File size: 58,633 Bytes
5697766 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | {"text": "\r\n { Transp.mpl }\r\n\r\n\r\nTITLE\r\n TransportationProblem;\r\n\r\nINDEX\r\n supply = (Wh1,Wh2,Wh3,Wh4,Wh5);\r\n dest = (A1,A2,B1,B2,B3,C1,C2,C3);\r\n\r\nDATA\r\n MaxCapacity[supply] := (200,300,250,450,350);\r\n Required[dest] := (188,214,137,199,225,200,177,185);\r\n\r\n ShippingCost[supply,dest] := (13, 22, 9, 14, 10, 32, 35, 36,\r\n 12, 10, 11, 13, 7, 11, 16, 15,\r\n 24, 22, 17, 11, 9, 8, 12, 8,\r\n 43, 40, 25, 17, 21, 24, 27, 22,\r\n 15, 9, 41, 38, 35, 8, 5, 13);\r\n\r\n\r\nDECISION VARIABLES\r\n VolumeShipped[supply,dest] -> \"\"\r\n\r\n\r\nMODEL\r\n\r\n MIN TotalCost = SUM(supply,dest: ShippingCost * VolumeShipped);\r\n\r\nSUBJECT TO\r\n\r\n Capacity[supply] : SUM(dest: VolumeShipped) < MaxCapacity ;\r\n Demand[dest] : SUM(supply: VolumeShipped) > Required ;\r\n\r\nEND\r\n", "meta": {"hexsha": "42cce4a4bcc4876210f327ce691d9118a118f510", "size": 918, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Transp.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Transp.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Transp.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.8108108108, "max_line_length": 69, "alphanum_fraction": 0.4782135076, "num_tokens": 329, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9669140216112958, "lm_q2_score": 0.8267118004748677, "lm_q1q2_score": 0.7993592317106695}}
{"text": "# Maple 2018.2 file to be called with\r\n# read \"log_trans_prob.mpl\"\r\n\r\n# we assume that b > 0!\r\n\r\nwith(LinearAlgebra):\r\n\r\ntrans_prob_unequal := proc(a, b, t, lambda, mu)\r\n local h, theta, psi, phi, alpha, beta, gamma:\r\n\r\n theta := lambda - mu:\r\n psi := lambda + mu:\r\n\r\n phi := (exp(theta * t) - 1) / (lambda * exp(theta * t) - mu):\r\n alpha := mu * phi:\r\n beta := lambda * phi:\r\n gamma := 1 - psi * phi:\r\n\r\n binomial(a + b - 1, a - 1) * alpha^a * beta^b + sum(binomial(a, h) * binomial(a + b - h - 1, a - 1) * alpha^(a - h) * beta^(b - h) * gamma^h, h = 1 .. min(a, b))\r\nend proc:\r\n\r\ntrans_prob_equal := proc(a, b, t, lambda)\r\n local h, theta, alpha, gamma:\r\n\r\n theta := lambda * t:\r\n\r\n alpha := theta / (1 + theta):\r\n gamma := (1 - theta) / (1 + theta):\r\n\r\n binomial(a + b - 1, a - 1) * alpha^(a + b) + sum(binomial(a, h) * binomial(a + b - h - 1, a - 1) * alpha^(a + b - 2 * h) * gamma^h, h = 1 .. min(a, b))\r\nend proc:\r\n\r\nlog_trans_prob := proc(a, b, t, lambda, mu)\r\n local s, lp:\r\n\r\n s := 0:\r\n lp := 0:\r\n\r\n if (lambda <> mu) then\r\n s := trans_prob_unequal(a, b, t, lambda, mu):\r\n else\r\n s := trans_prob_equal(a, b, t, lambda):\r\n end if:\r\n\r\n if evalf[20](s) > 0 then\r\n lp := ln(s):\r\n else\r\n lp := ln(normal(s)):\r\n end if:\r\n\r\n lp\r\nend proc:\r\n\r\nlog_trans_prob_float := proc(a, b, t, lambda, mu)\r\n evalf[100](log_trans_prob(a, b, t, lambda, mu))\r\nend proc:\r\n\r\n# generate data for Figures 1 and 3\r\nN := 1000:\r\nA := 25:\r\nB := 35:\r\nT := 2:\r\nL := 1:\r\nM := 3:\r\n\r\nvalues := Array([seq(0, i = 1 .. N)]):\r\n\r\nfor n to N do\r\n values[n] := log_trans_prob_float(A, B, T, L, n * M / N):\r\nend do:\r\n\r\nvalues := Transpose(Matrix(convert(values, list))):\r\n\r\nExport(\"log_trans_prob_values_univariate.csv\", values):\r\n\r\n# generate data for Figure 4 (beware: it takes a long time)\r\nN := 100:\r\nA := 200:\r\nB := 100:\r\nT := 1:\r\nL := 10:\r\nM := 10:\r\n\r\nvalues := Array([seq(0, i = 1 .. (N * N))]):\r\n\r\nc0 := 1:\r\nfor c1 to N do\r\n for c2 to N do\r\n values[c0] := log_trans_prob_float(A, B, T, c1 * L / N, c2 * M / N):\r\n c0 := c0 + 1:\r\n end do:\r\nend do:\r\n\r\nvalues := Transpose(Matrix(convert(values, list))):\r\n\r\nExport(\"log_trans_prob_values_bivariate.csv\", values):\r\n", "meta": {"hexsha": "299ac6ccc7e2ab9c31e7967f5279122e8e108b19", "size": 2178, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "log_trans_prob.mpl", "max_stars_repo_name": "albertopessia/numeric_bdp_support", "max_stars_repo_head_hexsha": "71323786cbdfeea410dedd21b06bbb1dbd43121b", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "log_trans_prob.mpl", "max_issues_repo_name": "albertopessia/numeric_bdp_support", "max_issues_repo_head_hexsha": "71323786cbdfeea410dedd21b06bbb1dbd43121b", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "log_trans_prob.mpl", "max_forks_repo_name": "albertopessia/numeric_bdp_support", "max_forks_repo_head_hexsha": "71323786cbdfeea410dedd21b06bbb1dbd43121b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.4536082474, "max_line_length": 164, "alphanum_fraction": 0.5381083563, "num_tokens": 775, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9473810511092412, "lm_q2_score": 0.8397339756938818, "lm_q1q2_score": 0.7955480565450117}}
{"text": "euler_angle_matrix := (t) -> \n<<cos(t[2])|\n -cos(t[3])*sin(t[2])|\n sin(t[2])*sin(t[3])>,\n <cos(t[1])*sin(t[2])|\n cos(t[1])*cos(t[2])*cos(t[3])-sin(t[1])*sin(t[3])|\n -cos(t[3])*sin(t[1])-cos(t[1])*cos(t[2])*sin(t[3])>,\n <sin(t[1])*sin(t[2])|\n cos(t[1])*sin(t[3])+cos(t[2])*cos(t[3])*sin(t[1])|\n cos(t[1])*cos(t[3])-cos(t[2])*sin(t[1])*sin(t[3])>\n>;\n\nmobius_embedding := (R,r) -> (t,u) ->\n (R + u*r*cos(2*Pi*t)) *~ [cos(4*Pi*t),sin(4*Pi*t),0] +~ [0,0,u *r* sin(2*Pi*t)];\n\ntorus_embedding := (R,r) -> (t,u) ->\n (R + r * cos(2*Pi*u)) *~ [cos(2*Pi*t),sin(2*Pi*t),0] +~ [0,0,(r * sin(2*Pi*u))];\n \nsimplex_embedding := proc(t)\n if nops(t) = 1 then\n return 0;\n elif nops(t) = 2 then\n return 2*t[1]-1;\n elif nops(t) = 3 then\n return [t[1]-t[2]/2-t[3]/2,sqrt(3)/2*(t[2]-t[3])];\n elif nops(t) = 4 then\n return [sqrt(2)*(2*t[2]-t[3]-t[4])/3,\n sqrt(2/3)*(t[3]-t[4]),\n\t t[1]-(t[2]+t[3]+t[4])/3];\n else\n error(\"Simplex embedding only defined in dim <= 3\");\n fi;\nend:\n\nmobius_arc := (R,r) -> proc(t1,u1,t2,u2)\n local s1,s2;\n if u1 = 0 then\n s2 := t2;\n s1 := t1 - round(2*(t1 - t2))/2;\n elif u2 = 0 then\n s1 := t1;\n s2 := t2 - round(2*(t2 - t1))/2;\n else \n s1 := t1;\n s2 := t2 - round(t2-t1);\n fi;\n return spacecurve(mobius_embedding(R,r)(s1 + p*(s2-s1),u1 + p*(u2-u1)),p=0..1,args[5..