{"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n(* prefix:\n mgga_x_tpss_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_tpss_params * ) (p->params);\n*)\n\n$ifdef mgga_x_revtpss_params\nparams_a_b := 0.40:\nparams_a_c := 2.35203946:\nparams_a_e := 2.16769874:\nparams_a_kappa := 0.804:\nparams_a_mu := 0.14:\nparams_a_BLOC_a := 3.0:\nparams_a_BLOC_b := 0.0:\n$endif\n\ntpss_ff := z -> params_a_BLOC_a + params_a_BLOC_b*z:\ntpss_kappa := (x, t) -> params_a_kappa:\n\n$include \"tpss_x.mpl\"\n\n(* Equation (5) *)\n\ntpss_a1 := (x, t) -> tpss_kappa(x, t)/(tpss_kappa(x, t) + tpss_fx(x, t)):\ntpss_f := (x, u, t) -> 1 + tpss_kappa(x, t)*(1 - tpss_a1(x, t)):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) -> mgga_exchange(tpss_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "b894640f7b43be0fdb449a4370708ab05c6cbb3b", "size": 992, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_tpss.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/mgga_exc/mgga_x_tpss.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/mgga_exc/mgga_x_tpss.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": 26.1052631579, "max_line_length": 101, "alphanum_fraction": 0.6320564516, "num_tokens": 384, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.900529786117893, "lm_q2_score": 0.6654105454764746, "lm_q1q2_score": 0.5992220161985202}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\n(* replace: \"br89_x\\(\" -> \"xc_mgga_x_br89_get_x(\" *)\n\n$include \"mgga_x_br89.mpl\"\n\nmbrxh_a1 := 0.23432:\nmbrxh_a2 := 0.089:\nmbrxh_a3 := 0.0053:\nparams_a_at := 0:\n\n(* new definition of Q. The rest of the functional remains the same *)\nbr89_Q := (x, u, t) ->\n mbrxh_a1*(2*t) - K_FACTOR_C + mbrxh_a2*x^2 + mbrxh_a3*x^4:", "meta": {"hexsha": "a116e39e660dabe67db4954af717acaae465b132", "size": 580, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_mbrxh_bg.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/mgga_exc/mgga_x_mbrxh_bg.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/mgga_exc/mgga_x_mbrxh_bg.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": 26.3636363636, "max_line_length": 70, "alphanum_fraction": 0.6672413793, "num_tokens": 217, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767906859264, "lm_q2_score": 0.6825737344123242, "lm_q1q2_score": 0.5989426098786341}} {"text": "\n# Base Parameter Energy Regressor for Robot based on MDH frames\n# Einleitung\n# Erstellung einer parameterlinearen und -minimalen Regressorform\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# chain -> Berechnung für eine serielle Struktur (nicht: Baumstruktur)\n# floatb -> floating base. Zusätzliche Betrachtung der Dynamikparameter der Basis.\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# energy -> Berechnung der Energie\n# regressor -> Regressorform (parameterlinear)\n# Authors\n# Alexander Tödtheide, toedtheide@irt.uni-hannover.de\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2017-02\n# \n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Quellen\n# [HRL_IDR] Skript Humanoid Robotics Lab - Serial Chain Robot Identification\n# [GautierKhalil1988] A Direct Determination of Minimum Inertial Parameters of Robots\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# [Gautier1990] M. Gautier: Numerical calculation of the base inertial parameters of robots\n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\ninterface(rtablesize=100): # Zur Anzeige von größeren Vektoren\n;\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"Generiere Minimalparameterregressor (Floating Base %s) der Energie für %s\\n\", base_method_name, robot_name):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name, base_method_name):\n# Ergebnisse der Energie laden\nread sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_worldframe_par2_maple.m\", robot_name, base_method_name):\nread sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_linkframe_par2_maple.m\", robot_name, base_method_name):\nT_floatb := T:\nU_floatb := U_grav:\n# Die kinetischen und potentiellen Energien aus (2) und (3) stehen ab hier durch T_floatb und U_floatb zur Verfügung. \n# Der Parametervektor 'PV2_vec' aus (13) wurde in 'robot_tree_floatb_twist_definitions.mw' aufgestellt. \n# Parameterlinearisierung\n# Parameterlinearisierung auf Basis von [HRL_IDR] (14) und (15)\n# Linearisierung\nt_ges := Matrix(1, 10*NL):\nu_ges := Matrix(1, 10*NL):\nfor i to 10*NL do \n t_ges[1,i] := diff(T_floatb,PV2_vec[i,1]);\n u_ges[1,i] := diff(U_floatb,PV2_vec[i,1]);\nend do: \n# Export\nsave t_ges, sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_regressor_maple.m\", robot_name, base_method_name):\nsave u_ges, sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_regressor_maple.m\", robot_name, base_method_name):\nif codegen_act then\n MatlabExport(convert_t_s(t_ges), sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_regressor_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\nif codegen_act then\n MatlabExport(convert_t_s(u_ges), sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_regressor_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n# Parameterminimierung\n# Minimalparametervekor\n# Definiere Parametermatrix\nXX := Matrix(NL, 1, PV2_mat[1 .. NL, 1]):\nXY := Matrix(NL, 1, PV2_mat[1 .. NL, 2]):\nXZ := Matrix(NL, 1, PV2_mat[1 .. NL, 3]):\nYY := Matrix(NL, 1, PV2_mat[1 .. NL, 4]):\nYZ := Matrix(NL, 1, PV2_mat[1 .. NL, 5]):\nZZ := Matrix(NL, 1, PV2_mat[1 .. NL, 6]):\nmX := Matrix(NL, 1, PV2_mat[1 .. NL, 7]):\nmY := Matrix(NL, 1, PV2_mat[1 .. NL, 8]):\nmZ := Matrix(NL, 1, PV2_mat[1 .. NL, 9]):\nm := Matrix(NL, 1, PV2_mat[1 .. NL, 10]):\n# Rekursive Berechnung der Minimalparameter\n# Rekursive Berechnung der Minimalparameter mit [HRL_IDR] (23), siehe Abbildung 1.\n# [GautierKhalil1990] (eq. 15, 16)\n# Die Sonderfälle (eq. 19, 20) für parallele oder senkrechte Schubachsen scheinen für Floating-Base-Modelle nicht zu gelten, da die dadurch gruppierten Dynamikparameter auf die Basis einen voneinander unabhängigen Einfluss haben.\n# Festgestellt durch Vergleich mit numerischer Berechnung der Minimalparameter nach [Gautier1990]\nfor i from NL by -1 to 2 do \n j := i-1: # Laufvariable für die MDH-Kinematikparameter (Inertialparameter von Segment 0 fangen auch bei 1 an).\n # printf(\"i=%d, j=%d, sigma=%d\\n\", i, j, sigma[j,1]):\n if sigma[j,1] = 0 then # Drehgelenk (eq. 15)\n XX[i,1] := XX[i,1]-YY[i,1]:\n XX[i-1,1] := XX[i-1,1] + YY[i,1]+d[j,1]^2*m[i,1]+2*d[j,1]*mZ[i,1]: \n XY[i-1,1] := XY[i-1,1] + a[j,1]*sin(alpha[j,1])*mZ[i,1]+a[j,1]*d[j,1]*sin(alpha[j,1])*m[i,1]: \n XZ[i-1,1] := XZ[i-1,1] - a[j,1]*cos(alpha[j,1])*mZ[i,1]-a[j,1]*d[j,1]*cos(alpha[j,1])*m[i,1]: \n YY[i-1,1] := YY[i-1,1] + cos(alpha[j,1])^2*YY[i,1]+2*d[j,1]*cos(alpha[j,1])^2*mZ[i,1]+(a[j,1]^2+d[j,1]^2*cos(alpha[j,1])^2)*m[i,1]:\n YZ[i-1,1] := YZ[i-1,1] + cos(alpha[j,1])*sin(alpha[j,1])*YY[i,1]+2*d[j,1]*cos(alpha[j,1])*sin(alpha[j,1])*mZ[i,1]+d[j,1]^2*cos(alpha[j,1])*sin(alpha[j,1])*m[i,1]:\n ZZ[i-1,1] := ZZ[i-1,1]+sin(alpha[j,1])^2*YY[i,1]+2*d[j,1]*sin(alpha[j,1])^2*mZ[i,1]+(a[j,1]^2+d[j,1]^2*sin(alpha[j,1])^2)*m[i,1]:\n mX[i-1,1] := a[j,1]*m[i,1]+mX[i-1,1]: \n mY[i-1,1] := mY[i-1,1]-sin(alpha[j,1])*mZ[i,1]-d[j,1]*sin(alpha[j,1])*m[i,1]:\n mZ[i-1,1] := mZ[i-1,1]+cos(alpha[j,1])*mZ[i,1]+d[j,1]*cos(alpha[j,1])*m[i,1]:\n m[i-1,1] := m[i-1,1]+m[i,1]:\n else: # Schubgelenk (eq. 16)\n XX[i-1,1] := XX[i-1,1] + cos(theta[j,1])^2*XX[i,1]\n - 2*cos(theta[j,1])*sin(theta[j,1])*XY[i,1]\n + sin(theta[j,1])^2*YY[i,1]:\n XY[i-1,1] := XY[i-1,1] + cos(theta[j,1])*sin(theta[j,1])*cos(alpha[j,1])*XX[i,1]\n + (cos(theta[j,1])^2-sin(theta[j,1])^2)*cos(alpha[j,1])*XY[i,1]\n - cos(theta[j,1])*sin(alpha[j,1])*XZ[i,1]\n - cos(theta[j,1])*sin(theta[j,1])*cos(alpha[j,1])*YY[i,1]\n + sin(theta[j,1])*sin(alpha[j,1])*YZ[i,1]:\n XZ[i-1,1] := XZ[i-1,1] + cos(theta[j,1])*sin(theta[j,1])*sin(alpha[j,1])*XX[i,1]\n + (cos(theta[j,1])^2-sin(theta[j,1])^2)*sin(alpha[j,1])*XY[i,1]\n + cos(theta[j,1])*cos(alpha[j,1])*XZ[i,1]\n - cos(theta[j,1])*sin(theta[j,1])*sin(alpha[j,1])*YY[i,1]\n - sin(theta[j,1])*cos(alpha[j,1])*YZ[i,1]:\n YY[i-1,1] := YY[i-1,1] + sin(theta[j,1])^2*cos(alpha[j,1])^2*XX[i,1]\n + 2*cos(theta[j,1])*sin(theta[j,1])*cos(alpha[j,1])^2*XY[i,1]\n - 2*sin(theta[j,1])*cos(alpha[j,1])*sin(alpha[j,1])*XZ[i,1]\n + cos(theta[j,1])^2*cos(alpha[j,1])^2*YY[i,1]\n - 2*cos(theta[j,1])*cos(alpha[j,1])*sin(alpha[j,1])*YZ[i,1]\n + sin(alpha[j,1])^2*ZZ[i,1]:\n YZ[i-1,1] := YZ[i-1,1] + sin(theta[j,1])^2*cos(alpha[j,1])*sin(alpha[j,1])*XX[i,1]\n + 2*cos(theta[j,1])*sin(theta[j,1])*cos(alpha[j,1])*sin(alpha[j,1])*XY[i,1]\n + sin(theta[j,1])*(cos(alpha[j,1])^2-sin(alpha[j,1])^2)*XZ[i,1]\n + cos(theta[j,1])^2*cos(alpha[j,1])*sin(alpha[j,1])*YY[i,1]\n + cos(theta[j,1])*(cos(alpha[j,1])^2-sin(alpha[j,1])^2)*YZ[i,1]\n - cos(alpha[j,1])*sin(alpha[j,1])*ZZ[i,1]:\n ZZ[i-1,1] := ZZ[i-1,1] + sin(theta[j,1])^2*sin(alpha[j,1])^2*XX[i,1]\n + 2*cos(theta[j,1])*sin(theta[j,1])*sin(alpha[j,1])^2*XY[i,1]\n + 2*sin(theta[j,1])*cos(alpha[j,1])*sin(alpha[j,1])*XZ[i,1]\n + cos(theta[j,1])^2*sin(alpha[j,1])^2*YY[i,1]\n + 2*cos(theta[j,1])*cos(alpha[j,1])*sin(alpha[j,1])*YZ[i,1]\n + cos(alpha[j,1])^2*ZZ[i,1]:\n # Keine Sonderregeln (eq. 19,20)\n end if:\nend do:\n# Parameter ohne Einfluss \"Markieren\"\n# Es kann keine Parameter mehr ohne Einfluss geben, da die Basis-Bewegung die Trägheit aller Segmente anregt.\n# Parametervektor in Richtiger Reihenfolge aufstellen und Entfernen von mZ, YY, m\n# Anwendung von [HRL_IDR] Regel 3 (S. 5) auf den Parametervektor\n# [GautierKhalil1990] (eq. 18)\nnt:=add(sigma[i,1],i=1..NJ): # Anzahl Translatorische Gelenke\nnr:=NJ-nt: # Anzahl rotatorische Gelenke\n;\nMPV_n_max := 10+7*nr+4*nt: # ignoriere Abzüge in der Formel\nParamvec := Matrix(MPV_n_max, 1):\n# Basis-Parameter direkt übernehmen\nParamvec(1..10,1) := :\n# Formel für Parameter, die durch Gelenke bewegt werden, anwenden\nii := 11: # Indizes 1..10 für Basis s.o.\nfor i from 1 to NJ do\n if sigma[i,1] = 0 then # Drehgelenk (eq. 15)\n Paramvec[ii, 1] := XX[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := XY[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := XZ[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := YZ[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := ZZ[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mX[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mY[i+1, 1]: ii:= ii+1:\n else: # Schubgelenk (eq. 16)\n # Keine Sonderregeln (eq. 19,20)\n Paramvec[ii, 1] := mX[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mY[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mZ[i+1, 1]: ii:= ii+1:\n Paramvec[ii, 1] := m[i+1, 1]: ii:= ii+1:\n end if:\nend do: \n# Entfernung von Nullelementen\n# Durch Entfernung der Nullelemente erfolgt 'beta_b' aus [HRL_IDR] (22)\np := 0:\nfor i to MPV_n_max do \n if Paramvec[i, 1] = 0 then \n p := p+1 \n end if:\nend do:\n# Determine size of matrix dependent on number of Zeroes\nParamvec_size := MPV_n_max-p:\nParamvec2 := Matrix(Paramvec_size, 1):\np := 0:\nfor i to MPV_n_max do \n # count Zeroes\n if Paramvec[i, 1] = 0 then \n p := p+1:\n else \n # Shift by number of currently found Zeroes\n Paramvec2[i-p, 1] := Paramvec[i, 1]:\n end if:\nend do: \nprintf(\"Dimension des Minimalparametervektors: %dx1\\n\", Paramvec_size):\nParamvec2;\n# Export - Minimalparametervektor\nsave Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_floatb_%s_maple\", robot_name, base_method_name):\nif codegen_act then\n MatlabExport(Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_floatb_%s_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if;\n# Minimal geometrievektor t_i und u_i\n# Markieren von t_mZ, t_YY, t_m, u_mZ, u_YY, u_m_j\n# Anwendung von [HRL_IDR] Regel 3 (S. 5) auf die Geometrievektoren t und u der Energien T und U\n# Die Regel bezieht sich auf Körper, die durch Drehgelenke bewegt werden. Einträge für den Basiskörper werden daher nicht geändert.\n# Die Parameter YY,MZ und M sind immer linear abhängig. Die entsprechenden Spalten der Regressormatrizen werden daher zum Entfernen markiert.\n# [GautierKhalil1990], p.369\nfor i from 1 to NL-1 do\n if sigma[i,1] = 0 then: # Drehgelenk\n t_ges[1,i*10+ 4]:=REMOVE; #YY\n t_ges[1,i*10+ 9]:=REMOVE; #MZ\n t_ges[1,i*10+10]:=REMOVE; #M\n u_ges[1,i*10+ 4]:=REMOVE; #YY\n u_ges[1,i*10+ 9]:=REMOVE; #MZ\n u_ges[1,i*10+10]:=REMOVE; #M\n else:\n t_ges[1,i*10+ 1]:=REMOVE; #XX\n t_ges[1,i*10+ 2]:=REMOVE; #XY\n t_ges[1,i*10+ 3]:=REMOVE; #XZ\n t_ges[1,i*10+ 4]:=REMOVE; #YY\n t_ges[1,i*10+ 5]:=REMOVE; #YZ\n t_ges[1,i*10+ 6]:=REMOVE; #ZZ\n\n u_ges[1,i*10+ 1]:=REMOVE; #XX\n u_ges[1,i*10+ 2]:=REMOVE; #XY\n u_ges[1,i*10+ 3]:=REMOVE; #XZ\n u_ges[1,i*10+ 4]:=REMOVE; #YY\n u_ges[1,i*10+ 5]:=REMOVE; #YZ\n u_ges[1,i*10+ 6]:=REMOVE; #ZZ\n end if:\nend do: \n# Entfernungen von markierten Elementen\n# Durch Entfernung der markierten Elemente, äquivalent zum Minimalparametervektor beta_b, haben t und u die gleiche Spaltenanzahl wie 'C_b'.\np:=0:\nfor i from 1 to 10*NL do #Nullen Zählen um die Matrixgröße von t_ges zu bestimmen \n if t_ges[1,i]=REMOVE and u_ges[1,i]=REMOVE then \n p:=p+1;\n end if\nend do: \nsize_Matrix:=10*NL-p: \nt_ges_minpar:=Matrix(1,size_Matrix):\nu_ges_minpar:=Matrix(1,size_Matrix):\nprintf(\"Dimension der Minimalparameter-Regressormatrix: 1x%d\\n\", size_Matrix):\np:=0:\nfor i from 1 to 10*NL do #Nullen Zählen \n if t_ges[1,i]=REMOVE and u_ges[1,i]=REMOVE then \n p:=p+1; \n else \n t_ges_minpar[1,i-p]:=t_ges[1,i]; #Um die Anzahl der im Iterationsschritt gezählten Nullen verschieben\n u_ges_minpar[1,i-p]:=u_ges[1,i]; #Um die Anzahl der im Iterationsschritt gezählten Nullen verschieben\n end if\nend do: \nsave t_ges_minpar, sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_regressor_minpar_maple.m\", robot_name, base_method_name):\nsave u_ges_minpar, sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_regressor_minpar_maple.m\", robot_name, base_method_name):\n# Export\nif codegen_act then\n MatlabExport(convert_t_s(t_ges_minpar), sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_regressor_minpar_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\nif codegen_act then\n MatlabExport(convert_t_s(u_ges_minpar), sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_regressor_minpar_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n\n", "meta": {"hexsha": "5560dcf26e448faa5ae7e3b295cf85b956ec58b2", "size": 13115, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_energy/robot_chain_floatb_rotmat_energy_regressor.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_energy/robot_chain_floatb_rotmat_energy_regressor.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_energy/robot_chain_floatb_rotmat_energy_regressor.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 51.431372549, "max_line_length": 229, "alphanum_fraction": 0.6408692337, "num_tokens": 4833, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8902942173896131, "lm_q2_score": 0.672331699179286, "lm_q1q2_score": 0.5985730239470513}} {"text": "#@ Not autoload\n# This is mostly superseded by alternating_five.mpl but some stuff at the end has not been transferred\n\nwith(group):\n\n# Generators\n\nx2 := [[1,2],[3,4]];\ny2 := [[1,3],[2,4]];\nz2 := [[2,3],[4,5]];\nx3 := [[1,2,3]];\nx5 := [[1,3,4,2,5]];\ny5 := [[1,2,3,4,5]];\n\nA5 := permgroup(5,{y2,x5});\n\n# Subgroups, named according to their order\n\nH[1 ] := permgroup(5,{}): \nH[2 ] := permgroup(5,{x2}):\nH[3 ] := permgroup(5,{x3}):\nH[4 ] := permgroup(5,{x2,y2}):\nH[5 ] := permgroup(5,{x5}):\nH[6 ] := permgroup(5,{z2,x3}):\nH[10] := permgroup(5,{x2,x5}):\nH[12] := permgroup(5,{x2,x3}):\nH[60] := A5:\n\nmp := proc()\n if nargs = 0 then\n return [];\n elif nargs = 1 then\n return args[1];\n elif nargs = 2 then\n return mulperms(args);\n else\n return mulperms(args[1],mp(args[2..-1]));\n fi;\nend:\n\nip := invperm:\npp := proc(sigma,n)\n local rho,tau,m;\n if (n >= 0) then\n tau := sigma; m := n;\n else \n tau := invperm(sigma);\n m := abs(n);\n fi;\n rho := [];\n while m > 0 do\n rho := mulperms(tau,rho);\n m := m-1;\n od;\n return(rho);\nend:\n\nccl := proc(x) map(g->mulperms(mulperms(g,x),invperm(g)),elements(A5)); end:\n\n# Conjugacy classes\n\nC[1] := {[]}:\nC[2] := ccl(x2):\nC[3] := ccl(x3):\nC[4] := ccl(mulperms(x5,x5)):\nC[5] := ccl(x5):\n\ntau := (1+sqrt(5))/2;\n\n# Dodecahedron representation\n\nRx1 := Matrix([[ 1,0,0],[0, 1,0],[0,0, 1]]):\nRx2 := Matrix([[ 1,0,0],[0,-1,0],[0,0,-1]]):\nRy2 := Matrix([[-1,0,0],[0,-1,0],[0,0, 1]]):\nRz2 := map(rationalize,Matrix([[1/tau,-tau,-1],[-tau,-1,1/tau],[-1,1/tau,-tau]])/2):\nRx3 := Matrix([[0,1,0],[0,0,1],[1,0,0]]):\nRx5 := map(rationalize,Matrix([[1/tau,tau,-1],[-tau,1,1/tau],[1,1/tau,tau]])/2):\nRy5 := map(rationalize,Matrix([[tau,-1,-1/tau],[1,1/tau,tau],[-1/tau,-tau,1]])/2):\n\nprels := {\n pp(x2,2),\n pp(y2,2),\n pp(z2,2),\n pp(x3,3),\n pp(x5,5),\n pp(mp(x2,y2),2),\n pp(mp(x2,mp(y2,z2)),3),\n pp(mp(mp(z2,x2),mp(z2,y2)),3),\n pp(mp(x2,z2),5),\n pp(mp(y2,z2),5),\n mp(ip(x3),mp(y2,mp(z2,mp(x2,mp(z2,mp(y2,z2)))))),\n mp(ip(x5),mp(y2,mp(z2,mp(x2,y2)))),\n mp(ip(y5),mp(y2,mp(z2,mp(x2,mp(z2,x2)))))\n};\n\nmrels := [\n Rx2^2 - Rx1,\n Ry2^2 - Rx1,\n Rz2^2 - Rx1,\n Rx3^3 - Rx1,\n Rx5^5 - Rx1,\n (Rx2 . Ry2)^2 - Rx1,\n (Rx2 . Ry2 . Rz2)^3 - Rx1,\n (Rz2 . Rx2 . Rz2 . Ry2)^3 - Rx1,\n (Rx2 . Rz2)^5 - 1,\n (Ry2 . Rz2)^5 - 1,\n Rx3 - Ry2 . Rz2 . Rx2 . Rz2 . Ry2 . Rz2,\n Rx5 - Ry2 . Rz2 . Rx2 . Ry2,\n Ry5 - Ry2 . Rz2 . Rx2 . Rz2 . Rx2\n]:\n\nmrels := map(M -> map(expand,M),mrels):\nrels := {op(map(expand,map(op,map(op,map(convert,mrels,listlist)))))};\n\nords := [1,2,4,3,6,12,5,10,60];\n\nfor n in ords do X[n] := [op(cosets(A5,H[n]))]: od:\n\nis_fixed1 := (g,x,H) -> groupmember(mulperms(mulperms(x,g),invperm(x)),H):\n\nis_fixed := proc(K,x,H)\n local gens,g;\n gens := op(2,K);\n for g in gens do\n if not(is_fixed1(g,x,H)) then return(false); end;\n od;\n return(true);\nend:\n\nphi := proc(i,j)\n local m,K,L,Y,y;\n K := H[i];\n L := H[j];\n Y := X[j];\n m := 0;\n for y in Y do\n if is_fixed(K,y,L) then\n m := m+1;\n fi;\n od;\n return(m); \nend:\n\n# Matrix of |(G/H_i)^{H_j}|\n\nM := Matrix(9,9,[seq(seq(phi(ords[i],ords[j]),j=1..9),i=1..9)]);\n\n# Cycle types of products of 5-cycles\nP := matrix(12,12,[0$144]):\nfor i from 1 to 12 do\n for j from 1 to 12 do\n g := mulperms(C[5][i],invperm(C[5][j])):\n P[i,j] := map(nops,g):\n od:\nod:\n\n# Edges and faces of the icosahedron\nE := []:\nF := []:\nfor i from 1 to 12 do\n for j from i+1 to 12 do\n if (P[i,j] = [3]) then\n E := [op(E),[i,j]]:\n for k from j+1 to 12 do\n if (P[i,k] = [3] and P[j,k] = [3]) then\n F := [op(F),[i,j,k]]:\n fi:\n od: \n fi:\n od:\nod:\nE;\nF;\n\n# Words for all elements of A5\nw[ 1] := []:\nw[ 2] := [X2]:\nw[ 3] := [Y2]:\nw[ 4] := [Z2]:\nw[ 5] := [X2,Y2]:\nw[ 6] := [X2,Z2]:\nw[ 7] := [Y2,Z2]:\nw[ 8] := [Z2,X2]:\nw[ 9] := [Z2,Y2]:\nw[10] := [X2,Y2,Z2]:\nw[11] := [X2,Z2,X2]:\nw[12] := [X2,Z2,Y2]:\nw[13] := [Y2,Z2,X2]:\nw[14] := [Y2,Z2,Y2]:\nw[15] := [Z2,X2,Y2]:\nw[16] := [Z2,X2,Z2]:\nw[17] := [Z2,Y2,Z2]:\nw[18] := [X2,Y2,Z2,X2]:\nw[19] := [X2,Y2,Z2,Y2]:\nw[20] := [X2,Z2,X2,Y2]:\nw[21] := [X2,Z2,X2,Z2]:\nw[22] := [X2,Z2,Y2,Z2]:\nw[23] := [Y2,Z2,X2,Y2]:\nw[24] := [Y2,Z2,X2,Z2]:\nw[25] := [Y2,Z2,Y2,Z2]:\nw[26] := [Z2,X2,Y2,Z2]:\nw[27] := [Z2,X2,Z2,X2]:\nw[28] := [Z2,X2,Z2,Y2]:\nw[29] := [Z2,Y2,Z2,X2]:\nw[30] := [Z2,Y2,Z2,Y2]:\nw[31] := [X2,Y2,Z2,X2,Z2]:\nw[32] := [X2,Y2,Z2,Y2,Z2]:\nw[33] := [X2,Z2,X2,Z2,X2]:\nw[34] := [X2,Z2,X2,Z2,Y2]:\nw[35] := [X2,Z2,Y2,Z2,X2]:\nw[36] := [X2,Z2,Y2,Z2,Y2]:\nw[37] := [Y2,Z2,X2,Z2,X2]:\nw[38] := [Y2,Z2,X2,Z2,Y2]:\nw[39] := [Y2,Z2,Y2,Z2,X2]:\nw[40] := [Y2,Z2,Y2,Z2,Y2]:\nw[41] := [Z2,X2,Z2,X2,Y2]:\nw[42] := [Z2,X2,Z2,Y2,Z2]:\nw[43] := [Z2,Y2,Z2,X2,Y2]:\nw[44] := [Z2,Y2,Z2,X2,Z2]:\nw[45] := [X2,Y2,Z2,X2,Z2,X2]:\nw[46] := [X2,Y2,Z2,X2,Z2,Y2]:\nw[47] := [X2,Y2,Z2,Y2,Z2,X2]:\nw[48] := [X2,Y2,Z2,Y2,Z2,Y2]:\nw[49] := [X2,Z2,X2,Z2,X2,Y2]:\nw[50] := [X2,Z2,X2,Z2,Y2,Z2]:\nw[51] := [X2,Z2,Y2,Z2,X2,Y2]:\nw[52] := [X2,Z2,Y2,Z2,X2,Z2]:\nw[53] := [Y2,Z2,X2,Z2,Y2,Z2]:\nw[54] := [Y2,Z2,Y2,Z2,X2,Y2]:\nw[55] := [Y2,Z2,Y2,Z2,X2,Z2]:\nw[56] := [Z2,X2,Z2,Y2,Z2,Y2]:\nw[57] := [Z2,Y2,Z2,X2,Z2,X2]:\nw[58] := [X2,Y2,Z2,Y2,Z2,X2,Y2]:\nw[59] := [Z2,Y2,Z2,Y2,Z2,X2,Z2]:\nw[60] := [X2,Z2,Y2,Z2,Y2,Z2,X2,Z2]:\n\n# Rotations for all elements\nRw[1] := IdentityMatrix(3):\nfor i from 2 to 60 do \n Rw[i] := map(expand,`.`(op(subs({X2=Rx2,Y2=Ry2,Z2=Rz2},w[i]))));\nod:\n\n# Permutations for all elements\nSw[1] := []:\nfor i from 2 to 60 do \n Sw[i] := mp(op(subs({X2=x2,Y2=y2,Z2=z2},w[i])));\nod:\n\n# Vertices of the icosahedron \n\nV[ 1] := < 0, 1, tau>: \nV[ 2] := < 0, -1, tau>:\nV[ 3] := < 0, 1,-tau>:\nV[ 4] := < 0, -1,-tau>: \nV[ 5] := < 1, tau, 0>: \nV[ 6] := < -1, tau, 0>:\nV[ 7] := < 1,-tau, 0>:\nV[ 8] := < -1,-tau, 0>:\nV[ 9] := < tau, 0, 1>: \nV[10] := < tau, 0, -1>:\nV[11] := <-tau, 0, 1>:\nV[12] := <-tau, 0, -1>: \n\nfor i from 1 to 12 do \n U := V[i];\n VV[U[1],U[2],U[3]] := i;\nod:\n\nVix := proc(T)\n local T1;\n T1 := map(expand,T);\n return(VV[T1[1],T1[2],T1[3]]);\nend:\n\n# Permutation action on vertices\n\nPx2 := convert([seq(Vix(Rx2 . V[i]),i=1..12)],disjcyc);\nPy2 := convert([seq(Vix(Ry2 . V[i]),i=1..12)],disjcyc);\nPz2 := convert([seq(Vix(Rz2 . V[i]),i=1..12)],disjcyc);\nPx3 := convert([seq(Vix(Rx3 . V[i]),i=1..12)],disjcyc);\nPx5 := convert([seq(Vix(Rx5 . V[i]),i=1..12)],disjcyc);\n", "meta": {"hexsha": "6ad365ed640d0e14ff9158fe23ddd26debd0c449", "size": 6123, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/groups/A5.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/groups/A5.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/groups/A5.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": 21.7127659574, "max_line_length": 102, "alphanum_fraction": 0.5075943165, "num_tokens": 3037, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8519528019683105, "lm_q2_score": 0.7025300449389326, "lm_q1q2_score": 0.5985224402526467}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2019 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(* prefix:\n gga_x_cap_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_cap_params * )(p->params);\n*)\n\ncap_f0 := s -> 1 - params_a_alphaoAx*s*log(1 + s)/(1 + params_a_c*log(1 + s)):\ncap_f := x -> cap_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(cap_f, rs, z, xs0, xs1):\n\n", "meta": {"hexsha": "576910af2dce691dd821900ceff1382e2f5c3d8e", "size": 589, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_cap.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_cap.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_cap.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": 25.6086956522, "max_line_length": 78, "alphanum_fraction": 0.6281833616, "num_tokens": 201, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086179043564153, "lm_q2_score": 0.658417487156366, "lm_q1q2_score": 0.5982499173716344}} {"text": "input := StringTools:-Trim(FileTools:-Text:-ReadFile(\"AoC-2021-15-input.txt\"));\ngrid := Matrix(map(s->parse~(StringTools:-Explode(s)),StringTools:-Split(input,\"\\n\"))):\n\n(gridw,gridl) := upperbound(grid);\n\nnbs := proc(i,j,gridsize)\nlocal out := NULL;\n if i < gridsize then out := out, [i+1, j]; end if;\n if j < gridsize then out := out, [i, j+1]; end if;\n if i > 1 then out := out, [i-1,j]; end if;\n if j > 1 then out := out, [i, j-1]; end if;\n return [out];\nend proc:\n\n# should really do this lazily\ninc := a -> (a mod 9) +~ 1;\nbiggrid:= Matrix([seq([seq((inc@@(i+j-2))(grid),j=1..5)],i=1..5)] );\n(biggridw,biggridl) := upperbound(biggrid);\n\nwith(GraphTheory):\nG := MakeWeighted(MakeDirected(SpecialGraphs:-GridGraph(gridl,gridw)));\nfor e in Edges(G) do\n SetEdgeWeight(G, e, grid[parse(e[2])]);\nend do:\nDijkstrasAlgorithm(G, \"1,1\", cat(\"\",gridl,\",\",gridw))[2];\n\nBG := MakeWeighted(MakeDirected(SpecialGraphs:-GridGraph(biggridl,biggridw)));\nfor i from 1 to biggridl do\n for j from 1 to biggridw do\n a := j + (i-1)*(biggridw);\n for n in nbs(i,j,biggridw) do\n b := n[2] + (n[1]-1)*biggridw;\n W[b,a] := biggrid[i,j];\n end do;\n end do;\nend do:\nDijkstrasAlgorithm(BG, \"1,1\", cat(\"\",biggridl,\",\",biggridw))[2];\n\n\n", "meta": {"hexsha": "72df073b20dd323e77c0883402ef3e6bd0d6eabd", "size": 1269, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day15/gt.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day15/gt.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day15/gt.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.725, "max_line_length": 87, "alphanum_fraction": 0.6028368794, "num_tokens": 451, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8633916099737806, "lm_q2_score": 0.6926419831347361, "lm_q1q2_score": 0.598021276954132}} {"text": "with(DifferentialAlgebra):\nring_diff := DifferentialRing(blocks = [[x2, x4, x1, x3], [y] ], derivations = [t]):\nsys := [\ndiff(x2(t), t) - (alpha*x1(t) - beta*x2(t)),\ndiff(x4(t), t) - ((gama*sigma*x2(t)*x4(t) - delta*sigma*x3(t)*x4(t)) / (x3(t))),\ndiff(x1(t), t) - ((-b*c*x1(t) - b*x1(t)*x4(t) + 1) / (c + x4(t))),\ndiff(x3(t), t) - (gama*x2(t) - delta*x3(t)),\ny(t) - (x1(t))\n];\nres := CodeTools[CPUTime](RosenfeldGroebner(sys, ring_diff, singsol=none));", "meta": {"hexsha": "11a583ed235d754693c4e003dda7a4a48881ce09", "size": 452, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/RosenfeldGroebner/Goodwin-oscillator.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/RosenfeldGroebner/Goodwin-oscillator.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/RosenfeldGroebner/Goodwin-oscillator.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 45.2, "max_line_length": 84, "alphanum_fraction": 0.564159292, "num_tokens": 191, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.921921841290738, "lm_q2_score": 0.6477982179521103, "lm_q1q2_score": 0.5972193258792683}} {"text": "# This function assumes that u is a symmetric polynomial in \n# x[1],...,x[n] and returns a polynomial in c[1],...,c[n] \n# that agrees with u after replacing the variables c[i] by\n# the elementary symmetric functions in x[1],...,x[n].\n# If the optional argument p_ is supplied, then the calculation\n# is done mod p_.\n\nnewton_rewrite := proc(u,n,x,c,p_)\n local p,f,i,v,w,a,m,k,cx,cxp,vars;\n\n p := `if`(nargs > 4,p_,0);\n\n f := expand(mul(t+x[i],i=1..n));\n for i from 1 to n do \n cx[i] := coeff(f,t,n-i);\n od:\n\n cxp := proc(i,j)\n option remember;\n local u;\n\n if j = 0 then\n return 1;\n else\n u := expand(cx[i]*cxp(i,j-1));\n if p > 0 then u := mods(u,p); fi;\n return u; \n fi;\n end:\n\n v := u;\n w := 0;\n vars := plex(seq(x[i],i=1..n));\n while v <> 0 do\n a,m := LeadingTerm(v,vars);\n k := [seq(degree(m,x[i]),i=1..n),0];\n w := w + a * mul(c[i]^(k[i]-k[i+1]),i=1..n);\n v := expand(v - a * mul(cxp(i,k[i]-k[i+1]),i=1..n));\n if nargs > 4 then v := modp(v,p_); fi;\n od:\n\n return w;\nend:\n\norbit_sum := proc(m,n,x)\n local S,R,v,C,c,r,i;\n S := combinat[permute](n);\n R := map(s -> [seq(x[i]=x[s[i]],i=1..n)],S);\n v := add(subs(r,m),r in R);\n C := {coeffs(v,{seq(x[i],i=1..n)})};\n c := igcd(op(C));\n v := expand(v/c);\n return v;\nend:", "meta": {"hexsha": "b7fcd7e095a0384e5db960d51f7de2718bf5ba57", "size": 1237, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/symfun.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/symfun.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/symfun.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": 22.9074074074, "max_line_length": 63, "alphanum_fraction": 0.5456750202, "num_tokens": 464, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8705972751232809, "lm_q2_score": 0.6859494485880927, "lm_q1q2_score": 0.5971857208131106}} {"text": "program gcd;\nbegin\nvar n1, n2: integer;\nread(n1);\nread(n2);\nif n2 > n1 then\nbegin\nvar tmp: integer;\ntmp := n1;\nn1 := n2;\nn2 := tmp;\nend;\nwhile n2 > 0 do\nbegin\nvar new: integer;\nnew := n1 % n2;\nn1 := n2;\nn2 := new;\nend;\nwriteln(n1);\nend.", "meta": {"hexsha": "9880f8572d312ae0646e4a9d0803aa02f9f40697", "size": 236, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "example_programs/gcd1.mpl", "max_stars_repo_name": "sebschmi/codegen-course", "max_stars_repo_head_hexsha": "c70dc9bf253558fb0a9c5e7b188c9556821cede5", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "example_programs/gcd1.mpl", "max_issues_repo_name": "sebschmi/codegen-course", "max_issues_repo_head_hexsha": "c70dc9bf253558fb0a9c5e7b188c9556821cede5", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "example_programs/gcd1.mpl", "max_forks_repo_name": "sebschmi/codegen-course", "max_forks_repo_head_hexsha": "c70dc9bf253558fb0a9c5e7b188c9556821cede5", "max_forks_repo_licenses": ["BSD-2-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 11.2380952381, "max_line_length": 20, "alphanum_fraction": 0.6144067797, "num_tokens": 97, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9019206765295399, "lm_q2_score": 0.6619228691808011, "lm_q1q2_score": 0.5970019219819223}} {"text": "\n# Base Parameter Energy Regressor for Robot based on MDH frames\n# Einleitung\n# Erstellung einer parameterlinearen und -minimalen Regressorform\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# chain -> Berechnung für eine serielle Struktur (nicht: Baumstruktur)\n# fixb -> fixed base. Kein Floating base Modell. Dort ist diese Form der Minimalparameterform nicht möglich.\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# energy -> Berechnung der Energie\n# regressor -> Regressorform (parameterlinear)\n# Authors\n# Alexander Tödtheide, toedtheide@irt.uni-hannover.de\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-03\n# \n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Quellen\n# [HRL_IDR] Skript Humanoid Robotics Lab - Serial Chain Robot Identification\n# [GautierKhalil1988] A Direct Determination of Minimum Inertial Parameters of Robots\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\ninterface(rtablesize=100): # Zur Anzeige von größeren Vektoren\n;\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"%s. Generiere Minimalparameterregressor der Energie für %s (geometrischer Ansatz)\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name, codegen_dynpar):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name, base_method_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name): \nkin_constraints_exist := kin_constraints_exist: # nur zum Abschätzen der Komplexität\n;\n# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(7)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardmäßig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 1: # standardmäßig simplify-Befehle anwenden\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(7): # siebter Eintrag ist für Energie-Regressor\nend if:\n\n# Ergebnisse der Energie laden\nread sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_worldframe_par2_maple.m\", robot_name, base_method_name):\nread sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_linkframe_par2_maple.m\", robot_name, base_method_name):\nT_floatb := T:\nU_floatb := U_grav:\n# Einfluss der Basis-Geschwindigkeit und -Position entfernen\nT_fixb:=T_floatb:\nU_fixb:=U_floatb:\nfor i from 1 to 6 do\n T_fixb := subs({V_base_t[i,1]=0},T_fixb):\n U_fixb := subs({X_base_t[i,1]=0},U_fixb):\nend do:\n# Die kinetischen und potentiellen Energien aus (2) und (3) stehen ab hier durch T_fixb und U_fixb zur Verfügung. \n# Der Parametervektor 'PV2_vec' aus (13) wurde in 'robot_tree_floatb_twist_definitions.mw' aufgestellt. \n\n# Parameterlinearisierung\n# Parameterlinearisierung auf Basis von [HRL_IDR] (14) und (15)\n# Linearisierung\nt_ges := Matrix(1, 10*(NL-1)):\nu_ges := Matrix(1, 10*(NL-1)):\nfor i to 10*(NL-1) do \n t_ges[1,i] := diff(T_fixb,PV2_vec[10+i,1]);\n u_ges[1,i] := diff(U_fixb,PV2_vec[10+i,1]);\nend do:\n# Terme vereinfachen\nif use_simplify=1 then\n tmp_t1:=time():\n tmp_l11 := length(t_ges):\n tmp_l12 := length(u_ges):\n t_ges := simplify2(t_ges):\n u_ges := simplify2(u_ges):\n tmp_t2:=time():\n tmp_l21 := length(t_ges):\n tmp_l22 := length(u_ges):\n printf(\"%s: Terme für Energie-Regressor vereinfacht. Länge: %d->%d / %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l11, tmp_l21, tmp_l12, tmp_l22, tmp_t2-tmp_t1):\nend if:\n# Export\nsave t_ges, sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_maple.m\", robot_name):\nsave u_ges, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_maple.m\", robot_name):\nif codegen_act then\n MatlabExport(convert_t_s(t_ges), sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_matlab.m\", robot_name), codegen_opt):\nend if:\nif codegen_act then\n MatlabExport(convert_t_s(u_ges), sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_matlab.m\", robot_name), codegen_opt):\nend if:\n# Parameterminimierung\n# Prüfe, ob der folgende Algorithmus funktionieren kann\n# Bestimme, ob es eine Baumstruktur ist. Wenn ja, funktioniert der Algorithmus (noch) nicht (nicht implementiert).\ntree:=false:\nfor i from 1 to NJ do\n if not v(i) = i-1 then\n tree := true: break:\n end if:\nend do:\n\nif assigned(user_CoM) or assigned(user_M) or assigned(user_inertia) \\ \n or kin_constraints_exist or tree then\n # es gibt einen Sonderfall, diese Berechnung der Minimalparameter funktioniert voraussichtlich nicht.\n printf(\"%s. Geometrische Berechnung der Minimalparameter nicht möglich.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch Löschung des Roboternamens.\nend if:\n# Minimalparametervekor\n# Definiere Parametermatrix\n# Nehme nur die Inertialparameter der bewegten Segmente, nicht die Basis.\nXX := Matrix(NJ, 1, PV2_mat[2 .. NL, 1]):\nXY := Matrix(NJ, 1, PV2_mat[2 .. NL, 2]):\nXZ := Matrix(NJ, 1, PV2_mat[2 .. NL, 3]):\nYY := Matrix(NJ, 1, PV2_mat[2 .. NL, 4]):\nYZ := Matrix(NJ, 1, PV2_mat[2 .. NL, 5]):\nZZ := Matrix(NJ, 1, PV2_mat[2 .. NL, 6]):\nmX := Matrix(NJ, 1, PV2_mat[2 .. NL, 7]):\nmY := Matrix(NJ, 1, PV2_mat[2 .. NL, 8]):\nmZ := Matrix(NJ, 1, PV2_mat[2 .. NL, 9]):\nm := Matrix(NJ, 1, PV2_mat[2 .. NL, 10]):\n\n# Rekursive Berechnung der Minimalparameter\n# Rekursive Berechnung der Minimalparameter mit [HRL_IDR] (23), siehe Abbildung 1.\n# [GautierKhalil1990] (eq. 15,16)\nfor i from NJ by -1 to 2 do\n # printf(\"i=%d, sigma=%d\\n\", i, sigma[i,1]): \n if sigma[i,1] = 0 then # Drehgelenk (eq. 15)\n XX[i, 1] := XX[i, 1]-YY[i,1]:\n XX[i-1,1] := XX[i-1,1] + YY[i,1] + d[i,1]^2*m[i,1]+2*d[i,1]*mZ[i,1]: \n XY[i-1,1] := XY[i-1,1] + a[i,1]*sin(alpha[i,1])*mZ[i,1]+a[i,1]*d[i,1]*sin(alpha[i,1])*m[i,1]: \n XZ[i-1,1] := XZ[i-1,1] - a[i,1]*cos(alpha[i,1])*mZ[i,1]-a[i,1]*d[i,1]*cos(alpha[i,1])*m[i,1]: \n YY[i-1,1] := YY[i-1,1] + cos(alpha[i,1])^2*YY[i,1]+2*d[i,1]*cos(alpha[i,1])^2*mZ[i,1]+(a[i,1]^2+d[i,1]^2*cos(alpha[i,1])^2)*m[i,1]:\n YZ[i-1,1] := YZ[i-1,1] + cos(alpha[i,1])*sin(alpha[i,1])*YY[i,1]+2*d[i,1]*cos(alpha[i,1])*sin(alpha[i,1])*mZ[i,1]+d[i,1]^2*cos(alpha[i,1])*sin(alpha[i,1])*m[i,1]:\n ZZ[i-1,1] := ZZ[i-1,1] + sin(alpha[i,1])^2*YY[i,1]+2*d[i,1]*sin(alpha[i,1])^2*mZ[i,1]+(a[i,1]^2+d[i,1]^2*sin(alpha[i,1])^2)*m[i,1]:\n mX[i-1,1] := mX[i-1,1] + a[i,1]*m[i,1]: \n mY[i-1,1] := mY[i-1,1] - sin(alpha[i,1])*mZ[i,1]-d[i,1]*sin(alpha[i,1])*m[i,1]:\n mZ[i-1,1] := mZ[i-1,1] + cos(alpha[i,1])*mZ[i,1]+d[i,1]*cos(alpha[i,1])*m[i,1]:\n m[i-1 ,1] := m[i-1 ,1] + m[i,1]:\n else: # Schubgelenk (eq. 16)\n # im Normalfall nicht geänderte Parameter initialisieren.\n # Wird durch Sonderregeln weiter unten überschrieben.\n mR_i := m[i-1 ,1]:\n mXR_i := mX[i-1,1]:\n mYR_i :=mY[i-1,1]:\n mZR_i:=mZ[i-1,1]:\n XXR_i := XX[i-1,1] + cos(theta[i,1])^2*XX[i,1]\n - 2*cos(theta[i,1])*sin(theta[i,1])*XY[i,1]+sin(theta[i,1])^2*YY[i,1]: \n XYR_i := XY[i-1,1] + cos(theta[i,1])*sin(theta[i,1])*cos(alpha[i,1])*XX[i,1]\n + (cos(theta[i,1])^2-sin(theta[i,1])^2)*cos(alpha[i,1])*XY[i,1]\n - cos(theta[i,1])*sin(alpha[i,1])*XZ[i,1]\n - cos(theta[i,1])*sin(theta[i,1])*cos(alpha[i,1])*YY[i,1]\n + sin(theta[i,1])*sin(alpha[i,1])*YZ[i,1]:\n XZR_i := XZ[i-1,1] + cos(theta[i,1])*sin(theta[i,1])*sin(alpha[i,1])*XX[i,1]\n + (cos(theta[i,1])^2-sin(theta[i,1])^2)*sin(alpha[i,1])*XY[i,1]\n + cos(theta[i,1])*cos(alpha[i,1])*XZ[i,1]\n - cos(theta[i,1])*sin(theta[i,1])*sin(alpha[i,1])*YY[i,1]\n - sin(theta[i,1])*cos(alpha[i,1])*YZ[i,1]:\n YYR_i := YY[i-1,1] + sin(theta[i,1])^2*cos(alpha[i,1])^2*XX[i,1]\n + 2*cos(theta[i,1])*sin(theta[i,1])*cos(alpha[i,1])^2*XY[i,1]\n - 2*sin(theta[i,1])*cos(alpha[i,1])*sin(alpha[i,1])*XZ[i,1]\n + cos(theta[i,1])^2*cos(alpha[i,1])^2*YY[i,1]\n - 2*cos(theta[i,1])*cos(alpha[i,1])*sin(alpha[i,1])*YZ[i,1]\n + sin(alpha[i,1])^2*ZZ[i,1]:\n YZR_i := YZ[i-1,1] + sin(theta[i,1])^2*cos(alpha[i,1])*sin(alpha[i,1])*XX[i,1]\n + 2*cos(theta[i,1])*sin(theta[i,1])*cos(alpha[i,1])*sin(alpha[i,1])*XY[i,1]\n + sin(theta[i,1])*(cos(alpha[i,1])^2-sin(alpha[i,1])^2)*XZ[i,1]\n + cos(theta[i,1])^2*cos(alpha[i,1])*sin(alpha[i,1])*YY[i,1]\n + cos(theta[i,1])*(cos(alpha[i,1])^2-sin(alpha[i,1])^2)*YZ[i,1]\n - cos(alpha[i,1])*sin(alpha[i,1])*ZZ[i,1]:\n ZZR_i := ZZ[i-1,1] + sin(theta[i,1])^2*sin(alpha[i,1])^2*XX[i,1]\n + 2*cos(theta[i,1])*sin(theta[i,1])*sin(alpha[i,1])^2*XY[i,1]\n + 2*sin(theta[i,1])*cos(alpha[i,1])*sin(alpha[i,1])*XZ[i,1]\n + cos(theta[i,1])^2*sin(alpha[i,1])^2*YY[i,1]\n + 2*cos(theta[i,1])*cos(alpha[i,1])*sin(alpha[i,1])*YZ[i,1]\n + cos(alpha[i,1])^2*ZZ[i,1]:\n # Im Kap. IV.C. sind Sonderfälle nur bezogen auf Schubgelenke definiert.\n # Diese scheinen aber noch überhaupt nicht gut zu funktionieren. Unklar, warum.\n # Sonderfall parallele Achsen (eq. 19)\n if sin(alpha[i,1]) = 0 and false then # deaktiviert. TODO: Klären, ob der Sonderfall sinnvoll ist\n ZZR_i := ZZ[i-1,1] + 2*a[i,1]*cos(theta[i,1])*mX[i,1] - 2*a[i,1]*sin(theta[i,1])*mY[i,1]:\n mXR_i := mX[i-1,1] + cos(theta[i,1])*mX[i,1] - sin(theta[i,1])*mY[i,1]:\n mYR_i := mY[i-1,1] + sin(theta[i,1])*cos(alpha[i,1])*mX[i,1] + cos(theta[i,1])*cos(alpha[i,1])*mY[i,1]:\n end if:\n # Sonderfall senkrechte Achsen (eq. 20)\n if cos(alpha[i,1]) = 0 and false then # deaktiviert.\n YYR_i := YY[i-1,1] + 2*a[i,1]*cos(theta[i,1])*mX[i,1] - 2*a[i,1]*sin(theta[i,1])*mY[i,1]:\n mXR_i := mX[i-1,1] + cos(theta[i,1])*mX[i,1] - sin(theta[i,1])*mY[i,1]:\n mZR_i := mZ[i-1,1] + sin(alpha[i,1])*sin(theta[i,1])*mX[i,1] + sin(alpha[i,1])*cos(theta[i,1])*mY[i,1]:\n end if:\n # Zuweisung der neuen Variable (wegen Fallunterscheidung parallel/senkrecht)\n # Nur für Schubgelenke notwendig\n m[i-1 ,1] := mR_i:\n mX[i-1,1] := mXR_i:\n mY[i-1,1] := mYR_i:\n mZ[i-1,1] := mZR_i:\n XX[i-1,1] := XXR_i:\n XY[i-1,1] := XYR_i:\n XZ[i-1,1] := XZR_i:\n YY[i-1,1] := YYR_i:\n YZ[i-1,1] := YZR_i:\n ZZ[i-1,1] := ZZR_i:\n end if: # Drehgelenk/Schubgelenk\nend do: \n\n# Parameter ohne Einfluss \"Markieren\"\n# Markierung von Parametern ohne Einfluss an Hand von [HRL_IDR] (18)\nprintf(\"The following parameters don't have any effect:\\n\"):\n\nfor i to 10*NJ do \n effect := 0:\n if not (t_ges[1,i]=0) then\n # printf(\"t_ges[1,%d] not Null\\n\", i):\n effect := 1:\n else\n for j to NQJ do\n if has(u_ges[1,i],{qJ_t(j,1)}) then\n # printf(\"u_ges[1,%d] not constant\\n\", i):\n effect := 1:\n break:\n end if:\n end do:\n end if:\n if effect = 0 then\n t_ges[1,i] := REMOVE:\n u_ges[1,i] := REMOVE:\n\n if `mod`(i, 10) = 1 then XX[trunc((1/10)*i)+1, 1] := 0; printf(\"XX%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 2 then XY[trunc((1/10)*i)+1, 1] := 0; printf(\"XY%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 3 then XZ[trunc((1/10)*i)+1, 1] := 0; printf(\"XZ%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 4 then YY[trunc((1/10)*i)+1, 1] := 0; printf(\"YY%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 5 then YZ[trunc((1/10)*i)+1, 1] := 0; printf(\"YZ%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 6 then ZZ[trunc((1/10)*i)+1, 1] := 0; printf(\"ZZ%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 7 then mX[trunc((1/10)*i)+1, 1] := 0; printf(\"MX%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 8 then mY[trunc((1/10)*i)+1, 1] := 0; printf(\"MY%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 9 then mZ[trunc((1/10)*i)+1, 1] := 0; printf(\"MZ%d \\n\", trunc((1/10)*i)+1): end if:\n if `mod`(i, 10) = 0 then m[trunc((1/10)*i), 1] := 0; printf(\" M%d \\n\", trunc((1/10)*i)): end if:\n end if:\nend do:\n# Speichere markierte Regressor-Vektoren\nsave t_ges, sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_marked_maple.m\", robot_name):\nsave u_ges, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_marked_maple.m\", robot_name):\n# Parametervektor in Richtiger Reihenfolge aufstellen und Entfernen von mZ, YY, m\n# Anwendung von [HRL_IDR] Regel 3 (S. 5) auf den Parametervektor\n# Bei Drehgelenken werden die Parameter YY, mZ und m mit denen des folgenden Körpers gruppiert. Bei Schubgelenken werden alle Trägheitsmomente gruppiert (da die Trägheitsmomente keinen Einfluss auf die translatorische Bewegung des Schubgelenkes haben).\n# [GautierKhalil1990] (eq. 18)\nnt:=add(sigma[i,1],i=1..NJ): # Anzahl Translatorische Gelenke\nnr:=NJ-nt: # Anzahl rotatorische Gelenke\n;\n#Anzahl der Einträge im Minimalparametervektor\nMPV_n_max := 7*nr+4*nt: # ignoriere Abzüge in der Formel\n;\nParamvec := Matrix(MPV_n_max, 1):\nii := 1:\nfor i to NJ do\n if sigma[i,1] = 0 then # Drehgelenk (eq. 15)\n Paramvec[ii, 1] := XX[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := XY[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := XZ[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := YZ[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := ZZ[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mX[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mY[i, 1]: ii:= ii+1:\n else: # Schubgelenk (eq. 16)\n if sin(alpha[i,1]) = 0 and false then # Sonderregel (eq. 19).\n # Parameter wurden mit denen der Basisnäheren Achse zusammengelegt und werden hier nicht betrachtet.\n # Parameter mZ fällt weg, also bleiben mX und mY übrig\n # TODO: Unklar, was das für das Programm heißt. Folgendes noch falsch.\n Paramvec[ii, 1] := mX[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mY[i, 1]: ii:= ii+1:\n elif cos(alpha[i,1]) = 0 and false then # Sonderregel (eq. 20)\n # Parameter mY fällt weg, also bleiben mX und mZ übrig\n # TODO: Unklar, was das für das Programm heißt. Folgendes noch falsch.\n Paramvec[ii, 1] := mX[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mZ[i, 1]: ii:= ii+1:\n else\n Paramvec[ii, 1] := mX[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mY[i, 1]: ii:= ii+1:\n Paramvec[ii, 1] := mZ[i, 1]: ii:= ii+1:\n end if:\n Paramvec[ii, 1] := m[i, 1]: ii:= ii+1:\n end if:\nend do:\n\n# Entfernung von Nullelementen\n# Durch Entfernung der Nullelemente erfolgt 'beta_b' aus [HRL_IDR] (22)\np := 0:\nfor i to MPV_n_max do \n if Paramvec[i, 1] = 0 then \n p := p+1 \n end if:\nend do:\n# Determine size of matrix dependent on number of Zeroes\nParamvec_size := MPV_n_max-p:\nParamvec2 := Matrix(Paramvec_size, 1):\np := 0:\nfor i to MPV_n_max do \n # count Zeroes\n if Paramvec[i, 1] = 0 then \n p := p+1:\n else \n # Shift by number of currently found Zeroes\n Paramvec2[i-p, 1] := Paramvec[i, 1]:\n end if:\nend do: \nprintf(\"Dimension des Minimalparametervektors: %dx1\\n\", Paramvec_size):\nParamvec2;\n# Export - Minimalparametervektor\nsave Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_maple\", robot_name):\nsave Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_maple_geom\", robot_name): # zum Testen gegen andere Implementierung\nif codegen_act then\n MatlabExport(Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_matlab.m\", robot_name), codegen_opt):\nend if;\n# Minimal geometrievektor t_i und u_i\n# Markieren von t_mZ, t_YY, t_m, u_mZ, u_YY, u_m_j\n# Anwendung von [HRL_IDR] Regel 3 (S. 5) auf die Geometrievektoren t und u der Energien T und U\n# Der Basis-Körper wird nicht gezählt. Daher ignorieren der ersten zehn Einträge in t_ges\n# [GautierKhalil1990], p.369 (rechts: \"As a conclusion ...\"\nfor i from 0 to NJ-1 do \n if sigma[i+1,1] = 0 then: # Drehgelenk\n t_ges[1,i*10+ 4]:=REMOVE; # YY\n t_ges[1,i*10+ 9]:=REMOVE; # mZ\n t_ges[1,i*10+10]:=REMOVE; # m\n u_ges[1,i*10+ 4]:=REMOVE; # YY\n u_ges[1,i*10+ 9]:=REMOVE; # mZ\n u_ges[1,i*10+10]:=REMOVE; # m\n else: # Schubgelenk\n u_ges[1,i*10+ 1]:=REMOVE; # XX\n u_ges[1,i*10+ 2]:=REMOVE; # XY\n u_ges[1,i*10+ 3]:=REMOVE; # XZ\n u_ges[1,i*10+ 4]:=REMOVE; # YY\n u_ges[1,i*10+ 5]:=REMOVE; # YZ\n u_ges[1,i*10+ 6]:=REMOVE; # ZZ\n t_ges[1,i*10+ 1]:=REMOVE; # XX\n t_ges[1,i*10+ 2]:=REMOVE; # XY\n t_ges[1,i*10+ 3]:=REMOVE; # XZ\n t_ges[1,i*10+ 4]:=REMOVE; # YY\n t_ges[1,i*10+ 5]:=REMOVE; # YZ\n t_ges[1,i*10+ 6]:=REMOVE; # ZZ\n # Sonderregel (eq. 19-20). Parameter zusammengelegt in Parametervektor. Werden daher hier entfernt.\n # Fälle vorerst auskommentiert (siehe oben). TODO: Das hat alles nicht funktioniert.\n if sin(alpha[i+1,1]) = 0 and false then # deaktiviert!\n u_ges[1,i*10+ 7]:=REMOVE; # mX\n t_ges[1,i*10+ 7]:=REMOVE; # mX\n u_ges[1,i*10+ 8]:=REMOVE; # mY\n t_ges[1,i*10+ 8]:=REMOVE; # mY\n end if:\n if cos(alpha[i+1,1]) = 0 and false then # deaktiviert!\n u_ges[1,i*10+ 7]:=REMOVE; # mX\n t_ges[1,i*10+ 7]:=REMOVE; # mX\n u_ges[1,i*10+ 9]:=REMOVE; # mZ\n t_ges[1,i*10+ 9]:=REMOVE; # mZ\n end if:\n end if:\nend do: \n# Entfernungen von markierten Elementen\n# Durch Entfernung der markierten Elemente, äquivalent zum Minimalparametervektor beta_b, haben t und u die gleiche Spaltenanzahl wie 'C_b'.\np:=0:\nfor i from 1 to 10*NJ do #Nullen Zählen um die Matrixgröße von t_ges zu bestimmen \n if t_ges[1,i]=REMOVE and u_ges[1,i]=REMOVE then \n p:=p+1;\n end if\nend do: \nsize_Matrix:=10*NJ-p: \nt_ges_minpar:=Matrix(1,size_Matrix):\nu_ges_minpar:=Matrix(1,size_Matrix):\nprintf(\"Dimension der Regressormatrix: 1x%d\\n\", size_Matrix):\n\nif size_Matrix <> Paramvec_size then\n printf(\"Achtung: Dimension der Regressormatrix passt nicht zu der des Parametervektors!\\n\"):\nend if:\n\np:=0:\nfor i from 1 to 10*NJ do #Nullen Zählen \n if t_ges[1,i]=REMOVE and u_ges[1,i]=REMOVE then \n p:=p+1; \n else \n t_ges_minpar[1,i-p]:=t_ges[1,i]; #Um die Anzahl der im Iterationsschritt gezählten Nullen verschieben\n u_ges_minpar[1,i-p]:=u_ges[1,i]; #Um die Anzahl der im Iterationsschritt gezählten Nullen verschieben\n end if\nend do: \nsave t_ges_minpar, sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_minpar_maple.m\", robot_name):\nsave u_ges_minpar, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_minpar_maple.m\", robot_name):\n# Zum symbolischen Testen des minimierten Regressors gegen den ursprünglichen\n(*\nread sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_maple.m\", robot_name):\nt_ges := t_ges: # Variable wurde im Arbeitsblatt verändert. Neu laden.\nread sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_maple.m\", robot_name):\nu_ges := u_ges:\n# Muss Null sein.\ntest_u := simplify(u_ges_minpar.Paramvec2 - u_ges.PV2_vec(11..,..)):\ntest_t := simplify(t_ges_minpar.Paramvec2 - t_ges.PV2_vec(11..,..)):\n*)\n;\n# Export\nif codegen_act then\n MatlabExport(convert_t_s(t_ges_minpar), sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_minpar_matlab.m\", robot_name), codegen_opt):\nend if:\nif codegen_act then\n MatlabExport(convert_t_s(u_ges_minpar), sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_minpar_matlab.m\", robot_name), codegen_opt):\nend if:\n\n\n", "meta": {"hexsha": "e905e242e9f0d1284146101bf368ef703f5db576", "size": 19783, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_energy/robot_chain_fixb_rotmat_energy_regressor.