.01882,0.01891,0.00856,0.11707,-0.09802,-0.06144,-0.11208,-0.01775,-0.00155,0.00655,-0.00965,-0.06733,0.02713,-0.06822,0.01082,-0.03614,0.01118,0.06407,-0.00393,-0.14204,-0.05738,-0.08678,-0.04235,0.06252,0.05079,0.0433,0.01558,0.11438,-0.11376,0.00875,0.10664,-0.08359,0.03024,0.02647,-0.00387,-0.04059,-0.02692,-0.04205,0.09816,0.05256,-0.0029,0.0233,-0.05086,-0.07132,-0.0746,0.03371,-0.07858,0.15635,0.10357,0.04046,-0.10203,0.02159,-0.01258,0.02372,-0.00271,0.17232,-0.04641,-0.09301,0.1407,0.03663,0.00537,0.0814,-0.01603,-0.03458,-0.05674,-0.01035,0.02887,0.05342,-0.01884,0.04705,0.0115,0.07417,0.07673,0.07606,0.03539,0.07226,-0.02312,0.04273,0.14924,-0.08842,-0.01276,-0.07878,-0.00045,0.00958,-0.04822,-0.02619,0.00652,-0.03463,0.07366,-0.00046,0.07682,0.01095,-0.09629,0.01822,0.00679,0.15701,-0.07632,-0.03986,0.02804,0.03589,0.03155,-0.03839,-0.08278,0.0141,0.00113,0.01721,-0.08913,-0.03074,-0.05326,-0.00955,-0.02071,0.01885,0.03444,-0.00524,0.02623,0.02293,-0.06181,0.08458,0.05459,0.01466,-0.02103,-0.05329,0.12778,-0.00562,0.07781,-0.00786,-0.11272,-0.0033,-0.04376,-0.02927,-0.09911,0.06915,0.0466,0.07929,-0.09894,-0.01167,0.01827,0.04191,-0.04273,0.02746,-0.0183,0.02026,-0.00064,0.05169,-0.05003,0.00743,0.04249,-0.08801,0.01355,-0.01191,0.06329,0.04107,-0.0082,-0.04779,0.01829,0.05318,0.04342,-0.03725,0.05437,0.04686,-0.02131,0.05495,0.03056,-0.01845]},{"domain":"data_science_ml","key":"ml_batch_norm_forward","name":"Batch 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naive Bayes prediction (binary features)","package":"data-science-ml-ai999x","example":"Bernoulli naive Bayes: X = [[1, 0, 1], [1, 1, 0], [0, 1, 1], [0, 0, 1], [1, 1, 1]], y = [0, 0, 1, 1, 0], x = [1, 0, 0], alpha = 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decomposition of predictions","package":"data-science-ml-ai999x","example":"Bias-variance decomposition: P = [[1, 2], [3, 2.5], [2, 3.5]], f = [1.5, 2.5]","v":[0.10674,0.0322,0.03691,-0.00985,-0.07731,0.05937,0.07489,0.00475,0.05719,-0.15014,0.05115,-0.06326,0.01716,-0.06868,-0.0621,-0.07012,0.17111,0.01141,0.09536,0.0377,-0.03298,-0.03299,0.10648,0.03916,-0.04157,-0.02208,-0.06104,-0.05667,0.01805,0.10588,-0.03194,-0.04202,0.06641,-0.05283,0.10426,-0.07404,0.04757,0.05663,-0.0434,0.06449,0.0303,0.04446,-0.0203,0.0557,0.02903,-0.07911,0.04029,0.06708,0.03554,0.01107,-0.01331,-0.00629,0.03508,0.14028,0.02207,-0.02002,0.1357,0.00657,0.00041,0.01924,0.03097,0.10303,-0.13508,0.04726,0.0228,-0.03496,0.0628,-0.13591,-0.0195,-0.08167,-0.00044,0.02356,0.00066,0.12548,0.03035,0.07034,-0.02116,-0.05581,-0.12875,-0.01844,0.05108,-0.03563,0.00249,-0.06894,-0.15232,-0.00845,-0.02609,-0.08403,-0.01852,-0.01568,-0.05682,0.02282,-0.02098,-0.03769,-0.04567,-0.03356,0.00493,0.05082,-0.19487,-0.05205,0.02621,-0.04845,-0.12446,-0.0286,-0.11884,0.06296,0.07676,0.08496,-0.04807,-0.01811,0.04317,0.05101,0.04407,0.02838,-0.08368,0.06852,-0.02224,-0.09114,0.021,0.02728,0.00016,-0.03627,-0.08833,-0.10592,0.04301,-0.03363,-0.07374,0.11465,-0.05508,0.02959,-0.06837,-0.09088,-0.10451,0.01653,0.0478,-0.05036,-0.06455,0.06018,-0.00592,0.06682,-0.09961,0.03818,0.04211,0.10562,0.05948,0.02094,0.05858,-0.00502,0.06862,-0.08813,-0.09603,0.0748,0.03769,-0.0005,-0.09191,0.00774,0.03454,-0.00491,-0.08902,0.07576,-0.00503,-0.03679,-0.00857,0.01376,0.07595,0.01163,-0.11635,0.03735,-0.03628,-0.07123,-0.05614,-0.0823,0.01157,0.03129,0.08275,0.00214,0.00303,0.01524,-0.07709,0.06973,-0.0282,-0.12977,-0.12242,-0.06036,0.05642,0.08872,0.05726,-0.06356,0.00809,0.04199,0.0023,0.01939,-0.06538,0.00196,0.08171,0.02859,-0.0204,0.05803,0.01832,-0.03516,0.02385,0.00113,-0.05026,-0.06154,-0.00435,-0.09836,-0.05855,0.0343,-0.00743,0.06216,0.04186,0.03293,0.04732,-0.04183,-0.015,-0.0493,-0.07488,-0.04298,-0.0152,0.0494,-0.04974,0.02419,0.03237,0.08837,0.0342,0.04367,0.06761,-0.04499,0.04483,0.12207,0.06988,-0.05445,-0.03761,0.05357,0.01232,0.08769,-0.02718,0.08968,-0.03424,0.00203,0.06458,0.0028,0.03516,0.06819,-0.06222,-0.02309,0.00703,0.12763,-0.0164,0.04836,-0.03066,-0.12535,-0.04656,-0.01677,0.02531,0.00849]},{"domain":"data_science_ml","key":"ml_binary_confusion_matrix","name":"Binary confusion matrix from labels","package":"data-science-ml-ai999x","example":"Binary confusion matrix: y_true = [1, 0, 1, 1, 0, 0, 1, 0], y_pred = [1, 0, 0, 1, 0, 1, 1, 0]","v":[0.14451,-0.08305,0.0288,0.03883,0.0317,-0.05363,0.13071,-0.0523,-0.02915,-0.01885,0.03626,0.05567,-0.0127,0.00077,-0.08031,0.09835,0.00944,-0.01643,0.07047,0.03375,-0.06345,0.00517,0.16425,0.10198,-0.02405,0.00901,-0.04738,0.01407,0.18317,0.01655,-0.07172,-0.00762,0.06436,0.01238,-0.08432,-0.12127,-0.00253,0.00234,0.05532,-0.00412,-0.03461,-0.04645,0.15568,0.01759,0.01809,-0.11003,0.04578,0.0413,0.04161,0.02763,-0.00229,-0.00119,0.03671,-0.00494,-0.08208,0.01768,-0.022,0.08378,0.05792,-0.0037,-0.00662,-0.08657,-0.02212,0.01583,-0.0578,0.06628,0.01257,-0.09746,-0.04745,-0.07255,0.01178,-0.10757,0.09815,0.01126,0.11225,-0.02988,0.02161,0.03643,-0.03047,-0.06976,-0.03993,-0.04185,0.1428,-0.05054,-0.06465,0.11141,0.06722,-0.0571,0.0062,-0.02201,0.03274,0.00186,-0.07181,0.0597,-0.07625,0.10732,0.02824,0.13062,-0.13903,0.08625,-0.00661,0.01031,-0.09958,-0.02504,-0.05486,0.01583,-0.01328,-0.01017,-0.03151,0.06905,-0.02484,-0.03278,-0.12615,-0.00491,0.00866,-0.04698,0.01706,-0.04673,0.12844,0.00752,0.05384,-0.07532,-0.03479,-0.03458,-0.05003,0.06185,0.00196,-0.0067,-0.09841,-0.02462,0.12051,-0.03231,-0.04096,0.01213,0.02797,-0.09614,0.09195,0.01222,-0.0793,-0.02137,0.07745,0.03288,-0.0613,0.01662,-0.01398,0.0229,0.03592,0.08833,0.0204,-0.05558,0.0467,0.01185,0.12273,0.03968,-0.08293,0.01018,-0.00583,-0.0486,-0.11706,-0.03638,-0.01854,-0.14848,-0.04701,-0.00476,0.04951,-0.04503,0.00261,0.07003,0.05504,-0.04612,0.02771,-0.05747,-0.0636,0.01487,0.15532,0.11133,-0.00078,-0.05624,0.12199,0.02027,0.06759,-0.06113,0.04828,-0.01063,-0.1019,0.00535,0.01223,0.04429,-0.08295,-0.02998,0.06957,-0.01111,-0.14004,-0.05026,-0.09043,-0.00316,-0.06271,0.08692,0.00341,-0.07507,0.03649,0.05856,-0.06937,-0.04453,0.01972,-0.0321,-0.05145,0.08005,0.02424,0.06044,-0.00816,0.00673,-0.07077,-0.00353,-0.06203,-0.06838,0.00423,0.01582,-0.01723,-0.08245,0.07141,-0.0406,0.0304,0.00426,-0.05148,-0.11991,0.03909,-0.01235,-0.01215,0.00811,-0.01347,-0.02466,0.0061,0.04285,-0.04351,0.07234,-0.10003,0.01174,-0.0758,0.11672,-0.04701,-0.00747,0.00689,0.08976,0.01773,-0.05306,0.08421,0.01948,0.11581,0.01093,0.02448,-0.04839,-0.05016,-0.00783,0.06413,-0.00241]},{"domain":"data_science_ml","key":"ml_binary_metrics_from_counts","name":"Binary classification metrics from confusion counts","package":"data-science-ml-ai999x","example":"Binary metrics from counts: TP = 40, FP = 10, FN = 5, TN = 45","v":[0.1385,-0.04555,-0.01381,0.01762,0.0097,-0.04407,0.10405,-0.02337,-0.01699,-0.01858,0.02942,0.07041,-0.04628,0.00367,-0.06872,0.12869,0.00792,0.03666,0.08995,0.02908,-0.06382,0.03416,0.12325,0.08617,-0.0468,-0.02377,-0.04377,-0.04955,0.17951,-0.05966,-0.09754,0.02149,0.06783,-0.03986,-0.09353,-0.09595,0.01309,-0.01601,0.05597,0.02389,-0.03989,-0.05112,0.15523,0.02253,0.01241,-0.10098,0.04598,0.03451,0.05183,0.00813,-0.01178,-0.01726,0.01096,0.02595,-0.09957,-0.0218,-0.03684,0.04444,0.05643,-0.01779,-0.0102,-0.0985,0.00959,0.03309,-0.08756,0.07187,-0.01418,-0.03592,-0.06061,-0.04634,-0.01719,-0.10783,0.06718,0.0164,0.11295,-0.02246,0.07336,-0.02634,-0.00036,-0.00448,-0.04226,-0.06411,0.12292,-0.03519,-0.06515,0.07365,0.06841,-0.08393,0.01108,-0.03285,0.02785,-0.0222,-0.07993,0.074,-0.08218,0.1369,-0.02721,0.1013,-0.09097,0.06426,0.0034,0.03356,-0.0448,-0.06274,-0.03202,0.04566,-0.00818,-0.01548,-0.00227,0.03406,-0.03034,-0.01968,-0.09812,-0.00587,0.01267,-0.07142,0.0514,0.00872,0.12271,0.01442,0.01715,-0.04794,-0.02553,-0.04242,-0.02917,0.08275,0.03771,-0.03109,-0.15631,-0.02307,0.07448,-0.05442,-0.01772,-0.00926,0.05738,-0.07946,0.07199,0.0307,-0.09404,0.02048,0.11812,0.01651,-0.02477,0.01567,0.00362,0.00853,0.03068,0.06423,0.0052,-0.01869,0.04786,-0.00644,0.09218,0.04841,-0.10865,0.02536,-0.00071,-0.06366,-0.15996,-0.02495,-0.0009,-0.15132,-0.03108,-0.02099,0.04314,-0.04632,0.02677,0.05909,0.07929,-0.01135,0.03066,-0.06097,-0.02977,0.02192,0.14129,0.09051,-0.0151,-0.02701,0.13318,0.06135,0.07372,-0.09079,0.06173,0.01407,-0.07864,0.02455,0.02436,0.05055,-0.07179,-0.01246,0.08699,-0.04588,-0.14326,-0.07088,-0.07233,0.00682,-0.04413,0.09236,0.01822,-0.06016,0.06569,0.00395,-0.07656,-0.04045,0.0032,-0.01153,-0.04111,0.06469,0.02462,0.06679,0.0276,0.03017,-0.06783,-0.0055,-0.05568,-0.03915,-0.00523,0.05217,-0.00126,-0.1287,0.09625,-0.04423,0.02579,0.0389,-0.04511,-0.11276,0.0213,-0.02877,-0.01857,0.03494,-0.02497,-0.00351,0.00182,0.0435,-0.1013,0.07571,-0.10793,-0.02553,-0.06443,0.17263,-0.04487,-0.01758,0.00045,0.08363,0.03191,-0.0395,0.06021,-0.03,0.12779,0.01768,0.01132,-0.07277,-0.06314,-0.0319,0.0571,0.04835]},{"domain":"data_science_ml","key":"ml_brier_score","name":"Brier score","package":"data-science-ml-ai999x","example":"Brier score: y_true = [1, 0, 1, 1], p = [0.9, 0.2, 0.7, 0.6]","v":[0.08634,-0.13235,0.07515,0.04405,0.12017,-0.05032,0.08235,0.04298,-0.03648,-0.12846,0.09567,0.01719,0.05142,-0.02569,-0.05497,-0.01406,0.10997,-0.09022,0.01717,0.0079,0.008,0.01409,0.1497,0.1321,0.01245,0.03788,-0.10092,0.02124,0.1842,0.06986,-0.00099,0.10086,-0.00388,-0.05926,-0.11872,-0.02788,0.06753,-0.08749,0.00143,-0.05619,-0.03871,-0.00544,0.10406,0.08605,0.03395,-0.13596,0.08449,-0.02153,0.03621,-0.09576,-0.08752,-0.03344,0.04392,-0.0286,-0.04839,-0.05158,0.01433,0.00768,0.00984,-0.00796,0.0207,-0.0903,-0.05007,-0.0521,0.0048,0.0016,0.00852,-0.07275,-0.02946,-0.00809,0.00712,-0.0526,-0.02861,-0.00499,-0.00798,0.08558,-0.01279,0.05192,-0.07264,-0.03661,-0.08402,-0.0278,0.16451,-0.00462,-0.16289,-0.01863,0.13031,0.01343,0.13918,-0.03224,-0.03324,-0.04725,-0.00359,0.00721,0.02201,0.03432,0.07902,0.09764,-0.03292,0.08103,-0.02292,-0.01982,-0.13101,-0.01827,-0.01243,-0.00118,-0.10721,0.08722,0.0681,0.03819,-0.00269,-0.01896,0.03099,-0.00203,0.03417,0.00175,-0.04707,-0.07349,0.07478,-0.02295,0.04595,0.00829,-0.05883,-0.06609,-0.04951,-0.05731,-0.06684,-0.06161,-0.08667,0.01426,0.15083,-0.00544,0.02805,-0.00894,-0.01644,-0.04292,0.0341,-0.01214,-0.0971,-0.05736,0.05693,0.04539,0.03761,0.06166,-0.04347,0.00483,0.03633,0.06877,0.05739,-0.0547,-0.09597,0.06854,0.05419,-0.04414,-0.07974,0.05702,0.00412,-0.06921,-0.02055,-0.01338,0.0329,-0.03755,0.06969,-0.03451,0.17525,-0.0744,-0.14486,0.04593,-0.00437,-0.04688,-0.01303,0.00919,-0.02025,0.01579,0.11023,-0.02581,0.02967,-0.00786,0.03422,0.01251,-0.04219,-0.03598,-0.00324,0.03813,0.01293,0.05819,0.01899,-0.00388,-0.09072,0.04033,-0.01627,-0.03178,-0.06386,0.00224,0.0425,0.02336,-0.05261,0.05295,0.01125,-0.01609,0.01449,0.08209,0.00263,0.00723,-0.03181,-0.08732,-0.01745,0.05565,0.11652,0.09106,-0.01951,0.02461,-0.0229,-0.0739,-0.03258,-0.09435,0.0349,0.05171,0.01379,-0.01436,-0.0938,0.12604,-0.01549,0.01996,0.01517,-0.11718,-0.02841,0.07608,0.07368,0.01028,0.04215,-0.04202,-0.02694,0.08779,0.0505,0.04418,0.03046,0.04889,-0.04004,0.02897,0.01866,-0.01839,-0.0198,0.11577,-0.07937,-0.11403,0.04738,-0.01376,0.04761,-0.11305,-0.03677,-0.04441,-0.1014,-0.01182,-0.01779,0.00984]},{"domain":"data_science_ml","key":"ml_calinski_harabasz_index","name":"Calinski-Harabasz index","package":"data-science-ml-ai999x","example":"Calinski-Harabasz index: X = [[1, 1], [1.5, 2], [3, 4], [5, 7], [3.5, 5], [4.5, 5]], labels = [0, 0, 1, 1, 1, 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output size","package":"data-science-ml-ai999x","example":"Convolution output size: n = 32, kernel = 3, stride = 1, padding = 1, dilation = 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50","v":[-0.04368,0.0739,-0.05529,-0.07086,-0.14277,-0.05037,0.0832,0.09974,0.01339,0.14169,-0.07708,-0.03586,0.02722,0.11503,-0.02082,0.01405,0.03168,0.0142,-0.00261,-0.14098,-0.00664,0.04282,-0.05091,-0.07869,0.09039,-0.01289,-0.0598,0.09691,-0.03666,-0.01352,-0.18019,0.01646,0.00597,-0.10382,0.0324,-0.00384,-0.05161,0.03622,-0.00502,0.07804,0.14527,-0.01426,0.00516,-0.08145,0.10532,0.03745,-0.00883,-0.00551,0.01558,-0.08266,0.05457,0.05458,-0.05369,0.03002,-0.00836,-0.00016,-0.01141,0.01746,-0.05956,-0.01127,0.0605,-0.05273,0.13771,0.10432,0.0571,0.01569,0.05362,-0.02277,-0.00917,0.02651,-0.03497,0.04032,-0.07116,-0.08077,-0.12281,-0.02436,0.02099,0.08443,-0.04523,-0.02128,0.06123,0.06047,-0.04915,-0.05315,0.01179,0.14519,-0.03711,-0.06573,-0.00385,-0.05524,0.16353,-0.00292,0.0192,-0.07811,-0.0206,-2e-05,0.00378,-0.01348,0.03606,-0.01499,-0.04405,-0.00786,-0.02656,-0.05362,0.01679,0.02142,0.00171,-0.0191,0.04821,-0.06935,0.01584,-0.00183,0.01935,-0.05919,-0.06117,0.09307,-0.09187,0.03373,-0.05639,0.01929,-0.02486,-0.01568,0.05971,-0.01789,-0.09228,-0.04545,0.01127,-0.05664,0.00084,0.01695,0.06309,0.04926,-0.00838,-0.06101,-0.01771,-0.01972,-0.0398,0.15164,0.06651,0.05662,0.08773,-0.01567,0.07779,0.0234,0.00787,-0.01904,0.04358,0.05612,-0.07561,0.09548,0.02119,-0.06231,-0.16755,-0.04946,0.0049,0.09404,0.00835,0.10646,-0.00957,0.19683,-0.07397,0.07299,0.01965,0.09046,0.00207,0.04632,0.08554,0.02557,-0.00357,-0.01069,0.06237,-0.01557,-0.07554,-0.0478,-0.00419,0.0248,0.10199,-0.03528,-0.04501,-0.08855,-0.03764,-0.05533,-0.06595,-0.03529,0.00965,-0.02846,-0.06938,0.0371,0.07447,0.07731,0.0595,0.0404,0.04128,-0.04306,-0.01636,0.06752,0.04588,-0.01836,0.00751,0.02003,-0.00763,0.00091,0.09663,-0.06044,-0.06632,-0.01573,-0.02206,0.00587,-0.01222,-0.01597,-0.0567,-0.07345,-0.03359,0.01313,-0.09389,0.04177,-0.08841,0.02691,-0.02061,-0.06524,-0.1394,0.00715,0.14588,0.04161,0.09344,0.02531,0.07447,-0.02413,-0.03831,-0.05081,-0.09778,-0.07921,0.0169,0.04977,-0.03707,-0.00441,0.01177,0.01616,0.03355,-0.0857,0.02039,0.05052,0.07472,-0.01693,-0.06536,0.12772,0.00962,-0.18657,-0.04711,0.06594,0.08996,-0.01714,0.02788,-0.0167,0.0357,-0.03811]},{"domain":"data_science_ml","key":"ml_cross_entropy_logits","name":"Cross-entropy 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index","package":"data-science-ml-ai999x","example":"Davies-Bouldin index: X = [[1, 1], [1.5, 2], [3, 4], [5, 7], [3.5, 5], [4.5, 5]], labels = [0, 0, 1, 1, 1, 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decision-tree split (classification, Gini or entropy)","package":"data-science-ml-ai999x","example":"Decision tree best split: X = [[2, 7], [3, 1], [10, 8], [11, 2], [4, 9], [12, 0]], y = [0, 0, 1, 1, 0, 1], criterion = gini","v":[-0.01652,0.01352,0.02832,0.01038,-0.03327,0.07143,0.05185,-0.04605,-0.02621,-0.00083,-0.03853,0.03027,-0.00406,-0.07512,0.01619,-0.06963,-0.00633,-0.04929,-0.04839,-0.04286,-0.114,-0.0658,0.04127,-0.04141,-0.0545,-0.00461,-0.03252,0.02502,0.10435,-0.01902,-0.05549,-0.0405,-0.02038,0.03169,-0.05211,0.07675,0.00642,-0.05572,-0.01421,0.03068,0.03219,0.03798,-0.01007,0.07525,0.06057,-0.02497,0.16975,-0.03942,-0.03827,0.04942,-0.06684,0.04934,-0.08755,-0.19676,-0.13479,0.07183,0.03999,0.02529,-0.00044,0.0116,-0.01243,0.03423,0.02226,-0.04845,0.04089,-0.00735,0.07558,-0.02103,-0.02253,0.07454,-0.02603,0.01093,-0.0699,0.15059,0.02341,0.00534,-0.12618,0.05303,-0.01017,-0.01975,0.04631,-0.00827,0.102,-0.01601,0.00759,0.08695,-0.00564,-0.00056,-0.16612,-0.02494,-0.09088,0.03142,-0.00836,-0.10698,0.0065,0.01063,-0.04624,-0.01143,-0.14025,-0.02098,-0.01221,0.02468,0.12282,-0.05042,-0.04998,-0.04036,-0.00507,0.01805,-0.08503,-0.02326,0.01168,-0.01699,-0.07389,0.23343,-0.00815,0.00593,-0.02171,0.01312,-0.02138,0.06075,-0.02611,0.18754,-0.00772,0.13983,0.02748,0.03302,0.01951,-0.00169,0.07715,-0.03426,0.01388,0.04403,-0.00942,-0.04943,-0.04532,0.08484,-0.104,0.03717,-0.04501,0.15699,0.06365,0.02631,-0.04106,-0.00199,0.00975,0.0625,0.03983,0.05582,0.07965,-0.12946,-0.01022,-0.14123,-0.01039,0.03078,0.0542,0.01371,0.04433,0.04186,-0.06633,0.0397,-0.03022,0.03308,0.05136,0.07482,-0.08449,-0.01369,0.05159,0.01683,0.05907,0.1139,0.05697,-0.11676,0.01707,0.03544,-0.07855,-0.01112,-0.0114,0.03245,-0.00917,-0.04682,0.02422,0.00247,-0.0929,-0.02583,-0.01498,-0.06348,0.07264,0.04104,-0.00618,0.09021,-0.00328,0.0016,-0.02316,0.0102,-0.0787,0.0334,-0.0498,-0.01116,-0.02192,0.04676,-0.10832,0.08523,-0.04548,-0.00284,0.01463,-0.00631,0.0081,0.02709,-0.00359,0.06824,-0.02367,0.02124,-0.05358,0.03506,0.15985,-0.04792,-0.02973,-0.0233,0.05544,0.074,-0.07487,-0.08599,-0.00837,-0.05551,-0.0924,0.05914,-0.04296,0.0261,-0.10928,0.00016,-0.00692,0.06724,-0.06656,-0.01068,0.17464,-0.05649,-0.04065,-0.10244,-0.11142,0.05019,-0.02865,-0.03552,0.14441,0.01966,-0.00613,-0.04472,-0.00643,0.04585,0.08673,-0.012,0.04935,0.00668,0.03586,0.06497,0.09171,0.01051]},{"domain":"data_science_ml","key":"ml_decision_stump_regression","name":"Best regression-tree split (squared error)","package":"data-science-ml-ai999x","example":"Regression tree best split: X = [[1], [2], [3], [10], [11], [12]], y = [1, 1.2, 0.8, 5, 5.4, 