-1]);\nend:\n\nsphere_arc := proc(a,b)\n local r,c,d,theta,i;\n r := evalf(sqrt(add(a[i]^2,i=1..3)));\n c := b -~ a;\n d := b +~ a;\n c := evalf(c *~ (r/sqrt(add(c[i]^2,i=1..3))));\n d := evalf(d *~ (r/sqrt(add(d[i]^2,i=1..3))));\n theta := evalf(arccos(add(a[i] * b[i],i=1..3)/r^2)/2);\n return spacecurve(d *~ cos(t) +~ c *~ sin(t),t = -theta..theta,args[3..-1]); \nend:\n\nspherical_angle := proc(a,b,c)\n local dp,ab,ac;\n dp := `dot/R`(3);\n ab := b -~ dp(b,a) *~ a;\n ac := c -~ dp(c,a) *~ a;\n return arccos(dp(ab,ac) /~ sqrt(dp(ab,ab) * dp(ac,ac))); \nend:\n\nspherical_triangle_area := proc(a,b,c)\n return spherical_angle(a,b,c) + \n spherical_angle(b,c,a) + \n spherical_angle(c,a,b) - Pi;\nend:\n\nspherical_triangle_area_alt := proc(a,b,c)\n local dp,f,x,y,z,F;\n dp := `dot/R`(3);\n f := (c) -> sqrt(1-c)/(sqrt(2) + sqrt(1+c));\n x,y,z := f(dp(b,c)),f(dp(c,a)),f(dp(a,b));\n F := (p,q,r) -> (p + q + r - p*q*r)/(1 - p*q - q*r - r*p);\n return 4 * arctan(sqrt(F( x, y, z) * F(-x, y, z) * F( x,-y, z) * F( x, y,-z)));\nend:\n\nsimplex_outline := proc(d)\n local e,i,j,opts;\n if d <> 2 and d <> 3 then\n error(\"Simplex outline is only defined in dimensions 2 and 3\");\n fi;\n \n e := table():\n for i from 0 to d do\n e[i] := simplex_embedding([0$i,1,0$(d-i)]);\n od:\n\n opts := [];\n if nargs > 1 then opts := [args[2..-1]]; fi;\n if d = 3 and opts = [] then opts := [colour=black]; fi;\n \n return display(seq(seq(line(e[i],e[j],op(opts)),j=i+1..d),i=0..d),\n scaling=constrained,axes=none);\nend:\n\ntrefoil_embedding := (R,r) -> proc(t,u)\n local x,y,z,i;\n x := [sin(t) + 2*sin(2*t),cos(t) - 2 * cos(2*t),-sin(3*t)];\n y := [72*sin(2*t)+3*sin(8*t)-13*sin(4*t)+3*sin(7*t)-14*sin(5*t)+3*sin(t),\n 3*cos(t)-3*cos(8*t)+3*cos(7*t)-72*cos(2*t)+14*cos(5*t)-13*cos(4*t),\n 10*sin(6*t)-34*sin(3*t)];\n z := [-391*cos(t)+2*cos(8*t)-29*cos(7*t)+85*cos(2*t)-99*cos(5*t)+24*cos(4*t)+9*cos(10*t)-9*cos(11*t),\n -9*sin(11*t)+29*sin(7*t)+85*sin(2*t)-9*sin(10*t)+2*sin(8*t)-24*sin(4*t)-99*sin(5*t)+391*sin(t),\n -570-34*cos(3*t)-94*cos(6*t)+18*cos(9*t)];\n y := y /~ sqrt(add(y[i]^2,i=1..3));\n z := z /~ sqrt(add(z[i]^2,i=1..3));\n return R *~ x +~ (r * cos(u)) *~ y +~ (r * sin(u)) *~ z;\nend:\n\n\n\ntrefoil_b := (t) -> [(2+cos(3*t))*cos(2*t),(2+cos(3*t))*sin(2*t),sin(3*t)];\n\nklein_embedding := (t,u) -> \n[(0.1*sin(3*Pi*t)+0.1*sin(Pi*t)+0.4*cos(Pi*t))*sin(2*Pi*u)-0.5*sin(4*Pi*t)+sin(2*Pi*t), \n 0.2*sin(2*Pi*u)*sin(3*Pi*t)+2.*cos(2*Pi*t)+0.5, \n 0.25*cos(2*Pi*u)*sin(2*Pi*t)+0.4*cos(2*Pi*u)];\n\nklein_seam_a := (t) -> [0.8621-0.0015*cos(4*Pi*t)+0.0171*sin(2*Pi*t)-0.0002*sin(6*Pi*t),t];\nklein_seam_b := (t) -> [0.1179+0.0031*cos(4*Pi*t)-0.0385*sin(2*Pi*t)+0.0005*sin(6*Pi*t), \n -0.25+0.0597*cos(2*Pi*t)-0.0004*cos(6*Pi*t)+0.0049*sin(4*Pi*t)];\nklein_seam := (t) -> [-0.2811+0.0051*cos(4*Pi*t)-0.1401*sin(2*Pi*t)+0.0005*sin(6*Pi*t), \n 1.7871-0.0061*cos(4*Pi*t)+0.3532*sin(2*Pi*t)-0.0005*sin(6*Pi*t), \n 0.2090*cos(2*Pi*t)-0.0010*cos(6*Pi*t)+0.0086*sin(4*Pi*t)];\n\norient_face := proc(ii,v)\n local dp,u0,u1,u2,vv,i;\n dp := (x,y) -> add(x[i] * y[i],i=1..3);\n u0 := [0,0,0];\n for i in ii do u0 := u0 +~ v[i]; od;\n u0 := evalf(u0 /~ sqrt(dp(u0,u0)));\n u1 := evalf(v[ii[1]]);\n u1 := u1 -~ dp(u1,u0) *~ u0;\n u1 := evalf(u1 /~ sqrt(dp(u1,u1)));\n u2 := [u0[2] * u1[3] - u0[3] * u1[2],\n u0[3] * u1[1] - u0[1] * u1[3],\n u0[1] * u1[2] - u0[2] * u1[1]];\n vv := map(i -> [evalf(arctan(dp(u2,v[i]),dp(u1,v[i]))),i],ii);\n return map(x -> x[2],sort(vv));\nend:\n", "meta": {"hexsha": "efda2cc4091585ea8c0843237939a46dd92355fd", "size": 4802, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/geometry/geometry.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/geometry/geometry.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/geometry/geometry.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.4459459459, "max_line_length": 102, "alphanum_fraction": 0.503331945, "num_tokens": 2191, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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{"text": "~ quaternions are represented as a vector(4)\n~ r + xi + yj + zk => [r, x, y, z]\n\nfunction quaternion_rotation(theta, v)\n st = sin(theta/2)\n return [cos(theta/2), st*v[0], st*v[1], st*v[2]]\nend\n\nfunction quaternion_add(x, y)\n return x + y\nend\n\nfunction quaternion_negate(x)\n return -x\nend\n\nfunction quaternion_subtract(x, y)\n return x - y\nend\n\nfunction quaternion_multiply(x, y)\n return [ x[0]*y[0] - x[1]*y[1] - x[2]*y[2] - x[3]*y[3], \\\n x[0]*y[1] + x[1]*y[0] + x[2]*y[3] - x[3]*y[2], \\\n\t x[0]*y[2] + x[2]*y[0] + x[3]*y[1] - x[1]*y[3], \\\n\t x[0]*y[3] + x[3]*y[0] + x[1]*y[2] - x[2]*y[1] ]\nend\n\nfunction quaternion_conjugate(x)\n return [x[0], -x[1], -x[2], -x[3]]\nend\n\nfunction quaternion_normalize(x)\n return x/sqrt(x*x)\nend\n\nfunction quaternion_inverse(x)\n return quaternion_conjugate(x)/(x*x)\nend\n\nfunction quaternion_divide(x, y)\n return quaternion_multiply(x, quaternion_inverse(y))\nend\n\nfunction quaternion_rotate(x, y)\n return quaternion_multiply(quaternion_multiply(x, y), quaternion_inverse(x))\nend\n\nfunction quaternion_from_matrix(m)\n if m[2,2] < 0 then\n if m[0,0] > m[1,1] then\n\t t = 1 + m[0,0] - m[1,1] - m[2,2]\n\t q = [m[2,1] - m[1,2], t, m[1,0] + m[0,1], m[0,2] + m[2,0]]\n\telse\n\t t = 1 - m[0,0] + m[1,1] - m[2,2]\n\t q = [m[0,2] - m[2,0], m[1,0] + m[0,1], t, m[2,1] + m[1,2]]\n\tend\n else if m[0,0] < -m[1,1] then\n t = 1 - m[0,0] - m[1,1] + m[2,2]\n\tq = [m[1,0] - m[0,1], m[0,2] + m[2,0], m[2,1] + m[1,2], t]\n else\n t = 1 + m[0,0] + m[1,1] + m[2,2]\n\tq = [t, m[2,1] - m[1,2], m[0,2] - m[2,0], m[1,0] - m[0,1]]\n end\n return q/(2*sqrt(t))\nend\n\nfunction quaternion_to_matrix(q)\n return [ 1 - 2*q[2]*q[2] - 2*q[3]*q[3], 2*q[1]*q[2] - 2*q[3]*q[0], 2*q[1]*q[3] + 2*q[2]*q[0]\n 2*q[1]*q[2] + 2*q[3]*q[0], 1 - 2*q[1]*q[1] - 2*q[3]*q[3], 2*q[2]*q[3] - 2*q[1]*q[0]\n\t 2*q[1]*q[3] - 2*q[2]*q[0], 2*q[2]*q[3] + 2*q[1]*q[0], 1 - 2*q[1]*q[1] - 2*q[2]*q[2] ]\nend\n\nfunction quaternion_slerp(xa, ya, t)\n x = quaternion_normalize(xa)\n y = quaternion_normalize(ya)\n dot = x*y\n if dot < 0 then\n x = -x\n\tdot = -dot\n end\n if dot > 0.9995 then\n return quaternion_normalize((1-t)*x + t*y)\n end\n theta0 = acos(dot)\n theta = t*theta0\n st = sin(theta)\n st0 = sin(theta0)\n s0 = cos(theta) - dot*st/st0\n s1 = st/st0\n return s0*x + s1*y\nend\n \n", "meta": {"hexsha": "b694e715d62bd13e1e832f67f457539d042af044", "size": 2404, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "quaternion.mpl", "max_stars_repo_name": "yugyfoog/MPL", "max_stars_repo_head_hexsha": "4159236c621fb823ada3d45b5b05368c60d8cb12", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-12-08T22:55:44.000Z", "max_stars_repo_stars_event_max_datetime": "2020-12-08T22:55:44.000Z", "max_issues_repo_path": "quaternion.mpl", "max_issues_repo_name": "yugyfoog/MPL", "max_issues_repo_head_hexsha": "4159236c621fb823ada3d45b5b05368c60d8cb12", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "quaternion.mpl", "max_forks_repo_name": "yugyfoog/MPL", "max_forks_repo_head_hexsha": "4159236c621fb823ada3d45b5b05368c60d8cb12", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.8494623656, "max_line_length": 96, "alphanum_fraction": 0.5170549085, "num_tokens": 1100, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750413739076, "lm_q2_score": 0.8267117876664789, "lm_q1q2_score": 0.7880837135920598}}
{"text": "# validate new test case (Figure8_7.java)\nwith(simplex);\n\nConstraints := [\n\n# conservation of units at each node\ne13+e14+e41+e15 = 400, # CHI\ne21+e23+e24+e25 = 400, # DC\n\ne13+e23 = 300, # HOU\ne14+e41+e24 = 200, # ATL\ne15+e25 = 300, # BOS\n\n# maximum flow on individual edges\n0 <= e13, e13 <= 200,\n0 <= e14, e14 <= 350,\n0 <= e41, e41 <= 200,\n0 <= e21, e21 <= 200,\n0 <= e23, e23 <= 280,\n0 <= e15, e15 <= 200,\n0 <= e24, e24 <= 200,\n0 <= e25, e25 <= 350\n];\n\nCost := 3*e41 + 7*e13 + 3*e14 + 4*e21 + 4*e23 + 7*e24 + 6*e15 + 6*e25;\n\n# Invoke linear programming to solve problem\nminimize (Cost, Constraints, NONNEGATIVE);\n", "meta": {"hexsha": "805b42e8afb161aa66bb14536048e416f810e083", "size": 621, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Code/Maple/Chapter-8/testCommands.mpl", "max_stars_repo_name": "konny0311/algorithms-nutshell-2ed", "max_stars_repo_head_hexsha": "760b0b8a296fb6be923c89406f61e773a48c59db", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 522, "max_stars_repo_stars_event_min_datetime": "2016-02-21T18:44:23.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-31T09:29:04.000Z", "max_issues_repo_path": "Code/Maple/Chapter-8/testCommands.mpl", "max_issues_repo_name": "linfachen/algorithms-nutshell-2ed", "max_issues_repo_head_hexsha": "17bd6e9cf9917727501f9eeadbfb2100f94eede0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2020-04-09T01:52:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-13T08:18:55.000Z", "max_forks_repo_path": "Code/Maple/Chapter-8/testCommands.mpl", "max_forks_repo_name": "linfachen/algorithms-nutshell-2ed", "max_forks_repo_head_hexsha": "17bd6e9cf9917727501f9eeadbfb2100f94eede0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 216, "max_forks_repo_forks_event_min_datetime": "2015-10-16T16:50:10.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-10T00:57:20.000Z", "avg_line_length": 21.4137931034, "max_line_length": 70, "alphanum_fraction": 0.5990338164, "num_tokens": 265, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632261523028, "lm_q2_score": 0.8244619263765707, "lm_q1q2_score": 0.7847749890805449}}
{"text": "# This is a row reduction algorithm for matrices over the p-local integers.\n# It returns a triple [L,P,x]. Here P is an invertible matrix with P.M = L,\n# so the row span of L is the same as that of M. All rows of zeros in L\n# appear at the bottom. Every nonzero row contains an entry called a pivot.\n# All pivot entries are powers of p. If a pivot entry is p^v, then\n# + all entries to the left are divisible by p^(v+1)\n# + all entries to the right are divisible by p^v\n# + all entries above or below are in the range {0,...,p^v - 1}\n# These conditions force many entries to be zero. I think that\n# they characterise the result up to reordering the rows. We use the\n# following ordering:\n# + If two rows have different valuations, then the one with lower\n# valuation comes first\n# + If two rows have the same valuation, then the one with the pivot\n# further to the left comes first.\n# The component x in the return value gives information abot the pivots.\n# Explicitly, if the i'th entry in x is [j,v] then there is a pivot entry\n# of p^v in position (i,j). \n\nZpl_reduce := proc(M,p)\n local L,L1,P,P1,r,c,i,j,k,h,m,J,K,v,v_min,v_min_pos,pivots,cmp,x;\n L := Copy(M);\n r,c := Dimension(M);\n P := Matrix(r,r);\n for i from 1 to r do P[i,i] := 1; od;\n v := Matrix(r,c);\n i := 0;\n J := {seq(j,j=1..r)};\n K := {seq(k,k=1..c)};\n pivots := NULL;\n v_min_pos := [0,0];\n while v_min_pos <> NULL do\n v_min := infinity;\n v_min_pos := NULL;\n for k in K do\n for j in J do\n v[j,k] := padic_val(L[j,k],p);\n if v[j,k] < v_min then\n v_min := v[j,k];\n v_min_pos := [j,k];\n fi;\n od;\n od;\n if v_min_pos = NULL then\n break;\n fi;\n j,k := op(v_min_pos);\n pivots := pivots,[j,k,v_min];\n m := p^v_min/L[j,k];\n RowOperation(L,j,m,inplace=true);\n RowOperation(P,j,m,inplace=true);\n for h from 1 to r do\n if h <> j then\n m := (L[h,k] - modp(L[h,k],p^v_min))/p^v_min;\n