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_energy/robot_chain_fixb_rotmat_energy_regressor.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_energy/robot_chain_fixb_rotmat_energy_regressor.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 47.6698795181, "max_line_length": 252, "alphanum_fraction": 0.6361017035, "num_tokens": 7424, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8577681122619883, "lm_q2_score": 0.6959583187272712, "lm_q1q2_score": 0.5969708532677186}} {"text": "`is_element/permutations` := (n::nonnegint) -> proc(s)\n type(s,list(posint)) and\n nops(s) = n and\n min(op(s)) = 1 and\n max(op(s)) = n and \n nops({op(s)}) = n;\nend:\n\n`is_equal/permutations` := (n) -> (s,t) -> evalb(s = t);\n\n`is_leq/permutations` := NULL;\n\n`random_element/permutations` := (n::nonnegint) ->\n combinat[randperm](n);\n \n`list_elements/permutations` := (n::nonnegint) ->\n combinat[permute](n);\n\n`count_elements/permutations` := (n::nonnegint) -> n!;\n\n`id/permutations` := proc(n::nonnegint) local i; [seq(i,i=1..n)]; end:\n\n`o/permutations` := (n::nonnegint) -> proc()\n local i;\n apply_assoc((s,t) -> [seq(s[t[i]],i=1..n)],\n [seq(i,i=1..n)])(args);\nend:\n\n`inv/permutations` := (n::nonnegint) -> proc(s)\n local i,t;\n t := table();\n for i from 1 to n do t[s[i]] := i; od;\n return [seq(t[i],i=1..n)];\nend:\n\n`length_set/permutations` := (n::nonnegint) -> proc(s)\n local L,i,j;\n\n L := [seq(seq([i,j],j=i+1..n),i=1..n-1)];\n L := select(ij -> s[ij[1]] > s[ij[2]],L);\n return L;\nend:\n\n`unordered_length_set/permutations` := (n::nonnegint) -> (s) ->\n map(u -> {op(u)},{op(`length_set/permutations`(n)(s))});\n\n`length/permutations` := (n::nonnegint) -> proc(s)\n nops(`length_set/permutations`(n)(s));\nend:\n\n`sgn/permutations` := (n::nonnegint) -> proc(s)\n local i,j;\n return signum(mul(mul(s[j]-s[i],j=i+1..n),i=1..n-1));\nend:\n\n`is_even/permutations` := (n::nonnegint) -> (s) ->\n evalb(`sgn/permutations`(n)(s) = 1);\n\n`is_odd/permutations` := (n::nonnegint) -> (s) ->\n evalb(`sgn/permutations`(n)(s) = -1);\n\n`switch/permutations` := (n::nonnegint) -> proc(i::posint)\n local j;\n if i >= n then error(\"Should have 1 <= i < n\"); fi;\n\n return [seq(j,j=1..i-1),i+1,i,seq(j,j=i+2..n)];\nend:\n\n`t/permutations` := (n::nonnegint) -> proc(k::posint)\n local i;\n [seq(i,i=1..k-1),seq(i+1,i=k..n-1),k];\nend:\n\n`t_inv/permutations` := (n::nonnegint) -> proc(k::posint)\n local i;\n [seq(i,i=1..k-1),n,seq(i-1,i=k+1..n)];\nend:\n\n`t_word/permutations` := (n::nonnegint) -> proc(k::posint)\n local i;\n [seq(i,i=k..n-1)];\nend:\n\n`to_coxeter_word/permutations` := (n::nonnegint) -> proc(w)\n local m,v;\n\n if n <= 1 then return []; fi;\n\n m := w[n];\n v := `o/permutations`(n)(`t_inv/permutations`(n)(m),w);\n v := [op(1..(n-1),v)];\n return [op(`t_word/permutations`(n)(m)),\n op(`to_coxeter_word/permutations`(n-1)(v))];\nend:\n\n`from_coxeter_word/permutations` := (n::nonnegint) -> proc(x)\n `o/permutations`(n)(op(map(`switch/permutations`(n),x)));\nend:\n\n# Here are two kinds of Coxeter words that reduce to the identity.\n# They are used in the proof of the completeness of the Coxeter relations.\n\n`long_coxeter_rel0/permutations` := (n) -> proc(l)\n local i;\n [seq(i,i=l..n-1),seq(i,i=l..n-1),seq(i,i=n-2..l,-1),seq(i,i=n-1..l+1,-1)];\nend:\n\n`long_coxeter_rel1/permutations` := (n) -> proc(k,l)\n local i;\n `if`(k <= l, \n [seq(i,i=k..n-1),seq(i,i=l..n-1),seq(i,i=n-2..k,-1),seq(i,i=n-1..l+1,-1)],\n [seq(i,i=k..n-1),seq(i,i=l..n-1),seq(i,i=n-2..k-1,-1),seq(i,i=n-1..l,-1)]);\nend:\n\n`coxeter_reduce_once/permutations` := (n) -> proc(x)\n local i,j,k,l,l0,l1,m,p,d,y,z,i0,p0,d0,z0,z1,z2;\n \n # Move s[p] left of s[q] if p < q - 1\n y := x;\n m := nops(y);\n z := [];\n i := 1;\n while i <= m do\n j := i + 1;\n while j <= m and y[j] < y[i] - 1 do\n z := [op(z),y[j]];\n j := j + 1;\n od;\n z := [op(z),y[i]];\n i := j;\n od;\n y := z;\n m := nops(y);\n \n z := [];\n i := 1;\n j := 1;\n while i <= m do \n while (j < m and y[j+1] = y[i]) do j := j + 1; od;\n if modp(j - i + 1,2) = 1 then z := [op(z),y[i]]; fi;\n i := j + 1;\n j := i;\n od;\n y := z;\n m := nops(y);\n\n d := table():\n l := table():\n i0 := 0;\n l0 := 0;\n\n for i from 1 to m do\n if i < m and abs(y[i+1] - y[i]) = 1 then\n d[i] := y[i+1] - y[i];\n j := i + 1;\n while j <= m and y[j] = y[i] + modp(j - i,2) * d[i] do j := j + 1; od;\n l[i] := j - i;\n else\n d[i] := 0;\n l[i] := 1;\n fi;\n if l[i] > l0 then\n i0 := i;\n l0 := l[i];\n fi;\n od:\n\n if l0 < 3 then return y; fi;\n\n z0 := [seq(y[i],i=1..i0-1)];\n z2 := [seq(y[i],i=i0+l0..m)];\n l1 := mods(l0,6);\n p0 := y[i0];\n d0 := d[i0];\n \n if l1 = 0 then z1 := []; \n elif l1 = 1 then z1 := [p0]; \n elif l1 = 2 then z1 := [p0,p0+d0];\n elif l1 = 3 and d0 = 1 then z1 := [p0,p0+1,p0];\n elif l1 = 3 and d0 = -1 then z1 := [p0-1,p0,p0-1];\n elif l1 = -2 then z1 := [p0+d0,p0];\n elif l1 = -1 then z1 := [p0+d0];\n fi;\n\n return [op(z0),op(z1),op(z2)];\nend:\n\n`coxeter_reduce/permutations` := (n) -> proc(w)\n local u,v;\n u := NULL;\n v := w;\n while u <> v do\n u := v;\n v := `coxeter_reduce_once/permutations`(n)(u);\n od:\n return u;\nend:", "meta": {"hexsha": "3face57a89188080cafabdae5327c864c17ba04f", "size": 4592, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/permutations.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/permutations.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/permutations.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": 23.3096446701, "max_line_length": 82, "alphanum_fraction": 0.5263501742, "num_tokens": 1844, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8267117983401363, "lm_q2_score": 0.7217432182679956, "lm_q1q2_score": 0.5966736339141322}} {"text": "######################################################################\n# simplex_interior(A) is the set of maps x : A -> (0,1] with sum = 1.\n\n`is_element/simplex_interior` := (A::set) -> proc(x)\n local a,u;\n global reason;\n\n if not `is_element/simplex`(A)(x) then\n reason := [convert(procname,string),\"x is not in the A-simplex\",x,A,reason];\n return false;\n fi;\n\n for a in A do if x[a] = 0 then\n reason := [convert(procname,string),\"x[a] = 0\",a];\n return false;\n fi; od;\n\n return true;\nend;\n\n`is_equal/simplex_interior` := (A::set) -> proc(x,y)\n `is_equal/simplex`(A)(x,y);\nend;\n\n`is_leq/simplex_interior` := NULL;\n\n`random_element/simplex_interior` := (A::set) -> proc()\n local x,a,r1,r2,u;\n if A = {} then return FAIL; fi;\n\n r1 := rand(1..5); \n r2 := rand(1..5);\n x := table();\n u := 0;\n for a in A do \n x[a] := r1()/r2();\n u := u + x[a];\n od;\n for a in A do x[a] := x[a]/u; od;\n\n return eval(x);\nend;\n\n`list_elements/simplex_interior` := NULL;\n`count_elements/simplex_interior` := NULL;\n", "meta": {"hexsha": "6e1e9c054a311ac1f4c324e34f20710e7b8493ba", "size": 996, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplex_interior.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/simplex_interior.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/simplex_interior.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": 21.652173913, "max_line_length": 78, "alphanum_fraction": 0.563253012, "num_tokens": 320, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.837619947119304, "lm_q2_score": 0.7122321720225278, "lm_q1q2_score": 0.5965798742661768}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2020 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(* prefix:\n gga_c_lm_params *params;\n\n assert(p->params != NULL);\n params = (gga_c_lm_params * )(p->params);\n*)\n\n$define lda_c_vbh_params\n$include \"lda_c_hl.mpl\"\n\n(* Constant after equation (2.25) in Hu-Langreth. It is equal to the\n numerical constant in equation (12) of the Langreth-Mehl paper,\n 4.28e-3, once one accounts for the factor 2 from the conversion\n from Rydberg to Hartree *)\nlm_J := Pi/(16*(3*Pi^2)^(4/3)):\n\n(* Equation (2.23) in Hu-Langreth *)\nlm_d := z -> sqrt(opz_pow_n(z, 5/3) + opz_pow_n(-z, 5/3))/sqrt(2):\n\n(* F parameter, see after eqn (2.25) in Hu-Langreth; this yields\n0.26181 which is rounds to 0.262 given by Langreth and Mehl. Hu and\nLangreth say the external parameter f = 0.15 for comparison with LM,\nbut that f = 0.17 is preferable *)\nlm_F := 2*sqrt(3)*params_a_lm_f / (2*(3/Pi)^(1/6)):\n\n(* First term in eqn (2.25) in Hu-Langreth *)\nlm_t1 := (z, xs0, xs1) ->\n -7/(9*2^(5/3)) * (xs0^2*opz_pow_n(z, 4/3) + xs1^2*opz_pow_n(-z, 4/3)):\n\n(* Second term in eqn (2.25) in Hu-Langreth *)\nlm_t2 := (rs, z, xt) ->\n 2/lm_d(z) * exp(-lm_F*xt*n_total(rs)^(1/6)) * xt^2:\n\nf := (rs, z, xt, xs0, xs1) ->\n + hl_f(rs, z)\n + lm_J*(lm_t1(z, xs0, xs1) + lm_t2(rs, z, xt))*n_total(rs)^(1/3):\n", "meta": {"hexsha": "55f01a4299a11d1bcf02dc3a84e68ab6f6c9621a", "size": 1505, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_lm.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_c_lm.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_c_lm.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": 32.0212765957, "max_line_length": 72, "alphanum_fraction": 0.6378737542, "num_tokens": 580, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297834483234, "lm_q2_score": 0.6619228891883799, "lm_q1q2_score": 0.5960812760603004}} {"text": "(*\n Copyright (C) 2020 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: mgga_exc *)\n\n(* prefix:\n mgga_x_jk_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_jk_params * ) (p->params);\n*)\n\n$include \"gga_x_b88.mpl\"\n\n(* equation 11 *)\ny := (x,u) -> x^2 - u:\n(* equation 5 *)\ngBecke := x -> b88_f(x)-1:\n(* equation 24 *)\njk_f := (x,u,t) -> 1 + gBecke(x)/(1 + 2*y(x,u)/x^2):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(jk_f, rs, z, xs0, xs1, u0, u1, t0, t1):", "meta": {"hexsha": "6e8101cb218a017d25bbaf8c7fa1e097e5aa3d6e", "size": 662, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_jk.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/mgga_exc/mgga_x_jk.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/mgga_exc/mgga_x_jk.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": 23.6428571429, "max_line_length": 68, "alphanum_fraction": 0.6042296073, "num_tokens": 253, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297914570319, "lm_q2_score": 0.6619228758499942, "lm_q1q2_score": 0.5960812693498341}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_mgga_x *)\n\nbr89_a := [0, 1, 0, -2, 0, 1]:\nfw := t -> mgga_series_w(br89_a, 6, t):\n\nbr89_gamma := 0.8:\nbr89_Q := (x, t, u) -> (u - 4*t*br89_gamma*Fermi_D(x, t))/6:\nbr89_y := (x, t, u) -> 2*Pi^(2/3)/(3*br89_Q(x, t, u)):\n\n(* lower piece *)\npgk_a1 := 1.5255251812009530:\npgk_a2 := 0.4576575543602858:\npgk_a3 := 0.4292036732051034:\n\npgk_b := [0.4771976183772063, -1.7799813494556270, 3.8433841862302150,\n -9.5912050880518490, 2.1730180285916720, -30.425133851603660]:\n\npgk_c := [0.7566445420735584, -2.6363977871370960, 5.4745159964232880,\n -12.657308127108290, 4.1250584725121360, -30.425133957163840]:\n\npgk_d := [0.00004435009886795587, 0.58128653604457910, 66.742764515940610,\n 434.26780897229770, 824.7765766052239000, 1657.9652731582120]:\n\npgk_e := [0.00003347285060926091, 0.47917931023971350, 62.392268338574240,\n 463.14816427938120, 785.2360350104029000, 1657.962968223273000000]:\n\npgk_UB := 2.085749716493756:\n\npgk_x_lower := y -> (-arctan(pgk_a1*y + pgk_a2) + pgk_a3) *\n add(pgk_c[i]*y^(i-1), i=1..6)/add(pgk_b[i]*y^(i-1), i=1..6):\n\npgk_x_upper := y -> (arccsch(pgk_UB*y) + 2) *\n add(pgk_d[i]*y^(i-1), i=1..6)/add(pgk_e[i]*y^(i-1), i=1..6):\n \npgk_x := (x, t, u) -> convert(piecewise(\n br89_y(x, t, u) <= 0, pgk_x_lower(br89_y(x, t, u)),\n pgk_x_upper(br89_y(x, t, u))), 'Heaviside'):\n\nbr89_v_full := x -> exp(x/3.0)*(1.0 - exp(-x)*(1.0 + x/2.0))/x:\nbr89_v_expa := x -> 1/2 + x/6 - x^2/18:\n\nbr89_v := (x, t, u) ->\n -2*Pi^(1/3)/X_FACTOR_C * br89_v_full(pgk_x(x, t, u)):\n\nf := (rs, x, t, u) -> -br89_v(x, t, u)/2:\n", "meta": {"hexsha": "b9f8cf15821d2814917bdbc635b95893c8a57960", "size": 1839, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_br89_explicit.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_x_br89_explicit.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_x_br89_explicit.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 34.0555555556, "max_line_length": 75, "alphanum_fraction": 0.6264274062, "num_tokens": 826, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070084811307, "lm_q2_score": 0.6548947357776795, "lm_q1q2_score": 0.5958933099015089}} {"text": "with(plots):\nwith(plottools):\n\ngreat_arc := proc(u,v,hue)\n local w,r,s,t,d,i;\n w := [u[2]*v[3]-u[3]*v[2],u[3]*v[1]-u[1]*v[3],u[1]*v[2]-u[2]*v[1]];\n r := evalf(sqrt(u[1]^2+u[2]^2+u[3]^2));\n d := u[1]*v[1]+u[2]*v[2]+u[3]*v[3];\n w := [v[1] - d * u[1]/r^2,v[2] - d * u[2]/r^2,v[3] - d * u[3]/r^2];\n s := evalf(sqrt(w[1]^2+w[2]^2+w[3]^2));\n w := [r*w[1]/s,r*w[2]/s,r*w[3]/s]; \n t := evalf(arccos(d/r^2))/10;\n return(CURVES(\n [seq([cos(i*t)*u[1]+sin(i*t)*w[1],\n cos(i*t)*u[2]+sin(i*t)*w[2],\n cos(i*t)*u[3]+sin(i*t)*w[3]],i=0..10)],\n COLOR(HUE,hue))); \nend:\n\n", "meta": {"hexsha": "966d1af10216e2c7b56a82adfe339b1c3f261788", "size": 592, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/plots.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/plots.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/plots.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": 29.6, "max_line_length": 68, "alphanum_fraction": 0.4290540541, "num_tokens": 304, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086179018818865, "lm_q2_score": 0.6548947223065755, "lm_q1q2_score": 0.5950490685357214}} {"text": "# The function brent_fsolve uses Brent's algorithm to find a root of\n# a real valued function of one variable. This code is based on the\n# Matlab implementation by John Burkardt, which is in turn based on the \n# original Fortran implementation by Richard Brent. However, this\n# version is designed for the case where we want to retain a lot\n# of additional information that is generated in the process of \n# evaluating the relevant function.\n#\n# The first argument F should be a function which accepts a single\n# real argument t and returns a table F(t). This should contain an \n# entry F(t)[\"err\"], which we want to be zero. The second and third\n# arguments should be numbers a and b such that F(a)[\"err\"] and \n# F(b)[\"err\"] have opposite signs. Other entries in F(t) can contain\n# auxiliary information generated during the calculation.\n#\n# If F(a) and/or F(b) have already been computed, then they can be \n# supplied as the arguments Fa_ and Fb_. Otherwise, these arguments\n# should be set to false.\n\n#@ brent_fsolve \nbrent_fsolve := proc(F,a,b,Fa_,Fb_,tol_,epsilon_) \n local tol,tol1,epsilon,c,sa,sb,sc,Fa,Fb,Fc,fa,fb,fc,d,e,m,p,q,r,s,steps,ret;\n\n tol := `if`(nargs > 5,tol_,10.^(-20));\n epsilon := `if`(nargs > 6,epsilon_,10.^(2 - Digits));\n\n sa := a;\n sb := b;\n if nargs < 4 or Fa_ = false then Fa := eval(F(sa)); else Fa := eval(Fa_); fi;\n if nargs < 5 or Fb_ = false then Fb := eval(F(sb)); else Fb := eval(Fb_); fi;\n fa := Fa[\"err\"];\n fb := Fb[\"err\"];\n\n if not((fa <= 0 and 0 <= fb) or \n (fb <= 0 and 0 <= fa)) then\n error(\"function has the same sign at endpoints\");\n fi;\n\n c := sa;\n fc := fa;\n Fc := eval(Fa);\n e := sb - sa;\n d := e;\n\n steps := 0;\n \n while true do\n steps := steps+1;\n \n if ( abs ( fc ) < abs ( fb ) ) then\n sa := sb;\n sb := c;\n c := sa;\n fa := fb;\n fb := fc;\n fc := fa;\n Fa := eval(Fb);\n Fb := eval(Fc);\n Fc := eval(Fa);\n fi;\n\n tol1 := 2.0 * epsilon * abs ( sb ) + tol;\n m := 0.5 * ( c - sb );\n\n if ( abs ( m ) <= tol or fb = 0.0 ) then\n break;\n fi;\n\n if ( abs ( e ) < tol or abs ( fa ) <= abs ( fb ) ) then\n e := m;\n d := e;\n else\n s := fb / fa;\n if ( sa = c ) then\n p := 2.0 * m * s;\n q := 1.0 - s;\n else\n q := fa / fc;\n r := fb / fc;\n p := s * ( 2.0 * m * q * ( q - r ) - ( sb - sa ) * ( r - 1.0 ) );\n q := ( q - 1.0 ) * ( r - 1.0 ) * ( s - 1.0 );\n fi;\n\n if ( 0.0 < p ) then\n q := - q;\n else\n p := - p;\n fi;\n\n s := e;\n e := d;\n\n if ( 2.0 * p < 3.0 * m * q - abs ( tol * q ) and p < abs ( 0.5 * s * q ) ) then\n d := p / q;\n else\n e := m;\n d := e;\n fi;\n fi;\n\n sa := sb;\n fa := fb;\n Fa := eval(Fb);\n\n if ( tol < abs ( d ) ) then\n sb := sb + d;\n elif ( 0.0 < m ) then\n sb := sb + tol;\n else\n sb := sb - tol;\n fi;\n\n Fb := eval(F(sb));\n fb := Fb[\"err\"];\n\n if ( ( 0.0 < fb and 0.0 < fc ) or ( fb <= 0.0 and fc <= 0.0 ) ) then\n c := sa;\n fc := fa;\n Fc := eval(Fa);\n e := sb - sa;\n d := e;\n fi;\n od;\n\n ret := eval(Fb);\n ret[\"steps\"] := steps;\n \n return [sb,eval(ret)];\nend:\n\n\n", "meta": {"hexsha": "31e9bbd39db73cc3bd443b20974d888c2fd42504", "size": 3031, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/brent.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/brent.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/brent.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": 22.9621212121, "max_line_length": 82, "alphanum_fraction": 0.5288683603, "num_tokens": 1078, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920068519378, "lm_q2_score": 0.7431680029241321, "lm_q1q2_score": 0.5950486796894701}} {"text": "######################################################################\n# prime_simplex(A) is the set of maps x : A -> [0,1] with max = 1.\n\n`is_element/prime_simplex` := (A::set) -> proc(x)\n local a,u,v;\n global reason;\n\n if not type(x,table) then\n reason := [convert(procname,string),\"x is not a table\",x];\n return false;\n fi;\n\n if map(op,{indices(x)}) <> A then\n reason := [convert(procname,string),\"x is not indexed by A\",x,A];\n return false;\n fi;\n\n v := 0;\n\n for a in A do\n u := x[a];\n\n if not (`is_element/RR`(u) and u >= 0 and u <= 1) then\n reason := [convert(procname,string),\"x[a] is not in the unit interval\",a,u];\n return false;\n fi;\n\n v := max(u,v);\n od;\n\n if simplify(v - 1) <> 0 then\n reason := [convert(procname,string),\"max(x[a] : a in A) <> 1\",a,v];\n return false;\n fi;\n\n return true;\nend;\n\n`is_equal/prime_simplex` := (A::set) -> proc(x,y)\n local a;\n global reason;\n\n for a in A do\n if simplify(x[a] - y[a]) <> 0 then\n reason := [convert(procname,string),\"x[a] <> y[a]\",a,x[a],y[a]];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n`is_leq/prime_simplex` := NULL;\n\n`random_element/prime_simplex` := (A::set) -> proc(d::posint := 5)\n local x,a,r1,r2,u;\n if A = {} then return FAIL; fi;\n\n r1 := rand(0..d); \n r2 := rand(1..d);\n x := table();\n u := 0;\n while u = 0 do\n for a in A do \n x[a] := r1()/r2();\n u := max(u,x[a]);\n od;\n od;\n\n for a in A do x[a] := x[a]/u; od;\n\n return eval(x);\nend;\n\n`list_elements/prime_simplex` := NULL;\n`count_elements/prime_simplex` := NULL;\n\n`phi/nonempty_subsets/prime_simplex` := (A::set) -> proc(U)\n local x,a;\n\n x := table();\n for a in A do x[a] := 0; od;\n for a in U do x[a] := 1; od;\n\n return eval(x);\nend;\n\n`supp/prime_simplex` := (A::set) -> proc(x)\n select(a -> x[a] > 0,A);\nend:\n\n`functor/prime_simplex` := (A::set,B::set) -> (f) -> proc(x)\n local a,b,y;\n \n y := table():\n for b in B do y[b] := 0; od:\n for a in A do y[f[a]] := max(y[f[a]],x[a]); od:\n return eval(y);\nend:\n", "meta": {"hexsha": "9ad69b10cf7604c0d6ae897355223a912cd188df", "size": 1951, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/prime_simplex.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/prime_simplex.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/prime_simplex.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": 19.51, "max_line_length": 79, "alphanum_fraction": 0.5463864685, "num_tokens": 666, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8267117769928211, "lm_q2_score": 0.7185944046238982, "lm_q1q2_score": 0.5940704571837212}} {"text": "with(DifferentialAlgebra):\nring_diff := DifferentialRing(blocks = [[v, x, z, w, y], [y2, y1] ], derivations = [t]):\nsys := [\ndiff(v(t), t) - (k*y(t) - v(t)*u),\ndiff(x(t), t) - (lm - x(t)*d - x(t)*v(t)*beta),\ndiff(z(t), t) - (c*w(t)*q*y(t) - h*z(t)),\ndiff(w(t), t) - (-b*w(t) + c*w(t)*x(t)*y(t) - c*w(t)*q*y(t)),\ndiff(y(t), t) - (x(t)*v(t)*beta - a*y(t)),\ny2(t) - (z(t)),\ny1(t) - (w(t))\n];\nres := CodeTools[CPUTime](RosenfeldGroebner(sys, ring_diff, singsol=none));", "meta": {"hexsha": "d570952a7b32fc00c7bac817c686c6da1c92ebf2", "size": 464, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/RosenfeldGroebner/HIV.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/RosenfeldGroebner/HIV.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/RosenfeldGroebner/HIV.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 38.6666666667, "max_line_length": 88, "alphanum_fraction": 0.5107758621, "num_tokens": 198, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218391455084, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5939251949956249}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_gga_c *)\n(* prefix:\n gga_x_hjs_b88_v2_params *params;\n \n assert(p->params != NULL);\n params = (gga_x_hjs_b88_v2_params * )(p->params);\n*)\n\n\nparams_a_a := [0.0253933, -0.0673075, 0.0891476, -0.0454168, -0.00765813, 0.0142506]:\nparams_a_b := [-2.6506, 3.91108, -3.31509, 1.54485, -0.198386, \n -0.136112, 0.0647862, 0.0159586, -0.000245066]:\n\n\nxi := 1/(exp(20) - 1):\nfs := s -> -log((exp(-s) + xi)/(1 + xi)):\n\n$include \"gga_x_hjs.mpl\"\n\nf := (rs, z, xt, xs0, xs1) -> \n f_lda(rs, z)*f1(rs, z, fs(X2S*xs0)) + f_lda(rs, -z)*f1(rs, -z, fs(X2S*xs1)):", "meta": {"hexsha": "af694d7db500de3561ae7ce7e4feec8ef5d3de8c", "size": 799, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_hjs_b88_v2.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_hjs_b88_v2.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_hjs_b88_v2.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 27.5517241379, "max_line_length": 85, "alphanum_fraction": 0.6257822278, "num_tokens": 340, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8615382094310357, "lm_q2_score": 0.6893056295505783, "lm_q1q2_score": 0.593863137833738}} {"text": "`is_element/morse_matchings` := (A::set) -> (R) -> proc(M)\n global reason;\n local e,H,F;\n \n if not(type(M,set)) then\n reason := [\"is_element/morse_matchings\",\"M is not a set\",M];\n return false;\n fi;\n\n for e in M do \n if not(type(e,list)) and nops(e) = 2 then\n reason := [\"is_element/morse_matchings\",\"M is not a set of lists of length 2\",M,e];\n return false;\n fi;\n\n if {op(e)} minus A <> {} then\n reason := [\"is_element/morse_matchings\",\"M is not a set of lists of length 2 in A\",M,e];\n return false;\n fi;\n od:\n\n H := `hasse_diagram/partord`(A)(R);\n\n if M minus H <> {} then\n reason := [\"is_element/morse_matchings\",\"M is not a subset of the Hasse diagram\",M,H];\n return false;\n fi;\n\n for e in M do\n if select(f -> {op(f)} intersect {op(e)} <> {}, M) <> {e} then\n reason := [\"is_element/morse_matchings\",\"edges in M are not disjoint\",M,e];\n return false;\n fi;\n od:\n\n F := M union map(e -> [e[2],e[1]],H minus M);\n F := `transitive_closure/autorel`(A)(F);\n F := F intersect `op/autorel`(A)(F);\n if F minus `id/autorel`(A) <> {} then\n reason := [\"is_element/morse_matchings\",\"M has cycles\",M,F];\n return false;\n fi;\n\n return true;\nend:\n", "meta": {"hexsha": "9621a11859680c9dddd2b9fd0b4e53f646bfa3a0", "size": 1158, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/morse.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/morse.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/morse.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": 25.1739130435, "max_line_length": 91, "alphanum_fraction": 0.6139896373, "num_tokens": 377, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8615382094310357, "lm_q2_score": 0.6893056231680122, "lm_q1q2_score": 0.5938631323349135}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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$include \"gga_c_gapc.mpl\"\n\n(* The two parameters were fixed by fitting to the exact correlation\nenergy per particle of the He atom *)\ngaploc_b := 14.709046:\ngaploc_a1 := 6.54613 + 2:\n\ngaploc_alpha := t -> (gaploc_a1 + 3*t^3)/(1 + t^3):\ngaploc_s := xt -> X2S*xt*2^(1/3):\n\n(* override definition of gap_G *)\n(* The pre-factor is completely different from the one in\n Equation (7). I used the \"gfac\" from the original code. *)\ngap_G := (rs, z, xt, par) -> (9*Pi/4)^(2/3)/2.0\n * gaploc_s(xt)^(gaploc_alpha(gap_t(rs, z, xt)))/rs^2\n * (gaploc_b + gaploc_s(xt)^2)/(1 + gaploc_s(xt)^(gaploc_alpha(gap_t(rs, z, xt)))):\n\n", "meta": {"hexsha": "b46004339ff79041ef470bd61e3e5d1662ea1210", "size": 882, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_gaploc.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_c_gaploc.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_c_gaploc.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": 31.5, "max_line_length": 84, "alphanum_fraction": 0.656462585, "num_tokens": 307, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070011518829, "lm_q2_score": 0.6513548782017745, "lm_q1q2_score": 0.5926723639102266}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\nux := (mgamma, x) -> mgamma*x^2/(1 + mgamma*x^2):\n\n(* article uses t = 2 tau convention *)\nwx_ss := (t, dummy) -> (K_FACTOR_C - t)/(K_FACTOR_C + t):\nwx_os := (ts0, ts1) -> (K_FACTOR_C*(ts0 + ts1) - 2*ts0*ts1)/(K_FACTOR_C*(ts0 + ts1) + 2*ts0*ts1):\n\nb97mv_g := (mgamma, wx, cc, n, xs, ts0, ts1) ->\n add(cc[i][1]*wx(ts0, ts1)^cc[i][2]*ux(mgamma, xs)^cc[i][3], i=1..n):\n\nb97mv_fpar := (lda_func, rs, z, xs0, xs1, ts0, ts1) ->\n + lda_stoll_par(lda_func, rs, z, 1) * b97mv_g(gamma_x, wx_ss, par_x, par_n, xs0, ts0, 0)\n + lda_stoll_par(f_pw , rs, z, 1) * b97mv_g(gamma_ss, wx_ss, par_ss, par_n, xs0, ts0, 0)\n + lda_stoll_par(lda_func, rs, -z, -1) * b97mv_g(gamma_x, wx_ss, par_x, par_n, xs1, ts1, 0)\n + lda_stoll_par(f_pw , rs, -z, -1) * b97mv_g(gamma_ss, wx_ss, par_ss, par_n, xs1, ts1, 0):\n\nb97mv_fos := (rs, z, xs0, xs1, ts0, ts1) ->\n lda_stoll_perp(f_pw, rs, z)\n * b97mv_g(gamma_os, wx_os, par_os, par_n, sqrt(xs0^2 + xs1^2)/sqrt(2), ts0, ts1):\n\nf_b97mv := (lda_func, rs, z, xt, xs0, xs1, ts0, ts1) ->\n + b97mv_fpar(lda_func, rs, z, xs0, xs1, ts0, ts1)\n + b97mv_fos(rs, z, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "f59f8ad8f89d68b296bfbedec8f6c7392246eece", "size": 1440, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/b97mv.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/b97mv.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/b97mv.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 41.1428571429, "max_line_length": 97, "alphanum_fraction": 0.6270833333, "num_tokens": 631, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070084811307, "lm_q2_score": 0.6513548646660542, "lm_q1q2_score": 0.5926723563679211}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2019 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$define lda_c_pw_params\n$include \"lda_c_pw.mpl\"\n\n(* Parameters from Table 6 *)\ngap_par0 := [\n 0.04953, 1.07924, 0.07928, (* a1, a2, a3 *)\n -2.504e-2, 7.026e-3, -1.268e-3, 1.136e-4, -3.841e-6, (* b3, b4, b5, b6, b7 *)\n 0.031091, (* params_a_a of lda_c_pw *)\n 0.23878 (* pre-factor of C = 0.06483*((9*Pi)/4)^(2/3) *)\n]:\ngap_par1 := [\n 0.0471985, 1.49676, 0.00179054,\n -3.24091e-2, 9.99978e-3, -1.93483e-3, 1.79118e-4, -6.15798e-6,\n 0.015545,\n 0.064535\n]:\n\n(* Equation (20): e'(rs) *)\ngap_eps_1 := (rs, par) ->\n par[1]*rs^(3/2)/(1 + sqrt(rs)*(par[2] + par[3]*sqrt(rs) + par[1]*rs)):\n(* Equation (21): e''(rs) *)\ngap_eps_2 := (rs, par) ->\n add(par[i+1]*rs^i, i=3..7):\n\n(* Equation (19) *)\ngap_C := (rs, par) -> par[10]/rs^2:\n\n(* Equation (17) *)\ngap_c2 := (rs, z, par) ->\n + (2*f_pw(rs, z)*gap_eps_1(rs, par) - gap_C(rs, par)*gap_eps_2(rs, par))\n / (2*(gap_C(rs, par)*gap_eps_1(rs, par) - f_pw(rs, z)^2)):\n(* Equation (18) *)\ngap_c3 := (rs, z, par) ->\n - (2*gap_eps_1(rs, par)^2 - f_pw(rs, z)*gap_eps_2(rs, par))\n / (2*(gap_C(rs, par)*gap_eps_1(rs, par) - f_pw(rs, z)^2)):\n(* Equation (16) *)\ngap_c1 := (rs, z, par) ->\n - gap_C(rs, par) * gap_c3(rs, z, par):\n\n(* after Equation (6): a = 30 is a parameter fixed by minimizing the\nvariance of the correlation energy error for the noble gas atoms He,\nNe, and Ar *)\ngap_par_a := 30:\n\n(* Equation (6) *)\ngap_H := (rs, t, par) ->\n (gap_par_a + par[9]*rs*log(rs)*t^2/beta_Hu_Langreth(rs))/(gap_par_a + t^2):\n\ngap_t := (rs, z, xt) ->\n xt*n_total(rs)^(1/6)/(4*mphi(z)*(3/Pi)^(1/6)):\n\n(* Gap function, Equation (5) *)\ngap_G := (rs, z, xt, par) ->\n + mphi(z)^3*beta_Hu_Langreth(rs)*gap_t(rs, z, xt)^2\n * gap_H(rs, gap_t(rs, z, xt), par)\n / (gap_c1(rs, z, par) - gap_c2(rs, z, par)*f_pw(rs, z)):\n\n(* Correlation energy per particle, Equation (4) *)\ngap_eps := (rs, z, xt, par) ->\n + (f_pw(rs, z) + gap_c1(rs, z, par)*gap_G(rs, z, xt, par))\n / (1 + gap_c2(rs, z, par)*gap_G(rs, z, xt, par) + gap_c3(rs, z, par)*gap_G(rs, z, xt, par)^2):\n\n(* Total energy, Equation (2) *)\nf_gap := (rs, z, xt) ->\n + gap_eps(rs, 0, xt, gap_par0)\n + f_zeta(z)*(gap_eps(rs, 1, xt, gap_par1) - gap_eps(rs, 0, xt, gap_par0)):\n\nf := (rs, z, xt, xs0, xs1) ->\n f_gap(rs, z, xt):\n", "meta": {"hexsha": "8cec140ca8e7f17623cf0179e30f4c2cd4de1f16", "size": 2516, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_gapc.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_c_gapc.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_c_gapc.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": 31.0617283951, "max_line_length": 96, "alphanum_fraction": 0.5715421304, "num_tokens": 1068, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9149009549929797, "lm_q2_score": 0.6477982179521105, "lm_q1q2_score": 0.5926712082471363}} {"text": "# Generated using bssn_4d_spher_matter.mw\n\nrestx:=expand(simplify((-2*b1(t, x)*alpha(t, x)*(diff(a1(t, x), t))-2*x*alpha(t, x)*(diff(a1(t, x), t))*(diff(b1(t, x), x))+2*x*(diff(diff(b1(t, x), t), x))*alpha(t, x)*a1(t, x)+2*(diff(b1(t, x), t))*alpha(t, x)*a1(t, x)+2*beta(t, x)*alpha(t, x)*b1(t, x)*(diff(a1(t, x), x))+b1(t, x)*x*alpha(t, x)*a1(t, x)*(diff(rpsi(t, x), x))*(diff(rpsi(t, x), t))+b1(t, x)*x*alpha(t, x)*a1(t, x)*(diff(ipsi(t, x), x))*(diff(ipsi(t, x), t))-b1(t, x)*x*alpha(t, x)*a1(t, x)*beta(t, x)*(diff(rpsi(t, x), x))^2-b1(t, x)*x*alpha(t, x)*a1(t, x)*beta(t, x)*(diff(ipsi(t, x), x))^2-2*beta(t, x)*alpha(t, x)*a1(t, x)*x*(diff(diff(b1(t, x), x), x))+2*beta(t, x)*alpha(t, x)*x*(diff(a1(t, x), x))*(diff(b1(t, x), x))-4*beta(t, x)*(diff(b1(t, x), x))*alpha(t, x)*a1(t, x)-2*x*(diff(b1(t, x), t))*a1(t, x)*(diff(alpha(t, x), x))+2*beta(t, x)*a1(t, x)*x*(diff(alpha(t, x), x))*(diff(b1(t, x), x))+2*beta(t, x)*a1(t, x)*b1(t, x)*(diff(alpha(t, x), x)))/(alpha(t, x)^3*b1(t, x)*x*a1(t, x))));\n\n\nire_rpsi_direct:=\n-2*(diff(rpsi(t, x), x))*beta(t, x)*(diff(beta(t, x), x))/alpha(t, x)^2+(diff(rpsi(t, x), t))*beta(t, x)*(diff(a1(t, x), x))/(alpha(t, x)^2*a1(t, x))-(diff(rpsi(t, x), t))*beta(t, x)*(diff(alpha(t, x), x))/alpha(t, x)^3-(diff(rpsi(t, x), x))*beta(t, x)*(diff(alpha(t, x), t))/alpha(t, x)^3+(diff(rpsi(t, x), x))*beta(t, x)^2*(diff(alpha(t, x), x))/alpha(t, x)^3+2*(diff(rpsi(t, x), t))*beta(t, x)*(diff(b1(t, x), x))/(alpha(t, x)^2*b1(t, x))+2*(diff(rpsi(t, x), x))*beta(t, x)*(diff(b1(t, x), t))/(alpha(t, x)^2*b1(t, x))-2*(diff(rpsi(t, x), x))*beta(t, x)^2*(diff(b1(t, x), x))/(alpha(t, x)^2*b1(t, x))+(diff(rpsi(t, x), x))*beta(t, x)*(diff(a1(t, x), t))/(alpha(t, x)^2*a1(t, x))-(diff(rpsi(t, x), x))*beta(t, x)^2*(diff(a1(t, x), x))/(alpha(t, x)^2*a1(t, x))-2*(diff(rpsi(t, x), t))*(diff(b1(t, x), t))/(alpha(t, x)^2*b1(t, x))+2*(diff(rpsi(t, x), t))*beta(t, x)/(alpha(t, x)^2*x)-2*(diff(rpsi(t, x), x))*beta(t, x)^2/(alpha(t, x)^2*x)+(diff(rpsi(t, x), t))*(diff(alpha(t, x), t))/alpha(t, x)^3+2*beta(t, x)*(diff(diff(rpsi(t, x), t), x))/alpha(t, x)^2+(diff(rpsi(t, x), t))*(diff(beta(t, x), x))/alpha(t, x)^2-(diff(rpsi(t, x), t))*(diff(a1(t, x), t))/(alpha(t, x)^2*a1(t, x))-beta(t, x)^2*(diff(diff(rpsi(t, x), x), x))/alpha(t, x)^2+(diff(rpsi(t, x), x))*(diff(beta(t, x), t))/alpha(t, x)^2-(diff(diff(rpsi(t, x), t), t))/alpha(t, x)^2+2*(diff(rpsi(t, x), x))/(a1(t, x)^2*x)+(diff(diff(rpsi(t, x), x), x))/a1(t, x)^2-(diff(rpsi(t, x), x))*(diff(a1(t, x), x))/a1(t, x)^3+2*(diff(rpsi(t, x), x))*(diff(b1(t, x), x))/(b1(t, x)*a1(t, x)^2)-mass*rpsi(t, x)+(diff(rpsi(t, x), x))*(diff(alpha(t, x), x))/(alpha(t, x)*a1(t, x)^2);\n\nresxx:=\n(1/2)*(-alpha(t, x)^3*b1(t, x)^2*x^2*(diff(rpsi(t, x), x))^2-alpha(t, x)^3*b1(t, x)^2*x^2*(diff(ipsi(t, x), x))^2+alpha(t, x)*b1(t, x)^2*x^2*(diff(rpsi(t, x), x))^2*a1(t, x)^2*beta(t, x)^2+alpha(t, x)*b1(t, x)^2*x^2*(diff(ipsi(t, x), x))^2*a1(t, x)^2*beta(t, x)^2-2*b1(t, x)^2*a1(t, x)^2*alpha(t, x)*beta(t, x)^2-2*(diff(b1(t, x), t))^2*a1(t, x)^2*alpha(t, x)*x^2+4*b1(t, x)^2*x*alpha(t, x)^2*(diff(alpha(t, x), x))+4*(diff(b1(t, x), x))*alpha(t, x)^3*x*b1(t, x)+2*(diff(b1(t, x), x))^2*alpha(t, x)^3*x^2+2*alpha(t, x)^3*b1(t, x)^2-2*a1(t, x)^2*alpha(t, x)^3+alpha(t, x)^3*b1(t, x)^2*x^2*U(t, x)*a1(t, x)^2-alpha(t, x)*b1(t, x)^2*x^2*(diff(rpsi(t, x), t))^2*a1(t, x)^2-alpha(t, x)*b1(t, x)^2*x^2*(diff(ipsi(t, x), t))^2*a1(t, x)^2+4*a1(t, x)*beta(t, x)*b1(t, x)*x^2*alpha(t, x)*(diff(a1(t, x), t))*(diff(b1(t, x), x))-4*a1(t, x)*beta(t, x)^2*alpha(t, x)*b1(t, x)*x^2*(diff(a1(t, x), x))*(diff(b1(t, x), x))-4*a1(t, x)*beta(t, x)^2*alpha(t, x)*b1(t, x)^2*x*(diff(a1(t, x), x))+4*a1(t, x)*beta(t, x)*b1(t, x)^2*x*alpha(t, x)*(diff(a1(t, x), t))-4*b1(t, x)*x^2*a1(t, x)^2*alpha(t, x)*(diff(diff(b1(t, x), t), t))+4*b1(t, x)^2*x*a1(t, x)^2*alpha(t, x)*(diff(beta(t, x), t))-2*(diff(b1(t, x), x))^2*x^2*a1(t, x)^2*alpha(t, x)*beta(t, x)^2+4*b1(t, x)*x^2*(diff(alpha(t, x), t))*a1(t, x)^2*(diff(b1(t, x), t))-4*b1(t, x)^2*x*(diff(alpha(t, x), t))*a1(t, x)^2*beta(t, x)+4*b1(t, x)*x^2*alpha(t, x)^2*(diff(alpha(t, x), x))*(diff(b1(t, x), x))+4*b1(t, x)*x^2*a1(t, x)^2*alpha(t, x)*(diff(beta(t, x), t))*(diff(b1(t, x), x))+4*b1(t, x)*x^2*a1(t, x)^2*alpha(t, x)*beta(t, x)*(diff(diff(b1(t, x), t), x))+8*b1(t, x)*x*a1(t, x)^2*alpha(t, x)*beta(t, x)*(diff(b1(t, x), t))+4*(diff(b1(t, x), x))*x^2*a1(t, x)^2*alpha(t, x)*beta(t, x)*(diff(b1(t, x), t))-4*(diff(b1(t, x), x))*x*a1(t, x)^2*alpha(t, x)*beta(t, x)^2*b1(t, x)-4*alpha(t, x)*b1(t, x)^2*x*beta(t, x)*a1(t, x)^2*(diff(beta(t, x), x))-4*b1(t, x)*x^2*(diff(alpha(t, x), t))*a1(t, x)^2*beta(t, x)*(diff(b1(t, x), x))-4*alpha(t, x)*b1(t, x)*x^2*beta(t, x)*a1(t, x)^2*(diff(beta(t, x), x))*(diff(b1(t, x), x)))/(alpha(t, x)^3*a1(t, x)^2*b1(t, x)^2*x^2);\n\n\nrestt:=\n(1/2)*(4*b1(t, x)^2*x*a1(t, x)^3*beta(t, x)^2*(diff(alpha(t, x), x))-2*(diff(b1(t, x), x))^2*x^2*a1(t, x)^3*alpha(t, x)*beta(t, x)^2+12*(diff(b1(t, x), x))*alpha(t, x)^3*a1(t, x)*x*b1(t, x)+4*alpha(t, x)^3*a1(t, x)*b1(t, x)*x^2*(diff(diff(b1(t, x), x), x))-4*alpha(t, x)^3*b1(t, x)*x^2*(diff(a1(t, x), x))*(diff(b1(t, x), x))-4*a1(t, x)^3*alpha(t, x)*b1(t, x)*x^2*beta(t, x)^2*(diff(diff(b1(t, x), x), x))+4*b1(t, x)*x^2*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(diff(b1(t, x), t), x))+8*b1(t, x)*x*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(b1(t, x), t))+4*(diff(b1(t, x), x))*x^2*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(b1(t, x), t))-12*(diff(b1(t, x), x))*x*a1(t, x)^3*alpha(t, x)*beta(t, x)^2*b1(t, x)+4*a1(t, x)^3*(diff(b1(t, x), t))*alpha(t, x)*b1(t, x)*x^2*(diff(beta(t, x), x))-4*a1(t, x)^2*(diff(b1(t, x), t))*alpha(t, x)*b1(t, x)*x^2*(diff(a1(t, x), t))-4*alpha(t, x)*b1(t, x)^2*x*beta(t, x)*a1(t, x)^3*(diff(beta(t, x), x))-4*b1(t, x)*x^2*a1(t, x)^3*(diff(b1(t, x), t))*beta(t, x)*(diff(alpha(t, x), x))+4*b1(t, x)*x^2*a1(t, x)^3*beta(t, x)^2*(diff(b1(t, x), x))*(diff(alpha(t, x), x))+4*a1(t, x)^2*(diff(b1(t, x), t))*alpha(t, x)*b1(t, x)*x^2*beta(t, x)*(diff(a1(t, x), x))-4*alpha(t, x)*b1(t, x)*x^2*beta(t, x)*a1(t, x)^3*(diff(beta(t, x), x))*(diff(b1(t, x), x))-2*b1(t, x)^2*a1(t, x)^3*alpha(t, x)*beta(t, x)^2-2*(diff(b1(t, x), t))^2*a1(t, x)^3*alpha(t, x)*x^2+2*(diff(b1(t, x), x))^2*alpha(t, x)^3*a1(t, x)*x^2-4*alpha(t, x)^3*b1(t, x)^2*x*(diff(a1(t, x), x))+2*alpha(t, x)^3*a1(t, x)*b1(t, x)^2-2*a1(t, x)^3*alpha(t, x)^3+b1(t, x)^2*x^2*alpha(t, x)*a1(t, x)^3*(diff(rpsi(t, x), t))^2+b1(t, x)^2*x^2*alpha(t, x)*a1(t, x)^3*(diff(ipsi(t, x), t))^2+b1(t, x)^2*x^2*alpha(t, x)^3*a1(t, x)^3*U(t, x)+b1(t, x)^2*x^2*alpha(t, x)^3*a1(t, x)*(diff(rpsi(t, x), x))^2+b1(t, x)^2*x^2*alpha(t, x)^3*a1(t, x)*(diff(ipsi(t, x), x))^2-b1(t, x)^2*x^2*alpha(t, x)*a1(t, x)^3*(diff(rpsi(t, x), x))^2*beta(t, x)^2-b1(t, x)^2*x^2*alpha(t, x)*a1(t, x)^3*(diff(ipsi(t, x), x))^2*beta(t, x)^2)/(alpha(t, x)^3*b1(t, x)^2*x^2*a1(t, x)^3);\n\nresthth:=\n(1/2)*(-2*a1(t, x)^2*alpha(t, x)*b1(t, x)*x*(diff(diff(a1(t, x), t), t))+2*alpha(t, x)^2*a1(t, x)*b1(t, x)*x*(diff(diff(alpha(t, x), x), x))-2*alpha(t, x)*a1(t, x)^3*b1(t, x)*x*(diff(beta(t, x), x))^2-2*b1(t, x)*x*(diff(a1(t, x), x))*alpha(t, x)^2*(diff(alpha(t, x), x))+2*(diff(alpha(t, x), x))*a1(t, x)^2*b1(t, x)*x*beta(t, x)^2*(diff(a1(t, x), x))+2*(diff(alpha(t, x), x))*a1(t, x)^3*b1(t, x)*x*beta(t, x)*(diff(beta(t, x), x))-2*(diff(alpha(t, x), x))*a1(t, x)^2*b1(t, x)*x*beta(t, x)*(diff(a1(t, x), t))+2*a1(t, x)^2*(diff(b1(t, x), t))*alpha(t, x)*x*beta(t, x)*(diff(a1(t, x), x))-2*alpha(t, x)*x*beta(t, x)^2*a1(t, x)^2*(diff(a1(t, x), x))*(diff(b1(t, x), x))-4*alpha(t, x)*x*beta(t, x)*a1(t, x)^3*(diff(beta(t, x), x))*(diff(b1(t, x), x))+2*alpha(t, x)*x*beta(t, x)*a1(t, x)^2*(diff(a1(t, x), t))*(diff(b1(t, x), x))-2*a1(t, x)^2*(diff(alpha(t, x), t))*b1(t, x)*x*beta(t, x)*(diff(a1(t, x), x))+4*(diff(a1(t, x), t))*alpha(t, x)*a1(t, x)^2*b1(t, x)*x*(diff(beta(t, x), x))+2*a1(t, x)^2*alpha(t, x)*b1(t, x)*x*(diff(beta(t, x), t))*(diff(a1(t, x), x))+4*a1(t, x)^2*alpha(t, x)*b1(t, x)*x*beta(t, x)*(diff(diff(a1(t, x), t), x))-2*alpha(t, x)*a1(t, x)^2*b1(t, x)*x*beta(t, x)^2*(diff(diff(a1(t, x), x), x))-2*alpha(t, x)*a1(t, x)^3*b1(t, x)*x*beta(t, x)*(diff(diff(beta(t, x), x), x))-6*alpha(t, x)*a1(t, x)^2*b1(t, x)*x*beta(t, x)*(diff(a1(t, x), x))*(diff(beta(t, x), x))+2*b1(t, x)*a1(t, x)^3*beta(t, x)^2*(diff(alpha(t, x), x))+4*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(b1(t, x), t))-4*(diff(b1(t, x), x))*a1(t, x)^3*alpha(t, x)*beta(t, x)^2-2*x*a1(t, x)^3*alpha(t, x)*(diff(diff(b1(t, x), t), t))+2*b1(t, x)*a1(t, x)^3*alpha(t, x)*(diff(beta(t, x), t))+2*a1(t, x)*b1(t, x)*alpha(t, x)^2*(diff(alpha(t, x), x))+2*x*(diff(alpha(t, x), t))*a1(t, x)^3*(diff(b1(t, x), t))-2*b1(t, x)*(diff(alpha(t, x), t))*a1(t, x)^3*beta(t, x)+2*alpha(t, x)^3*a1(t, x)*x*(diff(diff(b1(t, x), x), x))-2*alpha(t, x)^3*x*(diff(a1(t, x), x))*(diff(b1(t, x), x))+b1(t, x)*x*a1(t, x)^3*alpha(t, x)^3*U(t, x)-b1(t, x)*x*a1(t, x)^3*alpha(t, x)*(diff(rpsi(t, x), t))^2-b1(t, x)*x*a1(t, x)^3*alpha(t, x)*(diff(ipsi(t, x), t))^2+b1(t, x)*x*a1(t, x)*alpha(t, x)^3*(diff(rpsi(t, x), x))^2+b1(t, x)*x*a1(t, x)*alpha(t, x)^3*(diff(ipsi(t, x), x))^2-2*alpha(t, x)^3*b1(t, x)*(diff(a1(t, x), x))+4*(diff(b1(t, x), x))*alpha(t, x)^3*a1(t, x)+2*a1(t, x)^3*(diff(b1(t, x), t))*alpha(t, x)*x*(diff(beta(t, x), x))-2*a1(t, x)^2*(diff(b1(t, x), t))*alpha(t, x)*x*(diff(a1(t, x), t))-2*alpha(t, x)*b1(t, x)*beta(t, x)^2*a1(t, x)^2*(diff(a1(t, x), x))-4*alpha(t, x)*b1(t, x)*beta(t, x)*a1(t, x)^3*(diff(beta(t, x), x))+2*alpha(t, x)*b1(t, x)*beta(t, x)*a1(t, x)^2*(diff(a1(t, x), t))-2*a1(t, x)^3*(diff(alpha(t, x), t))*b1(t, x)*x*(diff(beta(t, x), x))+2*a1(t, x)^2*(diff(alpha(t, x), t))*b1(t, x)*x*(diff(a1(t, x), t))+2*a1(t, x)^3*alpha(t, x)*b1(t, x)*x*(diff(diff(beta(t, x), t), x))-2*a1(t, x)^3*alpha(t, x)*x*beta(t, x)^2*(diff(diff(b1(t, x), x), x))+2*x*a1(t, x)^3*alpha(t, x)*(diff(beta(t, x), t))*(diff(b1(t, x), x))+4*x*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(diff(b1(t, x), t), x))+2*a1(t, x)*x*alpha(t, x)^2*(diff(alpha(t, x), x))*(diff(b1(t, x), x))-2*x*(diff(alpha(t, x), t))*a1(t, x)^3*beta(t, x)*(diff(b1(t, x), x))-2*x*a1(t, x)^3*(diff(b1(t, x), t))*beta(t, x)*(diff(alpha(t, x), x))+2*x*a1(t, x)^3*beta(t, x)^2*(diff(b1(t, x), x))*(diff(alpha(t, x), x))-b1(t, x)*x*a1(t, x)^3*alpha(t, x)*(diff(rpsi(t, x), x))^2*beta(t, x)^2-b1(t, x)*x*a1(t, x)^3*alpha(t, x)*(diff(ipsi(t, x), x))^2*beta(t, x)^2+2*b1(t, x)*x*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(rpsi(t, x), t))*(diff(rpsi(t, x), x))+2*b1(t, x)*x*a1(t, x)^3*alpha(t, x)*beta(t, x)*(diff(ipsi(t, x), t))*(diff(ipsi(t, x), x)))/(b1(t, x)*x*alpha(t, x)^3*a1(t, x)^3);\n", "meta": {"hexsha": "2c8ee5f353ec3b6e910b5cea9cf217aed8f5370b", "size": 10507, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "eq_ire.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "eq_ire.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "eq_ire.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": 583.7222222222, "max_line_length": 3700, "alphanum_fraction": 0.4983344437, "num_tokens": 5310, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012671214071, "lm_q2_score": 0.6261241702517976, "lm_q1q2_score": 0.5921890335994898}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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\nlag_a1 := 0.041106:\nlag_a2 := 2.626712:\nlag_a3 := 0.092070:\nlag_a4 := 0.657946:\n\nlag_f0 := s-> lag_a1 * s^lag_a2/(1 + lag_a3 * s^lag_a2)^lag_a4:\nlag_f := x-> lag_f0(X2S*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(lag_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "e21fb217489b1f8c64311eac4c4d3d22a7e15589", "size": 517, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_lag.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_lag.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_lag.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": 25.85, "max_line_length": 73, "alphanum_fraction": 0.6421663443, "num_tokens": 201, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9032942119105695, "lm_q2_score": 0.6548947223065755, "lm_q1q2_score": 0.5915626120703094}} {"text": "# A striped preorder is one for which comparability is an equivalence relation\n\n######################################################################\n\n`is_element/striped_preord` := (A::set) -> proc(R)\n local E;\n global reason;\n\n if not `is_element/preord`(A)(R) then\n reason := [convert(procname,string),\"R is not a preorder on A\",R,A,reason];\n return false;\n fi;\n\n E := R union `op/autorel`(A)(R);\n \n if not(`is_transitive/autorel`(A)(E)) then\n reason := [convert(procname,string),\"R u R^op is not transitive\",R];\n return false;\n fi;\n \n return true;\nend;\n\n######################################################################\n\n`is_equal/striped_preord` := eval(`is_equal/autorel`);\n`is_leq/striped_preord` := eval(`is_leq/preord`);\n`is_separated/striped_preord` := eval(`is_separated/autorel`);\n\n`op/striped_preord` := eval(`op/autorel`);\n\n######################################################################\n# A075729\n\n`count_elements/striped_preord` := proc(A::set)\n local n,x,egf;\n n := nops(A);\n egf := convert(series(exp(1/(2-exp(x))-1),x=0,n+1),polynom,x):\n return n! * coeff(egf,x,n);\nend:\n\n######################################################################\n\n`list_elements/striped_preord` := proc(A::set)\n local RR,PI,pi,LL,QQ,B,Q,L;\n\n RR := [];\n\n PI := `list_elements/partitions`(A);\n for pi in PI do\n LL := [{}];\n for B in pi do\n QQ := `list_elements/total_preord`(B);\n LL := [seq(seq(L union Q,Q in QQ),L in LL)];\n od;\n RR := [op(RR),op(LL)];\n od:\n\n return RR;\nend:\n\n######################################################################\n# Note that the function below is not actually a rank function, but\n# it is an ingredient in certain rank functions to be defined \n# elsewhere.\n\n`rank/preord` := (A::set) -> proc(R)\n nops(`block_partition/preord`(A)(R));\nend:\n\n######################################################################\n\n`random_element/striped_preord` := (A::set) -> proc()\n local pi,Q,B;\n\n pi := `random_element/partitions`(A)();\n Q := {};\n for B in pi do \n Q := Q union `random_element/total_preord`(B)();\n od;\n return Q;\nend:\n\n\n######################################################################\n# Returns a striped preorder R0 > R with \n# (or FAIL if R is already maximal).\n\n`bump/striped_preord` := (A::set) -> proc(R)\n local pi,B,a,b,B0,R0;\n\n pi := `block_partition/preord`(A)(R);\n\n for B in pi do \n if nops(B) > 1 then\n a := B[1];\n B0 := B minus {a};\n R0 := R minus {seq([b,a],b in B0)};\n return R0;\n fi;\n od;\n\n return FAIL;\nend:\n\n######################################################################\n# Returns a striped preorder R1 with R < R0 <= S \n# (or FAIL if this is impossible)\n\n`relative_bump/striped_preord` := (A::set) -> proc(R,S)\n local pi,B,BB,SB,C,a,b,c,B0,R0;\n\n pi := `block_partition/preord`(A)(R);\n\n for B in pi do \n BB := `top/autorel`(B);\n SB := S intersect BB;\n if BB minus S <> {} then\n for a in B do\n C := select(b -> member([b,a],SB) and not(member([a,b],SB)),B);\n if C = {} then\n B0 := B minus {a};\n R0 := R minus {seq([b,a],b in B0)};\n return R0;\n fi;\n od;\n return FAIL; # should not happen\n fi;\n od;\n\n return FAIL;\nend:\n\n######################################################################\n\n`describe/striped_preord` := (A::set) -> proc(R)\n local s0,s1,s2,pi,B,C,r,m,j,k,c;\n\n s0 := \"\";\n pi := `block_partition/preord`(A)(R union `op/autorel`(A)(R));\n for B in pi do\n r := `rank_table/preord`(B)(R intersect `top/autorel`(B));\n m := max(map(b -> r[b],B));\n s1 := \"\";\n for j from 0 to m do \n C := select(b -> r[b]=j,B);\n s2 := \"\";\n for k from 1 to nops(C) do \n s2 := cat(s2,`if`(k>1,\"=\",\"\"),sprintf(\"%A\",C[k]));\n od:\n s1 := cat(s1,`if`(j>0,\"<\",\"\"),s2);\n od;\n s0 := cat(s0,`if`(s0=\"\",\"\",\",\"),s1);\n od:\n\n return s0;\nend:\n", "meta": {"hexsha": "01f64197ac80070818d7d18b3817bfec7006a9f5", "size": 3777, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/striped_preord.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/striped_preord.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/striped_preord.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": 23.9050632911, "max_line_length": 78, "alphanum_fraction": 0.4927190892, "num_tokens": 1111, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8499711718571774, "lm_q2_score": 0.6959583250334525, "lm_q1q2_score": 0.5915445130924419}} {"text": "with(DifferentialAlgebra):\nring_diff := DifferentialRing(blocks = [[EGF_EGFR, EGFR, pEGFR, pAkt_S6, pEGFR_Akt, pAkt, S6, pS6, Akt], [y1, y2, y3] , [pro_EGFR]], derivations = [t]):\nsys := [\ndiff(EGF_EGFR(t), t) - (reaction_1_k1*EGF_EGFR(t) - reaction_9_k1*EGF_EGFR(t) - reaction_1_k2*EGF_EGFR(t)),\ndiff(EGFR(t), t) - (-reaction_1_k1*EGF_EGFR(t) + reaction_1_k2*EGF_EGFR(t) - EGFR(t)*EGFR_turnover + EGFR_turnover*pro_EGFR(t)),\ndiff(pEGFR(t), t) - (-reaction_4_k1*pEGFR(t) + reaction_9_k1*EGF_EGFR(t) - pEGFR(t)*Akt(t)*reaction_2_k1 + reaction_3_k1*pEGFR_Akt(t) + pEGFR_Akt(t)*reaction_2_k2),\ndiff(pAkt_S6(t), t) - (pAkt(t)*reaction_5_k1*S6(t) - reaction_6_k1*pAkt_S6(t) - pAkt_S6(t)*reaction_5_k2),\ndiff(pEGFR_Akt(t), t) - (pEGFR(t)*Akt(t)*reaction_2_k1 - reaction_3_k1*pEGFR_Akt(t) - pEGFR_Akt(t)*reaction_2_k2),\ndiff(pAkt(t), t) - (-pAkt(t)*reaction_7_k1 - pAkt(t)*reaction_5_k1*S6(t) + reaction_6_k1*pAkt_S6(t) + reaction_3_k1*pEGFR_Akt(t) + pAkt_S6(t)*reaction_5_k2),\ndiff(S6(t), t) - (pS6(t)*reaction_8_k1 - pAkt(t)*reaction_5_k1*S6(t) + pAkt_S6(t)*reaction_5_k2),\ndiff(pS6(t), t) - (-pS6(t)*reaction_8_k1 + reaction_6_k1*pAkt_S6(t)),\ndiff(Akt(t), t) - (pAkt(t)*reaction_7_k1 - pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2),\ny1(t) - (pEGFR(t)*a1 + a1*pEGFR_Akt(t)),\ny2(t) - (a2*pAkt(t) + a2*pAkt_S6(t)),\ny3(t) - (pS6(t)*a3)\n];\nres := CodeTools[CPUTime](RosenfeldGroebner(sys, ring_diff, singsol=none));", "meta": {"hexsha": "e366a55b87554a08618e5c56fd16b893a5421d5a", "size": 1420, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/RosenfeldGroebner/Akt-pathway.