4.6]","v":[0.06381,0.01311,0.05476,0.00437,-0.06746,0.0886,-0.02642,-0.00897,-0.00432,-0.08948,-0.03314,-0.01315,0.06174,-0.08259,-0.04676,0.00496,0.14001,-0.11189,-0.01498,-0.02994,-0.13178,-0.01528,0.05715,-0.07864,-0.06318,0.02556,-0.05432,-0.03239,0.05975,-0.01231,-0.02991,-0.04955,0.02375,-0.01997,0.0101,-0.00264,0.0638,-0.04436,-0.05315,0.04235,-0.02669,0.13158,-0.03311,0.06518,0.08336,0.01958,0.19609,-0.00767,0.00123,-0.03233,-0.05969,0.09656,-0.0792,-0.13121,-0.07453,0.01118,0.06951,-0.01834,0.01904,0.09036,0.03681,0.06906,-0.05346,0.0238,0.10436,-0.03642,0.00784,-0.06048,-0.085,0.05709,-0.01921,-0.02566,-0.1277,0.02315,-0.03261,-0.02619,-0.02219,0.02873,-0.014,0.08693,0.03584,0.04108,0.11065,0.02006,-0.05676,0.04328,0.00109,0.01502,-0.09498,0.04783,-0.08754,0.0722,0.06398,-0.07957,0.01276,-0.03582,-0.06104,-0.00104,-0.19545,-0.02374,-0.00971,0.01834,0.08978,-0.00973,-0.16118,-0.00352,0.04246,-0.00484,0.03542,-0.04415,-0.00757,0.00321,-0.06212,0.10909,-0.05505,0.03245,-0.01399,-0.00443,-0.0149,0.04207,0.03499,0.21621,-0.03228,0.04374,0.01756,0.05676,0.07091,0.01383,0.09295,-0.02465,-0.03534,-0.02648,0.00974,-0.05811,0.01358,0.04111,-0.13075,-0.02747,0.01905,0.12695,0.02469,0.02793,0.04685,-0.00125,0.01272,-0.01791,0.0946,0.01068,0.13585,-0.18102,0.00991,-0.02238,-0.00333,0.03587,-0.02915,0.01782,-0.0097,0.05909,-0.1296,0.09525,-0.01173,0.09391,-0.00595,0.1018,-0.13725,0.04148,0.02369,-0.01899,0.01939,0.14105,-0.02906,-0.01189,0.0436,0.08294,-0.04153,-0.09751,0.03184,0.01595,-0.08918,0.00513,0.01938,0.00712,-0.14266,-0.08066,0.04214,-0.04279,0.05816,0.04251,-0.02578,0.10132,-0.02503,-0.0738,-0.04296,0.02999,0.00097,0.04921,0.00134,0.02658,0.00779,0.06125,-0.0145,0.10423,-0.05936,-0.02645,0.00831,-0.06852,0.02758,0.09606,-0.03708,0.07256,-0.01274,-0.02962,0.05328,0.01851,0.09395,-0.02018,-0.04719,-0.03378,0.11194,0.10635,-0.00956,-0.04058,-0.0543,-0.05068,0.00074,0.04079,0.0383,0.00469,-0.08328,0.01186,-0.00687,-0.01573,-0.05495,-0.06446,0.07901,-0.08844,-0.02187,0.01186,-0.07046,0.01844,-0.04989,-0.06345,0.04804,-0.01065,-0.07358,-0.05422,0.0096,0.05573,-0.01304,0.07333,-0.03478,-0.04438,-0.02128,0.03367,0.03114,-0.04682]},{"domain":"data_science_ml","key":"ml_dense_forward_pass","name":"Forward pass of a one-hidden-layer dense network","package":"data-science-ml-ai999x","example":"Dense network forward pass: x = [1, 2], W1 = [[0.5, -0.25], [0.1, 0.3]], b1 = [0.1, -0.2], activation = relu, W2 = [[1, -1]], b2 = [0.05], output = identity","v":[0.0304,-0.07197,0.02703,-0.01607,-0.04312,0.03914,-0.0521,-0.04613,0.08706,0.04742,0.0131,0.04955,-0.04691,0.00169,0.1339,0.04786,0.02919,-0.02947,0.03236,-0.06044,0.03245,-0.07712,0.03448,0.03353,-0.01859,-0.00803,-0.00298,0.06404,-0.13071,0.13612,-0.05498,-0.0605,0.01227,-0.08124,0.06979,0.09645,-0.00235,0.00784,0.01783,0.10996,0.01418,-0.00758,-0.00961,-0.02356,0.00145,-0.02671,-0.03014,-0.05689,-0.0553,-0.01049,0.00355,-0.05369,-0.02769,0.06708,0.01668,0.02292,0.04433,0.01802,-0.01769,0.01323,0.03305,-0.05279,0.1025,0.02361,0.12918,0.13827,0.02561,-0.07722,-0.02919,-0.07271,0.00128,-0.06954,-0.07424,0.06308,0.01462,0.00748,0.00922,0.0373,0.01333,0.02089,-0.08132,-0.00867,-0.04361,0.02172,-0.0777,0.07344,-0.19015,-0.05987,-0.00414,-0.03211,0.01118,-0.0512,0.09956,-0.09266,0.02686,-0.00305,0.07033,-0.06302,-0.00662,0.04321,-0.02927,0.01896,-0.04672,0.05032,0.00504,-0.03325,0.00897,0.04018,0.05389,0.0296,0.01208,0.07874,0.03456,-0.04651,0.04425,0.02219,-0.09801,0.04605,-0.04355,0.01197,-0.09047,-0.06879,-0.00101,-0.01499,0.01475,-0.12736,-0.15525,-0.01245,-0.031,-0.06442,-0.11552,-0.03362,0.03095,-0.12212,0.02599,0.0535,-0.16632,-0.10195,-0.03459,-0.11571,-0.04982,0.02136,0.10359,-0.02193,0.05887,0.01845,0.00247,-0.00109,-0.0336,-0.08188,-0.07908,-0.00749,0.04516,-0.0193,-0.05717,0.05299,0.00624,-0.00182,-0.00786,0.00146,-0.01704,-0.01232,-0.03337,0.04562,0.10211,0.1283,-0.00845,-0.02196,-0.09334,-0.06459,0.03802,-0.04597,0.07658,-0.02089,-0.04369,0.02639,-0.05159,-0.06058,0.09148,0.09581,0.11097,-0.05407,-0.07556,0.03582,0.00777,0.08857,0.03402,0.07276,-0.00122,-0.07507,0.18416,0.07499,-0.02265,-0.01569,-0.02318,0.05064,-0.03156,0.11852,-0.00821,-0.03317,-0.08135,0.03625,0.07275,0.03121,-0.0141,-0.07149,0.0305,0.07744,-0.02252,0.05627,0.13384,-0.0845,0.05967,-0.03236,0.03519,-0.01412,-0.04936,0.11411,0.02662,0.00704,0.1172,0.01758,0.01025,0.00394,0.1783,0.04561,0.09824,0.05035,0.04708,0.00646,-0.07426,0.03564,-0.07911,0.06198,-0.01809,-0.02083,-0.05248,0.06984,0.1088,-0.01052,-0.06195,0.17136,-0.03121,-0.01118,-0.11755,0.00034,-0.06063,0.11761,-0.00486,-0.02594,0.0495,0.00246,-0.01702,-0.008,-0.01154,-0.07557]},{"domain":"data_science_ml","key":"ml_dense_parameter_count","name":"Parameter count of a dense (fully connected) network","package":"data-science-ml-ai999x","example":"Dense network parameter count: sizes = [784, 128, 10], bias = yes","v":[0.0148,-0.07978,-0.00069,-0.0289,-0.08234,-0.05187,0.04884,-0.12147,0.11439,0.04141,0.05202,-0.06394,-0.02772,-0.05054,0.02181,0.07744,0.02938,0.10168,-0.02587,0.01476,0.03456,-0.07137,0.02495,0.04812,-0.04633,-0.05503,0.09983,0.01224,-0.13481,0.10719,-0.06325,-0.10562,0.00485,-0.26269,0.05467,-0.01509,0.05693,0.01956,0.08701,0.08668,0.05382,0.05874,0.01416,-0.00912,0.04057,0.05419,-0.16094,0.02838,0.03833,0.03011,-0.01105,-0.06641,-0.02736,0.08918,0.04735,0.02557,0.05229,0.04044,0.04861,-0.0497,-0.05799,0.00656,0.04788,-0.01418,0.0542,0.06896,-0.00116,-0.08392,-0.01781,-0.05471,-0.08654,0.00623,-0.09037,0.01981,-0.03182,-0.0132,-0.01376,0.0951,0.00135,0.04723,-0.03258,-0.1078,-0.06674,0.01521,-0.04081,0.07362,-0.10458,-0.11287,-0.03212,0.06174,0.04785,-0.0081,0.0075,-0.01687,-0.07432,-0.01526,0.00354,-0.03121,0.02364,0.01484,-0.04324,-0.00581,-0.05502,-0.02115,-0.0147,-0.01217,0.07287,-0.04403,0.03241,0.00995,-0.0838,0.0539,-0.03297,-0.05917,-0.09742,0.01862,-0.08458,0.05942,0.0215,0.09057,-0.06687,-0.0042,0.0403,0.05232,0.0993,-0.08273,-0.09035,0.07331,0.00105,-0.07039,-0.08312,0.05845,0.0342,-0.06303,-0.00486,0.02461,-0.11931,-0.06727,-0.03127,0.06973,-0.01246,0.08233,0.12447,-0.00816,0.04382,0.03021,-0.00054,0.01657,0.00339,-0.07138,0.02802,0.00305,-0.00182,-0.00876,0.03155,0.05457,-0.01639,-0.00245,0.03907,0.06031,0.08287,0.02295,-0.0988,0.11311,0.09731,0.13056,0.00403,-0.0413,-0.1585,-0.07813,0.06235,-0.10428,-0.0062,-0.07934,0.02842,-0.01635,-0.09063,0.00542,0.02003,0.12636,0.01361,-0.08877,0.02678,0.00895,-0.00977,0.13079,0.06569,0.0211,-0.07069,-0.07016,0.12445,0.09013,0.00708,-0.03339,-0.08672,-0.05836,-0.02846,0.04454,-0.04897,0.00281,-0.00351,0.03103,0.05527,0.05297,0.03383,-0.0579,0.02793,0.02366,-0.06356,0.07633,0.0416,-0.1336,0.07058,-0.0246,0.07543,-0.03098,-0.01295,0.06473,0.01718,0.02697,0.02731,0.08443,-0.03999,0.0147,0.14416,0.00554,0.00845,-0.08737,-0.02817,0.08349,-0.14102,0.0524,0.00324,0.07363,-0.02562,0.0051,0.05932,0.02303,0.00342,-0.06164,-0.04177,0.06093,0.03799,0.00482,-0.10307,0.04559,-0.02246,0.02565,0.00108,-0.06113,0.00969,0.05512,0.05733,0.06169,0.02406,-0.04028]},{"domain":"data_science_ml","key":"ml_distance_metrics","name":"Distances 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focal loss and its gradient","package":"data-science-ml-ai999x","example":"Focal loss: y = [1, 0, 1], z = [2, -1, -0.5], gamma = 2, alpha = 0.25","v":[0.09458,-0.05641,0.02965,-0.0873,-0.03833,-0.03427,-0.00211,0.02168,-0.08727,0.0788,-0.03582,-0.08228,0.023,-0.03198,-0.0583,0.08173,-0.07865,0.08124,0.07321,-0.01713,0.00412,0.02944,0.06003,0.04884,-0.02227,-0.04086,-0.02312,0.01999,0.10161,0.00251,-0.04121,-0.11685,-0.06755,-0.07152,0.12295,0.10501,0.00889,-0.04939,0.00524,0.00181,-0.02233,-0.06038,0.00767,-0.11863,0.03688,0.06374,-0.05466,-0.06017,0.05445,-0.0556,0.02038,0.0321,-0.0181,0.02993,0.07411,-0.03526,-0.12111,0.02842,-0.07676,-0.03503,-0.04077,-0.02167,-0.01232,0.02558,0.02379,0.03765,-0.01996,-0.13676,-0.04097,-0.01578,0.06072,0.03742,0.00356,-0.02481,0.00423,-0.00458,-0.08065,0.09202,-0.00902,-0.016,-0.01188,0.10441,0.04206,0.05019,-0.05626,0.10365,-0.02701,-0.04162,-0.08984,0.04118,0.13418,-0.13298,-0.00585,0.01919,0.0334,0.05795,-0.0583,-0.05834,-0.07285,-0.05119,0.03521,-0.07429,-0.07436,-0.02417,-0.01571,-0.03447,-0.05521,-0.00815,-0.01651,0.02684,0.01426,0.03102,0.06868,-0.07255,0.00574,-0.01397,0.03205,0.00262,0.0006,0.02476,-0.10475,-0.0858,0.03133,-0.01161,-0.00719,-0.01478,-0.173,-0.07392,-0.09368,0.01275,0.0716,0.06091,-0.07049,0.01994,-0.04864,0.01592,-0.16326,-0.01429,-0.01009,-0.07886,0.21325,-0.04978,0.01674,0.04665,-0.02106,-0.05959,0.05185,0.02599,-0.0795,0.09237,0.09654,-0.11264,-0.03098,-0.04365,0.05676,-0.08194,-0.00749,0.0127,-0.03317,-0.02669,-0.01564,-0.05005,0.0353,0.02223,0.02786,0.15452,-0.00318,0.04881,0.06259,-0.04815,-0.00862,0.06648,-0.00853,0.10804,0.02012,-0.04871,0.05818,-0.08659,0.04189,-0.02778,0.00923,-0.0084,-0.00423,-0.01886,0.05014,-0.05164,-0.04499,0.03481,-0.08782,-0.0031,0.00062,0.08598,-0.09694,-0.06902,0.03635,0.09072,-0.06584,-0.06324,0.02729,-0.04188,-0.01775,-0.05492,0.03995,-0.02659,0.12813,-0.12143,0.11079,0.07902,-0.01571,0.06672,0.01972,0.23082,0.00085,0.05199,0.00923,0.05138,0.04638,0.0357,0.00903,0.06944,-0.05893,-0.0691,-0.04633,0.17014,-0.04707,-0.01264,0.07023,0.03985,0.09133,0.03599,-0.0092,-0.05002,-0.03198,-0.01262,-0.03319,0.06373,0.02046,0.01117,0.0288,0.0355,0.04451,0.08486,0.05524,0.05748,-0.05535,0.03553,0.05004,-0.01375,0.11653,-0.0994,0.00983,-0.07042,-0.02092,-0.02228,0.02777,0.06885]},{"domain":"data_science_ml","key":"ml_gaussian_naive_bayes","name":"Gaussian naive Bayes prediction","package":"data-science-ml-ai999x","example":"Gaussian naive Bayes: X = [[6, 180, 12], [5.92, 190, 11], [5.58, 170, 12], [5.92, 165, 10], [5, 100, 6], [5.5, 150, 8], [5.42, 130, 7], [5.75, 150, 9]], y = [0, 0, 0, 0, 1, 1, 1, 1], x = [6, 130, 8]","v":[0.06734,0.03447,0.12299,-0.06479,-0.04945,-0.01245,0.05361,-0.05196,0.0341,-0.06921,-0.05578,0.05537,0.04516,0.00014,0.03711,-0.02898,-0.01393,-0.02531,0.00197,-0.02257,-0.15777,-0.08102,0.06473,0.03457,-0.11676,-0.13431,-0.08896,-0.04463,0.04209,0.1128,0.08379,0.01113,-0.01308,0.02648,-0.05267,0.01323,0.10427,-0.07701,-0.08148,-0.04035,0.06153,0.02831,0.02419,-0.03227,0.01952,0.04125,0.02954,-0.02062,-0.01408,0.02497,-0.01008,-0.00154,0.00577,0.01702,-0.13898,0.09215,0.08787,-0.03264,-0.02852,0.04535,-0.0243,-0.05977,-0.00787,0.00839,0.08909,0.06028,-0.01674,-0.06042,0.07227,-0.02273,0.04034,-0.1003,-0.08777,0.06102,0.00184,0.11743,-0.02963,0.04175,-0.0086,0.1162,0.08316,0.06607,-0.00308,0.03877,-0.05824,0.0855,-0.13689,-0.08498,0.0013,-0.05221,0.02965,0.03791,-0.07519,4e-05,0.00075,0.13338,-0.09476,-0.01391,0.01272,-0.14224,0.02254,0.04823,0.0843,-0.03738,-0.0422,0.00963,-0.02962,0.04009,0.00695,-0.0973,0.04216,-0.00822,0.04623,0.01335,0.0076,-0.02003,-0.01349,0.06215,-0.01142,-0.01055,-0.1144,0.06071,0.05399,-0.06612,0.00935,-0.01078,-0.00904,0.0257,0.03844,-0.01235,-0.01644,-0.11408,-0.04135,-0.03828,0.09351,-0.01192,-0.10462,0.03591,-0.08891,0.0772,-0.06593,0.09132,-0.0925,-0.09375,0.07637,0.07869,-0.08907,0.07691,0.02617,-0.12172,-0.04393,-0.00773,0.10113,0.08097,-0.07685,-0.03172,-0.02301,0.0719,-0.01914,0.13146,-0.11206,0.03487,0.06015,0.02693,0.06477,0.0636,-0.03003,0.01531,-0.13979,0.01349,0.02738,-0.07225,0.04356,-0.01631,-0.05314,0.09564,-0.01397,0.01306,0.01091,0.04996,-0.00708,0.04939,0.00429,0.05269,-0.04933,-0.05248,0.05435,0.02343,-0.06889,-0.11978,0.01421,0.09931,-0.0484,0.07466,0.05408,0.07564,0.0582,0.1114,-0.02425,0.05284,-0.0694,0.03544,-0.00901,-0.00619,0.12718,-0.09344,-0.05587,0.07885,-0.07841,-0.06137,0.06207,-0.04833,0.03032,-0.06763,0.07499,0.0072,-0.03186,0.0031,-0.04978,0.01915,-0.01072,0.06363,-0.12075,0.06572,0.03664,0.14264,-0.01796,-0.04475,-0.00876,-0.02273,-0.04943,0.03362,-0.02116,0.04926,-0.00034,0.02189,0.00842,0.03306,0.01449,0.06959,-0.01464,0.08249,0.03201,-0.01061,-0.0653,-0.10186,-0.0483,0.11833,0.02233,-0.11648,0.03522,0.00746,-0.07927,0.02625,0.04661,-0.07611]},{"domain":"data_science_ml","key":"ml_gini_split","name":"Gini impurity decrease of a split","package":"data-science-ml-ai999x","example":"Gini split: y = [0, 0, 0, 1, 1, 1, 1, 0], g = [0, 0, 0, 0, 1, 1, 1, 1]","v":[0.02845,0.07405,0.02741,-0.02133,0.00756,0.04154,0.08405,-0.06489,-0.09097,0.00508,-0.01561,0.0419,0.00574,-0.07153,0.01869,-0.05394,-0.04858,-0.01506,0.00552,-0.01422,-0.07725,-0.06851,0.03384,0.03095,0.00115,-0.01111,-0.00395,0.02085,0.10309,-0.05658,-0.11722,-0.06209,-0.06153,0.08047,-0.07871,0.09989,-0.05467,-0.03551,0.0226,-0.02276,0.01892,-0.02542,-0.05122,0.0792,0.06589,-0.04327,0.10141,0.00286,0.02144,-0.00199,-0.07136,-0.02232,-0.04888,-0.13518,-0.0614,0.05098,-0.07121,0.01177,-0.0523,-0.00151,0.03056,0.04769,0.04898,-0.10938,-0.0043,0.00958,0.01023,-0.06807,-0.03984,0.02974,-0.06929,-0.02269,-0.00473,0.09002,-0.00682,-0.00436,-0.17523,0.09317,-0.02314,-0.00432,0.07684,-0.09536,0.13813,0.04191,-0.05818,0.12598,0.02551,-0.00237,-0.10926,0.01275,-0.04182,0.00617,-0.02679,-0.04566,0.02669,0.06743,-0.07628,0.00491,-0.10913,-0.09472,-0.00212,0.02522,0.12335,-0.06648,-0.02189,-0.06018,0.05203,0.01136,-0.03942,0.02743,0.04553,-0.02672,-0.08405,0.17354,-0.0458,0.03979,0.00872,0.01673,0.02388,0.00503,-0.06332,0.086,-0.02609,0.08165,0.02633,0.04422,-0.04991,-0.02828,0.053,-0.00686,0.11863,0.08271,0.02185,-0.03161,-0.08155,0.01929,-0.00143,0.12839,-0.05186,0.14725,0.05406,0.01657,-0.03746,0.04281,0.03421,-0.01915,0.02573,-0.00456,0.029,-0.04351,0.024,-0.11506,-0.03919,0.02034,0.06952,0.02663,0.02125,0.05694,0.00311,-0.00713,-0.07232,0.01136,0.10389,0.02114,-0.00028,-0.03527,0.11634,0.07169,0.06851,0.07736,0.08125,-0.12025,-0.01332,-0.01747,-0.03294,-0.0696,-0.02263,-0.00254,-0.01067,-0.11291,0.02383,-0.05262,-0.08201,-0.06828,-0.05719,-0.0167,0.03418,0.02817,-0.06322,0.03577,0.00105,0.06113,0.0036,-0.02732,-0.12381,-0.00442,-0.03682,-0.02177,-0.02762,0.02469,-0.07555,-0.00078,-0.0448,-0.06008,0.01477,0.00351,0.02243,0.00246,0.01211,0.13579,-0.03833,0.08699,-0.0916,-0.01341,0.14535,-0.06952,0.04445,0.00575,0.05541,0.0926,-0.02845,-0.12468,0.01976,-0.04886,-0.11231,-0.03203,0.01608,-0.03515,-0.00436,0.01395,0.01112,0.05338,-0.07817,-0.04101,0.19004,-0.02779,-0.01092,-0.12772,-0.00354,-0.0142,0.07388,-0.02106,0.13396,0.07267,0.12069,-0.03169,0.04587,0.06783,0.15126,-0.06334,0.0463,-0.06776,-0.01593,0.0191,0.06457,0.09887]},{"domain":"data_science_ml","key":"ml_gradient_descent_step_linear","name":"One gradient-descent step for linear regression","package":"data-science-ml-ai999x","example":"Gradient descent step for linear regression: X = [[1], [2], [3], [4]], y = [2, 4, 6, 8], w = [1], b = 1, lr = 0.1","v":[0.0556,0.05332,0.00683,-0.07017,-0.08048,0.02459,-0.06599,-0.0677,0.06835,0.08053,-0.05944,-0.074,0.02526,0.06119,-0.11982,0.05753,0.02162,-0.06694,-0.07885,-0.01251,-0.05091,-0.10189,0.02062,0.07436,-0.11332,-0.0097,0.01287,-0.08306,-0.03929,0.07319,0.01676,-0.02932,-0.02613,0.00483,0.02108,0.07174,0.03402,-0.00182,-0.12131,0.09265,0.02353,0.01344,-0.0232,0.03098,-0.03555,0.08798,-0.01522,0.0015,-0.02112,0.06415,0.00402,0.12171,0.04802,0.05529,0.03911,0.07319,0.10518,-0.0727,-0.10269,0.04509,-0.02176,-0.09469,0.04665,-0.03364,0.07891,0.04472,0.03169,-0.06597,-0.08399,0.02458,0.06243,0.034,-0.05767,-0.03482,0.03676,0.04482,0.02791,-0.00108,0.01523,0.01377,-0.02796,0.04684,-0.02635,0.0018,-0.06549,0.04449,-0.04491,-0.09208,-0.1469,0.06841,0.01042,0.04438,0.01984,-0.03077,0.01813,0.02958,-0.00978,-0.08762,-0.10058,-0.04536,-0.01105,-0.0133,-0.03568,-0.04878,-0.03564,0.01173,0.14198,-0.03266,0.13867,-0.01179,0.0665,0.0271,-0.12317,-0.02891,-0.0381,0.06877,-0.09665,0.01229,-0.02403,-0.03325,-0.03355,-0.05206,-0.11685,-0.09264,0.06247,-0.08146,0.00455,0.0589,-0.00417,-0.01484,-0.00385,0.00666,0.07465,-0.05128,0.05822,0.04599,-0.0806,-0.01268,0.05349,-0.02988,-0.09909,-0.04818,-0.03525,0.00118,0.02342,0.06105,0.01926,-0.03108,0.01844,-0.15961,0.00264,0.02772,0.11204,0.06147,-0.00074,-0.00024,0.07822,0.02822,-0.01554,0.05365,0.02953,0.06412,-0.0095,0.02343,-0.04619,0.04769,0.02532,-0.0498,-0.09577,-0.02193,0.03396,-0.04461,0.00201,-0.0132,0.00659,0.01811,0.08619,-0.16608,-0.06934,-0.04544,0.02245,0.00022,0.0143,-0.08683,0.06542,0.06463,0.00591,0.06578,-0.09571,-0.08467,0.12874,0.12752,-0.07517,0.01946,0.02062,0.14022,0.03487,0.08391,0.03598,0.01516,-0.02169,0.10387,-0.01627,-0.03881,0.01001,-0.0345,0.08945,0.06311,-0.02872,0.05281,-0.01567,0.01092,0.10376,0.03053,-0.0281,-0.06141,0.13719,-0.00143,0.02328,0.05755,0.03066,0.0318,0.00043,0.1799,0.08534,0.07437,0.11036,0.03132,0.00357,0.08769,-0.07306,-0.09318,-0.11895,0.05045,-0.01078,-0.02544,-0.02268,0.07757,-0.1131,-0.05966,-0.00077,-0.04078,0.03612,-0.06189,-0.12456,-0.05863,0.11054,0.06101,-0.06003,0.00018,-0.00728,-0.11184,-0.04372,0.0179,0.03935,-0.04128]},{"domain":"data_science_ml","key":"ml_hamming_loss","name":"Hamming loss and subset accuracy (multi-label)","package":"data-science-ml-ai999x","example":"Hamming loss: Y_true = [[1, 0, 1], [0, 1, 0]], Y_pred = [[1, 0, 0], [0, 1, 