RowOperation(L,[h,j],-m,inplace=true);\n RowOperation(P,[h,j],-m,inplace=true);\n fi;\n od;\n J := sort(J minus {j});\n K := sort(K minus {k});\n od;\n cmp := proc(x,y)\n if x[3] < y[3] then return true; fi;\n if x[3] > y[3] then return false; fi;\n return evalb(x[2] < y[2]);\n end:\n pivots := sort([pivots],cmp);\n L1 := convert(L,listlist);\n P1 := convert(P,listlist);\n L1 := Matrix([seq(L1[x[1]],x in pivots),seq(L1[j],j in J)]);\n P1 := Matrix([seq(P1[x[1]],x in pivots),seq(P1[j],j in J)]);\n return [L1,P1,[seq([x[2],x[3]],x in pivots)]];\nend:\n\n\n######################################################################\n# This is an implementation of the p-local integers that can be\n# used with LinearAlgebra[Generic][SmithForm]. However, Smith\n# forms are not unique, and it does not seem easy to control which\n# version we get if we use LinearAlgebra[Generic][SmithForm].\n# The above function Zpl_reduce does essentially the same job\n# but with a more precisely specified result.\n\nZpl[`0`] := 0;\nZpl[`1`] := 1;\nZpl[`+`] := `+`;\nZpl[`-`] := `-`;\nZpl[`*`] := `*`;\nZpl[`=`] := `=`;\n\nZpl[Quo] := proc(a,b,r)\n local b0,q0,r0;\n b0 := p^padic_val(b,p);\n r0 := modp(a,b0);\n q0 := (a - r0)/b;\n if nargs >= 3 then r := r0; fi;\n return q0;\nend:\n\nZpl[Rem] := proc(a,b,q)\n local b0,q0,r0;\n b0 := p^padic_val(b,p);\n r0 := modp(a,b0);\n q0 := (a - r0)/b;\n if nargs >= 3 then q := q0; fi;\n return r0;\nend:\n\nZpl[EuclideanNorm] := ((m) -> padic_val(m,p));\nZpl[UnitPart] := ((m) -> m/p^padic_val(m,p));\nZpl[Gcdex] := proc(a,b,s,t)\n local u,v;\n u := padic_val(a,p);\n v := padic_val(b,p);\n if u <= v then\n if nargs >= 4 then\n s := p^u/a; t := 0;\n fi;\n return p^u;\n else\n if nargs >= 4 then\n s := 0; t := p^v/b;\n fi;\n return p^v;\n fi; \nend:\n", "meta": {"hexsha": "707b4804f7565068daa0fc3b005b8ad6ef253d38", "size": 3626, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/Zpl.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/Zpl.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/Zpl.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.5511811024, "max_line_length": 76, "alphanum_fraction": 0.5962493105, "num_tokens": 1239, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475699138558, "lm_q2_score": 0.8244619306896955, "lm_q1q2_score": 0.7777541588026101}}
{"text": "# We identify R^4 with the quaternions by the rule\n# [x1,x2,x3,x4] |-> x1 i + x2 j + x3 k + x4.\n\n`mu/H` := proc(a,b)\n if nargs = 0 then\n return [0,0,0,1];\n elif nargs = 1 then\n return args[1];\n elif nargs > 2 then\n return `mu/H`(a,`mu/H`(args[2..-1]));\n else\n return \n [ a[1]*b[4] + a[2]*b[3] - a[3]*b[2] + a[4]*b[1] ,\n - a[1]*b[3] + a[2]*b[4] + a[3]*b[1] + a[4]*b[2] ,\n a[1]*b[2] - a[2]*b[1] + a[3]*b[4] + a[4]*b[3] ,\n - a[1]*b[1] - a[2]*b[2] - a[3]*b[3] + a[4]*b[4]\n ];\n fi;\nend:\n\n`conj/H` := proc(a)\n [-a[1],-a[2],-a[3],a[4]];\nend:\n\n`square_norm/H` := proc(a) local i; return add(a[i]^2,i=1..4); end:\n\n`norm/H` := proc(a) local i; return sqrt(add(a[i]^2,i=1..4)); end:\n\n`inv/H` := (a) -> `conj/H`(a) /~ `square_norm/H`(a);\n\n`phi/angles/H` := (t) ->\n [cos(t[1])*cos(t[2]),cos(t[1])*sin(t[2]),sin(t[1])*cos(t[3]),sin(t[1])*sin(t[3])];\n\n# This is essentially a |-> a * i * (conjugate of a)\nhopf_map := (a) -> \n [a[1]^2-a[2]^2-a[3]^2+a[4]^2,\n 2*a[1]*a[2]+2*a[3]*a[4],\n 2*a[1]*a[3]-2*a[2]*a[4]];\n\n`rotation_matrix/H` := (a) -> Matrix(\n [[a[1]^2-a[2]^2-a[3]^2+a[4]^2,\n 2*a[1]*a[2]-2*a[3]*a[4],\n 2*a[1]*a[3]+2*a[2]*a[4]],\n [2*a[1]*a[2]+2*a[3]*a[4],\n -a[1]^2+a[2]^2-a[3]^2+a[4]^2,\n -2*a[1]*a[4]+2*a[2]*a[3]],\n [2*a[1]*a[3]-2*a[2]*a[4],\n 2*a[1]*a[4]+2*a[2]*a[3],\n -a[1]^2-a[2]^2+a[3]^2+a[4]^2]]\n ) / (a[1]^2+a[2]^2+a[3]^2+a[4]^2);\n\n", "meta": {"hexsha": "484be8ea080080d4eed45322f1591c5d2d2cf367", "size": 1358, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/quaternions.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/quaternions.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/quaternions.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.1153846154, "max_line_length": 83, "alphanum_fraction": 0.4455081001, "num_tokens": 743, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632261523028, "lm_q2_score": 0.8152324960856175, "lm_q1q2_score": 0.7759898337882505}}
{"text": "with(LinearAlgebra,\n Multiply, Transpose):\nwith(Groebner,\n Basis, Reduce, InterReduce, LeadingTerm, LeadingMonomial, TestOrder):\n\nwriteto(\"output.txt\"):\n\ntruncatePolynomial := proc (f, order_1, order_2)\nlocal poly, leading_coeff_1, leading_mon_1, leading_term,\n curr_index, polys:\n\n poly := expand(f):\n\n if evalb(type(poly, `+`)) then\n leading_coeff_1, leading_mon_1 := LeadingTerm(poly, order_1):\n leading_term := leading_coeff_1 * leading_mon_1:\n curr_index := 1:\n\n polys := sort([op(poly)], (b, a) -> TestOrder(a, b, order_2)):\n\n while evalb(polys[curr_index] <> leading_term) do\n curr_index := curr_index + 1:\n end do:\n\n if curr_index = 1 then\n return polys[1]:\n else\n return add(x, x in polys[1..curr_index]):\n end if:\n else\n return poly:\n end if:\nend proc:\n\nbasisConversion := proc (basis, order_1, order_2)\nlocal F_original, F_sanity_check, F, F_t, num_iter,\n F_t_gb, multipliers,\n G, repeat, curr_index, num_elements:\n\n F_original := Basis(basis, order_1):\n\n lprint(\"Step 1\"):\n F := Basis(basis, order_1):\n F_t := map(v -> truncatePolynomial(v, order_1, order_2), F):\n lprint(\"Current F\", F):\n lprint(\"Current F_t\", F_t):\n\n num_iter := 1:\n\n while true do\n lprint(\"Iteration \", num_iter):\n num_iter := num_iter + 1:\n\n lprint(\"Step 2\"):\n F_t_gb, multipliers := Basis(F_t, order_2, output=extended):\n lprint(\"Matrix of multipliers M': \", multipliers):\n lprint(\"H (= M' F_t): \", F_t_gb):\n\n lprint(\"Step 3\"):\n G := convert(simplify(\n