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/RosenfeldGroebner/Akt-pathway.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/RosenfeldGroebner/Akt-pathway.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 83.5294117647, "max_line_length": 164, "alphanum_fraction": 0.7007042254, "num_tokens": 641, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094032139577, "lm_q2_score": 0.66192288918838, "lm_q1q2_score": 0.5913019411145304}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_k_ol2_params *params;\n\n assert(p->params != NULL);\n params = (gga_k_ol2_params * )(p->params);\n*)\n\nol2_f := x ->\n + params_a_aa\n + params_a_bb*x^2/72.0\n + params_a_cc*x/(2^(1/3) + 4*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_kinetic(ol2_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "f6cb8c6d8b10dbb2d59efbdf4d5497334a3763e1", "size": 541, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_ol2.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_k_ol2.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_k_ol2.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": 23.5217391304, "max_line_length": 72, "alphanum_fraction": 0.6414048059, "num_tokens": 197, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933093975331751, "lm_q2_score": 0.6619228825191872, "lm_q1q2_score": 0.5913019313966377}} {"text": "# Number of subspaces of dimension d in F^n, if |F|=q\n\ngrassmann_count := (q::posint) -> proc(n,d)\n local i;\n return mul(q^(n-i)-1,i=0..d-1)/mul(q^(d-i)-1,i=0..d-1);\nend:\n\n# Number of splittings of F^(n+m) as a sum of subspaces of\n# dimensions n and m, if |F| = q.\n\nsplitting_count := (q::posint) -> (n,m) ->\n grassman_count(q)(n+m,n) * q^(n*m);\n\n# tanabe_N(p,n,r)(k) is the number of irreducible F-linear representations\n# of Z_p^n that have dimension p^k over F.\n\ntanabe_N := (p,n,r) -> (k) -> `if`(k = 0,p^(n*r),(p^n-1) * p^((n-1)*k + n*(r-1)));\n\n# The socle of K^0(BGL_{p^k}(F)) is generated by\n# euler(V)^{N-1}, where N = tanabe_N_bar(n,v,k)\n\ntanabe_N_bar := (p,n,r) -> proc(k)\n local j;\n p^(n*r) + (p^n-1)*p^(n*(r-1))*sum(p^((n-1)*j),j=1..k);\nend:\n\ntanabe_N_star := (p,n,r) -> proc(k)\n local j;\n p^(n*r-1) * (p-1) * sum(p^((n-1)*j),j=0..k-1);\nend:\n\ntanabe_N_lim := (p,n,r) -> (k) -> p^(n*r+n*k-k) * (1-p^(-n))/(1-p^(1-n));\n\n# The natural numbers can be partitioned as the disjoint union of\n# the sets tanabe_NN(p,n,r)(k), of size tanabe_N(p,n,r)(k).\n\ntanabe_NN := (p,n,r) -> proc(k::nonnegint)\n local i;\n if k = 0 then\n return [seq(i,i=0..tanabe_N_bar(p,n,r)(0)-1)];\n else\n return [seq(i,i=tanabe_N_bar(p,n,r)(k-1)..tanabe_N_bar(p,n,r)(k)-1)];\n fi;\nend:\n\n# tanabe_s(p,n,r)(m) is the unique k such that m lies in tanabe_NN(p,n,r)(k).\ntanabe_s := (p,n,r) -> proc(m)\n local k;\n k := 0;\n while m >= tanabe_N_bar(p,n,r)(k) do\n k := k+1;\n od;\n return k;\nend:\n\n# tanabe_X(p,n,r)(k) is the set of generators for E^0(BGL_*(F)) in\n# degree p^k.\n\ntanabe_X := (p,n,r) -> proc(k)\n local j;\n return [seq(c[p^k] ^ j, j = 0..tanabe_N(p,n,r)(k)-1)]; \nend:\n\n# tanabe_prim_gen(p,n,r)(k) is a generator for the primitives\n# in K^0(BGL_*(F)) in degree p^k\ntanabe_prim_gen := (p,n,r) -> (k) -> c[p^k] ^ tanabe_N_bar(p,n,r)(k-1);\n\n# tanabe_soc_gen(p,n,r)(k) is a generator for the socle of\n# K^0(BGL_{p^k}(F))\ntanabe_soc_gen := (p,n,r) -> (k) -> c[p^k] ^ (tanabe_N_bar(p,n,r)(k) - 1);\n\n# tanabe_m(p)(k) has p-adic valuation k and divides\n# tanabe_m(p)(k+1). Moreover, any positive integer n divides\n# tanabe_m(p)(k) when k is sufficiently large.\n\ntanabe_m := (p) -> proc(k) \n local m,i;\n m := 1;\n i := 1;\n while ithprime(i) <= p + k do\n m := m * ithprime(i) ^ k;\n i := i + 1;\n od:\n return m;\nend:\n\ncheck_tanabe_m := proc(p,k)\n _ASSERT(padic_val(tanabe_m(p)(k),p) = k,\n \"v_p(m[k])\");\n\n _ASSERT(type(tanabe_m(p)(k+1)/tanabe_m(p)(k),posint),\n \"m[k] divides m[k+1]\");\nend:\n\n# Given a polynomial f over the integers and a prime q, return\n# the first irreducible factor of f mod q, in the standard\n# Maple order.\n\nfirst_factor := proc(f,q)\n local F;\n F := :-Factor(f) mod q;\n if type(F,`*`) then F := [op(F)] else F := [F]; fi:\n F := sort(map(g -> `if`(type(g,`^`),op(1,g),g),F));\n return F[1];\nend:\n\n# Return an irreducible polynomial f[k](x) of degree v0 * p^k over\n# Z/q0. This gives a field F(k) of degree p^k over F = F(0),\n# where F(0) has order q = q0 ^ v0. The polynomials are arranged\n# so that the canonical primitive element x[k] in F(k) generates\n# the group of units, and there is an inclusion F(k) -> F(k+1)\n# sending x[k] to x[k+1] ^ m, where m = |F(k+1)^x|/|F(k)^x|.\ntanabe_FF_poly := (q0,v0,p) -> proc(k::nonnegint)\n option remember;\n local q,m,f;\n\n q := q0 ^ v0;\n if k = 0 then \n f := NumberTheory[CyclotomicPolynomial](q0 ^ v0 - 1,x);\n else\n m := (q ^ (p ^ k) - 1)/(q ^ (p ^ (k - 1)) - 1);\n f := subs(x = x ^ m, tanabe_FF_poly(q0,v0,p)(k - 1));\n end:\n\n return first_factor(f,q0);\nend:\n\n# tanabe_F(q0,v0)(m) is the field denoted by F[m] in the paper,\n# where q = q0 ^ v0 with q0 prime and v0 > 0.\n# tanabe_FF(q0,v0)(p,k) is F(k) = F[p^k].\n\ntanabe_F := (q0,v0) -> (m) -> GF(q0,v0 * m);\ntanabe_FF := (q0,v0) -> (p,k) -> GF(q0,v0 * p ^ k,tanabe_FF_poly);\n\n# Orders of various groups: G is the general linear group,\n# N is the subgroup of monomial matrices, H is the block\n# diagonal subgroup of p' index as in prop-non-p-power.\n\ntanabe_G_order := (q) -> proc(d)\n local k;\n return mul(q ^ d - q ^ k,k = 0..d-1);\nend:\n\ntanabe_N_order := (q) -> (d) -> d! * (q - 1)^d;\n\ntanabe_H_order := (q,p) -> proc(d)\n local dd,m,i;\n dd := digit_list(d,p);\n m := nops(dd);\n mul(tanabe_G_order(q)(p ^ i) ^ dd[i+1], i = 0..m-1);\nend:\n\n\n# The E^2 page of the AHSS converging to K_*(BV) has a trigrading\n# with E^2_{ijk} = H_i(BV_k;K_j). It has even generators\n# b[i] and u, and odd generators e[i] with\n# |b[i]| = tanabe_b_trideg(p,n,r)(i) = [2i,0,1]\n# |e[i]| = tanabe_e_trideg(p,n,r)(i) = [2i+1,0,1]\n# |u| = tanabe_u_trideg(p,n,r) = [0,2,0].\n\ntanabe_b_trideg := (p,n,r) -> (i) -> [2*i,0,1];\ntanabe_e_trideg := (p,n,r) -> (i) -> [2*i+1,0,1];\ntanabe_u_trideg := (p,n,r) -> [0,2,0];\n\n# The only nontrivial differentials have the form d_r, where\n# r = tanabe_AHSS_page(p,n,r)(k) for some k >= 0\n# [From now on we refer to this as the k'th differential,\n# and the page on which it occurs as the k'th page.]\n\ntanabe_AHSS_page := (p,n,r) -> (k) -> 2*p^(n*(r+k)) - 1;\n\n# Tridegree of the k'th differential\ntanabe_AHSS_d_trideg := (p,n,r) -> (k) ->\n [1-2*p^(n*(r+k)),2*p^(n*(r+k))-2,0];\n\n# The k'th page can be described in terms of generators\n# bb[m,i] and ee[m,i]\n\ntanabe_bb_defined := (p,n,r) -> (k) -> (m,i) ->\n m >= min(k,tanabe_s(p,n,r)(i));\n\ntanabe_bb_indec := (p,n,r) -> (k) -> (m,i) ->\n m = min(k,tanabe_s(p,n,r)(i));\n\ntanabe_ee_defined := (p,n,r) -> (k) -> (m,i) ->\n m = k and i >= tanabe_N_star(p,n,r)(k);\n\ntanabe_bb_trideg := (p,n,r) -> (m,i) -> [2*p^m*i,0,p^m];\ntanabe_ee_trideg := (p,n,r) -> (m,i) -> [2*p^m*i + 1,0,p^m];\n\ntanabe_dbb0 := (p,n,r) -> (k) -> (m,i) ->\n ee[k,i - tanabe_N_bar(p,n,r)(k) + tanabe_N_star(p,n,r)(k)] *\n u ^ (p^(n * (k + r)) - 1);\n\ntanabe_dbb := (p,n,r) -> (k) -> (m,i) ->\n `if`(m < k, 0, `if`(i < tanabe_N_bar(p,n,r)(k), 0, tanabe_dbb0(p,n,r)(k)(m,i)));\n\n# This is the part of the inverse Poincare series contributed by\n# irreducible representations of dimension at most p^k.\n\ntanabe_inverse_poincare_series := (p,n,r) -> proc(k)\n local j;\n (1-t)^(p^(n*r)) * mul((1 - t^(p^j))^(p^(n*(r+j))*(1-1/p^n)),j=1..k);\nend:\n\ntanabe_poincare_series := (p,n,r) -> (k) ->\n convert(series(1/tanabe_inverse_poincare_series(p,n,r)(k),t=0,p^k+1),\n polynom,t);\n\ntanabe_trideg := (p,n,r) -> proc(x)\n local d,d0,y;\n \n if type(x,indexed) then\n if op(0,x) = b then\n return tanabe_b_trideg(p,n,r)(op(x));\n elif op(0,x) = e then\n return tanabe_e_trideg(p,n,r)(op(x));\n elif op(0,x) = bb then\n return tanabe_bb_trideg(p,n,r)(op(x));\n elif op(0,x) = ee then\n return tanabe_ee_trideg(p,n,r)(op(x));\n else\n return [0,0,0];\n fi;\n elif x = u then\n return tanabe_u_trideg(p,n,r);\n elif type(x,`+`) then\n d := map(tanabe_trideg(p,n,r),{op(x)});\n if nops(d) = 1 then\n return op(d);\n else\n return FAIL;\n fi;\n elif type(x,`*`) then\n d := [0,0,0];\n for y in [op(x)] do\n d0 := tanabe_trideg(p,n,r)(y);\n if d0 = FAIL then return FAIL; fi;\n d := d +~ d0;\n od;\n return d;\n elif type(x,`^`) then\n return tanabe_trideg(p,n,r)(op(1,x)) *~ op(2,x);\n else\n return [0,0,0];\n fi;\nend:\n\n######################################################################\n\n# Check v_p(q ^ j - 1) = r + v_p(j) \ncheck_lem_vp := (p) -> proc(q::posint,j::posint)\n local r;\n r := padic_val(q - 1,p);\n _ASSERT(r > 0, \"r > 0\");\n\n _ASSERT(padic_val(q ^ j - 1,p) = r + padic_val(j,p),\n sprintf(\"v_{%d}(%d ^ %d - 1)\",p,q,j));\nend;\n\ncheck_tanabe_numbers := proc()\n local n,r,k,p,L,N,N_bar,N_star,N_lim,P,err;\n\n assume(n::posint);\n assume(r::posint);\n assume(k::posint);\n assume(p::posint);\n\n N := tanabe_N(p,n,r);\n N_bar := tanabe_N_bar(p,n,r);\n N_star := tanabe_N_star(p,n,r);\n N_lim := tanabe_N_lim(p,n,r);\n \n _ASSERT(\n simplify(N_bar(k) - N_bar(k-1) - N(k)) = 0,\n \"N_bar(k) - N_bar(k-1) = N(k)\"\n );\n\n _ASSERT(\n simplify(N_star(k) - (N_bar(k) - p^(n*k + n*r - k))) = 0,\n \"N_star(k) = N_bar(k) - p^(n*k + n*r - k)\"\n );\n\n _ASSERT(\n simplify(p^k * (N_bar(k) - N_star(k)) - p^(n * (k + r))) = 0,\n \"p^k * (N_bar(k) - N_star(k)) = p^(n * (k + r))\"\n );\n \n _ASSERT(\n simplify(p^(k + 1) * (N_bar(k) - N_star(k + 1)) - p^(n * (k + r))) = 0,\n \"p^(k + 1) * (N_bar(k) - N_star(k + 1)) = p^(n * (k + r))\"\n );\n \n _ASSERT(\n simplify(N(0) + sum(p^j * N(j),j=1..k) - p^(n*(r+k))) = 0,\n \"sum(p^j * N(j),j=0..k) = p^(n*(r+k))\"\n );\n\n _ASSERT(\n simplify((1 - p^(-k)) * N(0) +\n sum(expand((1 - p^(j - k)) * N(j)),j=1..k) - N_star(k)) = 0,\n \"sum((1 - p^(j-k)) * N(j),j=0..k) = N_star(k)\"\n );\n\n _ASSERT(\n simplify(p^(k + 1) * N_star(k + 1) - p^k * N_star(k) - (p - 1) * p^k * N_bar(k)) = 0,\n \"p^(k + 1) * N_star(k + 1) = p^k * N_star(k) + (p - 1) * p^k * N_bar(k)\"\n );\n\n _ASSERT(\n simplify(factor(N_bar(k) - (N_star(k)*(p^n-1)/(p-1) + p^(n*r)))) = 0,\n \"N_bar(k) = N_star(k)*(p^n-1)/(p-1) + p^(n*r)\"\n );\n\n _ASSERT(\n simplify(sum(p^j*(p-1)*N_bar(j),j=0..k-1) - p^k*N_bar(k) + p^(n*(r+k))) = 0,\n \"sum(p^j*(p-1)*N_bar(j),j=0..k-1)\"\n );\n \n _ASSERT(\n limit(simplify(N_bar(k)/N_lim(k)-1),k=infinity) = 0,\n \"N_bar(k) is asymptotic to N_lim(k)\"\n );\nend:\n\n\ncheck_factorial_congruences := proc() \n local p,i;\n p := ithprime(20);\n\n _ASSERT(\n {seq(modp((-1)^i * (i - 1)! * (p - i)!,p),i=1..p-1)} = {1},\n \"(-1)^i * (i - 1)! * (p - i)! = 1 mod p\"\n );\n\n _ASSERT(\n {seq(mods((-1)^i * binomial(p-1,i-1),p),i=1..p-1)} = {-1},\n \"(-1)^i * binomial(p-1,i-1) = -1 mod p\"\n );\nend:\n\n\ncheck_valuations := proc()\n local q0,v0,q,p,r,d,m;\n q0 := 19;\n v0 := 1;\n q := q0 ^ v0;\n p := 3;\n r := padic_val(q - 1, p);\n d := 20;\n \n _ASSERT(\n padic_val(tanabe_G_order(q)(d),p) - (d * r + (d - digit_sum(d,p))/(p - 1)) = 0,\n \"valuation of |G(d)|\"\n );\n\n m := tanabe_G_order(q)(d) / tanabe_N_order(q)(d):\n _ASSERT(type(m,posint) and padic_val(m,p) = 0,\n \"N(d) has p' index in G(d)\"\n );\n\n m := tanabe_G_order(q)(d) / tanabe_H_order(q,p)(d):\n _ASSERT(type(m,posint) and padic_val(m,p) = 0,\n \"H(d) has p' index in G(d)\"\n );\n\nend:\n\ncheck_diff_trideg := proc()\n local p,n,r,k,m,i,err,d0,d1,d2;\n\n d0 := tanabe_bb_trideg(p,n,r)(k,i);\n d1 := tanabe_AHSS_d_trideg(p,n,r)(k);\n d2 := tanabe_trideg(p,n,r)(tanabe_dbb0(p,n,r)(k)(m,i));\n\n err := simplify(d0 + d1 - d2, symbolic);\n\n _ASSERT(err = [0,0,0], \"differential respects tridegrees\");\nend:\n", "meta": {"hexsha": "57de413b798c8f461e268b19e7e7fc120677b53b", "size": 10169, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/tanabe/tanabe.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/tanabe/tanabe.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/tanabe/tanabe.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": 26.7605263158, "max_line_length": 87, "alphanum_fraction": 0.5513816501, "num_tokens": 4181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8221891392358015, "lm_q2_score": 0.7185943925708562, "lm_q1q2_score": 0.5908205050875059}} {"text": "with(Groebner):\nwith(PolynomialIdeals):\n\nJ := PolynomialIdeal({2*f1*f2*f3*f4*f5 - 9823275,\n5*f1*f2*f3*f4 + 24/5*f1*f2*f3*f5 + 21/5*f1*f2*f4*f5 + 16/5*f1*f3*f4*f5 + 9/5*f2*f3*f4*f5 - 4465125,\n4*f1*f2*f3 + 6*f1*f2*f4 + 18/5*f1*f2*f5 + 6*f1*f3*f4 + 24/5*f1*f3*f5 + 14/5*f1*f4*f5 + 4*f2*f3*f4 + 18/5*f2*f3*f5 + 14/5*f2*f4*f5 + 8/5*f3*f4*f5 - 441486,\n3*f1*f2 + 4*f1*f3 + 4*f1*f4 + 12/5*f1*f5 + 3*f2*f3 + 4*f2*f4 + 12/5*f2*f5 + 3*f3*f4 + 12/5*f3*f5 + 7/5*f4*f5 - 15498,\n2*f1 + 2*f2 + 2*f3 + 2*f4 + 6/5*f5 - 215,\nf1 + 2*f2 + 3*f3 + 4*f4 + 5*f5 + 6*t}):\nst := time[real]():\nBasis(J, tdeg(f1,f2,f3,f4,f5,t), characteristic=2^31-1):\ntime[real]() - st;\n\nJ := PolynomialIdeal({2*f1*f2*f3*f4*f5*f6 - 1404728325,\n6*f1*f2*f3*f4*f5 + 35/6*f1*f2*f3*f4*f6 + 16/3*f1*f2*f3*f5*f6 + 9/2*f1*f2*f4*f5*f6 + 10/3*f1*f3*f4*f5*f6 + 11/6*f2*f3*f4*f5*f6 - 648336150,\n5*f1*f2*f3*f4 + 8*f1*f2*f3*f5 + 14/3*f1*f2*f3*f6 + 9*f1*f2*f4*f5 + 7*f1*f2*f4*f6 + 4*f1*f2*f5*f6 + 8*f1*f3*f4*f5 + 7*f1*f3*f4*f6 + 16/3*f1*f3*f5*f6 + 3*f1*f4*f5*f6 + 5*f2*f3*f4*f5 + 14/3*f2*f3*f4*f6 + 4*f2*f3*f5*f6 + 3*f2*f4*f5*f6 +\n5/3*f3*f4*f5*f6 - 67597623,\n4*f1*f2*f3 + 6*f1*f2*f4 + 6*f1*f2*f5 + 7/2*f1*f2*f6 + 6*f1*f3*f4 + 8*f1*f3*f5 + 14/3*f1*f3*f6 + 6*f1*f4*f5 + 14/3*f1*f4*f6 + 8/3*f1*f5*f6 + 4*f2*f3*f4 + 6*f2*f3*f5 + 7/2*f2*f3*f6 + 6*f2*f4*f5 + 14/3*f2*f4*f6 + 8/3*f2*f5*f6 + 4*f3*f4*f5 + 7/2*f3*f4*f6 + 8/3*f3*f5*f6 +\n3/2*f4*f5*f6 - 2657700,\n3*f1*f2 + 4*f1*f3 + 4*f1*f4 + 4*f1*f5 + 7/3*f1*f6 + 3*f2*f3 + 4*f2*f4 + 4*f2*f5 + 7/3*f2*f6 + 3*f3*f4 + 4*f3*f5 + 7/3*f3*f6 + 3*f4*f5 + 7/3*f4*f6 + 4/3*f5*f6 - 46243,\n2*f1 + 2*f2 + 2*f3 + 2*f4 + 2*f5 + 7/6*f6 - 358}):\nst := time[real]():\nBasis(J, tdeg(f1,f2,f3,f4,f5,f6), characteristic=2^31-1):\ntime[real]() - st;\n\nJ := PolynomialIdeal({2*f1*f2*f3*f4*f5*f6*f7 - 273922023375, 7*f1*f2*f3*f4*f5*f6 + 48/7*f1*f2*f3*f4*f5*f7 + 45/7*f1*f2*f3*f4*f6*f7 + 40/7*f1*f2*f3*f5*f6*f7 + 33/7*f1*f2*f4*f5*f6*f7 + 24/7*f1*f3*f4*f5*f6*f7 + 13/7*f2*f3*f4*f5*f6*f7 - 127830277575,\n6*f1*f2*f3*f4*f5 + 10*f1*f2*f3*f4*f6 + 40/7*f1*f2*f3*f4*f7 + 12*f1*f2*f3*f5*f6 + 64/7*f1*f2*f3*f5*f7 + 36/7*f1*f2*f3*f6*f7 + 12*f1*f2*f4*f5*f6 + 72/7*f1*f2*f4*f5*f7 + 54/7*f1*f2*f4*f6*f7 + 30/7*f1*f2*f5*f6*f7 + 10*f1*f3*f4*f5*f6 + 64/7*f1*f3*f4*f5*f7 + 54/7*f1*f3*f4*f6*f7 + 40/7*f1*f3*f5*f6*f7 + 22/7f1*f4*f5*f6*f7 + 6*f2*f3*f4*f5*f6 + 40/7*f2*f3*f4*f5*f7 + 36/7*f2*f3*f4*f6*f7 + 30/7*f2*f3*f5*f6*f7 + 22/7*f2*f4*f5*f6*f7 + 12/7*f3*f4*f5*f6*f7 - 13829872635,\n5*f1*f2*f3*f4 + 8*f1*f2*f3*f5 + 8*f1*f2*f3*f6 + 32/7*f1*f2*f3*f7 + 9*f1*f2*f4*f5 + 12*f1*f2*f4*f6 + 48/7*f1*f2*f4*f7 + 9*f1*f2*f5*f6 + 48/7*f1*f2*f5*f7 + 27/7*f1*f2*f6*f7 + 8*f1*f3*f4*f5 + 12*f1*f3*f4*f6 +\n48/7*f1*f3*f4*f7 + 12*f1*f3*f5*f6 + 64/7*f1*f3*f5*f7 + 36/7*f1*f3*f6*f7 + 8*f1*f4*f5*f6 + 48/7*f1*f4*f5*f7 + 36/7*f1*f4*f6*f7 + 20/7*f1*f5*f6*f7 + 5*f2*f3*f4*f5 + 8*f2*f3*f4*f6 + 32/7*f2*f3*f4*f7 + 9*f2*f3*f5*f6 + 48/7*f2*f3*f5*f7 + 27/7*f2*f3*f6*f7 + 8*f2*f4*f5*f6 + 48/7*f2*f4*f5*f7 + 36/7*f2*f4*f6*f7 + 20/7*f2*f5*f6*f7 + 5*f3*f4*f5*f6 + 32/7*f3*f4*f5*f7 + 27/7*f3*f4*f6*f7 + 20/7*f3*f5*f6*f7 + 11/7*f4*f5*f6*f7 - 585849123,\n4*f1*f2*f3 + 6*f1*f2*f4 + 6*f1*f2*f5 + 6*f1*f2*f6 + 24/7*f1*f2*f7 + 6*f1*f3*f4 + 8*f1*f3*f5 + 8*f1*f3*f6 + 32/7*f1*f3*f7 + 6*f1*f4*f5 + 8*f1*f4*f6 + 32/7*f1*f4*f7 + 6*f1*f5*f6 + 32/7*f1*f5*f7 + 18/7*f1*f6*f7 + 4*f2*f3*f4 + 6*f2*f3*f5 + 6*f2*f3*f6 + 24/7*f2*f3*f7 + 6*f2*f4*f5 + 8*f2*f4*f6 + 32/7*f2*f4*f7 + 6*f2*f5*f6 + 32/7*f2*f5*f7 + 18/7*f2*f6*f7 + 4*f3*f4*f5 + 6*f3*f4*f6 + 24/7*f3*f4*f7 + 6*f3*f5*f6 + 32/7*f3*f5*f7 + 18/7*f3*f6*f7 + 4*f4*f5*f6 + 24/7*f4*f5*f7 + 18/7*f4*f6*f7 + 10/7*f5*f6*f7 - 11675085,\n3*f1*f2 + 4*f1*f3 + 4*f1*f4 + 4*f1*f5 + 4*f1*f6 + 16/7*f1*f7 + 3*f2*f3 + 4*f2*f4 + 4*f2*f5 + 4*f2*f6 + 16/7*f2*f7 + 3*f3*f4 + 4*f3*f5 + 4*f3*f6 + 16/7*f3*f7 + 3*f4*f5 + 4*f4*f6 + 16/7*f4*f7 + 3*f5*f6 + 16/7*f5*f7 + 9/7*f6*f7 - 116053,\n2*f1 + 2*f2 + 2*f3 + 2*f4 + 2*f5 + 2*f6 + 8/7*f7 - 553}):\nst := time[real]():\nBasis(J, tdeg(f1,f2,f3,f4,f5,f6,f7), characteristic=2^31-1):\ntime[real]() - st;\n", "meta": {"hexsha": "f247c9f9174fafd4d715bf99453073d11ff0ff81", "size": 3951, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmark/maplescripts/henrion.mpl", "max_stars_repo_name": "sumiya11/FastGroebner.jl", "max_stars_repo_head_hexsha": "5d3f39cec61bac0a9da8c63d1f6fa6fbea03e962", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2022-01-22T20:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-14T02:22:21.000Z", "max_issues_repo_path": "benchmark/maplescripts/henrion.mpl", "max_issues_repo_name": "sumiya11/Groebner.jl", "max_issues_repo_head_hexsha": "0b0e354a9d84a5f84a11b3d4c72dcd991859c752", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 13, "max_issues_repo_issues_event_min_datetime": "2022-01-17T01:16:26.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T16:44:38.000Z", "max_forks_repo_path": "benchmark/maplescripts/henrion.mpl", "max_forks_repo_name": "sumiya11/FastGroebner.jl", "max_forks_repo_head_hexsha": "5d3f39cec61bac0a9da8c63d1f6fa6fbea03e962", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-22T18:30:38.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-22T18:30:38.000Z", "avg_line_length": 109.75, "max_line_length": 509, "alphanum_fraction": 0.5722601873, "num_tokens": 2554, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107931567177, "lm_q2_score": 0.6297746213017459, "lm_q1q2_score": 0.5902315723401808}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\n(* replace: \"mbrxc_x\\(\" -> \"xc_mgga_x_mbrxc_get_x(\" *)\n\nmbrxc_a1 := 0.074746:\nmbrxc_a2 := 0.147:\nmbrxc_a3 := 0.0032:\n\n(* This is the derivative of f = (1+x)^(5/3)*exp(-2/3*x)/(x - 3) = (32*Pi)^(2/3)/(6*Q) *)\nmbrxc_aux_dfdx := x -> -2/3 * (1 + x)^(2/3) * exp(-2*x/3) * (x^2 - 3*x + 6) / (x - 3)^2:\n\n`diff/mbrxc_x` := proc(Q, g)\n - (32*Pi)^(2/3)/6 * diff(Q, g)/(Q^2 * mbrxc_aux_dfdx(mbrxc_x(Q)))\nend proc:\n\nmbrxc_Q := (x, t) ->\n mbrxc_a1*(2*t) - K_FACTOR_C + mbrxc_a2*x^2 + mbrxc_a3*x^4:\n\nmbrxc_min_Q := 5.0e-13:\nmbrxc_cQ := Q -> my_piecewise3(abs(Q) < mbrxc_min_Q,\n my_piecewise3(Q > 0, mbrxc_min_Q, -mbrxc_min_Q), Q):\n\nmbrxc_v := x ->\n - (32*Pi)^(1/3)/(8*X_FACTOR_C) * exp(x/3)*(8 - exp(-x)*(x^2 + 5*x + 8))/(x*(1 + x)^(1/3)):\n\nmbrxc_f := (x, u, t) ->\n - mbrxc_v(mbrxc_x(mbrxc_cQ(mbrxc_Q(x, t))))/2:\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(mbrxc_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "c8d9c53aa398b0519eaa68953bf706aed2de662f", "size": 1178, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_mbrxc_bg.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/mgga_exc/mgga_x_mbrxc_bg.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/mgga_exc/mgga_x_mbrxc_bg.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": 30.2051282051, "max_line_length": 92, "alphanum_fraction": 0.5755517827, "num_tokens": 549, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037262250327, "lm_q2_score": 0.6370307944803832, "lm_q1q2_score": 0.590083998647272}} {"text": "\n# Berechne kinematische Zwangsbedingungen für den Palettierroboter KUKA KR700PA aus 2 Viergelenkketten\n# Einleitung\n# Die kinematischen Zwangsbedingungen werden als Ersatzungsausdruck für die abhängigen Winkel aufgestellt.\n# \n# palh3m1TE->KUKA KR700PA, modellierung der Zwangsbedingungen mit Ausdrücken für trigonometrische Elimination\n# kinematic_constraint->Kinematische Zwangsbedingungen\n# Datenblatt des Roboters:\n# unter : https://www.kuka.com/en-de/products/robot-systems/industrial-robots/kr-700-pa\n# Voraussetzung(sehr wichtig!!!!!): \n# Viergelenkkette muss mit der Toolbox berechnet worden sein (Arbeitsblatt \"fourbar1TE_kinematic_constrains.mv\")\n# Quelle:\n# SA Shan: Shan2019_S828, \"Reduktion der Modellkomplexität von seriell-hybriden Palettierrobotern\"\n# Autor:\n# Weipu Shan\n# Studienarbeit bei: Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2018-08\n# (C) Institut fuer mechatronische Systeme, Leibniz Universitaet Hannover\n# Initialisierung\n# Import (Library)\ninterface(warnlevel=0): \t\t# Unterdrücke die folgende Warnung.\nrestart: \t\t\t\t# Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nkin_constraints_exist := true: # für Speicherung\n;\nwith(StringTools): # für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\n#with(ListTools):\ncodegen_act := true:\ncodegen_opt := 1: # Geringerer Optimierungsgrad. Sonst zu lange.\ncodegen_debug := 0: # Zur Code-Generierung auch für Nicht-Inert Ausdrücke\n;\n# Import(hybriddyn)\nread \"../helper/proc_MatlabExport\": #Matlab Export\nread \"../transformation/proc_rotx\": #Rotation um X\nread \"../transformation/proc_roty\": #Rotation um Y\nread \"../transformation/proc_rotz\": #Rotation um Z\nread \"../helper/proc_convert_s_t\": #zeitabhängige Variable für Ableitung\nread \"../helper/proc_convert_t_s\": #konstante Variable\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\": #substitute Spalte 1 mit Spalte 2\nwith (RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env\": #aktuelle Roboter, MDH-Tabelle\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\",robot_name): \n# Variable Initialisierung\n# Variable mit Winkeln der Nebenstruktur nur in Abhängigkeit der verallgemeinerten Koordinaten (Nur Aktive Gelenke)\nkintmp_qs := Matrix(RowDimension(kintmp_s),1): \t#kintmp_s von aktuellen Roboter, MDH\n;\n# \n# Konstante Winkel bereits hineinschreiben (Passive Gelenk)\nfor i from 1 to RowDimension(kintmp_s) do\n\tif diff(kintmp_s(i,1),t) = 0 then\n\t\t#konstante Variable, passive Winkel von aktuellem Roboter, MDH\n\t\tkimtmp_qs(i,1) := kintmp_s(i,1): \n \tend if:\nend do\n;\n# \n# Variable definieren für die Hilfswinkel\n# Ersetzungsausdrücke definieren\n# Speichere Sinus und Cosinus der Winkel direkt ab, da diese in den Rotationsmatrizen direkt auftreten.\n# Spalte 1: Zusuchender Ausdruck (sin oder cos eines Winkels)\t#第一列是要找到的三角函数表达\n# Spalte 2: Einzusetzender Ausdruck\t\t\t#第二列是代替的表达\n# Dadurch werden arctan-Ausdrücke in der direkten Kinematik reduziert.\n# Ähnliches Vorgehen wie in [1].\n# \n# #新建kintmp_subsexp 12X2, 第一列被动轴是sin cos 形式，第二列初始化和第一列相同，当前机器人的sin cos\nkintmp_subsexp := Matrix(2*RowDimension(kintmp_s),2):\nfor i from 1 to RowDimension(kintmp_s) do \t\t\t#kintmp_s von aktuellen Roboter\n\tkintmp_subsexp(2*i-1,1) := sin(kintmp_s(i,1)):\n\tkintmp_subsexp(2*i, 1) := cos(kintmp_s(i,1)):\n\t# Initialisierung der rechten Spalte mit gleichen Werten. Später nur Ersetzung, wenn Vorteilhaft.\n\tkintmp_subsexp(2*i-1,2) := kintmp_subsexp(2*i-1, 1):\n\tkintmp_subsexp(2*i, 2) := kintmp_subsexp(2*i, 1):\nend do:\n# \n# Sicherung der aktuelle Daten\nbackup_kintmp_qs := kintmp_qs:\t\t#Backup von aktuellem Roboter, konstante Variable\nbackup_kintmp_qt := kintmp_qt:\t\t#Backup von aktuellem Roboter, zeitabhängige Variable\nbackup_kintmp_subsexp := kintmp_subsexp: \t#Backup von aktuellem Roboter, sin, cos von 4 Winkeln\n \n;\n# Daten von Fourbar übernehmen\nread sprintf(\"../codeexport/fourbar1TE/tmp/kinematic_constraints_maple_inert.m\"): \t\n# Winkeln von Fourbar会先覆盖原先的变量 kintmp_subsexp, kintmp_qs, kintmp_qt,所以一开始需要备份\n\n;\n# Speichern WInkeln von Fourbar, mit Fourbar Variable\nkintmp_subsexp_fourbar := kintmp_subsexp: \t#sin,cos von 4 Winkeln, Fourbar\nkintmp_qs_fourbar := kintmp_qs:\t\t#konstante Variable, Fourbar\nkintmp_qt_fourbar := kintmp_qt:\t\t#zeitabhängige Variable, Fourbar\n;\n# \n# 以下内容有疑问 Was ist der Sinn darunten\n#kintmp_subsexp_fourbar:\n#winkel(6,2):\n#kintmp_subsexp_fourbar(6,2):\n#kintmp_subsexp_fourbar(3,3):\n#winkel_neu := Matrix(6,2):\nwinkel_neu(1,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(3,2)):\nwinkel_neu(2,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(4,2)):\nwinkel_neu(3,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(1,2)):\nwinkel_neu(4,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(2,2)):\nwinkel_neu(5,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(5,2)):\nwinkel_neu(6,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(6,2)):\n# \n# Vorherige Werte für dieses System wieder herstellen\nkintmp_qs := backup_kintmp_qs:\t\t#aktuellem Roboter, konstante Variable\nkintmp_qt := backup_kintmp_qt:\t\t#aktuellem Roboter, zeitabhängige Variable\nkintmp_subsexp := backup_kintmp_subsexp:\t\t#aktuellem Roboter, sin, cos von 4 Winkeln\n\n;\nwinkel_neu(1..6,1);\n# Viergelenkkette 1: A-B-C-D\n# Von ABCD: eta1, eta3, eta4 -----> Von Fourbar: rho, eta, xi\nwinkel1 := <;;;;;>:\n# Ausdrücke von Fourbar in aktuellem Roboter mitbringen\nfor i from 1 to 6 do\n\twinkel1(i,2) := kintmp_subsexp_fourbar(i,2): \t\t#Subsexpress von Fourbar übernehmen\n\tcos_phi_s := sin(qJ2s)*sin(phi2) - cos(qJ2s)*cos(phi2):\t#phi_s ist unabhängige Winkel von VGK, hier ist phi_s = eta2_s\n\tsin_phi_s := sin(qJ2s)*cos(phi2) + cos(qJ2s)*sin(phi2):\t#qJ2s ist echte aktive Winkel von Roboter, eta2 ^= phi = Pi - qJ2 - phi2\n\twinkel1(i,2) := subs({sin(qJ1s)=sin_phi_s},winkel1(i,2)):\t\n\twinkel1(i,2) := subs({cos(qJ1s)=cos_phi_s},winkel1(i,2)):\n\twinkel1(i,2) := subs({l1=AB}, winkel1(i,2)):\n\twinkel1(i,2) := subs({l2=DA}, winkel1(i,2)):\n\twinkel1(i,2) := subs({l3=DC}, winkel1(i,2)):\n\twinkel1(i,2) := subs({l4=BC}, winkel1(i,2)):\nend do:\nwinkel1(1..6,1):\n# eta1, eta3, eta4 wird wie rho, eta, xi in Fourbar darstellen\nsin_eta1_s := winkel1(1,2):\t#eta1 = qJ2s = rho\n;\ncos_eta1_s := winkel1(2,2):\t\nsin_eta3_s := winkel1(3,2):\t#eta3 = qJ3s = eta\n;\ncos_eta3_s := winkel1(4,2):\t\nsin_eta4_s := winkel1(5,2):\t#eta4 = qJ4s = xi\n;\ncos_eta4_s := winkel1(6,2):\t\n# eta16, eta79, eta27, abhängige Winkeln von aktuellem Roboter\ncos_eta16_s := cos_eta1_s*cos(phi1) + sin_eta1_s*sin(phi1):\t#eta16 = eta1 - phi1\n;\nsin_eta16_s := sin_eta1_s*cos(phi1) - cos_eta1_s*sin(phi1):\ncos_eta79_s := - cos_eta4_s:\t\t\t\t#eta79 = Pi-eta4\n;\nsin_eta79_s := sin_eta4_s:\ncos_eta27_s := cos_eta3_s*cos(phi79) + sin_eta3_s*sin(phi79):\t#eta27 = eta3 - phi79\n;\nsin_eta27_s := sin_eta3_s*cos(phi79) - cos_eta3_s*sin(phi79):\n# Viergelenkkette 2: B-E-F-G\nwinkel2 := <;;;;\n;>:\n# Ausdrücke von Fourbar in aktuellem Roboter mitbringen\nfor i from 1 to 6 do\n\twinkel2(i,2) := kintmp_subsexp_fourbar(i,2): \t\t\t#Subsexpress von Fourbar übernehmen\n\t#phi_s ist unabhängige Winkel von VGK, hier ist phi_s = xi2_s\n\t#qJ3s ist echte aktive Winkel von Roboter, xi2 ^= phi = Pi - qJ3 - (phi78-eta27)\n\tcos_phi_s := -cos(phi78+phi79)*(cos_eta3_s*cos(qJ3s)+sin_eta3_s*sin(qJ3s))-sin(phi78+phi79)*(sin_eta3_s*cos(qJ3s)-cos_eta3_s*sin(qJ3s)):\n\tsin_phi_s := sin(phi78+phi79)*(cos_eta3_s*cos(qJ3s)+sin_eta3_s*sin(qJ3s))-cos(phi78+phi79)*(sin_eta3_s*cos(qJ3s)-cos_eta3_s*sin(qJ3s)):\n\t#\n\twinkel2(i,2) := subs({sin(qJ1s)=sin_phi_s},winkel2(i,2)):\t\n\twinkel2(i,2) := subs({cos(qJ1s)=cos_phi_s},winkel2(i,2)):\n\twinkel2(i,2) := subs({l1=BG}, winkel2(i,2)):\n\twinkel2(i,2) := subs({l2=BE}, winkel2(i,2)):\n\twinkel2(i,2) := subs({l3=EP}, winkel2(i,2)):\n\twinkel2(i,2) := subs({l4=GP}, winkel2(i,2)):\nend do:\nwinkel2(1..6,1):\n# xi1, xi3, xi4 wird wie rho, eta, xi in Fourbar darstellen\nsin_xi1_s := winkel2(1,2):\t#xi1 = qJ2s = rho\n;\ncos_xi1_s := winkel2(2,2):\nsin_xi3_s := winkel2(3,2):\t#xi3 = qJ3s = eta\n;\ncos_xi3_s := winkel2(4,2):\nsin_xi4_s := winkel2(5,2):\t#xi4 = qJ4s = xi\n;\ncos_xi4_s := winkel2(6,2):\n# xi78, xi34, xi410, abhängige Winkeln von aktuellem Roboter\ncos_xi78_s := cos_xi1_s:\t\t\t\t#xi78 = xi1\n;\nsin_xi78_s := sin_xi1_s:\ncos_xi34_s := cos_xi3_s*cos(phi410) + sin_xi3_s*sin(phi410):\t#xi34 = xi3 - phi410\n;\nsin_xi34_s := sin_xi3_s*cos(phi410) - cos_xi3_s*sin(phi410):\ncos_xi410_s := -cos_xi4_s:\t\t\t\t#xi410 = Pi - xi4\n;\nsin_xi410_s := sin_xi4_s:\n# Kintmp_subsexp\nkintmp_subsexp(1, 2) := sin_xi34_s:\nkintmp_subsexp(2, 2) := cos_xi34_s:\nkintmp_subsexp(3, 2) := sin_eta16_s:\nkintmp_subsexp(4, 2) := cos_eta16_s:\nkintmp_subsexp(5, 2) := sin_eta27_s:\nkintmp_subsexp(6, 2) := cos_eta27_s:\nkintmp_subsexp(7, 2) := sin_xi78_s:\nkintmp_subsexp(8, 2) := cos_xi78_s:\nkintmp_subsexp(9, 2) := sin_eta79_s:\nkintmp_subsexp(10, 2) := cos_eta79_s:\nkintmp_subsexp(11, 2) := sin_xi410_s:\nkintmp_subsexp(12, 2) := cos_xi410_s:\nkintmp_subsexp:\n\n# Kintmp_qs\nkintmp_qs(1,1) := %arctan(sin_xi34_s,cos_xi34_s):\nkintmp_qs(2,1) := %arctan(sin_eta16_s,cos_eta16_s):\nkintmp_qs(3,1) := %arctan(sin_eta27_s,cos_eta27_s):\nkintmp_qs(4,1) := %arctan(sin_xi78_s,cos_xi78_s):\nkintmp_qs(5,1) := %arctan(sin_eta79_s,cos_eta79_s):\nkintmp_qs(6,1) := %arctan(sin_xi410_s,cos_xi410_s):\n\nkintmp_subsexp:\n# Export\nwinkel := <; ; ; ;; ;;;;;;>:\nsave winkel, sprintf(\"../codeexport/palh3m1TE/tmp/kinematic_constraints_maple_inert\"):\n\n\n\nkintmp_qt := convert_s_t(kintmp_qs):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple\", robot_name)\n;\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple.m\", robot_name)\n;\n#printf(\"Ausdrücke für kintmp_subsexp gespeichert (Maple). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\nfor i from 1 to RowDimension(kintmp_s) do\n tmp := kintmp_qs(i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d\",robot_name, i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d.m\", robot_name, i):\nend do:\nsave kin_constraints_exist, kintmp_qs, kintmp_qt,kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert\" ,robot_name):\nsave kin_constraints_exist, kintmp_qs, kintmp_qt, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nsave kintmp_qs, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_qs_maple_inert\", robot_name):\n#printf(\"Ausdrücke mit Inert-Arctan exportiert (Matlab). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Liste mit abhängigen konstanten Kinematikparametern erstellen (wichtig für Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\ninterface(rtablesize=20):\nkc_symbols := Matrix(list_constant_expressions( kintmp_subsexp ));\n#kc_symbols :=Transpose(kc_symbols);\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_maple\", robot_name):\nkc_symbols:\nMatlabExport(kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_matlab.m\",robot_name),2);\n#printf(\"Fertig. %s. CPU-Zeit bis hier: %1.2fs. \\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time() - st):\n\n", "meta": {"hexsha": "990b510376abe0a94aaa7023c1b8120cd8d29611", "size": 11944, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "systems/palh3m1/codegen/palh3m1TE_kinematic_constraints.mpl", "max_stars_repo_name": "SchapplM/robsynth-serhybroblib", "max_stars_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/palh3m1/codegen/palh3m1TE_kinematic_constraints.mpl", "max_issues_repo_name": "SchapplM/robsynth-serhybroblib", "max_issues_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/palh3m1/codegen/palh3m1TE_kinematic_constraints.mpl", "max_forks_repo_name": "SchapplM/robsynth-serhybroblib", "max_forks_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": 48.7510204082, "max_line_length": 304, "alphanum_fraction": 0.7370227729, "num_tokens": 4568, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8397339596505965, "lm_q2_score": 0.7025300698514777, "lm_q1q2_score": 0.5899383573299916}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_x_hjs_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_hjs_params * )(p->params);\n*)\n\nhjs_AA := 0.757211:\nhjs_BB := -0.106364:\nhjs_CC := -0.118649:\nhjs_DD := 0.609650:\n\nhjs_fH := s -> add(params_a_a[i]*s^(1+i), i=1..6)/(1 + add(params_a_b[i]*s^i, i=1..9)):\n\n(* The m_max functions are necessary as in some cases the arguments of the\n sqrt become negative *)\nhjs_zeta := s -> m_max(s^2*hjs_fH(s), 1e-10):\nhjs_eta := s -> m_max(hjs_AA + hjs_zeta(s), 1e-10):\nhjs_lambda := s -> hjs_DD + hjs_zeta(s):\nhjs_chi := (rs, z, s) -> nu(rs, z)/sqrt(hjs_lambda(s) + nu(rs, z)^2):\n\nhjs_fF := (rs, z, s) ->\n 1 - s^2/(27*hjs_CC*(1 + s^2/4)) - hjs_zeta(s)/(2*hjs_CC):\n\nhjs_fG := (rs, z, s) ->\n - 2/5 * hjs_CC*hjs_fF(rs, z, s)*hjs_lambda(s)\n - 4/15 * hjs_BB*hjs_lambda(s)^2\n - 6/5 * hjs_AA*hjs_lambda(s)^3\n - hjs_lambda(s)^(7/2)*(4/5*sqrt(Pi) + 12/5*(sqrt(hjs_zeta(s)) - sqrt(hjs_eta(s)))):\n\nhjs_f1 := (rs, z, s) ->\n + hjs_AA\n - 4/9 * hjs_BB*(1 - hjs_chi(rs, z, s))/hjs_lambda(s)\n - 2/9 * hjs_CC*hjs_fF(rs, z, s)*(2 - 3*hjs_chi(rs, z, s) + hjs_chi(rs, z, s)^3)/hjs_lambda(s)^2\n - 1/9 * hjs_fG(rs, z, s)*(8 - 15*hjs_chi(rs, z, s) + 10*hjs_chi(rs, z, s)^3 - 3*hjs_chi(rs, z, s)^5)/hjs_lambda(s)^3\n + 2*nu(rs, z)*(sqrt(hjs_zeta(s) + nu(rs, z)^2) - sqrt(hjs_eta(s) + nu(rs, z)^2))\n + 2*hjs_zeta(s)*log((nu(rs, z) + sqrt(hjs_zeta(s) + nu(rs, z)^2))/(nu(rs, z) + sqrt(hjs_lambda(s) + nu(rs, z)^2)))\n - 2*hjs_eta(s)*log((nu(rs, z) + sqrt(hjs_eta(s) + nu(rs, z)^2))/(nu(rs, z) + sqrt(hjs_lambda(s) + nu(rs, z)^2))):\n\nhjs_fx := (rs, z, x) -> hjs_f1(rs, z, X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange_nsp(hjs_fx, rs, z, xs0, xs1):\n", "meta": {"hexsha": "8550e5da4633bf89dd174b278267262c9a5cda43", "size": 1936, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_hjs.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_hjs.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_hjs.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": 37.2307692308, "max_line_length": 119, "alphanum_fraction": 0.5795454545, "num_tokens": 847, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070060380482, "lm_q2_score": 0.6477982247516797, "lm_q1q2_score": 0.5894361432005635}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2019 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(* prefix:\n gga_c_optc_params *params;\n\n assert(p->params != NULL);\n params = (gga_c_optc_params * )(p->params);\n*)\n\n$include \"gga_c_pw91.mpl\"\n\noptc_f2 := (rs, z, xt, xs0, xs1) ->\n + f_pw91(rs*(2/(1 + z))^(1/3), 1, xs0, xs0, 0)*opz_pow_n( z,1)/2\n + f_pw91(rs*(2/(1 - z))^(1/3), -1, xs1, 0, xs1)*opz_pow_n(-z,1)/2:\n\nf := (rs, z, xt, xs0, xs1) ->\n + params_a_c1*f_pw91(rs, z, xt, xs0, xs1) + (params_a_c2 - params_a_c1)*optc_f2(rs, z, xt, xs0, xs1):\n", "meta": {"hexsha": "c9088dfb5f887a920bc9564d16926804c96cfa96", "size": 748, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_optc.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_c_optc.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_c_optc.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": 28.7692307692, "max_line_length": 103, "alphanum_fraction": 0.6082887701, "num_tokens": 303, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8976952866333483, "lm_q2_score": 0.6548947425132314, "lm_q1q2_score": 0.5878959235950881}} {"text": "# This is supposed to be a toy 2D model for issues that arise in\n# computational geometry for computer aided design.\n# We work everywhere in the real projective plane, and consider\n# only straight lines and conic curves and segments thereof.\n# This is supposed to make everything nicely computable.\n\ndp3 := proc(x,y) local i; add(x[i]*y[i],i=1..3); end;\nnm3 := proc(x) local i; sqrt(add(x[i]^2,i=1..3)); end;\nxp3 := (u,v) -> [u[2]*v[3]-u[3]*v[2],\n u[3]*v[1]-u[1]*v[3],\n u[1]*v[2]-u[2]*v[1]];\ntp3 := (u,v,w) -> Determinant(Matrix([u,v,w]));\neq3 := (u,v) -> evalb(xp3(u,v) = [0$3]);\nsp3 := (u) -> [u[1]/u[3],u[2]/u[3]];\n\n`plane_stereo/RP` := (x) -> [x[1]/x[3],x[2]/x[3]];\n`plane_unstereo/RP` := (u) -> [u[1],u[2],1];\n\n`disc_stereo/RP` := (x) -> [x[1],x[2]] *~ (signum(x[3])/nm3(x));\n\n`disc_unstereo/RP` := (u) ->\n [u[1],u[2],sqrt(1-u[1]^2-u[2]^2)];\n\n######################################################################\n\n`is_element/RP_points` := proc(x)\n type(x,[numeric,numeric,numeric]);\nend:\n\n`is_leq/RP_points` := NULL:\n`list_elements/RP_points` := NULL:\n`count_elements/RP_points` := NULL:\n\n`random_element/RP_points` := () -> `random_element/R`(3)();\n\n`dist/RP_points` := proc(x,y)\n local i;\n 1 - add(x[i]*y[i],i=1..3)^2/add(x[i]^2,i=1..3)\nend:\n\n`is_equal/RP_points` := (x,y) -> evalb(xp3(x,y) = [0$3]);\n\n`in_general_position/RP_points` :=\n (u,v,w) -> evalb(Determinant(Matrix([u,v,w])) = 0);\n\n`disc_plot/point` := (x) -> point(`disc_stereo/RP`(x),args[2..-1]);\n\n######################################################################\n\n`is_element/RP_lines` := proc(x)\n type(x,[numeric,numeric,numeric]);\nend:\n\n`is_leq/RP_lines` := NULL:\n`list_elements/RP_lines` := NULL:\n`count_elements/RP_lines` := NULL:\n\n`random_element/RP_lines` := () -> `random_element/R`(3)();\n\n`dist/RP_lines` := proc(x,y)\n local i;\n 1 - add(x[i]*y[i],i=1..3)^2/add(x[i]^2,i=1..3)\nend:\n\n`is_equal/RP_lines` := (x,y) -> evalb(xp3(x,y) = [0$3]);\n\n`in_general_position/RP_lines` :=\n (u,v,w) -> evalb(Determinant(Matrix([u,v,w])) = 0);\n\n`track/RP_lines` := proc(x,t)\n local u,v;\n u,v := op(NullSpace(Matrix(x)));\n return (1-t) *~ u +~ t *~ v;\nend:\n\n`disc_plot/line` := proc(x)\n local u,v,w,p,t,t0,R;\n u,v := op(NullSpace(Matrix(x)));\n w := cos(Pi*t) *~ u +~ sin(Pi*t) *~ v;\n t0 := fsolve(w[3]);\n if evalf(subs(t = t0,diff(w[3],t))) > 0 then\n R := (t0 + 0.0001) .. (t0 + 0.9999);\n else \n R := (t0 - 0.9999) .. (t0 - 0.0001);\n fi;\n p := simplify(`disc_stereo/RP`(w));\n plot([op(p),t=R],args[2..-1]);\nend:\n\n######################################################################\n\n`is_incident/RP` := proc(x,y) local i; evalb(add(x[i]*y[i],i=1..3) = 0); end;\n\n`point_join/RP` := (x,y) -> xp3(x,y);\n\n`line_meet/RP` := (x,y) -> xp3(x,y);\n\n######################################################################\n\n`is_element/RP_conics` := proc(q)\n local c;\n if not(type(q,[numeric$6])) then\n return false;\n fi;\n\n # We now need to check whether the associated quadratic form\n # has one negative and two positive eigenvalues. This works\n # out as follows.\n \n c := [-q[1]-q[2]-q[3],\n (q[1]*q[2]+q[2]*q[3]+q[3]*q[1]) - (q[4]^2+q[5]^2+q[6]^2)/4,\n (q[1]*q[4]^2+q[2]*q[5]^2+q[3]*q[6]^2-q[4]*q[5]*q[6])/4\n - q[1]*q[2]*q[3]\n ];\n\n if c[3] > 0 and (c[1] <= 0 or c[2] <= 0) then\n return true;\n fi;\n\n return false;\nend:\n\n`is_leq/RP_conics` := NULL:\n`list_elements/RP_conics` := NULL:\n`count_elements/RP_conics` := NULL:\n\n`random_element/RP_conics` := proc()\n local q;\n\n q := `random_element/R`(6)();\n while not(`is_element/RP_conics`(q)) do\n q := `random_element/R`(6)();\n od:\n\n return q;\nend:\n\n\n`dist/RP_conics` := proc(q,r)\n local i,j;\n sqrt(add(add((q[i]*r[j]-q[j]*r[i])^2,j=i+1..6),i=1..6)/\n (add(q[i]^2,i=1..6) * add(r[i]^2,i=1..6)));\nend:\n\n`is_equal/RP_conics` := proc(q,r)\n evalb(`dist/RP_conics`(q,r) = 0);\nend:\n\n`conic_matrix/RP` := (q) -> \n <,,>;\n\n`conic_unmatrix/RP` := (Q) ->\n [Q[1,1],Q[2,2],Q[3,3],2*Q[2,3],2*Q[3,1],2*Q[1,2]];\n\n`conic_eval/RP` := (q) -> (x) ->\n q[1]*x[1]^2 + q[2]*x[2]^2 + q[3]*x[3]^2 +\n q[4]*x[2]*x[3] + q[5]*x[3]*x[1] + q[6]*x[1]*x[2];\n\n`conic_bilin/RP` := (q) -> (x,y) ->\n (`conic_eval/RP`(q)(x +~ y) - `conic_eval/RP`(q)(x -~ y))/4; \n\n`conic_coeffs/RP` := (qx,x) -> [\n coeff(qx,x[1],2),\n coeff(qx,x[2],2),\n coeff(qx,x[3],2),\n coeff(coeff(qx,x[2],1),x[3],1),\n coeff(coeff(qx,x[3],1),x[1],1),\n coeff(coeff(qx,x[1],1),x[2],1)\n];\n\n`disc_implicitplot/conic` := proc(q)\n local u,v,qq;\n \n qq := numer(simplify(`conic_eval/RP`(q)(`disc_unstereo/RP`([u,v]))));\n implicitplot(qq,u=-1.1..1.1,v=-1.1..1.1,args[2..-1]);\nend:\n\n######################################################################\n\n`is_element/RP_arcs` := proc(xxc)\n if not(type(xxc,[[numeric$3]$3])) then\n return false;\n fi;\n\n if Determinant(Matrix(xxc)) = 0 then return false; fi;\n\n return true;\nend:\n\n`random_element/RP_arcs` := proc()\n local xxc,i,j;\n xxc := [[0$3]$3];\n\n while Determinant(Matrix(xxc)) = 0 do\n xxc := [seq([seq(rand(-10..10)(),i=1..3)],j=1..3)];\n od;\n\n return xxc;\nend:\n\n`ratio/RP_arcs` := proc(xxc1,xxc2)\n local u,v,w,i;\n \n u := [seq(dp3(xxc1[i],xxc2[i]),i=1..3)];\n v := [seq(dp3(xxc1[i],xxc1[i]),i=1..3)];\n w := [seq(dp3(xxc2[i],xxc2[i]),i=1..3)];\n\n if (u *~ u = v *~ w) then\n return u /~ w;\n else\n return NULL;\n fi;\nend:\n\n`is_equal/RP_arcs` := proc(xxc1,xxc2)\n local r;\n r := `ratio/RP_arcs`(xxc1,xxc2);\n\n if r = NULL then return false; fi;\n if r[1] <> r[2] or r[2] <> r[3] then\n return false;\n fi;\n\n return true;\nend:\n\n`is_similar/RP_arcs` := proc(xxc1,xxc2)\n local r;\n r := `ratio/RP_arcs`(xxc1,xxc2);\n\n if r = NULL then return false; fi;\n if r[1]*r[2] - r[3]^2 <> 0 then\n return false;\n fi;\n\n return true; \nend:\n\n`is_leq/RP_arcs` := NULL:\n`list_elements/RP_arcs` := NULL:\n`count_elements/RP_arcs` := NULL:\n\n`arc_eval/RP` := (xxc) -> (t) ->\n (1-t)^2 *~ xxc[1] +~ t^2 *~ xxc[2] +~ (t*(1-t)) *~ xxc[3];\n\n`conic_arc_eval/RP` := (q,xxc) -> (t) ->\n `conic_eval/RP`(q)(`arc_eval/RP`(xxc)(t));\n\n`conic_contains_point/RP` := proc(q,x)\n local err;\n err := abs(`conic_eval/RP`(q)(x));\n return evalb(err = 0);\nend:\n\n`conic_contains_arc/RP` := proc(q,xxc)\n local t,err;\n err := max(map(abs,[coeffs(expand(`conic_arc_eval/RP`(q,xxc)(t)),t)]));\n return evalb(err = 0);\nend:\n\n`normalise_similar/RP_arcs` := proc(xxc)\n local x,c,n;\n x[1] := xxc[1];\n x[2] := xxc[2];\n c := xxc[3];\n n[1] := nm3(x[1]);\n n[2] := nm3(x[2]);\n return [x[1]/~n[1],x[2]/~n[2],c/~sqrt(n[1]*n[2])];\nend:\n\n`arc_coeffs/RP` := proc(st,t)\n local su,u;\n su := factor((1+u)^2 *~ subs(t=u/(1+u),st));\n [map(coeff,su,u,0),\n map(coeff,su,u,2),\n map(coeff,su,u,1)];\nend:\n\n`arc_from_tangents/RP` := proc(x1,x2,u1,u2)\n local m1,m2,n,c;\n m1 := Determinant(Matrix([x1,x2,u2]));\n m2 := Determinant(Matrix([x1,x2,u1]));\n n := - Determinant(Matrix([x1,u1,u2])) * m2/m1;\n c := n *~ x2 +~ m2 *~ u2;\n return [m1 *~ x1,m2 *~ x2,n *~ c];\nend:\n\n`arc_inv/RP` := (xxc) -> proc(y)\n local u1,u2,u3;\n u1 := Determinant(Matrix(x1,x2,y));\n u2 := Determinant(Matrix(x2,c ,y));\n u3 := Determinant(Matrix(c ,x1,y));\n return u2/(u1+u2); # or u1/(u1+u3);\nend:\n\n`conic_from_arc/RP` := proc(xxc)\n local x1,x2,c,M;\n x1,x2,c := op(xxc);\n \n M := Matrix(\n [[x1[1]^2, x1[2]^2, x1[3]^2,\n x1[2]*x1[3], x1[1]*x1[3], x1[1]*x1[2]],\n [x2[1]^2, x2[2]^2, x2[3]^2,\n x2[2]*x2[3], x2[1]*x2[3], x2[1]*x2[2]],\n [2*c[1]*x1[1], 2*c[2]*x1[2], 2*c[3]*x1[3], c[2]*x1[3]+c[3]*x1[2],\n c[1]*x1[3]+c[3]*x1[1], c[1]*x1[2]+c[2]*x1[1]],\n [2*c[1]*x2[1], 2*c[2]*x2[2], 2*c[3]*x2[3], c[2]*x2[3]+c[3]*x2[2],\n c[1]*x2[3]+c[3]*x2[1], c[1]*x2[2]+c[2]*x2[1]],\n [c[1]^2+2*x1[1]*x2[1], c[2]^2+2*x1[2]*x2[2], c[3]^2+2*x1[3]*x2[3],\n c[2]*c[3]+x1[2]*x2[3]+x1[3]*x2[2],\n c[1]*c[3]+x1[1]*x2[3]+x1[3]*x2[1],\n c[1]*c[2]+x1[1]*x2[2]+x1[2]*x2[1]]]\n );\n return NullSpace(M)[1];\nend:\n\n`arc_from_rational_conic/RP` := proc(q)\n local x,y,z,f,sol,u0,u1,u2,u,t,Z;\n if not(type(q,[rational$6])) then\n return NULL;\n fi;\n\n f := `conic_eval/RP`(q)([x,y,z]);\n sol := isolve(f);\n if sol = NULL then return NULL; fi;\n\n u0 := subs(sol,[x,y,z]);\n u1 := eval(subs(igcd = (() -> 1),u0));\n u2 := u1;\n for Z in indets(u1) do\n if degree(u1[1],Z) = 1 then u2 := subs(Z = 1,u2); fi;\n od:\n u := subs({indets(u2)[1] = t,indets(u2)[2] = 1-t},u2);\n return `arc_coeffs/RP`(u,t);\nend:\n\n`arc_from_conic_eigenvalues/RP` := proc(q)\n local Q,E,V,i,v,xxc;\n Q := evalf(Matrix(`conic_matrix/RP`(q),shape=symmetric));\n E,V := Eigenvectors(Q);\n for i from 1 to 3 do \n v[i] := convert(Column(V,i)/sqrt(abs(E[i])),list); \n od;\n xxc := [(v[1] +~ v[2])/~2,(v[1] -~ v[2])/~2,v[3]];\n return xxc;\nend:\n\n`cut_arc/RP` := proc(xxc,t1,t2)\n local y1,y2,d;\n y1 := `arc_eval/RP`(xxc)(t1);\n y2 := `arc_eval/RP`(xxc)(t2);\n d := (2*(1-t1)*(1-t2)) *~ xxc[1] +~\n (2*t1*t2) *~ xxc[2] +~\n (t1 + t2 - 2*t1*t2) *~ xxc[3];\n return [y1,y2,d];\nend:\n\n`shift_arc/RP` := proc(xxc,u)\n [exp(u),exp(-u),1] *~ xxc;\nend:\n\n`bulge_arc/RP` := proc(xxc,u)\n local x1,x2,c;\n x1,x2,c := op(xxc);\n if u >= 0 then\n return [x1,x2,u*~c];\n else\n return [x1,x2,u*~c];\n fi;\nend:\n\n`disc_plot/arc` := proc(xxc)\n local u,v,tt,m,i,P,e,t0,t1;\n u := `arc_eval/RP`(xxc)(t);\n tt := sort(evalf([op({0,1,fsolve(u[3],t=0..1)})]));\n m := nops(tt);\n P := NULL;\n e := 10.^(-4);\n for i from 1 to m-1 do\n t0 := (1-e) *~ tt[i] +~ e *~ tt[i+1];\n t1 := e *~ tt[i] +~ (1-e) *~ tt[i+1];\n v := simplify(`disc_stereo/RP`(u)) assuming t > t0 and t < t1;\n P := P,plot([op(v),t=t0..t1],args[2..-1]);\n od:\n display(P);\nend:\n\n`disc_point_plot/arc` := proc(xxc)\n local i,N,P,u,v,p;\n N := 12;\n P := NULL;\n for i from 0 to N do\n u := evalf(`arc_eval/RP`(xxc)(i/N));\n v := `disc_stereo/RP`(u);\n p := point(v,args[2..-1]);\n P := P,p;\n od:\n display(P);\nend:\n", "meta": {"hexsha": "afc7871e3c1499d1565e2cbdaaa8692d719f5317", "size": 9679, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/plane_cad.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/plane_cad.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/plane_cad.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": 24.1975, "max_line_length": 77, "alphanum_fraction": 0.5240210766, "num_tokens": 4160, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8652240895276223, "lm_q2_score": 0.6791787056691698, "lm_q1q2_score": 0.5876417772391564}} {"text": "with(Groebner):\nwith(Ore_algebra):\n\n\nfind_koszul_homology := proc(rels,vars_,p_)\n local vars,char,A,T,P,ix_P,S,B0,B1,d,i,j,k,u,e_K,e_Z,e_B,de_K,ee_K,dd,K,\n K_basis,K_rank,Z_basis,Z_rank,B_basis,B_rank,BZ_basis,BZ_rank;\n\n if nargs > 1 then\n vars := vars_;\n else\n vars := [op(indets(rels,symbol))];\n fi;\n\n if nargs > 2 then\n char := (characteristic = p_);\n else\n char := NULL;\n fi;\n\n A := poly_algebra(op(vars),e_K,e_Z,e_B,char);\n T := MonomialOrder(A,lexdeg([e_K,e_B],vars,[e_Z]),{e_K,e_Z,e_B});\n\n d := nops(rels);\n # P = list of all subsets of 1,..,d\n P := combinat[powerset]([seq(i,i=1..d)]);\n\n # Now build index for P e.g. if {1,4,6} appears as 10th\n # element of P then if_P[{1,4,6}] should be 10.\n ix_P := table():\n for i from 1 to 2^d do ix_P[P[i]] := i; od:\n\n # de_K[i] will be the differential applied to the i'th basis\n # element of the exterior algebra (for 1 <= i <= 2^d).