0]]","v":[0.14576,-0.02843,0.01413,-0.00613,0.01435,-0.03157,0.21496,0.00754,0.00245,0.02086,0.02065,0.0299,0.07743,0.06718,-0.09703,0.02907,0.0413,-0.0387,0.0325,0.05076,-0.04474,0.08223,0.16166,-0.05735,0.05656,0.0204,-0.04396,-0.00745,0.0344,0.03036,-0.03434,-0.02743,0.00632,0.03,-0.08236,-0.0548,-0.01399,0.06496,-0.06212,-0.02594,0.03083,-0.07898,0.07028,0.00309,0.07465,-0.04458,0.0394,0.0393,0.01753,0.04128,0.00504,0.05725,0.00161,0.072,0.05726,0.0659,0.06943,0.0906,-0.01788,-0.00802,0.02751,-0.04758,-0.03598,0.04777,-0.00088,-0.02291,0.12152,-0.0538,0.00177,0.01319,0.09241,-0.02543,0.14954,0.06439,-0.00725,0.06475,-0.06571,0.02612,-0.04528,-0.098,0.02324,0.05635,0.12598,-0.11371,-0.11721,0.05037,0.00541,-0.13027,-0.09429,0.0512,-0.04732,-0.08094,-0.07311,0.02413,-0.01649,0.07808,0.03531,0.01665,-0.12943,0.05038,0.02276,-0.09204,-0.04168,-0.06062,-0.14229,-2e-05,-0.06231,0.03448,-0.14287,0.04786,0.02038,-0.03023,-0.02539,0.03286,-0.01995,-0.00297,-0.01538,-0.02275,-0.04233,-0.02067,-0.08586,-0.07023,-0.00818,-0.0072,-0.00237,0.0298,-0.11433,0.00933,-0.05895,0.04276,0.15804,-0.0687,-0.07528,0.03538,0.03744,0.01898,-0.05775,0.04507,-0.02395,0.0282,-0.04294,0.01335,-0.01558,0.09371,0.08768,0.00553,0.10395,0.01167,-0.04422,-0.05933,-0.0181,-0.02121,0.07295,0.03519,-0.03223,-0.12697,0.07387,0.0496,-0.11074,-0.03618,-0.0626,-0.0282,0.02958,-0.03864,0.01605,-0.07262,-0.02698,-0.10271,0.09253,-0.07383,-0.06625,-0.1514,-0.04404,-0.07518,0.079,0.04764,0.10652,0.0288,0.06863,-0.02427,0.02591,0.00357,-0.05053,-0.01247,-0.07605,-0.02162,0.06463,-0.0381,-0.10755,0.01658,-0.00283,0.03694,-0.14761,-0.06783,-0.10318,0.05193,-0.08248,0.05602,-0.04161,-0.07984,0.02339,0.07846,-0.03062,-0.00703,-0.03377,-0.09688,-0.02409,0.03102,-0.03128,0.05032,-0.04623,-0.06,-0.03988,0.07647,-0.05339,0.02922,-0.04641,0.0012,-0.00449,-0.0106,0.10975,-0.04319,0.02499,0.03335,-0.07601,-0.04441,0.08159,-0.04277,0.0362,-0.06252,0.03176,0.02897,-0.04654,0.06066,0.09182,0.0374,-0.09589,0.05925,-0.03502,-0.01985,0.04785,0.03935,-0.06648,0.06353,0.00585,-0.01918,0.05105,0.10371,0.13413,0.06873,-0.03729,0.02792,-0.01909,-0.01217,0.05806,0.00975]},{"domain":"data_science_ml","key":"ml_hierarchical_clustering","name":"Agglomerative hierarchical clustering merge heights","package":"data-science-ml-ai999x","example":"Hierarchical clustering: X = [[0, 0], [0, 1], [4, 0], [4, 1.5], [10, 10]], method = 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impurity from class counts (entropy, Gini, misclassification)","package":"data-science-ml-ai999x","example":"Impurity from class counts: counts = [9, 5]","v":[-0.00144,0.03172,-0.02308,0.02174,0.0578,-0.03592,0.15172,-0.01778,-0.02382,0.02879,0.01398,-0.02046,-0.03973,-0.04374,-0.04792,0.00462,0.01384,-0.03461,-0.02515,-0.03256,-0.05,-0.07737,-0.00763,0.02825,-0.06968,0.03634,0.01934,-0.00162,0.09102,-0.02012,-0.11765,0.01099,0.01231,0.01677,-0.06165,0.01727,-0.04046,-0.03752,0.06667,0.0291,-0.01811,-0.0559,0.04157,0.12151,0.05879,-0.01403,0.02628,0.00708,0.01223,0.01119,-0.07931,0.00179,-0.04453,-0.11544,-0.10464,0.10078,-0.08529,0.02675,0.03187,-0.11353,0.03873,0.04565,0.00309,-0.01934,-0.04412,0.00603,0.03325,0.02667,-0.03392,0.07625,-0.12474,0.02792,-0.01934,0.16811,0.13287,0.06141,-0.07825,0.07184,-0.08866,-0.09065,-0.00686,-0.05848,0.04081,0.03594,0.03579,0.07586,-0.01552,-0.03238,-0.09184,-0.07403,0.02052,-0.07322,-0.07454,-0.07645,-0.09848,0.06869,-0.0632,-0.03956,-0.03393,0.00442,-0.00414,-0.00041,0.09023,-0.09052,0.01769,-0.01046,-0.00857,-0.00892,-0.08838,0.02598,0.05362,-0.03775,-0.0729,0.16282,-0.04069,-0.03009,0.04104,0.00966,0.02858,0.13832,0.01745,0.09321,0.00812,0.07271,0.0511,-0.011,0.02573,-0.08277,0.00631,-0.04521,0.12878,0.08577,-0.05904,-0.00735,-0.02953,0.10274,0.00665,0.04476,-0.05505,0.16395,0.0491,0.01982,-0.0847,-0.00796,0.00601,-0.00938,-0.02361,0.08258,-0.0064,-0.0979,-0.04662,-0.12674,-0.03585,-0.00783,0.07967,0.17515,-0.08646,0.02541,-0.01763,0.05419,-0.041,-0.04924,-0.01231,0.07927,0.0627,-0.09321,-0.00104,0.03066,0.06813,0.02242,0.06921,-0.17258,0.04313,-0.00584,-0.02421,0.03019,-0.0678,0.03387,0.0508,-0.01218,-0.00742,-0.06118,0.02567,0.0692,-0.03928,-0.00951,0.03548,0.11039,-0.0638,0.08259,0.01258,0.00523,0.00435,0.01208,-0.14956,0.00414,-0.07935,0.00465,-0.07076,-0.02097,-0.07869,-0.00339,0.01475,0.03271,-0.08658,0.04184,0.01077,-0.01164,0.03932,0.13729,0.01876,0.03671,-0.05341,-0.00186,0.10494,-0.08554,0.04693,0.03543,0.01472,-0.04146,-0.03391,-0.02524,-0.00761,-0.01735,-0.12847,-0.07195,-0.01519,-0.01157,-0.10453,-0.01317,0.01802,0.06589,0.00703,-0.00355,0.12608,0.01692,-0.07197,-0.0631,-0.10221,0.01357,0.00368,-0.0502,0.11488,0.12074,0.12345,-0.02569,0.09955,0.0418,0.08348,-0.08925,0.04166,-0.00315,-0.00198,-0.01761,-0.01171,0.04933]},{"domain":"data_science_ml","key":"ml_information_gain","name":"Information gain and gain ratio of a split","package":"data-science-ml-ai999x","example":"Information gain: y = [1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0], x = [0, 0, 1, 2, 2, 2, 1, 0, 0, 2, 0, 1, 1, 2]","v":[0.06123,-0.03784,0.0366,-0.02492,0.05461,0.06483,0.02993,-0.00942,-0.07328,0.00266,-0.01087,0.02011,-0.01208,-0.08696,0.03443,0.06006,-0.05,-0.13165,-0.186,-0.02997,-0.14192,-0.03669,-0.00045,-0.0288,-0.02681,-0.03334,-0.04847,-0.02923,0.08755,0.06598,-0.0125,-0.03018,-0.06113,0.01575,-0.03726,0.10139,-0.01821,-0.04167,-0.05451,0.0218,0.04761,0.02764,0.03692,0.03838,0.11383,0.05777,0.08346,0.02005,-0.09805,0.04786,-0.09845,0.01052,-0.10373,-0.15442,-0.09095,0.157,0.01154,0.01202,-0.04231,0.01133,-0.05259,-0.00938,0.07351,-0.11997,-0.02396,-0.01831,0.00418,0.02368,0.02525,0.05269,0.02814,-0.0261,-0.06013,0.08112,-0.02013,0.03671,-0.15142,0.06263,0.03647,-0.04892,-0.04841,0.02924,0.06223,0.02795,0.04049,0.08791,-0.00058,0.09241,-0.05485,-0.00699,0.01503,-0.02328,0.00618,-0.08735,0.03166,0.04192,-0.14166,-0.05805,0.00964,-0.07294,-0.02926,-0.00404,0.12965,-0.05351,-0.02079,-0.06308,0.09045,0.03687,-0.05555,0.03093,0.02835,-0.03333,-0.09698,0.17231,0.02576,0.0702,-0.07027,-0.04089,0.00777,0.02154,-0.0151,0.06312,0.01113,0.08545,0.04915,0.05937,-0.02742,-0.033,0.02997,-0.06223,0.0766,0.06315,0.08861,-0.08319,0.00716,0.07865,-0.00895,0.02792,-0.05238,0.04369,0.16939,0.05219,-0.02494,-0.06829,0.01519,0.01952,-0.03094,0.07421,0.08635,-0.11519,0.00451,-0.13331,0.01988,-0.01562,0.08319,-0.06492,0.02678,0.0482,0.05679,-0.01139,0.05029,-0.00223,0.10094,0.04204,-0.01107,0.01126,0.02163,0.06686,0.03453,0.1283,0.05966,-0.08037,0.01005,0.06502,-0.13226,0.02541,-0.05769,0.06298,0.0181,-0.04187,0.01119,0.05472,-0.02193,0.00692,-0.00734,-0.10633,0.05815,0.06135,-0.06498,0.04759,0.00546,-0.02738,-0.00075,-0.02219,-0.06888,-0.03381,-0.06095,0.05372,-0.13538,0.04971,-0.05244,0.03226,0.05292,0.02726,0.02568,-0.04018,-0.02053,0.0715,0.04846,0.11528,-0.04937,-0.00043,-0.07804,-0.01165,0.09936,-0.04238,0.05196,-0.00246,0.02027,0.0812,-0.07898,0.01479,-0.10582,0.0189,-0.11414,0.00168,0.01426,0.07099,-0.06438,-0.01786,-0.05853,0.00335,-0.07659,-0.0057,0.13757,-0.04752,0.04067,-0.03361,-0.08541,0.03646,-0.02995,-0.04246,0.13533,-0.01206,0.05822,-0.0015,0.05067,0.04294,0.05419,-0.10266,-0.00263,-0.03651,-0.00795,0.05745,0.0392,-0.01065]},{"domain":"data_science_ml","key":"ml_joint_conditional_entropy","name":"Joint, marginal and conditional entropy and mutual information","package":"data-science-ml-ai999x","example":"Joint and conditional entropy: P = [[0.25, 0.25], [0.5, 0]], unit = bits","v":[-0.08834,-0.13989,0.02367,0.01393,0.03065,-0.02995,0.12284,0.03928,0.07037,-0.05368,-0.01447,0.0218,0.03285,-0.05736,0.00881,-0.07006,-0.03087,-0.14015,-0.04901,-0.00627,-0.0875,0.05242,0.05364,-0.01731,-0.07865,0.02417,-0.1152,0.08383,-0.0073,0.03524,0.02244,0.02002,-0.09929,0.01014,0.04,0.07424,0.02842,-0.01971,-0.01918,0.12914,0.04788,-0.01625,0.02149,-0.00911,-0.00646,-0.04899,0.00178,0.0797,-0.07904,0.1132,-0.13779,-0.0333,-0.03713,-0.10347,-0.16932,0.0853,0.12835,-0.02557,-0.07478,-0.01742,-0.03927,-0.062,-0.03711,-0.09817,-0.00626,-0.07692,0.04065,0.14287,0.09356,0.04553,0.02813,-0.06457,0.01196,-0.01358,-0.03009,0.01535,-0.01443,0.00346,0.05634,-0.0573,-0.03271,-0.06326,0.03562,0.03137,-0.00045,-0.02951,-0.0083,0.1161,-0.01473,0.04023,0.02028,-0.09816,-0.10053,0.03553,0.05299,-0.051,-0.0184,-0.07252,0.03303,0.018,0.05003,-0.01646,0.07557,-0.0641,-0.01179,-0.07396,-0.02138,0.04724,-0.02638,0.00011,-0.01157,-0.03686,0.01395,-0.0152,0.02512,0.02359,-0.03655,0.00958,-0.00498,-0.01258,-0.0428,0.04546,0.06118,0.07562,0.03518,0.08005,-0.06253,-0.07833,0.04031,0.02738,0.07258,-0.0117,-0.07311,-0.00834,0.01054,0.05106,-0.04142,0.07675,-0.01648,0.02245,0.14037,-0.02121,0.05319,-0.04136,0.02218,0.06332,0.04227,0.03145,0.0688,-0.04248,-0.05373,-0.0999,-0.06263,-0.05302,0.11393,-0.02282,0.07989,-0.00947,0.10757,0.09327,0.03323,-0.00667,0.08588,-0.0128,0.10284,-0.03641,-0.12088,0.04326,-0.06855,0.10468,0.07013,-0.00095,0.0117,-0.07561,-0.07269,0.06401,0.02274,-0.01008,0.02489,-0.01864,-0.06624,0.08069,-0.04957,0.10671,-0.02861,0.02812,0.02921,-0.04545,-0.10025,0.08293,-0.03676,0.1279,0.01639,0.06936,-0.06589,-0.02712,-0.04403,0.03924,-0.04981,-0.00856,0.0068,0.00912,0.01234,0.03267,0.00776,-0.04537,-0.06332,0.09025,0.0821,0.10247,-0.06101,-0.09771,-0.09227,-0.05321,-0.03428,0.03056,0.00353,-0.03156,0.02803,0.04867,-0.05218,0.09608,-0.09016,0.05072,-0.09786,0.08032,-0.03285,0.04601,-0.02675,-0.02002,-0.0923,0.07391,0.00474,0.01285,0.12459,-0.07785,0.11464,-0.02567,-0.14809,0.13564,-0.01632,-0.01718,0.06528,0.09331,-0.06429,-0.09788,0.03042,-0.00041,0.02799,-0.12659,-0.05269,0.03282,-0.01839,0.01058,-0.06163,0.04667]},{"domain":"data_science_ml","key":"ml_kfold_cv_linear_regression","name":"k-fold cross-validated MSE of linear regression","package":"data-science-ml-ai999x","example":"K-fold cross-validation of linear regression: X = [[1], [2], [3], [4], [5], [6]], y = [1.1, 1.9, 3.2, 3.9, 5.1, 5.8], k = 3","v":[0.09821,0.08466,0.03087,-0.02998,-0.14092,-0.04538,-0.04312,-0.02186,0.06522,-0.02246,-0.04455,-0.08761,0.09007,-0.00908,-0.05059,0.01184,0.10083,-0.04542,0.01809,0.00332,-0.10443,0.06795,0.07707,-0.07833,-0.01897,-0.02095,-0.00824,-0.08289,0.00366,0.01008,-0.03163,-0.07324,0.03522,0.00051,0.04305,-0.03536,0.09625,0.03001,-0.09062,0.0975,0.01363,0.06299,-0.0425,0.00493,0.02473,0.00339,0.12673,0.08651,-0.00608,-0.04191,-0.03842,0.0741,-0.02244,0.0162,0.02552,-0.02726,0.12401,0.02372,0.04507,0.11883,0.07087,0.04186,-0.0493,0.04735,0.17192,-0.01563,0.03998,-0.0829,-0.01613,-0.00668,0.09273,0.02886,-0.10896,0.08814,-0.02968,0.15939,0.0355,0.01595,-0.01222,0.07191,0.03956,0.04373,0.01794,-0.06661,-0.08055,-0.01839,-0.02858,-0.02903,-0.08794,0.02224,-0.04767,0.0691,0.07313,-0.0875,0.00039,-0.0077,-0.02411,-0.04314,-0.17145,-0.03164,0.06487,-0.04178,0.04653,0.03438,-0.12029,0.03273,0.05653,-0.01945,0.10411,-0.05086,0.00274,-0.0227,0.03032,0.02892,-0.10389,0.11305,-0.01694,0.07769,-0.03552,-0.04146,-0.07484,0.07359,-0.05536,0.0272,-0.00332,-0.02776,-0.00115,0.05919,0.0232,0.08282,-0.03412,-0.16229,-0.09461,-0.03334,0.11557,-0.08919,-0.13273,-0.00258,0.05322,0.10225,-0.0829,0.03318,0.02494,0.10252,0.04431,0.01569,0.02058,0.04329,0.06939,-0.11316,-0.03671,0.03407,0.01829,0.05216,-0.06779,-0.1059,-0.00411,0.03304,-0.04754,0.09288,-0.05194,0.06576,0.04975,0.07442,-0.09055,0.08778,-0.06434,-0.06007,-0.00785,0.03682,-0.09508,-0.00584,0.03659,0.11068,-0.04083,-0.02763,0.03254,-0.05612,-0.12774,-0.01712,-0.04993,0.01115,-0.1305,-0.08545,0.07596,0.00158,-0.02823,-0.03364,-0.0338,0.00744,-0.00938,-0.01461,-0.02948,-0.04016,0.04367,0.09294,0.05629,0.06828,-0.0097,-0.0035,-0.04637,0.06684,-0.05771,-0.09151,-0.01751,-0.08951,-0.01428,0.038,-0.0572,0.03464,0.02266,-0.06713,0.10924,0.05736,-0.01152,0.00193,-0.04696,0.01307,0.04122,0.03999,-0.01841,-0.01921,0.00803,0.133,0.02035,0.06844,0.09316,-0.02028,-0.05654,0.06232,-0.11454,-0.00335,-0.08242,-0.01696,0.02956,-0.04772,0.00439,-0.06309,-0.02749,0.00105,0.01914,-0.04318,0.03415,-0.02733,-0.03887,-0.04208,0.09446,0.07069,0.00394,0.02756,-0.05018,-0.05746,-0.06878,0.01802,0.03007,-0.10145]},{"domain":"data_science_ml","key":"ml_kfold_sizes","name":"k-fold cross-validation fold sizes","package":"data-science-ml-ai999x","example":"K-fold sizes: n = 10, k = 3","v":[0.00687,0.10369,0.0824,-0.02283,-0.12979,-0.06604,-0.0086,-0.00392,0.00751,0.02179,-0.058,0.04693,0.02608,-0.10582,0.06863,-0.03053,-0.02441,0.03866,0.10985,-0.07311,-0.04727,0.15394,0.06928,-0.02082,-0.02629,-0.0706,-0.02435,-0.07745,0.03051,-0.06629,-0.11009,-0.01558,0.00571,0.01117,-0.01647,-0.0766,-0.01221,0.07202,0.01306,0.06889,0.02022,0.05381,-0.00086,-0.04554,0.06288,-0.01713,-0.04928,0.02924,0.02726,-0.02762,-0.04824,0.13314,-0.06992,0.04424,0.03812,-0.03028,0.03768,0.03475,0.05766,-0.00849,-0.09856,0.01994,0.03329,-0.02071,0.07248,0.08952,0.01438,-0.02785,0.09496,-0.0119,-0.01398,0.02825,-0.06703,0.12584,-0.14042,0.0593,-0.02934,0.07365,0.03546,0.10573,0.00375,-0.10571,0.01866,-0.08535,-0.06703,0.10585,-0.08899,0.05028,-0.04826,0.01132,0.03716,-0.00833,0.07213,-0.05888,0.05232,0.02766,-0.07048,0.01337,-0.04026,-0.04748,0.0279,0.04397,0.08347,-0.00315,-0.05799,0.06402,0.06727,-0.06378,0.08738,0.00198,-0.03904,-0.08962,-0.06737,-0.00039,-0.03143,0.15706,0.02942,0.14762,0.07454,-0.03972,-0.03525,0.04978,0.00754,0.09321,0.06101,0.04145,-0.03433,0.12161,-0.01432,0.06104,0.02546,-0.06812,0.02915,-0.11727,0.05128,-0.11963,0.0016,0.02362,0.01691,0.10027,-0.06314,0.06046,-0.01077,0.04958,0.01071,0.01106,-0.00518,0.02471,-0.04685,-0.0116,0.01595,-0.06136,-0.04514,0.00754,0.01034,-0.12211,-0.08225,-0.00637,-0.00456,-0.01478,-0.02149,0.08965,-0.05313,0.05547,-0.05165,0.04875,0.0006,-0.04491,0.03674,0.04359,-0.0351,-0.03499,-0.05217,0.07945,0.09479,0.00643,-0.07878,-0.00283,-0.15352,-0.06548,0.01497,-0.02938,-0.00799,-0.03504,-0.07479,-0.04319,0.03693,-0.01651,-0.01417,0.00777,0.00544,0.05679,0.04498,-0.06747,-0.12439,0.0168,0.01886,0.03792,-0.11193,0.05264,0.00918,0.03033,-0.09,-0.03979,0.13733,-0.01093,-0.0566,-0.06087,-0.08504,0.00936,-0.01565,-0.06714,-0.08277,0.11204,0.01669,-0.00906,0.01193,0.03906,0.04927,0.00226,-0.08831,-0.00035,0.11468,0.00652,-0.01183,0.08349,0.01088,-0.03449,0.04646,0.05466,-0.12124,0.03136,-0.04706,-0.00885,0.01089,-0.01257,0.10033,-0.19394,0.0214,0.04603,0.0003,-0.16237,0.00561,0.0204,0.1235,0.02994,0.08187,0.11037,0.04887,0.04985,-0.05876,-0.0269,-0.01762,0.03525,0.09638,-0.02473]},{"domain":"data_science_ml","key":"ml_kl_divergence_discrete","name":"KL divergence, Jensen-Shannon divergence and cross-entropy of discrete distributions","package":"data-science-ml-ai999x","example":"KL divergence: p = [0.5, 0.5], q = [0.9, 0.1], unit = 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6]]","v":[0.05092,0.06008,-0.01703,-0.10875,-0.07816,-0.03654,-0.08554,0.01857,0.01861,-0.04174,-0.11154,-0.06519,0.04308,0.01084,-0.0247,-0.13064,0.0051,0.06834,0.04159,0.00927,0.0072,0.04065,0.0087,-0.06299,-0.00352,-0.00442,0.03332,0.10767,0.03764,-0.05624,0.01234,-0.0971,-0.01141,-0.07838,0.05395,-0.05527,0.01158,-0.00277,-0.07424,0.06369,-0.00106,0.08342,-0.15423,0.04413,-0.04586,0.05075,0.00912,0.04273,-0.03881,-0.08878,0.01452,-0.06767,0.15976,0.04361,-0.07158,0.02042,0.05514,0.01924,0.04431,0.03867,0.114,-0.01379,-0.01106,0.03349,0.0301,-0.00437,0.02115,0.00819,0.08786,0.06677,-0.02879,0.08998,-0.0253,0.03907,-0.08381,0.17482,0.04873,0.05896,0.04377,0.04275,0.01391,0.0762,0.05564,0.00269,-0.04334,-0.04215,-0.08254,-0.02009,-0.10776,-0.07367,-0.06588,0.14322,-0.03309,0.01137,0.00113,-0.02412,-0.00961,0.00889,-0.06868,-0.10334,-0.00132,-0.0348,0.01069,-0.0617,-0.00704,0.0558,-0.03206,-0.10472,-0.06214,0.02694,0.11898,-0.0529,0.07213,0.01131,-0.03468,0.04254,0.07009,0.04638,-0.05209,0.07549,-0.11124,0.02842,-0.0215,0.07418,-0.05849,-0.03746,0.03392,-0.03044,0.1333,-0.03963,0.08393,-0.11658,-0.19286,0.04356,0.06058,-0.09819,-0.05759,0.05412,-0.01139,-0.04607,-0.04256,0.11508,-0.03843,0.08283,0.04258,-0.03446,-0.03404,0.12829,-0.00294,-0.09128,-0.02805,0.06818,-0.00938,-0.00814,-0.02655,-0.06147,-0.02355,0.06994,0.00056,0.07467,-0.07887,-0.02382,0.05727,0.15138,0.03856,-0.01426,0.0019,-0.04168,-0.02071,-0.03544,0.03483,-0.00669,0.00772,0.01375,-0.10138,-0.05454,-0.05295,-0.02527,-0.03296,0.05018,-0.01019,0.00973,-0.02269,0.07543,-0.04195,-0.07259,-0.03173,-0.05109,0.04681,0.02003,-0.01511,0.04787,-0.03644,-0.01043,0.06748,0.10237,0.04017,-0.02727,0.02897,-0.16075,-0.18291,0.07323,-0.0172,-0.02873,0.00161,0.00207,0.01136,-0.07835,0.00448,0.02584,0.03604,-0.0335,0.13145,0.01966,-0.07355,-0.0371,-0.07879,0.00845,-0.02806,0.08765,-0.07576,-0.03531,0.04058,0.11449,0.00785,0.10104,-0.08564,-0.05603,-0.01503,0.08191,0.04092,0.00291,-0.10105,0.0116,-0.07363,-0.02497,0.01468,-0.043,0.03964,0.05901,0.06433,-0.03055,0.02404,0.06775,-0.0364,-0.00872,-0.01542,0.11784,0.03551,-0.07414,0.10396,0.0091,-0.06111,0.02801,-0.0493,-0.03316]},{"domain":"data_science_ml","key":"ml_kmeans_step","name":"One 