Multiply(convert(multipliers, Matrix), Transpose(convert(F, Matrix)))), list):\n lprint(\"G (= M' * F): \", G):\n\n lprint(\"Step 4\"):\n repeat := false:\n curr_index := 1:\n num_elements := numelems(F_t_gb):\n while curr_index < num_elements do\n if evalb(LeadingMonomial(F_t_gb[curr_index], order_2)\n <> LeadingMonomial(G[curr_index], order_2)) then\n lprint(\"There are the witness polynomials that prove\"\\\n \"G_s is not empty (g_j, h_j) respectively \",\n F_t_gb[curr_index], G[curr_index]):\n repeat := true:\n break:\n end if:\n curr_index := curr_index + 1:\n end do:\n\n #F := G:\n F := InterReduce(G, order_2):\n\n F_sanity_check := Basis(F, order_1):\n lprint(\"GB w.r.t. >1 of current F\", F_sanity_check):\n lprint(\"GB w.r.t. >1 of original input\", F_original):\n ASSERT(evalb(F_original = F_sanity_check)):\n\n if repeat = false then\n lprint(\"Done\"):\n return F:\n else\n F_t := map(v -> truncatePolynomial(v, order_1, order_2), F):\n lprint(\"Current F\", F):\n lprint(\"Current F_t\", F_t):\n end if:\n end do:\n\nend proc:\n\ntestBasisConversion := proc (basis, order_1, order_2)\nlocal output_1, output_2:\n lprint():\n lprint(\"Basis conversion of \", basis, \" from \", order_1, \" to \", order_2):\n output_1 := basisConversion(basis, order_1, order_2):\n output_2 := Basis(basis, order_2):\n lprint(\"Result obtained using implemented algorithm \", output_1):\n lprint(\"Result obtained using Maple Basis algorithm \", output_2):\n lprint(\"Are these results the same? \", evalb(output_1 = output_2)):\nend proc:\n\n# ---------------------------------------------------------------------------\n# Testing\ntestBasisConversion([y^2-x,x^2-y*z-1,z^2-x], grlex(x, y, z), plex(x, y, z)):\n#testBasisConversion([y^2-x,x^2-y*z-1,z^2-x], grlex(x, y, z), plex(x, z, y)):\n#testBasisConversion([y^2-x,x^2-y*z-1,z^2-x], grlex(x, y, z), plex(y, x, z)):\n#testBasisConversion([y^2-x,x^2-y*z-1,z^2-x], grlex(x, y, z), plex(y, z, x)):\n#testBasisConversion([y^2-x,x^2-y*z-1,z^2-x], grlex(x, y, z), plex(z, x, y)):\n#testBasisConversion([y^2-x,x^2-y*z-1,z^2-x], grlex(x, y, z), plex(z, y, x)):\n#testBasisConversion([y^2-x,x^2-y*z-1,z^2-x], plex(x, y, z), grlex(x, y, z)):\n#testBasisConversion([x*y+z-x*z, x^2-z, 2*x^3-x^2*y*z-1], tdeg(x, y, z), plex(z, y, x)):\n#testBasisConversion([x + y + z, x*y + y*z + z*x, x*y*z-1], grlex(x, y, z), plex(x, y, z)):\n#testBasisConversion([x + y + z + u, x*y + y*z + z*u + u*x, x*y*z + y*z*u + z*u*x + u*x*y, x*y*z*u-1], grlex(x, y, z, u), plex(x, y, z, u)):\n# ---------------------------------------------------------------------------\n", "meta": {"hexsha": "89fce7805bdd419b21a7432f0158112da17cc5c4", "size": 4544, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "basisConversion.mpl", "max_stars_repo_name": "typesAreSpaces/Basis-Conversion", "max_stars_repo_head_hexsha": "e5aec90e139f19f874fe4e40b823d28551c773ff", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "basisConversion.mpl", "max_issues_repo_name": "typesAreSpaces/Basis-Conversion", "max_issues_repo_head_hexsha": "e5aec90e139f19f874fe4e40b823d28551c773ff", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "basisConversion.mpl", "max_forks_repo_name": "typesAreSpaces/Basis-Conversion", "max_forks_repo_head_hexsha": "e5aec90e139f19f874fe4e40b823d28551c773ff", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.6451612903, "max_line_length": 140, "alphanum_fraction": 0.5501760563, "num_tokens": 1373, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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{"text": "# Andrews-Paule identity. See §7.1 in “Multiple binomial sums”.\n\nS := Sum(z^n*Sum(Sum(Multinomial([i,j])^2*Multinomial([2*n-2*j,2*n-2*i]), i=0..infinity), j=0..infinity), n=0..infinity);\n\nR, ord := BinomSums[sumtores](S, u);\n\n# Checking\nBinomSums[rser](R, ord, 6);\nBinomSums[computesum](S, 5);\n\n# We obtain the following differential operator annihilating the generating function S:\ndop := 1048576*D^6*z^8 + 2883584*D^6*z^7-40960*D^6*z^6 +\n22020096*D^5*z^7-29696*D^6*z^5 + 64225280*D^5*z^6 + 1296*D^6*z^4 +\n1269760*D^5*z^5 + 146407424*D^4*z^6-605184*D^5*z^4 + 455041024*D^4*z^5 +\n16848*D^5*z^3 + 24412672*D^4*z^4 + 363069440*D^3*z^5-3632352*D^4*z^3 +\n1211465728*D^3*z^4 + 59292*D^4*z^2 + 106845184*D^3*z^3 +\n305827840*D^2*z^4-7352832*D^3*z^2 + 1109626112*D^2*z^3 + 58320*D^3*z +\n139138736*D^2*z^2 + 60272640*D*z^3-4247073*D^2*z + 244005120*D*z^2 + 9720*D^2 +\n42117840*D*z + 691200*z^2-374625*D + 3369600*z + 996300;\n\n# Conversion to a differential equation with initial condition\ninit := BinomSums[computesum](S, 6):\ndeq := {\n DETools[diffop2de](dop, y(z), [D,z]),\n seq( (D@@i)(y)(0) = i!*coeff(init, z, i), i=0..4 )\n };\n\n# Conversion to a recurrence.\nrec := gfun[diffeqtorec](deq, y(z), u(n));\n\n# Resolution of the recurrence.\nrsolve(rec, u(n));\n\n", "meta": {"hexsha": "36b09b2eaa08ac1219935dc30ac62b7ffc7dbb78", "size": 1251, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/andrews-paule-identity.mpl", "max_stars_repo_name": "lairez/binomsum", "max_stars_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2015-10-28T00:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2021-05-27T07:47:59.000Z", "max_issues_repo_path": "examples/andrews-paule-identity.mpl", "max_issues_repo_name": "lairez/binomsum", "max_issues_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "examples/andrews-paule-identity.mpl", "max_forks_repo_name": "lairez/binomsum", "max_forks_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 36.7941176471, "max_line_length": 121, "alphanum_fraction": 0.6522781775, "num_tokens": 550, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111796979521253, "lm_q2_score": 0.8376199572530448, "lm_q1q2_score": 0.7632222996485015}}