\n de_K := table():\n for i from 1 to 2^d do\n S := P[i];\n de_K[i] := add((-1)^(j-1) * e_K^ix_P[subsop(j=NULL,S)] * rels[S[j]],j=1..nops(S));\n ee_K[i] := e_K^i + e_K^(2^d+1) * de_K[i];\n od:\n\n # dd = the differential = linear extension of the map\n # sending e_K^i to de_K[i]\n dd := (u) -> add(coeff(u,e_K,i) * de_K[i],i=1..2^d);\n\n # Basis() calculates Groebner basis\n B0 := Basis([seq(ee_K[i],i=1..2^d)],T,char);\n K_basis := [seq(e_K^i,i=1..2^d)];\n K_rank := 2^d;\n Z_basis := select(u -> degree(u,e_K) <= 2^d,B0);\n Z_rank := nops(Z_basis);\n B_basis := select(u -> u <> 0,expand(map(quo,B0,e_K^(2^d+1),e_K)));\n B_rank := nops(B_basis);\n\n B1 := Basis([seq(e_B^i + B_basis[i],i=1..B_rank),\n seq(e_Z^i + Z_basis[i],i=1..Z_rank)],T,char);\n\n BZ_basis := [seq(NormalForm(e_B^i,B1,T,char),i=1..B_rank)];\n BZ_rank := nops(BZ_basis);\n\n K := table():\n K[\"num_rels\"] := d;\n K[\"A\"] := A;\n K[\"T\"] := T;\n K[\"P\"] := P;\n K[\"ix_P\"] := eval(ix_P);\n K[\"de_K\"] := eval(de_K);\n K[\"K_basis\"] := K_basis;\n K[\"K_rank\"] := K_rank;\n K[\"Z_basis\"] := Z_basis;\n K[\"Z_rank\"] := Z_rank;\n K[\"B_basis\"] := B_basis;\n K[\"B_rank\"] := B_rank;\n K[\"BZ_basis\"] := BZ_basis;\n K[\"BZ_rank\"] := BZ_rank;\n\n K[\"Z_basis_matrix\"] := \n Matrix([seq([seq(coeff(u,e_K,i),i=1..2^d)],u in Z_basis)]);\n K[\"B_basis_matrix\"] := \n Matrix([seq([seq(coeff(u,e_K,i),i=1..2^d)],u in B_basis)]);\n K[\"BZ_basis_matrix\"] := \n Matrix([seq([seq(coeff(u,e_Z,i),i=1..Z_rank)],u in BZ_basis)]);\n\n K[\"B0\"] := B0;\n K[\"B1\"] := B1;\n\n return eval(K);\nend:\n\n", "meta": {"hexsha": "60204dbe2b4f4b335c87560828857f33e0c276d4", "size": 2390, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/koszul.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/koszul.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/koszul.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": 26.5555555556, "max_line_length": 84, "alphanum_fraction": 0.5824267782, "num_tokens": 926, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8652240825770432, "lm_q2_score": 0.679178699175393, "lm_q1q2_score": 0.587641766899899}} {"text": "DPH_expr:=-1/6*alpha(t,x)*K(t,x)+beta(t,x)*diff(phi(t,x),x)+1/6*diff(beta(t,x),x);\ndgxx_expr:=-2*alpha(t,x)*Axx(t,x)+beta(t,x)*diff(A(t,x),x)+4/3*A(t,x)*diff(beta(t,x),x);\ndgthetatheta_expr:=-1/3*x*(6*alpha(t,x)*x*Athth(t,x)-6*beta(t,x)*B(t,x)-3*beta(t,x)*x*diff(B(t,x),x)+2*x*B(t,x)*diff(beta(t,x),x));\nmetxx_expr:=exp(phi(t,x))^4*A(t,x);\nmetthetatheta_expr:=exp(phi(t,x))^4*B(t,x);\ninvmetxx_expr:=1/exp(phi(t,x))^4/A(t,x);\ninvmetthetatheta_expr:=1/exp(phi(t,x))^4/B(t,x);\nDDLxx_expr:=-1/2*(-2*diff(diff(alpha(t,x),x),x)*metxx(t,x)+diff(metxx(t,x),x)*diff(alpha(t,x),x))/metxx(t,x);\nDDLthetatheta_expr:=1/2*x*(2*metthetatheta(t,x)+x*diff(metthetatheta(t,x),x))/metxx(t,x)*diff(alpha(t,x),x);\nDTK_expr:=-1/metxx(t,x)*DDLxx(t,x)-2/metthetatheta(t,x)*DDLthetatheta(t,x)+1/3*alpha(t,x)*K(t,x)^2+1/2*alpha(t,x)*rho(t,x)+1/2*alpha(t,x)*TS(t,x)+beta(t,x)*diff(K(t,x),x)+1/A(t,x)^2*alpha(t,x)*Axx(t,x)^2+2/B(t,x)^2*alpha(t,x)*Athth(t,x)^2;\nRRxx_expr:=3/4/A(t,x)^2*diff(A(t,x),x)^2-2/x^2-2/x/B(t,x)*diff(B(t,x),x)-1/2/B(t,x)^2*diff(B(t,x),x)^2+A(t,x)*diff(Lamx(t,x),x)+2/x^2*A(t,x)/B(t,x)+2/x*A(t,x)/B(t,x)^2*diff(B(t,x),x)+1/2*diff(A(t,x),x)*Lamx(t,x)-1/x/B(t,x)*diff(A(t,x),x)-1/2/A(t,x)*diff(diff(A(t,x),x),x)-4*diff(diff(phi(t,x),x),x)+2/A(t,x)*diff(phi(t,x),x)*diff(A(t,x),x)-4/x*diff(phi(t,x),x)-2/B(t,x)*diff(phi(t,x),x)*diff(B(t,x),x);\nRRthetatheta_expr:=1/A(t,x)*B(t,x)+1/2/A(t,x)/B(t,x)*diff(B(t,x),x)^2*x^2+Lamx(t,x)*x*B(t,x)+1/2*x^2*Lamx(t,x)*diff(B(t,x),x)-1/B(t,x)*x*diff(B(t,x),x)-1/2/A(t,x)*x^2*diff(diff(B(t,x),x),x)-1-6/A(t,x)*B(t,x)*x*diff(phi(t,x),x)-3/A(t,x)*x^2*diff(phi(t,x),x)*diff(B(t,x),x)-2/A(t,x)*B(t,x)*x^2*diff(diff(phi(t,x),x),x)+1/A(t,x)^2*B(t,x)*x^2*diff(phi(t,x),x)*diff(A(t,x),x)-4/A(t,x)*B(t,x)*x^2*diff(phi(t,x),x)^2;\nUxx_expr:=alpha(t,x)*Axx(t,x)*K(t,x)-2*alpha(t,x)*Axx(t,x)^2/A(t,x);\nUthetatheta_expr:=alpha(t,x)*x^2*Athth(t,x)*K(t,x)-2*alpha(t,x)*x^2*Athth(t,x)^2/B(t,x);\nPxx_expr:=beta(t,x)*diff(Axx(t,x),x)+4/3*Axx(t,x)*diff(beta(t,x),x);\nPthetatheta_expr:=2*beta(t,x)*x*Athth(t,x)+beta(t,x)*x^2*diff(Athth(t,x),x)-2/3*x^2*Athth(t,x)*diff(beta(t,x),x);\nDAAxx_expr:=-2/3*em4phi(t,x)*DDLxx(t,x)+2/3/metthetatheta(t,x)*em4phi(t,x)*DDLthetatheta(t,x)*metxx(t,x)+2/3*em4phi(t,x)*alpha(t,x)*RRxx(t,x)-2/3/metthetatheta(t,x)*em4phi(t,x)*alpha(t,x)*RRthetatheta(t,x)*metxx(t,x)-2/3*em4phi(t,x)*alpha(t,x)*JSxx(t,x)+2/3/metthetatheta(t,x)*em4phi(t,x)*alpha(t,x)*JSthth(t,x)*metxx(t,x)+alpha(t,x)*Uxx(t,x)+Pxx(t,x);\nDAAthetatheta_expr:=1/3*x^2/metxx(t,x)*em4phi(t,x)*DDLxx(t,x)*metthetatheta(t,x)-1/3*x^2*em4phi(t,x)*DDLthetatheta(t,x)-1/3*x^2/metxx(t,x)*em4phi(t,x)*alpha(t,x)*RRxx(t,x)*metthetatheta(t,x)+1/3*x^2*em4phi(t,x)*alpha(t,x)*RRthetatheta(t,x)-1/3*x^2*em4phi(t,x)*alpha(t,x)*JSthth(t,x)+1/3*x^2/metxx(t,x)*em4phi(t,x)*alpha(t,x)*JSxx(t,x)*metthetatheta(t,x)+x^2*alpha(t,x)*Uthetatheta(t,x)+x^2*Pthetatheta(t,x);\nDLAMx_expr:=-2/A(t,x)^2*Axx(t,x)*diff(alpha(t,x),x)-4/3/A(t,x)*alpha(t,x)*diff(K(t,x),x)-2/A(t,x)*alpha(t,x)*Sx(t,x)+12/A(t,x)^2*alpha(t,x)*Axx(t,x)*diff(phi(t,x),x)+beta(t,x)*diff(Lamx(t,x),x)-2/x^2/B(t,x)*beta(t,x)-1/3*diff(beta(t,x),x)*Lamx(t,x)+2/x/B(t,x)*diff(beta(t,x),x)+1/A(t,x)^3*alpha(t,x)*diff(A(t,x),x)*Axx(t,x)+4/3/A(t,x)*diff(diff(beta(t,x),x),x)-4/A(t,x)/x/B(t,x)*alpha(t,x)*Athth(t,x)-2/A(t,x)/B(t,x)^2*alpha(t,x)*Athth(t,x)*diff(B(t,x),x)+4/x/B(t,x)^2*alpha(t,x)*Athth(t,x);\nDLAMtheta_expr:=0;\nC1_expr:=-3/32/A(t,x)^3*diff(A(t,x),x)^2+1/4/x/A(t,x)/B(t,x)*diff(B(t,x),x)-1/16/A(t,x)/B(t,x)^2*diff(B(t,x),x)^2-1/8*diff(Lamx(t,x),x)-1/16/A(t,x)*diff(A(t,x),x)*Lamx(t,x)+1/8/x/A(t,x)/B(t,x)*diff(A(t,x),x)+1/16/A(t,x)^2*diff(diff(A(t,x),x),x)-1/4/x*Lamx(t,x)-1/8/B(t,x)*Lamx(t,x)*diff(B(t,x),x)+1/8/A(t,x)/B(t,x)*diff(diff(B(t,x),x),x);\nC5_expr:=-1/12*K(t,x)^2+1/4*rho(t,x)+1/8/A(t,x)^2*Axx(t,x)^2+1/4/B(t,x)^2*Athth(t,x)^2;\nHS_expr:=C5s(t,x)*psi(t,x)^5+C1s(t,x)*psi(t,x)+1/A(t,x)*diff(diff(psi(t,x),x),x)-1/2/A(t,x)^2*diff(psi(t,x),x)*diff(A(t,x),x)+2/A(t,x)/x*diff(psi(t,x),x)+1/A(t,x)/B(t,x)*diff(psi(t,x),x)*diff(B(t,x),x);\n\n", "meta": {"hexsha": "b50dba8c39991370834b0741212bb60874d46e14", "size": 3991, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "archive/allequations.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "archive/allequations.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "archive/allequations.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": 159.64, "max_line_length": 491, "alphanum_fraction": 0.5933350038, "num_tokens": 1973, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632936392131, "lm_q2_score": 0.6334102775181399, "lm_q1q2_score": 0.5874014411841503}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_x_mpbe_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_mpbe_params * )(p->params);\n*)\n\nmpbe_f0 := s -> s^2/(1 + params_a_a*s^2):\nmpbe_f := x -> 1\n + params_a_c1*mpbe_f0(X2S*x)\n + params_a_c2*mpbe_f0(X2S*x)^2\n + params_a_c3*mpbe_f0(X2S*x)^3:\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(mpbe_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "2a45249ee6699a7c00e90d2bcbb538b4ae28232a", "size": 606, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_mpbe.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_mpbe.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_mpbe.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": 25.25, "max_line_length": 68, "alphanum_fraction": 0.6501650165, "num_tokens": 228, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797075998822, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5870048441567532}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-14-input.txt\" ):\n\nsplit := StringTools:-Split(input,\"\\n\"):\npolymer := split[1];\nrules := table(map(`=`@op,\n map(s->StringTools:-Split(s)[[1,3]], split[3..-1]))):\n\n# initial count\npaircount := table(sparse=0):\nfor i to length(polymer)-1 do\n paircount[polymer[i..i+1]] += 1;\nend do:\n\nfor i to 40 do\n update := indices(paircount, 'pairs');\n paircount := table(sparse=0):\n lettercount := table(sparse=0):\n for u in update do\n b := lhs(u); c := rules[lhs(u)];\n paircount[ cat(b[1],c) ] += rhs(u);\n paircount[ cat(c,b[2]) ] += rhs(u);\n lettercount[ b[1] ] += rhs(u);\n lettercount[ b[2] ] += rhs(u);\n lettercount[ c ] += 2*rhs(u);\n end do:\n lettercount[polymer[1]] += 1; lettercount[polymer[-1]] += 1;\n if i = 10 or i = 40 then\n t:=[entries(lettercount, 'nolist')];\n print( i=(t[max[index](t)] - t[min[index](t)]) / 2);\n end if;\nend do:\n", "meta": {"hexsha": "b27a6080682c8b6dfaa83f56c289994c64382549", "size": 960, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day14/AoC14-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day14/AoC14-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day14/AoC14-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.0, "max_line_length": 64, "alphanum_fraction": 0.55, "num_tokens": 323, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8354835207180245, "lm_q2_score": 0.7025300573952052, "lm_q1q2_score": 0.5869522857627819}} {"text": "#@ Not autoload\n\nwith(GroupTheory):\nwith(LinearAlgebra):\n\nS4 := SymmetricGroup(4);\n\nx2 := [[1,2]];\ny2 := [[2,3]];\nz2 := [[3,4]];\nu2 := [[1,2],[3,4]];\nv2 := [[1,3],[2,4]];\nx3 := [[1,2,3]];\nx4 := [[1,3,2,4]];\n\nH[ 1] := Subgroup({},S4);\nH[ 2] := Subgroup({x2},S4);\nK[ 2] := Subgroup({u2},S4);\nH[ 3] := Subgroup({x3},S4);\nH[ 4] := Subgroup({x4},S4);\nK[ 4] := Subgroup({x2,z2},S4);\nL[ 4] := Subgroup({u2,v2},S4);\nH[ 6] := Subgroup({x2,x3},S4);\nH[ 8] := Subgroup({x2,x4},S4);\nH[12] := Subgroup({u2,x3},S4);\nH[24] := S4;\n\nS4_subgroups := [H[1],H[2],K[2],H[3],H[4],K[4],L[4],H[6],H[8],H[12],H[24]]:\n\n# Burnside matrix of numbers |Map_G(G/H_i,G/H_j)|\nn := nops(S4_subgroups);\nM := Matrix(n,n):\nfor i from 1 to n do\n for j from 1 to n do\n Hi := S4_subgroups[i];\n Zi := {op(Generators(Hi))};\n Hj := S4_subgroups[j];\n C := map(Representative,LeftCosets(Hj,S4));\n M[i,j] := nops(select(c -> `and`(op(map(x -> SubgroupMembership(c^(-1) . x . c,Hj),Zi))),C));\n od:\nod:\n\nunassign('C'):\n\n# Skeleton of the poset of conjugacy classes of subgroups\nN := {seq(i,i=1..n)};\nR := select(ij -> M[ij[1],ij[2]] <> 0,{seq(seq([i,j],j=1..n),i=1..n)});\n\n# Conjugacy classes\n\nC[1] := ConjugacyClass([],S4);\nC[2] := ConjugacyClass(x2,S4);\nC[3] := ConjugacyClass(u2,S4);\nC[4] := ConjugacyClass(x3,S4);\nC[5] := ConjugacyClass(x4,S4);\n\nchars := [\n [ 1, 1, 1, 1, 1],\n [ 1,-1, 1, 1,-1],\n [ 2, 0, 2,-1, 0],\n [ 3, 1,-1, 0,-1],\n [ 3,-1,-1, 0, 1]\n];\n\nchar_names := [1,epsilon,sigma,rho,epsilon*rho];\n\nchar_rels := [\n epsilon^2 - 1,\n epsilon * sigma - sigma,\n sigma^2 - 1 - epsilon - sigma,\n sigma * rho - rho - epsilon * rho,\n rho^2 - 1 - sigma - rho - epsilon * rho\n];\n\nchar_psi_rels := [\n psi(2,epsilon) = 1,\n psi(2,sigma) = 1 - epsilon + sigma,\n psi(3,sigma) = 1 + epsilon,\n psi(2,rho) = 1 + sigma + rho - epsilon * rho,\n psi(3,rho) = 1 + epsilon - sigma + rho\n];\n\nchar_lambda_rels := [\n lambda(2,sigma) = epsilon,\n lambda(2,rho) = epsilon * rho,\n lambda(3,rho) = epsilon\n];", "meta": {"hexsha": "6b504f28ddeaaca68cfd62c68a0849fafa093e27", "size": 1941, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/groups/S4.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/groups/S4.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/groups/S4.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": 22.3103448276, "max_line_length": 95, "alphanum_fraction": 0.5486862442, "num_tokens": 854, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8723473746782093, "lm_q2_score": 0.6723317057447908, "lm_q1q2_score": 0.5865067984193907}} {"text": "Q := [b*c+a, a*c-b, b*c-c^2+a-1, b*c+c^2+a+1, a*c-c^2-b-1, a*c+c^2-b+1, a*c-b*\nc-a-b, a*c+b*c+a-b, a^2+b^2-3*c^2-3, a^2+b^2-c^2-1, 3*a^2+3*b^2-c^2-1, a^2+b^2\n-b*c-a, a^2+b^2+b*c+a, a^2-a*c+b^2+b, a^2+a*c+b^2-b, a^2+b^2-4*b*c+c^2-4*a+1,\na^2+b^2-2*b*c-c^2-2*a-1, a^2+b^2+2*b*c-c^2+2*a-1, a^2+b^2+4*b*c+c^2+4*a+1, a^2\n-4*a*c+b^2+c^2+4*b+1, a^2-2*a*c+b^2-c^2+2*b-1, a^2+2*a*c+b^2-c^2-2*b-1, a^2+4*\na*c+b^2+c^2-4*b+1, a^2-2*a*c+b^2-2*b*c+c^2-2*a+2*b+1, a^2-2*a*c+b^2+2*b*c+c^2+\n2*a+2*b+1, a^2+2*a*c+b^2-2*b*c+c^2-2*a-2*b+1, a^2+2*a*c+b^2+2*b*c+c^2+2*a-2*b+\n1, -b*c+a, a*b+c, -b^2-b*c+a-1, b^2-b*c+a+1, a*b-b*c+a+c, a*b+b*c-a+c, a*b-b^2\n+c-1, a*b+b^2+c+1, a^2-b*c+c^2+a, a^2+b*c+c^2-a, a^2-3*b^2+c^2-3, a^2-b^2+c^2-\\\n1, 3*a^2-b^2+3*c^2-1, a^2-a*b+c^2-c, a^2+a*b+c^2+c, a^2-b^2-2*b*c+c^2+2*a-1, a\n^2-b^2+2*b*c+c^2-2*a-1, a^2+b^2-4*b*c+c^2+4*a+1, a^2+b^2+4*b*c+c^2-4*a+1, a^2-\\\n4*a*b+b^2+c^2-4*c+1, a^2-2*a*b-b^2+c^2-2*c-1, a^2+2*a*b-b^2+c^2+2*c-1, a^2+4*a\n*b+b^2+c^2+4*c+1, a^2-2*a*b+b^2-2*b*c+c^2+2*a-2*c+1, a^2-2*a*b+b^2+2*b*c+c^2-2\n*a-2*c+1, a^2+2*a*b+b^2-2*b*c+c^2+2*a+2*c+1, a^2+2*a*b+b^2+2*b*c+c^2-2*a+2*c+1\n, a*c+b, a*b-c, a*c-b^2-c^2+b, a*c+b^2+c^2+b, a*b-b^2-c^2-c, a*b+b^2+c^2-c, a*\nb-a*c-b-c, a*b+a*c+b-c, a^2-3*b^2-3*c^2+1, a^2-b^2-c^2+1, 3*a^2-b^2-c^2+3, a^2\n-a*c-b+1, a^2+a*c+b+1, a^2-a*b+c+1, a^2+a*b-c+1, a^2-4*a*c+b^2+c^2-4*b+1, a^2-\\\n2*a*c-b^2-c^2-2*b+1, a^2+2*a*c-b^2-c^2+2*b+1, a^2+4*a*c+b^2+c^2+4*b+1, a^2-4*a\n*b+b^2+c^2+4*c+1, a^2-2*a*b-b^2-c^2+2*c+1, a^2+2*a*b-b^2-c^2-2*c+1, a^2+4*a*b+\nb^2+c^2-4*c+1, a^2-2*a*b-2*a*c+b^2+c^2-2*b+2*c+1, a^2-2*a*b+2*a*c+b^2+c^2+2*b+\n2*c+1, a^2+2*a*b-2*a*c+b^2+c^2-2*b-2*c+1, a^2+2*a*b+2*a*c+b^2+c^2+2*b-2*c+1];\n", "meta": {"hexsha": "a3b9f32cf55045d88d22eaacefde5cb2250686d7", "size": 1660, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "files/quadrics_N1.mpl", "max_stars_repo_name": "copyme/copyme.github.io", "max_stars_repo_head_hexsha": "112c2a9eac8ca155224d86d390d5cf701e16db6b", "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": "files/quadrics_N1.mpl", "max_issues_repo_name": "copyme/copyme.github.io", "max_issues_repo_head_hexsha": "112c2a9eac8ca155224d86d390d5cf701e16db6b", "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": "files/quadrics_N1.mpl", "max_forks_repo_name": "copyme/copyme.github.io", "max_forks_repo_head_hexsha": "112c2a9eac8ca155224d86d390d5cf701e16db6b", "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": 75.4545454545, "max_line_length": 79, "alphanum_fraction": 0.4668674699, "num_tokens": 1209, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070035949657, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5861849362836603}} {"text": "A_infinity_rel := (m) -> proc(n::posint)\n local p,r,s,t,u,i;\n p := 0;\n for r from 0 to n do\n for s from 1 to n-r do\n t := n - r - s;\n u := r + 1 + t;\n p := p + (-1)^(r+s*t) *\n m(u)(seq(x[i],i=1..r),\n m(s)(seq(x[i],i=r+1..r+s)),\n seq(x[i],i=r+s+1..n));\n od;\n od;\n return unapply(p,seq(x[i],i=1..n));\nend:\n\nA_infinity_deg := (n) -> n - 2;\n\ntwisted_complex_rel := (d) -> proc(u) local i; \n unapply(add((-1)^i * d(i)(d(u-i)(x)),i=0..u),x);\nend:\n\ntwisted_complex_bideg := (i) -> [i,i-1];\n\nDA_infinity_rel := (mm) -> proc(i::nonnegint,n::posint) \n local p,r,s,t,u,j,k,l,x;\n p := 0;\n for r from 0 to n do\n for s from 1 to n-r do\n for j from 0 to i do\n t := n - r - s;\n u := r + 1 + t;\n k := i - j;\n p := p + (-1)^(r*s+t+k*u) *\n mm(j,u)(seq(x[l],l=1..r),\n mm(k,s)(seq(x[l],l=r+1..r+s)),\n seq(x[l],l=r+s+1..n));\n od;\n od;\n od;\n return unapply(p,seq(x[l],l=1..n));\nend:\n\nDA_infinity_bideg := (i,n) -> [i,i+n-2];\n\n", "meta": {"hexsha": "9edd042b86735b02b6831d74ed95587bcf81dc65", "size": 958, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/a_infinity.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/a_infinity.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/a_infinity.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": 20.8260869565, "max_line_length": 56, "alphanum_fraction": 0.4665970772, "num_tokens": 418, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894745194281, "lm_q2_score": 0.6548947290421275, "lm_q1q2_score": 0.5859929104651486}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_gga_c *)\n(* prefix:\n gga_c_zvpbeint_params *params;\n\n assert(p->params != NULL);\n params = (gga_c_zvpbeint_params * )(p->params);\n*)\n\nparams_a_gamma := (1 - log(2))/Pi^2:\nparams_a_BB := 1:\n$include \"gga_c_pbe.mpl\"\n\nnu := (rs, z, t) ->\n t*mphi(z)*(3/rs)^(1/6):\nff := (rs, z, t) ->\n exp(-params_a_alpha*nu(rs, z, t)^3*m_abs(1*z)^params_a_omega):\n\nf := (rs, z, xt, xs0, xs1) ->\n f_pw(rs, z) + ff(rs, z, tp(rs, z, xt))*fH(rs, z, tp(rs, z, xt)):\n", "meta": {"hexsha": "548e4816ab8ec53030973fd98fe6d201a5242ee0", "size": 704, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_c_zvpbeint.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_c_zvpbeint.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_c_zvpbeint.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 25.1428571429, "max_line_length": 68, "alphanum_fraction": 0.6122159091, "num_tokens": 263, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8887587875995483, "lm_q2_score": 0.6584175072643413, "lm_q1q2_score": 0.5851743454905728}} {"text": "\nrestart;\nwriteto(terminal);\nNULL;\nS := readdata(\"s.txt\", float, 3)[1];\nX1 := S[1];\nX2 := S[2];\nT := S[3];\nY_str := parse(readdata(\"y.txt\", string, 3)[1][1], statement);\ny := unapply(Y_str, x1, x2, t);\ny(0, 0, 42);\nL_str := parse(readdata(\"L_eq.txt\", string, 100)[1][1], statement);\nG_str := parse(readdata(\"G.txt\", string, 100)[1][1], statement);\nc := 1;\nL := unapply(L_str, x1, x2, t);\nu := (x1, x2, t) -> L(x1, x2, t);\nG := unapply(G_str, x1, x2, t);\n;\nu(0.5, 0.5, 0.5);\nG(0, 1/5, 0.3);\ny(0, 0, 42);\n\nplotsetup(maplet);\nwith(plots);\nanimate3d(y(x1, x2, t), x1 = -X1 .. X1, x2 = -X2 .. X2, t = 0 .. 1, color = sin(x1*x2));\nY0rl := Matrix([[1/2, 1/2, 0], [1/3, 1/3, 0], [1/4, 1/4, 0], [1/5, 1/5, 0], [1/6, 1/6, 0]]);\nL0 := 5;\nY0i := Vector(5);\nfor i to 5 do\n Y0i[i] := y(Y0rl[i, 1], Y0rl[i, 2], Y0rl[i, 3]);\nend do;\nYGrl := Matrix([[1/2, 1, 1/7], [0, 0, 1/2], [0, 1/3, 1/5], [1/2, 0, 1/4], [0, 1/2, 1/8]]);\nLG := 5;\nYGi := Vector(5);\nfor i to 5 do\n YGi[i] := evalf(y(YGrl[i, 1], YGrl[i, 2], YGrl[i, 3]));\nend do;\nSm0 := Matrix([[1/2, 1/2, -1], [1/3, 1/3, -2]]);\nM0 := 2;\nSmG := Matrix([[1.1, 1.5, 1/2], [-0.5, 2, 1/2]]);\nMG := 2;\n\nyI := 0;\nfor i1 to 10 do\n for i2 to 10 do for i3 to 10 do yI1 := piecewise(c(i3/10)^4 + (-(i1/10)^2 - (i2/10)^2) <> 0, 0.001*1/(2*Pi*c*(c(t - i3/10)^4 + (-(x1 - i1/10)^2 - (x2 - i2/10)^2)))*L(i1/10, i2/10, i3/10), 0); yI := yI + yI1; end do; end do;\nend do;\nyInf := unapply(yI, x1, x2, t);\nevalf(yInf(0, 0.65, 0.3));\nY0 := Vector(L0);\nfor l to L0 do\n Y0[l] := Y0i[l] - evalf(yInf(Y0rl[l, 1], Y0rl[l, 2], Y0rl[l, 3]));\nend do;\nYG := Vector(LG);\nfor l to LG do\n YG[l] := YGi[l] - evalf(yInf(YGrl[l, 1], YGrl[l, 2], YGrl[l, 3]));\nend do;\nYbar := Vector(L0 + LG);\nfor i to L0 do\n Ybar[i] := Y0[i];\nend do;\nfor i to LG do\n Ybar[L0 + i] := YG[i];\nend do;\nA11 := Matrix(L0, M0);\nA := Matrix(L0 + LG, M0 + MG);\nfor i to L0 do\n for j to M0 do A11[i, j] := evalf(G(Y0rl[i, 1] - Sm0[j, 1], Y0rl[i, 2] - Sm0[j, 2], Y0rl[i, 3] - Sm0[j, 3])); A[i, j] := A11[i, j]; end do;\nend do;\nA11;\nA12 := Matrix(L0, MG);\nfor i to L0 do\n for j to MG do A12[i, j] := evalf(G(Y0rl[i, 1] - SmG[j, 1], Y0rl[i, 2] - SmG[j, 2], Y0rl[i, 3] - SmG[j, 3])); A[i, j + M0] := A12[i, j]; end do;\nend do;\ni := 2;\nj := 1;\nA12[i, j] := evalf(G(Y0rl[i, 1] - SmG[j, 1], Y0rl[i, 2] - SmG[j, 2], Y0rl[i, 3] - SmG[j, 3]));\nA12;\nA21 := Matrix(LG, M0);\nfor i to LG do\n for j to M0 do A21[i, j] := evalf(G(YGrl[i, 1] - Sm0[j, 1], YGrl[i, 2] - Sm0[j, 2], YGrl[i, 3] - Sm0[j, 3])); A[L0 + i, j] := A21[i, j]; end do;\nend do;\nA21;\nA22 := Matrix(LG, MG);\nfor i to LG do\n for j to MG do A22[i, j] := evalf(G(YGrl[i, 1] - SmG[j, 1], YGrl[i, 2] - SmG[j, 2], YGrl[i, 3] - SmG[j, 3])); A[i + L0, j + M0] := A22[i, j]; end do;\nend do;\nA22;\nA;\n# Псевдообернена:\nwith(LinearAlgebra);\nAt := Multiply(Transpose(A), MatrixInverse(Multiply(A, Transpose(A))));\nufinal := Multiply(At, Ybar);\nu0 := Vector(M0);\ny0 := 0;\nfor i to M0 do\n u0[i] := ufinal[i];\nend do;\nfor i to M0 do\n y0 := y0 + G(x1 - Sm0[i, 1], x2 - Sm0[i, 2], t - Sm0[i, 3])*u0[i];\nend do;\nuG := Vector(MG);\nfor i to MG do\n uG[i] := ufinal[M0 + i];\nend do;\nyG := 0;\nfor i to MG do\n yG := yG + G(x1 - SmG[i, 1], x2 - SmG[i, 2], t - SmG[i, 3])*uG[i];\nend do;\nyfinal := unapply(evalf(yInf(x1, x2, t) + y0 + yG), x1, x2, t);\n\nsave yfinal, \"y_final.log\";\nanimate3d(yfinal(x1, x2, t), x1 = -X1 .. X1, x2 = -X2 .. X2, t = 0 .. T, color = sin(x1*x2));\n\n", "meta": {"hexsha": "f2b891aec64257e799d9444f20da1222452f834f", "size": 3417, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "engine.mpl", "max_stars_repo_name": "Via-R/statistic_modeling", "max_stars_repo_head_hexsha": "4d5982ccd1a87ffd7df5d8df1d08480648713e67", "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": "engine.mpl", "max_issues_repo_name": "Via-R/statistic_modeling", "max_issues_repo_head_hexsha": "4d5982ccd1a87ffd7df5d8df1d08480648713e67", "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": "engine.mpl", "max_forks_repo_name": "Via-R/statistic_modeling", "max_forks_repo_head_hexsha": "4d5982ccd1a87ffd7df5d8df1d08480648713e67", "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": 29.9736842105, "max_line_length": 227, "alphanum_fraction": 0.5086333041, "num_tokens": 1756, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8615382094310357, "lm_q2_score": 0.6791786991753929, "lm_q1q2_score": 0.585138400371268}} {"text": "# This code is for the cohomology of F(A,R^3), or F(A,R^{2n+1}) for\n# any n > 0. This is concentrated in even degrees so we do not\n# need to worry about sign rules or gradings.\n\nwith(Groebner):\n\n`vars/poisson` := proc(A::set)\n local a,b;\n [seq(seq(u[a,b],b in A),a in A)];\nend:\n\n`rels/poisson` := proc(A::set)\n local n,i,j,k,uf;\n n := nops(A);\n uf := (i,j) -> u[A[i],A[j]];\n\n return \n [seq(uf(i,i),i = 1..n),\n seq(seq(uf(i,j)+uf(j,i),j=i+1..n),i=1..n-1),\n seq(seq(uf(i,j)^2,j=1..n),i=1..n),\n seq(seq(seq(\n uf(i,j)*uf(j,k) + uj(j,k)*uf(k,i) + uf(k,i)*uf(i,j),\n k=j+1..n),j=i+1..n),i=1..n)\n ];\nend:\n\n`groebner_basis/poisson` := proc(A::set)\n Basis(`rels/poisson`(A),tdeg(`vars/poisson`(A)));\nend:\n\n`basis/poisson` := proc(A::set)\n local n,a,x,v,B,U,V;\n \n n := nops(A);\n if n <= 1 then\n return [1];\n fi;\n a := A[n];\n B := A minus {a};\n U := `basis/poisson`(A minus {a});\n V := [1,seq(u[x,a],x in B)];\n return map(op,[seq(U *~ v,v in V)]);\nend:\n", "meta": {"hexsha": "0b88dd9e6f4dd9fdf4a5ea4cec4c121214ecd8b5", "size": 957, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/poisson.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/poisson.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/poisson.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": 21.75, "max_line_length": 67, "alphanum_fraction": 0.5370950888, "num_tokens": 392, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8791467770088162, "lm_q2_score": 0.6654105653819835, "lm_q1q2_score": 0.584993553943185}} {"text": "program sample16;\t/* prime numbers */\r\nvar furui : array[20000] of boolean;\r\n i, j : integer;\r\nbegin\r\n i := 2;\r\n while i < 20000 do begin\r\n furui[i] := true;\r\n i := i + 1\r\n end;\r\n furui[0] := false;\r\n furui[1] := false;\r\n i := 2;\r\n while i < 20000 do begin\r\n if furui[i] then begin\r\n writeln(i, ' is a prime number');\r\n j := i;\r\n if i < 16384 then\r\n while j < 20000 do begin\r\n furui[j] := false;\r\n j := j + i\r\n end\r\n end;\r\n i := i + 1\r\n end\r\nend.\r\n", "meta": {"hexsha": "5c188cb1a75b2e8d08f105414c530614984945b0", "size": 521, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "data/sample16.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": "task1_sample/sample16.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/program1/sample16.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": 20.0384615385, "max_line_length": 40, "alphanum_fraction": 0.472168906, "num_tokens": 176, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7931059707450325, "lm_q2_score": 0.7371581626286834, "lm_q1q2_score": 0.5846445401642465}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n(* prefix:\n mgga_x_tau_hcth_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_tau_hcth_params * ) (p->params);\n*)\n\nhcth_coeff_a := [0, 1, 0, -2, 0, 1]:\n\n(* Equation (29) *)\nhcth_gamX := 0.004:\nhcth_ux := x -> hcth_gamX*x^2/(1 + hcth_gamX*x^2):\n\nhcth_gxl := x -> add(params_a_cx_local [i]*hcth_ux(x)^(i-1), i=1..4):\nhcth_gxnl := x -> add(params_a_cx_nlocal[i]*hcth_ux(x)^(i-1), i=1..4):\n\nhcth_f := (x, u, t) -> hcth_gxl(x) + hcth_gxnl(x)*mgga_series_w(hcth_coeff_a, 6, t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) -> mgga_exchange(hcth_f, rs, z, xs0, xs1, u0, u1, t0, t1):", "meta": {"hexsha": "04ccc833e8ad7d1f51dcd5d1bfcf15197c0385c2", "size": 856, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_tau_hcth.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/mgga_exc/mgga_x_tau_hcth.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/mgga_exc/mgga_x_tau_hcth.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": 30.5714285714, "max_line_length": 101, "alphanum_fraction": 0.6285046729, "num_tokens": 351, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218284193595, "lm_q2_score": 0.6334102636778401, "lm_q1q2_score": 0.583954748429463}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-5-input.txt\" ):\nlines:=map(l->[[parse(l[1])],[parse(l[-1])]],\n {op(map(StringTools:-Split, StringTools:-Split(input,\"\\n\"), \"->\"))}):\n\npointcounts1 := table(sparse=0):\npointcounts2 := table(sparse=0):\n\nfor l in lines do\n step := signum~(l[2] - l[1]);\n ls := l[1];\n pointcounts2[op(ls)] += 1;\n if 0 in step then \n pointcounts1[op(ls)] += 1;\n end if;\n while ls <> l[2] do\n ls := ls + step;\n pointcounts2[op(ls)] += 1;\n if 0 in step then \n pointcounts1[op(ls)] += 1;\n end if;\n end do;\nend do:\n\nanswer1:=nops(select(i->i>1,[entries(pointcounts1, nolist)]));\nanswer2:=nops(select(i->i>1,[entries(pointcounts2, nolist)]));\n\n# Visualization\n\n# just the lines\nplots:-display(seq(plottools:-line(l[], thickness=0.01),l in lines));\n\n# fancy hotspots\nrng := [min,max](entries(pointcounts2,nolist));\ncolors := [ColorTools:-Color(\"CVD 8\"),ColorTools:-Gradient(\"CVD 2\"..\"CVD 9\", number=rng[2]-rng[1]-2)[]];\nepc := [seq(Array(map([lhs], select(p->rhs(p)=i,[entries(pointcounts2,pairs)]))),i=rng[1]..rng[2])]:\n\nplots:-display(\n seq(plottools:-point(epc[i], symbol=solidcircle, color=colors[i], symbolsize=i),i=rng[1]..rng[2] ),\n size=[5000,5000], axes=none, background=\"Black\");\n\n", "meta": {"hexsha": "4e02fdd1badac4a7479241b18e014ce668a84026", "size": 1296, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day5/AoC5-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day5/AoC5-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day5/AoC5-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.6097560976, "max_line_length": 104, "alphanum_fraction": 0.5987654321, "num_tokens": 427, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8596637505099167, "lm_q2_score": 0.6791786926816161, "lm_q1q2_score": 0.5838653022171002}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_xc_th3_params *params;\n\n assert(p->params != NULL);\n params = (gga_xc_th3_params * )(p->params);\n*)\n\nparams_a_n := 19:\n\nparams_a_a := [\n 7/6, 8/6, 9/6, 10/6, 17/12, 9/6, 10/6, 11/6,\n 10/6, 11/6, 12/6, 10/6, 11/6, 12/6, 7/6, 8/6,\n 9/6, 10/6, 13/12.0\n]:\n\nparams_a_b := [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0]:\nparams_a_c := [0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0]:\nparams_a_d := [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]:\n\n$include \"th.mpl\"\n\nf := (rs, z, xt, xs0, xs1) -> f_th(rs, z, xt, xs0, xs1):\n", "meta": {"hexsha": "eb90133b5910dbe68f6186f12c52df1c38b9fbff", "size": 839, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_xc_th3.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_xc_th3.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_xc_th3.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.21875, "max_line_length": 72, "alphanum_fraction": 0.5446960667, "num_tokens": 453, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8902942319436397, "lm_q2_score": 0.6548947223065755, "lm_q1q2_score": 0.5830489937998758}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n$include \"gga_c_zvpbeint.mpl\"\n$include \"gga_c_pbeloc.mpl\"\n\nparams_a_alpha := 0.5:\nparams_a_omega := 2:\n\n(* redefine nu of zbpbeint *)\nzvpbeint_nu := (rs, z, t) ->\n 2*(4/(3*Pi^2))^(1/18) * rs^(1/3):\n\n(* Note that f_pbe here is, in fact, pbeloc *)\nf := (rs, z, xt, xs0, xs1) ->\n zvpbeint_ff(rs, z, 0) * f_pbe(rs, z, xt, xs0, xs1):\n", "meta": {"hexsha": "fff8b1693a7708e93009035cb51cbcff00d5c54b", "size": 592, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_zvpbeloc.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_c_zvpbeloc.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_c_zvpbeloc.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": 24.6666666667, "max_line_length": 68, "alphanum_fraction": 0.6402027027, "num_tokens": 228, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8807970842359877, "lm_q2_score": 0.6619228691808012, "lm_q1q2_score": 0.5830197331635688}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_x_kt_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_kt_params * )(p->params);\n*)\n\nkt_fx := (rs, z, xs) ->\n 1 - params_a_gamma/X_FACTOR_C*n_spin(rs, z)^(4/3)*xs^2/(n_spin(rs, z)^(4/3) + params_a_delta):\n\n(* we want energy per particle *)\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange_nsp(kt_fx, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "6cd59a6ba7a184554d57775f1f6cd366f913dc9b", "size": 610, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_kt.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_kt.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_kt.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": 27.7272727273, "max_line_length": 97, "alphanum_fraction": 0.6508196721, "num_tokens": 210, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9046505376715775, "lm_q2_score": 0.6442250928250375, "lm_q1q2_score": 0.5827985766056921}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\nmbeef_n := 5:\nmbeef_coefs := [\n [ 1.17114923e+00, 1.15594371e-01, -5.32167416e-02, -2.01131648e-02, 1.41417107e-03],\n [-6.76157938e-02, 4.53837246e-02, -2.22650139e-02, 1.92374554e-02, 9.19317034e-07],\n [ 1.48659502e-02, 3.18024096e-02, -5.21818079e-03, 1.33707403e-07, -5.00749348e-07],\n [ 1.40794142e-03, -6.08338264e-03, -6.57949254e-07, -5.49909413e-08, 5.74317889e-08],\n [ 1.41530486e-04, -1.00478906e-07, 2.01895739e-07, 3.97324768e-09, -3.40722258e-09]\n]:\n\n$include \"mbeef.mpl\"\n\nmbeefvdw_f := (x, u, t) -> mbeef_expansion(x, t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(mbeefvdw_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "9cb6a30249f0250275568aa071981ba1a10473fb", "size": 931, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_mbeefvdw.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/mgga_exc/mgga_x_mbeefvdw.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/mgga_exc/mgga_x_mbeefvdw.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": 35.8076923077, "max_line_length": 90, "alphanum_fraction": 0.6498388829, "num_tokens": 455, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9046505351008906, "lm_q2_score": 0.6442250928250376, "lm_q1q2_score": 0.5827985749495912}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_c_zvpbeint_params *params;\n\n assert(p->params != NULL);\n params = (gga_c_zvpbeint_params * )(p->params);\n*)\n\nparams_a_gamma := (1 - log(2))/Pi^2:\nparams_a_BB := 1:\n$include \"gga_c_pbe.mpl\"\n\nzvpbeint_nu := (rs, z, t) ->\n t*mphi(z)*(3/rs)^(1/6):\n\n(* we write (z^2)^(omega/2) instead of z^omega in order to\n avoid the use of abs(z). Max is required not to get float\n exceptions for z->0 *)\nzvpbeint_ff := (rs, z, t) ->\n exp(-params_a_alpha*zvpbeint_nu(rs, z, t)^3*m_max(z^2, 1e-20)^(params_a_omega/2)):\n\nf := (rs, z, xt, xs0, xs1) ->\n f_pw(rs, z) + zvpbeint_ff(rs, z, tp(rs, z, xt))*fH(rs, z, tp(rs, z, xt)):\n", "meta": {"hexsha": "0c60f3d431828d03c91db5039dbeff70dcbea538", "size": 895, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_zvpbeint.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_c_zvpbeint.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_c_zvpbeint.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": 27.96875, "max_line_length": 84, "alphanum_fraction": 0.6324022346, "num_tokens": 334, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.903294209307224, "lm_q2_score": 0.6442251133170356, "lm_q1q2_score": 0.5819248143495684}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_gga_c *)\n(* prefix:\n gga_x_kt_params *params;\n \n assert(p->params != NULL);\n params = (gga_x_kt_params * )(p->params);\n*)\n\nfx := (rs, z, xs) -> \n params_a_gamma*n_spin(rs, z)^(4/3)*xs^2/(n_spin(rs, z)^(4/3) + params_a_delta):\n\nf0 := (rs, zeta, xt, xs0, xs1) -> \n - (X_FACTOR_C - fx(rs, zeta, xs0))*n_spin(rs, zeta)^(4/3) \n - (X_FACTOR_C - fx(rs, -zeta, xs1))*n_spin(rs, -zeta)^(4/3):\n\n(* we want energy per particle *)\nf := (rs, zeta, xt, xs0, xs1) -> f0(rs, zeta, xt, xs0, xs1)/n_total(rs):\n", "meta": {"hexsha": "46189e1ed0bbe8b006fb63c6aa0c9b7f65606fca", "size": 754, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_kt.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_kt.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_kt.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 29.0, "max_line_length": 82, "alphanum_fraction": 0.6153846154, "num_tokens": 285, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9032941962904956, "lm_q2_score": 0.6442250928250375, "lm_q1q2_score": 0.5819247874535621}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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# Minimum and maximum functions that I can differentiate\n\nm_min := (x1, x2) -> my_piecewise3(x1 > x2, x2, x1):\nm_max := (x1, x2) -> my_piecewise3(x1 > x2, x1, x2):\nm_abs := (x) -> my_piecewise3(x > 0, x, -x):\n\n# Teach maple to differentiate piecewise functions\n\n`diff/my_piecewise3` :=\n proc(c, x1, x2, x) my_piecewise3(c, diff(x1, x), diff(x2, x)) end proc:\n\n`diff/my_piecewise5` :=\n proc(c1, x1, c2, x2, x3, x) my_piecewise5(c1, diff(x1, x), c2, diff(x2, x), diff(x3,x)) end proc:\n\n# This is the derivative of xc_E1_scaled = -exp(x)*Ei(-x) = exp(x)E1(x)\n\n`diff/xc_E1_scaled` :=\n proc(y, x) (xc_E1_scaled(y) - 1/y) * diff(y, x) end proc:\n\n# The derivative of xc_erfcx = exp(x^2)*erfc(x) = 2*x*xc_erfcx(x) - 2/sqrt(Pi)\n`diff/xc_erfcx` :=\n proc(y, x) (2*y*xc_erfcx(y) - 2/sqrt(Pi)) * diff(y, x) end proc:\n\n\n# a series of useful definitions\n\nM_C := 137.0359996287515: (* speed of light *)\n\nX2S := 1/(2*(6*Pi^2)^(1/3)):\nX2S_2D := 1/(2*(4*Pi)^(1/2)):\n\nX_FACTOR_C := 3/8*(3/Pi)^(1/3)*4^(2/3):\nX_FACTOR_2D_C := 8/(3*sqrt(Pi)):\nK_FACTOR_C := 3/10*(6*Pi^2)^(2/3):\n\nMU_GE := 10/81:\nMU_PBE := 0.06672455060314922*(Pi^2)/3:\nKAPPA_PBE := 0.8040:\n\n# generic conversion functions\n\n$ifdef xc_dimensions_1d\nDIMENSIONS := 1:\nRS_FACTOR := 1/2:\n$elif xc_dimensions_2d\nDIMENSIONS := 2:\nRS_FACTOR := 1/sqrt(Pi):\nLDA_X_FACTOR := -X_FACTOR_2D_C:\n$else\nDIMENSIONS := 3:\nRS_FACTOR := (3/(4*Pi))^(1/3):\nLDA_X_FACTOR := -X_FACTOR_C:\n$endif\n\nr_ws := n -> RS_FACTOR/n^(1/DIMENSIONS):\nn_total := rs -> (RS_FACTOR/rs)^DIMENSIONS:\n\nn_spin := (rs, z) -> simplify((1 + z)*n_total(rs)/2):\nsigma_spin := (rs, z, xs) -> simplify(xs^2*n_spin(rs, z)^(8/3)):\nt_total := (z, ts0, ts1) ->\n (ts0*((1 + z)/2)^(5/3) + ts1*((1 - z)/2)^(5/3)):\nu_total := (z, us0, us1) -> t_total(z, us0, us1):\n\n# useful formulas that enter several functionals follow\n\n# von Weizsäcker term\nt_vw := (z, xt, us0, us1) -> (xt^2 - u_total(z, us0, us1))/8:\n\n# Screening for extreme values of zeta\nz_thr := z -> my_piecewise5(\n 1 + z <= p_a_zeta_threshold, p_a_zeta_threshold - 1,\n 1 - z <= p_a_zeta_threshold, 1 - p_a_zeta_threshold,\n z):\n\nopz_pow_n := (z, n) -> my_piecewise3(1 + z <= p_a_zeta_threshold, (p_a_zeta_threshold)^n, (1 + z)^n):\n\n# See Eq. (9) of Perdew1992_13244\nf_zeta := z -> (opz_pow_n(z,4/3) + opz_pow_n(-z,4/3) - 2)/(2^(4/3) - 2):\nf_zeta_2d := z -> 1/2*(opz_pow_n(z,3/2) + opz_pow_n(-z,3/2)):\n\n# used in several correlation functionals\nmphi := z -> (opz_pow_n(z,2/3) + opz_pow_n(-z,2/3))/2:\ntt := (rs, z, xt) -> xt/(4*2^(1/3)*mphi(z)*sqrt(rs)):\n\n# in the paper it is beta_a = 0.066725\nbeta_Hu_Langreth := rs -> 0.066724550603149220*(1 + 0.1*rs)/(1 + 0.1778*rs):\n\n# Generate exchange and kinetic functionals from the expression for the\n# enhancement factor\nlda_x_spin := (rs, z) -> simplify(LDA_X_FACTOR*opz_pow_n(z,1 + 1/DIMENSIONS)*2^(-1-1/DIMENSIONS)*(RS_FACTOR/rs)):\nlda_k_spin := (rs, z) -> simplify(K_FACTOR_C*opz_pow_n(z,5/3)*2^(-5/3)*(RS_FACTOR/rs)^2):\n\n# Screen out small densities as well as the zero component from fully spin polarized densities due to terms of the form (1+z)^{-n}\nscreen_dens := (rs, z) -> (n_spin(rs, z) <= p_a_dens_threshold):\n\n# For most functionals zeta screening occurs inside the funcitonal,\n# but for B88 and B94 correlation need to screen out also outside\nscreen_dens_zeta := (rs, z) -> screen_dens(rs, z) or (1 + z <= p_a_zeta_threshold):\n\n# non-separable GGA exchange\ngga_exchange_nsp := (func, rs, z, xs0, xs1) ->\n + my_piecewise3(screen_dens(rs, z), 0, lda_x_spin(rs, z_thr( z))*func(rs, z_thr( z), xs0))\n + my_piecewise3(screen_dens(rs, -z), 0, lda_x_spin(rs, z_thr(-z))*func(rs, z_thr(-z), xs1)):\n# GGA exchange\ngga_exchange := (func, rs, z, xs0, xs1) ->\n + my_piecewise3(screen_dens(rs, z), 0, lda_x_spin(rs, z_thr( z))*func(xs0))\n + my_piecewise3(screen_dens(rs, -z), 0, lda_x_spin(rs, z_thr(-z))*func(xs1)):\n# GGA kinetic energy\ngga_kinetic := (func, rs, z, xs0, xs1) ->\n + my_piecewise3(screen_dens(rs, z), 0, lda_k_spin(rs, z_thr( z))*func(xs0))\n + my_piecewise3(screen_dens(rs, -z), 0, lda_k_spin(rs, z_thr(-z))*func(xs1)):\n\n# non-separable meta-GGA exchange\nmgga_exchange_nsp := (func, rs, z, xs0, xs1, u0, u1, t0, t1) ->\n + my_piecewise3(screen_dens(rs, z), 0, lda_x_spin(rs, z_thr( z))*func(rs, z_thr( z), xs0, u0, t0))\n + my_piecewise3(screen_dens(rs, -z), 0, lda_x_spin(rs, z_thr(-z))*func(rs, z_thr(-z), xs1, u1, t1)):\n# meta-GGA exchange\nmgga_exchange := (func, rs, z, xs0, xs1, u0, u1, t0, t1) ->\n + my_piecewise3(screen_dens(rs, z), 0, lda_x_spin(rs, z_thr( z))*func(xs0, u0, t0))\n + my_piecewise3(screen_dens(rs, -z), 0, lda_x_spin(rs, z_thr(-z))*func(xs1, u1, t1)):\n# meta-GGA kinetic energy\nmgga_kinetic := (func, rs, z, xs0, xs1, u0, u1) ->\n + my_piecewise3(screen_dens(rs, z), 0, lda_k_spin(rs, z_thr( z))*func(xs0, u0))\n + my_piecewise3(screen_dens(rs, -z), 0, lda_k_spin(rs, z_thr(-z))*func(xs1, u1)):\n\n# This is the Stoll decomposition in our language\nlda_stoll_par := (lda_func, rs, z) ->\n my_piecewise3(screen_dens_zeta(rs, z), 0, opz_pow_n(z, 1)/2 * lda_func(rs*2^(1/3)*opz_pow_n(z, -1/3), 1)):\n\nlda_stoll_perp := (lda_func, rs, z) ->\n + lda_func(rs, z)\n - lda_stoll_par(lda_func, rs, z)\n - lda_stoll_par(lda_func, rs, -z):\n\ngga_stoll_par := (gga_func, rs, z, xs, spin) ->\n my_piecewise3(screen_dens_zeta(rs, z), 0,\n gga_func(rs*2^(1/3)*opz_pow_n(z,-1/3), spin, xs, xs*(1 + spin)/2, xs*(1 - spin)/2) * opz_pow_n(z,1)/2):\n\n# Curvature of the Fermi hole (without the current term)\nFermi_D := (xs, ts) -> 1 - xs^2/(8*ts):\n\n# correction to Fermi_D similar to the one found in\n# JCP 127, 214103 (2007); doi: http://dx.doi.org/10.1063/1.2800011\nFermi_D_corrected := (xs, ts) -> (1 - xs^2/(8*ts)) * (1 - exp(-4*ts^2/params_a_Fermi_D_cnst^2)):\n\n# Becke function used in several correlation functionals\nb88_R_F := (f_x, rs, z, xs) -> 1/(2*X_FACTOR_C*n_spin(rs, z)^(1/3)*f_x(xs)):\nb88_zss := (css, f_x, rs, z, xs) -> 2*css*b88_R_F(f_x, rs, z, xs):\nb88_zab := (cab, f_x, rs, z, xs0, xs1) -> cab*(\n + my_piecewise3(screen_dens(rs, z), 0, b88_R_F(f_x, rs, z_thr( z), xs0))\n + my_piecewise3(screen_dens(rs, -z), 0, b88_R_F(f_x, rs, z_thr(-z), xs1))\n ):\n\n# The meta-GGA version\nb94_R_F := (f_x, rs, z, xs, us, ts) -> 1/(2*X_FACTOR_C*n_spin(rs, z)^(1/3)*f_x(xs,us,ts)):\nb94_zss := (css, f_x, rs, z, xs, us, ts) -> 2*css*b94_R_F(f_x, rs, z, xs, us, ts):\nb94_zab := (cab, f_x, rs, z, xs0, xs1, us0, us1, ts0, ts1) -> cab*(\n + my_piecewise3(screen_dens(rs, z), 0, b94_R_F(f_x, rs, z_thr( z), xs0, us0, ts0))\n + my_piecewise3(screen_dens(rs, -z), 0, b94_R_F(f_x, rs, z_thr(-z), xs1, us1, ts1))\n ):\n\n# Power series often used in mggas\nmgga_w := t -> (K_FACTOR_C - t)/(K_FACTOR_C + t):\nmgga_series_w := (a, n, t) -> add(a[i]*mgga_w(t)^(i-1), i=1..n):\n\n# Used in screened functionals\nkF := (rs, z) -> (3*Pi^2)^(1/3) * opz_pow_n(z,1/3) * RS_FACTOR/rs:\nnu := (rs, z) -> p_a_hyb_omega_0_/kF(rs, z):\n\n\n(* Maple 2020 has a bug where series aren't computed to the order requested; this circumvents that *)\npadding_order := 30:\n\n(* Cap polynomial expansion to given order (throws out the padded terms, if any) *)\nthrow_out_large_n := proc(X,n) select(t -> abs(degree(t,{b}))<=n, X); end proc:\n\n(* Function that makes f(a) smooth for a->infty *)\nenforce_smooth_lr := proc(f, a, a_cutoff, expansion_order);\n (* Calculate large-a expansion *)\n f_large := a -> eval(throw_out_large_n(convert(series(f(b), b=infinity, expansion_order+padding_order), polynom), expansion_order), b=a):\n (* Return the series expansion for large a; also remove any numerical overflows from the original branch *)\n my_piecewise3(a >= a_cutoff, f_large(m_max(a, a_cutoff)), f(m_min(a, a_cutoff))):\nend proc:\n", "meta": {"hexsha": "ebe1e251726e2cadb8238a0536e4389a5ccf7ced", "size": 7952, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/util.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/util.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/util.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": 41.4166666667, "max_line_length": 139, "alphanum_fraction": 0.6404678068, "num_tokens": 3123, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8558511543206819, "lm_q2_score": 0.679178699175393, "lm_q1q2_score": 0.5812758736792792}} {"text": "######################################################################\n# single_cubes(k) is the usual set of injective maps [0,1]^k -> [0,1]^k\n\n`is_element/single_cubes` := (k::posint) -> proc(xy)\n local i,x,y;\n global reason;\n\n if not(type(xy,[[realcons$k],[realcons$k]])) then\n reason := [convert(procname,string),\"xy is not in R^k x R^k\",xy];\n return false;\n fi;\n\n x,y := op(xy);\n for i from 1 to k do\n if not(0 <= x[i] and x[i] < y[i] and y[i] <= 1) then\n reason := [convert(procname,string),\"not (0 <= x[i] < y[i] <= 1)\",i,x[i],y[i]];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n`is_equal/single_cubes` := (k::posint) -> proc(xy1,xy2)\n global reason;\n\n if xy1 <> xy2 then\n reason := [convert(procname,string),\"xy1 <> xy2\",xy1,xy2];\n return false;\n fi;\n\n return true;\nend:\n\n`is_leq/single_cubes` := NULL;\n\n`random_element/single_cubes` := (k::posint) -> proc(d := 6) \n local r,x,y,i,s,t;\n\n r := rand(0..d);\n x := NULL;\n y := NULL;\n for i from 1 to k do\n s := 0;\n t := 0;\n while s = t do s := r(); t := r(); od;\n x := x,min(s,t)/d;\n y := y,max(s,t)/d;\n od;\n return [[x],[y]];\nend;\n\n`list_elements/single_cubes` := NULL;\n`count_elements/single_cubes` := NULL;\n\n`act/single_cubes` := (k::posint) -> (xy) -> (t) ->\n xy[1] +~ (t *~ (xy[2] -~ xy[1]));\n\n`id/single_cubes` := (k::posint) -> [[0$k],[1$k]];\n\n`compose/single_cubes` := (k::posint) -> (xy,uv) -> \n map(`act/single_cubes`(k)(xy),uv);\n\n`overlap/single_cubes` := (k::posint) -> proc(xy,uv)\n local x,y,u,v,i;\n\n x,y := op(xy);\n u,v := op(uv);\n for i from 1 to k do\n if max(x[i],u[i]) >= min(y[i],v[i]) then\n return false;\n fi;\n od;\n return true;\nend;\n\n`centre/single_cubes` := (k::posint) -> proc(xy)\n (xy[1] +~ xy[2]) /~ 2;\nend;\n\n", "meta": {"hexsha": "5c860802379f42555f9faf91b92dc436e42343df", "size": 1707, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/single_cubes.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/single_cubes.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/single_cubes.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": 21.0740740741, "max_line_length": 82, "alphanum_fraction": 0.5348564733, "num_tokens": 613, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7745833841649233, "lm_q2_score": 0.7490872075132152, "lm_q1q2_score": 0.5802305042302385}} {"text": "with(DifferentialThomas):\nwith(Tools):\nRanking([t], [[S, A, E, C, Ninv, J, I], [y2, y] ]):\nsys := [\ndiff(S(t), t) - (-b*S(t)*Ninv(t)*A(t)*q - b*S(t)*Ninv(t)*II(t) - b*S(t)*Ninv(t)*J(t)),\ndiff(A(t), t) - (-E(t)*k*r + E(t)*k - A(t)*g1),\ndiff(E(t), t) - (b*S(t)*Ninv(t)*A(t)*q + b*S(t)*Ninv(t)*II(t) + b*S(t)*Ninv(t)*J(t) - E(t)*k),\ndiff(C(t), t) - (alpha*II(t)),\ndiff(Ninv(t), t) - (0),\ndiff(J(t), t) - (alpha*II(t) - g2*J(t)),\ndiff(II(t), t) - (-alpha*II(t) + E(t)*k*r - g1*II(t)),\ny2(t) - (Ninv(t)),\ny(t) - (C(t))\n];\nres := CodeTools[CPUTime](ThomasDecomposition(sys));", "meta": {"hexsha": "d92e9f22f0a4832c603287afa500c79540f7505b", "size": 569, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/DifferentialThomas/SEAIJRC-Covid-model.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/DifferentialThomas/SEAIJRC-Covid-model.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/DifferentialThomas/SEAIJRC-Covid-model.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 37.9333333333, "max_line_length": 94, "alphanum_fraction": 0.4868189807, "num_tokens": 264, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9046505351008906, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.5795515688857302}} {"text": "# https://www.reddit.com/r/adventofcode/comments/ra3f5i/2021_day_6_part_3_day_googol/\n# Get the 10^100th generation of Lantern fish \n\ninput := \"3,1,1,0,3,7,5,5,2,4,2,1,0,2,6,4,3,0,2,1,5,1,4,2,3,0,6,3,0,5,0,5,6,0,0,6,7,0,1,6,3,2,1,1,2,2,0,1,1,1,6,0,2,1,0,5,1,4,7,6,3,0,7,2,0,0,2,0,2,7,3,7,2,4,6,1,6,6,1,1,6,3,3,1,0,4,5,0,5,1,2,0,2,0,7,4,6,1,6,1,5,0,0,2,3\":\ntally := table(sparse=0,Statistics:-Tally(StringTools:-Split(input,\",\"))):\nlanternfish := Vector([seq(tally[cat(\"\",i)],i=0..8)]):\n\nU := Matrix([\n [0, 1, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0, 0],\n [1, 0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 1],\n [1, 0, 0, 0, 0, 0, 0, 0, 0]]):\n\nminpoly := LinearAlgebra:-MinimalPolynomial(U,x);\n\nq:=10^20:\nn := 10^100: # googol\n\n# reduce x^n modulo the minpoly to get g so g(U) = U^n\ng := Powmod(x, n, minpoly, x) mod q:\n\nadd(eval(g, x=U) . lanternfish) mod q;\n# 80595178351181834124\n\n", "meta": {"hexsha": "1658e2972ec06cc405fc0ea9945bbd25d47293a8", "size": 1014, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day6/Part3-reddit.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day6/Part3-reddit.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day6/Part3-reddit.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.8, "max_line_length": 221, "alphanum_fraction": 0.5414201183, "num_tokens": 638, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094117351309, "lm_q2_score": 0.6477982179521103, "lm_q1q2_score": 0.5786842450018658}} {"text": "#@ Not autoload\n\nwith(LinearAlgebra):\nwith(Groebner):\n\nQ8 := table():\n\nQ8[\"element_names\"] := [\"1\",\"-1\",\"i\",\"-i\",\"j\",\"-j\",\"k\",\"-k\"];\nQ8[\"conjugacy_classes\"] := [[1],[2],[3,4],[5,6],[7,8]];\nQ8[\"character_table\"] := \n [[1$8],\n [ 1, 1,-1,-1, 1, 1,-1,-1],\n [ 1, 1, 1, 1,-1,-1,-1,-1],\n [ 1, 1,-1,-1,-1,-1, 1, 1],\n [ 2,-2, 0, 0, 0, 0, 0, 0]];\nQ8[\"character_names\"] := [1,alpha,beta,gamma,rho];\n\nQ8[\"character_relations\"] := \n [alpha^2-1,beta^2-1,gamma^2-1,alpha*beta*gamma-1,\n (alpha-1)*rho,(beta-1)*rho,(gamma-1)*rho,\n rho^2-1-alpha-beta-gamma];\n\nQ8[\"euler_class\"] := table([\n 1 = 0,\n alpha = x,\n beta = y,\n gamma = z,\n rho = c2\n]):\n\n# Morava K-theory information from the Chern approximations paper\n\np := 2;\nn := 3;\nq := p^n;\n\nQ8[\"morava_K_vars\"] := plex(v,x,y,c2);\nQ8[\"morava_K_vars_alt\"] := plex(v,c2,x,y);\n \nQ8[\"morava_K_rels\"] := [\n c2^((q^2+q)/2),\n c2^((q^2-q)/2) * x,\n c2^((q^2-q)/2) * y,\n x^2 - v*x,\n y^2 - v*y,\n x*y - v*x - v*y - c2^q,\n v - add(c2^(q^2/2 - 2^i*(q-1)),i=0..n-1)\n];\n\nQ8[\"morava_K_groebner\"] :=\n Basis(Q8[\"morava_K_rels\"],Q8[\"morava_K_vars\"],characteristic=p);\n\nQ8[\"morava_K_basis\"] := \n [seq(c2^i,i=0..