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6]]","v":[0.01471,0.04549,0.01176,-0.07684,-0.12375,-0.01398,-0.09083,0.00383,0.04232,0.00048,-0.1477,-0.05424,0.05923,0.0009,-0.04498,-0.08778,-0.00217,0.06123,0.02947,-0.02883,0.03204,0.00955,0.02489,-0.07506,-0.0147,0.02677,0.00208,0.07265,0.03643,-0.06168,0.02575,-0.04083,-0.00624,-0.03714,-0.00216,-0.04379,0.04549,0.0306,-0.04825,0.06519,0.04201,0.06015,-0.1232,0.00116,-0.07311,0.05572,0.0625,-0.02102,-0.02491,-0.05178,0.07498,-0.0241,0.08798,0.04283,-0.09687,-0.01109,0.11005,0.02949,0.01578,0.02618,0.0875,-0.08489,-0.04175,0.04242,0.05669,0.04009,-0.02264,0.05844,0.07947,0.14324,-0.02393,0.03945,-0.00072,-0.02183,-0.09359,0.16853,-0.01522,0.02063,0.07557,0.05182,0.0255,0.08991,0.05109,0.00176,-0.13255,-0.00562,-0.04451,-0.11883,-0.13978,-0.08575,-0.03529,0.13433,-0.0321,0.05354,0.02171,-0.00674,-0.02814,0.03408,-0.08807,-0.03594,-0.02544,-0.03712,0.03232,-0.04042,-0.0179,0.00693,-0.02748,-0.09143,-0.07449,-0.05657,0.14407,-0.07638,0.02229,0.01096,-0.00486,0.04774,0.08676,0.07766,-0.07735,0.06276,-0.04296,0.00473,0.04181,0.04651,-0.04651,-0.06425,0.03451,-0.01008,0.10611,-0.05962,0.07706,-0.08126,-0.156,0.02306,0.05605,-0.008,-0.08683,0.07286,-0.01501,-0.01715,-0.075,0.09629,-0.06136,0.06094,0.04582,0.00503,-0.01642,0.08334,-0.01191,-0.1176,-0.01148,0.04065,0.04641,0.04515,-0.0332,-0.10484,0.02584,0.0703,-0.05432,0.09022,-0.11409,0.06123,0.0426,0.13375,0.04821,-0.05535,0.03117,-0.12308,-0.01143,-0.02221,0.01311,-0.09247,0.01878,-0.05131,-0.0339,-0.00325,0.00321,-0.00091,-0.01695,0.00931,-0.01968,0.03037,-0.04767,0.0539,-0.0526,-0.05556,-0.00419,0.0124,-0.00975,-0.0208,0.03826,0.03178,-0.01529,-0.00745,0.02596,0.16641,0.04501,0.0507,0.00903,-0.12055,-0.20723,0.12155,-0.01452,-0.06029,-0.00156,-0.01386,0.03474,-0.06098,-0.02508,0.00449,0.01559,-0.05501,0.09366,0.05259,-0.07636,-0.02425,-0.04043,0.01927,0.04587,0.06217,-0.02438,-0.00124,0.00937,0.10228,-0.01795,0.15962,-0.03397,-0.10189,0.00053,0.03151,0.0511,0.06143,-0.09046,0.02834,-0.04862,0.008,-0.02286,-0.0223,0.0222,0.02993,0.05514,-0.05605,-0.02086,0.05301,-0.03317,-0.07552,-0.01831,0.11638,-0.00116,-0.04132,0.09958,0.06213,-0.11225,-0.00695,-0.00102,-0.07169]},{"domain":"data_science_ml","key":"ml_knn_classify","name":"k-nearest-neighbour classification of a query point","package":"data-science-ml-ai999x","example":"kNN classification: X = [[1, 1], [2, 1], [4, 3], [5, 4], [1, 2], [6, 5]], y = [0, 0, 1, 1, 0, 1], x = [3, 2.2], k = 3, metric = euclidean","v":[-0.02304,-0.03168,0.0513,-0.11954,-0.07413,-0.10094,-0.01486,-0.01316,0.04563,-0.09833,-0.09202,0.00323,0.01732,0.02668,-0.02481,-0.08214,0.0173,0.01457,-0.01513,-0.00622,-0.04922,-0.0931,0.03597,-0.11251,-0.01822,-0.0037,-0.02217,-0.01992,0.00401,-0.03969,0.06776,0.00705,-0.02328,0.00073,-0.01371,-0.09452,0.10217,0.02447,-0.00544,-0.0171,0.09934,0.03577,-0.02159,0.01289,-0.12595,0.05809,0.01242,-0.00835,-0.00768,-0.01116,0.08792,0.04168,-0.06703,0.01393,-0.07747,-0.01498,0.0827,0.06963,0.03343,0.05117,0.00094,-0.114,-0.08201,0.00135,-0.00508,0.08499,0.04147,0.03464,0.04191,0.20415,-0.0013,-0.04791,-0.041,0.02938,-0.09175,0.1055,-0.02957,-0.06144,0.03539,0.01587,0.02271,0.03564,0.01112,-0.00938,-0.09429,0.0663,-0.07462,-0.08084,-0.06987,-0.0978,0.00254,0.02065,0.00815,0.03965,-0.01882,0.05149,-0.04516,-0.00017,-0.09186,-0.04638,0.00557,-0.02687,0.02611,-0.11472,-0.1001,-0.03057,-0.02071,-0.04901,-0.07293,-0.1113,0.04044,-0.15243,-0.00671,0.07197,0.03743,0.0161,0.10889,0.19036,-0.08422,0.09207,-0.07474,0.01947,0.06606,-0.01548,0.03184,-0.02971,0.04638,0.02967,0.07954,-0.08149,0.02976,-0.01742,-0.09633,0.01162,0.08974,0.00954,-0.04094,0.0713,-0.04714,0.11238,-0.07369,0.11138,-0.08661,-0.01295,0.03033,0.00506,-0.00327,0.1263,-0.02567,-0.10935,0.02656,0.07299,0.07,0.06401,0.00471,-0.06828,0.03767,0.05284,-0.04924,0.14448,-0.14539,0.03387,-0.06287,0.11855,0.1236,0.01381,-0.0307,-0.13736,0.0167,-0.00444,-0.02984,-0.09527,-0.02268,-0.0423,-0.00299,0.02648,-0.00369,0.03396,-0.00628,0.12957,0.02697,0.03982,-0.01338,0.08096,-0.05093,-0.03468,0.09781,0.03699,-0.01081,-0.00438,0.07212,0.00299,-0.01475,0.05901,-0.04597,0.1207,0.00939,0.02471,-0.0085,-0.00957,-0.12534,0.09439,0.05665,0.01286,0.09692,-0.02973,-0.0179,-0.05478,-0.01574,0.07109,0.01515,-0.07619,0.04804,-0.00255,-0.04458,0.03238,-0.07383,0.01634,-0.0069,0.06001,-0.02025,0.00275,0.00981,0.07231,0.05703,0.1658,-0.03706,-0.13198,0.03854,-0.00365,0.01387,0.08052,-0.01707,0.04367,-0.01474,-0.00276,-0.01163,0.0258,-0.03372,0.03603,0.02391,-0.04126,0.01469,-0.0068,-0.07837,-0.05001,-0.0489,0.08771,0.03021,-0.02435,0.05579,0.06604,-0.08767,-0.00676,-0.01221,-0.08508]},{"domain":"data_science_ml","key":"ml_knn_regress","name":"k-nearest-neighbour regression of a query point","package":"data-science-ml-ai999x","example":"kNN regression: X = [[1], [2], [3], [10]], y = [1.5, 2.5, 3, 9], x = [2.4], k = 2, metric = euclidean, weights = uniform","v":[0.04561,-0.05476,0.03254,-0.106,-0.00236,-0.01318,-0.04462,-0.00929,0.01306,-0.14956,-0.0709,0.00645,0.02913,0.00215,-0.02722,0.01195,0.10622,-0.07253,-0.07444,-0.01289,-0.05834,-0.16641,0.02592,-0.02062,-0.04956,0.00842,-0.05086,-0.12166,0.05633,-0.06242,0.11455,0.02553,-0.0105,-0.06954,0.03853,-0.07225,0.10238,0.04242,-0.00131,0.08332,0.0525,0.06216,-0.0542,0.01643,-0.13419,0.0639,0.03588,0.02614,0.00874,-0.0295,0.03336,0.03528,-0.02213,0.05818,0.00933,-0.10712,0.08249,0.03164,-0.00437,0.06338,-0.03572,-0.01972,-0.18813,-0.0652,0.05155,0.04641,-0.07,0.03556,-0.00671,0.08171,0.02874,-0.02692,-0.1221,-0.08216,-0.05565,0.0878,-0.02342,-0.02361,-0.00423,0.08545,-0.01891,0.08593,0.01845,0.03835,-0.07889,0.04482,0.02033,-0.02733,0.03121,-0.04733,-0.00169,0.00693,0.0997,0.02935,-0.01936,0.0451,0.00767,0.05237,-0.12378,-0.04113,0.08064,-0.04263,-0.04967,-0.0191,-0.14586,-0.04843,0.01004,-0.00427,0.07078,-0.08152,0.04604,-0.10317,-0.07799,0.0119,0.00054,0.10141,0.08964,0.1358,-0.02125,0.03723,0.01188,-0.03945,-0.0184,-0.13127,0.04138,-0.02144,0.02009,0.00242,0.02392,-0.09418,-0.03845,-0.045,0.0571,-0.0335,0.0855,-0.02396,-0.02083,-0.0045,-0.04067,0.06926,-0.04216,0.02044,-0.00173,0.01895,-0.00813,-0.00807,0.03338,0.01948,0.0524,-0.14631,0.01543,0.09091,0.14693,0.05949,0.01504,-0.06178,0.05659,-0.05278,-0.01254,0.15062,-0.10995,0.03043,-0.03536,0.0802,0.12537,0.04394,0.01951,-0.09973,-0.02916,0.0126,-0.0234,-0.0429,0.00042,-0.0389,0.01743,-0.04123,0.02205,-0.00544,-0.03433,0.13161,0.05514,-0.00154,-0.02929,0.00089,0.05551,0.01425,0.01799,0.07357,0.00421,-0.03347,0.01364,-0.05473,0.03106,0.04724,0.04712,0.12722,0.00684,0.03969,-0.01218,-0.014,-0.06935,0.01425,0.04071,-0.1116,0.07073,-0.06903,-0.00438,-0.01204,-0.03398,0.09272,0.08975,-0.01325,0.11815,-0.08261,-0.02404,0.03412,0.04836,0.00817,0.03614,0.13334,-0.00746,0.03337,-0.00793,0.07774,0.0839,0.10396,0.00381,-0.05378,0.04716,0.05833,0.0456,0.03289,-0.04885,-0.02099,0.00032,-0.0065,-0.04288,0.12626,-0.02876,-0.03547,0.0476,0.00169,-0.05668,-0.05196,-0.09613,-0.09317,0.0084,0.12534,-0.09384,0.02286,0.0285,0.00051,-0.14113,-0.0705,-0.0493,-0.07413]},{"domain":"data_science_ml","key":"ml_label_smoothing_cross_entropy","name":"Cross-entropy with label smoothing","package":"data-science-ml-ai999x","example":"Label smoothing cross-entropy: z = [2, 1, 0.1], y = 0, epsilon = 0.1","v":[0.09309,0.0116,0.09128,-0.03882,-0.07983,-0.12744,0.04901,0.05665,-0.10648,-0.02056,0.0276,-0.03094,0.00148,-0.01864,0.02642,0.10185,-0.0087,0.0102,0.10158,-0.00597,0.02551,0.09039,0.08204,-0.09105,-0.02614,0.03982,-0.0762,0.02676,2e-05,-0.0182,-0.14969,-0.05216,0.01247,-0.01575,0.02523,0.1057,0.05238,-0.12952,0.02429,-0.04854,-0.02446,-0.09441,0.02368,-0.05175,0.08849,0.03211,0.05325,-0.08999,-0.05784,-0.0565,-0.01475,-0.08564,-0.01333,0.03654,0.06134,-0.08893,-0.00341,0.07418,-0.03826,-0.00159,-0.00733,-0.04893,0.0448,0.16243,0.01628,-0.01581,-0.0619,-0.0655,0.01937,0.03128,0.0215,0.03033,0.01607,0.09176,-0.06669,0.06849,0.00559,0.10318,-0.03326,0.02215,0.01496,0.1454,0.07582,0.08159,-0.10296,0.14698,-0.12356,-0.03344,0.00455,-0.03011,0.10373,-0.11609,0.02795,-0.00601,0.045,0.06693,0.02996,-0.11569,0.05853,-0.00463,0.03485,0.02538,-0.00715,-0.05158,0.00487,-0.02204,-0.11983,-0.02585,0.04345,-0.02444,0.05891,-0.03998,0.09998,-0.09027,0.03981,0.05717,0.00369,0.00114,-0.10447,-0.02025,-0.09238,-0.03434,0.04052,-0.01215,-0.0738,-0.06705,-0.07249,-0.0769,-0.05961,-0.01432,0.05939,-0.04812,-0.12556,-0.03912,-0.02506,0.06545,-0.10064,0.01184,-0.03809,0.0142,0.04722,-0.02997,0.03869,-0.02878,0.0497,-0.04469,0.07933,0.09647,-0.19324,0.07172,0.02925,-0.08347,-0.00964,-0.06583,0.00475,0.06387,-0.0104,0.07952,0.01536,-0.06252,-0.1083,0.04977,0.0707,0.12455,0.06066,0.05785,-0.03562,-0.04101,-0.00159,-0.02887,-0.05722,-0.06627,-0.02305,-0.01736,0.0191,-0.04807,0.00885,0.06616,0.05764,0.01643,0.04376,-0.04169,0.01843,0.0835,0.07415,-0.01687,-0.0643,0.0704,-0.12552,0.07512,0.0939,0.07155,-0.06963,-0.00185,-0.07725,-0.04319,-0.11281,-0.0519,-0.03193,-0.04443,-0.0263,0.05033,-0.02313,-0.05048,-0.02403,-0.08792,0.18934,0.08105,0.02744,0.08794,-0.03501,0.1184,0.02545,0.02202,9e-05,0.00233,-0.02706,0.01338,-0.10002,0.01343,-0.02964,-0.03913,0.07955,0.0481,0.07725,0.02728,-0.02984,0.03552,0.03286,0.0185,0.04324,0.04031,0.05914,-0.10549,0.07626,-0.06475,-0.0454,0.04044,0.07189,-0.00101,-0.01307,0.02342,-0.03959,0.00348,0.00914,0.02914,0.03006,-0.02156,0.03789,-0.01221,-0.01415,0.00638,0.01387,-0.03555,0.01358,0.05975]},{"domain":"data_science_ml","key":"ml_lasso_regression","name":"Lasso 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0.1","v":[0.05512,0.04922,-0.07294,-0.02884,-0.14903,0.02746,-0.07694,-0.0571,0.05275,-0.04376,-0.0809,-0.06979,0.08748,0.01893,-0.07018,-0.00934,0.11261,-0.02971,-0.04328,-0.03185,-0.13419,0.0412,0.03058,-0.02974,-0.0534,-0.02867,0.01912,-0.03323,0.00712,0.06958,-0.07755,-0.0768,0.03233,-0.01503,0.05841,-0.01556,0.10897,-0.02965,-0.10907,0.12004,-0.02536,0.04452,-0.04621,-0.00834,0.04141,0.07386,0.11462,-0.01546,-0.04204,-0.02491,0.02699,0.09576,-0.01666,-0.01984,-0.07468,0.0239,0.15052,-0.07897,0.02003,0.15992,0.0626,0.03804,-0.07363,0.0773,0.10902,-0.01298,-0.00757,-0.0514,-0.02248,-0.00564,0.03253,-0.00474,-0.02298,-0.017,0.03974,0.09831,0.08781,0.00161,0.03644,0.06856,0.01664,0.08855,-0.00505,-0.0026,0.0177,0.00942,-0.03762,-0.06149,-0.13629,0.08516,0.00781,0.03589,0.01318,-0.10649,0.02932,-0.02826,-0.04997,-0.0031,-0.13724,-0.05272,0.03352,-0.04986,0.05376,-0.01501,-0.09059,-0.0365,-0.00952,-0.02122,0.11475,-0.02793,0.00108,0.0399,-0.02336,-0.0069,-0.05134,-0.01441,-0.01926,0.02343,-0.06846,0.06722,-0.05825,0.09083,0.06072,0.00676,0.02118,0.03992,-0.00011,0.09073,0.03558,-0.03164,-0.14654,-0.04504,-0.1061,-0.05937,0.01993,-0.02197,-0.18193,-0.04299,-0.01084,0.10835,-0.01824,-0.01872,-0.0264,0.01356,0.13737,0.01377,0.08734,0.07083,0.08607,-0.11773,-0.00888,0.04882,-0.00868,0.02973,-0.0125,-0.095,0.02826,0.0467,-0.04688,0.17024,-0.02963,0.0244,0.00545,0.10088,-0.02581,0.0628,-0.00374,0.00096,-0.09558,0.09331,-0.04254,0.00052,0.03143,0.05251,-0.07916,-0.02491,0.04868,-0.06148,-0.02888,-0.06768,-0.01201,0.02646,-0.05244,-0.04251,0.09571,-0.03289,0.00819,0.01663,-0.06811,0.06802,-0.00154,-0.00382,0.02011,0.03086,-0.01351,0.03089,0.04411,-0.01152,0.07289,-0.0349,-0.00999,0.10609,-0.04803,-0.07586,-0.01206,-0.05339,0.06346,0.06649,-0.02974,0.02627,0.00031,-0.06238,0.14723,0.03982,0.03816,0.0356,0.00675,-0.05487,0.00995,0.07652,-0.06073,0.00093,-0.06959,0.11865,0.02791,0.16723,0.06474,0.02212,-0.09372,0.03199,-0.16527,-0.01007,-0.03558,-0.06764,-0.01001,-0.00842,-0.04478,0.0032,-0.0516,-0.0283,-0.00226,-0.04612,0.09255,-0.01909,-0.10822,-0.00406,0.06993,0.02445,-0.05232,0.07638,-0.05369,-0.07373,0.0434,0.04251,0.04528,-0.06401]},{"domain":"data_science_ml","key":"ml_linear_svm_decision","name":"Linear SVM decision values, classes and margin","package":"data-science-ml-ai999x","example":"Linear SVM decision: w = [2, -1], b = -1, X = [[1, 0], [0, 1], [2, 2]]","v":[0.00193,0.02574,0.00797,-0.03654,-0.0507,-0.00777,0.02252,-0.08279,-0.01461,0.05826,-0.10188,0.05152,0.02546,0.01139,-0.0707,-0.01032,-0.07608,0.02223,-0.0835,-0.03806,-0.00854,-0.08177,0.00285,-0.04764,-0.00545,-0.06412,0.03762,-0.01867,0.05635,-0.02474,0.06119,0.07577,-0.05998,0.00066,-0.03427,0.01452,0.0135,-0.06581,-0.12756,0.06581,-0.04547,-0.06487,0.03695,0.07301,-0.03551,-0.01459,0.01232,-0.03102,-0.04849,0.00891,0.01741,0.06539,0.02969,0.08475,0.05693,0.11361,0.07751,0.05851,-0.07859,0.09012,-0.07378,-0.11169,0.00217,-0.0469,0.0459,0.00388,0.01558,-0.10823,-0.05845,-0.0373,0.11563,0.02916,-0.04195,0.08161,0.09311,0.03378,-0.06122,-0.02056,0.1187,0.02399,0.02051,0.02919,0.02523,-0.08462,-0.09306,0.06044,-0.04355,-0.04998,-0.1149,-0.03621,0.0669,0.06014,-0.02243,-0.01484,0.02635,0.01614,0.0753,-0.09952,-0.03495,-0.00453,-0.04194,0.00202,-0.00721,-0.07462,0.04753,-0.01528,0.00381,-0.02446,0.03251,0.03883,0.13438,-0.08355,-0.0756,0.13994,0.02039,-0.02991,-0.10384,0.045,-0.07162,0.02322,-0.05644,0.02203,-0.12226,0.02179,0.01736,-0.0359,0.02425,0.03332,0.01096,-0.016,-0.02971,0.09957,0.00778,-0.07074,0.01591,0.03988,-0.11926,-0.0483,-0.0443,0.00782,-0.01033,-0.0808,-0.04378,-0.03378,0.03444,0.02625,-0.02618,0.05769,-0.04357,-0.1206,0.01616,0.03652,0.16639,0.04505,-0.09436,-0.08502,0.14762,0.03702,-0.01154,0.07575,0.02254,-0.0177,-0.01914,-0.04212,0.02689,-0.02138,-0.0506,-0.12107,0.01987,-0.02034,-0.03551,-0.04354,-0.01948,0.01557,-0.08069,0.00687,0.01176,-0.18226,0.07895,0.00644,0.15609,-0.03643,0.02883,-0.05047,0.01235,0.01532,0.11078,0.05726,0.02361,-0.10628,0.05197,0.07854,-0.16954,0.0278,0.0351,0.07281,-0.01026,0.07921,0.05427,0.04051,-0.08008,0.11614,-0.07227,-0.02079,-0.01967,0.03336,0.06547,0.06431,-0.05454,-0.01667,-0.03073,0.00808,0.15441,0.02197,0.06459,-0.00949,0.04021,0.05365,-0.04555,0.02836,-0.0252,-0.00175,0.04377,0.11771,0.02942,0.09851,-0.02313,0.00536,-0.02607,0.12357,-0.02852,0.01226,-0.02498,0.09853,0.02823,0.00734,-0.09098,0.02099,-0.04303,-0.07286,0.04351,0.04068,0.08975,0.01035,-0.07775,-0.10398,0.01002,0.08708,0.05305,-0.05643,0.13288,0.00847,0.07209,0.09945,-0.03074,-0.07673]},{"domain":"data_science_ml","key":"ml_log_loss_binary","name":"Binary log loss (cross-entropy)","package":"data-science-ml-ai999x","example":"Binary log loss: y_true = [1, 0, 1, 1], p = [0.9, 0.2, 0.7, 0.6]","v":[0.06159,-0.16313,0.07614,-0.04095,0.10758,-0.03704,0.09678,0.00636,-0.09579,0.06429,0.06118,0.03608,0.05723,-0.03338,0.03346,0.09515,0.04543,-0.03508,0.01746,-0.04706,-0.03957,0.04371,0.16665,-0.04668,0.0373,0.01066,-0.07174,0.05161,0.21515,0.05825,-0.09689,-0.00768,-0.03452,-0.05852,-0.03982,0.07619,0.01419,-0.0989,-0.02711,0.00633,-0.00874,-0.11781,0.10174,-0.01665,0.08143,-0.03377,0.11438,-0.05113,-0.01531,-0.03378,-0.04789,-0.09413,-0.00506,-0.03124,-0.02445,-0.09216,0.01079,0.08211,-0.05263,-0.02855,0.02534,-0.03698,-0.07827,0.06743,0.03721,0.05087,0.02056,-0.05901,0.06721,0.01926,0.01021,-0.02539,-0.01017,0.02588,0.00252,0.05078,-0.09676,0.05804,-0.03552,-0.07279,0.02514,0.06227,0.16979,0.05972,-0.15225,0.08578,0.01234,0.0164,0.03374,-0.06596,0.07005,-0.1067,-0.03615,-0.04338,0.02923,0.13064,-0.01138,-0.0019,0.00552,-0.03432,0.02212,-0.07433,-0.00856,-0.1155,-0.02425,-0.0453,-0.12018,0.09051,-0.02828,0.00144,0.01798,0.00951,0.09505,-0.02673,0.02017,-0.00992,-0.05081,0.05175,-0.00027,-0.07224,-0.05988,0.03573,-0.00842,-0.00794,-0.01833,-0.02044,-0.13895,-0.01713,-0.1223,0.01896,0.09791,-0.01308,-0.00452,0.03685,-0.06085,0.02631,-0.0197,0.01479,-0.05006,-0.04586,0.05389,0.07222,0.02293,0.06142,-0.02281,0.00672,0.06551,0.00961,-0.09335,-0.05475,-0.05028,-0.05307,0.08625,-0.07577,0.00703,0.03272,-0.02832,-0.01101,0.0189,-0.00732,-0.05851,0.0168,0.17179,0.02773,0.07092,-0.01665,-0.07038,-0.05514,-0.04103,-0.04711,0.01363,-0.09596,-0.05962,-0.00761,0.04105,-0.0577,-0.00964,-0.03161,0.04741,-0.0594,-0.02931,-0.02264,-0.04824,0.04601,0.05137,-0.00438,-0.03109,-0.06597,-0.12751,0.08456,-0.07133,0.04739,-0.07235,-0.03346,-0.07723,-0.05298,-0.07074,0.05749,-0.07385,-0.06034,-0.04702,0.03755,-0.05468,-0.06996,0.04542,-0.09327,0.094,0.06153,0.06126,0.07822,0.00636,0.11361,0.02124,-0.01498,0.06812,-0.07255,0.05007,0.12069,-0.0263,0.01908,-0.10143,0.03878,-0.03833,0.02907,-0.06185,-0.0466,-0.00542,0.07001,0.02678,-0.06433,0.05585,-0.02925,-0.06024,0.05278,0.05245,0.0455,-0.01025,0.06413,-0.01419,-0.00278,0.00084,0.04091,0.00936,0.17548,0.04655,-0.047,0.08055,0.02278,0.08362,-0.11368,0.01539,0.01374,0.00861,0.04087,-0.00365,0.03321]},{"domain":"data_science_ml","key":"ml_log_loss_multiclass","name":"Multi-class log loss (categorical cross-entropy)","package":"data-science-ml-ai999x","example":"Multiclass log loss: y_true = [0, 2, 1], P = [[0.7, 0.2, 0.1], [0.1, 0.3, 0.6], [0.25, 0.5, 