{"text": "program sample29;\r\n\t/* Calculator program\t*/\r\n\t/* c n : clear & set n\t*/\r\n\t/* + n : add n\t\t\t*/\r\n\t/* - n : subtract n\t*/\r\n\t/* * n : multiply n\t*/\r\n\t/* / n : divide by n\t\t*/\r\n\t/* o : off\t\t\t\t*/\r\nvar unused1: integer;\r\n UnusedArrayForTest: array[200] of char;\r\nprocedure gcmlcm(m, n, gc, lc : integer);\r\n\t/* gc := GCM(m,n), lc := LCM(m,n) */\r\n\t/* m and n are not changed */\r\nvar a,b,r : integer;\r\nbegin\r\na := m;\r\nb := n;\r\nwhile b <> 0 do begin\r\nr := a - (a div b) * b;\r\na := b;\r\nb := r\r\nend;\r\ngc := a;\r\nlc := (m div gc) * n\r\nend;\r\nprocedure abs(a, b : integer);\r\nbegin\r\nif a < 0 then b := -a else b := a\r\nend;\r\nprocedure gcm(a, b, gc : integer);\r\nvar lc, aa, bb : integer;\r\nbegin\r\nif (a = 0) or (b = 0) then gc := 1\r\nelse begin\r\ncall abs(a,aa); call abs(b,bb);\r\ncall gcmlcm(aa, bb, gc, lc)\r\nend\r\nend;\r\nprocedure lcm(a, b, lc : integer);\r\nvar gc, aa, bb : integer;\r\nbegin\r\nif (a = 0) or (b = 0) then lc := 1\r\nelse begin\r\ncall abs(a,aa); call abs(b,bb);\r\ncall gcmlcm(aa, bb, gc, lc)\r\nend\r\nend;\r\nvar unusedchar : char;\r\nprocedure reduce(a1, a2 : integer);\r\n var gc:integer;\r\nbegin\r\nif a1 = 0 then begin a2 := 1; return end;\r\nif a2 = 0 then begin a1 := 1; return end;\r\nif a2 < 0 then begin a1 := -a1; a2 := - a2 end;\r\n call gcm(a1, a2, gc);\r\na1 := a1 div gc;\r\na2 := a2 div gc\r\nend;\r\n\r\nprocedure sum(x1, x2, y1, y2 : integer);\r\nvar lc, y11 : integer;\r\nbegin\r\ncall lcm(x2, y2, lc);\r\nx1 := x1 * (lc div x2);\r\ny11 := y1 * (lc div y2);\r\nx1 := x1 + y11;\r\nx2 := lc;\r\ncall reduce(x1, x2)\r\nend;\r\nprocedure sub(x1, x2, y1, y2 : integer);\r\nvar lc, y11 : integer;\r\nbegin\r\ncall sum(x1, x2, -y1, y2)\r\nend;\r\nprocedure mult(x1, x2, y1, y2 : integer);\r\nvar gc,y22,y11 : integer;\r\nbegin\r\ncall gcm(x1, y2, gc);\r\nx1 := x1 div gc;\r\ny22 := y2 div gc;\r\ncall gcm(x2, y1, gc);\r\nx2 := x2 div gc;\r\ny11 := y1 div gc;\r\nx1 := x1 * y11;\r\nx2 := x2 * y22;\r\ncall reduce(x1, x2)\r\nend;\r\nprocedure divide(x1, x2, y1, y2 : integer);\r\nbegin\r\ncall mult(x1, x2, y2, y1)\r\nend;\r\nvar unusedarray : array[100] of char;\r\nprocedure printfinal(a, b : integer);\r\nbegin\r\nif a = 0 then writeln('Final Result =', a)\r\nelse if b = 1 then writeln('Final Result =', a)\r\nelse writeln('Final Result =', a, '/', b)\r\nend;\r\nprocedure printtemp(a, b : integer);\r\nbegin\r\nif a = 0 then writeln('Temporary Result =', a)\r\nelse if b = 1 then writeln('Temporary Result =', a)\r\nelse writeln('Temporary Result =', a, '/', b)\r\nend;\r\n\r\nvar\tx1, x2, y1,y2 : integer;\r\nvar\tcom :char;\r\nendflag : boolean;\r\nbegin\r\nwriteln(' *** Calculator -- h for help ***');\r\nx1 := 0; x2 :=1;\r\nendflag := false;\r\nwhile not endflag do begin\r\nwriteln(' Please input command :');\r\nreadln(com, y1); y2 := 1;\r\nif (com = 'c') or (com = 'C') then begin x1 := y1; x2 := y2 end\r\nelse if com = '+' then call sum(x1, x2, y1, y2)\r\nelse if com = '-' then call sub(x1, x2, y1, y2)\r\nelse if com = '*' then call mult(x1, x2, y1, y2)\r\nelse if com = '/' then call divide(x1, x2, y1, y2)\r\nelse if (com = 'o') or (com = 'O') then endflag := true\r\nelse begin\r\nwriteln;\r\nwriteln('Calculator Usage:');\r\nwriteln(' c number : clear & set it');\r\nwriteln(' + number : add it');\r\nwriteln(' - number : subtract it');\r\nwriteln(' * number : multiply it');\r\nwriteln(' / number : divide by it');\r\nwriteln(' o : off(terminate execution)');\r\nwriteln\r\nend;\r\nif endflag then call printfinal(x1, x2)\r\nelse call printtemp(x1, x2)\r\nend\r\nend.\r\n", "meta": {"hexsha": "99329f379253b2048cbcb488d6860d19f2fbcc8d", "size": 3346, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "data/sample29p.mpl", "max_stars_repo_name": "naru380/SoftwareExperience5", "max_stars_repo_head_hexsha": "89020bf73d9fc6b58f8d564c7aaed52a0e02f371", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-02-10T01:27:36.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-10T01:27:36.000Z", "max_issues_repo_path": "task2_sample/sample29p.mpl", "max_issues_repo_name": "shouth/LanguageProcessing", "max_issues_repo_head_hexsha": "7d4f751b5babb97857310990e746740f884fa5e5", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 14, "max_issues_repo_issues_event_min_datetime": "2020-10-04T11:15:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-01-20T02:11:14.000Z", "max_forks_repo_path": "samples/program2/sample29p.mpl", "max_forks_repo_name": "Hiroya-W/lang-processing", "max_forks_repo_head_hexsha": "c93ef2d5757e560c4df2335f07ac25552750140c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.4233576642, "max_line_length": 65, "alphanum_fraction": 0.5750149432, "num_tokens": 1187, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. 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{"text": "# Strehl's identity. See §7.2.1 in “Multiple binomial sums”.\n\n# The identity is S1 = S2.\nS1 := Sum(z^n*Sum(Binomial3(n,k)*Multinomial([n,k])*Sum(Binomial3(k,j)^3, j=0..infinity), k=0..infinity), n=0..infinity);\nS2 := Sum(z^n*Sum(Binomial3(n,k)^2*Binomial3(n+k,k)^2, k=0..infinity), n=0..infinity);\n\n# Quick check\nBinomSums[computesum](S1, 5) - BinomSums[computesum](S2, 5);\n\nR1, ord1 := BinomSums[sumtores](S1, u);\n\n# Consistency check\nBinomSums[rser](R1, ord1, 6);\n\nR2, ord2 := BinomSums[sumtores](S2, u);\n\n# Consistency check\nBinomSums[rser](R2, ord2, 6);\n\n# For R1 and R2 we find the same Picard Fuchs equation :\n# D^3 + (6*t^2 - 153*t + 3)/(t^3 - 34*t^2 + t)*D^2 + (7*t^2 - 112*t + 1)/(t^4 - 34*t^3 + t^2)*D + (t - 5)/(t^4 - 34*t^3 + t^2)\n# Since the initial conditions are the same, S1 = S2.\n", "meta": {"hexsha": "88d211df75186b87400b3ea316d6e2a49692f0a6", "size": 797, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/strehl-identity.mpl", "max_stars_repo_name": "lairez/binomsum", "max_stars_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2015-10-28T00:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2021-05-27T07:47:59.000Z", "max_issues_repo_path": "examples/strehl-identity.mpl", "max_issues_repo_name": "lairez/binomsum", "max_issues_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "examples/strehl-identity.mpl", "max_forks_repo_name": "lairez/binomsum", "max_forks_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.652173913, "max_line_length": 126, "alphanum_fraction": 0.626097867, "num_tokens": 351, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9572778024535095, "lm_q2_score": 0.7931059414036511, "lm_q1q2_score": 0.759222712699709}}