(q^2+q)/2-1),\n seq(c2^i*x,i=0..(q^2-q)/2-1),\n seq(c2^i*y,i=0..(q^2-q)/2-1)\n ];\n\nQ8[\"vec_table\"] := table():\nd := nops(Q8[\"morava_K_basis\"]):\nfor i from 1 to d do \n Q8[\"vec_table\"][Q8[\"morava_K_basis\"][i]] := [0$(i-1),1,0$(d-i)];\nod:\n\nQ8[\"vec\"] := proc(u)\n local ub,uc;\n if u = 0 then\n return [0$d];\n elif type(u,`+`) then\n return modp(map(Q8[\"vec\"],u),p); \n else\n if type(u,`*`) then\n uc,ub := selectremove(type,u,integer);\n else\n ub := u;\n uc := 1;\n fi;\n return modp(uc *~ Q8[\"vec_table\"][u],p);\n fi;\nend:\n\nQ8[\"morava_K_groebner_alt\"] :=\n Basis(Q8[\"morava_K_rels\"],Q8[\"morava_K_vars_alt\"],characteristic=p);\n\nQ8[\"morava_K_basis_alt\"] := \n [seq(seq(seq(x^i*y^j*c2^k,k=0..3),j=0..1),i=0..7),\n seq(seq(y^j*c2^k,k=0..3),j=2..7),\n seq(c2^k,k=4..7)\n ];", "meta": {"hexsha": "361b702be821456bbfed0ab80dfea13d315d003c", "size": 1894, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/morava/Q8.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/morava/Q8.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/morava/Q8.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": 21.2808988764, "max_line_length": 69, "alphanum_fraction": 0.540654699, "num_tokens": 871, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767906859264, "lm_q2_score": 0.658417500561683, "lm_q1q2_score": 0.5777460753243148}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\ngvt4_alpha := 0.00186726:\ngvt4_coeff_d := [-9.800683e-01, -3.556788e-03, 6.250326e-03, -2.354518e-05, -1.282732e-04, 3.574822e-04]:\n\n$include \"gvt4.mpl\"\n\ngvt4_f := (x, u, t) -> -gtv4(gvt4_alpha, gvt4_coeff_d, x, 2*(t - K_FACTOR_C))/X_FACTOR_C:\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(gvt4_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "04a7893403ab884ea0d661d5344ab8e576a6137a", "size": 611, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_gvt4.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/mgga_exc/mgga_x_gvt4.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/mgga_exc/mgga_x_gvt4.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": 30.55, "max_line_length": 105, "alphanum_fraction": 0.6546644845, "num_tokens": 260, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026528034426, "lm_q2_score": 0.6297746004557471, "lm_q1q2_score": 0.5776939116662849}} {"text": " ReparamDetermined := proc(lo :: LO(name, anything))\n local h;\n h := op(1,lo);\n LO(h,\n evalindets(op(2,lo),\n 'And'('specfunc({Int,int})',\n 'anyfunc'(anything, 'name=anything')),\n g -> `if`(determined(op(1,g),h), Reparam(g,h), g)))\n end proc;\n\n determined := proc(e, h :: name)\n local i;\n for i in indets(e, 'specfunc({Int,int})') do\n if hastype(IntegrationTools:-GetIntegrand(i),\n 'applyintegrand'('identical'(h),\n 'dependent'(IntegrationTools:-GetVariable(i)))) then\n return false\n end if\n end do;\n return true\n end proc;\n\n #Beginning of Carl's code devoted to disintegration and the reparametrization (aka change\n #of variables) of integrals and sums.\n\n #Finds the innermost Ints or Sums in an expression, that is, those which\n #don't contain further Ints or Sums\n innermostIntSum:= proc(e::anything, $)::set(specfunc({Int,Sum}));\n select(IS-> nops(indets(IS, specfunc({Int,Sum}))) = 1, indets(e, specfunc({Int,Sum})))\n end proc;\n\n #my substitute for IntegrationTools:-Change\n ChangeVarInt:= proc(J::specfunc(Int), target::algebraic, $)\n local\n newJ, #What J will become.\n x::name:= op([2,1], J),\n u::name:= gensym('u'), #new variable of integration\n s, #What x will become\n F #Boolean: flip integral?\n ;\n s:= {solve({u = target}, {x})};\n if nops(s) = 0 then\n userinfo(1, reparam, \"Can't solve substitution target.\");\n return e\n end if;\n if nops(s) > 1 then\n userinfo(1, reparam, \"Case of multi-branched substitution not handled.\");\n return e\n end if;\n s:= s[];\n\n newJ:= Int(\n eval(implicitdiff(u = target, x, u)*op(1,J), s),\n u=\n limit(target, x= op([2,2,1], J), right).. #lower limit\n limit(target, x= op([2,2,2], J), left), #upper limit\n op(3.., J) #optional Int args (unlikely to be used)\n );\n\n #If lower limit > upper limit, then flip limits of integration.\n F:= is(op([2,2,1], newJ) > op([2,2,2], newJ));\n if F::truefalse then\n if F then\n userinfo(2, reparam, \"Switching limits:\", op([2,2], newJ));\n newJ:= IntegrationTools:-Flip(newJ)\n end if\n else #If inequality can't be decided, then don't reverse.\n userinfo(1, reparam, \"Can't order new limits:\", op([2,2], newJ))\n end if;\n\n newJ\n end proc;\n\n #main procedure for int/sum reparamterizations\n reparam:= proc(e::LO(symbol, algebraic), {ctx::list:= []}, $)\n local\n J:= innermostIntSum(e), #the integral or sum\n newJ, #What J will become\n #possible subs target(s)\n oldarg::{algebraic, set(algebraic)}:= map2(op, 2, indets(e, specfunc(applyintegrand)))\n ;\n if nops(J) = 0 then\n userinfo(2, procname, \"No sum or integral found.\");\n return e\n end if;\n if nops(J) > 1 then\n userinfo(1, reparam, \"Case of multiple innermost Int or Sums not yet handled.\");\n return 'procname'(e)\n end if;\n J:= J[];\n if J::specfunc(Sum) then\n userinfo(1, reparam, \"Sums not yet handled.\");\n return 'procname'(e)\n end if;\n\n if nops(oldarg) <> 1 then\n userinfo(1, thisproc, \"More than 1 reparam possible:\", oldarg);\n return 'procname'(e)\n end if;\n oldarg:= oldarg[]; #Extract the reparam target.\n\n #If the target is simply a name, return input unchanged.\n if oldarg::symbol then\n userinfo(2, procname, \"No need for a reparameterization.\");\n return e\n end if;\n\n #Make the change of vars.\n newJ:= simplify_assuming('ChangeVarInt(J, oldarg)', build_kb(ctx,\"reparam\"));\n\n if newJ = 0 then\n WARNING(\"Integral is 0, likely due to improper handling of an infinity issue.\");\n userinfo(\n 1, procname, \"u subs:\",\n print(\n #Reformat the ChangeVarInt command for readability.\n subs(\n x= ':-x',\n 'ChangeVarInt'(\n subsindets(\n J,\n specfunc(applyintegrand),\n f-> ':-h'(op(2,f))\n )\n ),\n oldarg\n )\n )\n )\n end if;\n\n subs(J= newJ, e)\n end proc;\n", "meta": {"hexsha": "c611fab85fbd4fefc527cb0a638813d888ed50ce", "size": 4705, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/Reparam.mpl", "max_stars_repo_name": "zaxtax/hakaru", "max_stars_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2015-02-07T17:57:04.000Z", "max_stars_repo_stars_event_max_datetime": "2016-01-29T19:40:24.000Z", "max_issues_repo_path": "maple/NewSLO/Reparam.mpl", "max_issues_repo_name": "zaxtax/hakaru", "max_issues_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/NewSLO/Reparam.mpl", "max_forks_repo_name": "zaxtax/hakaru", "max_forks_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.1119402985, "max_line_length": 93, "alphanum_fraction": 0.5058448459, "num_tokens": 1228, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8438950907764118, "lm_q2_score": 0.6825737279551494, "lm_q1q2_score": 0.5760206181143046}} {"text": "(*\n Copyright (C) 2019 M.A.L. Marques\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: mgga_exc *)\n\n$include \"hyb_mgga_x_pjs18.mpl\"\n\n(* This expression (10) has \\tilde A, and not A *)\njs18_f_SR := (rs, z, x, t) -> tm_w(x, t)*js18_DME_SR(rs, z, x, t)\n + (1 - tm_w(x, t))*attenuation_erf(a_cnst*rs/opz_pow_n(z,1/3))*tm_fx_SC(x, t):\n\njs18_f := (rs, z, x, u, t) -> -p_a_hyb_coeff_0_*js18_f_SR(rs, z, x, t) + tm_f(x, u, t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange_nsp(js18_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "dd2087eb874f2341fe38227748d6481a3a16a8df", "size": 690, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_js18.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/mgga_exc/hyb_mgga_x_js18.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/mgga_exc/hyb_mgga_x_js18.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": 32.8571428571, "max_line_length": 87, "alphanum_fraction": 0.631884058, "num_tokens": 285, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9032942119105696, "lm_q2_score": 0.6370308013713525, "lm_q1q2_score": 0.5754262356874944}} {"text": "bc := \n[\n [\n [2-7*x1+x1^2*x2-1/2*(x3-x1),\n 6*x1-x1^2*x2-5*(x4-x2),\n 2-7*x3+x3^2*x4-1/2*(x1-x3),\n 6*x3-x3^2*x4+1+1/2*(x2-x4)\n ], \n [x4,x3,x2,x1]\n ],\n [\n [1-c*x-x*y^2-x*z^2,\n 1-c*y-y*x^2-y*z^2,\n 1-c*z-z*x^2-z*y^2,\n 8*c^6+378*c^3-27\n ],\n [z, y, x, c]\n ],\n [ \n [a+b+c+d+h1,\n a*b+b*c+c*d+d*h1+h1*a,\n a*b*c+b*c*d+c*d*h1+d*h1*a+h1*a*b,\n a*b*c*d+b*c*d*h1+c*d*h1*a+d*h1*a*b+h1*a*b*c,\n a*b*c*d*h1-1\n ],\n [h1, d, c, b, a]\n ],\n [\n [2*x1*(2-x1-y1)+x2-x1,\n 2*x2*(2-x2-y2)+x1-x2,\n 2*y1*(5-x1-2*y1)+y2-y1,\n y2*(3-2*x2-4*y2)+y1-y2\n ],\n [x2, x1, y2, y1]\n ],\n [\n [1/100-4*s*(s-1)*(s-b)*(s-c),\n 1/5-b*c,\n 2*s-1-b-c\n ],\n [s, c, b]\n ],\n [\n [x^2+y^2-x*y-1,\n y^2+z^2-y*z-a^2,\n z^2+x^2-z*x-b^2,\n a^2-1+b-b^2,\n 3*b^6+56*b^4-122*b^3+56*b^2+3\n ],\n [z, y, x, b, a]\n ]\n]:", "meta": {"hexsha": "d02e723cb0e403caa8b1b0347b6cc11b2860298d", "size": 1065, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Examples/xia2006.mpl", "max_stars_repo_name": "lihaokun/StrongSfTriDec", "max_stars_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2022-03-21T11:48:40.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-21T11:50:26.000Z", "max_issues_repo_path": "Examples/xia2006.mpl", "max_issues_repo_name": "lihaokun/StrongSfTriDec", "max_issues_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "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/xia2006.mpl", "max_forks_repo_name": "lihaokun/StrongSfTriDec", "max_forks_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "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": 20.4807692308, "max_line_length": 53, "alphanum_fraction": 0.2957746479, "num_tokens": 516, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111796979521252, "lm_q2_score": 0.6297746143530797, "lm_q1q2_score": 0.5738378428841553}} {"text": "(*\n Copyright (C) 2020 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(* prefix:\n gga_k_rational_p_params *params;\n\n assert(p->params != NULL);\n params = (gga_k_rational_p_params * )(p->params);\n*)\n\nrational_p_f0 := s -> (1 + params_a_C2/params_a_p * s^2)^(-params_a_p):\nrational_p_f := x -> rational_p_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_kinetic(rational_p_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "ca3b2bac9dcea3793637db6c451802555d1d561f", "size": 579, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "external/libxc-5.1.6/maple/gga_exc/gga_k_rational_p.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/gga_exc/gga_k_rational_p.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/gga_exc/gga_k_rational_p.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": 27.5714285714, "max_line_length": 73, "alphanum_fraction": 0.6753022453, "num_tokens": 196, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.857768108626046, "lm_q2_score": 0.668880247169804, "lm_q1q2_score": 0.5737441445121649}} {"text": "$ifndef _GEN_SOL_\n$define _GEN_SOL_\n\n$include \"Utils.mpl\"\n\n# 寻找一般解,考虑存在常数约束和多个单变量非零约束\n# 若只存在一个极大元，则直接返回下标\n# 否则分组返回极大元，相等的极大元放在一组中\nfindGenSolInd:=proc(icons::list(set),n::posint)\n return findGenVec(con2vec~(icons,n));\nend proc:\n\n# 将约束条件转化为向量\ncon2vec:=proc(c::set,n::posint)\n local v,t;\n v:=Array(1..n,2);\n for t in c do\n if op(0,t)=`=` then\n v[op([1,1],indets(t,name))]:=0;\n elif op(0,t)=`<>` then\n v[op([1,1],indets(t,name))]:=1;\n end if;\n end do;\n return convert(v,list);\nend proc:\n\n# 寻找一般解\n# 等价于寻找偏序集的极大元\n# 返回下标的list\nfindGenVec:=proc(v::list)\n local mInd,i,j,n,isAdd,ind,t,gen,mgen,maxind;\n n:=numelems(v);\n mInd:=table();\n mInd[1]:=1;\n for i from 2 to n do\n isAdd:=true;\n for j in indices(mInd,nolist) do\n if v[i] &> v[j] then\n unassign(evaln(mInd[j]));\n elif v[j] &> v[i] then\n isAdd:=false;\n break;\n end if;\n end do;\n if isAdd then\n mInd[i]:=1;\n end if;\n end do;\n ind:=[indices(mInd,nolist)];\n if numelems(ind)=1 then\n return ind[1];\n else\n # 分组返回，相等的元素放在一组\n t:=table();\n for i in ind do\n tappend(t,v[i],i);\n end do;\n ind:=[entries(t,nolist)];\n # 选择一般性最大的分组\n gen:=map(x->add(v[x[1]]),ind);\n mgen:=max(gen);\n maxind:=find(gen,mgen);\n ind:=ind[maxind];\n return ind;\n end if;\nend proc:\n\n`&>=`:=proc(x::list,y::list)\n local n:=numelems(x);\n return andmap(k->evalb(x[k]>=y[k]),[seq(1..n)]);\nend proc:\n\n`&>`:=proc(x::list,y::list)\n local n:=numelems(x);\n return x &>= y and ormap(k->evalb(x[k]>y[k]),[seq(1..n)]);\nend proc:\n\n$endif", "meta": {"hexsha": "33f5b7d798eba9ee97ca3d143c56cb24275a0ecb", "size": 1753, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "InvClassify/GenSol.mpl", "max_stars_repo_name": "yu961549745/InvariantClassify", "max_stars_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "InvClassify/GenSol.mpl", "max_issues_repo_name": "yu961549745/InvariantClassify", "max_issues_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "InvClassify/GenSol.mpl", "max_forks_repo_name": "yu961549745/InvariantClassify", "max_forks_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.4743589744, "max_line_length": 62, "alphanum_fraction": 0.515687393, "num_tokens": 663, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8128673133042217, "lm_q2_score": 0.7057850278370112, "lm_q1q2_score": 0.5737095793482166}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_gga_x *)\n\nc1 := 0.003:\n\nf := x -> 1 + c1/X_FACTOR_C * x^2:\n", "meta": {"hexsha": "1f619799a5035b1e348c5769c22610c8d1cf1917", "size": 312, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_herman.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_herman.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_herman.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 22.2857142857, "max_line_length": 68, "alphanum_fraction": 0.6602564103, "num_tokens": 102, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.86153820232079, "lm_q2_score": 0.6654105521116443, "lm_q1q2_score": 0.5732766108715505}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\n$include \"gga_c_scan_e0.mpl\"\n$include \"mgga_x_scan.mpl\"\n\nscan_b1c := 0.0285764:\nscan_b2c := 0.0889:\nscan_b3c := 0.125541:\nscan_eclda0 := rs -> -scan_b1c/(1 + scan_b2c*sqrt(rs) + scan_b3c*rs):\n\nscan_chi_infty := 0.12802585262625815:\nscan_g_infty := s -> 1/(1 + 4*scan_chi_infty*s^2)^(1/4):\n\n(* in the paper it is 2.3631 *)\nscan_G_cnst := 2.363:\nscan_Gc := z -> (1 - scan_G_cnst*(2^(1/3) - 1)*f_zeta(z))*(1 - z^12):\n\nscan_H0 := (rs, s) ->\n scan_b1c*log(1 + (exp(-scan_eclda0(rs)/scan_b1c) - 1)*(1 - scan_g_infty(s))):\nscan_e0 := (rs, z, s) ->\n (scan_eclda0(rs) + scan_H0(rs, s))*scan_Gc(z):\n\nscan_alpha := (z, xt, ts0, ts1) ->\n (t_total(z, ts0, ts1) - xt^2/8)/(K_FACTOR_C*t_total(z, 1, 1)):\n\n(* set parameters of f_alpha *)\nparams_a_c1 := 0.64:\nparams_a_c2 := 1.5:\nparams_a_d := 0.7:\n\nscan_f := (rs, z, xt, xs0, xs1, ts0, ts1) ->\n f_pbe(rs, z, xt, xs0, xs1) + scan_f_alpha(scan_alpha(z, xt, ts0, ts1))*(\n + scan_e0(rs, z, X2S*2^(1/3)*xt)\n - f_pbe(rs, z, xt, xs0, xs1)\n ):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n scan_f(rs, z, xt, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "1a812eddc2dc80fa23b8d9276aa4fcc1bebce8f2", "size": 1335, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_scan.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/mgga_exc/mgga_c_scan.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/mgga_exc/mgga_c_scan.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": 28.4042553191, "max_line_length": 79, "alphanum_fraction": 0.6157303371, "num_tokens": 571, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.894789457685656, "lm_q2_score": 0.640635861701035, "lm_q1q2_score": 0.573234215265452}} {"text": "# 尽可能的化简解的约束\n\n$ifndef _CON_REFINE_\n$define _CON_REFINE_\n\n$include \"Condition.mpl\"\n$include \"../seg/Seg.mpl\"\n\n# 总的简化函数\nconRefine:=proc(r::RepSol)\n signRefine(r);\n epRefine(r);\n uniqueAndSort(r);# 简化之后重新对条件进行排序\n return;\nend proc:\n\n# 对于代表元v[k]删去a[k]>0.\n# 对于代表元-v[k]删去a[k]<0.\n# 这里只删去了acon的条件，对于osol并没有进行修改\nsignRefine:=proc(r::RepSol)\n local vs,k,rc;\n vs:=indets(r:-rep,name);\n if numelems(vs)<>1 then\n return;\n end if;\n k:=op([1,1],vs);\n rc:=eval({a[k]>0,a[k]<0});\n r:-acon:=map(x->x minus rc,r:-acon);\n return;\nend proc:\n\n# 尽可能删去和epsilon有关的约束\nepRefine:=proc(r::RepSol)\n r:-acon:=epDeal~(r:-acon);\nend proc:\n\n# 处理每个可能情况的约束条件\nepDeal:=proc(s::set)\n local ca,ce,r;\n ce,ca:=selectremove(has,s,epsilon);\n ce:=ceDeal~(ce);\n r:=ce union ca;\n r:=classifySolve(r);\n return r;\nend proc:\n\n# 单个关于epsilon的条件处理\nceDeal:=proc(e)\n local rs;\n # 有的时候solve会抽，对于这种情况不做处理\n try\n rs:=conSolve(e);\n catch :\n return e;\n end try;\n if numelems(rs)=0 then\n # 无解则原样返回\n return e;\n elif numelems(rs)=1 then\n # 只有一个解，则不论有多少条件都可以\n return rs[][];\n else\n return multiConRefine(rs);\n end if;\nend proc:\n\nmultiConRefine:=proc(rs)\n local s;\n # 单变量约束的并集，只处理无约束和，x<>c的约束\n if numelems(indets(rs,name))=1 and \n andmap(x->evalb(numelems(x)=1),rs) then\n s:=`union`(seq(Seg(x),x in rs));\n if s=real then\n return NULL;\n end if;\n s:=&C s;\n if type(s:-bound,numeric) then\n return indets(rs,name)[]<>s:-bound;\n else\n return e;\n end if;\n # 删去一个共同条件之后能够构成单变量约束的并集\n elif numelems(`intersect`(rs[]))=1 then\n s:=`intersect`(rs[]);\n return s[],multiConRefine(map(x->x minus s,rs));\n else\n return e;\n end if;\nend proc:\n\n# 求解不等式，\n# 在解中删除自由变量\n# 删除和epsilon有关的约束\nconSolve:=proc(c)\n local r;\n r:=[RealDomain:-solve(c)];\n r:=map(x->remove(t->evalb(lhs(t)=rhs(t)),x),r);\n r:=map(x->remove(has,x,epsilon),r);\n r:=[{r[]}[]];# 去重\n return r;\nend proc:\n\n$endif", "meta": {"hexsha": "e1462faa9b7b0ff03768459757d13dc2f13934be", "size": 2074, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "old/ConRefine.mpl", "max_stars_repo_name": "yu961549745/InvariantClassify", "max_stars_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "old/ConRefine.mpl", "max_issues_repo_name": "yu961549745/InvariantClassify", "max_issues_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "old/ConRefine.mpl", "max_forks_repo_name": "yu961549745/InvariantClassify", "max_forks_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.1359223301, "max_line_length": 56, "alphanum_fraction": 0.5713596914, "num_tokens": 825, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7905303186696748, "lm_q2_score": 0.724870282120402, "lm_q1q2_score": 0.5730319351188186}} {"text": "\n# NewtonEuler Formulation for Robot based on MDH frames\n\n# Einleitung\n# Berechnung der inversen Dynamik in Rückwärtsrekursive\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# tree -> Berechnung für eine beliebige Baumstruktur (ohne Schleifen)\n# fixb -> Fixed Base Modell der Basis.\n# dynamics -> Berechnung der Dynamik\n# NewtonEuler->Newton - Euler Bewegungsgleichung\n# Linkframe->Berechnung der Newton Euler im Körper-KS(KSi)\n# par12 -> Parametersatz 1 (Schwerpunkt als Parameter: SX,SY,SZ) oder Parametersatz 2 (1. und 2. Moment MX,MY,MZ,...)\n\n# Sources\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I\n# \n# Initialization\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\nread \"../transformation/proc_rotx\": \nread \"../transformation/proc_roty\": \nread \"../transformation/proc_rotz\": \nread \"../transformation/proc_trotx\": \nread \"../transformation/proc_troty\": \nread \"../transformation/proc_trotz\": \nread \"../transformation/proc_transl\": \nread \"../transformation/proc_trafo_mdh\": \n# Einstellungen für Code-Export: Optimierungsgrad (2=höchster) und Aktivierung jedes Terms.\ncodegen_opt := 2:\ncodeexport_grav := true: \ncodeexport_corvec := true:\ncodeexport_cormat := true:\ncodeexport_inertia := true:\ncodeexport_inertiaD := true:\ncodeexport_invdyn := true:\ncodegen_act := true:\ncodegen_dynpar := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"Generiere Dynamikgleichungen für %s (Herleitung im Körper-KS)\\n\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name): \nkin_constraints_exist := kin_constraints_exist: # nur zum Abschätzen der Komplexität\n;\n# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(9)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardmäßig aus\n else # mit kinematischen Zwangsbedingungen\n if NJ <= 5 then # nur bei einfachen Systemen Term-Vereinfachung durchführen\n use_simplify := 1:\n else\n use_simplify := 0: # Annahme: Dauert zu lange bzw. zu rechenintensiv (nicht geprüft)\n end if:\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(9): # neunter Eintrag ist für Dynamik\nend if:\n\nread \"../helper/proc_index_symmat2vector\":\nread \"../helper/proc_symmat2vector\":\n# Ergebnisse der Kinematik laden\nread sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name, base_method_name):\nTrf := Trf:\nTrf_c := Trf_c:\n# Ergebnisse der Geschwindigkeit laden\nread sprintf(\"../codeexport/%s/tmp/velocity_linkframe_floatb_%s_maple.m\", robot_name, base_method_name):\nomega_i_i:= omega_i_i:\nrD_i_i:= rD_i_i:\n# Zeitableitungen der MDH-Drehwinkel laden.\n# Die Berechnung soll nur an einer Stelle erfolgen. Siehe robot_tree_velocity_mdh_angles.mw.\nread sprintf(\"../codeexport/%s/tmp/velocity_mdh_angles_maple.m\", robot_name):\nthetaD := thetaD:\ndD :=dD:\n# Zeitableitungen der Geschwindigkeit laden.\n# Die Berechnung soll nur an einer Stelle erfolgen. Siehe robot_tree_acceleration_mdh_angles.mw.\nread sprintf(\"../codeexport/%s/tmp/acceleration_mdh_angles_maple.m\", robot_name):\nthetaDD :=thetaDD:\ndDD := dDD:\n# Ergebnisse der Geschwindigkeit laden. TODO: Warum doppelt?\nread sprintf(\"../codeexport/%s/tmp/velocity_linkframe_floatb_%s_maple.m\", robot_name, base_method_name):\nomega_i_i:= omega_i_i:\nrD_i_i:= rD_i_i:\n# Ergebnisse der Beschleunigung laden\naccfile := sprintf(\"../codeexport/%s/tmp/acceleration_linkframe_floatb_%s_maple.m\", robot_name, base_method_name):\nif FileTools[Exists](accfile) then\n read accfile:\nelse\n printf(\"%s. Schwerpunktsbeschleunigung wurde nicht berechnet. Abbruch der Newton-Euler-Berechnung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch Löschung des Roboternamens.\nend if:\nomegaD_i_i:= omegaD_i_i: \nrDD_i_i:= rDD_i_i:\nrDD_i_Si:= rDD_i_Si:\n# Mit diesem Arbeitsblatt werden die Vorwärtsrekursive für Fixed-Base Modelle generiert. Erkenne welche Basis-Modellierung aktiv ist\nif base_method_name=\"twist\" then # Basis-Methode \"twist\" wird (hier) nur für fixed Base benutzt\n expstring:=\"fixb\":\nelif base_method_name=\"eulxyz\" then \n expstring:=\"floatb_eulxyz\":\nelse\n printf(\"Nicht behandelte Basis-Methode: %s\\n\", base_method_name):\nend if:\n# Schalter zur Auswahl der unterschiedlichen Terme, die exportiert werden sollen.\n\n# Newton-Euler formulation(mit Funktion)\nOutputNewtonEuler:= NewtonEuler(f_i_i,m_i_i):\n# Backward recursive computation\n# Force exerted on link i by link i-1(unbekannte Kraft zwischen Teilkörper n-1 und Teilkörper n)\nf_i_i:= Matrix(3,NJ+1):\n# Moment exerted on link i by link i-1(unbekannte Moment zwischen Teilkörper n-1 und Teilkörper n)\nm_i_i:=Matrix(3,NJ+1):\n\n# Schnittmomente/Kräfte\ntau_B := Matrix(6,1):\ntau_J := Matrix(NQJ,1):\ntau := Matrix(6+NQJ,1):\n\n\nI_i_i_m:= Matrix(3,3,NL):\nfor i from 1 to NL do\n I_i_i_m(1..3,1..3,i):=Matrix(3,3):\n end do:\n\nfor i from 1 to NL do\n I_i_i_m[1,1,i]:=I_i_i[1,i]:\n I_i_i_m[1,2,i]:=I_i_i[2,i]:\n I_i_i_m[1,3,i]:=I_i_i[3,i]:\n I_i_i_m[2,1,i]:=I_i_i[2,i]:\n I_i_i_m[2,2,i]:=I_i_i[4,i]:\n I_i_i_m[2,3,i]:=I_i_i[5,i]:\n I_i_i_m[3,1,i]:=I_i_i[3,i]:\n I_i_i_m[3,2,i]:=I_i_i[5,i]:\n I_i_i_m[3,3,i]:=I_i_i[6,i]:\nend do:\n\nF_i:= Matrix(3,NL):\nM_i:= Matrix(3,NL):\nfor i from 1 to NL do\n # External forces and moment on link i\n #Betrachte dazu nur die durch Gelenke angetriebenen Körper, nicht die Basis\n # [Khali2002](9.5.3) (9.88) & (9.89)\n F_i(1..3,i):= M(i,1)*rDD_i_i(1..3,i)+CrossProduct(omegaD_i_i(1..3,i),mr_i_i_Si(1..3,i))+ CrossProduct(omega_i_i(1..3,i), CrossProduct(omega_i_i(1..3,i), mr_i_i_Si(1..3,i))):\n M_i(1..3,i):= I_i_i_m(1..3,1..3,i).omegaD_i_i(1..3,i)+ CrossProduct(omega_i_i(1..3,i),(I_i_i_m(1..3,1..3,i).omega_i_i(1..3,i))) + CrossProduct(mr_i_i_Si(1..3,i),rDD_i_i(1..3,i)):#CrossProduct(r,F_i(1..3,i)):####\n # Terme vereinfachen\n if use_simplify>=1 then\n tmp_t1:=time():\n tmp_l11 := length(F_i(1..3,i)):\n tmp_l12 := length(M_i(1..3,i)):\n F_i(1..3,i) := simplify2(F_i(1..3,i)):\n M_i(1..3,i) := simplify2(M_i(1..3,i)):\n tmp_l21 := length(F_i(1..3,i)):\n tmp_l22 := length(M_i(1..3,i)):\n tmp_t2:=time():\n printf(\"%s: Terme für inneres Kraft/Moment %d vereinfacht. Länge: %d->%d / %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l11, tmp_l21, tmp_l12, tmp_l22, tmp_t2-tmp_t1):\n end if:\nend do :\n\n# Forces and moment exerted on link i by link i-1\n\nfor i from NL by -1 to 1 do\n f_i_i_part:= F_i(1..3,i):\n m_i_i_part:= M_i(1..3,i):# + CrossProduct(r_i_i_Si(1..3,i),(F_i(1..3,i))):\n\n I_nf := Matrix([ListTools[SearchAll](i-1,convert(v,list))]):\n \n for tmp from 1 to ColumnDimension(I_nf) do\n I_nf(tmp) := I_nf(tmp)+1:\n end do:\n\n if ColumnDimension(I_nf) <> 0 then\n for tmp from 1 to RowDimension(v) do\n j := I_nf(tmp): \n \n R_i_j := Matrix(Trf(1..3,1..3,j-1)): \n r_i_i_j := Matrix(Trf(1 .. 3, 4, j-1)):\n f_j_j := f_i_i(1..3,j):\n m_j_j := m_i_i(1..3,j):\n \n f_i_i_part := f_i_i_part + R_i_j.f_j_j:\n m_i_i_part := m_i_i_part + R_i_j.m_j_j + CrossProduct(r_i_i_j, R_i_j.f_j_j):\n \n if tmp = ColumnDimension(I_nf) then\n break: #Abbruch. Alle Nachfolger untersucht.\n end if:\n end do:\n end if:\n\n f_i_i(1..3,i) := f_i_i_part;\n m_i_i(1..3,i) := m_i_i_part;\n # Terme vereinfachen\n if use_simplify>=1 then\n tmp_t1:=time():\n tmp_l11 := length(f_i_i(1..3,i)):\n tmp_l12 := length(m_i_i(1..3,i)):\n f_i_i(1..3,i) := simplify2(f_i_i(1..3,i)):\n m_i_i(1..3,i) := simplify2(m_i_i(1..3,i)):\n tmp_l21 := length(f_i_i(1..3,i)):\n tmp_l22 := length(m_i_i(1..3,i)):\n tmp_t2:=time():\n printf(\"%s: Rekursive Terme für Kraft/Moment %d vereinfacht. Länge: %d->%d / %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l11, tmp_l21, tmp_l12, tmp_l22, tmp_t2-tmp_t1):\n end if:\nend do:\n\nfor i from 2 to NL do # Schleife über Anzahl der Körper\n if sigma(i-1) <> 2 then\n if sigma(i-1) = 0 then # Drehgelenk\n tau_J(i-1,1) := <0,0,1>.m_i_i(1..3,i):\n else # Schubgelenk\n tau_J(i-1,1) := <0,0,1>.f_i_i(1..3,i):\n end if:\n end if:\nend do:\n# Unbekannten Kräfte und Momente zwischen den Teilkörpern bestimmen\ntau_B [1..3,1]:= Transpose(Trf_c(1..3, 1..3, 1)).f_i_i(1..3,1) :\ntau_B [4..6,1]:= Transpose(T_basevel).Trf_c(1..3, 1..3, 1).m_i_i(1..3,1):\n\ntau[1..6,1]:= tau_B:\ntau[7..6+NQJ,1]:= tau_J:\n# Export\nf_i_i := convert_t_s(f_i_i):\nm_i_i := convert_t_s(m_i_i):\ntau_J := convert_t_s(tau_J):\ntau_B := convert_t_s(tau_B):\ntau := convert_t_s(tau):\n# Floating Base\nf_i_i_floatb := copy(f_i_i):\nm_i_i_floatb := copy(m_i_i):\ntau_J_floatb := copy(tau_J):\ntau_B_floatb := copy(tau_B):\ntau_floatb := copy(tau):\nfor i from 1 to 6 do\n if i < 4 then\n var := VD_base_s[i,1] - g_world[i,1];\n else\n var := VD_base_s[i,1]:\n end if:\n f_i_i_floatb := subs({VD_base_s[i,1]=var},f_i_i_floatb):\n m_i_i_floatb := subs({VD_base_s[i,1]=var},m_i_i_floatb):\n tau_J_floatb := subs({VD_base_s[i,1]=var},tau_J_floatb):\n tau_B_floatb := subs({VD_base_s[i,1]=var},tau_B_floatb):\n tau_floatb := subs({VD_base_s[i,1]=var},tau_floatb):\nend do:\n# Maple Export # TODO: Wieso Bedingung \"twist\" gewählt?\nif not(base_method_name=\"twist\") then\n save f_i_i_floatb,m_i_i_floatb,tau_J_floatb, tau_B_floatb, tau_floatb,sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_linkframe_maple.m\", robot_name, base_method_name):\n printf(\"%s. Maple-Ausdrücke exportiert.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nend if:\n# Matlab Export\nif codegen_act and codeexport_invdyn and not(base_method_name=\"twist\") then\n MatlabExport(convert_t_s(f_i_i_floatb), sprintf(\"../codeexport/%s/tmp/invdyn_floatb_%s_NewtonEuler_linkframe_f_i_i_par%d_matlab.m\", robot_name, base_method_name, codegen_dynpar), codegen_opt):\n MatlabExport(convert_t_s(m_i_i_floatb), sprintf(\"../codeexport/%s/tmp/invdyn_floatb_%s_NewtonEuler_linkframe_m_i_i_par%d_matlab.m\", robot_name, base_method_name, codegen_dynpar), codegen_opt):\n MatlabExport(convert_t_s(tau_J_floatb), sprintf(\"../codeexport/%s/tmp/invdyn_floatb_%s_NewtonEuler_linkframe_tauJ_par%d_matlab.m\", robot_name, base_method_name, codegen_dynpar), codegen_opt):\n MatlabExport(convert_t_s(tau_B_floatb), sprintf(\"../codeexport/%s/tmp/invdyn_floatb_%s_NewtonEuler_linkframe_tauB_par%d_matlab.m\", robot_name, base_method_name, codegen_dynpar), codegen_opt):\n MatlabExport(convert_t_s(tau_floatb), sprintf(\"../codeexport/%s/tmp/invdyn_floatb_%s_NewtonEuler_linkframe_tauJB_par%d_matlab.m\", robot_name, base_method_name, codegen_dynpar), codegen_opt):\nend if:\n# Fixed Base\nfor i from 1 to NQB do\n f_i_i := subs({X_base_s[i,1]=0},f_i_i):\n m_i_i := subs({X_base_s[i,1]=0},m_i_i):\n tau_J := subs({X_base_s[i,1]=0},tau_J):\n tau_B := subs({X_base_s[i,1]=0},tau_B):\n tau := subs({X_base_s[i,1]=0},tau):\nend do:\nfor i from 1 to 6 do\n f_i_i := subs({V_base_s[i,1]=0},f_i_i):\n m_i_i := subs({V_base_s[i,1]=0},m_i_i):\n tau_J := subs({V_base_s[i,1]=0},tau_J):\n tau_B := subs({V_base_s[i,1]=0},tau_B):\n tau := subs({V_base_s[i,1]=0},tau):\n if i < 4 then\n var := -g_world[i,1];\n else\n var := 0:\n end if:\n f_i_i := subs({VD_base_s[i,1]=var},f_i_i):\n m_i_i := subs({VD_base_s[i,1]=var},m_i_i):\n tau_J := subs({VD_base_s[i,1]=var},tau_J):\n tau_B := subs({VD_base_s[i,1]=var},tau_B):\n tau := subs({VD_base_s[i,1]=var},tau):\nend do:\n# Maple Export\nsave f_i_i,m_i_i,tau_J, tau_B, tau,sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_linkframe_par%d_maple.m\", robot_name, base_method_name, codegen_dynpar):\nprintf(\"%s. Maple-Ausdrücke exportiert.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n# Matlab Export\nif codegen_act and codeexport_invdyn then\n MatlabExport(f_i_i, sprintf(\"../codeexport/%s/tmp/invdyn_fixb_NewtonEuler_linkframe_f_i_i_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt):\n MatlabExport(m_i_i, sprintf(\"../codeexport/%s/tmp/invdyn_fixb_NewtonEuler_linkframe_m_i_i_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt):\n MatlabExport(tau_J, sprintf(\"../codeexport/%s/tmp/invdyn_fixb_NewtonEuler_linkframe_tauJ_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt):\n MatlabExport(tau_B, sprintf(\"../codeexport/%s/tmp/invdyn_fixb_NewtonEuler_linkframe_tauB_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt):\n MatlabExport(tau, sprintf(\"../codeexport/%s/tmp/invdyn_fixb_NewtonEuler_linkframe_tauJB_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt):\nend if:\n\n", "meta": {"hexsha": "ea1cc1d46dbca4840c8028a51851db93a4ca9798", "size": 13023, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_dynamics/robot_tree_fixb_dynamics_NewtonEuler_linkframe_par12.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_dynamics/robot_tree_fixb_dynamics_NewtonEuler_linkframe_par12.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_dynamics/robot_tree_fixb_dynamics_NewtonEuler_linkframe_par12.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 42.145631068, "max_line_length": 213, "alphanum_fraction": 0.7145051064, "num_tokens": 4546, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8479677545357568, "lm_q2_score": 0.6757646075489392, "lm_q1q2_score": 0.5730265968580109}} {"text": "(*\n Copyright (C) 2019 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(* prefix:\n gga_x_ncap_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_ncap_params * )(p->params);\n*)\n\nncap_f0 := s -> 1 + params_a_mu*tanh(s)*arcsinh(s)*( 1 + params_a_alpha*((1-params_a_zeta)*s*log(1+s) + params_a_zeta*s))/(1 + params_a_beta*tanh(s)*arcsinh(s)):\nncap_f := x -> ncap_f0(X2S*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(ncap_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "cf6c2c690bfcd1ee3c21e117449cbe363cdc3a4a", "size": 647, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_ncap.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_ncap.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_ncap.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": 30.8095238095, "max_line_length": 161, "alphanum_fraction": 0.6630602782, "num_tokens": 227, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9046505299595163, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.5730149244576377}} {"text": "(*\n Copyright (C) 2019 M.A.L. Marques\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: mgga_exc *)\n(* prefix:\n mgga_x_task_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_task_params * )(p->params);\n*)\n\ntask_alpha := (x, t) -> (t/K_FACTOR_C) * m_max(1 - x^2/(8*t), 1e-10):\n\ntask_gx0 := x -> 1 - exp(-params_a_task_c*x^(-1/4)):\ntask_gx := x -> my_piecewise3(x > 0, task_gx0(m_max(x, 0)), 0):\n\ntask_hx1 := r -> simplify(add(params_a_task_anu[i+1]*ChebyshevT(i, (r - 1)/(r + 1)), i=0..2)):\n\ntask_fx := r -> simplify(add(params_a_task_bnu[i+1]*ChebyshevT(i, (r - 1)/(r + 1)), i=0..4)):\n\ntask_f0 := (s, a) -> params_a_task_h0x*task_gx(s^2) +\n (1.0 - task_fx(a))*(task_hx1(s^2) - params_a_task_h0x)*task_gx(s^2)^params_a_task_d:\n\ntask_f := (x, u, t) -> task_f0(X2S*x, task_alpha(x, t)):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(task_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "9afc0b7e4d0de277b59809b28e4e211115ff0b36", "size": 1067, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_task.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/mgga_exc/mgga_x_task.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/mgga_exc/mgga_x_task.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": 32.3333333333, "max_line_length": 94, "alphanum_fraction": 0.6213683224, "num_tokens": 429, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9149009549929797, "lm_q2_score": 0.6261241842048092, "lm_q1q2_score": 0.5728416140731803}} {"text": "with(DifferentialAlgebra):\nring_diff := DifferentialRing(blocks = [[x3, x1, x2, x0], [y1] ], derivations = [t]):\nsys := [\ndiff(x3(t), t) - (-b2*x3(t) + b2*x2(t)),\ndiff(x1(t), t) - (a2*x0(t) - a2*x1(t)),\ndiff(x2(t), t) - ((ka*kc*b1*x3(t) - ka*kc*b1*x2(t) + ka*b1*x0(t)*x3(t) - ka*b1*x0(t)*x2(t) - n*kc*x2(t) + kc*b1*x3(t)*x2(t) - kc*b1*x2(t)^2) / (ka*kc + ka*x0(t) + kc*x2(t))),\ndiff(x0(t), t) - ((-ka*n*x0(t) - ka*kc*a1*x0(t) + ka*kc*a1*x1(t) - ka*a1*x0(t)^2 + ka*a1*x0(t)*x1(t) - kc*a1*x0(t)*x2(t) + kc*a1*x1(t)*x2(t)) / (ka*kc + ka*x0(t) + kc*x2(t))),\ny1(t) - (x0(t))\n];\nres := CodeTools[CPUTime](RosenfeldGroebner(sys, ring_diff, singsol=none));", "meta": {"hexsha": "7aaed92e4657033e39b23e494062e5cd686d9dd3", "size": 648, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/RosenfeldGroebner/Pharm.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/RosenfeldGroebner/Pharm.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/RosenfeldGroebner/Pharm.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 64.8, "max_line_length": 175, "alphanum_fraction": 0.537037037, "num_tokens": 316, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299591537478, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.5725141954379608}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\n$define lda_c_pw_params\n$include \"lda_c_pw.mpl\"\n\n$define lda_x_params\n$include \"lda_x.mpl\"\n\ncc06_cnst := (3/(4*Pi))^(2/3):\n\ncc06_alpha := -0.0007:\ncc06_beta := 0.0080*cc06_cnst:\ncc06_gamma := 0.026 *cc06_cnst:\n\ncc06_f := (rs, z, us0, us1) ->\n (f_lda_x(rs, z) + f_pw(rs, z))*(1 +\n (cc06_alpha + cc06_beta*u_total(z, us0, us1))/(1 + cc06_gamma*u_total(z, us0, us1))\n ):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n cc06_f(rs, z, us0, us1):\n", "meta": {"hexsha": "a7b76c7c280cd8191d81b0021a5ae91753980584", "size": 716, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_xc_cc06.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/mgga_exc/mgga_xc_cc06.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/mgga_exc/mgga_xc_cc06.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": 23.8666666667, "max_line_length": 87, "alphanum_fraction": 0.6410614525, "num_tokens": 279, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.893309411735131, "lm_q2_score": 0.6406358411176238, "lm_q1q2_score": 0.5722860263652254}} {"text": "# A cactus lobe is a map f : R/Z -> R/Z of degree one that has \n# constant speed on some finite collection of half-open intervals,\n# and speed zero on the complement of those intervals. We encode\n# f as a pair [c,T], where c = f(0) is in R/Z (as defined by\n# `is_element/RZ`) and T is the half-open interval where the \n# speed is nonzero (as defined by `is_element/RZ_set`).\n\n`is_element/cactus_lobes` := proc(cT)\n global reason;\n local c,T;\n\n if not(type(cT,list) and nops(cT) = 2) then\n reason := [\"is_element/cactus_lobes\",\"cT is not a list of length 2\",cT];\n return false; \n fi;\n\n c,T := op(cT);\n\n if not `is_element/RZ`(c) then\n reason := [\"is_element/cactus_lobes\",\"c is not in R/Z\",c,cT];\n return false; \n fi;\n\n if not `is_element/RZ_set`(T) then\n reason := [\"is_element/cactus_lobes\",\"T is not an RZ_set\",T,cT];\n return false; \n fi;\n\n if T = `empty/RZ` then\n reason := [\"is_element/cactus_lobes\",\"T is empty\",T,cT];\n return false; \n fi;\n\n return true;\nend:\n\n`is_equal/cactus_lobes` := proc(cT0,cT1)\n return `is_equal/RZ`(cT0[1],cT1[1]) and\n `is_equal/RZ_set`(cT0[2],cT1[2]);\nend:\n\n`random_element/cactus_lobes` := proc()\n local T;\n T := `empty/RZ_set`;\n while T = `empty/RZ_set` do T := `random_element/RZ_set`(); od:\n return [`random_element/RZ`(),T];\nend:\n\n`is_leq/cactus_lobes` := NULL:\n`list_elements/cactus_lobes` := NULL:\n`count_elements/cactus_lobes` := NULL:\n\n`start/cactus_lobes` := (cT) -> cT[1];\n`motion_set/cactus_lobes` := (cT) -> cT[2];\n`speed/cactus_lobes` := (cT) -> 1/`length/RZ_set`(cT[2]);\n\n`eval/cactus_lobes` := (cT) -> proc(t)\n local t0,c,T,n,i,u,s;\n\n c,T := op(cT);\n n := nops(T)/2;\n i := 1;\n u := c;\n s := 1/`length/RZ_set`(T);\n t0 := t - floor(t);\n while i <= n and T[2*i-1] <= t0 do\n u := u + s*(min(t0,T[2*i]) - T[2*i-1]);\n i := i+1;\n od: \n\n u := u - floor(u);\n return u;\nend:\n\n`id/cactus_lobes` := [0,[0,1]];\n\n`o/cactus_lobes` := proc(cT,dU)\n local c,T,d,U,n,m,sT,sU,T1,T2,n1,V,a,b,y,z,i,j,aa,bb;\n c,T := op(cT);\n d,U := op(dU);\n n := nops(T)/2;\n m := nops(U)/2;\n sT := 1/`length/RZ_set`(T);\n sU := 1/`length/RZ_set`(U);\n T1 := `unroll/RZ_set`(T);\n n1 := nops(T1)/2;\n V := NULL;\n y := d;\n for i from 1 to m do\n a := U[2*i-1];\n b := U[2*i];\n z := y + sU * (b - a);\n T2 := (T1 -~ y)/~sU +~ a; \n for j from 1 to n1 do\n if T2[2*j] >= a and T2[2*j-1] <= b then\n aa := max(T2[2*j-1],a);\n bb := min(T2[2*j],b);\n if aa < bb then \n V := V,aa,bb;\n fi;\n fi;\n od;\n y := z;\n od;\n\n return [`eval/cactus_lobes`(cT)(d),[V]];\nend:\n\n`source_shift/cactus_lobes` := (t) -> proc(cT)\n local c,d,T,U;\n c,T := op(cT);\n U := `shift/RZ_set`(t)(T);\n d := `eval/cactus_lobes`(cT)(-t);\n return [d,U];\nend:\n\n`target_shift/cactus_lobes` := (t) -> proc(cT)\n local c,d,T;\n c,T := op(cT);\n d := c+t;\n d := d - floor(d);\n return [d,T];\nend:\n\n`plot/cactus_lobes` := proc(cT)\n local c,T,L,x,y,z,a,b,n,i,s,A;\n c,T := op(cT);\n L := NULL;\n if T[1] > 0 then\n L := L,[[0,c],[T[1],c]];\n fi;\n y := c;\n n := nops(T)/2;\n s := 1/`length/RZ_set`(T);\n for i from 1 to n do\n a := T[2*i-1];\n b := T[2*i];\n z := y + s * (b-a);\n if z <= 1 then\n L := L,[[a,y],[b,z]];\n y := z;\n else\n x := a + (1 - y)/s;\n L := L,[[a,y],[x,1]],[[x,0],[b,z-1]];\n y := z-1;\n fi;\n x := `if`(i < n,T[2*i+1],1);\n if b < x then\n L := L,[[b,y],[x,y]];\n fi;\n od;\n\n A := args[2..-1];\n return\n display(map(u -> line(u[1],u[2],A),[L]),scaling=constrained,axes=none);\nend:\n\n`full_plot/cactus_lobes` := proc(cT)\n local x;\n \n display(\n `plot/cactus_lobes`(cT),\n seq(line([x,0],[x,1],colour=red),x in [0,1]),\n seq(line([x,0],[x,1],colour=red,linestyle=dot),x in cT[2]),\n line([0,0],[1,0],colour=blue),\n line([0,1],[1,1],colour=blue),\n line([0,cT[1]],[1,cT[1]],colour=green,linestyle=dash)\n );\nend:\n\n", "meta": {"hexsha": "6a9125ca670f297a245be4cae300b27bd20eef66", "size": 3726, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/cacti/cactus_lobes.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/operads/cacti/cactus_lobes.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/operads/cacti/cactus_lobes.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": 21.7894736842, "max_line_length": 74, "alphanum_fraction": 0.5528717123, "num_tokens": 1530, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.782662489091802, "lm_q2_score": 0.7310585786300049, "lm_q1q2_score": 0.5721721268224745}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\n$define lda_c_pw_params\n$include \"lda_c_pw.mpl\"\n\n$define lda_x_params\n$include \"lda_x.mpl\"\n\nb98_gamma_x := 0.11:\nb98_gamma_ss := 1.6:\nb98_gamma_ab := 0.14:\n\nparams_a_c_x := [0.8085, 0.6682, 0.1420]:\nparams_a_c_ss := [0.2606, -0.9608, 0.9023]:\nparams_a_c_ab := [1.2033, -2.2717, 0.9596]:\n\nb98_q := (x, u, t) -> 1 - (t - x^2/8 - u/4)/K_FACTOR_C:\n\nb98_g := (gamma, cc, q) -> add(cc[i]*(gamma*q/sqrt(1 + gamma^2*q^2))^(i-1), i=1..3):\n\nb98_f := (rs, z, xs0, xs1, us0, us1, ts0, ts1) ->\n + lda_x_spin(rs, z)\n * b98_g( b98_gamma_x, params_a_c_x, b98_q(xs0, us0, ts0))\n + lda_x_spin(rs, -z)\n * b98_g( b98_gamma_x, params_a_c_x, b98_q(xs1, us1, ts1))\n + lda_stoll_par(f_pw, rs, z, 1)\n * b98_g(b98_gamma_ss, params_a_c_ss, b98_q(xs0, us0, ts0)) * Fermi_D(xs0, ts0)\n + lda_stoll_par(f_pw, rs, -z, -1)\n * b98_g(b98_gamma_ss, params_a_c_ss, b98_q(xs1, us1, ts1)) * Fermi_D(xs1, ts1)\n + lda_stoll_perp(f_pw, rs, z)\n * b98_g(b98_gamma_ab, params_a_c_ab, (b98_q(xs0, us0, ts0) + b98_q(xs1, us1, ts1))/2):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n b98_f(rs, z, xs0, xs1, us0, us1, ts0, ts1):", "meta": {"hexsha": "c7c45ed2994191009e97717bab779c43f9de268d", "size": 1372, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_xc_b98.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/mgga_exc/mgga_xc_b98.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/mgga_exc/mgga_xc_b98.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": 32.6666666667, "max_line_length": 90, "alphanum_fraction": 0.6333819242, "num_tokens": 605, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.92414182206801, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.5718408775000752}} {"text": "# A full flag of subspaces in (Z/p)^d is represented by a list\n# [w[1],...,w[d]] where the subspace of dimension i is\n# spanned by [w[1],...,w[i]] and the last nonzero entry in\n# w[i] is a 1 in position h[i] say, and w[i+1],...,w[d]\n# all have zero in position h[i].\n\n\n`count_elements/vectors` := (p,d) -> p^d;\n\n`list_elements/vectors` := proc(p,d)\n local L,i,j,u;\n \n L := [[]];\n for i from 1 to d do\n L := [seq(seq([op(u),j],j=0..p-1),u in L)];\n od:\n return L;\nend:\n\n`height/vectors` := (p,d) -> proc(u)\n local h;\n \n h := d;\n while h > 0 and u[h] = 0 do h := h - 1; od;\n return h;\nend:\n\n`count_elements/monic_vectors` := (p,d) -> (p^d - 1)/(p - 1);\n\n`list_elements/monic_vectors` := proc(p,d)\n local i,u;\n \n [seq(seq([op(u),1,0$(d-1-i)],u in `list_elements/vectors`(p,i)),i=0..d-1)];\nend:\n\n`count_elements/full_flags` := proc(p,d) local i; mul((p^i-1)/(p-1),i=1..d); end:\n\n`list_elements/full_flags` := proc(p,d)\n local L,L1,nL,H,V,i,j,k,u,v,q;\n L := [[]];\n H := [[]];\n \n for i from 1 to d do\n nL := nops(L);\n L1 := L;\n L := [];\n V := `list_elements/monic_vectors`(p,d - i + 1);\n H := map(W -> sort(map(`height/vectors`(p,d),W)),L1);\n for j from 1 to nL do \n for v in V do\n u := [];\n q := 1;\n for k from 1 to d do\n if member(k,H[j]) then\n u := [op(u),0];\n else\n u := [op(u),v[q]];\n q := q + 1;\n fi;\n od:\n L := [op(L),[op(L1[j]),u]];\n od;\n od:\n od:\n\n return L;\nend:\n\n`random_element/full_flags` := (p,d) -> proc()\n local V,i,v;\n V := table():\n V[0] := `bot/subspaces`(p,d);\n for i from 1 to d do \n v := [0$d];\n while `is_member/subspaces`(p,d)(v,V[i-1]) do \n v := [seq(rand(0..p-1)(),i=1..d)];\n od;\n V[i] := `span/subspaces`(p,d)([op(V[i-1][1]),v]);\n end:\n return `from_subspace_list/full_flags`(p,d)([seq(V[i],i=1..d)]);\nend:\n\n`is_element/full_flags` := (p,d) -> proc(W)\n local h,i,j;\n\n if not(type(W,list(list(integer)))) then \n return false;\n fi;\n\n if map(nops,W) <> [d$d] then \n return false;\n fi;\n\n if W <> modp(W,p) then\n return false;\n fi;\n\n h := table():\n for i from 1 to d do \n if W[i] = [0$d] then return false; fi;\n j := d; \n while W[i][j] = 0 do j := j - 1; od;\n if W[i][j] <> 1 then \n return false;\n fi;\n h[i] := j;\n od:\n\n for i from 1 to d do \n for j from i+1 to d do \n if W[j][h[i]] <> 0 then return false; fi;\n od;\n od;\n\n return true;\nend:\n\n`count_elements/full_flags` := proc(p,d) local i; mul((p^i-1)/(p-1),i = 1..d); end:\n\n`basepoint/full_flags` := (p,d) -> convert(IdentityMatrix(d),listlist);\n\n`to_subspace_list/full_flags` := (p,d) -> proc(W)\n local i;\n [seq(`span/subspaces`(p,d)([op(1..i,W)]),i=1..d)];\nend:\n\n`from_subspace_list/full_flags` := (p,d) -> proc(V)\n local i,j,h,v,W;\n\n v := V[1][1][1];\n j := d; while j > 0 and v[j] = 0 do j := j - 1; od; \n v := modp(v /~ v[j],p);\n W := [v];\n h := [j];\n for i from 2 to d do \n j := 1;\n while j < i and `is_member/subspaces`(p,d)(V[i][1][j],V[i-1]) do \n j := j + 1;\n od;\n v := V[i][1][j];\n for j from 1 to i-1 do \n v := modp(v -~ v[h[j]] *~ W[j],p);\n od:\n j := d; while j > 0 and v[j] = 0 do j := j - 1; od; \n v := modp(v /~ v[j],p);\n W := [op(W),v];\n h := [op(h),j];\n od:\n return W;\nend:\n\n# It would be better to do this directly and use it in the\n# `from_subspace/full_flags` procedure.\n`from_generators/full_flags` := (p,d) -> proc(U)\n local V,i;\n V := [seq(`span/subspaces`(p,d)([op(1..i,U)]),i=1..d)];\n return `from_subspace_list/full_flags`(p,d)(V);\nend:\n\n`matrix_act/full_flags` := (p,d) -> proc(g,W)\n local gW,V,i;\n\n gW := convert(Transpose(Matrix(g) . Transpose(Matrix(W))),listlist);\n V := [seq(`span/subspaces`(p,d)([op(1..i,gW)]),i=1..d)];\n return `from_subspace_list/full_flags`(p,d)(V);\nend:\n\n`jordan_permutation/full_flags` := (p,d) -> proc(U,V)\n local U0,V0,UV,UV1,i,j,w;\n U0 := `to_subspace_list/full_flags`(p,d)(U);\n U0 := table([0 = `bot/subspaces`(p,d),seq(i = U0[i],i=1..d)]);\n V0 := `to_subspace_list/full_flags`(p,d)(V);\n V0 := table([0 = `bot/subspaces`(p,d),seq(i = V0[i],i=1..d)]);\n UV := table():\n for i from 0 to d do \n for j from 0 to d do \n UV[i,j] := `inter/subspaces`(p,d)(U0[i],V0[j]);\n od;\n od;\n UV1 := table();\n w := table():\n for i from 1 to d do \n for j from 1 to d do \n UV1[i,j] := `sum/subspaces`(p,d)(UV[i-1,j],UV[i,j-1]);\n if `dim/subspaces`(p,d)(UV[i,j]) > `dim/subspaces`(p,d)(UV1[i,j]) then\n w[i] := j;\n fi;\n od;\n od;\n return [seq(w[i],i=1..d)];\nend:\n", "meta": {"hexsha": "4d3f2f73338cc5d72cf015f87258ec49db18bda4", "size": 4368, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/full_flags.