0.25]]","v":[0.03161,-0.08196,0.08844,-0.02194,0.00099,-0.06444,0.10824,-0.00208,-0.0632,0.05001,0.06129,0.0186,0.08542,0.01672,0.0083,0.03069,0.0364,0.04529,0.05678,-0.0357,-0.0284,0.05635,0.16464,-0.09614,0.00651,0.0031,-0.05479,0.06351,0.10941,0.02787,-0.11106,-0.0257,0.02873,-0.02142,-0.01774,0.04861,0.06497,-0.05479,-0.04295,0.00835,-0.00867,-0.11251,0.05641,0.04136,0.06002,-0.04119,0.0886,-0.02362,-0.00229,-0.05547,-0.04871,-0.08912,0.03312,-0.01729,-0.00687,-0.09051,0.03269,0.01965,-0.04629,-0.04363,0.05075,-0.02019,-0.04465,0.05845,0.0187,-0.02047,0.04926,-0.03692,0.0775,0.04126,0.035,0.03157,0.02416,0.06441,-0.06532,0.1218,-0.08096,0.03597,0.00339,-0.04208,0.06918,0.01317,0.1482,0.03664,-0.18509,0.03839,-0.02201,-0.10116,-0.00056,-0.04461,0.01031,-0.06717,-0.06896,-0.03667,0.04071,0.0851,-0.01556,-0.02867,-0.0522,-0.00778,0.03392,-0.09583,-0.01408,-0.1178,-0.01868,0.0015,-0.14366,0.05699,-0.02947,0.04551,0.07793,-0.00735,0.1576,-0.00536,-0.02441,0.03412,-0.03756,0.01514,-0.04641,-0.05584,-0.14612,0.06112,-0.0155,0.01478,0.01436,-0.02915,-0.13378,-0.0295,-0.13431,0.09884,0.09437,-0.09364,-0.06809,0.06041,0.02037,0.03914,-0.09304,0.04001,-0.03527,0.02398,0.01418,0.00633,0.0179,0.09608,0.01394,0.02711,0.06567,-0.00492,-0.11279,-0.0591,-0.1096,-0.04363,0.05202,-0.06495,-0.02879,0.00969,-0.01322,0.02313,-0.02853,-0.00806,-0.12812,0.00701,0.15415,0.04013,0.08043,-0.02311,-0.12933,-0.12464,-0.02443,-0.03414,-0.01479,-0.09461,-0.02064,-0.02084,0.05224,-0.03303,-0.00958,-0.0422,0.07106,0.01539,-0.02023,-0.0648,-0.08155,0.0608,0.02411,0.05678,-0.01919,-0.12155,-0.12482,0.05847,-0.00588,0.11055,-0.14129,-0.00541,-0.09001,0.02602,-0.03849,0.04885,-0.07455,-0.08288,-0.07713,0.04333,-0.05151,-0.00959,-0.04028,-0.08883,0.08342,0.07126,0.05074,0.06969,-0.02036,0.06849,0.03144,0.00973,0.05144,-0.05101,0.02175,0.03751,-0.02661,0.03958,-0.09046,0.00695,-0.00053,0.10816,-0.02887,-0.01769,-0.05379,0.04249,0.00192,-0.05997,0.05707,0.04893,-0.04594,0.0282,0.10288,0.04832,-0.02108,0.02369,-0.01188,0.01331,0.05856,0.05596,0.00777,0.15049,0.02028,-0.03865,0.03674,-0.00048,0.11425,-0.07198,-0.00733,0.06117,0.01824,0.03028,-0.01461,0.04398]},{"domain":"data_science_ml","key":"ml_log_softmax","name":"Log-softmax","package":"data-science-ml-ai999x","example":"Log-softmax: z = [1, 2, 3]","v":[-0.06159,-0.04017,0.03309,0.00711,-0.00976,-0.06328,-0.05826,0.10025,-0.06698,-0.00421,0.05072,-0.03095,-0.02512,-0.03088,0.09624,0.06924,-0.0658,0.06608,0.08192,-0.06483,0.08285,0.00143,0.04638,-0.08983,-0.07223,0.00412,-0.07003,0.11308,0.0419,0.04952,-0.08717,0.0384,0.0228,-0.11067,-0.00987,0.07244,0.06844,-0.095,-0.04305,0.04379,-0.01232,-0.07789,0.01086,-0.0449,0.04,-0.02159,-0.01079,-0.09595,-0.09803,-0.02746,-0.09425,-0.11306,0.06346,0.07725,0.02414,-0.10217,-0.02458,-0.0333,-0.02011,0.00653,0.01027,-0.02457,0.02364,0.0503,0.03309,0.01342,-0.03062,0.05006,0.0558,0.06422,0.10869,0.02368,-0.09634,0.08765,-0.09922,0.06278,0.00932,-0.10291,-0.05338,-0.00383,-0.01104,0.08521,0.04282,0.06483,-0.04664,0.03065,-0.03691,0.07893,0.05295,-0.10776,0.078,-0.04089,-0.08253,0.0192,0.12892,0.03624,0.02166,-0.02429,0.10953,-0.11161,0.00435,0.02673,0.00827,-0.02871,0.04522,0.04677,-0.08376,-0.01517,0.00095,-0.08852,-0.00225,0.06683,0.1495,0.05631,0.07435,-0.0273,-0.10959,0.09485,-0.0487,-0.05769,-0.06118,0.00834,0.06798,0.01521,0.04455,-0.07269,-0.06915,-0.01182,-0.08064,0.00826,-0.01373,-0.02728,-0.09656,-0.00331,0.00437,0.04663,-0.13918,-0.05708,0.01573,-0.09175,0.09413,0.02588,0.03147,0.08966,0.00543,0.07166,-0.01829,0.03582,-0.19994,0.07911,-0.05964,0.00777,-0.06658,-0.08743,-0.04446,0.00182,-0.09316,0.03049,-0.01717,-0.06033,-0.09366,-0.03013,0.08814,0.12746,0.10314,0.08005,-0.0479,-0.04413,-0.02831,-0.07705,-0.01606,-0.01601,0.00853,0.03942,-0.05701,-0.10067,-0.02293,-0.03135,0.04804,0.14783,-0.05228,-0.02141,0.07843,0.12156,0.05831,0.04727,-0.11501,-0.01192,-0.02571,0.06638,-0.00671,0.09199,-0.07743,-0.00851,-0.06411,0.00525,-0.10679,0.04096,-0.01701,0.00518,-0.0863,-0.0371,0.00373,0.0672,-0.05393,-0.06583,0.07468,0.09389,0.04308,0.07383,0.01039,0.08232,0.03465,-0.05116,0.0208,-0.01449,-0.04708,0.06791,-0.11603,0.00993,-0.03436,-0.05513,0.03221,0.03345,0.11865,0.02628,0.01426,-0.01476,-0.00085,-0.04582,0.07878,-0.04031,0.08145,-0.03176,0.03268,0.04245,0.06479,-0.00987,0.04055,-0.00379,-0.01249,0.07789,-0.07662,0.01488,-0.04274,-0.04159,0.03525,0.01365,0.05003,-0.04675,0.07174,0.0509,0.05052,0.00962,-0.01809,0.06034]},{"domain":"data_science_ml","key":"ml_logistic_loss_gradient","name":"Logistic regression loss and gradient (L2-regularised)","package":"data-science-ml-ai999x","example":"Logistic regression gradient: X = [[1, 2], [2, 1], [3, 3]], y = [0, 1, 1], w = [0.5, -0.25], b = 0.1, lam = 0","v":[0.0395,-0.095,0.03948,-0.09125,-0.11395,-0.03198,-0.04841,-0.10881,0.03478,0.1265,-0.01186,-0.04623,0.05011,0.08355,-0.01984,0.01601,-0.13069,-0.0049,-0.05191,-0.03839,-0.0597,-0.06104,0.05461,0.02927,-0.0341,-0.12082,0.04035,-0.01761,0.05328,0.13224,-0.02507,-0.02382,-0.00356,-0.06361,0.01582,0.03697,0.0707,-0.10991,-0.06441,0.08476,0.06209,-0.08212,0.05396,0.02182,0.05843,0.05615,0.01534,-0.01732,-0.03451,0.01296,-0.07236,0.04119,0.02046,-0.00045,0.08881,0.0645,-0.01413,-0.0506,-0.10301,0.11769,0.03162,-0.0578,0.07953,-0.01093,0.0188,0.02002,0.03397,-0.064,0.02199,0.04829,0.03566,0.00309,-0.09972,-0.00052,0.05134,0.00105,-0.11046,-0.00506,-0.06012,-0.10054,-0.0616,0.13044,-0.00054,0.02031,-0.06698,0.06765,-0.01641,-0.14804,-0.12225,0.07278,-0.01859,0.00715,-0.00979,-0.04933,0.09661,0.08318,-0.06006,-0.07984,-0.0966,-0.11234,0.01426,0.02268,-0.05331,-0.04568,0.00833,-0.0432,0.0379,-0.02364,0.07606,-0.03682,0.05,-0.04699,0.04795,-0.00111,-0.02711,0.03527,-0.03714,0.01028,-0.07498,0.02463,-0.09072,-0.08637,-0.04914,-0.04314,0.01706,-0.08102,-0.04751,0.01781,-0.0883,0.0427,-0.00951,0.01527,0.0907,-0.07822,-0.02977,0.06765,-0.06776,-0.01457,0.038,0.02114,0.10127,-0.03462,0.04108,0.0055,0.01152,0.06073,-0.00455,0.0242,-0.08267,-0.07567,0.01877,-0.00056,0.08181,-0.02472,0.06317,-0.07242,0.10869,0.00627,-0.01839,0.10903,-0.03083,0.03967,0.0408,0.05836,-0.02627,0.13389,0.02811,-0.03461,-0.02581,-0.03862,0.02508,-0.00428,-0.02494,0.02202,-0.04701,-0.05394,0.09488,-0.13493,-0.05038,-0.06111,0.02857,-0.00371,-0.02318,-0.08024,0.11472,-0.07199,-0.00669,0.09649,-0.04648,-0.0238,0.12789,0.13584,-0.03913,-0.01821,-0.04422,0.04714,-0.0507,0.0819,0.03038,0.02485,-0.00583,0.12359,0.01126,-0.03217,0.0261,-0.06615,0.14983,0.13652,0.0109,0.03913,-0.04719,0.10706,0.12063,-0.00663,0.05229,0.01563,0.09063,0.04778,0.01333,0.01736,-0.09737,-0.00881,0.0025,0.16806,0.02622,0.08559,0.07114,-0.02077,-0.01087,-0.03761,-0.03506,-0.08641,-0.04954,0.01706,0.07927,0.05925,0.02082,0.03822,-0.06247,-0.03269,0.00981,0.01023,0.10265,0.05303,-0.09969,0.02302,0.07046,0.02774,-0.00688,-0.0626,0.02745,-0.06783,0.01333,0.06871,-0.01045,-0.03406]},{"domain":"data_science_ml","key":"ml_logistic_regression_fit","name":"Logistic regression fit (L2, stated C)","package":"data-science-ml-ai999x","example":"Logistic regression fit: X = [[0.5], [1], [1.5], [2], [2.5], [3], [3.5], [4]], y = [0, 0, 1, 0, 1, 0, 1, 1], C = 1","v":[0.06733,-0.03332,0.01874,-0.04849,-0.10754,0.00072,-0.01092,-0.11313,0.02606,0.0075,-0.04137,0.0013,0.08301,0.04517,-0.02578,-0.00017,-0.00492,-0.01651,-0.03154,-0.06984,-0.11087,-0.04747,0.07738,-0.02372,-0.07104,-0.07242,-0.03535,-0.03668,0.06231,0.13525,-0.02822,-0.06824,0.02968,-0.07876,0.03416,-0.00465,0.15576,-0.07865,-0.06518,0.09377,0.02459,-0.04951,0.00499,-0.0025,0.01494,0.02371,0.09709,-0.00871,-0.08754,0.00114,-0.07312,0.04163,-0.01052,-0.01643,-0.03093,0.04693,0.09126,-0.03295,-0.01369,0.19265,0.05345,0.00147,-0.05376,0.06974,0.06066,0.05962,-0.00616,-0.06601,-0.00346,0.01928,0.04985,-0.03877,-0.09398,0.00189,0.01672,0.04456,-0.04997,0.04468,-0.0684,-0.00224,0.05778,0.1218,0.02865,0.04172,-0.02104,0.09497,-0.04479,-0.10487,-0.10767,0.01679,0.04563,0.04152,-0.00829,-0.06805,0.06054,0.10002,-0.06109,0.00978,-0.16637,-0.11918,0.04581,0.0325,0.00059,-0.01973,-0.07475,-0.10158,-0.00862,0.00527,0.06268,-0.01297,-0.01148,-0.01172,0.02021,0.03206,-0.02144,0.01581,-0.03188,0.04906,-0.08879,0.05065,-0.11738,0.02677,0.02904,-0.05063,-0.00602,-0.02773,-0.05391,0.06225,-0.06269,-0.01825,-0.07297,-0.03822,-0.04048,-0.09649,0.03756,0.01788,-0.15958,0.00622,0.01917,0.07705,0.05845,0.0278,-0.01068,0.01544,0.04433,0.06281,0.00686,0.09639,0.03966,-0.12639,-0.04085,-0.02054,0.07741,-0.00986,0.02712,-0.08726,0.0095,-0.00819,-0.03653,0.15181,-0.11197,0.08521,0.04164,0.12387,-0.00557,0.14573,0.03371,-0.02764,-0.06718,0.01012,-0.01888,-0.02764,0.06775,0.04399,-0.0839,-0.02325,0.11073,-0.10416,-0.02865,-0.02871,0.01831,0.00736,-0.03061,-0.05878,0.09827,-0.05768,-0.00623,0.07871,-0.07005,0.03827,0.02525,0.06918,-0.05089,0.04771,-0.03309,0.02606,-0.01432,0.08069,0.03611,-0.04288,-0.04491,0.10352,-0.04098,-0.10868,0.01791,-0.07312,0.09278,0.12547,-0.00144,0.0194,-0.03765,-0.01156,0.16057,-0.02223,0.07286,0.07177,0.07366,0.02138,-0.0266,0.06629,-0.08476,0.02767,-0.03565,0.13448,0.04413,0.14327,0.0445,0.03722,-0.09218,-0.01448,-0.08166,-0.06181,-0.04617,0.00213,0.05763,0.03335,0.03723,0.03838,0.00959,-0.03124,-0.01483,-0.01527,0.0798,0.03766,-0.1238,-0.01374,0.05114,0.04699,-0.02944,-0.05455,0.01441,-0.03012,0.02409,0.05959,0.01597,-0.06646]},{"domain":"data_science_ml","key":"ml_logistic_regression_predict","name":"Logistic regression prediction from given weights","package":"data-science-ml-ai999x","example":"Logistic regression prediction: w = [0.8, -0.4], b = -0.2, X = [[1, 2], [3, 1], [0, 0]]","v":[0.04505,-0.04114,0.03037,-0.01008,0.01197,0.07389,0.0049,-0.12994,-0.04622,-0.03034,0.02504,0.10303,-0.00401,0.02775,0.05851,0.01153,-0.02891,-0.0999,-0.00971,-0.06408,-0.05502,-0.06375,0.10266,0.08115,-0.11151,-0.0334,-0.05984,-0.0705,0.08835,0.1189,0.05605,-0.01402,-0.00462,0.02698,0.01871,0.0032,0.05842,-0.06282,-0.10703,0.0828,0.00954,-0.06743,0.04797,0.0412,-0.10155,-0.04293,0.0417,-0.04589,-0.11317,0.00113,-0.05032,0.02261,0.02828,0.02112,0.02537,0.0293,0.05565,-0.05856,-0.06959,0.11313,-0.01908,0.00115,-0.0603,-0.03865,0.06225,0.05294,-0.02833,-0.0203,0.12589,-0.07253,0.05562,-0.05471,-0.09436,-0.03886,0.01907,0.06701,-0.03211,-0.01754,0.03086,-0.01198,-0.01015,0.02424,0.05392,0.03702,-0.09566,0.07243,-0.03976,-0.01037,-0.05147,-0.03074,0.09696,-0.05866,-0.04297,-0.08225,0.07884,0.09039,0.00213,0.04149,-0.10534,-0.06054,0.04306,0.00858,-0.04012,-0.04082,0.03947,-0.10619,-0.00645,0.08055,0.16228,0.00497,0.03062,-0.01699,-0.04156,-0.02497,0.01976,0.01285,-0.03908,0.01896,-0.00913,-0.03314,-0.06601,-0.00604,-0.06575,-0.10948,-0.04332,-0.07905,-0.06528,-0.02348,-0.12493,-0.0172,-0.05724,-0.02532,0.07741,-0.11856,0.03366,0.0171,-0.08046,-0.0016,-0.03374,-0.00413,0.00011,-0.01361,-0.02534,0.0044,-0.06348,0.03902,-0.01339,0.04001,-0.00749,-0.11706,-0.06896,0.02326,0.12646,-0.00311,-0.00195,-0.01698,0.03754,-0.10047,-0.02175,0.05658,-0.09096,0.00675,0.09176,0.05001,0.16935,0.08392,-0.03012,-0.03351,-0.11075,0.05151,0.0941,0.01881,0.01562,0.04057,-0.01175,0.01078,0.04682,-0.20347,0.0243,0.03629,0.08101,0.01562,-0.00052,-0.00503,0.04086,-0.0129,0.02506,0.09466,-0.0569,-0.05609,0.03741,0.13759,-0.09596,0.07601,-0.05528,0.05678,-0.033,0.10515,0.00435,0.07281,-0.09473,0.01229,-0.06509,0.031,0.03751,-0.05414,0.03408,0.1346,-0.03456,0.06718,0.05582,0.05099,0.08908,-0.03432,0.07065,0.02023,0.10461,-0.02304,-0.0412,0.12038,0.01442,0.06629,-0.11382,0.10459,0.10078,0.0936,0.05034,0.03722,0.03844,0.011,-0.05038,0.00871,-0.01078,-0.00491,0.04568,0.02309,0.05971,0.08203,-0.00015,-0.04361,-0.02094,-0.00439,-0.00627,0.06978,-0.10677,-0.0793,0.09974,0.11341,-0.03207,-0.07551,0.03828,-0.03712,-0.02677,0.07302,-0.05071,0.00797]},{"domain":"data_science_ml","key":"ml_loocv_linear_regression","name":"Leave-one-out 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5.8]","v":[0.0209,0.10723,-0.03682,-0.14325,-0.03179,0.03692,-0.01425,-0.01287,0.04365,-0.01743,-0.11538,-0.08329,0.07145,0.01601,-0.11621,0.03081,0.13487,0.02555,-0.03979,0.0642,-0.12348,-0.01568,0.0372,-0.0176,-0.03424,0.00925,-0.01506,-0.06541,0.05398,0.07305,-0.04848,-0.05283,0.07708,0.0199,0.04922,0.00454,0.10488,-0.02638,-0.16736,0.08733,0.01112,0.01244,-0.06961,0.04075,-0.03428,0.06397,0.08557,0.02512,-0.03857,-0.04888,0.03328,0.008,-0.00391,0.00054,-0.0337,-0.02867,0.17713,-0.04561,0.0359,0.11055,0.09881,0.00616,-0.15699,0.02482,0.06152,-0.00294,0.02898,-0.04702,-0.02901,0.00414,0.0236,0.0192,-0.0971,0.03802,-0.01665,0.11921,0.13905,0.00143,0.01946,0.09085,0.04794,0.08226,0.03949,0.01861,-0.01792,-0.07062,-0.0384,-0.04941,-0.0682,0.02378,0.02245,0.10524,0.00394,-0.06242,0.01244,0.06413,0.01961,0.00207,-0.11045,-0.05365,0.05252,-0.01897,0.08481,-0.03397,-0.07706,-0.029,0.03838,-0.02129,0.09915,-0.04069,0.01119,0.01556,-0.02188,0.01067,-0.04921,0.00301,-0.00484,0.05578,-0.0541,-0.00148,-0.10487,0.10121,-0.06295,0.02002,0.04774,0.00227,0.00192,0.11063,0.0573,0.00237,-0.08384,-0.10622,-0.0892,-0.00329,0.10881,-0.04146,-0.18689,0.01659,0.00499,0.10364,-0.11171,0.01318,0.01017,0.03941,0.09717,0.05275,0.04794,0.06875,0.07014,-0.11649,-0.03464,0.07141,0.03135,0.05474,-0.04796,-0.02256,-0.0143,0.07045,-0.02236,0.08371,-0.07464,0.0363,0.05781,0.05518,-0.02348,0.00942,0.01089,-0.03065,-0.0792,-0.00137,-0.13022,-0.05412,0.0502,0.03343,-0.03153,-0.00265,-0.00298,-0.05717,-0.03094,0.02637,-0.06766,0.04826,-0.01265,-0.05154,0.09348,0.01904,0.00153,-0.0756,-0.10344,0.01366,0.00631,0.01304,-0.04107,0.03608,0.03224,0.06349,0.04772,-0.02942,-0.00208,-0.00471,-0.05562,0.07971,-0.08253,-0.08927,-0.06095,-0.08978,0.05676,0.06247,-0.02273,0.09926,0.00764,-0.04004,0.15227,-0.0224,0.03565,-0.00275,-0.01083,-0.02347,-0.01211,0.01751,8e-05,-0.0272,-0.04019,0.14856,0.00284,0.06503,0.05454,-0.03291,-0.106,0.09109,-0.06352,0.00581,-0.06755,-0.01947,-0.00244,0.0032,-0.12308,0.0053,-0.08856,-0.04824,-0.05492,-0.08537,0.05118,-0.04708,-0.06737,-0.09671,0.05881,0.02495,0.00585,0.00154,-0.07782,-0.0729,0.0428,0.08984,0.03688,-0.05607]},{"domain":"data_science_ml","key":"ml_mape","name":"Mean absolute percentage error","package":"data-science-ml-ai999x","example":"Mean absolute percentage error: y_true = [100, 200, 300], y_pred = [110, 190, 330]","v":[0.16162,0.03231,0.05232,0.0687,0.05231,0.0108,0.04692,-0.0073,-0.00914,-0.09892,0.0694,-0.02678,0.03776,-0.06534,-0.06193,0.04139,0.13995,-0.08344,0.00789,0.00179,0.04998,0.04827,0.03046,0.01573,0.01679,0.06189,-0.07528,-0.06355,0.07093,0.05242,0.00426,0.00306,0.08456,-0.03198,-0.04555,-0.10877,-0.04,0.04583,0.10718,0.02191,-0.04362,0.03752,0.07903,0.11242,0.06384,-0.10212,0.06837,-0.00667,0.17247,-0.01252,-0.02124,-0.01348,-0.0048,0.08025,0.09561,-0.07566,0.06907,-9e-05,0.03294,-0.0868,-0.00948,-0.06873,-0.09281,-0.01406,0.07997,-0.11081,-0.05112,-0.05493,-0.01177,-0.02604,0.04813,0.04455,0.06493,-0.20815,0.00758,0.01412,0.00271,0.0186,-0.0825,-0.01852,-0.00632,-0.03549,0.10115,-0.04114,-0.04109,0.05458,0.06335,-0.03242,0.02975,0.0034,-0.01018,0.00339,0.04002,0.03962,-0.03574,-0.00574,-0.01356,0.08528,-0.08442,0.08163,-0.02544,-0.0976,-0.03662,0.03829,-0.11661,0.0388,0.00884,0.06651,0.08141,0.11969,-0.01619,-0.02885,-0.02771,-0.09918,-0.11383,0.039,-0.02582,-0.00435,0.14326,-0.01935,0.16111,-0.05201,-0.05143,-0.10018,0.00033,0.03633,-0.00727,-0.01005,-0.06302,0.05087,0.06166,-0.05373,-0.01217,-0.04548,-0.0441,-0.08623,0.06237,-0.07693,-0.02759,0.01305,-0.01279,-0.06234,0.06964,0.09399,0.05773,0.01928,0.06094,-0.08297,0.05053,-0.06576,-0.05784,0.05644,0.07314,-0.02234,-0.05826,-0.04191,0.00308,-0.00432,-0.02443,-0.05037,0.055,0.0408,-0.02032,-0.06198,-0.00351,-0.0681,0.02348,0.02245,0.05968,0.009,-0.02574,-0.17515,0.03872,-0.04738,0.20516,0.02458,0.04926,-0.00286,0.15726,0.01554,0.03508,-0.04049,-0.0156,-0.00355,-0.0144,0.092,0.00234,0.05446,-0.07851,-0.00821,0.02674,-0.07296,-0.02681,-0.02829,-0.06819,0.05583,0.00099,0.04399,-0.07725,-0.01063,0.07735,0.00541,-0.01215,0.0537,-0.01131,-0.10879,0.02366,-0.02755,-0.05965,0.1079,-0.03404,-0.01761,-0.02817,-0.03079,-0.06495,-0.05704,0.0489,0.01321,-0.05029,0.02429,0.05121,-0.01278,0.03974,0.02105,-0.04633,-0.12817,0.05782,0.03225,0.05109,-0.0351,0.11322,-0.02696,-0.02024,0.00398,0.04513,0.05384,-0.06297,0.02881,-0.0114,-0.08833,0.00334,0.07652,-0.07734,0.06386,-0.03317,-0.11788,0.03909,-0.00218,-0.03228,-0.03519,-0.03939,-0.02926,-0.09679,-0.11419,0.03782,0.04098]},{"domain":"data_science_ml","key":"ml_matthews_correlation","name":"Matthews correlation coefficient","package":"data-science-ml-ai999x","example":"Matthews correlation coefficient: TP = 40, FP = 10, FN = 5, TN = 45","v":[0.01409,-0.00774,0.02,0.18489,-0.08409,-0.07302,0.07803,0.03841,0.12239,0.00639,0.02239,-0.04375,0.0059,-0.0697,-0.1123,0.09941,0.01603,0.00226,0.08201,-0.0183,-0.08112,0.11759,0.06813,0.05029,-0.05061,-0.00054,0.03716,-0.04831,-0.00979,0.01688,-0.05995,-0.02726,0.0437,0.02874,-0.08366,-0.03183,0.01158,-0.00712,0.00269,-0.00584,-0.06216,0.03859,0.03502,0.00657,-0.00805,-0.15157,0.12234,-0.01248,0.00117,0.10137,0.03717,0.06062,0.09308,-0.02751,-0.05773,0.01916,-0.08073,0.02079,0.06949,-0.00084,0.02205,-0.08243,0.0565,-0.06566,-0.12476,-0.02857,-0.01342,0.02842,-0.01528,-0.10968,-0.0163,-0.08964,0.11286,0.04746,0.06474,-0.03073,-0.01496,-0.0364,-0.00934,0.02689,-0.00753,-0.06068,0.02965,0.00028,0.03589,0.00758,0.02537,0.0169,-0.01936,-0.03601,-0.02914,-0.0726,-0.06668,0.06048,-0.05923,-0.01001,0.0153,0.08786,-0.07332,0.14429,0.02836,-0.08006,-0.0629,0.02058,-0.0612,0.0574,-0.02531,0.09465,7e-05,0.04183,-0.06891,-0.02689,-0.04163,0.03613,0.0023,0.08452,0.09914,-0.03051,0.09973,0.0456,0.01663,-0.00114,0.079,0.049,-0.1197,0.03703,-0.00162,-0.11864,-0.05853,0.08926,0.07238,0.05637,-0.08384,0.06226,0.06135,-0.05636,0.01676,-0.03133,-0.04748,0.04383,-0.03499,-0.12068,0.05612,0.02907,0.00092,-0.06911,0.00674,0.12473,0.0331,0.01031,0.06289,-0.04856,0.00463,0.01111,-0.11226,-0.0525,0.06518,-0.11213,-0.09428,0.12226,-0.04,-0.10078,-0.03682,-0.02323,0.03677,0.01431,-0.03128,0.05755,-0.01722,0.07897,0.04707,-0.02824,-0.06777,-0.02138,0.0834,0.02896,0.01674,-0.02289,0.09524,0.03168,0.12709,-0.04376,0.03866,0.02057,0.01633,0.01469,-0.0779,0.01036,-0.10334,0.03478,0.10824,0.04202,-0.04721,-0.05353,-0.205,0.04225,-0.0199,0.03164,0.0121,-0.0925,0.01748,0.04957,0.00323,0.02366,-0.00451,-0.01223,-0.1011,0.00637,0.1052,-0.02447,-0.12008,-0.18941,-0.02812,-0.01695,0.00017,-0.02466,-0.10477,-0.05422,-0.04403,0.04993,0.0716,-0.16037,-0.04636,0.03303,0.02813,-0.09056,0.08262,-0.02171,-0.01019,0.02862,-0.05304,0.09051,0.02932,-0.00485,-0.01048,-0.01609,-0.08977,0.07042,0.00812,0.05519,0.01853,-0.04118,-0.02824,0.01879,0.01518,-0.04658,0.05452,0.00903,0.00161,0.05551,0.06123,0.05422,-0.08908,-0.02524,-0.04937,0.0042]},{"domain":"data_science_ml","key":"ml_mean_average_precision","name":"Mean