{"text": "TITLE\n\tSNDP_stochastic_MIP;\n\nSTOCHASTIC\n\nSCENARIO\n\tSCEN := 1..3;\n\nINDEX\n\tVAR_INDEX := (_A12, _B12, _A13, _B13, _A32, _A33, _C24, _C34) : 4;\t! index should be created from 4 letters (avoid letter conflict)\n\tBIN_VAR_INDEX := (_C2, _C3) : 3;\n\tCONSTR_INDEX := 1..11;\n\nPROBABILITIES\n\tProb[SCEN] := (0.25, 0.5, 0.25);\n\nDATA\n\tCost[VAR_INDEX] := (2, 2, 2, 2, 1, 0, -11, -10);\t\t!vector qT, transportation costs, selling price (signs are reverted in order to transform to MIN problem)\n\tFixed_Cost[BIN_VAR_INDEX] := (2000, 2000);\t\t\t!vector c, set up costs (signs are reverted in order to transform to MIN problem)\n\tT[CONSTR_INDEX, BIN_VAR_INDEX] := (\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t0,\t\t0\n\t\t\t\t\t\t5000,\t\t0\n\t\t\t\t\t\t0,\t\t5000);\t!matrix T (technological in 2 stage model)\n\tW[CONSTR_INDEX, VAR_INDEX] := (\t1, 0, 0, 0, 1, 0, -2, 0,\n\t\t\t\t\t-1, 0, 0, 0, -1, 0, 2, 0,\n\t\t\t\t\t0, 0, 1, 0, 0, 1, 0, -2,\n\t\t\t\t\t0, 0, -1, 0, 0, -1, 0, 2,\n\t\t\t\t\t0, 1, 0, 0, 0, 0, -3, 0,\n\t\t\t\t\t0, -1, 0, 0, 0, 0, 3, 0,\n\t\t\t\t\t0, 0, 0, 1, 0, 0, 0, -3,\n\t\t\t\t\t0, 0, 0, -1, 0, 0, 0, 3,\n\t\t\t\t\t0, 0, 0, 0, 0, 0, -1, -1,\n\t\t\t\t\t0, 0, 0, 0, 0, 0, -1, 0,\n\t\t\t\t\t0, 0, 0, 0, 0, 0, 0, -1);\t!matrix W (recourse in 2 stage model)\nRANDOM DATA\n\th[SCEN, CONSTR_INDEX] := (0, 0, 0, 0, 0, 0, 0, 0, -2000, 0, 0\n\t\t\t\t0, 0, 0, 0, 0, 0, 0, 0, -5000, 0, 0\n\t\t\t\t0, 0, 0, 0, 0, 0, 0, 0, -8000, 0, 0);\n\nSTAGE1 BINARY VARIABLES\n\ty[BIN_VAR_INDEX];\n\nSTAGE2 VARIABLES\n\tx[VAR_INDEX];\n\nMIN\t\t\t\t\t\t\t\t\t!MAX was transformed to MIN\n\tObjective = sum(BIN_VAR_INDEX: Fixed_Cost * y) + sum(VAR_INDEX: Cost * x);\n\nSUBJECT TO\n \tConstr[CONSTR_INDEX]: sum(VAR_INDEX: W * x) >= h - sum(BIN_VAR_INDEX: T * y);\n\nEND", "meta": {"hexsha": "a4ed654f172c9d0de3a0d3d60284abfcfeb8ecf4", "size": 1667, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/SNDP_stochastic_MIP.mpl", "max_stars_repo_name": "pashtetGP/optconvert", "max_stars_repo_head_hexsha": "6dacf2d177c26f3e7f20bce34362878db53bfa13", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "tests/SNDP_stochastic_MIP.mpl", "max_issues_repo_name": "pashtetGP/optconvert", "max_issues_repo_head_hexsha": "6dacf2d177c26f3e7f20bce34362878db53bfa13", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "tests/SNDP_stochastic_MIP.mpl", "max_forks_repo_name": "pashtetGP/optconvert", "max_forks_repo_head_hexsha": "6dacf2d177c26f3e7f20bce34362878db53bfa13", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.2542372881, "max_line_length": 156, "alphanum_fraction": 0.5464907019, "num_tokens": 858, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218391455084, "lm_q2_score": 0.8221891370573388, "lm_q1q2_score": 0.7579941213613602}}
{"text": "(* 2020 Susi Lehtola and Miguel A. L. Marques\n\n This script is used to check the convergence of the series\n expansions of the various attenuation functions, and to\n establish cutoff values for their series expansions.\n*)\n\n$include \"attenuation.mpl\"\n\n(* For exact results we use 1000 digit *)\nexact_digits := 1000:\n(* Double precision has 15 digits *)\ndouble_digits := 15:\n(* An acceptable relative error at double precision is 1e-13 *)\nerror_thr := 1e-13:\n\ncheck_asymptotics := proc(f, a);\n (* Grid spacing *)\n da := 0.01:\n (* Value for a to start with *)\n amax := 5:\n\n (* First, we compare we find a point where to make the cutoff *)\n for acut from amax by -da to da do\n (* Exact result *)\n Digits := exact_digits:\n exact := evalf(f(acut)):\n (* Double precision *)\n Digits := double_digits:\n local doubleprec := evalf(f(acut)):\n (* Error *)\n local err := doubleprec/exact-1:\n #printf(\"Cutoff %e exact % e double % e error % e\\n\", acut, exact, doubleprec, err):\n if (abs(err) < error_thr) then\n break:\n end if:\n end do:\n\n (* Now we find the series expansion that has the same level of agreement *)\n for expord from 4 to 1000 by 2 do\n f_series := a -> eval(throw_out_large_n(convert(series(f(b), b=infinity, expord+padding_order), polynom), expord), b=a):\n local ser := evalf(f_series(acut)):\n local err := ser/exact-1:\n #printf(\"Expansion order %3d original % e asymptotic % e error % \"\n # \"e\\n\", expord, exact, ser, err);\n if (abs(err) < error_thr) then\n (* Check if the expansion is accurate everywhere *)\n accurate := true:\n for aval from acut by da to amax do\n (* Exact result *)\n Digits := exact_digits:\n lexact := evalf(f(aval)):\n (* Double precision *)\n Digits := double_digits:\n lser := evalf(f_series(aval)):\n (* Error *)\n local lerr := lser/lexact-1:\n #printf(\"a= %e exact % e double % e error % e\\n\", aval, lexact, lser, lerr):\n if (abs(lerr) > error_thr) then\n accurate := false:\n break:\n end if:\n end do:\n if accurate then\n break:\n end if:\n end if:\n end do:\n\n printf(\"Cutoff should be at a= %.2f and use a series expansion of \"\n \"order %d\\n\", acut, expord):\nend proc:\n\nprintf(\"attenuation_erf\\n\"):\ncheck_asymptotics(attenuation_erf0, a):\n\nprintf(\"\\nattenuation_erf_f2\\n\"):\ncheck_asymptotics(attenuation_erf_f20, a):\n\nprintf(\"\\nattenuation_erf_f3\\n\"):\ncheck_asymptotics(attenuation_erf_f30, a):\n\nprintf(\"\\nattenuation_gau\\n\"):\ncheck_asymptotics(attenuation_gau0, a):\n\nprintf(\"\\nattenuation_yukawa\\n\"):\ncheck_asymptotics(attenuation_yukawa0, a):\n\n", "meta": {"hexsha": "136c005a30d77bbb389cd98e124d27790d42376d", "size": 2934, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "external/libxc-5.1.6/maple/check_attenuation.mpl", "max_stars_repo_name": "pmu2022/lsms", "max_stars_repo_head_hexsha": "3c5f266812cad0b6d570bef9f5abb590d044ef92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-01-27T14:45:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-27T14:45:51.000Z", "max_issues_repo_path": "external/libxc-5.1.6/maple/check_attenuation.mpl", "max_issues_repo_name": "pmu2022/lsms", "max_issues_repo_head_hexsha": "3c5f266812cad0b6d570bef9f5abb590d044ef92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2021-09-14T01:30:26.