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/full_flags.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/full_flags.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": 22.75, "max_line_length": 83, "alphanum_fraction": 0.538003663, "num_tokens": 1699, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581097540519, "lm_q2_score": 0.718594386544335, "lm_q1q2_score": 0.5717554512777382}} {"text": "######################################################################\n# F(N)(A) is Inj(A,RR^N) modulo translation and scaling.\n#\n# Elements are represented as tables indexed by A, whose values \n# are lists of length N of real numbers. The equivalence relation\n# is built into the definition of the function `is_equal/F` rather\n# than the representation of the elements.\n\n`is_element/F` := (N::posint) -> (A::set) -> proc(x)\n local a;\n global reason;\n\n if not(type(x,table)) then\n reason := [convert(procname,string),\"x is not a table\",x];\n return false; \n fi;\n\n if map(op,{indices(x)}) <> A then\n reason := [convert(procname,string),\"x is not indexed by A\",x,A];\n return false;\n fi;\n\n for a in A do\n if not `is_element/R`(N)(x[a]) then\n reason := [convert(procname,string),\"x[a] is not in R^N\",a,x[a],N];\n return false;\n fi;\n od;\n\n if nops(map(op,{entries(x)})) <> nops(A) then\n reason := [convert(procname,string),\"x is not injective\",x];\n return false; \n fi;\n\n return true;\nend;\n\n######################################################################\n# This function normalises the infinity norm. This is convenient\n# because it preserves rationality, but it is geometrically unpleasant.\n\n`normalise/F` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,r,a;\n\n x0 := table();\n u := [0$N];\n\n for a in A do\n x0[a] := x[a];\n u := u +~ x[a];\n od;\n u := u /~ nops(A);\n r := 0;\n for a in A do\n x0[a] := x0[a] -~ u;\n r := max(r,op(map(abs,x0[a])));\n od;\n for a in A do\n x0[a] := x0[a] /~ r;\n od;\n\n return(eval(x0));\nend;\n\n######################################################################\n# This function normalises the euclidean norm\n`normalise_2/F` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,r2,r,a;\n\n x0 := table();\n u := [0$N];\n\n for a in A do\n x0[a] := x[a];\n u := u +~ x[a];\n od;\n u := u /~ nops(A);\n r2 := 0;\n for a in A do\n x0[a] := x0[a] -~ u;\n r2 := r2 + `norm_2/R`(N)(x0[a])^2;\n od;\n r := sqrt(r2);\n\n for a in A do\n x0[a] := x0[a] /~ r;\n od;\n\n return(eval(x0));\nend;\n\n######################################################################\n\n`is_equal/F` := (N::posint) -> (A::set) -> proc(x,y) \n local x0,y0,a;\n global reason;\n\n x0 := `normalise/F`(N)(A)(x);\n y0 := `normalise/F`(N)(A)(y);\n\n for a in A do\n if not(`is_equal/R`(N)(x0[a],y0[a])) then\n reason := [convert(procname,string),\"x0[a] <> y0[a]\",a,x0[a],y0[a]];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_leq/F` := NULL;\n\n######################################################################\n\n`random_element/F` := (N::posint) -> (A::set) -> proc()\n local ok,x,a;\n\n ok := false;\n while not(ok) do\n x := table();\n for a in A do\n x[a] := `random_element/R`(N)();\n od:\n ok := `is_element/F`(N)(A)(x);\n od;\n\n return eval(x);\nend;\n\n######################################################################\n\n`list_elements/F` := NULL;\n\n######################################################################\n\n`count_elements/F` := NULL;\n\n######################################################################\n\n`separation_infinity/F` := (N::posint) -> (A::set) -> proc(x)\n local x0,d,n,i,j;\n\n x0 := `normalise/F`(N)(A)(x);\n d := 2;\n n := nops(A);\n\n for i from 1 to n-1 do \n for j from i+1 to n do\n d := min(d,`d_infinity/R`(N)(x0[A[i]],x0[A[j]]));\n od;\n od;\n\n return d;\nend;\n\n######################################################################\n\n`fatten/F` := (N::posint) -> (A::set) -> proc(x)\n local x0,d,m,a,i,e,u;\n\n x0 := `normalise/F`(N)(A)(x);\n d := `separation_infinity/F`(N)(A)(x0);\n m := 0;\n for a in A do\n for i from 1 to N do\n m := max(m,d/2+abs(x0[a][i]));\n od;\n od;\n \n e := [1 $ N];\n\n for a in A do\n u[a] := [((x0[a] -~ ((d/2) *~ e)) /~ m +~ e) /~ 2,\n ((x0[a] +~ ((d/2) *~ e)) /~ m +~ e) /~ 2];\n od;\n\n return eval(u);\nend;\n\n######################################################################\n\n`inc/F/Fbar` := (N::posint) -> (A::set) -> proc(x)\n local y,P,T,t;\n\n y := table();\n\n P := `list_elements/big_subsets`(A);\n\n for T in P do\n y[T] := table([seq(t = x[t],t in T)]);\n od:\n\n return eval(y);\nend;\n\n######################################################################\n\n`gaps/F` := (N::posint) -> (A::set) -> proc(x)\n local G,V,W,m,i,j,a;\n \n G := NULL;\n m := nops(A);\n \n for i from 1 to N do \n V := sort([seq(x[a][i],a in A)]);\n W := [seq(V[j+1] - V[j],j = 1 .. m-1)];\n G := G,max(W);\n od;\n\n G := [G];\n return G;\nend;\n\n######################################################################\n\n`gap/F` := (N::posint) -> (A::set) -> proc(x)\n return max(`gaps/F`(N)(A)(x));\nend;\n\n######################################################################\n\n`normalise_gap/F` := (N::posint) -> (A::set) -> proc(x)\n local m,g,x0,a,i;\n \n m := [seq(min(seq(x[a][i],a in A)),i=1..N)];\n g := `gap/F`(N)(A)(x);\n \n x0 := table();\n for a in A do\n x0[a] := (x[a] -~ m) /~ g;\n od;\n\n return eval(x0);\nend;\n\n######################################################################\n\n`delta/F` := (N::posint) -> (A::set) -> (a,b) -> proc(x)\n local u,n,i;\n u := x[b] -~ x[a];\n n := sqrt(add(u[i]^2,i=1..N));\n return u /~ n;\nend:\n\n######################################################################\n\n`draw_unnormalised/F` := (A::set) -> proc(x)\n local a;\n display(seq(point(x[a]),a in A),scaling=constrained,axes=none);\nend;\n\n######################################################################\n\n`draw/F` := (A::set) -> proc(x)\n display(`draw_unnormalised/F`(A)(`normalise/F`(2)(A)(x)),view=[-1..1,-1..1]);\nend;\n\n", "meta": {"hexsha": "fc1d42c5c4e1c3f35ef757ed4045d62c0d6ba888", "size": 5514, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/F.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/operads/F.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/operads/F.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": 21.2076923077, "max_line_length": 78, "alphanum_fraction": 0.4143997098, "num_tokens": 1685, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8459424373085146, "lm_q2_score": 0.6757646075489392, "lm_q1q2_score": 0.5716579591567814}} {"text": "\n# Kinematik-Berechnung 3. Arm KAS5 Modell 7\n# Beschreibung\n# \n# Berechnung der kinematischen Zwangsbedingungen des Systems KAS5m7 in impliziter Form.\n# Ansatz: Schließen von Gelenkketten nach [1] und Anwendung der Zahnrad-Zwangsbedingungen.\n# \n# Quellen\n# [1] Khalil and Bennis: Symbolic calculation of the base inertial parameters of closed-loop robots (1995)\n# Autor\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2018-02\n# Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Initialisierung\nrestart:\nkin_constraints_exist := true: # Für Speicherung\n;\nwith(StringTools): # Für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\ncodegen_act := true:\ncodegen_opt := 1: # Geringerer Optimierungsgrad. Sonst zu lange.\ncodegen_debug := 0: # Zur Code-Generierung auch für Nicht-Inert-Ausdrücke\n;\nread \"../helper/proc_MatlabExport\":\nread \"../transformation/proc_rotx\":\nread \"../transformation/proc_roty\":\nread \"../transformation/proc_rotz\":\nread \"../transformation/proc_trotz\":\nread \"../transformation/proc_transl\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\nread \"../helper/proc_intersect_circle\":\nwith(RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env_IC\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name_OL):\n# Ergebnisse der Kinematik laden\nread sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name_OL, base_method_name);\nread \"../robot_codegen_definitions/robot_env_IC\":\nTrf := Trf:\nTrf_c := Trf_c:\n# Schleife über B-C-D\n# 3-4-12-13-17\nT_3_17 := combine( Matrix(Trf(1..4,1..4, 4)) . Matrix(Trf(1..4,1..4,12)) . Matrix(Trf(1..4,1..4,13)) . Matrix(Trf(1..4,1..4,17)) ):\n# 3-10-11-20\nT_3_20 := combine( Matrix(Trf(1..4,1..4, 10)) . Matrix(Trf(1..4,1..4,11)) . Matrix(Trf(1..4,1..4,20)) ):\nh1 := T_3_17(1..3,4) - T_3_20(1..3,4):\n# Schleife über 2-F-E\n# \n# 2-3-10-16\nT_2_16 := combine( Matrix(Trf(1..4,1..4, 3)) . Matrix(Trf(1..4,1..4,10)) . Matrix(Trf(1..4,1..4,16)) ):\n# 2-8-9-19\nT_2_19 := combine( Matrix(Trf(1..4,1..4, 8)) . Matrix(Trf(1..4,1..4,9)) . Matrix(Trf(1..4,1..4,19)) ):\n# Vektorkette\nh2 := T_2_16(1..3,4) - T_2_19(1..3,4):\n# Schleife über 5-B-A\n\n# 4-5-6-18\nT_4_18 := combine( Matrix(Trf(1..4,1..4, 5)) . Matrix(Trf(1..4,1..4,6)) . Matrix(Trf(1..4,1..4,18)) ):\n# 4-12-13-14-15-21\nT_4_21 := combine( Matrix(Trf(1..4,1..4, 12)) . Matrix(Trf(1..4,1..4,13)) . Matrix(Trf(1..4,1..4,14)) . Matrix(Trf(1..4,1..4,15)) . Matrix(Trf(1..4,1..4,21)) ):\n# Vektorkette\nh3 := T_4_18(1..3,4) - T_4_21(1..3,4):\n# Zahnrad-Kontakt\n# \nhz1 := -qJ_t(4) + qJ_t(11):\nhz2 := -qJ_t(6) + qJ_t(5) - qJ_t(4) + delta18:\nh_user := :\n# Zusammenstellen aller Zwangsbedingungen\n# \nimplconstr_t := :\nimplconstr_s := convert_t_s(implconstr_t):\n# Exportiere Code für folgende Skripte\n# \n# \nkin_constraints_exist:=true:\nsave implconstr_t, implconstr_s, kin_constraints_exist, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_implicit_maple.m\", robot_name):\n# Exportieren des vollständigen Ausdruckes\nif codegen_act then\n MatlabExport(implconstr_s, sprintf(\"../codeexport/%s/tmp/kinconstr_impl_matlab.m\", robot_name), 2):\nend if:\n# Liste mit abhängigen konstanten Kinematikparametern erstellen (wichtig für Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\nkc_symbols := Matrix(list_constant_expressions( implconstr_s )):\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_implicit_constraints_symbols_list_maple\", robot_name):\nMatlabExport(Transpose(kc_symbols), sprintf(\"../codeexport/%s/tmp/kinematic_implicit_constraints_symbols_list_matlab.m\", robot_name), 2):\ninterface(rtablesize=100):\nkc_symbols\n;\n", "meta": {"hexsha": "787089e770dbcbd8b1eda1ff179bf0380d7c3ab0", "size": 3880, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "exoskeleton_model/model_generation/constraints/KAS5m7IC_kinematic_constraints_implicit.mpl", "max_stars_repo_name": "SchapplM/robsynth-paper_iftommwc2019_dynamics_hybridrobots", "max_stars_repo_head_hexsha": "b3d83b4c99bb5bccb3076ca93790b079fc4e1d2f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-19T14:12:45.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-19T14:12:45.000Z", "max_issues_repo_path": "exoskeleton_model/model_generation/constraints/KAS5m7IC_kinematic_constraints_implicit.mpl", "max_issues_repo_name": "SchapplM/robsynth-paper_iftommwc2019_dynamics_hybridrobots", "max_issues_repo_head_hexsha": "b3d83b4c99bb5bccb3076ca93790b079fc4e1d2f", "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": "exoskeleton_model/model_generation/constraints/KAS5m7IC_kinematic_constraints_implicit.mpl", "max_forks_repo_name": "SchapplM/robsynth-paper_iftommwc2019_dynamics_hybridrobots", "max_forks_repo_head_hexsha": "b3d83b4c99bb5bccb3076ca93790b079fc4e1d2f", "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": 42.1739130435, "max_line_length": 160, "alphanum_fraction": 0.7219072165, "num_tokens": 1426, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357666736773, "lm_q2_score": 0.658417500561683, "lm_q1q2_score": 0.5708715223908652}} {"text": "\n# Energy Calculation for Atlas Robot based on MDH frames\n# Introduction\n# Berechnung von potentieller Energie für den Roboter.\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# tree -> Berechnung für eine beliebige Baumstruktur (ohne Schleifen)\n# floatb -> floating base wird durch base twist (Geschwindigkeit der Basis) oder vollständige Orientierung (Euler-Winkel) berücksichtigt\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# energy -> Berechnung der Energie\n# worldframe -> Berechnung der Positionen und Geschwindigkeiten im Welt-KS (KS W) anstatt im Basis-KS (KS 0)\n# par2 -> Parametersatz 2 (erstes Moment anstelle von Schwerpunkt als Parameter)\n\n# Anmerkung\n# Nur potentielle Energie möglich\n# Kinetische Energie stimmt nicht überein. Funktioniert nicht mit diesem Parametervektor und Geschwindigkeiten im Basis-KS\n# Für die kinetische Energie sollte robot_tree_floatb_twist_rotmat_energy_linkframe_par2.mw genommen werden!\n# Authors\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-03\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# \n# Sources\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I\n# Initialization\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../transformation/proc_rotx\": \nread \"../transformation/proc_roty\": \nread \"../transformation/proc_rotz\": \nread \"../transformation/proc_trotx\": \nread \"../transformation/proc_troty\": \nread \"../transformation/proc_trotz\": \nread \"../transformation/proc_transl\": \nread \"../transformation/proc_trafo_mdh\": \nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nkin_constraints_exist := kin_constraints_exist: # Laden zur Einstellung der Term-Vereinfachung\n;\n# Einstellungen für Term-Vereinfachungen: 0=keine, 1=E_pot(einzelne), 2=auch E_pot (komplett)\nif not assigned(simplify_options) or simplify_options(6)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardmäßig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 2: # standardmäßig alle simplify-Befehle anwenden\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(6): # sechster Eintrag ist für Energie\nend if:\n# Ergebnisse der Kinematik laden\nread sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name, base_method_name):\nTrf_c := Trf_c:\nread sprintf(\"../codeexport/%s/tmp/kinematics_com_worldframe_floatb_%s_par1_maple.m\", robot_name, base_method_name):\nr_W_i_Si := r_W_i_Si:\nmr_W_i_Si := mr_W_i_Si:\n\n# Potential Energy\nU_b := Matrix(NL, 1):\nU_grav := 0:\nfor i to NL do \n r_W_W_i := Matrix(3,1,Trf_c(1 .. 3, 4, i)):\n U_b[i] := -Multiply(Transpose(g_world), M[i, 1]*r_W_W_i+Matrix(3,1,mr_W_i_Si(1 .. 3, i))):\n printf(\"%s. Potentielle Energie aus Gravitation für Körper %d berechnet (im Welt-KS, mit Parametersatz 2).\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1):#0=Basis\n # Terme vereinfachen (nur einzelne Energien und nicht die Summe.\n # Annahme: Zusammenfassung verschiedener Körper nicht zielführend\n if use_simplify>=1 then\n tmp_t1:=time(): tmp_l1 := length(U_b[i,1]):\n printf(\"%s. Beginne Vereinfachung für potentielle Energie (Param. 2; Körper %d). Länge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l1):\n U_b[i,1] := simplify2(U_b[i,1]):\n tmp_t2:=time(): tmp_l2 := length(U_b[i,1]):\n printf(\"%s: Terme für potentielle Energie (Param. 2) vereinfacht (Körper %d). Länge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end if:\n U_grav := U_grav+U_b[i, 1]:\n # Terme nochmal in Gesamtsumme zusammenfassen (zusätzlich)\n if use_simplify>=2 then\n tmp_t1:=time(): tmp_l1 := length(U_grav):\n printf(\"%s. Beginne Vereinfachung für potentielle Energie (Param. 2; Summe bis Körper %d). Länge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l1):\n U_grav := simplify2(U_grav):\n tmp_t2:=time(): tmp_l2 := length(U_grav):\n printf(\"%s: Terme für potentielle Energie (Param. 2) vereinfacht (Summe bis Körper %d). Länge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end if:\nend do:\n# Maple Export\nsave U_grav, sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_worldframe_par2_maple.m\", robot_name, base_method_name):\n# Kinetic Energy\n# Using velocities in world frame and MX,MY,MZ as a parameter does not work.\n# Only calculation of potential energy in this worksheet\n# Matlab Export\nprintf(\"%s: Potentielle Energie (Param. 2) berechnet und gespeichert. Beginne Matlab-Export.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n# Potential Energy\n# Floating Base\nU_s := convert_t_s(U_grav):\nif codegen_act then\n MatlabExport(U_s, sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_worldframe_par2_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n# Fixed Base\nU_s_fixb:=U_s:\nfor i from 1 to NQB do\n U_s_fixb := subs({X_base_s[i,1]=0},U_s_fixb):\nend do:\nfor i from 1 to 6 do\n U_s_fixb := subs({V_base_s[i,1]=0},U_s_fixb):\nend do:\nif codegen_act then\n MatlabExport(U_s_fixb, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_worldframe_par2_matlab.m\", robot_name), codegen_opt):\nend if:\n\n", "meta": {"hexsha": "63be453a9f30b0e801dcfb89f9ddca36c4150ffd", "size": 5944, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_energy/robot_tree_floatb_rotmat_energy_worldframe_par2.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_energy/robot_tree_floatb_rotmat_energy_worldframe_par2.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_energy/robot_tree_floatb_rotmat_energy_worldframe_par2.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 46.0775193798, "max_line_length": 148, "alphanum_fraction": 0.7394010767, "num_tokens": 1901, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8577681049901036, "lm_q2_score": 0.665410572017153, "lm_q1q2_score": 0.5707679653995342}} {"text": "(*\n Copyright (C) 2020 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(* prefix:\n gga_k_lkt_params *params;\n\n assert(p->params != NULL);\n params = (gga_k_lkt_params * )(p->params);\n*)\n\n(* The m_min avoids divisions by zero *)\nlkt_f0 := s -> 1/cosh(params_a_a * m_min(200, s)) + 5*s^2/3 :\nlkt_f := x -> lkt_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_kinetic(lkt_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "f91671bba91cd9096d0e55d83db8eb7dab0e3b38", "size": 575, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_lkt.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_k_lkt.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_k_lkt.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": 26.1363636364, "max_line_length": 68, "alphanum_fraction": 0.6469565217, "num_tokens": 203, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9059898305367525, "lm_q2_score": 0.6297746074044134, "lm_q1q2_score": 0.5705693898386743}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\nlp90_c0 := 0.80569:\nlp90_d0 := 3.0124e-3:\nlp90_k := 4.0743e-3:\n\n(* Equation (60) *)\nlp90_f := (rs, z, xt, us0, us1) ->\n - (lp90_c0 + lp90_d0*t_vw(z, xt, us0, us1))/(rs/RS_FACTOR + lp90_k):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n lp90_f(rs, z, xt, us0, us1):\n", "meta": {"hexsha": "a0dc905a1bd65e1c1e318275e389a2e640f8da29", "size": 534, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_xc_lp90.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/mgga_exc/mgga_xc_lp90.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/mgga_exc/mgga_xc_lp90.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": 25.4285714286, "max_line_length": 70, "alphanum_fraction": 0.6235955056, "num_tokens": 217, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797075998822, "lm_q2_score": 0.6261241772283034, "lm_q1q2_score": 0.5705116447281023}} {"text": "\n# Berechnungen für Systeme mit kinematischen Zwangsbedingungen\n# Beschreibung\n# Dieses Arbeitsblatt ist für Systeme mit kinematischen Zwangsbedingungen relevant.\n# Es werden die Zusammenhänge zwischen den Minimalkoordinaten des Systems mit Zwangsbedingungen mit dem offenen System ohne Zwangsbedingungen hergestellt (nach [NakamuraGho1989], [ParkChoPlo1999]).\n# Das System ohne Zwangsbedingungen kann durch die Erstellung einer neuen robot_env definiert werden (Weglassen der Zwangsbedingungen, offene Baumstruktur).\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# kinematic_constraints_calculations -> Berechnungen bezüglich kinematischer Zwangsbedingungen\n# Quellen\n# [KhalilKle1986] Khalil, W. & Kleinfinger, J.: A new geometric notation for open and closed-loop robots (1986)\n# [NakamuraGho1989] Nakamura, Yoshihiko and Ghodoussi, Modjtaba: Dynamics computation of closed-link robot mechanisms with nonredundant and redundant actuators (1989)\n# [ParkChoPlo1999] Park, FC and Choi, Jihyeon and Ploen, SR: Symbolic formulation of closed chain dynamics in independent coordinates (1999)\n# Autor\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2017-12\n# Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\ninterface(rtablesize=30):\nwith(StringTools): # Für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\ncodegen_act := true:\ncodegen_opt := 2: # Hoher Optimierungsgrad.\n;\nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nwith(RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\n# Definition und Zwangsbedingeun\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nif not assigned(simplify_options) or simplify_options(1)=-1 then\n if NJ <= 5 then\n use_simplify := 1: # Nur bei sehr einfachen Systemen (Viergelenkkette). Sonst hängt es sich auf.\n else\n use_simplify := 0: # Sonst keine Vereinfachung.\n end if:\nelse\n use_simplify := simplify_options(1): # erster Eintrag ist für Zwangsbedingungen\nend if:\n# Lesen der Zwangsbedingungen\nkin_constraints_exist := false:\nconstrfile := sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nif FileTools[Exists](constrfile) then\n read constrfile:\nend if:\nif kin_constraints_exist = true then:\n kintmp_qs := kintmp_qs: # gelesene Variable sonst nicht sichtbar\n kintmp_qt := kintmp_qt: # gelesene Variable sonst nicht sichtbar\n kintmp_subsexp := kintmp_subsexp: # gelesene Variable sonst nicht sichtbar\n printf(\"%s. Kinematische Zwangsbedingungen gelesen.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nelse\n printf(\"%s. Es gibt keine Zwangsbedingungen. Offene Struktur. Keine weiteren Berechnungen notwendig.\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n restart: # Funktioniert nicht. Gedacht, damit im worksheet-Modus nichts mehr passieren kann.\n robot_name := \"\": # Damit werden die Export-Befehle ungültig\n codegen_act := false:\n quit:\nend if:\n# Abhängige Koordinaten definieren\n# Nicht alle Ersetzungsausdrücke sind auch Koordinaten\nNSE := RowDimension(kintmp_s):\n# temporäre kinematische Ausdrücke (die auch die Zwangsbedingungen enthalten)\nkintmp_s:\n# Gelenkvariable für Drehgelenke (nach [KhalilKle1986])\ntheta_s := convert_t_s(theta):\n# Gelenkvariable für Schubgelenke (nach [KhalilKle1986])\nd_s := convert_t_s(d):\n# Finde und zähle die Vorkommnisse von kintmp_s in theta_s und d_s. Die Anzahl der abhängigen Gelenkvariablen muss mit den definierten Minimalkoordinaten übereinstimmen, sonst ist das benutzerspezifizierte Modell falsch.\n# Zähle, welche Zwangsbedingungen tatsächlich vorkommen\nkintmp_zaehler := Matrix(NSE,1):\nfor i from 1 to NSE do\n if has(has~(, kintmp_s(i,1)), true) then\n kintmp_zaehler(i,1) := 1:\n end if:\nend do:\n# Zähle, welche Gelenke abhängig sind (durch ZB beschrieben).\n# (in der Gelenkvariablen stehen die Inhalte von kintmp)\njv_zaehler := Matrix(NJ,1):\nfor i from 1 to NJ do\n if has(has~(theta_s(i,1), kintmp_s), true) or has(has~(d_s(i,1), kintmp_s), true) then\n jv_zaehler(i,1) := 1:\n end if:\nend do:\n# Zählen, welche Gelenke statische Transformationen sind\nsigma2_zaehler := Matrix(NJ,1):\nfor i from 1 to NJ do\n if sigma(i,1)=2 then\n sigma2_zaehler(i,1) := 1:\n end if:\nend do:\n# Anzahl der abhängigen Gelenkvariablen (Zählmethode: Gelenkkoordinaten durchgehen)\nNC1 := add(jv_zaehler(n), n = 1 .. NJ):\n# Anzahl der abhängigen Gelenkvariablen (Zählmethode: Zwangsbedingungen durchgehen)\nNC2 := add(kintmp_zaehler(n), n = 1 .. NSE):\n# Anzahl der konstanten Transformationen\nNS := add(sigma2_zaehler(n), n = 1 .. NJ):\n# Anzahl der \"realen\" Gelenke (statische Transformationen herausrechnen)\nNRJ := NJ - NS:\n# Es gibt (NL - 1) durch Gelenke bewegte Körper, NVJ/2 Koordinatensysteme (hier als \"Gelenk\" gezählt) sind statisch aufgrund der Schleifenschlussbedingungen\nif NQJ+NC1 <> NRJ then\n printf(\"%s. Fehler: Anzahl der Abhängigen Gelenke %d (aus Gelenkvariablen) passt nicht zur Anzahl der Gelenke %d und der Minimalkoordinaten %d\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), NC1, NRJ, NQJ):\nend if:\nif NC1 <> NC2 then\n printf(\"%s. Fehler: Anzahl der Abhängigen Gelenke %d (aus Gelenkvariablen) passt nicht zur Anzahl der Zwangsbedingungen %d (aus Verwendung der Zwangsbedingungs-Variablen)\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), NC1, NC2):\nend if:\n# Indizes der Zwangsbedingungen (in kintmp_s), die wirklich verwendet werden. Wird später nicht mehr benötigt.\nInd_ZB := Matrix(NC,1):\nj := 1:\nfor i from 1 to NSE do\n if kintmp_zaehler(i,1) = 1 then\n Ind_ZB(j,1) := i:\n j := j + 1:\n end if:\nend do:\n# Koordinaten der offenen Struktur (MDH-Gelenkvariablen)\n# Darstellung der Gelenkvariablen in abhängigkeit der Minimalkoordinaten. Diese Gelenkvariablen sind die Minimalkoordinaten des offenen Systems (ohne Zwangsbedingungen)\njv_s := theta_s*~(Matrix(NJ,1,1)-sigma) + d_s*~sigma - qoffset:\njv_qs := jv_s: # Initialisierung\njv_qt := Matrix(NJ,1): # Initialisierung\n;\n# Ersetzen der abhängigen Gelenkkoordinaten\nfor i from 1 to NJ do # Index über alle Gelenkvariablen\n # Substituiere sin und cos der Winkel (einfachere Ausdrücke. Sollten aber hier nicht drin sein.)\n jv_qs(i,1) := subs_kintmp_exp(jv_qs(i,1)):\n # Substituiere die verbleibenden Winkel direkt\n for jj from 1 to NSE do # Index über zu ersetzende Winkel\n jv_qs(i,1) := subs( { kintmp_s(jj, 1) = kintmp_qs(jj, 1) }, jv_qs(i,1) ): \n end do:\n jv_qt(i,1) := convert_s_t( jv_qs(i,1) ):\nend do:\n# Jacobi-Matrix der abhängigen Winkel\n# Ableitung der Gelenkkoordinaten nach den Minimalkoordinaten.\n# Wird benötigt, um die Geschwindigkeit der Gelenkkoordinaten der offenen Struktur zu berechnen und um die Momente der offenen Struktur auf die geschlossene Struktur umzurechnen.\n# Ist Matrix Phi aus [ParkChoPlo1999]. qJ hier ist qa dort. qr dort entspricht den Koordinaten desselben Systems ohne Zwangsbedingungen.\n# Entspricht der Matrix W aus [NakamuraGho1989] (nur dass hier die Aufteilung q1,q2 nicht gestapelt in q auftreten muss).\n# Wenn statische Transformationen definiert sind (mit sigma=2), dann werden die entsprechenden Spalten hier trotzdem angegeben (das ist nicht unbedingt intuitiv, aber von der Programmierung bedeutend einfach)\nPhi_s := Matrix(NJ, NQJ):\n# Jacobi-Matrix berechnen\nfor i from 1 to NJ do\n for j from 1 to NQJ do\n Phi_s(i,j) := diff(jv_qs(i,1), qJ_s(j,1)):\n end do:\nend do:\n# Term vereinfachen\nif use_simplify >= 1 then\n tmp_t1 := time(): tmp_l1 := length(Phi_s):\n printf(\"%s. Vereinfache Passiv-Gelenk-Jacobi (Dimension %d x %d). Länge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), NJ, NQJ, tmp_l1):\n for i from 1 to NJ do\n for j from 1 to NQJ do\n tmp_t1ij := time(): tmp_l1ij := length(Phi_s(i,j)):\n printf(\"%s. Vereinfache Passiv-Gelenk-Jacobi Eintrag %d,%d. Länge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, j, tmp_l1ij):\n Phi_s(i,j) := simplify2(Phi_s(i,j)):\n tmp_t2ij := time(): tmp_l2ij := length(Phi_s(i,j)):\n printf(\"%s. Passiv-Gelenk-Jacobi der ZB Eintrag %d,%d vereinfacht. Länge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, j, tmp_l1ij, tmp_l2ij, tmp_t2ij-tmp_t1ij):\n end do:\n end do:\n tmp_t2 := time(): tmp_l2 := length(Phi_s):\n printf(\"%s. Passiv-Gelenk-Jacobi der ZB vereinfacht. Länge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l1, tmp_l2, tmp_t2-tmp_t1):\nend if:\n# Zeitableitung der Jacobi-Matrix\n# Wird benötigt, um die Beschleunigung der Gelenkkoordinaten der offenen Struktur zu berechnen.\nPhi_t := convert_s_t(Phi_s):\nPhiD_t := diff~(Phi_t, t):\nPhiD_s := convert_t_s(PhiD_t):\n# Exportiere Code für folgende Skripte\n# Speichere Maple-Ausdruck (Eingabe-Format und internes Format)\nsave jv_s, jv_qs, jv_qt, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_explicit_maple.m\", robot_name):\nsave Phi_s, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_explicit_jacobian_maple.m\", robot_name):\nsave PhiD_s, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_explicit_jacobian_time_derivative_maple.m\", robot_name):\nprintf(\"%s. Ausdrücke für Kinematische ZB gespeichert (Maple)\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nif codegen_act = true then\n MatlabExport(jv_zaehler, sprintf(\"../codeexport/%s/tmp/kinconstr_index_dependant_joints_matlab.m\", robot_name), 2):\n MatlabExport(jv_qs, sprintf(\"../codeexport/%s/tmp/kinconstr_expl_matlab.m\", robot_name), 2):\n MatlabExport(Phi_s, sprintf(\"../codeexport/%s/tmp/kinconstr_expl_jacobian_matlab.m\", robot_name), 2):\n MatlabExport(PhiD_s, sprintf(\"../codeexport/%s/tmp/kinconstr_expl_jacobianD_matlab.m\", robot_name), 2):\n printf(\"%s. Ausdrücke für Kinematische ZB gespeichert (Matlab)\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nend if:\n\n\n\n", "meta": {"hexsha": "d357bd34e253dd6d4b8ebc407b633a398e8b9569", "size": 10100, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_constraints/robot_kinematic_constraints_calculations.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_constraints/robot_kinematic_constraints_calculations.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_constraints/robot_kinematic_constraints_calculations.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 52.3316062176, "max_line_length": 220, "alphanum_fraction": 0.747029703, "num_tokens": 3373, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8397339797047029, "lm_q2_score": 0.6791787056691697, "lm_q1q2_score": 0.570329437442261}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(x2(t), t) = alpha*x1(t) - beta*x2(t),\ndiff(x4(t), t) = (gama*sigma*x2(t)*x4(t) - delta*sigma*x3(t)*x4(t)) / (x3(t)),\ndiff(x1(t), t) = (-b*c*x1(t) - b*x1(t)*x4(t) + 1) / (c + x4(t)),\ndiff(x3(t), t) = gama*x2(t) - delta*x3(t),\ny(t) = x1(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "f46344a2c7560c8573598653ec40766486d5bf7d", "size": 354, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/Goodwin-oscillator.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/Goodwin-oscillator.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/Goodwin-oscillator.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 35.4, "max_line_length": 78, "alphanum_fraction": 0.5621468927, "num_tokens": 152, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9161096204605947, "lm_q2_score": 0.622459338205511, "lm_q1q2_score": 0.5702409880756036}} {"text": "# Recall that $\\Lambda^*$ is defined to be the monoid of lists of\n# finite sets of natural numbers. Such a list can be represented\n# in Maple like [{1,4,6},{2,3,4,5},{1}], for example. Similarly,\n# if $N$ is a finite set of natural numbers, then $\\Lambda^*[N]$\n# is the submonoid generated by the subses of $N$.\n\n# The function `is_element/itloc`(N)(AA) will return true iff\n# AA is an element of $\\Lambda^*[N]$.\n\n`is_element/itloc` := (N::set) -> proc(AA)\n return type(AA,list(set(nonnegint)));\nend:\n\n# The function `is_small_element/itloc`(N)(l)(AA) will return true\n# iff AA is an element of $\\Lambda^*[N]$ and has length $l$.\n\n`is_small_element/itloc` := (N::set) -> (l::nonnegint) -> proc(AA)\n local A;\n \n if not(`is_element/itloc`(N)(AA)) then\n return false;\n fi;\n\n if nops(AA) > l then return false; fi;\n A := map(op,{op(AA)});\n if A minus N <> {} then return false; fi;\n return true;\nend:\n\n# The function `list_small_elements/itloc`(N)(l) will produce a\n# list of all the elements of $\\Lambda^*[N]$ that have length l.\n# (This will obviously be unmanageably large unless N and l are\n# very small.)\n\n`list_small_elements/itloc` := (N::set) -> proc(l::nonnegint)\n option remember;\n local PN,L,i;\n\n PN := combinat[powerset](N);\n if l = 0 then\n return [[]];\n else\n L := `list_small_elements/itloc`(N)(l-1);\n return [seq(seq([op(AA),A],A in PN),AA in L)];\n fi;\nend:\n\n# The function `list_smaller_elements/itloc`(N)(l) lists\n# elements of length <= l.\n\n`list_smaller_elements/itloc` := (N::set) -> proc(l::nonnegint)\n [seq(op(`list_small_elements/itloc`(N)(k)),k=0..l)];\nend:\n\n# The function `count_small_elements/itloc`(N)(l) returns\n# the number of elements of length l.\n\n`count_small_elements/itloc` := (N::set) -> (l::nonnegint) ->\n 2^(nops(N) * l);\n\n# The function `random_small_element/itloc`(N)(l)() returns\n# a randomly chosen element of $\\Lambda^*[N]$ of length l.\n# (Note the extra pair of brackets in the syntax.)\n\n`random_small_element/itloc` := (N::set) -> (l::nonnegint) -> proc()\n local r;\n \n r := `random_element/subsets`(N);\n return [seq(r(),i=1..l)];\nend:\n\n# The function `o/itloc` is the multiplication law for the\n# monoid $\\Lambda^*$: so for example `o/itloc`(AA,BB,CC) is\n# just the list obtained by concatenating AA, BB and CC.\n\n`o/itloc` := () -> map(op,[args]);\n\n# `id/itloc` is the empty list, which is the identity element\n# of the monoid $\\Lambda^*$.\n\n`id/itloc` := [];\n\n# `omega/itloc`(AA) is the union of all the sets in the list AA.\n# `cap/itloc`(AA,B) is the sequence of intersections of sets in\n# AA with the fixed set B. (This is defn-om in the LaTeX file.)\n\n`omega/itloc` := (AA) -> map(op,{op(AA)});\n`cap/itloc` := (AA,B) -> map(A -> `intersect`(A,B),AA);\n\n# `sigma/itloc`(N)(AA) is the intersection of all the sets in the\n# list AA, to be interpreted as N if the list AA is empty.\n# This is essentially the same as in rem-sg-xi in the LaTeX file.\n\n`sigma/itloc` := (N::set) -> (AA) -> `intersect`(N,op(AA));\n\n# `prec/itloc`(A,B) returns true if every element of A is strictly\n# less than every element of B. The function `preceq/itloc`(A,B)\n# returns true if every element of A is less than or equal to\n# every element of B. These are in defn-prec in the LaTeX file.\n`prec/itloc` := proc(A::set,B::set)\n if A = {} or B = {} then return true; fi;\n return evalb(max(op(A)) < min(op(B)));\nend:\n\n`preceq/itloc` := proc(A::set,B::set)\n if A = {} or B = {} then return true; fi;\n return evalb(max(op(A)) <= min(op(B)));\nend:\n\n# The next five definitions correspond to defn-reduced in the LaTeX file.\n\n`is_top_reduced/itloc` := proc(AA)\n local t;\n t := map(A -> max(-infinity,op(A)),AA);\n return evalb(t = sort(t));\nend:\n\n`is_bottom_reduced/itloc` := proc(AA)\n local b;\n b := map(A -> min(op(A),infinity),AA);\n return evalb(b = sort(b));\nend:\n\n`is_unnested/itloc` := proc(AA)\n local r,i;\n r := nops(AA);\n for i from 1 to r-1 do\n if AA[i] minus AA[i+1] = {} then\n return false;\n fi;\n if AA[i+1] minus AA[i] = {} then\n return false;\n fi;\n od;\n return true;\nend:\n\n`is_end_reduced/itloc` := proc(AA)\n `is_top_reduced/itloc`(AA) and\n `is_bottom_reduced/itloc`(AA);\nend:\n\n`is_reduced/itloc` := proc(AA)\n `is_top_reduced/itloc`(AA) and\n `is_bottom_reduced/itloc`(AA) and\n `is_unnested/itloc`(AA);\nend:\n\n# The next three definitions correspond to defn-reductions and\n# lem-trimming-confluent\n`beta/itloc` := proc(AA)\n local r,i,n,BB;\n\n r := nops(AA);\n if r = 0 then return []; fi;\n BB := table();\n BB[1] := AA[1];\n for i from 2 to r do \n if BB[i-1] = [] then \n return [[]];\n fi;\n n := min(BB[i-1]);\n BB[i] := select(j -> evalb(j >= n),AA[i]);\n od;\n return [seq(BB[i],i=1..r)];\nend:\n\n`tau/itloc` := proc(AA)\n local r,i,n,BB;\n\n r := nops(AA);\n if r = 0 then return []; fi;\n BB := table();\n BB[r] := AA[r];\n for i from r-1 to 1 by -1 do \n if BB[i+1] = [] then \n return [[]];\n fi;\n n := max(BB[i+1]);\n BB[i] := select(j -> evalb(j <= n),AA[i]);\n od;\n return [seq(BB[i],i=1..r)];\nend:\n\n`delta/itloc` := proc(AA) \n local r,m,i,BB,CC,Bi,Cm,U,V,ok;\n\n r := nops(AA);\n if r = 0 then return []; fi;\n\n ok := false;\n CC := AA;\n while not(ok) do\n BB := CC;\n r := nops(BB);\n CC := [BB[1]];\n m := 1;\n for i from 2 to r do\n Bi := {op(BB[i])};\n Cm := {op(CC[m])};\n U := Bi minus Cm;\n V := Cm minus Bi;\n if U = {} then\n CC := [seq(CC[j],j=1..m-1),BB[i]];\n elif V <> {} then\n CC := [op(CC),BB[i]];\n m := m+1;\n fi;\n od: \n ok := evalb(CC = BB);\n od;\n \n return BB;\nend:\n\n`end_reduce/itloc` := (AA) -> `tau/itloc`(`beta/itloc`(AA)):\n\n`reduce/itloc` := (AA) -> `delta/itloc`(`tau/itloc`(`beta/itloc`(AA))):\n\n`rho/itloc` := eval(`reduce/itloc`):\n\n# `oo/itloc` concatenates its arguments, and then applies the\n# reduction map.\n\n`oo/itloc` := proc()\n `reduce/itloc`(`o/itloc`(args));\nend:\n\n######################################################################\n\n# The set $\\Theta(AA)$ of threads is defined in defn-threads.\n# The function `is_element/threads/itloc`(AA)(a) returns true\n# iff a is a thread for AA.\n\n`is_element/threads/itloc` := (AA) -> proc(a)\n local r,i;\n\n r := nops(AA);\n if not(type(a,list) and nops(a) = r) then\n return false;\n fi;\n\n for i from 1 to r do\n if not(member(a[i],AA[i])) then\n return false;\n fi;\n od;\n\n if a <> sort(a) then\n return false;\n fi;\n\n return true;\nend:\n\n# The function `is_leq/threads/itloc`(AA)(a,b) returns true iff\n# a[i] <= b[i] for all i.\n\n`is_leq/threads/itloc` := (AA) -> proc(a,b)\n local i;\n for i from 1 to nops(AA) do\n if a[i] > b[i] then return false; fi;\n od;\n return true;\nend:\n\n# The function `list_elements/threads/itloc`(AA) returns a list\n# of all the threads for AA.\n\n`list_elements/threads/itloc` := proc(AA)\n local r,AA0,L0,L,U,a0;\n\n r := nops(AA);\n\n if r = 0 then\n return [[]];\n elif r = 1 then\n return [op(map(a -> [a],AA[1]))];\n fi;\n\n AA0 := [seq(AA[i],i=1..r-1)];\n L0 := `list_elements/threads/itloc`(AA0);\n L := NULL;\n for a0 in L0 do\n U := select(a -> a0[r-1] <= a,AA[r]);\n L := L,seq([op(a0),a],a in U);\n od:\n return [L];\nend:\n\n# The function `random_element/threads`(AA)() attempts to return\n# a randomly chosen thread for AA. It is not very intelligent,\n# so it may fail to find a thread even if one exists. It will\n# return the symbol FAIL if it does not find a thread.\n\n`random_element/threads/itloc` := (AA) -> proc(num_tries::posint := 10)\n local k,n,a,i,B;\n\n if min(op(map(nops,AA))) = 0 then return FAIL; fi;\n\n k := num_tries;\n n := nops(AA);\n\n while k > 0 do\n k := k-1;\n a := [random_element_of(AA[1])];\n for i from 2 to n do\n B := select(b -> b >= a[-1],AA[i]);\n if B = {} then\n break;\n else\n a := [op(a),random_element_of(B)];\n fi;\n od;\n if nops(a) = n then return a; fi;\n od;\n\n return FAIL;\nend:\n\n# We do not know an efficient method to compute the number of threads,\n# so we set `count_elements/threads/itloc` to NULL. \n`count_elements/threads/itloc` := NULL:\n\n# If the poset of threads is nonempty then it will have a smallest\n# element, which will be returned by the function\n# `bot/threads/itloc`(AA).\n\n`bot/threads/itloc` := proc(AA)\n local BB;\n BB := `beta/itloc`(AA);\n if member({},BB) then\n return FAIL;\n else\n return map(min,BB);\n fi;\nend:\n\n# If the poset of threads is nonempty then it will have a largest\n# element, which will be returned by the function\n# `top/threads/itloc`(AA).\n\n`top/threads/itloc` := proc(AA)\n local CC;\n CC := `tau/itloc`(AA);\n if member({},CC) then\n return FAIL;\n else\n return map(max,BB);\n fi;\nend:\n\n# `is_threadable/itloc`(AA) returns true iff AA has a thread\n`is_threadable/itloc` :=\n (AA) -> (`bot/threads/itloc`(AA) <> FAIL);\n\n# `min_thread_sets/itloc`(AA) returns the minimal elements of the\n# poset of thread sets for AA (as in defn-threads)\n`min_thread_sets/itloc` := proc(AA)\n local U,V,W,a,b;\n U := {op(`list_elements/threads/itloc`(AA))};\n U := map(u -> {op(u)},U);\n U := [op(U)];\n U := sort(U,(a,b) -> evalb(nops(a) < nops(b)));\n V := [];\n for a in U do\n W := select(b -> b minus a = {},V);\n if W = [] then V := [op(V),a]; fi;\n od;\n return {op(V)};\nend:\n \n######################################################################\n\n# $\\Phi_0[N]$ is the submonoid of $\\Lambda[N]$ generated by the\n# functors $L_{K(n)}$. It bijects naturally with the subset of\n# $\\Lambda^*[N]$ consisting of the zero element [{}], together\n# with all elements [{a[1]},...,{a[r]}] with a[1] <= ... <= a[r].\n\n`is_element/Phi0/itloc` := (N::set(nonnegint)) -> proc(AA)\n local P;\n \n if not(`is_element/itloc`(N)(AA)) then\n return false;\n fi;\n \n if AA = [{}] then return true; fi;\n\n if {1,op(map(nops,AA))} <> {1} then\n return false; # not all singletons\n fi;\n\n P := map(op,AA);\n if sort(P) <> P then\n return false;\n fi;\n \n return true;\nend:\n\n`is_leq/Phi0/itloc` := (N::set(nonnegint)) -> proc(AA,BB)\n local P,Q;\n \n if AA = [{}] then return true; fi;\n if BB = [{}] then return false; fi;\n P := {op(map(op,AA))};\n Q := {op(map(op,AA))};\n \n return evalb(P minus Q = {});\nend:\n\n`list_elements/Phi0/itloc` := proc(N::set(nonnegint))\n local L;\n L := combinat[choose](sort([op(N)]));\n L := map(P -> map(i -> {i},P),L);\n L := [[{}],op(L)];\n return L;\nend:\n\n`random_element/Phi0/itloc` := proc(N::set(nonnegint))\n local P,AA;\n \n if rand(1..6)() = 1 then\n return [{}];\n else\n P := sort([op(random_subset_of(N)())]);\n AA := map(u -> {u},P);\n return AA;\n fi;\nend:\n\n`count_elements/Phi0/itloc` := proc(N::set(nonnegint))\n 1 + 2^nops(N);\nend:\n\n`o/Phi0/itloc` := proc()\n local AA,P;\n\n if member([{}],[args]) then\n return [{}];\n fi;\n\n AA := map(op,[args]);\n P := map(op,AA);\n if P <> sort(P) then\n return [{}];\n fi;\n\n return AA;\nend:\n\n`id/Phi0/itloc` := [];\n\n######################################################################\n\n# M11/itloc(N)(A) is the set $M'_{N,A}$ from defn-M-prime\n\n`is_element/M11/itloc` := (N::set(nonnegint)) -> (A::set(nonnegint)) -> proc(T)\n evalb(type(T,set) and (T minus N = {}) and (T intersect A <> {})); \nend:\n\n`is_leq/M11/itloc` := (N) -> (A) -> (T0,T1) -> evalb(T0 minus T1 = {}):\n\n`list_elements/M11/itloc` := (N::set(nonnegint)) -> proc(A::set(nonnegint))\n return [op(select(T -> T intersect A <> {},combinat[powerset](N)))];\nend:\n\n`random_element/M11/itloc` := (N::set(nonnegint)) -> (A::set(nonnegint)) -> proc()\n local U,V;\n \n U := `random_element/nonempty_subsets`(A)();\n V := `random_element/subsets`(N minus A)();\n return U union V;\nend:\n\n`count_elements/M11/itloc` := (N::set(nonnegint)) -> proc(A::set(nonnegint))\n 2^nops(N) - 2^nops(N minus A);\nend:\n\n######################################################################\n\n# M1/itloc(N)(AA) is the set $M'_{N,AA}$ from defn-M-prime-multi\n\n`is_element/M1/itloc` := (N::set(nonnegint)) -> (AA) -> proc(TT)\n local r,i;\n\n r := nops(AA);\n\n if not(type(TT,list(set(nonnegint)))) then\n return false;\n fi;\n \n if nops(TT) <> r then\n return false;\n fi;\n\n if map(op,{op(TT)}) minus N <> {} then\n return false;\n fi;\n \n for i from 1 to r do\n if TT[i] intersect AA[i] = {} then\n return false;\n fi;\n od;\n\n for i from 1 to r-1 do\n if not(`preceq/itloc`(TT[i],TT[i+1])) then\n return false;\n fi;\n od;\n\n return true;\nend:\n\n`is_leq/M1/itloc` := (N) -> (AA) -> proc(TT0,TT1) \n `and`(seq(TT0[i] minus TT1[i] = {},i=1..nops(TT0)));\nend:\n\n`list_elements/M1/itloc` := (N::set(nonnegint)) -> proc(AA)\n local r,m,L,L0,L1,L2,AA0,TT0;\n r := nops(AA);\n if r = 0 then\n return [[]];\n fi;\n\n L1 := `list_elements/M11/itloc`(N)(AA[r]);\n\n if r = 1 then\n return map(T -> [T],L1);\n fi;\n\n AA0 := [seq(AA[i],i=1..r-1)];\n L0 := `list_elements/M1/itloc`(N)(AA0);\n L := NULL;\n for TT0 in L0 do\n m := max(TT0[r-1]);\n L2 := select(T -> min(T) >= m,L1);\n L := L,seq([op(TT0),T],T in L2);\n od:\n L := [L];\n return L;\nend:\n\n`random_element/M1/itloc` := (N::set(nonnegint)) -> (AA) -> proc(num_tries := 10)\n local r,k,AA0,TT0,m,N0,A0,T;\n r := nops(AA);\n if r = 0 then\n return [];\n fi;\n\n k := num_tries;\n while k > 0 do\n k := k-1;\n AA0 := [seq(AA[i],i=1..r-1)];\n TT0 := `random_element/M1/itloc`(N)(AA0)(num_tries);\n if TT0 <> FAIL then\n N0 := N;\n if r > 1 then\n m := max(op(TT0[r-1])); \n N0 := select(i -> (i >= m),N);\n fi;\n A0 := N0 intersect AA[r];\n if A0 <> {} then \n T := `random_element/M11/itloc`(N0)(A0)();\n if T <> FAIL then\n return [op(TT0),T];\n fi;\n fi;\n fi;\n od;\n\n return FAIL;\nend:\n\n`count_elements/M1/itloc` := NULL:\n\n######################################################################\n\n`is_element/M2/itloc` := (N::set(nonnegint)) -> (AA) -> proc(T::set(nonnegint)) \n `is_threadable/itloc`(`cap/itloc`(AA,T)) and\n (T minus N) = {};\nend:\n\n`is_leq/M2/itloc` := (N::set(nonnegint)) -> (AA) -> proc(T0,T1) \n evalb(T0 minus T1 = {});\nend:\n\n`list_elements/M2/itloc` := (N::set(nonnegint)) -> proc(AA)\n local L;\n\n L := `list_elements/threads/itloc`(AA);\n L := map(a -> {op(a)},L);\n return [seq(seq(T union U,U in combinat[powerset](N minus T)),T in L)];\nend:\n\n`random_element/M2/itloc` := (N::set(nonnegint)) -> (AA) -> proc()\n local a,T;\n a := `random_element/threads/itloc`(AA)();\n if a = FAIL then return FAIL; fi;\n T := {op(a)};\n T := {op(T),op(random_subset_of(N minus T))};\n return T;\nend:\n\n`count_elements/M2/itloc` := NULL:\n\n######################################################################\n\n`is_element/M3/itloc` := (N::set(nonnegint)) -> (AA) -> (T) -> proc(TT)\n `is_element/M1/itloc`(N)(AA)(TT) and\n `omega/itloc`(TT) minus T = {};\nend:\n\n`is_leq/M3/itloc` := (N::set(nonnegint)) -> (AA) -> (T) -> proc(TT0,TT1)\n `and`(seq(evalb(TT0[i] minus TT1[i] = {}),i=1..nops(TT0)));\nend:\n\n`list_elements/M3/itloc` := (N::set(nonnegint)) -> (AA) -> proc(T)\n local BB,L;\n\n BB := `cap/itloc`(AA,T);\n L := `list_elements/M1/itloc`(T)(BB);\n return L;\nend:\n\n`phi/itloc` := (N::set(nonnegint)) -> (AA) -> (T) -> (TT) -> proc(k)\n local r,i,BB,b;\n r := nops(AA);\n if k < 0 or k > 2*r then error(\"k is out of range\"); fi;\n i := ceil(k/2);\n BB := `beta/itloc`(`cap/itloc`(AA,T));\n if member({},BB) then error(\"T is not a thread set for AA\"); fi;\n b := map(min,BB);\n if k = 0 then\n return TT;\n elif k = 2*i then \n return [seq({b[j]},j=1..i),seq(TT[j],j=i+1..r)];\n else\n return [seq({b[j]},j=1..i-1),TT[i] union {b[i]},seq(TT[j],j=i+1..r)];\n fi;\nend:\n", "meta": {"hexsha": "ca45c414fb6a3800c4d1cbf9c30018052761fc56", "size": 15048, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/itloc_old.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/itloc_old.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/itloc_old.