average precision (MAP) of rankings","package":"data-science-ml-ai999x","example":"Mean average precision: R = [[1, 0, 1, 0, 0], [0, 1, 0, 0, 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reciprocal rank (MRR)","package":"data-science-ml-ai999x","example":"Mean reciprocal rank: R = [[0, 0, 1], [0, 1, 0], [1, 0, 0]]","v":[0.03129,-0.03381,-0.09613,0.10013,-0.1496,-0.0997,-0.09119,-0.01217,0.04563,0.02276,-0.02451,0.03128,-0.05435,0.02297,0.04876,-0.02954,-0.01199,-0.01271,-0.01722,-0.00677,-0.02209,-0.00167,0.03267,0.05266,-0.01074,0.05749,-0.01419,-0.14734,0.06917,-0.05797,0.00031,0.10117,0.03529,-0.06161,-0.00632,0.01094,0.0684,0.06941,0.03413,0.05606,0.04162,0.08179,0.04362,-0.08762,-0.0033,0.00531,0.04469,-0.05268,-0.03996,0.0663,-0.08725,0.06398,-0.03907,0.06009,-0.08481,-0.00268,0.06343,0.02174,0.06304,-0.02867,-0.09821,-0.01184,0.0036,-0.02507,-0.00546,0.01157,-0.03192,-0.01171,-0.03708,0.05533,0.06314,0.09473,0.06126,-0.02709,-0.06158,0.14654,-0.00074,0.04856,-0.02626,-0.022,-0.06368,0.1091,0.07622,-0.1183,0.00658,0.04342,0.04266,-0.06788,-0.03261,0.04328,-0.03595,0.06634,-0.0167,-0.02045,0.04862,0.03698,0.0401,0.03973,-0.03716,0.13077,0.04757,-0.03371,-0.07677,0.07576,-0.00786,0.06917,0.00468,0.08893,-0.02545,0.00189,-0.10296,-0.06427,-0.07972,0.05107,-0.0293,0.11458,-0.11232,-0.06321,-0.02459,0.01594,0.01391,-0.08054,-0.01756,0.03054,-0.01134,-0.03313,0.05678,0.01367,-0.05499,0.14983,-0.03078,0.02908,-0.04977,-2e-05,0.09864,-0.0762,-0.04488,0.00933,-0.07536,0.00534,0.01781,0.04361,-0.08057,0.13277,-0.00334,-0.0382,0.10196,-0.03386,0.14246,-0.03883,-0.05785,0.02501,-0.00936,0.02985,-0.02019,-0.18316,0.07137,0.00775,-0.04639,0.05851,0.04066,-0.04528,0.00595,-0.07608,0.03015,0.06425,-0.07172,-0.05866,0.14951,0.0704,-0.06482,0.04424,-0.00927,0.03635,-0.04338,-0.00664,0.12439,-0.02058,0.03915,0.0259,-0.03691,0.00111,0.0092,-0.01108,0.09634,-0.03268,-0.02854,0.02655,0.02238,-0.05501,-0.04088,-0.0071,-0.00827,-0.06908,0.02106,0.12097,-0.15267,0.09787,-0.01534,-0.10862,-0.04032,-0.09853,0.05823,0.02702,0.02299,-0.01483,0.0269,0.01352,-0.07994,-0.08115,-0.00806,0.00534,-0.08168,0.11251,-0.00984,-0.07757,-0.09541,-0.14471,0.00286,-0.02257,0.03109,-0.05306,0.09278,0.08265,0.06012,-0.00098,-0.00418,-0.02528,-0.01919,-0.04884,-0.07631,0.08217,-0.02814,0.01236,-0.01342,0.02985,0.01913,0.05181,-0.07737,0.07107,-0.01159,-0.00315,-0.02849,-0.17527,-0.04366,0.03249,0.01976,0.03655,0.03806,0.20523,-0.01111,-0.01632,-0.0929,0.00637,0.00286,-0.06376]},{"domain":"data_science_ml","key":"ml_mean_squared_log_error","name":"Mean 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8]","v":[0.08938,-0.059,0.06682,0.01228,0.05069,-0.00582,-0.03128,0.09674,-0.03681,-0.11634,0.1032,-0.05268,0.04519,-0.03502,-0.01452,0.13451,0.20241,-0.08682,0.03922,-0.01339,-0.0314,-0.05498,0.11148,0.0239,-0.06935,0.10515,-0.09787,-0.02509,0.09094,0.04746,-0.09873,-0.0415,0.07087,-0.09262,-0.00272,-0.01293,0.05109,0.05214,0.053,0.04224,-0.04475,0.02231,0.08856,0.04847,0.04465,-0.03654,0.13395,-0.04007,-0.00039,-0.03619,-0.05992,-0.00237,0.03714,0.07145,-0.01894,-0.14139,0.08164,0.0217,-0.00176,0.0018,0.02643,0.0741,-0.16525,0.13501,0.14423,-0.01978,-0.06264,-0.0851,-0.04273,0.00934,0.01096,-0.03051,-0.07165,-0.0112,0.03154,0.00727,-0.00493,0.01778,-0.16894,-0.03187,0.02399,0.04313,0.08274,0.05515,-0.07674,0.06705,0.03065,0.07572,0.04597,-0.0669,0.01201,-0.08841,0.04407,-0.04592,-0.05814,0.02708,0.00382,0.05905,-0.08988,0.00923,0.00979,-0.015,-0.11812,0.02761,-0.09636,-0.03077,-0.0384,0.03129,0.08714,0.01796,-0.049,-0.04179,0.0369,-0.0429,-0.07292,0.0483,-0.05483,0.05001,0.04697,-0.04309,0.12585,0.00728,-0.00951,-0.08699,-0.0739,-0.02303,-0.04051,0.02774,-0.04083,0.01594,-0.0067,-0.01578,-0.08143,-0.0515,-0.01979,0.00157,-0.07217,-0.04316,0.06729,-0.0346,0.0144,0.01594,0.1235,0.1125,-0.03949,-0.05697,0.04043,0.01132,0.06459,-0.07978,-0.01015,0.0589,0.01098,-0.05565,-0.0329,0.081,-0.02413,0.01509,-0.04317,0.07392,1e-05,0.03997,0.03921,0.09386,-0.02496,0.00734,-0.04064,0.01356,0.01021,-0.0136,-0.07275,-0.06262,0.00707,-0.01534,0.07791,-0.13516,0.04631,0.02142,-0.03024,-0.00956,-0.031,-0.05567,-0.03711,0.03913,0.16074,0.05605,-0.04588,0.01956,-0.09223,0.10659,-0.0779,-0.08426,0.03529,0.00994,0.00377,0.00728,-0.12711,0.03735,-0.09513,0.01843,0.08534,0.00429,-0.11946,-0.0518,0.01813,-0.07724,0.04652,0.03722,0.06756,0.05805,0.04549,0.09129,0.05247,-0.04257,-0.01511,-0.04534,0.03053,-0.03242,0.01994,0.0448,-0.01487,-0.01645,-0.00571,0.02732,0.04926,-0.1378,0.02403,0.04236,-0.04024,-0.05702,0.11112,-0.02694,0.07795,-0.00243,0.03779,0.04095,0.01004,0.07235,0.03478,-0.05297,-0.00751,0.01377,-0.07015,0.12832,-0.07468,-0.10476,0.04469,0.02117,-0.0796,0.05534,-0.021,-0.01286,-0.06993,-0.02766,-0.03247,0.03404]},{"domain":"data_science_ml","key":"ml_minmax_scaler","name":"Min-max 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30]]","v":[-0.01058,0.0491,-0.0095,0.04191,-0.12957,0.0384,-0.05601,-0.00208,0.05356,-0.09906,0.01665,0.01562,-0.02767,0.02686,0.00169,-0.03455,-0.071,0.02896,0.00284,-0.00428,0.01261,0.13781,-0.00728,-0.11855,-0.01783,0.03929,-0.0331,-0.01299,-0.10598,0.07811,0.05252,-0.02378,-0.01033,-0.05124,0.04285,-0.09539,0.07414,0.04878,-0.05253,0.02606,0.01439,-0.01318,-0.08943,-0.03055,-0.03128,0.0408,-0.0214,-0.01946,-0.01417,0.01466,0.01607,0.0302,0.00164,-0.03222,-0.07313,0.0415,0.15207,-0.04317,0.06741,0.02758,0.01427,-0.06709,0.04863,0.05566,0.04244,0.00515,-0.06117,0.0947,0.04425,0.13192,0.03306,0.02841,-0.00228,0.02594,-0.12535,0.17097,0.0231,-0.05022,0.05077,-0.05469,0.11606,0.06523,-0.03898,-0.0607,0.0748,0.0553,-0.15453,-0.03453,-0.06973,-0.04882,0.02163,0.10588,-0.00696,-0.00574,0.04935,-0.00135,0.1094,-0.00753,-0.03277,0.07813,-0.03838,-0.0747,-0.06844,-0.04897,0.00368,0.01933,-0.1088,-0.04988,-0.01009,-0.10333,-0.04982,-0.00453,0.07174,-0.05056,-0.11339,0.02805,-0.05558,0.00404,-0.12711,0.05526,-0.04766,-0.02366,0.07274,-0.02845,0.03718,-0.11054,-0.01017,0.05608,0.02427,0.01001,-0.08317,-0.10836,-0.06653,0.02121,0.03456,-0.01181,-0.07733,0.07438,-0.03806,0.07731,-0.0572,0.0395,-0.06442,0.08106,-0.04334,0.08526,-0.0376,-0.04183,0.00743,0.01863,-0.05612,-0.06032,-0.05251,-0.03413,-0.05271,-0.08075,0.07748,0.05924,-0.12794,0.14273,-0.0518,0.17621,0.07863,0.01544,-0.01197,-0.04919,-0.10951,0.0114,-0.0119,0.01366,-0.01846,-0.03538,0.11629,0.07485,-0.11262,0.01435,0.06155,-0.05659,-0.04187,0.0186,-0.06889,0.07849,0.02876,0.09462,-0.01416,-0.01874,0.02097,0.00754,0.00405,0.04988,0.03371,-0.0007,-0.00017,-0.04903,0.0306,0.06887,0.07955,-7e-05,-0.08262,0.02926,-0.07307,-0.04074,-0.03665,0.02196,0.01022,-0.10741,-0.05681,0.04832,-0.00257,0.00464,-0.01991,-0.06427,-0.05938,0.07874,-0.01149,0.05627,-0.01839,0.02229,0.02481,-0.05067,0.00143,-0.0007,-0.08331,0.04724,0.11027,0.16149,0.04126,-0.04416,-0.0313,-0.01417,-0.00702,0.06563,-0.03522,0.19849,0.02615,0.05456,-0.02674,0.0572,-0.10123,-0.0033,-0.08735,0.04017,-0.01642,-0.01395,-0.03752,0.0271,-0.00179,0.01857,-0.10866,-0.02002,0.00541,0.09187,-0.00822,0.15768,0.04922,-0.03438]},{"domain":"data_science_ml","key":"ml_mse_gradient","name":"Mean 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confusion matrix","package":"data-science-ml-ai999x","example":"Multiclass confusion matrix: y_true = [0, 1, 2, 2, 1, 0, 2, 1], y_pred = [0, 2, 2, 2, 1, 0, 1, 1]","v":[0.13063,0.01442,0.06615,0.01235,0.05085,-0.04681,0.10163,-0.06521,0.0028,-0.05818,0.01787,0.07204,0.0273,-0.01643,-0.07393,-0.02447,-0.01096,0.02004,0.07633,-0.01983,-0.06594,0.04005,0.13161,0.04099,-0.05765,0.01622,-0.03569,0.03136,0.08879,0.08151,-0.00216,-0.03927,0.07119,0.04706,-0.08531,-0.15869,0.01402,0.05757,0.08352,-0.07382,-0.01503,-0.0559,0.13981,0.03457,-0.02956,-0.12447,-0.01475,0.04942,0.04634,0.00521,-0.04309,0.05854,0.02659,-0.04239,-0.08401,0.03754,0.06237,0.06587,0.05131,-0.01182,0.01529,-0.01244,0.0153,0.00179,-0.0059,0.03163,0.08757,-0.07118,-0.00374,0.02052,0.00625,-0.09707,0.04594,0.0569,0.03624,0.00154,-0.07288,0.0627,-0.01558,-0.06133,-0.02956,-0.07226,0.15303,-0.04587,-0.04138,0.11871,0.02357,-0.09187,0.00783,-0.04067,0.05057,0.01438,-0.04946,0.01531,-0.07795,0.06089,0.04154,0.10504,-0.22228,0.07935,0.01695,0.04642,-0.07503,-0.05702,-0.03576,0.011,-0.04131,0.0086,-0.08734,0.07931,-0.0121,-0.05614,-0.12688,0.002,-0.02906,-0.00934,0.07998,-0.08882,0.0479,0.03442,0.00016,-0.05732,0.00912,-0.01336,-0.01438,0.06105,0.02,0.01136,-0.07793,0.02377,0.17386,-0.06594,-0.11584,0.03815,0.03284,-0.09102,0.01688,0.0848,-0.05272,0.05208,-0.03548,-0.01665,-0.07903,0.03071,-0.00161,0.06849,0.03302,0.13814,0.02217,-0.07657,-0.00749,0.03403,0.05176,0.03572,-0.04539,0.04673,-0.03385,-0.02923,-0.10061,0.01584,-0.03093,-0.11647,-0.06753,0.01157,0.13815,-0.03721,-0.02835,0.01025,0.06336,-0.03501,0.03548,-0.07766,-0.06965,-0.00914,0.09308,0.10028,-0.00899,-0.08814,0.1098,0.03284,0.0798,-0.04244,0.01294,-0.00879,-0.12527,-0.00298,0.04319,0.05872,-0.08681,-0.03086,0.09509,0.01149,-0.16024,0.00306,-0.13335,-0.00617,-0.06018,0.08466,-0.0632,-0.0334,0.01283,0.07803,-0.0556,0.01574,-0.04642,-0.05582,-0.03508,0.09162,0.00063,0.06584,0.00525,-0.03959,-0.09152,-0.00431,-0.07321,-0.04534,0.0611,-0.01979,-0.04545,-0.0687,0.07141,-0.01926,0.04137,0.00874,-0.06905,-0.05303,-0.00126,-0.0452,-0.03158,-0.06272,-0.01772,0.03688,0.00665,0.04348,0.02968,0.05866,-0.10306,-0.02063,-0.05128,0.06219,-0.04705,-0.03908,0.00395,0.0941,0.002,-0.03076,0.07624,0.06282,0.112,-0.01815,-0.00581,-0.01418,-0.09974,0.0334,0.0642,0.00177]},{"domain":"data_science_ml","key":"ml_multiclass_hinge_loss","name":"Multi-class hinge loss (Crammer-Singer and Weston-Watkins)","package":"data-science-ml-ai999x","example":"Multiclass hinge loss: y_true = [0, 1, 2], D = [[1.2, 0.3, -0.5], [0.4, 0.9, 1.1], [-0.2, 0.1, 2]]","v":[0.01552,0.04452,0.00226,-0.00033,-0.1008,0.00056,0.06922,-0.04238,0.02774,0.12241,-0.07111,0.00904,0.08748,-0.02368,-0.06292,-0.08266,-0.02511,0.02549,0.02233,-0.00678,-0.07119,0.00962,0.09323,-0.08797,-0.01149,0.02016,-0.00953,0.07804,0.06157,-0.01035,-0.06436,0.01723,-0.06566,0.0317,-0.07634,0.00979,0.02232,-0.06174,-0.08708,-0.04915,0.06738,-0.06032,-0.04982,-0.01587,0.07591,-0.03867,0.06393,-0.00391,-0.00922,0.02626,0.01291,0.04935,0.08286,0.00941,0.12431,0.01029,-0.01493,0.04417,-0.02252,-0.00304,0.03738,-0.05741,-0.00449,0.06667,0.04518,-0.04478,0.05818,-0.08658,-0.02161,-0.03238,0.12335,0.02679,0.01997,0.14575,-0.02292,0.04508,-0.07464,0.01236,0.03525,-0.01163,0.02136,0.03734,0.0867,-0.09915,-0.15187,0.07449,-0.05874,-0.12594,-0.1198,-0.00468,0.00342,-0.00492,0.03594,-0.02867,-0.00943,-0.00621,0.07602,-0.06346,-0.11809,0.00776,-0.00398,-0.01924,-0.03588,-0.03179,-0.01986,0.05486,-0.08866,0.01751,-0.09633,0.13865,0.0973,0.00867,0.06597,0.10458,-0.05836,0.00606,-0.05193,-0.00394,-0.14204,0.00037,-0.13279,-0.01609,-0.02653,0.0636,0.01001,-0.03555,-0.1287,0.02409,-0.05455,0.03984,0.03509,0.01637,-0.14797,0.04216,0.01891,-0.0292,-0.17764,-0.01262,0.02373,0.03366,-0.05257,-0.09992,-0.01366,0.09242,0.07199,-0.03266,0.09535,0.03656,-0.07788,-0.02039,-0.02089,-0.09248,0.04234,0.00901,-0.04347,-0.05011,0.10099,0.10297,-0.0741,0.09386,-0.0402,0.02087,0.04619,-0.00982,-0.00453,-0.00293,-0.03301,-0.07147,0.08578,-0.0833,-0.04467,-0.06658,-0.011,-0.11155,0.05194,-0.06144,0.03691,-0.0441,0.07962,-0.04682,0.07955,-0.02962,-0.07579,-0.05604,0.00101,-0.01888,-0.01581,-0.08952,-0.05218,0.01959,0.0729,0.07499,-0.13138,0.05874,0.03857,0.14096,-0.00626,0.03383,-0.0143,-0.08831,-0.06442,0.01252,-0.02629,0.01445,-0.0459,-0.07697,0.02705,0.10981,-0.02637,-0.04938,-0.01198,0.05062,0.09424,0.05761,0.03836,0.0232,-0.01291,0.07365,-0.0146,-0.03421,-0.04416,-0.05385,0.08111,0.13425,-0.01031,0.05668,-0.04419,-0.00613,-0.03307,-0.01709,0.0251,0.08779,-0.09037,0.08008,0.10403,0.05562,-0.1036,-0.00421,0.03157,-0.06112,0.11178,0.0857,-0.0208,0.04257,-0.07724,0.01177,-0.01931,0.03966,0.11647,0.02059,0.00407,0.06271,0.06717,0.04992,0.00381,-0.05173]},{"domain":"data_science_ml","key":"ml_multihead_attention","name":"Multi-head attention (identity projections)","package":"data-science-ml-ai999x","example":"Multi-head attention: Q = [[1, 0, 1, 0]], K = [[1, 0, 0, 1], [0, 1, 1, 0]], V = [[1, 2, 3, 4], [5, 6, 7, 8]], heads = 2","v":[-0.05048,0.10055,-0.03582,-0.09329,0.00309,-0.00593,0.06984,0.05467,0.04093,-0.09112,0.05394,-0.0188,0.03683,0.00163,-0.02655,0.08865,0.01849,0.12579,0.11604,0.00059,0.04977,0.15664,0.04289,-0.04487,-0.02878,-0.01127,0.06289,0.03536,-0.07226,0.01211,-0.07948,0.02403,0.02622,-0.02835,-0.003,-0.02142,0.0181,0.06659,-0.02774,0.10694,-0.08475,-0.00775,-0.11174,-0.12125,-0.00132,0.03655,-0.00446,-0.02643,7e-05,0.01321,-0.07623,-0.09264,-0.03742,-0.02685,0.04468,-0.06831,0.0782,0.08597,0.02097,-0.04151,-0.0452,-0.01809,0.01205,0.00823,0.02779,0.04369,0.05951,-0.07856,0.06072,0.05381,0.05937,0.0459,-0.02639,0.14691,-0.15166,0.02185,0.11283,0.06966,-0.01411,0.04636,-0.05169,0.02654,0.04847,-0.01632,0.01203,-0.03783,0.01115,-0.03425,0.03766,-0.10773,0.06861,-0.05592,0.00981,-0.03145,0.11011,-0.06047,0.02662,-0.06358,0.08486,-0.00875,0.0234,-0.04362,0.04421,0.02511,-0.03052,0.05016,0.04236,0.0082,-0.0179,-0.05417,-0.02166,-0.05571,0.15056,0.06224,-0.0296,0.04634,-0.02973,0.04574,-0.04624,-0.05751,-0.035,-0.06302,0.06273,0.03008,0.07279,-0.10036,-0.07258,0.01463,-0.05093,-0.0321,-0.05341,-0.11094,-0.09825,-0.05585,0.1118,-0.08667,-0.11656,0.04996,-0.17165,0.05965,0.0486,-0.03496,0.1204,0.05273,0.05364,0.05811,-0.05176,0.01265,-0.05436,0.02309,0.02057,0.04989,-0.21221,-0.04198,-0.05678,-0.06063,-0.06817,-0.0584,0.00505,-0.0927,-0.02528,-0.15996,0.07791,-0.00575,-0.01836,0.1213,-0.09484,0.08373,0.01281,-0.14314,-0.09169,0.02659,-0.06509,0.00092,-0.03801,-0.01356,-0.01512,-0.05885,0.00112,0.03995,0.09859,-0.00656,0.02048,0.00467,0.00842,-0.01977,-0.01703,-0.00956,-0.00554,-0.02457,0.07349,0.09885,-0.01026,0.06421,-0.02536,-0.04533,-0.03405,0.0358,-0.08827,-0.02627,-0.05511,0.01445,-0.01195,0.16219,-0.01841,-0.09781,-0.00515,0.01662,0.05792,0.04989,0.08077,-0.07127,-0.01143,0.04665,-0.02783,0.05486,-0.09306,0.04502,0.05974,0.04908,-0.02742,-0.01182,0.08696,0.03803,0.08154,-0.02446,0.05666,-0.10246,0.06394,0.09252,-0.02653,0.1306,-0.00098,-0.06587,0.00597,-0.03432,-0.01394,0.00893,0.03981,-0.05564,0.05994,0.02416,-0.05825,0.00942,-0.05305,0.05256,0.01046,0.04174,0.06344,0.03768,-0.02088,-0.02354,-0.02087,-0.0168,0.00081,0.06963]},{"domain":"data_science_ml","key":"ml_multinomial_naive_bayes","name":"Multinomial naive Bayes prediction (word counts)","package":"data-science-ml-ai999x","example":"Multinomial naive Bayes: X = [[2, 1, 0, 0], [1, 1, 0, 1], [0, 0, 3, 1], [0, 1, 2, 2]], y = [0, 0, 1, 1], x = [1, 0, 1, 0], alpha = 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information between two label sequences","package":"data-science-ml-ai999x","example":"Mutual information of labels: x = [0, 0, 1, 1, 2, 2], y = [0, 0, 1, 1, 1, 1], unit = 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5","v":[0.09759,-0.06511,-0.06737,-0.01415,-0.11433,-0.09532,-0.06129,-0.0188,-0.02992,0.01456,-0.05565,0.08861,-0.1378,-0.00752,0.10698,-0.01611,-0.03065,-0.00674,0.0069,-0.03801,-0.01711,0.09404,0.10371,-0.04085,0.02009,0.02677,0.008,-0.05159,0.11782,-0.09266,-0.05956,0.03741,0.07182,-0.06495,0.01768,-0.01331,0.03511,0.04026,0.01238,0.00632,0.00627,0.05288,0.04738,-0.00057,-0.00012,0.03071,0.05978,-0.03982,0.00979,0.01683,-0.09684,0.07424,-0.05978,0.02414,-0.09424,0.00302,0.03915,0.01914,0.09088,0.02095,-0.12041,0.01244,0.05672,0.02222,-0.04537,0.00926,0.02259,-0.00515,-0.06612,-0.01091,0.02152,0.00931,0.08492,0.07081,-0.1162,0.1381,0.03255,-0.00537,-0.0296,0.03244,-0.04134,0.05639,0.07981,-0.06805,0.02323,0.05007,0.04686,-0.06473,-0.02174,0.05615,0.0124,0.0822,-0.04303,-0.00173,0.02794,0.0077,0.01255,-0.01392,-0.076,0.03265,-0.01866,-0.01281,-0.04203,0.06688,-0.05305,0.13928,0.00607,0.05337,0.00093,-0.01801,-0.05341,-0.04587,-0.07154,0.13703,-0.00336,0.05611,-0.0444,-0.06911,0.02059,0.03723,0.00998,-0.08059,0.01513,0.05738,0.03247,-0.04295,0.10047,0.02363,-0.05705,0.09338,0.05528,-0.00486,-0.08861,-0.03111,0.01628,-0.05181,-0.04411,0.06235,-0.07751,0.07661,-0.00377,0.09365,-0.09226,0.11515,-0.00623,-0.11334,0.1067,0.02686,0.07138,-0.0925,0.04953,0.02856,-0.0081,0.07908,-0.02724,-0.17977,0.06316,-0.01386,-0.05685,-0.04027,0.05465,-0.01918,-0.04943,0.02943,0.0122,0.09657,0.01554,-0.06059,0.12309,0.05948,-0.11793,-0.0045,-0.06168,-0.00443,-0.04065,0.01582,0.03197,-0.03021,0.07673,0.03434,0.08451,-0.04827,0.01803,-0.00125,0.04564,-0.09514,-0.01202,-0.00647,0.03692,0.01309,-0.03608,0.0198,-0.06257,-0.08997,-0.05706,0.03275,-0.1132,0.12981,0.04309,-0.11562,0.02167,-0.04977,0.05231,0.02275,0.08527,-0.02938,0.05875,0.0376,-0.04011,-0.06671,0.00029,-0.01989,-0.02489,0.14587,0.03787,0.00819,-0.11142,-0.05586,-0.02406,-0.05386,-0.00091,-0.09369,0.12479,0.00092,0.02083,-0.0241,-0.00591,-0.08646,-0.06325,0.02509,-0.11996,0.02763,-0.07272,-0.06182,-0.06201,-0.0397,0.01809,0.01759,-0.04384,0.08908,-0.00281,-0.03264,-0.00982,-0.10565,-0.03429,0.13355,-0.02266,0.02976,0.10863,0.24317,-0.04301,-0.05618,-0.03854,0.01024,0.03799,-0.04687]},{"domain":"data_science_ml","key":"ml_precision_recall_f1_averaged","name":"Averaged 