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-25T14:05:10.000Z", "max_forks_repo_path": "external/libxc-5.1.6/maple/check_attenuation.mpl", "max_forks_repo_name": "pmu2022/lsms", "max_forks_repo_head_hexsha": "3c5f266812cad0b6d570bef9f5abb590d044ef92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-03T18:16:26.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-03T18:16:26.000Z", "avg_line_length": 32.9662921348, "max_line_length": 128, "alphanum_fraction": 0.5814587594, "num_tokens": 766, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094145755218, "lm_q2_score": 0.8459424431344437, "lm_q1q2_score": 0.7556883486410165}}
{"text": "(*\n Copyright (C) 2018 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n(* x has a different definition in the Chachiyo paper *)\nchachiyo_x := x -> 2/9 * (Pi/3)**(1/3) * (2**(-1/3) * x):\n\n(* equation 1 *)\nchachiyo_f0 := x -> (3*x^2 + Pi^2*log(x+1)) / ((3*x + Pi^2)*log(x+1)):\n\nchachiyo_f := x -> chachiyo_f0(chachiyo_x(x)):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(chachiyo_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "c4c0194369292481f1ba890b3163eb8721ab8a85", "size": 585, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_chachiyo.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_chachiyo.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_chachiyo.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 29.25, "max_line_length": 72, "alphanum_fraction": 0.6205128205, "num_tokens": 218, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9637799441350253, "lm_q2_score": 0.7826624840223698, "lm_q1q2_score": 0.7543144051276597}}
{"text": "#If X ~ Exp(λ) then kX ~ Exp(λ/k).\n\n#Equivalent: If X ~ Exp(α) then kX ~ Exp(kα)\n\n#Proof:\nPDF_exponential := (alpha, x) -> exp(-x/alpha)/alpha;\n\nPDF_kX := (alpha, x, k) -> PDF_exponential(alpha, x/k)/k;\nsimplify(PDF_kX(alpha, x, k));\n\nPDF_exp_scaled := (alpha, x, k) -> PDF_exponential(k*alpha, x);\nsimplify(PDF_exp_scaled(alpha, x, k));\n\nevalb(PDF_kX(alpha, x, k) = PDF_exp_scaled(alpha, x, k));\n", "meta": {"hexsha": "2c0cb942e295fde5ddb2f61a607d779b2fe5b011", "size": 397, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip/t_exponential_scale_closure.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip/t_exponential_scale_closure.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip/t_exponential_scale_closure.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 26.4666666667, "max_line_length": 63, "alphanum_fraction": 0.6397984887, "num_tokens": 145, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9465966702001758, "lm_q2_score": 0.7956581049086031, "lm_q1q2_score": 0.7531673127242658}}
{"text": "(*\n Copyright (C) 2021 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n\n(* Data in table 1 *)\nw20_a0 := proc(z)\n if (z=0) then\n (1-log(2))/Pi^2\n elif (z=1) then\n (1-log(2))/(2*Pi^2)\n end if\nend proc:\n\nw20_a1 := proc(z)\n if (z=0) then\n (9*Pi/4)^(-1/3) * 1/(4*Pi^3) * ( 7*Pi^2/6 - 12*log(2) - 1 )\n elif (z=1) then\n 2^(-4/3) * (9*Pi/4)^(-1/3) * 1/(4*Pi^3) * ( 13*Pi^2/12 - 12*log(2) + 1/2 )\n end if\nend proc:\n\nw20_b0 := proc(z)\n if (z=0) then\n -0.071100 + log(2)/6 - 3/(4*Pi^2)*evalf(Zeta(3))\n elif (z=1) then\n -0.049917 + log(2)/6 - 3/(4*Pi^2)*evalf(Zeta(3))\n end if\nend proc:\n\nw20_b1 := proc(z)\n if (z=0) then\n -0.01\n elif (z=1) then\n (* Compare eq 12 to eqs 15 and 16 *)\n 0\n end if\nend proc:\n\nw20_f0 := -0.9:\nw20_f1 := 1.5:\nw20_f2 := 0:\n\n(* eq 6 *)\nw20_cs := z -> 3/10*(9*Pi/4)^(2/3) * 1/2*((1+z)^(5/3) + (1-z)^(5/3)):\n(* eq 7 *)\nw20_cx := z -> -3/(4*Pi)*(9*Pi/4)^(1/3) * 1/2*((1+z)^(4/3) + (1-z)^(4/3)):\n\n(* eq 8 *)\nw20_ec := (rs, z) -> -w20_a0(z)/2 * log(1 + w20_DF(rs,z,w20_f0-w20_cx(z))/rs + w20_E(rs,z)/rs^(3/2) + w20_DF(rs,z,w20_f2-w20_cs(z))/rs^2) + w20_G(rs,z):\n\n(* eqs 9 and 11 only differ by the f_i - c_j(z) term *)\nw20_DF := (rs, z, cfterm) -> exp(-2*w20_b0(z)/w20_a0(z)) - 2 * (1 - exp(-(rs/100)^2))*( cfterm/w20_a0(z) + 1/2 * exp(-2*w20_b0(z)/w20_a0(z)) ):\n\n(* eq 10 *)\nw20_E := (rs, z) -> - 2*(1 - exp(-(rs/100)^2))*w20_f1 / w20_a0(z):\n\n(* eq 12, rewritten in terms of a decaying exponential to avoid overflow *)\nw20_G := (rs, z) -> rs*exp(-(rs/100)^2) / (exp(-(rs/100)^2) + 10*rs^(5/4)) * ( -w20_a1(z)*log(1 + 1/rs) + w20_b1(z) ):\n\n(* eq 17 *)\nf_w20 := (rs, zeta) -> w20_ec(rs,0) + (w20_ec(rs,1) - w20_ec(rs,0))*f_zeta(zeta):\n\nf := (rs, zeta) -> f_w20(rs, zeta):\n", "meta": {"hexsha": "8635162b0edd130511fdcee24c412e39d295868a", "size": 1904, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_w20.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_w20.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_w20.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 27.2, "max_line_length": 152, "alphanum_fraction": 0.531512605, "num_tokens": 917, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475683211323, "lm_q2_score": 0.7981867729389246, "lm_q1q2_score": 0.7529675513180263}}
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