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": 23.4027993779, "max_line_length": 82, "alphanum_fraction": 0.5802099947, "num_tokens": 5290, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8840392878563335, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5695203043573808}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(KS01(t), t) = c0001*KS00(t) + FS11(t)*gamma1101 - F(t)*alpha01*S01(t) + FS01(t)*beta01 - K(t)*S01(t)*a01 + KS01(t)*b01,\ndiff(FS10(t), t) = -c0001*KS00(t) - b00*KS00(t) + S00(t)*K(t)*a00 - c0011*KS00(t) - c0010*KS00(t),\ndiff(S11(t), t) = FS11(t)*beta11 + FS11(t)*gamma1100 + FS11(t)*gamma1101 + FS11(t)*gamma1110 - F(t)*alpha10*S10(t) - F(t)*alpha11*S11(t) - F(t)*alpha01*S01(t) + gamma1000*FS10(t) + FS01(t)*beta01 + FS01(t)*gamma0100 + beta10*FS10(t),\ndiff(S00(t), t) = F(t)*alpha10*S10(t) - gamma1000*FS10(t) - beta10*FS10(t),\ndiff(S10(t), t) = c0001*KS00(t) - a10*K(t)*S10(t) + KS10(t)*b10 + KS10(t)*c1011 + b00*KS00(t) + c0111*KS01(t) - S00(t)*K(t)*a00 - K(t)*S01(t)*a01 + c0011*KS00(t) + c0010*KS00(t) + KS01(t)*b01,\ndiff(F(t), t) = F(t)*alpha01*S01(t) - FS01(t)*beta01 - FS01(t)*gamma0100,\ndiff(KS00(t), t) = FS11(t)*gamma1100 + gamma1000*FS10(t) + FS01(t)*gamma0100 + b00*KS00(t) - S00(t)*K(t)*a00,\ndiff(S01(t), t) = -FS11(t)*beta11 - FS11(t)*gamma1100 - FS11(t)*gamma1101 - FS11(t)*gamma1110 + F(t)*alpha11*S11(t),\ndiff(KS10(t), t) = -a10*K(t)*S10(t) + FS11(t)*gamma1110 - F(t)*alpha10*S10(t) + KS10(t)*b10 + beta10*FS10(t) + c0010*KS00(t),\ndiff(FS01(t), t) = FS11(t)*beta11 - F(t)*alpha11*S11(t) + KS10(t)*c1011 + c0111*KS01(t) + c0011*KS00(t),\ndiff(FS11(t), t) = -c0111*KS01(t) + K(t)*S01(t)*a01 - KS01(t)*b01,\ndiff(K(t), t) = a10*K(t)*S10(t) - KS10(t)*b10 - KS10(t)*c1011,\ny1(t) = F(t),\ny5(t) = S11(t),\ny3(t) = S01(t),\ny0(t) = K(t),\ny4(t) = S10(t),\ny2(t) = S00(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "1a300258010fea36d7c9eb17d26a1c8406f39660", "size": 1591, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/MAPK-model-(6-outputs).mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/MAPK-model-(6-outputs).mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/MAPK-model-(6-outputs).mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 69.1739130435, "max_line_length": 233, "alphanum_fraction": 0.6021370207, "num_tokens": 746, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213799730774, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.5695127041450756}} {"text": "with(Groebner):\nwith(PolynomialIdeals):\n\nJ := PolynomialIdeal({10*x1*x2^2 + 10*x1*x3^2 + 10*x1*x4^2 + 10*x1*x5^2 + 10*x1*x6^2 + 10*x1*x7^2 - 11*x1 + 10, 10*x1^2*x2 + 10*x2*x3^2 + 10*x2*x4^2 + 10*x2*x5^2 + 10*x2*x6^2 + 10*x2*x7^2 - 11*x2 + 10, 10*x1^2*x3 + 10*x2^2*x3 + 10*x3*x4^2 + 10*x3*x5^2 + 10*x3*x6^2 + 10*x3*x7^2 - 11*x3 + 10, 10*x1^2*x4 + 10*x2^2*x4 + 10*x3^2*x4 + 10*x4*x5^2 + 10*x4*x6^2 + 10*x4*x7^2 - 11*x4 + 10, 10*x1^2*x5 + 10*x2^2*x5 + 10*x3^2*x5 + 10*x4^2*x5 + 10*x5*x6^2 + 10*x5*x7^2 - 11*x5 + 10, 10*x1^2*x6 + 10*x2^2*x6 + 10*x3^2*x6 + 10*x4^2*x6 + 10*x5^2*x6 + 10*x6*x7^2 - 11*x6 + 10, 10*x1^2*x7 + 10*x2^2*x7 + 10*x3^2*x7 + 10*x4^2*x7 + 10*x5^2*x7 + 10*x6^2*x7 - 11*x7 + 10}):\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7), charactesistic=2^31-1):\ntime[real]() - st;\n\n\nJ := PolynomialIdeal({10*x1*x2^2 + 10*x1*x3^2 + 10*x1*x4^2 + 10*x1*x5^2 + 10*x1*x6^2 + 10*x1*x7^2 + 10*x1*x8^2 - 11*x1 + 10, 10*x1^2*x2 + 10*x2*x3^2 + 10*x2*x4^2 + 10*x2*x5^2 + 10*x2*x6^2 + 10*x2*x7^2 + 10*x2*x8^2 - 11*x2 + 10, 10*x1^2*x3 + 10*x2^2*x3 + 10*x3*x4^2 + 10*x3*x5^2 + 10*x3*x6^2 + 10*x3*x7^2 + 10*x3*x8^2 - 11*x3 + 10, 10*x1^2*x4 + 10*x2^2*x4 + 10*x3^2*x4 + 10*x4*x5^2 + 10*x4*x6^2 + 10*x4*x7^2 + 10*x4*x8^2 - 11*x4 + 10, 10*x1^2*x5 + 10*x2^2*x5 + 10*x3^2*x5 + 10*x4^2*x5 + 10*x5*x6^2 + 10*x5*x7^2 + 10*x5*x8^2 - 11*x5 + 10, 10*x1^2*x6 + 10*x2^2*x6 + 10*x3^2*x6 + 10*x4^2*x6 + 10*x5^2*x6 + 10*x6*x7^2 + 10*x6*x8^2 - 11*x6 + 10, 10*x1^2*x7 + 10*x2^2*x7 + 10*x3^2*x7 + 10*x4^2*x7 + 10*x5^2*x7 + 10*x6^2*x7 + 10*x7*x8^2 - 11*x7 + 10, 10*x1^2*x8 + 10*x2^2*x8 + 10*x3^2*x8 + 10*x4^2*x8 + 10*x5^2*x8 + 10*x6^2*x8 + 10*x7^2*x8 - 11*x8 + 10}):\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7,x8), characteristic=2^31-1):\ntime[real]() - st;\n\n\nJ := PolynomialIdeal({10*x1*x2^2 + 10*x1*x3^2 + 10*x1*x4^2 + 10*x1*x5^2 + 10*x1*x6^2 + 10*x1*x7^2 + 10*x1*x8^2 + 10*x1*x9^2 - 11*x1 + 10,\n10*x1^2*x2 + 10*x2*x3^2 + 10*x2*x4^2 + 10*x2*x5^2 + 10*x2*x6^2 + 10*x2*x7^2 + 10*x2*x8^2 + 10*x2*x9^2 - 11*x2 + 10,\n10*x1^2*x3 + 10*x2^2*x3 + 10*x3*x4^2 + 10*x3*x5^2 + 10*x3*x6^2 + 10*x3*x7^2 + 10*x3*x8^2 + 10*x3*x9^2 - 11*x3 + 10,\n10*x1^2*x4 + 10*x2^2*x4 + 10*x3^2*x4 + 10*x4*x5^2 + 10*x4*x6^2 + 10*x4*x7^2 + 10*x4*x8^2 + 10*x4*x9^2 - 11*x4 + 10,\n10*x1^2*x5 + 10*x2^2*x5 + 10*x3^2*x5 + 10*x4^2*x5 + 10*x5*x6^2 + 10*x5*x7^2 + 10*x5*x8^2 + 10*x5*x9^2 - 11*x5 + 10,\n10*x1^2*x6 + 10*x2^2*x6 + 10*x3^2*x6 + 10*x4^2*x6 + 10*x5^2*x6 + 10*x6*x7^2 + 10*x6*x8^2 + 10*x6*x9^2 - 11*x6 + 10,\n10*x1^2*x7 + 10*x2^2*x7 + 10*x3^2*x7 + 10*x4^2*x7 + 10*x5^2*x7 + 10*x6^2*x7 + 10*x7*x8^2 + 10*x7*x9^2 - 11*x7 + 10,\n10*x1^2*x8 + 10*x2^2*x8 + 10*x3^2*x8 + 10*x4^2*x8 + 10*x5^2*x8 + 10*x6^2*x8 + 10*x7^2*x8 + 10*x8*x9^2 - 11*x8 + 10,\n10*x1^2*x9 + 10*x2^2*x9 + 10*x3^2*x9 + 10*x4^2*x9 + 10*x5^2*x9 + 10*x6^2*x9 + 10*x7^2*x9 + 10*x8^2*x9 - 11*x9 + 10}):\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7,x8,x9), characteristic=2^31-1):\ntime[real]() - st;\n", "meta": {"hexsha": "b0cc53f0a4e1ed82f6578396f93291a9ab8b8b3f", "size": 2924, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmark/maplescripts/noon.mpl", "max_stars_repo_name": "sumiya11/FastGroebner.jl", "max_stars_repo_head_hexsha": "5d3f39cec61bac0a9da8c63d1f6fa6fbea03e962", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2022-01-22T20:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-14T02:22:21.000Z", "max_issues_repo_path": "benchmark/maplescripts/noon.mpl", "max_issues_repo_name": "sumiya11/Groebner.jl", "max_issues_repo_head_hexsha": "0b0e354a9d84a5f84a11b3d4c72dcd991859c752", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 13, "max_issues_repo_issues_event_min_datetime": "2022-01-17T01:16:26.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T16:44:38.000Z", "max_forks_repo_path": "benchmark/maplescripts/noon.mpl", "max_forks_repo_name": "sumiya11/FastGroebner.jl", "max_forks_repo_head_hexsha": "5d3f39cec61bac0a9da8c63d1f6fa6fbea03e962", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-22T18:30:38.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-22T18:30:38.000Z", "avg_line_length": 104.4285714286, "max_line_length": 847, "alphanum_fraction": 0.549247606, "num_tokens": 1879, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9149009526726544, "lm_q2_score": 0.6224593382055109, "lm_q1q2_score": 0.5694886415242119}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_lda *)\n(* prefix:\n lda_xc_1d_ehwlrg_params *params;\n \n assert(p->params != NULL);\n params = (lda_xc_1d_ehwlrg_params * )(p->params);\n*)\n\nn := rs -> 1/(2*rs):\n\nf := (rs, zeta) -> \\\n (params_a_a1 + params_a_a2*n(rs) + params_a_a3*n(rs)^2) * n(rs)^params_a_alpha:\n", "meta": {"hexsha": "559d4340e963190a047b1680e3cfb5ffb91f7a85", "size": 517, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/lda_xc_1d_ehwlrg.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/lda_xc_1d_ehwlrg.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/lda_xc_1d_ehwlrg.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 24.619047619, "max_line_length": 80, "alphanum_fraction": 0.6576402321, "num_tokens": 177, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8740772482857833, "lm_q2_score": 0.6513548578981939, "lm_q1q2_score": 0.5693344618492308}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_mgga_c *)\n\n$define gga_x_b88_params\n$include \"gga_x_b88.mpl\"\n\ncab := 0.63:\ncss := 0.96:\n\nb88_cab := (rs, z, xs0, xs1) ->\n - 0.8 * (1 - z^2)/4 * n_total(rs)\n * b88_zab(cab, f_b88, rs, z, xs0, xs1)^2 * (\n 1 - log(1 + b88_zab(cab, f_b88, rs, z, xs0, xs1))\n / b88_zab(cab, f_b88, rs, z, xs0, xs1)\n ):\n\nb88_css := (rs, z, xs, ts) ->\n - 0.01 * (1 + z)/2 * n_spin(rs, z)^(5/3) * 2*ts * Fermi_D(xs, ts)\n * b88_zss(css, f_b88, rs, z, xs)^4 * (\n 1 - 2*log(1 + b88_zss(css, f_b88, rs, z, xs)/2)\n / b88_zss(css, f_b88, rs, z, xs)\n ):\n\nf_b88_c := (rs, z, xs0, xs1, ts0, ts1) ->\n + b88_cab(rs, z, xs0, xs1)\n + b88_css(rs, z, xs0, ts0)\n + b88_css(rs, -z, xs1, ts1):\n\nf := (rs, z, xt, xs0, xs1, ts0, ts1, us0, us1) ->\n f_b88_c(rs, z, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "e25f59edeb3f02449d5fc89bc5b8885cae0cbb09", "size": 1024, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_c_b88.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_c_b88.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_c_b88.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 26.9473684211, "max_line_length": 68, "alphanum_fraction": 0.5615234375, "num_tokens": 471, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086179068309441, "lm_q2_score": 0.6261241772283034, "lm_q1q2_score": 0.5689076393294281}} {"text": "# Example from Section 5.3\nread \"../ComputeIdentifiableFunctions.mpl\";\n\n#------------------------------------------------------------------------------\n# Auxiliary function for counting nonconstant coefficients\n\nCountNonNumeric := proc(p, var)\n local result, c:\n result := 0:\n for c in coeffs(p, var) do\n if not type(c, numeric) then\n result := result + 1:\n end if:\n end do:\n return result:\nend proc:\n\n#------------------------------------------------------------------------------\n\nmodel_original := [\n diff(x1(t), t) = (a * x1(t) - b * x1(t) * x2(t)),\n diff(x2(t), t) = (-c * x2(t) + d * x1(t) * x2(t)),\n diff(f(t), t) = 0,\n y1(t) = (e * x1(t) + f(t) * x2(t)),\n y2(t) = f(t)\n]:\n\nprintf(\"We are interested in computing ME-identifiable functions and the bound for ME-identifiablility\\n\"):\nME_identifiable_functions := MultiExperimentIdentifiableFunctions(model_original, no_bound=true, simplified_generators=true)[3]:\nprintf(\"The field of multi-experiment identifiable functions is generated by %a\\n\", ME_identifiable_functions):\n\nprintf(\"To find a good bound for the number of experiments we consider the following model (as described in Section 5.3)\\n\"):\nmodel := [\n diff(x1(t), t) = (a * x1(t) - b * x1(t) * x2(t)),\n diff(x2(t), t) = (-c * x2(t) + d * x1(t) * x2(t)),\n y(t) = (e * x1(t) + f * x2(t))\n]:\nprint(model):\n\nprintf(\"First we compute the bound and IO-equations considering f just as a parameter\\n\"):\nresult := MultiExperimentIdentifiableFunctions(model, simplified_generators=true):\nprintf(\"If we consider a different system with f being an unknown parameter with the same value for different experiments, the bound from the theorem will be %a\\n\", result[1]):\n# In the notation of Section 5.3\nio_eq_coeffs := [expand(denom(result[2][1])), op(map(p -> expand(simplify(p * denom(result[2][1]))), result[2]))]:\nprint(io_eq_coeffs):\nns := sort(map(p -> CountNonNumeric(p, f), io_eq_coeffs)):\nn := ns[1]:\nprintf(\"The number of non-numeric coefficients with respect to f (in the notation of Section 5.3: n, n1, n2, ...) in the coefficients of the only input-output equation are: %a\\n\", ns):\nprintf(\"Section 5.3 implies that the number of experiments for the case when f is a known parameter different in different experiments is %a\\n\", max(n + min(ns[2...]), max(ns[2..]))):\n\n", "meta": {"hexsha": "4340c56c16c7995a7ad969d4580ba1edee367829", "size": 2346, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/LV_mix.mpl", "max_stars_repo_name": "iliailmer/AllIdentifiableFunctions", "max_stars_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-03-19T18:42:30.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-19T18:42:30.000Z", "max_issues_repo_path": "examples/LV_mix.mpl", "max_issues_repo_name": "iliailmer/AllIdentifiableFunctions", "max_issues_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-03-20T15:22:40.000Z", "max_issues_repo_issues_event_max_datetime": "2021-03-21T01:07:04.000Z", "max_forks_repo_path": "examples/LV_mix.mpl", "max_forks_repo_name": "iliailmer/AllIdentifiableFunctions", "max_forks_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-03-04T20:30:13.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-04T20:30:13.000Z", "avg_line_length": 46.0, "max_line_length": 184, "alphanum_fraction": 0.6227621483, "num_tokens": 623, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8244619177503206, "lm_q2_score": 0.6893056231680122, "lm_q1q2_score": 0.5683062359931792}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(v(t), t) = k*y(t) - v(t)*u,\ndiff(x(t), t) = lm - x(t)*d - x(t)*v(t)*beta,\ndiff(z(t), t) = c*w(t)*q*y(t) - h*z(t),\ndiff(w(t), t) = -b*w(t) + c*w(t)*x(t)*y(t) - c*w(t)*q*y(t),\ndiff(y(t), t) = x(t)*v(t)*beta - a*y(t),\ny2(t) = z(t),\ny1(t) = w(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "fc6071327371b63702a085b4d4f0662575473768", "size": 358, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/HIV.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/HIV.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/HIV.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 29.8333333333, "max_line_length": 64, "alphanum_fraction": 0.5055865922, "num_tokens": 155, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8918110425624791, "lm_q2_score": 0.6370307944803832, "lm_q1q2_score": 0.568111096969955}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(x3(t), t) = -b2*x3(t) + b2*x2(t),\ndiff(x1(t), t) = a2*x0(t) - a2*x1(t),\ndiff(x2(t), t) = (ka*kc*b1*x3(t) - ka*kc*b1*x2(t) + ka*b1*x0(t)*x3(t) - ka*b1*x0(t)*x2(t) - n*kc*x2(t) + kc*b1*x3(t)*x2(t) - kc*b1*x2(t)^2) / (ka*kc + ka*x0(t) + kc*x2(t)),\ndiff(x0(t), t) = (-ka*n*x0(t) - ka*kc*a1*x0(t) + ka*kc*a1*x1(t) - ka*a1*x0(t)^2 + ka*a1*x0(t)*x1(t) - kc*a1*x0(t)*x2(t) + kc*a1*x1(t)*x2(t)) / (ka*kc + ka*x0(t) + kc*x2(t)),\ny1(t) = x0(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "6a4b15e4013c86b866c0bfe368cd19d8483de116", "size": 549, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/Pharm.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/Pharm.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/Pharm.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 54.9, "max_line_length": 173, "alphanum_fraction": 0.5300546448, "num_tokens": 277, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206738932333, "lm_q2_score": 0.6297746074044134, "lm_q1q2_score": 0.5680067383110349}} {"text": "toy_input := \"start-A\n start-b\n A-c\n A-b\n b-d\n A-end\n b-end\":\n\ntoy2_input:=\"dc-end\n HN-start\n start-kj\n dc-start\n dc-HN\n LN-dc\n HN-end\n kj-sa\n kj-HN\n kj-dc\":\n\nsample_input := \"fs-end\n he-DX\n fs-he\n start-DX\n pj-DX\n end-zg\n zg-sl\n zg-pj\n pj-he\n RW-he\n fs-DX\n pj-RW\n zg-RW\n start-pj\n he-WI\n zg-he\n pj-fs\n start-RW\":\n\ninput := FileTools:-Text:-ReadFile(\"AoC-2021-12-input.txt\" ):\n\nnodes := map(s->{StringTools:-Split(s,\"-\")[]}, StringTools:-Split(input)):\nG := GraphTheory:-Graph( {nodes[]} );\nsmall := select(StringTools:-IsLower,{map(op, nodes)[]}) minus {\"end\"};\n\nnumpaths := proc(a, s2:=FAIL, visited_s2:=false,\n excluding:={\"start\"}, path:=[] )\nglobal G, small;\nlocal newex, newvs2;\n\n if a = \"end\" then\n if s2<>FAIL and numboccur(path, s2) <> 2 then\n return 0;\n end if;\n# print([path[],\"end\"]);\n return 1;\n end if;\n\n local nb := {GraphTheory:-Neighborhood(G, a)[]} minus excluding;\n if a = s2 and visited_s2 = false then\n newex := excluding;\n newvs2 := true;\n elif a in small then\n newex := excluding union {a};\n newvs2 := visited_s2;\n else\n newex := excluding;\n newvs2 := visited_s2;\n end if;\n\n return add(numpaths(i, s2, newvs2, newex, [path[],a]), i in nb);\n\n end proc:\n\nanswer1 := numpaths(\"start\");\nanswer2 := answer1 + add(numpaths(\"start\", pp), pp in small minus {\"start\"});\n\n", "meta": {"hexsha": "651b30dde3eef7b2a09d90e5c11de7cab12ef06b", "size": 1502, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day12/AoC12-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day12/AoC12-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day12/AoC12-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.5064935065, "max_line_length": 77, "alphanum_fraction": 0.5419440746, "num_tokens": 494, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8152324983301568, "lm_q2_score": 0.6959583250334526, "lm_q1q2_score": 0.5673678440506928}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(S(t), t) = -bi*S(t)*II(t) - S(t)*mu - S(t)*bw*W(t) + R(t)*a + mu,\ndiff(II(t), t) = bi*S(t)*II(t) - gam*II(t) + S(t)*bw*W(t) - mu*II(t),\ndiff(W(t), t) = xi*II(t) - xi*W(t),\ndiff(R(t), t) = gam*II(t) - R(t)*mu - R(t)*a,\ny(t) = k*II(t),\ny2(t) = S(t) + R(t) + II(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "69eeeb526970e7313d5ead36f9a425cc4087b0a0", "size": 378, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/SIWR-with-extra-output.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/SIWR-with-extra-output.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/SIWR-with-extra-output.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 34.3636363636, "max_line_length": 70, "alphanum_fraction": 0.5132275132, "num_tokens": 168, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8976952921073469, "lm_q2_score": 0.6297746143530797, "lm_q1q2_score": 0.5653457063934796}} {"text": "\n# Kinematik-Berechnung Modell PalH2m1 (Hybrider Palettierer, Variante 2, Modellierung 1)\n# Beschreibung\n# Ein Palettierroboter mit fünf Achsen als Näherung für einen Palettierroboter mit Viergelenkketten\n# Die vierte Achse des Ersatzmodells wird als abhängiges Gelenk in Abhängigkeit der Achsen 2 und 3 beschrieben.\n# Dadurch wird der Effekt der Parallelogramme kinematisch nachgebildet.\n# Die Gelenkmomente sollten genauso wie durch die Parallelogramme übertragen werden (als ob deren Dynamikparameter Null sind).\n# Quellen\n# Autor\n# Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2018-12\n# (C) Institut für Mechatronische Systeme, Universität Hannover\n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nkin_constraints_exist := true: # Für Speicherung\n;\nwith(StringTools): # Für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\ncodegen_act := true:\ncodegen_opt := 2: # Hoher Optimierungsgrad.\n;\nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nwith(RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\n# Variable mit Winkeln der Zwangsbedingungen nur in Abhängigkeit der verallgemeinerten Koordinaten\nkintmp_qs := Matrix(RowDimension(kintmp_s),1):\nkintmp_qt := Matrix(RowDimension(kintmp_s),1):\n# Ersetzungsausdrücke definieren.\n# Variable zum speichern des Sinus und Cosinus der Winkel. Für dieses System ist das eigentlich nicht notwendig. Erstelle Variable, da sie von den anderen Skripten erwartet wird\nkintmp_subsexp := Matrix(2*RowDimension(kintmp_s),2):\n# Zwangsbedingung für abhängigen Gelenkwinkel\n# Der vierte Winkel ist der passive Winkel nahe des Endeffektors. Er wird durch die Parallelstruktur (aus zwei Parallelogrammen) bei hybriden Palettierrobotern bestimmt.\n# Durch die Parallelogramme ergibt sich ein konstantes Verhältnis zu den Gelenkwinkeln der Achsen 2 und 3, die auch in derselben Ebene liegen.\nrho4_qt := -theta(2) -theta(3):\nkintmp_qt(1,1) := rho4_qt:\nkintmp_qs := convert_t_s(kintmp_qt):\n# Exportiere Code für folgende Skripte\n# Speichere Maple-Ausdruck (Eingabe-Format und internes Format)\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple\", robot_name):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple.m\", robot_name):\nprintf(\"Ausdrücke für kintmp_subsexp gespeichert (Maple)\\n\"):\nsave kintmp_qs, kintmp_qt, kin_constraints_exist, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert\", robot_name):\nsave kintmp_qs, kintmp_qt, kin_constraints_exist, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nsave kintmp_qs, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_qs_maple_inert\", robot_name):\n# Liste mit abhängigen konstanten Kinematikparametern erstellen (wichtig für Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\nkc_symbols := Matrix(list_constant_expressions( kintmp_qs )):\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_maple\", robot_name):\nMatlabExport(Transpose(kc_symbols), sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_matlab.m\", robot_name), 2):\nprintf(\"Fertig\\n\"):\n\n", "meta": {"hexsha": "db1168bb6ba8e7e83259e883e03ea074842c7f55", "size": 3600, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "systems/palh2m1/codegen/palh2m1_kinematic_constraints.mpl", "max_stars_repo_name": "SchapplM/robsynth-serhybroblib", "max_stars_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/palh2m1/codegen/palh2m1_kinematic_constraints.mpl", "max_issues_repo_name": "SchapplM/robsynth-serhybroblib", "max_issues_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/palh2m1/codegen/palh2m1_kinematic_constraints.mpl", "max_forks_repo_name": "SchapplM/robsynth-serhybroblib", "max_forks_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": 61.0169491525, "max_line_length": 177, "alphanum_fraction": 0.8105555556, "num_tokens": 1053, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.835483553488848, "lm_q2_score": 0.6757646075489392, "lm_q1q2_score": 0.5645902156369845}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_mgga_x *)\n\nn_mbeef := 5:\ncoefs_mbeef := [\n [ 1.17114923e+00, 1.15594371e-01, -5.32167416e-02, -2.01131648e-02, 1.41417107e-03],\n [-6.76157938e-02, 4.53837246e-02, -2.22650139e-02, 1.92374554e-02, 9.19317034e-07],\n [ 1.48659502e-02, 3.18024096e-02, -5.21818079e-03, 1.33707403e-07, -5.00749348e-07],\n [ 1.40794142e-03, -6.08338264e-03, -6.57949254e-07, -5.49909413e-08, 5.74317889e-08],\n [ 1.41530486e-04, -1.00478906e-07, 2.01895739e-07, 3.97324768e-09, -3.40722258e-09]\n]:\n\n$include \"mbeef.mpl\"\n\nf := (rs, x, t, u) ->\n mgga_mbeef(x, t):\n", "meta": {"hexsha": "9a39f7a01fc10ad0dbcf34e82209e8cce7b53b22", "size": 817, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_mbeefvdw.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_x_mbeefvdw.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_x_mbeefvdw.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 34.0416666667, "max_line_length": 90, "alphanum_fraction": 0.6560587515, "num_tokens": 394, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8479677545357568, "lm_q2_score": 0.6654105653819835, "lm_q1q2_score": 0.564246702971329}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_gga_x *)\n(* prefix:\n gga_x_mpbe_params *params;\n \n assert(p->params != NULL);\n params = (gga_x_mpbe_params * )(p->params);\n*)\n\nf0 := s -> s^2/(1 + params_a_a*s^2):\nf := x -> 1\n + params_a_c1*f0(X2S*x)\n + params_a_c2*f0(X2S*x)^2\n + params_a_c3*f0(X2S*x)^3:", "meta": {"hexsha": "e742eb734b6d499107881e626d35679dc304ecc9", "size": 514, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_mpbe.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_mpbe.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/gga_x_mpbe.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 24.4761904762, "max_line_length": 68, "alphanum_fraction": 0.6478599222, "num_tokens": 184, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8757869819218865, "lm_q2_score": 0.6442251201477016, "lm_q1q2_score": 0.5642039736524204}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2019 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: mgga_exc *)\n(* prefix:\n mgga_x_gdme_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_gdme_params * )(p->params);\n*)\n\ngdme_at := (params_a_AA + 3/5*params_a_BB)*2^(1/3)/(X_FACTOR_C*(3*Pi^2)^(2/3)):\ngdme_bt := params_a_BB/(X_FACTOR_C*2^(1/3)*(3*Pi^2)^(4/3)):\n\ngdme_f := (x, u, t) -> gdme_at + gdme_bt*((params_a_a^2 - params_a_a + 1/2)*u - 2*t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(gdme_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "16877b8fd8aaa3bbd88cf81554a3f2389e5dcc8a", "size": 747, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_gdme.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/mgga_exc/mgga_x_gdme.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/mgga_exc/mgga_x_gdme.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": 29.88, "max_line_length": 85, "alphanum_fraction": 0.6238286479, "num_tokens": 295, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797100118214, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.5638201761797104}} {"text": "######################################\n# Implementation of the lapse choices\n# in standard G-BSSN\n# Gamma drive and 1 + log\n# Also some experimental other lapse\n# choices\n######################################\n\nread \"/home/arman/FD/FD.mpl\":\n\nCFD();\nMFD();\n\ngrid_functions:= {alpha,K,beta,Lamx,DLamx,BB,ctfmp};\n\n# A generalization of 1 + log\neq1 := diff(alpha(t,x),t) = -gma*alpha(t,x)^gmb*K(t,x);\n\nAVGT := f -> (FD(f,[[1],[0,0,0]]) + FD(f,[[0],[0,0,0]]))/2 ;\nFD_table[t] := [ [0] , [0,1] ];\n\n\nspec := [ \n { i = [1,1,1] , b=xmin } = Gen_Sten(lhs(eq1)) - AVGT(Gen_Sten(rhs(eq1))) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq1)) - AVGT(Gen_Sten(rhs(eq1))),\n { i=[Nx,Nx,1], b=xmax } = alpha(n+1,i) + myzero*x(i) - 1\n];\n\n\nA_Gen_Solve_Code(spec,{alpha(n+1,i)},proc_name=\"evol_alphaopl\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_alphaopl\");\n\n# Some kinda generalization of 1 + log\neq2:= diff(alpha(t,x),t) + epsal*diff(K(t,x),t) = -epsal*ck*K(t,x);\n\n\n\nspec2 := [ \n { i = [1,1,1] , b=xmin } = Gen_Sten(lhs(eq2)) - AVGT(Gen_Sten(rhs(eq2))) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq2)) - AVGT(Gen_Sten(rhs(eq2))),\n { i=[Nx,Nx,1], b=xmax } = alpha(n+1,i) + myzero*x(i) - 1\n];\n\n\nA_Gen_Solve_Code(spec2,{alpha(n+1,i)},proc_name=\"evol_alphakd\");\nA_Gen_Res_Code(spec2,input=\"d\",proc_name=\"resid_alphakd\");\n\n\n# This is gamma drive\n\neq3 := diff(beta(t,x),t) = mus*Lamx(t,x) - eta*beta(t,x);\neq4 := diff(alpha(t,x),t) = -2*alpha(t,x)*K(t,x);\n\nspec := [ \n { i = [1,1,1] , b=xmin } = Gen_Sten(lhs(eq4)) - AVGT(Gen_Sten(rhs(eq4))) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq4)) - AVGT(Gen_Sten(rhs(eq4))),\n { i=[Nx,Nx,1], b=xmax } = alpha(n+1,i) + myzero*x(i) - 1\n];\n\n\nA_Gen_Solve_Code(spec,{alpha(n+1,i)},proc_name=\"evol_alphadyopl\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_alphadyopl\");\n\n\nspec := [ \n { i = [1,1,1] , b=xmin } = Gen_Sten(lhs(eq3)) - AVGT(Gen_Sten(rhs(eq3))) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq3)) - AVGT(Gen_Sten(rhs(eq3))),\n { i=[Nx,Nx,1], b=xmax } = beta(n+1,i) + myzero*x(i) \n];\n\nA_Gen_Solve_Code(spec,{beta(n+1,i)},proc_name=\"evol_betagd\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_betagd\");\n\n\n# Some strange driver, for testing\neq5 := diff(beta(t,x),t) = mus*diff(K(t,x),x) - eta*beta(t,x);\n\nspec := [ \n { i = [1,1,1] , b=xmin } = beta(n+1,i) + myzero*x(i) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq5)) - AVGT(Gen_Sten(rhs(eq5))),\n { i=[Nx,Nx,1], b=xmax } = beta(n+1,i) + myzero*x(i) \n];\n\nA_Gen_Solve_Code(spec,{beta(n+1,i)},proc_name=\"evol_betakd\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_betakd\");\n\n\n# More playing around with shift condition\neq6:= diff(beta(t,x),t) + epsal*diff(Lamx(t,x),t) = -epsal*ck*Lamx(t,x);\n\n\nspec2 := [ \n { i = [1,1,1] , b=xmin } = Gen_Sten(lhs(eq6)) - AVGT(Gen_Sten(rhs(eq6))) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq6)) - AVGT(Gen_Sten(rhs(eq6))),\n { i=[Nx,Nx,1], b=xmax } = beta(n+1,i) + myzero*x(i)\n];\n\n\nA_Gen_Solve_Code(spec2,{beta(n+1,i)},proc_name=\"evol_betagd2\");\nA_Gen_Res_Code(spec2,input=\"d\",proc_name=\"resid_betagd2\");\n\n\neq7 := diff(beta(t,x),t) = advc*beta(t,x)*diff(beta(t,x),x)/ctfmp(x) + mus*BB(t,x); \neq8 := diff(BB(t,x),t) = advc*beta(t,x)*diff(BB(t,x),x)/ctfmp(x) - eta*BB(t,x) + DLamx(t,x);\neq9 := diff(alpha(t,x),t) = advc*beta(t,x)*diff(alpha(t,x),x)/ctfmp(x) - 2*alpha(t,x)*K(t,x);\n\nspec := [ \n { i = [1,1,1] , b=xmin } = beta(n+1,i)+myzero*x(i) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq7)) - AVGT(Gen_Sten(rhs(eq7))),\n { i=[Nx,Nx,1], b=xmax } = beta(n+1,i) + myzero*x(i)\n];\n\nA_Gen_Solve_Code(spec,{beta(n+1,i)},proc_name=\"evol_beta_hgd_adv\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_beta_hgd_adv\");\n\n\nspec := [ \n { i = [1,1,1] , b=xmin } = BB(n+1,i)+myzero*x(i) ,\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq8)) - AVGT(Gen_Sten(rhs(eq8))),\n { i=[Nx,Nx,1], b=xmax } = BB(n+1,i) + myzero*x(i)\n];\n\nA_Gen_Solve_Code(spec,{BB(n+1,i)},proc_name=\"evol_BB_hgd_adv\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_BB_hgd_adv\");\n\nspec := [ \n { i = [1,1,1] , b=xmin } = Gen_Sten(lhs(eq9)) - AVGT(Gen_Sten(rhs(eq9))),\n { i = [2,Nx-1,1] } = Gen_Sten(lhs(eq9)) - AVGT(Gen_Sten(rhs(eq9))),\n { i=[Nx,Nx,1], b=xmax } = alpha(n+1,i) - 1 + myzero*x(i)\n];\n\nA_Gen_Solve_Code(spec,{alpha(n+1,i)},proc_name=\"evol_alpha_hgd_adv\");\nA_Gen_Res_Code(spec,input=\"d\",proc_name=\"resid_alpha_hgd_adv\");\n\n\n", "meta": {"hexsha": "9abcda8bf426cd0a42d65110d1dd1e57fe1d0d8c", "size": 4339, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "coord_choices.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "coord_choices.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "coord_choices.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": 31.9044117647, "max_line_length": 93, "alphanum_fraction": 0.5768610279, "num_tokens": 1786, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894548800271, "lm_q2_score": 0.6297746074044134, "lm_q1q2_score": 0.5635156776566782}} {"text": "######################################################\n# Performing the compactificatoin and non-uniform\n# coordinate transformation on the tensor expressions\n######################################################\n\nall_pdes:=[ \n [DPH,0,dn] , [dg,2,dn] , \n [DDL,2,dn],\n [DTK,0,dn],\n [RR,2,dn], [P,2,dn],\n [DLAM,1,up],\n [C1,0,dn],\n [HS,0,dn], \n [DB,0,dn],\n [HS3,0,dn], \n [MK,1,up],\n [EQRPIb2,0,dn], \n [EQIPIb2,0,dn],\n [DRPSI,0,dn],\n [DIPSI,0,dn]\n ];\n\n# Going from x -> ctfm(x) using DEtools\nwith(DEtools);\naddcoords(compact,[t,x],[t,ctfm(x)]);\n\n\n# See built_eqns.mpl for how 'tt' table is defined\n\nfor ii from 1 to nops(all_pdes) do\n nm := all_pdes[ii][1]:\n rank := all_pdes[ii][2]:\n tp := all_pdes[ii][3]:\n printf(\"Transforming %a\\n\",nm);\n if rank <> 0 then\n\n for jj from 1 to nops(coord) do\n if (tt[nm][all][coord[jj]] <> 0 ) then\n tt[nm][allcomp][coord[jj]] := PDEchangecoords(tt[nm][all][coord[jj]],[t,x],compact,[t,x]);\n tt[nm][regcomp][coord[jj]] := PDEchangecoords(tt[nm][reg][coord[jj]],[t,x],compact,[t,x]);\n\n\t # Symbolically replacing derivatives of compactification function \n # since we do not want to finite difference them)\n\n tt[nm][allcomp][coord[jj]] := subs({diff(ctfm(x),x)=ctfmp(x),diff(ctfm(x),x,x)=ctfmpp(x)},tt[nm][allcomp][coord[jj]]);\n tt[nm][regcomp][coord[jj]] := subs({diff(ctfm(x),x)=ctfmp(x),diff(ctfm(x),x,x)=ctfmpp(x)},tt[nm][regcomp][coord[jj]]);\n\n # DEtools will replace x with ctfm(x) symbolically in our expressions, but ctfm(x) is our new x, fixing that\n for kk from 1 to nops(grid_functions) do\n fn := grid_functions[kk];\n tt[nm][allcomp][coord[jj]] := subs(fn(t,ctfm(x))=fn(t,x),tt[nm][allcomp][coord[jj]]);\n tt[nm][regcomp][coord[jj]] := subs(fn(t,ctfm(x))=fn(t,x),tt[nm][regcomp][coord[jj]]);\n end do;\n\n end if;\n\n end do;\n else\n\n # Same as above, symbolically replacing derivatives of compactification function\n if ( tt[nm][all] <> 0 ) then\n tt[nm][allcomp] := PDEchangecoords(tt[nm][all],[t,x],compact,[t,x]);\n tt[nm][regcomp] := PDEchangecoords(tt[nm][reg],[t,x],compact,[t,x]);\n tt[nm][allcomp] := subs({diff(ctfm(x),x)=ctfmp(x),diff(ctfm(x),x,x)=ctfmpp(x)},tt[nm][allcomp]);\n tt[nm][regcomp] := subs({diff(ctfm(x),x)=ctfmp(x),diff(ctfm(x),x,x)=ctfmpp(x)},tt[nm][regcomp]);\n\n # Same as above, fixing DEtools mess!\n for kk from 1 to nops(grid_functions) do \n fn := grid_functions[kk];\n tt[nm][allcomp] := subs(fn(t,ctfm(x))=fn(t,x),tt[nm][allcomp]);\n tt[nm][regcomp] := subs(fn(t,ctfm(x))=fn(t,x),tt[nm][regcomp]);\n end do;\n\n end if;\n\n end if;\nend do:\n\n# Checking if everything is transformed properly at the limit ctfm(x) = x\n\nfor ii from 1 to nops(all_pdes) do\n nm := all_pdes[ii][1]:\n rank := all_pdes[ii][2]:\n tp := all_pdes[ii][3]:\n if rank <> 0 then\n\n\t\t\t for jj from 1 to nops(coord) do\n if ( tt[nm][all][coord[jj]] <> 0 ) then\n\t\t\t\tres := simplify(tt[nm][all][coord[jj]] - eval(tt[nm][allcomp][coord[jj]],{ctfm(x) = x, ctfmp(x) = 1, ctfmpp(x) = 0}));\n\t\t\t\tprintf(\"res = %a\\n\",res);\n\t\t\t\tres := simplify(tt[nm][reg][coord[jj]] - eval(tt[nm][regcomp][coord[jj]],{ctfm(x) = x, ctfmp(x) = 1, ctfmpp(x) = 0}));\n\t\t\t\tprintf(\"res = %a\\n\",res);\n end if;\n\t\t\t end do;\n\n else\n res := simplify(tt[nm][all] - eval(tt[nm][allcomp],{ctfm(x) = x, ctfmp(x) = 1, ctfmpp(x) = 0}));\n printf(\"res = %a\\n\",res);\n res := simplify(tt[nm][reg] - eval(tt[nm][regcomp],{ctfm(x) = x, ctfmp(x) = 1, ctfmpp(x) = 0}));\n printf(\"res = %a\\n\",res);\n end if;\nend do:\n\n##################################################\n# Performing a collection operation, i.e. \n# powers of ctfm(x) function, this will help the\n# intel c and fortran compiler a lot! \n#################################################\n\nfor ii from 1 to nops(all_pdes) do\n nm := all_pdes[ii][1]:\n rank := all_pdes[ii][2]:\n tp := all_pdes[ii][3]:\n if rank <> 0 then\n\n\t\t\t for jj from 1 to nops(coord) do\n if (tt[nm][all][coord[jj]] <> 0 ) then\n \t\t\t tt[nm][all][coord[jj]] := collect(collect(eval(expand(tt[nm][allcomp][coord[jj]]),{ctfmpp(x)=octfmp(x)*ctfmp(x)^2}),1/ctfmp(x)),1/ctfm(x));\n\t\t\t tt[nm][reg][coord[jj]] := collect(collect(eval(expand(tt[nm][regcomp][coord[jj]]),{ctfmpp(x)=octfmp(x)*ctfmp(x)^2}),1/ctfmp(x)),1/ctfm(x));\n\t\t\t\tprint(tt[nm][all][coord[jj]]);\n print(tt[nm][reg][coord[jj]]);\n end if;\n\t\t\t end do;\n\t \n else\n tt[nm][all] := collect(collect(eval(expand(tt[nm][allcomp]),{ctfmpp(x)=octfmp(x)*ctfmp(x)^2}),1/ctfmp(x)),1/ctfm(x));\n tt[nm][reg] := collect(collect(eval(expand(tt[nm][regcomp]),{ctfmpp(x)=octfmp(x)*ctfmp(x)^2}),1/ctfmp(x)),1/ctfm(x));\n\t print(tt[nm][all]);\n\t print(tt[nm][reg]);\n end if;\nend do:\n\n# Adding new members of grid functions to our set:\ngrid_functions := grid_functions union {ctfm,ctfmp,octfmp};\n\n", "meta": {"hexsha": "4530eca399eff45f9e9fb8f3a37d7ba30a8567a0", "size": 4945, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "compactify.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "compactify.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "compactify.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": 36.3602941176, "max_line_length": 147, "alphanum_fraction": 0.5557128413, "num_tokens": 1724, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7772998611746912, "lm_q2_score": 0.7248702761768248, "lm_q1q2_score": 0.5634415650419059}} {"text": "###############################################################################\n# Part 1: Algorithms for computation with subfields of rational functions\n###############################################################################\n\nwith(PolynomialIdeals):\n#------------------------------------------------------------------------------\n\nIdealsEq := proc(A, B)\n # Checks whether polynomial ideals are equal\n return evalb((A subset B) and (B subset A)):\nend:\n\n#------------------------------------------------------------------------------\n\nFieldToIdeal := proc(gens)\n # Input: generators of a subfield of the field of rational functions\n # Computes the MQS ideal of the field with the new variables of the form x_aux\n # See: https://mediatum.ub.tum.de/doc/685465/document.pdf Definition 2.16\n # https://doi.org/10.1016/j.jsc.2005.09.010 Lemma 2.1\n local all_vars, subs_dupl, all_dupl, common_denom, polys, f, gb:\n all_vars := indets(gens):\n subs_dupl := map(v -> v = cat(v, _aux), all_vars):\n all_dupl := map(v -> subs(subs_dupl, v), all_vars):\n common_denom := 1:\n polys := []:\n for f in gens do\n common_denom := lcm(common_denom, denom(f)):\n polys := [op(polys), numer(f) * subs(subs_dupl, denom(f)) - subs(subs_dupl, numer(f)) * denom(f)]:\n end do:\n #gb := Groebner[Basis]([op(polys), common_denom * t - 1], plex(t, op(all_dupl))):\n\n gb := Groebner[Basis]([op(polys), common_denom * t - 1], tdeg(t, op(all_dupl))):\n gb := Groebner[Walk](gb, tdeg(t, op(all_dupl)), lexdeg([t], [op(all_dupl)])):\n \n gb := select(p -> not (t in indets(p)), gb):\n return PolynomialIdeal(gb, variables=all_dupl):\nend proc:\n\n#------------------------------------------------------------------------------\n\nFieldCoefficientRestriction := proc(J, msq_for_subfield)\n # Input: J - a polynomial ideals over a field of rational functions\n # msq_for_subfield - the MQS ideal for a subfield E of coefficients (see FieldToIdeal)\n # Computes the radical of the restriction of the ideal to the subfield E \n # in the sense of https://doi.org/10.1016/j.jsc.2005.09.010 (MSQ-paper in what follows)\n #\n # NOTE: unlike the algorithm in the MQS-paper, we compute the radical, not the restriction itself\n # one can obtain the algorithm MQS-paper by replacing PrimeDecomposition with PrimaryDecomposition \n # in the code below\n local poly_vars, coeff_vars, subs_aux, coeff_aux, gens, subs_aux_msq, gens_msq, msq_ideal_aux, \n msq_components, J_ext, components, primes_to_keep, P, elim_P, comp, cleaned_ideal:\n\n poly_vars := IdealInfo[Variables](J):\n coeff_vars := IdealInfo[Parameters](J) union IdealInfo[Parameters](msq_for_subfield):\n subs_aux := map(v -> v = parse(cat(v, _aux_aux)), coeff_vars):\n coeff_aux := subs(subs_aux, coeff_vars):\n\n # list F of polynomials in the notation of the MSQ-paper, page 375\n gens := map(p -> subs(subs_aux, p * denom(p)), IdealInfo[Generators](J)):\n\n # Substitution to avoid names clashing between the aux variables in the msq ideal and the variables in J\n subs_aux_msq := map(v -> v = parse(cat(v, _aux)), IdealInfo[Variables](msq_for_subfield)):\n gens_msq := map(p -> subs(subs_aux_msq, p), IdealInfo[Generators](msq_for_subfield)):\n msq_ideal_aux := PolynomialIdeal(gens_msq, variables=map(s -> rhs(s), subs_aux_msq)):\n msq_components := [PrimeDecomposition(msq_ideal_aux)]:\n\n J_ext := PolynomialIdeal([op(gens), op(gens_msq)], variables=poly_vars union coeff_aux): \n components := [PrimeDecomposition(J_ext)]:\n \n # Selecting prime components as in Remark on page 377 in MSQ-paper\n primes_to_keep := []:\n for P in components do\n # Going through the prime decomposition of the MSQ-deal mimics the\n # working over the restricted field (which is what has been done in the MSQ-paper)\n elim_P := EliminationIdeal(P, coeff_aux):\n for comp in msq_components do\n if elim_P subset comp then\n primes_to_keep := [op(primes_to_keep), P]:\n end if:\n end do: \n end do:\n if nops(primes_to_keep) > 0 then\n cleaned_ideal := Intersect(op(primes_to_keep)):\n else\n cleaned_ideal := PolynomialIdeal([0], variables = poly_vars):\n end if:\n\n # Applying Lemma 2.2 from the MSQ-paper\n return EliminationIdeal(cleaned_ideal, poly_vars):\nend proc:\n\n#------------------------------------------------------------------------------\n\n\nFilterGenerators := proc(ideal)\n # Input: ideal over a rational function field\n # Computes a simplified set of generators of the field of definition\n local gb, gens, p, cf, lc, gsorted, result, big_ideal, cur_ideal, g, new_ideal:\n gb := Groebner[Basis](ideal, tdeg(op(IdealInfo[Variables](ideal)))):\n gens := {}:\n for p in gb do\n cf := sort([coeffs(p, IdealInfo[Variables](ideal))], (a, b) -> length(convert(a, string)) < length(convert(b, string))):\n lc := cf[1]:\n cf := map(c -> c / lc, cf):\n gens := {op(gens), op(cf[2..nops(cf)])}:\n end do:\n gsorted := sort([op(gens)], (a, b) -> length(convert(a, string)) < length(convert(b, string)));\n result := {}:\n big_ideal := FieldToIdeal(gens):\n cur_ideal := FieldToIdeal(result):\n for g in gsorted do\n if big_ideal = cur_ideal then\n return result:\n end if:\n new_ideal := FieldToIdeal({op(result), g}):\n if new_ideal <> cur_ideal then\n \t # a dirty hack to transform -1/a to a\n if convert(g, string)[1] = \"-\" then\n g := -g:\n end:\n if convert(g, string)[1] = \"1\" then\n g := 1 / g:\n end:\n result := {op(result), g}:\n cur_ideal := new_ideal:\n end if:\n end do:\n return result:\nend proc:\n\n#------------------------------------------------------------------------------\n\nFieldIntersection := proc(gens_left, gens_right)\n # Input: gens_left and gens_right - generators of a subfields E and F of a field of rational functions\n # If terminates, resturns an ideal with field of definition being the intersection of generators of E and F\n # Is guaranteed to terminate if at least one of E and F is algebraically closed in rational functions (see REF)\n # Implementation below is a version of Algorithm 2.38 from https://mediatum.ub.tum.de/doc/685465/document.pdf\n local msq_left, msq_right, poly_vars, coeff_vars, Ii, Ji, gb, result, p, cf, lc;\n\n msq_left := FieldToIdeal(gens_left):\n msq_right := FieldToIdeal(gens_right):\n poly_vars := IdealInfo[Variables](msq_left) union IdealInfo[Variables](msq_right):\n coeff_vars := IdealInfo[Parameters](msq_left) union IdealInfo[Parameters](msq_right):\n\n Ii := PolynomialIdeal([1], variables=poly_vars):\n Ji := msq_left:\n\n while not IdealsEq(Ii, Ji) do\n Ii := FieldCoefficientRestriction(Ji, msq_right):\n Ji := FieldCoefficientRestriction(Ii, msq_left):\n end do:\n\n return Ji:\nend proc:\n\n#------------------------------------------------------------------------------\n\nCompareFields := proc(gens_l, gens_r)\n # Checks whether gens_l and gens_r generate the same subfield of rational functions\n return IdealsEq(FieldToIdeal(gens_l), FieldToIdeal(gens_r)):\nend proc:\n\n\n#------------------------------------------------------------------------------\n\n###############################################################################\n# Part 2: Algorithm for computing identifiable functions\n###############################################################################\n\nwith(DifferentialAlgebra):\n\n#===============================================================================\n\nExtractDenominator := proc(model)\n # Input: model a list of rational functions\n # returns the function multiplied by their denominators and \n # an inequality corresponding to the LCM of the denominators\n local common_denom, r;\n common_denom := 1:\n for r in model do\n common_denom := lcm(common_denom, denom(r)):\n end do:\n return [op(map(p -> denom(p) * p, model)), common_denom <> 0]:\nend proc:\n\n#===============================================================================\nCheckReducibilitySet := proc(polys, charset)\n # Input: polys - list of differential polynomials\n # charset - a characteristic set\n # Returns true iff all the polynomials are reduced to zero wrt to the charset\n local result, e:\n result := true:\n for e in polys do\n if NormalForm(e, charset) <> 0 then\n result := false:\n break:\n end if:\n end do:\n return result:\nend proc:\n#===============================================================================\n\nGetIOEquations := proc(model, states, inputs, outputs, params, use_brackets, infolevel, target)\n # Input: model - list of differential polynomials defining the model\n # states, ios, params - list of names of state variables, input-output variables\n # and parameter, respectively\n # Computes a list of input-output equations of the model\n local Relim, Rorig, charsets, chset_orig, general_comps, general, c, e, gen_comp, io_eqs:\n Relim := DifferentialRing(blocks = [[op(states)], [op(outputs)], [op(inputs)]], derivations = [t], arbitrary = params):\n if not use_brackets then\n Relim := DifferentialRing(blocks = [[op(states)], op(outputs), [op(inputs)]], derivations = [t], arbitrary = params):\n end if:\n Rorig := DifferentialRing(blocks = [[op(outputs)], [op(states)], [op(inputs)]], derivations = [t], arbitrary = params):\n # DifferentialRing(blocks = [[op(inputs)], [op(outputs)], [op(states)]], derivations = [t], arbitrary = params):\n chset_orig := RosenfeldGroebner(model, Rorig)[1]:\n \n \n if infolevel > 0 then\n LogText(sprintf(\" Computing the characteristic set (singsol = none)\\n\"), target):\n end if:\n charsets := RosenfeldGroebner(model, Relim, singsol = none):\n if CheckReducibilitySet(Equations(charsets[1]), chset_orig) then \n gen_comp := charsets[1]:\n else\n if infolevel > 0 then\n LogText(sprintf(\" Did not pick the right component. Using singsol = all\\n\"), target):\n end if:\n charsets := RosenfeldGroebner(model, Relim):\n if infolevel > 0 then\n LogText(sprint(\" Selecting the general component\\n\"), target):\n end if:\n general_comps := []:\n for c in charsets do\n general := true:\n for e in Equations(c) do\n if NormalForm(e, chset_orig) <> 0 then\n general := false:\n break:\n end if:\n end do:\n if general then\n general_comps := [op(general_comps), c]:\n end if:\n end do:\n if nops(general_comps) > 1 then\n LogText(sprintf(\"More than one component is considered general!\", general_comps), target):\n end if:\n gen_comp := general_comps[1]:\n end if:\n io_eqs := Equations(gen_comp, leader < parse(cat(states[-1], \"(t)\"))):\n return io_eqs:\nend proc:\n\n#===============================================================================\n\n# Adapted from \n# https://www.mapleprimes.com/questions/36772-Extract-Specific-Coefficients-Of-A-Multivariate\n# by Kitonum 15364\ncoefff:=proc(P, t)\n local L, H, i, k:\n L:=[coeffs(P, indets(P), 'h_aux_for_coef')]: H:=[h_aux_for_coef]: k:=0:\n for i from 1 to nops(H) do\n if H[i]=t then k:=L[i] fi:\n end do:\n return k;\nend proc:\n\n#===============================================================================\n\nDecomposePolynomial := proc(p, vars_main, vars_coef, infolevel, target)\n # Input: p - polynomial in two groups of variables: vars_main and vars_coef\n # Computes a decomposition of minimal length of p as a linear combination \n # of products A * B, where A is a polynomial in vars_main and B \n # is a polynomial in vars_coef return two lists: list of A's and list of B's\n local cf, monoms, result_cf, result_monom, i, c, m, j, lc, lm, coeff_in_c:\n cf := [coeffs(collect(p, vars_main, 'distributed'), vars_main, 'monoms')]:\n monoms := [monoms]:\n result_cf := []:\n result_monom := Array([]):\n if infolevel > 0 then\n LogText(sprintf(\" Number of monomials: %a\\n\", nops(cf)), target):\n end:\n for i from 1 to nops(cf) do\n c := cf[i]:\n m := monoms[i]:\n for j from 1 to nops(result_cf) do\n lc, lm := Groebner[LeadingTerm](result_cf[j], plex(op(vars_coef))):\n coeff_in_c := coefff(c, lm):\n c := c - coeff_in_c / lc * result_cf[j]:\n result_monom[j] := result_monom[j] + coeff_in_c / lc * m:\n end do:\n if c <> 0 then\n result_cf := [op(result_cf), c]:\n ArrayTools[Append](result_monom, m):\n end if:\n end do:\n if infolevel > 0 then\n LogText(sprintf(\" Reduced to: %a\\n\", nops(result_cf)), target):\n end:\n return [result_cf, convert(result_monom, list)]:\nend proc:\n\n#===============================================================================\n\nConstructWronskian := proc(io_eq, model, states, inputs, outputs, params, state_space, infolevel, target)\n # Input - the same as for GetIOEquations + one IO-equation + flag subs_param\n # Computes the Wronskian for this equation using the representation\n # given by DecomposePolynomial. Return a pair of the Wronskian\n # reduced modulo the original system and a list of coefficients\n # of the compressed io_eq\n local getNormalForm, diff_to_ord, v, vt, h, v_ord, vd, p, decomp, diff_polys, Rorig, chset_orig,\n M, yus, yus_reduced, yus_list, M_sub, roll, params_sub, ios, ps_sol, ps, i:\n\n diff_to_ord := {}:\n ios := [op(inputs), op(outputs)]:\n for v in ios do\n vt := parse(cat(v, \"(t)\")):\n diff_to_ord := {op(diff_to_ord), vt = v}:\n for h from 1 to nops(states) + 1 do\n v_ord := parse(cat(v, \"_\", h)):\n vd := diff(vt, t$h):\n diff_to_ord := {op(diff_to_ord), vd = v_ord}:\n end do:\n end do:\n p := subs(diff_to_ord, io_eq):\n if infolevel > 0 then\n LogText(sprintf(\" Combining monomials to reduce the dimension\\n\"), target):\n end if:\n decomp := DecomposePolynomial(p, map(e -> rhs(e), diff_to_ord), params, infolevel, target):\n diff_polys := map(p -> subs(map(e -> rhs(e) = lhs(e), diff_to_ord), p), decomp[2]):\n Rorig := DifferentialRing(blocks = [[op(outputs)], [op(states)], [op(inputs)]], derivations = [t], arbitrary = params):\n # DifferentialRing(blocks = [[op(inputs)], [op(outputs)], [op(states)]], derivations = [t], arbitrary = params):\n chset_orig := RosenfeldGroebner(model, Rorig)[1]:\n \n if infolevel > 0 then\n LogText(sprintf(\" Computing the Wronskian\\n\"), target):\n end if:\n M := VectorCalculus[Wronskian](diff_polys, t):\n yus := indets(M) minus {t}:\n\n if infolevel > 0 then\n LogText(sprintf(\" Reducing the Wronskian\\n\"), target):\n end if:\n if state_space <> [] then\n ps_sol := GetPSSolution(state_space, nops(yus)):\n yus_reduced := []:\n for v in ios do\n vt := parse(cat(v, \"(t)\")):\n ps := subs(ps_sol, v(t)):\n for i from 0 to nops(yus) - 1 do\n yus_reduced := [op(yus_reduced), vt = subs({t = 0}, ps)]:\n vt := diff(vt, t):\n ps := diff(ps, t):\n end do:\n end do:\n else\n getNormalForm := proc (p, chset_orig)\n return p=DifferentialAlgebra:-NormalForm(p, chset_orig):\n end proc:\n Rorig := DifferentialRing(blocks = [[op(outputs)], [op(states)], [op(inputs)]], derivations = [t], arbitrary = params):\n # DifferentialRing(blocks = [[op(inputs)], [op(outputs)], [op(states)]], derivations = [t], arbitrary = params):\n chset_orig := RosenfeldGroebner(model, Rorig)[1]:\n yus_list := convert(yus, list):\n yus_reduced:=Threads:-Seq[tasksize=nops(yus_list)](getNormalForm(yus_list[i], chset_orig), i =1..nops(yus_list)):\n # yus_reduced := map(p -> p = NormalForm(p, chset_orig), yus):\n end if:\n \n # iofun:=map(y->parse(cat(convert(y, string), \"(t)\")), ios):\n # derivative_orders:=table([seq(p=0, p in iofun)]):\n # for each in yus_list do\n # indets_ := indets(each) minus {t}: # get indets of derivative to compute order\n # function_ := op(indets_ intersect {op(iofun)}): # for which function?