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metrics (MAE, MSE, RMSE, R^2, explained variance)","package":"data-science-ml-ai999x","example":"Regression metrics: y_true = [3, -0.5, 2, 7], y_pred = [2.5, 0, 2, 8]","v":[0.16166,-0.00671,0.01815,0.09204,0.04994,0.04382,0.02338,0.00896,-0.00503,-0.15988,0.08893,-0.03196,0.06306,-0.04807,-0.06489,0.01551,0.23933,-0.08376,0.03853,0.0069,0.00332,0.01441,0.07726,0.0408,-0.012,0.07419,-0.00146,-0.0731,0.03793,0.02525,-0.00774,-0.00707,0.06429,-0.07655,-0.00341,-0.102,0.00023,0.08284,0.03352,0.02139,-0.04231,-0.00494,0.06755,0.12551,0.03171,-0.07385,0.09765,-0.00713,0.09033,-0.05418,-0.00878,0.03393,0.04116,0.15351,0.06654,-0.11712,0.11204,-0.00878,0.02452,-0.02066,-0.00122,0.02856,-0.12528,0.03223,0.10982,-0.11466,0.02099,-0.069,-0.0909,-0.06557,0.03416,0.03406,0.00709,-0.06653,0.03843,0.0122,0.06126,-0.01776,-0.07927,-0.02056,-0.00356,-0.00381,0.05027,-0.06788,-0.03698,0.07906,0.05741,0.00098,0.03216,-0.03324,-0.0416,-0.00494,0.03402,0.01267,-0.03183,-0.06482,0.01358,0.04228,-0.16781,0.03005,0.02072,-0.04947,-0.11109,0.03185,-0.15325,0.03142,-0.00757,0.06617,0.04959,0.07147,-0.00281,0.00062,-0.03896,-0.01347,-0.11627,0.01765,-0.04908,-0.06783,0.12807,-0.04171,0.16445,0.04674,-0.11513,-0.11424,0.0011,-0.03863,-0.01329,0.04572,-0.0472,0.03788,-0.05162,-0.06939,-0.04954,-0.01849,0.00197,-0.09817,-0.02661,-0.06482,0.01339,0.00869,-0.06551,-0.001,0.07847,0.11741,0.00773,-0.03871,0.05565,-0.04401,0.12116,-0.11243,-0.05412,0.12523,0.00549,-0.02863,-0.12551,0.08158,0.03996,0.02772,-0.08723,0.03938,0.02718,0.02173,-0.03813,0.00371,-0.03509,-0.02151,-0.03603,0.01369,0.0056,0.00299,-0.11107,-0.08203,-0.0101,0.04227,0.07887,-0.07137,0.0428,-0.00359,0.00834,0.00091,0.06785,-0.08659,-0.07692,-0.01545,0.08816,0.08833,-0.01618,-0.02411,-0.02864,0.03771,-0.03833,-0.07939,-0.04799,-0.01564,0.03493,0.03692,-0.03814,0.11291,-0.04726,-0.00882,0.13884,0.02206,-0.02239,-0.00953,-0.05255,-0.06315,-0.04592,0.02444,0.0083,0.05218,0.03272,0.0283,0.03558,-0.00417,-0.10133,-0.0458,-0.03913,-0.08577,0.00556,0.02936,0.03147,0.02533,0.01353,0.01328,-0.02057,-0.09492,0.06798,0.01136,0.02844,0.00665,0.09139,-0.04041,0.02927,0.03746,0.02589,0.04106,-0.05083,0.08107,-0.03817,-0.0414,0.04466,0.04498,-0.08609,0.09261,-0.06015,-0.06279,0.05887,0.04801,-0.05731,0.04834,0.00637,-0.08612,-0.05343,-0.03729,-0.01618,0.00381]},{"domain":"data_science_ml","key":"ml_ridge_regression","name":"Ridge regression coefficients (stated alpha)","package":"data-science-ml-ai999x","example":"Ridge regression: X = [[1], [2], [3], [4], [5]], y = [1.2, 1.9, 3.1, 3.9, 5.2], alpha = 1","v":[0.07547,0.0141,-0.05034,-0.00803,-0.1511,0.04212,-0.07852,-0.0493,0.0739,-0.06551,-0.07671,0.00112,0.08996,0.02366,-0.07096,-0.05943,0.0993,-0.05497,-0.04308,-0.04586,-0.10481,-0.01038,0.05614,-0.01214,-0.03033,0.00398,-0.00583,-0.06488,-0.01581,0.03478,0.01767,-0.05232,-0.00229,-0.08213,0.07995,-0.00762,0.11938,0.01772,-0.09018,0.08759,0.01619,0.06903,-0.04211,-0.0091,0.01804,0.06379,0.11214,0.00829,-0.02525,-0.01178,0.03283,0.13543,0.01023,0.00184,-0.03829,0.00763,0.14465,-0.057,0.05757,0.13518,0.06738,0.03571,-0.05067,0.08184,0.14882,0.00658,0.01401,-0.03786,-0.05505,-0.03643,0.05888,-0.00803,-0.10677,0.02947,0.02401,0.08384,0.04013,0.01289,-0.01754,0.09264,0.0526,0.08366,-0.02805,-0.0275,0.00279,0.04421,-0.04177,-0.0426,-0.1073,0.0466,-0.01248,0.05181,0.04033,-0.07513,0.00314,-0.02228,-0.04474,-0.01109,-0.18734,-0.02924,0.03837,-0.05772,0.03047,0.04281,-0.11874,-0.04161,0.00027,0.01253,0.07602,-0.02744,-0.01923,0.02536,-0.02407,0.01534,-0.06366,0.01701,-0.038,0.03067,-0.02643,0.05205,-0.06228,0.06369,0.0236,-0.00943,0.0004,0.00671,-0.03031,0.08072,0.02408,-0.0408,-0.17409,-0.07986,-0.10806,-0.043,0.00051,-0.0177,-0.15353,-0.04161,0.00312,0.10694,-0.06379,0.00645,-0.05067,0.04008,0.06833,0.02646,0.07849,0.09265,0.10799,-0.11308,-0.03542,0.03133,0.00089,0.02425,-0.03545,-0.10357,0.0147,0.03121,-0.04297,0.19179,-0.00948,0.03182,-0.02593,0.10791,-0.0396,0.10903,-0.01988,-0.00505,-0.06707,0.08568,-0.03602,0.00315,0.03875,0.06162,-0.09109,-0.05604,0.06212,-0.08135,-0.06553,-0.03629,-0.00705,0.0543,-0.10674,-0.07004,0.09207,-0.04585,-0.01901,0.0137,-0.01139,0.05342,-0.04799,-0.0351,0.02201,0.03203,0.05334,0.05378,0.05246,0.02283,0.0865,-0.02738,0.0171,0.08934,-0.0141,-0.06592,-0.0199,-0.09906,0.01264,0.0588,-0.05391,-0.01017,0.00321,-0.09823,0.13063,0.04331,0.01599,0.03713,-0.02308,-0.05062,0.03024,0.08291,-0.04379,0.02319,-0.07022,0.09713,0.05115,0.16212,0.06054,0.04087,-0.05587,0.03267,-0.13228,-0.01547,-0.04119,0.02287,-0.05909,-0.0159,-0.01223,0.0152,-0.02809,-0.01235,0.03599,-0.03772,0.04208,-0.06673,-0.11304,0.00587,0.01909,0.06078,-0.09028,0.07712,-0.04331,-0.05081,-0.01068,0.08064,0.0259,-0.07835]},{"domain":"data_science_ml","key":"ml_rnn_parameter_count","name":"Parameter 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no","v":[-0.1155,-0.03862,-0.03175,-0.0109,-0.10107,0.01064,0.10425,-0.08946,0.06673,0.06632,0.056,-0.01212,0.01676,0.04751,0.05672,0.01324,-0.01944,0.06985,-0.03144,0.00334,-0.02934,-0.0431,0.00717,0.04212,0.01816,-0.13237,0.08414,-0.03696,-0.0629,0.09586,-0.04368,-0.06841,-0.00116,-0.1427,0.0729,-0.01242,0.01707,0.0496,-0.04683,0.10017,0.09163,-0.03816,0.05384,0.0114,0.05319,0.0747,-0.07631,0.04817,-0.00911,-0.04187,-0.05901,0.05947,-0.00985,0.014,0.04133,0.00701,0.05872,-0.04325,0.0258,0.08337,-0.06336,0.04345,0.07649,-0.04619,0.08044,0.05902,0.01953,-0.02026,-0.01598,-0.04281,-0.02209,0.07506,-0.13052,0.11744,0.00075,0.03654,-0.02064,0.10647,-0.07771,0.04829,0.00055,0.01126,-0.03397,0.0014,-0.05614,0.09864,-0.07823,-0.05302,0.00877,0.08957,-0.01561,0.02059,0.02886,-0.00567,-0.00733,0.01368,-0.12294,-0.0294,-0.03829,-0.14796,0.04876,-0.00525,-0.00313,0.11225,-0.04899,0.00623,0.05211,-0.06791,0.0627,-0.06525,-0.06152,-0.02447,0.01911,-0.05676,-0.02131,0.03098,-0.01585,-0.00874,-0.00937,0.03168,-0.05295,-0.0178,0.08679,0.06775,0.00349,-0.12849,-0.02879,0.09529,-0.01613,-0.01511,-0.10861,-0.0549,0.04981,-0.10175,0.09377,-0.00089,-0.11077,-0.09698,-0.10332,-0.01634,0.06959,0.02506,0.01652,-0.04857,0.03356,-0.0666,-0.06293,0.06803,0.00421,-0.01829,-0.02529,0.00087,-0.02958,0.01417,-0.10789,0.04875,0.00713,0.02272,0.08631,0.03221,0.01565,-0.04139,-0.08982,0.08536,0.05893,0.15099,0.02365,0.01908,-0.11901,-0.02391,0.03691,-0.06954,0.0392,-0.02269,-0.05379,0.01776,-0.04809,-0.03274,0.00771,0.09759,0.06976,-0.05852,0.06266,-0.03323,0.09844,0.06024,0.06483,0.0819,-0.08563,-0.10788,0.04348,0.12894,-0.00984,-0.00366,0.01819,0.02858,-0.128,0.06778,-0.08067,0.02373,0.01734,0.06168,0.0195,0.13348,0.0694,-0.09905,0.05369,0.07997,-0.10202,-0.01503,0.00611,-0.06588,0.15318,0.01039,0.03765,-0.0205,-0.01879,0.02137,0.04011,-0.03749,0.06245,0.01382,0.0108,0.07649,0.11793,0.01715,0.08133,-0.02758,-0.08216,0.05005,-0.17291,-0.05395,0.01806,-0.04209,-0.04185,0.06043,0.0817,0.01715,0.05851,-0.04168,0.05146,0.01364,0.00891,-0.076,-0.09192,0.08437,0.03917,0.00231,-0.03591,-0.03124,0.02384,-0.04781,0.00201,0.07908,-0.07183,-0.10914]},{"domain":"data_science_ml","key":"ml_robust_scaler","name":"Robust 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[100]]","v":[0.04748,0.06179,0.03746,-0.07247,-0.08601,0.04033,-0.08721,0.00063,0.02324,0.00125,0.02084,-0.02997,0.02219,0.02414,-0.03236,0.01055,-0.0643,0.07389,-0.04281,0.03811,0.03846,0.04816,-0.06216,-0.11133,-0.06047,-0.03782,0.02173,-0.13346,-0.03804,0.01454,0.0539,0.02343,-0.01531,-0.08552,0.03136,-0.03548,0.09234,-0.10385,-0.09408,0.04248,-0.04115,-0.03878,-0.0646,0.07042,-0.04615,0.09801,0.00196,-0.03739,-0.00299,-0.07694,-0.05055,0.03853,-0.01936,-0.05766,-0.00393,0.05623,0.13769,-0.02454,-0.00844,0.02876,0.02274,-0.12174,0.02596,0.05129,0.13409,-0.01722,0.06353,0.01845,0.01628,0.16086,0.06282,0.0418,-0.08219,0.04738,-0.07518,0.14843,0.06575,-0.02543,0.0597,-0.03159,0.05294,0.03051,-0.00072,0.03076,0.02706,0.00663,-0.03494,-0.12667,-0.08113,0.02692,0.03759,0.15979,-0.00112,-0.04304,0.0611,0.04147,0.02773,-0.02447,-0.09552,-0.0162,0.02,-0.0195,0.03878,-0.04725,-0.00913,0.02173,-0.01218,-0.08485,0.08648,-0.12594,0.01147,-0.02431,0.03723,-0.04554,-0.02212,0.01072,-0.03177,0.05387,-0.1397,0.06887,-0.08691,0.01915,0.00063,-0.00848,0.04014,-0.05998,0.06136,0.08359,-0.01986,0.02743,-0.0515,-0.14888,-0.03575,-0.07955,0.00467,-0.02459,-0.10658,0.01673,-0.0096,0.0035,-0.04264,-0.01895,-0.06729,0.02297,-0.01706,0.09289,-0.0464,0.00393,-0.00914,-0.05166,0.08038,0.03625,0.02222,-0.01136,0.0034,-0.03253,0.04367,0.02441,-0.09278,0.12602,-0.06105,0.13176,0.03967,0.0213,-0.01926,0.00099,0.03977,-0.02304,-0.03776,-0.00465,-0.10769,-0.01711,0.08849,0.08154,-0.1568,-0.00363,0.06529,-0.11611,-0.0946,0.0166,0.0519,0.07545,0.10335,0.03306,0.07177,-0.03997,0.05854,0.02946,0.05043,-0.01504,0.09132,0.03571,-0.01842,-0.0481,-0.01833,0.05681,0.03652,0.09028,-0.15299,0.07435,-0.07857,0.0573,-0.01217,0.04502,-0.04762,-0.085,-0.02333,0.08383,-0.03184,0.08457,-0.00799,0.0037,0.07981,0.13467,-0.01532,0.03428,0.02036,0.09004,-0.0044,-0.04155,0.02224,-0.03669,0.00526,0.06611,0.00115,0.13423,0.03662,-0.09935,-0.08591,0.08845,-0.02778,0.03237,-0.0366,0.15971,0.00986,-0.00695,-0.02342,-0.03659,-0.05425,0.057,-0.08989,-0.07612,0.00988,-0.08126,-0.02165,-0.04897,0.05089,-0.00752,-0.04194,-0.02052,-0.03896,-0.00101,0.03943,0.15255,0.02241,-0.05521]},{"domain":"data_science_ml","key":"ml_roc_auc","name":"ROC 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0.2]","v":[0.07976,-0.09879,0.03879,-0.01488,0.01919,-0.02367,0.05413,-0.0035,-0.04508,-0.00665,0.03718,0.03521,-0.04748,0.00994,0.02055,0.05768,0.0689,-0.01625,0.07947,-0.01,-0.0329,-0.0576,0.14318,0.06999,0.04081,0.05081,-0.01342,0.10013,0.16553,-0.02031,-0.13736,0.05299,0.047,0.01532,-0.14884,0.02333,-0.06007,-0.04445,0.0184,-0.08392,-0.04551,0.00265,0.0339,0.05011,0.03542,-0.10504,0.16599,-0.01455,0.00993,0.00033,0.02791,-0.02026,0.06472,0.02321,-0.08041,-0.00309,-0.00825,0.05557,0.03,0.02671,0.07036,-0.07337,0.02713,-0.01626,0.02446,-0.04554,0.07446,-0.06244,0.01284,-0.05119,-0.05448,-0.03037,-0.00478,0.0704,0.09851,0.10212,-0.10145,0.07658,0.00282,0.04015,-0.04432,0.03103,0.1277,-0.05077,-0.09113,0.09151,0.04122,-0.04131,-0.03231,-0.05945,-0.01042,-0.05055,-0.033,0.02026,-0.03427,0.10001,0.07121,0.05793,-0.11462,0.01258,0.02388,-0.03017,-0.0958,0.00421,0.03785,-0.07463,-0.13872,0.03184,-0.03493,0.11524,-0.02263,-0.0571,-0.0306,0.10272,0.02289,-0.03671,0.04122,-0.12747,0.00278,0.03386,-0.00479,-0.01256,-0.02838,0.03639,-0.13161,-0.04196,-0.14675,-0.02363,-0.10324,0.06006,0.11386,0.02185,-0.04381,-0.02788,-0.04406,-0.01981,0.00701,0.08078,-0.13464,0.0579,0.02562,0.00896,-0.02785,0.13436,-0.00712,-0.11,0.06531,0.06666,0.05336,-0.05286,0.00031,-0.0197,0.08867,0.02267,-0.17993,0.06207,-0.02769,-0.06151,-0.00974,-0.04116,-0.13098,-0.07761,0.02839,0.05743,0.15498,-0.06773,-0.08828,0.07487,0.03488,-0.02193,0.03719,-0.07199,0.00754,-0.08443,0.11192,0.00263,-0.0381,0.00474,0.10734,0.00057,0.06997,-0.08676,-0.0094,-0.0731,-0.00893,-0.00847,0.00759,-0.00943,-0.04419,-0.00501,-0.01842,-0.01123,-0.08727,0.00847,-0.0787,0.06305,-0.01119,0.06864,0.06744,-0.09498,-0.00576,0.0011,-0.06842,-0.01222,0.03827,0.00661,-0.04664,-0.00063,0.01623,0.06671,0.04236,0.05598,-0.03362,0.05234,0.03787,-0.07113,-0.0307,-0.02878,-0.09008,-0.00924,-0.00361,0.01206,0.02497,-0.00688,-0.03863,-0.05345,-0.0198,0.04506,0.0067,-0.05621,0.00057,0.02309,-0.03644,-0.00738,0.02357,0.09876,-0.04735,-0.02227,-0.00919,0.00269,0.00699,0.07051,0.06762,0.02491,0.05548,-0.0159,0.02065,0.11869,0.15981,-0.05791,-0.01949,0.02055,-0.08944,-0.02084,0.11954,-0.04774]},{"domain":"data_science_ml","key":"ml_roc_curve","name":"ROC curve points","package":"data-science-ml-ai999x","example":"ROC curve: y_true = [0, 1, 1, 0, 1], scores = [0.1, 0.9, 0.8, 0.3, 0.2]","v":[0.08954,-0.13464,0.0529,-0.01788,-0.05429,0.01499,-0.03367,0.01954,-0.0312,-0.02137,0.00549,0.05956,-0.01517,-0.0161,0.00635,0.09425,0.08882,0.0009,0.03685,-0.02728,-0.06906,-0.1093,0.10155,0.07873,0.01323,0.0198,-0.01363,0.10378,0.16115,-0.04762,-0.12275,0.04487,0.02816,-0.04968,-0.11367,0.00629,0.01141,-0.00268,0.04477,-0.07262,-0.02067,-0.00223,0.03882,0.04468,0.05856,-0.09973,0.1318,0.01222,0.06779,-0.0142,0.00711,-0.01062,0.05614,-0.01311,-0.02075,-0.01399,-0.00068,0.031,0.05617,0.0359,0.05348,-0.12292,0.03893,0.04465,0.04111,0.0062,0.00522,-0.09306,-0.01549,-0.06335,-0.00882,-0.00304,0.03973,0.04814,0.08055,0.06585,-0.02394,0.04739,-0.02844,0.06013,-0.03706,0.01222,0.12104,-0.07412,-0.08675,0.06188,0.00877,-0.04288,-0.04789,-0.05462,0.02777,-0.01811,-0.0217,0.09377,-0.0488,0.10519,0.04729,0.12796,-0.11608,0.02627,0.00972,-0.06953,-0.1595,0.03,0.02495,-0.01735,-0.06846,0.00318,-0.02535,0.07279,-0.028,-0.03178,-0.01138,0.07081,0.03621,-0.00111,-0.02333,-0.08463,0.04664,0.03816,0.00574,-0.00218,-0.01839,-0.005,-0.1221,-0.00911,-0.12885,-0.01955,-0.09769,0.03393,0.05505,0.00098,-0.03327,-0.02334,0.03866,-0.06457,-0.01866,0.06652,-0.08195,0.02731,0.04106,0.00346,-0.079,0.11776,0.00702,-0.08772,0.05692,0.05979,0.07196,-0.05365,0.00075,0.04564,0.07285,0.0315,-0.20128,0.02484,0.01505,-0.02843,-0.06697,-0.04024,-0.10518,-0.13376,0.0012,0.09416,0.1253,-0.04286,-0.12281,0.07012,0.06948,-0.05348,-0.0028,-0.07662,0.0238,-0.06876,0.18239,0.02469,-0.00328,-0.02185,0.09696,0.04791,0.05916,-0.0427,0.00103,-0.0986,-0.03075,-0.05775,0.03521,0.01578,-0.00848,-0.05718,-0.0185,-0.05781,-0.11402,0.06714,0.00555,0.09924,-0.00144,0.04983,0.1086,-0.08695,-0.01518,0.00482,-0.05894,-0.04405,0.03302,0.05439,-0.07011,0.03074,0.00071,0.00457,0.04809,0.11635,-0.00875,0.02772,0.0076,-0.04084,-0.08037,-0.02819,-0.11321,0.00188,-0.01206,-0.02834,0.04759,0.04689,0.0092,-0.03042,-0.04529,0.04976,-0.03237,0.00494,-0.00729,-0.05546,0.01188,-0.00563,-0.0512,0.08646,-0.08458,0.05417,-0.05899,0.05096,-0.05353,0.08885,0.06418,0.00237,0.01106,0.0145,-0.04689,0.1165,0.10102,-0.03203,0.05212,0.02001,-0.0769,-0.00287,0.12236,-0.12402]},{"domain":"data_science_ml","key":"ml_scaled_dot_product_attention","name":"Scaled dot-product attention","package":"data-science-ml-ai999x","example":"Scaled dot-product attention: Q = [[1, 0], [0, 1]], K = [[1, 0], [0, 1], [1, 1]], V = [[1, 2], [3, 4], [5, 6]], causal = no","v":[-0.02128,0.06218,-0.04279,-0.0665,-0.04221,-0.06951,-0.02967,0.0828,0.038,-0.10695,0.10351,-0.07882,0.00259,0.00629,-0.02218,0.11497,-0.05881,0.09496,0.00123,0.01851,0.03913,0.02522,-0.00696,0.02081,-0.11791,-0.02288,0.03034,0.0025,-0.10969,0.03112,0.01982,0.01284,-0.0057,-0.03468,0.0549,0.02581,0.05141,0.01686,0.01473,0.14352,-0.05883,-0.01371,-0.11558,-0.03662,-0.08022,0.01818,-0.03804,-0.07485,0.00665,-0.02182,-0.02671,-0.10078,-0.01777,-0.05581,0.10446,-0.08089,0.08691,0.03895,0.0685,0.01109,-0.02447,-0.06793,0.00984,0.01713,-0.02373,0.03327,-0.01828,0.00951,0.01125,0.09008,0.06847,0.02413,0.00628,0.06233,-0.13867,0.0341,0.09726,0.03203,-0.10089,0.03791,-0.08164,0.05105,0.03563,0.02798,0.03501,-0.02957,-0.02533,-0.08984,0.05439,-0.08118,0.05376,-0.01903,0.0437,0.00387,0.06258,-0.08135,0.03379,-0.05904,0.09935,-0.0114,0.03871,-0.07583,-0.03753,0.00535,-0.05926,0.04145,-0.01122,-0.00544,0.028,-0.09052,0.01488,-0.05802,0.1756,-8e-05,-0.02207,0.07608,-0.03907,0.04766,-0.05467,-0.04102,-0.0756,-0.09265,0.0645,-0.02773,0.03735,-0.09591,-0.10142,-0.01445,-0.03201,0.00676,-0.04814,-0.07275,-0.10986,-0.00038,0.13512,-0.04133,-0.15448,0.0372,-0.06203,0.02646,0.01994,-0.01935,0.12302,0.09725,-0.01334,0.07321,-0.03654,0.00549,-0.08405,0.04604,0.0125,0.05379,-0.13817,-0.07853,-0.08398,-0.07042,0.01198,-0.03721,-0.02193,-0.0802,-0.06829,-0.04956,0.06143,0.0087,0.04851,0.10967,-0.11854,0.04194,-0.05998,-0.1193,-0.08579,0.00581,-0.03649,0.02974,-0.05412,-0.00139,-0.02058,-0.09184,0.03171,0.09078,0.09202,0.04397,0.05748,0.10928,0.03541,-0.02677,-0.09173,0.0252,-0.02111,0.04032,0.06696,0.11372,-0.01854,0.01858,-0.05839,0.01427,-0.02805,0.04925,-0.01497,-0.00486,-0.06207,-0.02943,0.04571,0.11564,-0.06532,-0.09996,-0.01256,0.04122,0.08002,0.02137,0.07801,-0.10264,0.02354,0.09037,-0.01368,0.06438,-0.09858,-0.00953,0.00467,0.03602,0.05,-0.03746,0.03017,0.08668,0.08963,0.05559,0.06674,-0.11048,0.09122,0.08628,-0.02304,0.14596,0.03064,-0.08399,0.00261,-0.05927,0.04679,0.07701,0.01194,-0.05125,0.02315,0.06777,-0.03651,-0.05483,-0.07929,0.04941,0.02188,0.06306,0.03951,0.04008,0.02818,0.07737,-0.06461,-0.00082,-0.02087,0.04911]},{"domain":"data_science_ml","key":"ml_sgd_momentum_step","name":"SGD with momentum: one update","package":"data-science-ml-ai999x","example":"SGD momentum step: w = [1, -2], grad = [0.5, -1], buf = [0.1, 0.2], lr = 0.1, momentum = 0.9, nesterov = no, weight_decay = 0","v":[-0.07582,0.07431,-0.02867,-0.07089,-0.00366,-0.03352,0.02905,0.00389,-0.03267,0.06102,-0.00347,0.01358,-0.06362,0.04029,-0.0978,0.01104,-0.04412,-0.06758,-0.02323,0.00117,0.04678,-0.12962,-0.07012,0.06112,-0.05464,-0.02844,0.00182,-0.02043,-0.08965,0.09331,0.03615,-0.04751,-0.0556,-0.05658,0.0713,0.08818,-0.12574,-0.03179,0.06203,-0.04742,0.05162,-0.06152,-0.02721,-0.01877,-0.02957,0.10693,-0.07102,-0.04399,0.03022,0.01388,-0.04925,0.04595,0.03333,0.062,0.07758,0.00599,-0.076,-0.07121,-0.06124,-0.08377,-0.13054,-0.0737,0.07639,-0.03652,-0.09447,0.07872,0.14445,-0.05463,-0.06626,0.03623,0.02961,-0.00114,-0.11255,-0.03028,0.0194,-0.0612,0.02275,0.04266,-0.07977,0.02847,-0.06934,0.06195,-0.09007,0.00966,0.08027,0.07106,-0.00541,-0.03475,-0.01724,0.05837,0.0235,0.06546,-0.00233,0.07844,-0.00439,-0.04112,0.01225,-0.04974,0.00128,-0.09446,-0.00815,-0.00581,-0.01616,0.01633,0.02921,-0.03553,0.06676,-0.01864,0.04814,0.06661,0.14627,0.04328,-0.07484,0.0021,-0.07137,0.01351,-0.07642,0.01553,-0.0051,-0.05692,-0.02003,-0.07987,-0.01706,0.09309,0.01022,-0.19562,-0.03476,-0.07194,0.03452,-0.016,0.05104,0.0603,0.07942,-0.06007,0.0411,0.11192,-0.09605,0.02861,0.04042,-0.06039,0.04883,-0.14097,0.08434,-0.04944,0.04979,0.02934,-0.02792,-0.01154,-0.04539,-0.00301,0.02086,-0.04731,-0.06933,0.02554,-0.02154,0.05814,0.05007,0.03115,0.05873,-0.00332,0.04159,-0.03676,-0.03576,0.01779,0.00135,0.09537,0.11481,0.04568,-0.00755,-0.09666,0.09194,0.06053,-0.02078,-0.08882,0.0077,0.09367,0.08759,-0.10357,0.01224,-0.02717,0.12098,-0.00406,0.09113,-0.03177,0.0846,0.02702,-0.00092,0.08409,-0.07454,-0.05838,0.1545,0.18554,-0.13132,-0.03765,-0.01054,0.05551,-0.04696,0.03557,0.09937,-0.00716,-0.06608,0.0381,0.10137,0.02274,0.00016,0.04726,0.1433,0.04561,-0.00253,0.04054,-0.03904,0.10375,0.04794,-0.06387,-0.05038,-0.04796,0.01456,0.04559,0.0142,-0.00558,0.06843,0.03669,0.04027,0.1659,0.00866,-0.01194,0.05581,0.0222,0.02876,0.00485,-0.07047,-0.00752,0.03544,0.01569,-0.02204,-0.05213,-0.03199,0.09646,-0.00648,-0.04416,0.04057,0.06652,-0.02207,-0.02378,-0.05717,-0.01665,0.0221,0.05416,0.03709,0.00936,-0.01499,-0.11613,0.05304,-0.05558,-0.07916,-0.10393]},{"domain":"data_science_ml","key":"ml_sigmoid","name":"Sigmoid (logistic function) and its derivative","package":"data-science-ml-ai999x","example":"Sigmoid: z = 0","v":[-0.00453,-0.06429,0.06092,-0.00713,-0.04208,0.01194,-0.11376,-0.03595,-0.03405,0.05265,0.04498,-0.0219,0.00826,-0.0529,0.11426,0.06397,-0.02743,0.02749,0.08786,-0.0723,0.04874,-0.06307,0.0081,-0.07687,-0.0897,-0.05458,-0.01836,0.01695,0.06166,0.12273,-0.14498,0.04025,0.007,-0.07245,0.06159,-0.02223,0.04989,-0.14636,0.07787,0.06766,0.03111,-0.02746,0.02636,0.00753,0.09767,-0.03721,0.03426,-0.01823,-0.05062,-0.05511,-0.08095,-0.08387,-0.0258,-0.02205,0.01037,0.03808,-0.05938,0.00039,-0.05211,0.03362,0.02865,-0.07697,0.00216,0.01672,0.06617,0.08557,-0.05933,-0.02495,0.04258,0.06785,0.05636,-0.06337,-0.07021,0.09232,0.09743,-0.02899,-0.03246,-0.09293,-0.01933,-0.11976,-0.00136,0.13506,0.02489,0.05022,-0.07871,0.05747,-0.09366,0.01334,-0.02063,-0.06549,0.10589,-0.11216,0.02359,-0.04262,0.06886,0.06802,0.06145,-0.03133,0.07974,-0.13396,-0.00864,0.07015,0.01257,0.05677,0.04118,0.03702,0.07742,0.01095,0.04535,-0.04844,-0.01569,0.12021,0.08337,-0.01058,0.10892,-0.04142,-0.11631,0.06016,-0.05115,-0.0651,0.00169,-0.05004,0.01268,0.02172,-0.04374,-0.09332,-0.07667,-0.03483,-0.11297,0.01714,-0.05217,-0.00453,0.05313,-0.14259,0.02172,0.05694,-0.05892,-0.02957,-0.05608,-0.02826,0.05109,0.0393,0.07862,0.01564,0.01903,-0.00682,-0.04107,0.02963,-0.09029,0.03638,-0.02997,-0.06591,0.02884,-0.10033,0.00083,-0.08436,0.04962,-0.03383,-0.00383,0.01085,-0.01704,-0.00388,-0.03056,0.10025,0.09015,0.11295,-0.0749,-0.00816,-0.00998,0.01143,-0.01855,0.00504,0.10395,0.02493,0.0215,-0.11124,0.05102,0.0105,0.03465,0.07062,0.03137,-0.08723,0.09431,-0.01261,0.0722,0.01042,0.05513,0.07709,0.07231,0.05814,0.08483,0.06067,-0.05148,0.00221,-0.06777,-0.02266,-0.12573,0.16651,0.01918,0.04247,-0.10202,0.00274,-0.03762,-0.04697,0.02412,-0.02621,0.07385,0.09604,0.02961,-0.00542,0.02857,0.09826,0.06861,-0.10712,0.02714,-0.01812,-0.10452,0.13304,-0.03431,0.00968,0.01652,-0.0266,0.09292,-0.02935,0.11705,0.03922,0.06377,-0.00727,-0.001,-0.08926,0.05137,-0.06084,-0.03635,-0.03456,-0.00339,0.01181,0.04634,0.09357,0.06591,0.01689,-0.09378,0.10724,0.00519,0.04744,-0.0581,0.03735,-0.02694,-0.00308,-0.03688,-0.06709,0.1119,0.06014,-0.03905,-0.05523,-0.04067,0.02502]},{"domain":"data_science_ml","key":"ml_silhouette_score","name":"Silhouette score","package":"data-science-ml-ai999x","example":"Silhouette score: X = [[1, 1], [1.5, 2], [3, 4], [5, 7], [3.5, 5], [4.5, 5]], labels = [0, 0, 1, 1, 1, 1]","v":[0.02187,-0.02039,0.02334,-0.09179,-0.09667,-0.08059,-0.0178,0.02523,0.01252,0.00179,-0.07666,-0.06136,-0.05639,0.04501,0.0025,-0.15247,0.04044,0.03038,0.02707,-0.02632,0.01676,0.02664,0.09493,-0.08746,0.03356,-0.02965,0.12316,0.05084,0.07856,-0.0576,0.07508,-0.01134,-0.00849,-0.05646,-0.0558,-0.07578,-0.01601,-0.09887,-0.07561,0.06822,-0.04831,0.10047,-0.08808,0.07292,0.00102,0.07115,0.04411,0.08574,-0.0662,-0.01932,0.10965,0.0012,0.08087,0.01218,-0.03952,0.08608,-0.00033,0.05146,0.03301,0.08126,0.10585,-0.02841,-0.02744,0.00586,0.05239,-0.02188,0.10235,-0.01771,0.14293,0.07568,-0.03798,0.00493,-0.02006,-0.02276,0.00503,0.16603,0.00536,-0.04872,0.12508,-0.04669,-0.01771,0.03343,0.02733,-0.02019,-0.01882,-0.07158,-0.01081,-0.1045,-0.13654,-0.06775,-0.05033,0.05839,-0.06525,-0.02729,0.04024,0.01045,0.01715,-0.03513,-0.11557,-0.01925,-0.00539,-0.08984,0.06969,-0.0705,-0.00994,-0.00357,0.04761,-0.10101,-0.03043,-0.01428,0.11195,-0.07763,0.0339,-0.01282,0.00966,0.01506,0.0927,0.07712,-0.07211,0.04013,-0.07274,-0.02427,-0.03402,0.15656,-0.01685,-0.03134,-0.0458,-0.00967,0.08955,-0.04167,0.07905,-0.02884,-0.08395,0.01414,0.07325,-0.01191,0.04383,0.00184,-0.11426,-0.01481,-0.01884,0.04595,0.00587,0.03973,0.07095,-0.01119,-0.0064,0.11211,-0.07266,-0.02327,0.01129,0.00528,0.12617,-0.01137,-0.04411,-0.0739,0.0764,0.04535,-0.02334,0.10621,-0.00394,-0.04964,-0.02705,0.10184,0.08575,-0.08194,-0.04038,-0.13851,0.01965,-0.03778,0.03707,0.04684,-0.0362,0.03061,-0.1207,-0.04925,-0.03793,-0.02907,0.01511,0.06611,0.01991,0.07656,-0.06816,-0.00078,-0.04969,-0.08585,-0.01253,-0.03006,0.12406,-0.01144,0.02594,0.01988,-0.03531,-0.05547,-0.01374,0.09812,0.04694,0.05556,0.04172,-0.09913,-0.12631,0.09718,0.00119,-0.02167,0.07379,-0.0214,-0.04659,-0.13269,0.00774,0.01559,-0.02926,-0.05071,0.10826,0.06503,-0.04052,0.00299,-0.1082,0.02908,0.01426,0.08285,-0.08857,-0.0931,0.06246,0.05027,-0.04119,0.10219,-0.07603,-0.06387,0.04362,0.07274,0.02298,0.0097,-0.07968,0.02895,-0.04924,0.00089,-0.07549,-0.02901,0.05108,0.05064,0.04358,-0.02559,0.02851,0.04388,0.04319,0.00927,-0.06021,0.08464,0.07123,-0.07183,0.05802,-0.01158,-0.07697,0.00666,-0.05671,-0.09471]},{"domain":"data_science_ml","key":"ml_softmax","name":"Softmax","package":"data-science-ml-ai999x","example":"Softmax: z = [1, 2, 3]","v":[-0.04942,-0.09368,0.05828,0.05902,-0.00528,-0.08772,-0.04055,0.06657,-0.08084,-0.06454,0.05148,-0.00848,-0.03086,-0.03637,0.05079,-0.02229,-0.03696,0.06075,0.09394,-0.05207,0.05953,-0.01558,0.05937,-0.03523,-0.0547,0.03706,-0.0691,0.10494,0.03444,0.04199,-0.12337,0.07921,0.02382,-0.04653,0.04929,-0.01197,0.10687,-0.09436,-0.00311,0.02364,-0.03825,-0.05659,-0.00377,-0.04912,-0.02607,-0.02764,-0.0417,-0.06336,-0.1253,0.00223,-0.16195,-0.10534,0.03647,-0.00379,-0.02854,-0.12197,-0.0086,-0.07103,-0.00211,-0.0176,0.02463,-0.00733,0.00267,0.03898,0.00933,0.05502,-0.01028,0.02748,0.0443,0.08847,0.05258,0.01372,-0.09195,0.05125,-0.08901,0.08335,0.02767,-0.01659,-0.01976,-0.02122,-0.01588,0.0689,0.10815,0.08384,-0.04686,0.03843,-0.02525,0.13435,0.07537,-0.10976,0.01745,-0.06126,-0.06529,-0.0324,0.08738,-0.01272,0.05836,0.00168,0.09289,-0.05802,-0.01149,0.03905,-0.01159,-0.05744,0.06727,0.00933,-0.12368,0.00316,-0.00202,-0.02902,-0.04057,-0.00125,0.15215,0.04547,0.08798,-0.03513,-0.11107,0.02683,0.00829,0.0095,-0.10312,0.04712,0.08149,0.00023,0.03994,-0.05157,-0.03376,-0.02297,-0.04984,-0.00937,0.06193,-0.04884,-0.13761,0.00383,0.01221,0.00516,-0.10957,-0.03243,-0.0142,-0.02436,0.02707,0.06007,-0.03891,0.10534,0.02818,0.10383,0.01571,0.0814,-0.09421,0.03573,-0.13984,0.02403,-0.1157,-0.10357,-0.00946,0.02059,-0.1195,-0.01461,-0.01139,-0.03018,-0.06098,-0.0626,0.04598,0.12174,0.16902,0.05457,-0.10486,0.00361,-0.02332,-0.06829,0.04736,-0.02573,0.05047,-0.0053,-0.04788,-0.08896,0.00149,-0.05669,0.01773,0.12586,-0.08743,-0.01964,0.09753,0.12579,0.00412,0.09266,-0.08083,0.00968,0.02802,0.09145,-0.07951,0.10058,-0.0654,0.071,-0.06026,-0.03558,-0.07365,0.01298,0.01289,-0.07467,-0.09219,0.00938,-0.01205,0.04888,-0.05975,-0.02619,0.07339,0.11271,0.05045,0.06698,0.0321,0.0811,0.01784,-0.08417,0.00221,-0.00125,0.00332,0.0023,-0.13668,0.00279,-0.06683,0.01387,0.05152,-0.00164,0.10884,0.03347,-0.04086,0.02911,0.0199,0.03395,0.12564,0.01038,0.07226,-0.02472,0.04877,0.05495,0.08816,0.01402,0.00542,0.00442,-0.01303,-0.02648,-0.02529,0.06942,-0.01181,-0.02982,-0.01461,-0.00917,0.04202,-0.09636,0.0245,0.04895,0.03108,0.01113,-0.04834,0.08109]},{"domain":"data_science_ml","key":"ml_softmax_temperature","name":"Softmax with temperature","package":"data-science-ml-ai999x","example":"Softmax with temperature: z = [1, 2, 3], T = 2","v":[-0.10103,-0.11037,0.07382,-0.018,-0.06365,-0.07363,0.02037,0.05902,-0.02236,-0.03991,-6e-05,-0.01693,-0.05547,0.00547,0.11114,0.0543,-0.00687,-0.00208,0.06199,-0.04848,0.01617,0.01183,0.02037,-0.08423,-0.02574,0.00342,-0.06449,0.03608,0.14351,0.01276,-0.11989,0.08598,0.07365,-0.06751,-0.03199,0.14124,-0.01497,-0.13731,-0.06078,0.02653,-0.06157,-0.12948,0.02902,0.04955,-0.02361,-0.02418,0.00892,-0.05865,-0.10216,0.06004,-0.09572,-0.09109,-0.07972,-0.13015,0.07755,-0.09595,0.02047,0.00328,-0.02389,-0.02397,-0.04483,0.01392,0.04013,0.01198,0.02707,-0.02805,-0.02506,0.08971,0.06798,0.05205,-0.04038,0.00175,-0.08372,0.10668,-0.03548,0.10862,-0.03643,0.03858,-0.05656,-0.07877,-0.0523,0.05398,0.09717,0.07794,-0.01118,0.07595,-0.10437,0.06363,0.02629,-0.13713,0.10154,-0.07962,-0.0374,-0.10401,0.06423,0.01458,-0.00977,-0.06638,0.1104,0.04294,-0.01643,-0.00489,0.08599,-0.02265,0.02867,-0.02807,-0.03933,0.08014,-0.00562,0.00663,-0.05018,0.00351,0.09644,-0.07563,0.08528,0.0231,-0.03731,0.07245,-0.00485,0.016,-0.02278,0.08954,0.13271,-0.0036,-0.00173,0.00578,-0.0485,-0.05038,-0.05839,-0.00647,0.0283,-0.03823,-0.02954,-0.01937,0.04063,0.05232,0.0093,0.01368,-0.08642,-0.03438,0.03531,0.04008,-0.02812,0.08683,0.021,0.06771,0.02211,0.109,-0.1531,0.07181,-0.02871,-0.10356,-0.11629,-0.10124,-0.0005,0.01725,-0.10423,0.00137,0.02776,-0.00218,-0.06865,-0.01327,-0.01504,0.10088,0.03427,0.05871,-0.09578,-0.03928,-0.06664,-0.03936,0.14408,-0.0334,-0.01939,0.04166,-0.06614,-0.02584,-0.02977,0.01458,0.03472,0.16655,0.07862,-0.07365,0.00729,0.07902,0.02307,0.04946,-0.0253,0.08315,-0.02462,0.07629,0.00961,0.06982,-0.05527,0.01895,-0.05845,0.02378,-0.00202,-0.00128,-0.04328,0.02712,-0.09192,-0.04819,0.03201,-0.03349,0.00376,0.01791,0.10518,0.05774,-0.00565,-0.04783,0.09958,0.11464,-0.01914,-0.01147,0.05952,-0.05027,-0.00977,0.06415,-0.02692,-0.02789,-0.1434,0.01082,0.08216,-0.04009,-0.0015,-0.01249,-0.01356,-0.07556,-0.03244,0.04879,0.11348,0.00138,0.03921,-0.04648,0.02353,0.07523,0.00532,-0.00617,0.026,0.11035,0.01107,0.0088,0.01459,0.06961,-0.02529,0.03113,0.02471,0.02416,0.04039,-0.1576,0.00154,0.05124,-0.07413,-0.03722,-0.0059,0.07237]},{"domain":"data_science_ml","key":"ml_standard_scaler","name":"Standardisation (z-scores of features)","package":"data-science-ml-ai999x","example":"Standard scaler: X = [[1, 10], [2, 20], [3, 30], [4, 40]]","v":[-1e-05,-0.0123,-0.02843,-0.02902,-0.06284,0.06091,-0.16225,0.0238,0.0299,-0.07868,0.09503,-0.03761,-0.03519,-0.00621,-0.02451,-0.05357,-0.07359,0.08318,-0.06366,-0.00333,0.0085,0.03454,0.02919,-0.00417,-0.08361,0.00012,0.02518,-0.11258,-0.08178,0.06099,0.0914,-0.06299,0.06305,-0.07963,0.09794,-0.09179,0.10698,0.03228,-0.0201,0.09453,0.01071,0.02697,-0.11494,0.03604,-0.0289,0.03615,-0.02533,-0.05521,-0.01176,0.0302,-0.02524,-0.03779,0.06157,-0.07384,-0.04533,0.01808,0.12538,-0.06541,-0.00402,0.03894,0.00841,-0.01082,0.0354,-0.00441,0.12376,0.04873,-0.0201,0.05811,0.11808,0.1251,3e-05,0.03758,-0.0538,0.05371,-0.09516,0.17611,-0.00416,-0.08321,0.02483,-0.00964,0.0225,0.07591,0.00118,0.0165,0.07567,0.01753,-0.09569,-0.06383,-0.087,-0.04981,-0.01835,0.0629,-0.0322,0.02962,0.04409,-0.00994,-0.00873,0.01966,-0.08568,0.02025,0.01822,-0.10509,-0.04829,-0.05523,0.03997,-0.00722,0.04113,-0.05885,0.08876,-0.09345,-0.00839,0.00465,0.04063,-0.10843,-0.11394,0.09518,0.01079,0.00198,-0.06504,-0.01522,-0.04009,-0.02927,0.0281,-0.00452,0.04634,-0.10469,-0.0502,0.02466,-0.06243,-0.00703,-0.12045,-0.13092,0.00084,-0.03823,0.08618,-0.03979,-0.06546,0.04154,-0.05624,0.02644,-0.04818,0.03157,-0.12086,0.07769,-0.01296,0.09514,-0.10558,-0.02991,0.05391,0.01082,-0.02602,0.01082,0.00954,-0.00761,-0.02643,-0.09147,0.13675,0.01165,-0.05519,0.12466,-0.05027,0.13105,0.08377,0.08138,-0.01735,-0.03707,-0.13683,0.01887,-0.03734,-0.01338,0.06315,-0.00635,0.10713,0.05807,-0.04693,0.01532,0.02329,-0.06078,-0.0884,0.05984,-0.01034,0.08122,0.04719,0.03499,0.02863,0.00778,-0.00327,-0.01508,-0.00884,-0.06543,0.07641,-0.02856,0.01088,-0.06241,0.08558,0.12425,0.0741,0.06217,-0.14413,0.09354,-0.07444,-0.07107,-0.04868,-0.02093,0.03086,-0.06147,-0.07283,0.05686,-0.01356,0.01507,0.02925,0.03743,-0.01849,0.0366,-0.01886,0.03116,-0.00794,-0.02051,0.03511,0.00596,0.0229,-0.0046,-0.06881,0.04328,0.10789,0.09965,0.05765,-0.08879,0.00806,0.03344,0.00826,0.03261,-0.01029,0.16998,-0.04086,0.04128,0.05663,0.10004,-0.02511,0.04415,-0.04185,0.01619,-0.05095,0.0152,0.00736,0.00104,0.0687,0.06995,-0.0778,-0.0252,-0.01479,0.04709,-0.16174,0.05526,0.03946,-0.03929]},{"domain":"data_science_ml","key":"ml_step_lr_schedule","name":"Step 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65","v":[0.0292,0.05397,-0.06124,-0.06727,-0.03255,-0.03475,0.0038,0.03289,-0.04548,0.12913,-0.0163,-0.06705,-0.03436,0.15122,-0.03149,0.08716,0.00903,0.01108,-0.00426,-0.02299,-0.01001,-0.04286,-0.03547,-0.01373,0.02272,-0.01327,-0.03151,0.00012,-0.03275,0.00846,-0.15698,-0.04819,-0.04506,-0.11248,0.00696,0.10451,-0.04998,0.07333,-0.06973,0.0695,0.13811,0.0521,0.03984,-0.0898,0.02341,0.13631,-0.01638,0.01388,0.05215,0.02816,0.01491,0.05632,-0.02578,0.03421,0.05245,0.00661,-0.05184,-0.01699,-0.05222,-0.06548,-0.0159,-0.09872,0.09703,-0.008,-0.02251,0.03665,0.09091,-0.0242,0.03786,-0.00826,0.03319,0.02865,-0.10754,-0.03037,-0.08165,-0.04746,-0.01562,0.11387,-0.08398,-0.03533,-0.00132,0.05912,-0.05333,-0.01095,0.00045,0.15732,-0.0458,-0.00994,0.03312,-0.04162,0.0597,-0.00362,0.03724,-0.08431,-0.00889,0.06684,-0.03015,-0.00913,0.09084,-0.05289,0.00978,-0.02116,-0.08123,-0.11834,-0.05203,-0.00344,0.06153,-0.04493,0.07469,-0.00299,0.01346,-0.01047,-0.05468,-0.02363,-0.10193,0.13418,-0.05701,0.09247,-0.01552,-0.04292,-0.00149,-0.01144,0.03989,-0.00442,-0.06178,-0.10151,-0.09259,-0.01294,-0.02567,0.05096,0.02164,0.11755,0.05558,-0.10509,0.00323,0.02259,-0.04681,0.06358,0.10511,0.04919,0.0892,0.00151,0.03211,0.07523,0.0014,-0.0115,-0.01338,-0.02455,-0.06485,0.08399,0.04012,-0.13675,-0.08449,-0.04412,0.07912,0.01383,-0.06259,0.06869,0.02956,0.10826,-0.05311,0.14312,0.03044,0.0505,0.00438,-0.00521,0.18089,0.02052,0.00872,0.00069,0.03868,-0.00875,-0.09863,-0.03656,0.14845,0.05467,0.05442,0.01159,-0.03994,-0.03052,0.02265,-0.01778,0.0408,-0.05172,0.09374,-0.09177,-0.03712,0.00481,0.03513,-0.01472,0.07439,0.03651,-0.02502,-0.04982,0.0029,0.07124,-0.03696,-0.00824,-0.06495,0.01513,-0.0278,-0.02823,0.13613,-0.01406,0.01634,0.0537,-0.05727,-0.01411,-0.06262,0.04375,-0.09237,0.02351,-0.06124,0.00732,-0.06654,0.03172,-0.07784,-0.00758,-0.08711,0.0499,-0.06815,0.00418,0.11553,0.10284,0.06913,0.02638,0.10397,0.02966,-0.0629,-0.035,-0.05642,-0.10392,-0.03476,0.07964,-0.04441,-0.0125,0.02794,-0.00708,0.0074,-0.10788,0.0117,0.07582,-0.01614,-0.08782,-0.03551,0.09899,0.0891,-0.10766,-0.02406,0.07004,0.12012,-0.11076,0.02716,0.02317,0.09417,-0.06992]},{"domain":"data_science_ml","key":"ml_threshold_metrics","name":"Confusion counts, precision and recall at a score threshold","package":"data-science-ml-ai999x","example":"Metrics at a threshold: y_true = [0, 1, 1, 0, 1], scores = [0.1, 0.9, 0.8, 0.3, 0.2], threshold = 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accuracy","package":"data-science-ml-ai999x","example":"Top-k accuracy: y_true = [0, 1, 2, 2], S = [[0.5, 0.2, 0.2001], [0.3, 0.4, 0.2], [0.2, 0.4, 0.3], [0.7, 0.2, 0.1]], k = 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