\n # order:=numelems(indets_): # compute order\n # if derivative_orders[function_] parse(cat(x, \"(t)\")) = x, states), M_sub):\n return [M_sub, decomp[1]]:\nend proc:\n\n#===============================================================================\n\nSingleExperimentIdentifiableFunctions := proc(model, output_targets, {infolevel := 1})\n # Input: model - ODE model represented as a list of differential polynomials\n # Computes generators of the field of single-identifiable functions\n local result, start, finish, states, inputs, outputs, model_eq, ios, params, io_eqs, si_gens, eq, wrnsk, echelon_form, model_denomfree, target: \t\n states, inputs, outputs, params, model_eq := op(ParseInput_(model)): # states, ios, params := op(ParseInput_(model)):\n ios := [op(inputs), op(outputs)]:\n\n # Step 1\n if infolevel > 0 then\n LogText(sprintf(\"SE Step 1: Computing input-output equations\\n\"), output_targets[log]):\n end if:\n model_denomfree := ExtractDenominator(model_eq):\n io_eqs := GetIOEquations(model_denomfree, states, inputs, outputs, params, false, infolevel, output_targets[log]):\n if infolevel > 0 then\n LogText(sprintf(\"SE Total number of io-equations: %a\\n\", nops(io_eqs)), output_targets[log]):\n end if:\n\n \t si_gens := {}:\n\t for eq in io_eqs do\n\t # Step 2\n\t if infolevel > 0 then\n\t LogText(sprintf(\"SE Step 2: Constructing the Wronskian\\n\"), output_targets[log]):\n\t end if:\n\t wrnsk := ConstructWronskian(eq, model_denomfree, states, inputs, outputs, params, [], infolevel, output_targets[log])[1]:\n\t # Step 3\n\t if infolevel > 0 then\n\t LogText(sprintf(\"SE Step 3: Computing the reduced row echelon form of the Wronskian\\n\"), output_targets[log]):\n\t end if:\n\t echelon_form := LinearAlgebra[ReducedRowEchelonForm](wrnsk):\n\t si_gens := {op(si_gens), op(select(x -> not type(x, numeric), convert(echelon_form, list)))}:\n\t end do:\n\n # Step 4\n if infolevel > 0 then\n LogText(sprintf(\"SE Step 4: restricting to the field of parameters\"), output_targets[log]):\n end if:\n \tresult:=map(simplify, convert(FilterGenerators(FieldIntersection(si_gens, params)), list)):\n\tDocumentTools:-SetProperty(output_targets[single], expression, result, 'refresh'):\n\treturn result:\nend proc:\n\n#===============================================================================\n# Adapted from https://github.com/pogudingleb/SIAN\nFunctionToVariable_ := proc(f):\n convert(convert(f, string)[1..-4], symbol):\nend proc:\n\nParseInput_ := proc(model)\n local all_symbols, x_functions, io_functions, params, states, ios, diff_polys, lhss, out_functions, in_functions, inputs, outputs:\n diff_polys := map(eq -> lhs(eq) - rhs(eq), model):\n all_symbols := foldl(`union`, op( map(e -> indets(e), diff_polys) )) minus {t}:\n x_functions := map(f -> int(f, t), select( f -> type(int(f, t), function(name)), all_symbols )):\n io_functions := select( f -> not type(int(f, t), function(name)) and type(f, function(name)) and not f in x_functions, all_symbols ):\n lhss := map(eq -> lhs(eq), model):\n out_functions := select(f -> f in lhss, io_functions):\n in_functions := select(f -> not (f in lhss), io_functions):\n params := [op(select(f -> not type(f, function(name)) and not type(int(f, t), function(name)), all_symbols))]:\n states := [op(map(FunctionToVariable_, x_functions))]:\n inputs := [op(map(FunctionToVariable_, in_functions))]:\n outputs := [op(map(FunctionToVariable_, out_functions))]:\n return [states, inputs, outputs, params, diff_polys]:\nend proc:\n\n#===============================================================================\n\nMultiExperimentIdentifiableFunctions := proc(model, simplified_generators, no_bound, simplify_bound, max_perms, output_targets): # {simplified_generators := false, no_bound := false})\n # Input: model - ODE model in the state-space form\n # Computes the bound from Theorem REF. Returns a list containing\n # 1. the bound\n # 2. the list of lists of coefficients of the IO-equations (after compression)\n # 3. (optional) simplified set of generators of the field of multi-experiment identifiable functions\n #\n # Optional keyword arguments:\n # 1. simplified_generators - if False, then just the coefficients of the IO-equations are returned.\n # if True, they are being simplified (maybe be a substantial simplification)\n # but this takes time\n # 2. no_bound - if True, then bound for the number of experiments is not computed (may save a lot of time)\n\n local states, inputs, outputs, ios, params, model_eqs, io_eqs, io_coeffs, io_coef, wrnsk, s, roll, wrnsk_sub, r, bound, \n generators, i, eq, result, model_denomfree, target, start, finish, infolevel, use_brackets, output_permutations, \n outputs_, io_coeffs_sb, io_eqs_sb, bound_sb, skip_simplify, result_sb, best_output_ordering, returned_generators, idx, old_bound:\n\n states, inputs, outputs, params, model_eqs := op(ParseInput_(model)):\n use_brackets:=false:\n output_permutations := combinat[permute](outputs):\n output_permutations:= output_permutations[..min(nops(output_permutations),max_perms)];\n \n infolevel := 1:\n model_denomfree := ExtractDenominator(model_eqs):\n skip_simplify := false:\n old_bound := 10: # this will be replaced by a smaller boud every time\n idx:=0:\n for use_brackets in [true, false] do\n for outputs in output_permutations do\n \tLogText(sprintf(\"Permutation:\\t%a\\n\", outputs), output_targets[log]):\n \t# the first iteration is default permutation\n\t \t LogText(sprintf(\"Use Brackets?\\t%a\\n\", use_brackets), output_targets[log]):\n\t if infolevel > 0 then\n\t LogText(sprintf(\"ME Computing input-output equations\\n\"), output_targets[log]):\n\t \t end if:\n\t \t io_eqs := GetIOEquations(model_denomfree, states, inputs, outputs, params, use_brackets, infolevel, output_targets[log]):\n\t \t if infolevel > 0 then\n\t LogText(sprintf(\"ME Total number of io-equations: %a\\n\", nops(io_eqs)), output_targets[log]):\n\t end if:\n\t io_coeffs := []:\n\t \n\t for eq in io_eqs do\n\t io_coef := DecomposePolynomial(eq, indets(eq) minus {op(params)}, params, infolevel, output_targets[log])[1]:\n\t io_coeffs := [op(io_coeffs), io_coef]:\n\t end do:\n\n\t generators := {}:\n \t for io_coef in io_coeffs do\n io_coef := sort(io_coef, (a, b) -> length(convert(a, string)) < length(convert(b, string)));\n for i from 2 to nops(io_coef) do\n generators := {op(generators), io_coef[i] / io_coef[1]}:\n end do:\n end do:\n bound := 0:\n\t\t if no_bound = false then\n for eq in io_eqs do\n if infolevel > 0 then\n LogText(sprintf(\"ME Constructing the Wronskian\\n\"), output_targets[log]):\n end if:\n wrnsk, io_coef := op(ConstructWronskian(eq, model_denomfree, states, inputs, outputs, params, model, infolevel, output_targets[log])):\n # in the notation of the theorem\n s := nops(io_coef) - 1:\n # substitution does not increase the rank, so the resulting bound will be correct\n roll := rand(1..15):\n wrnsk_sub := map(v -> v = roll(), indets(wrnsk)):\n r := LinearAlgebra[Rank](subs(wrnsk_sub, wrnsk)):\n bound := max(bound, s - r + 1):\n end do:\n end if:\n if bound 0 then\n\t\t LogText(sprintf(\"ME WARNING: Entering simplification of generators! if this takes too long, try unchecking \\\"Simplified Generators\\\"\\n\"), output_targets[log]):\n end if:\n result := [op(result), FilterGenerators(FieldToIdeal(generators))]:\n DocumentTools:-SetProperty(output_targets[multi], expression, map(simplify, convert(result[3], list)), 'refresh'):\n returned_generators := result[3]:\n else\n DocumentTools:-SetProperty(output_targets[multi], expression, map(simplify, convert(result[2], list)), 'refresh'):\n returned_generators := result[2]:\n end if:\n if old_bound > 0 then\n \t DocumentTools:-SetProperty(output_targets[bound_], expression, old_bound, 'refresh'):\n \t if old_bound=1 then\n \t \t skip_simplify := true:\n \t \t if simplify_bound then\n \t \t\t LogText(sprintf(\"Bound on the number of experiments = 1, \\\"Try to refine bound\\\" was selected but it will be skipped\"), output_targets[log]):\n \t \t end if:\n\t \t if simplified_generators then\n \t\t DocumentTools:-SetProperty(output_targets[single], expression, map(simplify, convert(result[3], list)), 'refresh'):\n \t\t else\n \t \t\t DocumentTools:-SetProperty(output_targets[single], expression, map(simplify, convert(result[2], list)), 'refresh'):\n \t\t end if:\n \t end if:\n else\n\t DocumentTools:-SetProperty(output_targets[bound_], expression, \"\",'refresh'):\n end if:\n if skip_simplify or not simplify_bound then\n \tbreak:\n \telse\n \t\tDocumentTools:-SetProperty(\"being_refined\", caption, \"being refined\", 'refresh'):\n end if:\n end do: # loop over outputs\n if skip_simplify or not simplify_bound then\n # only breaks if we do not simplify. the code runs at most once\n break:\n end if:\n end do:\n DocumentTools:-SetProperty(\"being_refined\", caption, \"\", 'refresh'):\n return [bound, returned_generators];#table([bd=bound]):\nend proc:\n\nGetPSSolution := proc(model, ord)\n # Input: model and integer ord\n # Output: a truncated power series solution with random parameter values\n # and initial conditions of order ord\n local roll, states, inputs, outputs, params, model_eqs, model_sub,\n x_funcs, x_sols, x_eqs, cur_ord, i, rhs_eval, total_sub, y_funcs, y_sols,\n params_subs, input_subs:\n roll := rand(1..15):\n states, inputs, outputs, params, model_eqs := op(ParseInput_(model)):\n params_subs := map(p -> p = roll(), params):\n input_subs := map(u -> parse(cat(u, \"(t)\")) = add([seq(roll() * t^i, i=0..ord)]), inputs):\n model_sub := subs(params_subs, model):\n model_sub := subs(input_subs, model_sub):\n x_funcs := map(x -> parse(cat(x, \"(t)\")), states):\n x_sols := map(x -> x = roll(), x_funcs):\n x_eqs := map(x -> subs(model_sub, diff(x, t)), x_funcs):\n \n for cur_ord from 1 to ord do\n for i from 1 to nops(x_funcs) do\n rhs_eval := series(subs(x_sols, x_eqs[i]), t, ord + 1):\n x_sols[i] := (lhs(x_sols[i]) = (rhs(x_sols[i]) + t^cur_ord * coeff(rhs_eval, t, cur_ord - 1) / cur_ord)):\n end do:\n end do:\n \n total_sub := [op(x_sols), op(params_subs), op(input_subs)]:\n y_funcs := map(y -> parse(cat(y, \"(t)\")), outputs):\n y_sols := map(y -> y = subs(total_sub, subs(model_sub, y)), y_funcs):\n \n return [op(y_sols), op(input_subs), op(params_subs), op(x_sols)]:\nend proc:\n\n#===============================================================================\n\n#===============================================================================\nIdentifiabilityODE := proc(system_ODEs, params_to_assess, output_targets, {char:=0, p := 0.99, count_solutions:=true, infolevel := 1, method := 2, num_nodes := 6})\n#IdentifiabilityODE := proc(system_ODEs, params_to_assess, p, output_targets, count_solutions, char)\n\t#{p := 0.99, count_solutions:=true, infolevel := 1, method := 2, num_nodes := 6}) \n#===============================================================================\n local i, j, k, n, m, s, all_params, all_vars, eqs, Q, X, Y, poly, d0, D1, \n sample, all_subs,alpha, beta, Et, x_theta_vars, prolongation_possible, \n eqs_i, JacX, vars, vars_to_add, ord_var, var_index, deg_variety, D2, \n y_hat, u_hat, theta_hat, Et_hat, Q_hat, theta_l, theta_g, gb, v, X_eq, Y_eq, \n poly_d, separant, leader, x_functions, y_functions, u_functions,\n all_symbols_rhs, mu, x_vars, y_vars, u_vars, theta, subst_first_order,\n subst_zero_order, x_eqs, y_eqs, param, other_params, to_add, at_node,\n prime, max_rank, R, tr, e, p_local, xy_ders, polys_to_process, new_to_process, start, finish,\n Et_x_vars, out_sian, var, G, P, solutions_table, check:\n\n #----------------------------------------------\n # 0. Extract inputs, outputs, states, and parameters from the system\n #----------------------------------------------\n if SearchText(\".\", convert(system_ODEs, string)) <> 0 then\n LogText(sprintf(\"WARNING: It looks like your system involves floating-point numbers. This may result into a non-meaninful result, please convert them to rationals (e.g., 0.2 -> 1/5)\"), \"LogAreaSIAN\"):\n WARNING(\"WARNING: It looks like your system involves floating-point numbers. This may result into a non-meaninful result, please convert them to rationals (e.g., 0.2 -> 1/5)\"):\n end if:\n \n if not (indets(system_ODEs, name) subset indets(system_ODEs)) then\n LogText(sprintf(cat(\"ERROR: you are using reserved maple symbols: \", convert(indets(system_ODEs, name) minus indets(system_ODEs), string))), output_targets[log]):\n DocumentTools:-SetProperty(\"GlobalParams1\", expression, Error(BadName)):\n DocumentTools:-SetProperty(\"LocalParams1\", expression, Error(BadName)):\n DocumentTools:-SetProperty(\"NoIDParams1\", expression, Error(BadName)):\n error (cat(\"ERROR: you are using reserved maple symbols: \", convert(indets(system_ODEs, name) minus indets(system_ODEs), string))):\n return;\n end if:\n \n randomize():\n# infolevel:=1:\n# num_nodes:=1:\n if infolevel > 0 then\n PrintHeader(\"0. Extracting states, inputs, outputs, and parameters from the system\", output_targets[log]):\n end if:\n x_functions := map(f -> int(f, t), select( f -> type(int(f, t), function(name)), map(lhs, system_ODEs) )):\n y_functions := select( f -> not type(int(f, t), function(name)), map(lhs, system_ODEs) ):\n all_symbols_rhs := foldl(`union`, op( map(e -> indets(rhs(e)), system_ODEs) )) minus {t}:\n xy_ders := {op(x_functions), op(y_functions), op(select(f -> (f in all_symbols_rhs), map(lhs, system_ODEs)))}:\n u_functions := select( f -> type(f, function), convert(all_symbols_rhs minus xy_ders, list)):\n mu := convert(all_symbols_rhs minus {op(xy_ders), op(u_functions)}, list):\n\n x_vars := map(FunctionToVariable, x_functions):\n y_vars := map(FunctionToVariable, y_functions):\n u_vars := map(FunctionToVariable, u_functions):\n theta := map(ParamToInner, params_to_assess):\n subst_first_order := {seq(diff(x_functions[i], t) = MakeDerivative(x_vars[i], 1), i = 1 .. nops(x_vars))}:\n subst_zero_order := {\n seq(x_functions[i] = MakeDerivative(x_vars[i], 0), i = 1 .. nops(x_vars)),\n seq(y_functions[i] = MakeDerivative(y_vars[i], 0), i = 1 .. nops(y_vars)),\n seq(u_functions[i] = MakeDerivative(u_vars[i], 0), i = 1 .. nops(u_vars))\n }:\n x_eqs := subs(subst_zero_order, subs(subst_first_order, select(e -> type(int(lhs(e), t), function(name)), system_ODEs))):\n y_eqs := subs(subst_zero_order, select(e -> not type(int(lhs(e), t), function(name)), system_ODEs)):\n\n # taking into account that fact that Groebner[Basis] is Monte Carlo with probability of error \n # at most 10^(-18) (for Maple 2017)\n p_local := p + nops(params_to_assess) * 10^(-18):\n if p_local >= 1 then\n LogText(\"The probability of success cannot exceed 1 - #params_to_assess 10^{-18}. We reset it to 0.99\", output_targets[log]);\n p_local := 0.99:\n end if:\n\n if infolevel > 0 then\n LogText(sprintf(\"\\n===== Input info =====\\n\"), output_targets[log]): \n LogText(sprintf(\"%s %a\\n\", `State variables: `, x_functions), output_targets[log]): \n LogText(sprintf(\"%s %a\\n\", `Output variables: `, y_functions), output_targets[log]): \n LogText(sprintf(\"%s %a\\n\", `Input variables: `, u_functions), output_targets[log]): \n LogText(sprintf(\"%s %a\\n\", `Parameters in equations: `, mu), output_targets[log]): \n LogText(sprintf(\"===================\\n\\n\"), output_targets[log]): \n end if:\n\n #----------------------------------------------\n # 1. Construct the maximal system.\n #----------------------------------------------\n\n if infolevel > 0 then\n PrintHeader(\"1. Constructing the maximal polynomial system\",output_targets[log]):\n end if:\n\n # (a) ---------------\n n := nops(x_vars):\n m := nops(y_vars):\n s := nops(mu) + n:\n all_params := [op(mu), op(map(x -> MakeDerivative(x, 0), x_vars ))]:\n all_vars := [ op(x_vars), op(y_vars), op(u_vars) ]:\n eqs := [op(x_eqs), op(y_eqs)]:\n Q := foldl( (f, g) -> lcm(f, g), op( map(f -> denom(rhs(f)), eqs) )):\n \n\n # (b,c) ---------------\n X := []:\n X_eq := []:\n for i from 1 to n do\n X := [op(X), []]:\n poly := numer(lhs(x_eqs[i]) - rhs(x_eqs[i])):\n for j from 0 to s + 1 do\n poly_d := Differentiate(poly, all_vars, j):\n leader := MakeDerivative(x_vars[i], j + 1):\n separant := diff(poly_d, leader):\n X[i] := [op(X[i]), poly_d]:\n X_eq := [op(X_eq), leader = -(poly_d - separant * leader) / separant]:\n end do:\n end do:\n # LogExpression(X[1]);\n \n # (d,e) ---------------\n Y := []:\n Y_eq := []:\n for i from 1 to m do\n Y := [op(Y), []]:\n poly := numer(lhs(y_eqs[i]) - rhs(y_eqs[i])):\n for j from 0 to s + 1 do\n poly_d := Differentiate(poly, all_vars, j):\n leader := MakeDerivative(y_vars[i], j):\n separant := diff(poly_d, leader):\n Y[i] := [op(Y[i]), poly_d]:\n Y_eq := [op(Y_eq), leader = -(poly_d - separant * leader) / separant]:\n end do:\n end do:\n\n\n #----------------------------------------------\n # 2. Truncate.\n #----------------------------------------------\n\n if infolevel > 0 then\n PrintHeader(\"2. Truncating the polynomial system based on the Jacobian condition\", output_targets[log]):\n end if:\n\n # (a) ---------------\n d0 := max(op( map(f -> degree( simplify(Q * rhs(f)) ), eqs) ), degree(Q)):\n\n # (b) ---------------\n # extra factor nops(theta) + 1 compared to the formula in the paper is to\n # provide probability gaurantee to the local identifiability test\n D1 := floor( (nops(theta) + 1) * 2 * d0 * s * (n + 1) * (1 + 2 * d0 * s) / (1 - p_local) ):\n # prime := nextprime(D1):\n if infolevel > 1 then\n LogText(sprintf(\"%s %a\\n\", `Bound D_1 for testing the rank of the Jacobian probabilistically: `, D1), output_targets[log]);\n end if:\n\n # (c, d) ---------------\n sample := SamplePoint(D1, x_vars, y_vars, u_vars, mu, X_eq, Y_eq, Q):\n all_subs := sample[4]:\n u_hat := sample[2]:\n y_hat := sample[1]:\n \n # (e) ------------------\n alpha := [seq(1, i = 1..n)]:\n beta := [seq(0, i = 1..m)]:\n Et := [];\n # TODO: improve for arbitrary derivatives\n x_theta_vars := all_params:\n prolongation_possible := [seq(1, i = 1..m)]:\n\n # (f) ------------------\n while add(prolongation_possible) > 0 do\n for i from 1 to m do\n if prolongation_possible[i] = 1 then\n eqs_i := [op(Et), Y[i][beta[i] + 1]]:\n JacX := VectorCalculus[Jacobian](subs({op(u_hat), op(y_hat)}, eqs_i), x_theta_vars = subs(all_subs, x_theta_vars)):\n if LinearAlgebra[Rank](JacX) = nops(eqs_i) then\n Et := [op(Et), Y[i][beta[i] + 1]]:\n beta[i] := beta[i] + 1:\n # adding necessary X-equations\n polys_to_process := [op(Et), seq(Y[k][beta[k] + 1], k=1..m)]:\n while nops(polys_to_process) <> 0 do\n new_to_process := []:\n vars := {};\n for poly in polys_to_process do\n vars := vars union { op(GetVars(poly, x_vars)) }:\n end do:\n vars_to_add := { op(remove(v -> evalb(v in x_theta_vars), vars)) };\n for v in vars_to_add do\n x_theta_vars := [op(x_theta_vars), v];\n ord_var := GetOrderVar(v);\n var_index := ListTools[Search](ord_var[1], x_vars):\n poly := X[ var_index ][ ord_var[2] ]:\n Et := [op(Et), poly]:\n new_to_process := [op(new_to_process), poly]:\n alpha[ var_index ] := max(alpha[ var_index ], ord_var[2] + 1):\n end do:\n polys_to_process := new_to_process:\n end do:\n else\n prolongation_possible[i] := 0;\n end if:\n end if: \n end do:\n end do:\n # is used for assessing local identifiabilty\n max_rank := nops(Et):\n\n # (g) --------------\n for i from 1 to m do\n for j from beta[i] + 1 to nops(Y[i]) do\n to_add := true:\n for v in GetVars(Y[i][j], x_vars) do\n if not (v in x_theta_vars) then\n to_add := false:\n end if:\n end do:\n if to_add = true then\n beta[i] := beta[i] + 1:\n Et := [op(Et), Y[i][j]]:\n end if:\n end do:\n end do:\n \n if infolevel > 1 then\n LogText(sprintf(\"%s %a\\n\", `Orders of prolongations of the outputs (beta) = `, beta), output_targets[log]):\n LogText(sprintf(\"%s %a\\n\", `Orders of prolongations of the state variables (alpha) = `, alpha), output_targets[log]):\n end if:\n ##############################\n\n if infolevel > 0 then\n PrintHeader(\"3. Assessing local identifiability\", output_targets[log]):\n end if:\n \n theta_l := []:\n for param in theta do\n other_params := subs(param = NULL, x_theta_vars):\n JacX := VectorCalculus[Jacobian]( \n subs( { op(u_hat), param = subs(all_subs, param), op(y_hat) }, Et), \n other_params = subs(all_subs, other_params)\n ):\n if LinearAlgebra[Rank](JacX) <> max_rank then\n theta_l := [op(theta_l), param]:\n end if:\n end do:\n DocumentTools:-SetProperty(\"LocalLabel\" , caption, \"Locally Identifiable Paramters\");\n if infolevel > 1 then\n LogText(sprintf(\"%s %a\\n\", `Locally identifiable paramters: `, map(x -> ParamToOuter(x, all_vars), theta_l)), output_targets[log]);\n LogText(sprintf(\"%s %a\\n\", `Nonidentifiable parameter: `, map(x -> ParamToOuter(x, all_vars), [op({op(theta)} minus {op(theta_l)})])), output_targets[log]);\n end if:\n\n DocumentTools:-SetProperty(output_targets[localparams], expression, map(x -> ParamToOuter(x, all_vars), theta_l), 'refresh'): # local\n DocumentTools:-SetProperty(output_targets[noidparams], expression, map(x -> ParamToOuter(x, all_vars), [op({op(theta)} minus {op(theta_l)})]), 'refresh'): # no id\n\n #----------------------------------------------\n # 3. Randomize.\n #----------------------------------------------\n\n if infolevel > 0 then\n PrintHeader(\"4. Randomizing the truncated system\", output_targets[log]):\n end if:\n\n # (a) ------------\n deg_variety := foldl(`*`, op( map(e -> degree(e), Et) )):\n D2 := floor( 6 * nops(theta_l) * deg_variety * (1 + 2 * d0 * max(op(beta))) / (1 - p_local) ):\n if infolevel > 1 then\n LogText(sprintf(\"%s %a\\n\", `Bound D_2 for assessing global identifiability: `, D2), output_targets[log]):\n end if:\n\n # (b, c) ---------\n sample := SamplePoint(D2, x_vars, y_vars, u_vars, mu, X_eq, Y_eq, Q):\n y_hat := sample[1]:\n u_hat := sample[2]:\n theta_hat := sample[3]:\n if infolevel > 1 then\n LogText(sprintf(\"%s %a\\n\", `Random sample for the outputs and inputs is generated from `, theta_hat), output_targets[log]):\n end if:\n\n # (d) ------------\n Et_hat := map(e -> subs([op(y_hat), op(u_hat)], e), Et):\n Et_x_vars := {}:\n for poly in Et_hat do\n Et_x_vars := Et_x_vars union { op(GetVars(poly, x_vars)) }:\n end do:\n if infolevel > 1 then\n LogText(sprintf(\"%s %a %s %a %s\\n\", \"The polynomial system contains\", nops(Et_hat), \"equations in \", nops(Et_x_vars) + nops(mu), \" variables\"), output_targets[log]);\n end if:\n Q_hat := subs(u_hat, Q):\n\n vars := [\n op(sort([op(Et_x_vars)], (a, b) -> CompareDiffVar(a, b, x_vars))),\n z_aux, w_aux,\n op(sort(mu))\n ]:\n if infolevel > 1 then\n LogText(sprintf(\"Variable ordering to be used for Groebner basis computation %a\\n\", vars), output_targets[log]);\n end if:\n \n #----------------------------------------------\n # 4. Determine.\n #----------------------------------------------\n\n if infolevel > 0 then\n PrintHeader(\"5. Assessing global identifiability\", output_targets[log]):\n end if:\n theta_g := []:\n if method = 1 then\n at_node := proc(var, args_node)\n local gb_loc, fname;\n gb_loc := Groebner[Basis](op(args_node)):\n gb_loc;\n end proc:\n\n if nops(theta_l) > 1 and num_nodes > 1 then\n Grid[Setup](\"local\", numnodes = num_nodes):\n Grid[Set](at_node):\n gb := Grid[Seq](\n at_node(theta_l[i], [\n [op(Et_hat), z_aux * Q_hat - 1, (theta_l[i] - subs(theta_hat, theta_l[i])) * w_aux - 1],\n tdeg(vars)\n ]),\n i = 1..nops(theta_l)\n ):\n else\n gb := []:\n for i from 1 to nops(theta_l) do\n gb := [\n op(gb), \n at_node(\n theta_l[i], \n [[op(Et_hat), z_aux * Q_hat - 1, (theta_l[i] - subs(theta_hat, theta_l[i])) * w_aux - 1], tdeg(op(vars))]\n ) \n ]:\n end do:\n end if:\n for i from 1 to nops(theta_l) do\n if gb[i] = [1] then\n theta_g := [op(theta_g), theta_l[i]]:\n else\n if infolevel > 1 then\n LogText(sprintf(\"%s %a %s %a\\n\", `Groebner basis corresponding to the parameter `, theta_l[i], ` is `, gb[i]), output_targets[log]):\n end if:\n end if:\n end do: \n elif method = 2 then\n LogText(sprintf(\"%s %a\\n\", `Computing Groebner Basis with characteristic`, char), output_targets[log]):\n \tgb := Groebner[Basis]([op(Et_hat), z_aux * Q_hat - 1], tdeg(op(vars)), characteristic=char);\n for i from 1 to nops(theta_l) do\n if char>0 then\n \tcheck := subs(theta_hat, theta_l[i]) mod char:\n else\n \tcheck := subs(theta_hat, theta_l[i]):\n end if:\n if Groebner[NormalForm](theta_l[i], gb, tdeg(op(vars)), characteristic=char) = check then\n theta_g := [ op(theta_g), theta_l[i] ]:\n end if:\n end do:\n\n if count_solutions then\n LogParameters(\"\",output_targets[parameters]):\n \tfor var in theta_g do\n \t\tLogText(sprintf(\"%s %a, %s %a\\n\",`The number of solutions for`, var, `is`, 1), output_targets[log]):\n\t\tLogParameters(sprintf(\"%s %a, %s %a\\n\",`Parameter`, ParamToOuter(var, all_vars), `number of solutions:`, 1), output_targets[parameters]):\n\t\tsolutions_table[var]:=1:\n \tend do:\n\t\n \tfor var in select(p -> not p in theta_g, theta_l) do\n\t\tG := Groebner[Walk](gb, tdeg(op(vars)), lexdeg([op({op(vars)} minus {var})], [var]), characteristic=char):\n\t\tP := select(x->evalb(indets(x)={var}), G):\n\t\tsolutions_table[var]:=degree(P[1], [op(indets(P))]): \n\t\tLogText(sprintf(\"%s %a, %s %a\\n\",`The number of solutions for`, var, `is`, degree(P[1], [op(indets(P))])), output_targets[log]):\n\t\tLogParameters(sprintf(\"%s %a, %s %a\\n\",`Parameter`, ParamToOuter(var, all_vars), `number of solutions:`, degree(P[1], [op(indets(P))])), output_targets[parameters])\n \tend do:\n fi:\n \tDocumentTools:-SetProperty(output_targets[globalparams], value, [op(map(x -> ParamToOuter(x, all_vars), theta_g))], 'refresh'): # global\n \tDocumentTools:-SetProperty(output_targets[localparams], value, [op(map(x -> ParamToOuter(x, all_vars), select(p -> not p in theta_g, theta_l)))], 'refresh'): # global\n else\n LogText(sprintf(`No such method`), output_targets[log]):\n LogText(sprintf(\"%q\\n\", \"Provided method: %d, allowed methods: 1, 2\", method), output_targets[log]):\n end if:\n\n if infolevel > 0 then\n LogText(sprintf(\"\\n=== Summary ===\\n\"), output_targets[log]):\n LogText(sprintf(\"%s %a\\n\", `Globally identifiable parameters: `, map(x -> ParamToOuter(x, all_vars), theta_g)), output_targets[log]):\n LogText(sprintf(\"%s %a\\n\", `Locally but not globally identifiable parameters: `, map(x -> ParamToOuter(x, all_vars), select(p -> not p in theta_g, theta_l))), output_targets[log]):\n LogText(sprintf(\"%s %a\\n\", `Not identifiable parameters: `, map(x -> ParamToOuter(x, all_vars), select(p -> not p in theta_l, theta))), output_targets[log]):\n LogText(sprintf(\"===============\\n\\n\"), output_targets[log]):\n end if:\n DocumentTools:-SetProperty(\"LocalLabel\" , caption, \"Locally but not Globally Identifiable Paramters\");\n out_sian := table([\n globally = [op(map(x -> ParamToOuter(x, all_vars), theta_g))],\n locally_not_globally = {op(map(x -> ParamToOuter(x, all_vars), select(p -> not p in theta_g, theta_l)))},\n non_identifiable = {op(map(x -> ParamToOuter(x, all_vars), select(p -> not p in theta_l, theta)))},\n parameters = mu,\n basis=gb,\n varordering=tdeg(op(vars)),\n allvars=vars,\n for_outer=all_vars\n ]):\n if count_solutions then\n PrintHeader(\"WARNING: The result of solution counting is guaranteed with high probability, however it NOT the same probability 'p' as provided in the input.\", output_targets[log]):\n end if:\n out_sian[num_solutions] := solutions_table:\n return out_sian;\nend proc:\n\n#===============================================================================\nPrintHeader := proc(text, output_target):\n#===============================================================================\n LogText(sprintf(\"\\n=======================================================\\n\"), output_target):\n LogText(sprintf(text), output_target):\n LogText(sprintf(\"\\n=======================================================\\n\"), output_target):\nend proc:\n\n#===============================================================================\nGetParameters := proc(system_ODEs, initial_conditions) local initial_values, all_symbols_rhs, mu:\n#===============================================================================\n initial_values := map(f -> subs({t = 0}, int(f, t)), select( f -> type(int(f, t), function(name)), map(lhs, system_ODEs) )):\n all_symbols_rhs := foldl(`union`, op( map(e -> indets(rhs(e)), system_ODEs) )) minus {t}:\n mu := select(s -> not type(s, function), all_symbols_rhs):\n if initial_conditions then\n return [op(mu), op(initial_values)]:\n else\n return [op(mu)]:\n end if:\nend proc:\n\n#===============================================================================\nFunctionToVariable := proc(f):\n#===============================================================================\n convert(cat(convert(f, string)[1..-4], \"_\"), symbol):\nend proc:\n\n#===============================================================================\nParamToInner := proc(p) local s:\n#===============================================================================\n s := convert(p, string):\n if length(s) > 3 and s[-3..-1] = \"(0)\" then\n MakeDerivative(FunctionToVariable(p), 0):\n else\n p:\n end if:\nend proc:\n\n#===============================================================================\nParamToOuter := proc(p, varnames) local s:\n#===============================================================================\n s := convert(p, string):\n if length(s) > 2 and s[-2..-1] = \"_0\" and parse(s[1..-2] )in varnames then\n parse(cat(s[1..-3], \"(0)\")):\n else\n p:\n end if:\nend proc:\n\n#===============================================================================\nMakeDerivative := proc(var_name, der_order):\n#===============================================================================\n cat(var_name, der_order):\nend proc:\n\n\n#===============================================================================\nDifferentiateOnce := proc(diff_poly, var_list) \n#===============================================================================\n local result, aux, v, h, diff_v:\n result := 0:\n for diff_v in indets(diff_poly) do\n aux := GetOrderVar(diff_v):\n # seems that Maple does not have unpacking\n v := aux[1]:\n h := aux[2]:\n if v in var_list then\n result := result + diff(diff_poly, MakeDerivative(v, h)) * MakeDerivative(v, h + 1):\n end if:\n end do:\n simplify(result):\nend proc:\n\n\n#===============================================================================\nDifferentiate := proc(diff_poly, var_list, ord := 1) \n#===============================================================================\n local result, i;\n result := diff_poly:\n for i from 1 to ord do\n result := DifferentiateOnce(result, var_list):\n end do:\n result:\nend proc:\n\n\n#===============================================================================\nGetVars := proc(diff_poly, var_list)\n#===============================================================================\n local result;\n result := select(v -> evalb(GetOrderVar(v)[1] in var_list), indets(diff_poly)):\n return result:\nend proc:\n\n\n#===============================================================================\nGetOrderVar := proc(diff_var)\n#===============================================================================\n local s, v, h;\n if not StringTools[RegMatch](\"^(.*_)([0-9]+)$\", diff_var, s, v, h) then\n return [\"\", \"\"]:\n end if:\n return [parse(v), parse(h)]:\nend proc:\n\n\n#===============================================================================\nSamplePoint := proc(bound, x_vars, y_vars, u_vars, mu, X_eq, Y_eq, Q)\n#===============================================================================\n local n, m, s, all_params, all_vars, theta_hat, u_variables, \n u_hat, x_hat, y_hat, eq, eq_num, eq_denom, \n v, poly, i, j, all_subs, roll, to_compute;\n n := nops(x_vars):\n m := nops(y_vars):\n s := nops(mu) + n:\n all_params := [op(mu), op(map(x -> MakeDerivative(x, 0), x_vars ))]:\n all_vars := [ op(x_vars), op(y_vars), op(u_vars) ]:\n\n roll := rand(0 .. bound):\n while true do\n theta_hat := map(p -> p = roll(), all_params): \n u_variables := [];\n for i from 1 to nops(u_vars) do\n u_variables := [ op(u_variables), seq(MakeDerivative(u_vars[i], j), j = 0..s + 1) ]:\n end do:\n u_hat := map(p -> p = roll(), u_variables) : \n \n all_subs := [op(theta_hat), op(u_hat)]:\n if subs(all_subs, Q) = 0 then\n next\n end if:\n to_compute := [op(X_eq), op(Y_eq)]:\n while nops(to_compute) <> 0 do\n to_compute := map(e -> lhs(e) = subs(all_subs, rhs(e)), to_compute);\n all_subs := [ op(all_subs), op(select(e -> type(rhs(e), numeric), to_compute)) ]:\n to_compute := remove(e -> type(rhs(e), numeric), to_compute):\n end do:\n y_hat := map(e -> lhs(e) = subs(all_subs, rhs(e)), Y_eq):\n x_hat := map(e -> lhs(e) = subs(all_subs, rhs(e)), X_eq):\n break:\n end do:\n\n return [y_hat, u_hat, theta_hat, all_subs];\nend proc:\n\n#===============================================================================\nGenerateReplica := proc(equations, r)\n#===============================================================================\n # generates a system of equations corresponding to r independent trajectories of\n # the original system. Time-dependent variabes are replicated, parameters are not\n local all_functions, zero_order, first_order, funcs, without_t, result, i, subst:\n all_functions := select(f -> type(f, function), foldl(`union`, op( map(indets, equations) ))):\n zero_order := select(f -> not type(int(f, t), function(name)), all_functions):\n first_order := map(f -> int(f, t), select(f -> type(int(f, t), function(name)), all_functions)):\n funcs := {op(zero_order), op(first_order)}:\n without_t := map(f -> convert(convert(f, string)[1..-4], symbol), funcs):\n result := []:\n for i from 1 to r do\n subst := map(f -> f = convert(cat(convert(f, string), \"_r\", i), symbol), without_t):\n result := [op(result), op(map(e -> subs(subst, e), equations))]:\n end do: \n return result:\nend proc:\n\n#===============================================================================\nCompareDiffVar := proc(dvl, dvr, var_list)\n#===============================================================================\n local vl, vr, hl, hr;\n vl, hl := op(GetOrderVar(dvl, var_list)):\n vr, hr := op(GetOrderVar(dvr, var_list)):\n if evalb(hl <> hr) then\n return evalb(hl > hr):\n end if:\n if evalb(length(vl) <> length(vr)) then\n return evalb(length(vl) > length(vr)):\n end if:\n return StringTools[Compare](vr, vl):\nend proc:\n\n\nLogText:= proc(text, target)\n\t# must pass text as sprintf(text)!!!\n\tUpdateLog(text, target);\nend proc:\n\nLogExpression:= proc(text, target)\n\t# must pass text as sprintf(\"%q\\n\", text)!!!\n\tUpdateLog(text, target);\nend proc:\n\n#LogTextSIAN := ()->UpdateLog(sprintf(_passed), \"LogAreaSIAN\");\n#LogExpressionSIAN := ()->UpdateLog(sprintf(\"%q\\n\", _passed), \"SIAN\");\n\n#LogTextME := ()->UpdateLog(sprintf(_passed), \"LogAreaME\");\n#LogExpressionME := ()->UpdateLog(sprintf(\"%q\\n\", _passed), \"LogAreaME\");\n\n#LogTextSE := ()->UpdateLog(sprintf(_passed), \"LogAreaSE\");\n#LogExpressionSE := ()->UpdateLog(sprintf(\"%q\\n\", _passed), \"LogAreaSE\");\n\nUpdateLog := proc(s, target)\nlocal logsofar;\n\n\tlogsofar := DocumentTools:-GetProperty(target, value);\n\tif logsofar <> \"\" then\n\t\tlogsofar := logsofar, \"\\n\";\n\tend if;\n\t\n\tDocumentTools:-SetProperty(target, value, cat(logsofar,s), 'refresh');\n\nend proc:\n\nexamples := table([ \n \t\"Biohydrogenation\" = [ \"Taken from R. Munoz-Tamayo, L. Puillet, J.B. Daniel, D. Sauvant, O. Martin, M. Taghipoor, P. Blavy\\n Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?\\ndoi.org/10.1017/S1751731117002774\\nSystem (3) in Supplementary Material 2, initial conditions are assumed to be unknown\",\n \t[\n \"dx4/dt = - k5 * x4 / (k6 + x4);\\n\",\n \"dx5/dt = k5 * x4 / (k6 + x4) - k7 * x5/(k8 + x5 + x6);\\n\",\n \"dx6/dt = k7 * x5 / (k8 + x5 + x6) - k9 * x6 * (k10 - x6) / k10;\\n\",\n \"dx7/dt = k9 * x6 * (k10 - x6) / k10;\\n\",\n \"y1 = x4;\\n\",\n \"y2 = x5\"]],\n\n \t\"Chemical Reaction Network\" = [\"Taken from Conradi, C., Shiu, A., Dynamics of post-translational modification systems: recent progress and future directions Eq. 3.4\",\n\t[\n \"dx1/dt = -k1 * x1 * x2 + k2 * x4 + k4 * x6;\\n\",\n \"dx2/dt = k1 * x1 * x2 + k2 * x4 + k3 * x4;\\n\",\n \"dx3/dt = k3 * x4 + k5 * x6 - k6 * x3 * x5;\\n\",\n \"dx4/dt = k1 * x1 * x2 - k2 * x4 - k3 * x4;\\n\",\n \"dx5/dt = k4 * x6 + k5 * x6 - k6 * x3 * x5;\\n\",\n \"dx6/dt = -k4 * x6 - k5 * x6 + k6 * x3 * x5;\\n\",\n \"y1 = x3;\\n\"\n \"y2 = x2;\\n\" ]],\n\n\t\"DAISY Ex. 3\" = [\"DAISY Example 3\", [\n \"dx1/dt = -1 * p1 * x1 + p2 * x2 + u(t);\\n\",\n \"dx2/dt = p3 * x1 - p4 * x2 + p5 * x3;\\n\",\n \"dx3/dt = p6 * x1 - p7 * x3;\\n\",\n \"y1 = x1;\\n\"]],\n\n\t\"DAISY_mamil3\" = [\"DAISY mamil 3\",\n\t[\n \"dx1/dt = -(a21 + a31 + a01) * x1 + a12 * x2 + a13 * x3 + u(t);\\n\",\n \"dx2/dt = a21 * x1 - a12 * x2;\\n\",\n \"dx3/dt = a31 * x1 - a13 * x3;\\n\",\n \"y = x1\"]],\n \n\t\"DAISY_mamil4\" = [\"DAISY mamil 4\", [\n \"dx1/dt = -k01 * x1 + k12 * x2 + k13 * x3 + k14 * x4 - k21 * x1 - k31 * x1 - k41 * x1 + u(t);\\n\",\n \"dx2/dt = -k12 * x2 + k21 * x1;\\n\",\n \"dx3/dt = -k13 * x3 + k31 * x1;\\n\",\n \"dx4/dt = -k14 * x4 + k41 * x1;\\n\",\n \"y = x1\"]],\n\n\t\"HIV\" = [\"Example (with initial conditions assumed being unknown) from Section IV of 'DAISY: an Efficient Tool to Test Global Identifiability. Some Case Studies' by G. Bellu, M.P. Saccomani\",\n\t[\n \"dx1/dt = -b * x1 * x4 - d * x1 + s;\\n\",\n \"dx2/dt = b * q1 * x1 * x4 - k1 * x2 - mu1 * x2;\\n\",\n \"dx3/dt = b * q2 * x1 * x4 + k1 * x2 - mu2 * x3;\\n\",\n \"dx4/dt = -c * x4 + k2 * x3;\\n\",\n \"y1 = x1;\\n\",\n \"y2 = x4\"]],\n\n\t\"HIV2\" = [\"The system is taken from Wodarz, D., Nowak, M.\\nSpecific therapy regimes could lead to long-term immunological control of HIV\\nhttps://doi.org/10.1073/pnas.96.25.14464\\nPage 1\",\n\t[\n \"dx/dt = lm - d * x - beta * x * v;\\n\",\n \"dy/dt = beta * x * v - a * y;\\n\",\n \"dv/dt = k * y - u * v;\\n\",\n \"dw/dt = c * x * y * w - c * q * y * w - b * w;\\n\",\n \"dz/dt = c * q * y * w - h * z;\\n\",\n \"y1 = w;\\n\",\n \"y2 = z\"]],\n\n\t\"Lipolysis\" = [\"Taken from R. Munoz-Tamayo, L. Puillet, J.B. Daniel, D. Sauvant, O. Martin, M. Taghipoor, P. Blavy\\nReview: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?\\ndoi.org/10.1017/S1751731117002774\\nSystem (1) in Supplementary Material 2, initial conditions are assumed to be unknown\\nbrought to the rational function form by introducing new state variable x5 = k1 e^(-k3 t)\",\n\t[\n \"dx1/dt = -x1 * x5 / (k2 + x1);\\n\",\n \"dx2/dt = 2 * x1 * x5 / ((k2 + x1) * 3) - k4 * x2;\\n\",\n \"dx3/dt = k4*(x2)/2 - k4*x3;\\n\",\n \"dx4/dt = x1 * x5 / (3 * (k2 + x1)) + k4 * (x2)/2 + k4 * x3;\\n\",\n \"dx5/dt = -k3 * x5;\\n\",\n \"y1 = x1;\\n\",\n \"y2 = x2 + x3;\\n\",\n \"y3 = x4\"]],\n\n \t\"LV\" = [\"Lotka-Volterra System\",[\n \t\"dx1/dt = a*x1 - b*x1*x2;\\n\", \n \t\"dx2/dt = -c*x2 + d*x1*x2;\\n\",\n \t\"y = x1;\\n\"]],\n\t\"OralGlucose\" = [\"Example (with initial conditions assumed being unknown) from Section III of 'DAISY: an Efficient Tool to Test Global Identifiability. Some Case Studies'\\nby G. Bellu, M.P. Saccomani\",\n\t[\n \"dG/dt = -(p1 + X) * G + p1 * Gb + v * R;\\n\",\n \"dX/dt = -p2 * X + p3 * (u(t) - Ib);\\n\",\n \"dR/dt = k;\\n\",\n \"dIb/dt = 0;\\n\",\n \"dGb/dt = 0;\\n\",\n \"y1 = G;\\n\",\n \"y2 = Ib;\\n\",\n \"y3 = Gb;\\n\"]],\n\n\t\"SEIR\" = [\"Taken from N. Tuncer, T. Le\\n'Structural and practical identifiability analysis of outbreak models'\\nhttps://doi.org/10.1016/j.mbs.2018.02.004\\nEquation (2.2) with prevalence observations\",\n[\n \"dS/dt = -b * S * In / N;\\n\",\n \"dE/dt = b * S * In / N - nu * E;\\n\",\n \"dIn/dt = nu * E - a * In;\\n\",\n \"dN/dt = 0;\\n\",\n \"y1 = In;\\n\",\n \"y2 = N;\\n\"]],\n\n\t\"SEIR2\" = [\"Taken from N. Tuncer, T. Le\\n'Structural and practical identifiability analysis of outbreak models'\\nhttps://doi.org/10.1016/j.mbs.2018.02.004\\nEquation (2.2) with cumulative incidence observations\",\n\t[\n \"dS/dt = -b * S * In / N;\\n\",\n \"dE/dt = b * S * In / N - nu * E;\\n\",\n \"dIn/dt = nu * E - a * In;\\n\",\n \"dN/dt = 0;\\n\",\n \"dCu/dt = nu * E;\\n\",\n \"y1 = Cu;\\n\",\n \"y2 = N\"]],\n\n\t\"SIR_R0\" = [\"SIR R0\",[\n \"dS/dt = -b * In * S;\\n\",\n \"dIn/dt = b * In * S - g * In;\\n\",\n \"dR/dt = g * In;\\n\",\n \"daux/dt = 0;\\n\",\n \"y1 = In;\\n\",\n \"y2 = b / g + aux;\"]],\n\n\t\"SIRSForced\" = [\"Taken from Capistran M., Moreles M., Lara B.\\n'Parameter Estimation of Some Epidemic Models.\\n The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus'\\ndoi.org/10.1007/s11538-009-9429-3\\nEquations (7)-(11)\",\n[\n \"ds/dt = mu - mu * s - b0 * (1 + b1 * x1) * i * s + g * r;\\n\",\n \"di/dt = b0 * (1 + b1 * x1) * i * s - (nu + mu) * i;\\n\",\n \"dr/dt = nu * i - (mu + g) * r;\\n\",\n \"dx1/dt = -M * x2;\\n\",\n \"dx2/dt = M * x1;\\n\",\n \"y1 = i;\\n\",\n \"y2 = r;\\n\"]],\n\n\t\"SlowFast\" = [\"Taken from Vajda S., Rabitz H.\\n'Identifiability and Distinguishability of First-Order Reaction Systems', p. 701\\nWe added an extra output x_C\",\n\t[\n \"dxA/dt = -k1 * xA;\\n\",\n \"dxB/dt = k1 * xA - k2 * xB;\\n\",\n \"dxC/dt = k2 * xB;\\n\",\n \"deA/dt = 0;\\n\",\n \"deC/dt = 0;\\n\",\n \"y1 = eA * xA + eB * xB + eC * xC;\\n\",\n \"y2 = xC;\\n\",\n \"y3 = eA;\\n\",\n \"y4 = eC\"]],\n\t\n\t\"Treatment\" = [\"Taken from N. Tuncer, T. Le\\nStructural and practical identifiability analysis of outbreak models'\\nhttps://doi.org/10.1016/j.mbs.2018.02.004\\nEquation (2.3) with observed treatment\",\n\t[\n \"dS/dt = -b * S * In / N - d * b * S * Tr / N;\\n\",\n \"dIn/dt = b * S * In / N + d * b * S * Tr / N - (a + g) * In;\\n\",\n \"dTr/dt = g * In - nu * Tr;\\n\",\n \"dN/dt = 0;\\n\",\n \"y1 = Tr;\\n\",\n \"y2 = N\"]],\n\n\t\"Tumor\" = [\"Example (with initial conditions assumed being unknown) from Section 3 of\\n'Examples of testing global identifiability of biological and biomedical models with the DAISY software'\\nby M.P. Saccomani, S. Audoly, G. Bellu, L. D'Angio\",\n[ \"dx1/dt = -(k3 + k7) * x1 + k4 * x2;\\n\",\n \"dx2/dt = k3 * x1 - (k4 + a * k5 + b * d1 * k5) * x2 + k6 * x3 + k6 * x4 + k5 * x2 * x3 + k5 * x2 * x4;\\n\",\n \"dx3/dt = a * k5 * x2 - k6 * x3 - k5 * x2 * x3;\\n\",\n \"dx4/dt = b * d1 * k5 * x2 - k6 * x4 - k5 * x2 * x4;\\n\",\n \"dx5/dt = k7 * x1;\\n\",\n \"da/dt = 0;\\n\",\n \"db/dt = 0;\\n\",\n \"dd1/dt = 0;\\n\",\n \"y1 = x5;\\n\",\n \"y2 = a;\\n\",\n \"y3 = b;\\n\",\n \"y4 = d1;\\n\"]]\n]):\n\n# Setup\n\ntimed_SIAN:=proc(sigma, params_to_assess, p, output_targets_sian, count_solutions, char)\n\tlocal output, data, start, finish:\n\tstart:= time():\n #IdentifiabilityODE := proc(system_ODEs, params_to_assess, output_targets_sian, {char:=0, p := 0.99, count_solutions:=true, infolevel := 1, method := 2, num_nodes := 6})\n\toutput := IdentifiabilityODE(sigma, params_to_assess, output_targets_sian, char=char, p=p, count_solutions=count_solutions, infolevel=1, method=2, num_nodes=1):\n\tfinish:= time():\n\tDocumentTools:-SetProperty(output_targets_sian[runningtime], value, convert(finish-start, string), 'refresh'): # time\n\treturn output:\nend proc:\n\ntimed_Multi:=proc(model, simplified_generators, no_bound, simplify_bound, max_perms, output_targets_multi)\n\tlocal start, output, finish, data, bound, generators:\n\tstart:=time():\n\tbound, generators := op(MultiExperimentIdentifiableFunctions(model, simplified_generators, no_bound, simplify_bound, max_perms, output_targets_multi)):\n\tfinish:=time():\n\tDocumentTools:-SetProperty(output_targets_multi[runningtime], value, convert(finish-start, string), 'refresh'):\n\treturn [bound, finish-start, generators]: #table([output=bound, runtime=finish-start]):\nend proc:\n\ntimed_Single:=proc(model, output_targets_single)\n\tlocal start, output, finish, data:\n\tstart:=time():\n\toutput := SingleExperimentIdentifiableFunctions(model, output_targets_single):\n\tfinish:=time():\n\tDocumentTools:-SetProperty(output_targets_single[runningtime], value, convert(finish-start, string), 'refresh'):\n\treturn output:\nend proc:\n\nwith(StringTools):\n\nsigmaParser := proc(sigma)\n\tlocal states, state_eqs, outputs, output_eqs;\n\tif SearchText(\"diff\", sigma)>0 then\n\t\tsigma := [map(x->parse(x), Split(sigma, \";\"))]:\n\telse\n\t\tLogExpression(sprintf(\"%q \\n\", Split(sigma, \";\")), \"LogAreaSIAN\"):\n\t\tsigma := Split(sigma, \";\"):\n\t\t\n\t\tstates := map(x->Trim(RegSubs(\"d([a-zA-Z0-9]+)/dt(.*)\" = \"\\\\1\", x)), select(x->SearchText(x, \"/dt\")>0, sigma)):\n\t\tstate_eqs := select(x->Has(x, \"/dt\"), sigma):\n\t\t\n\t\toutputs := map(x->Trim(Split(x, \"=\")[1]), select(x->not Has(x, \"/dt\"), sigma)):\n\t\toutput_eqs := select(x->not SearchText(x, \"/dt\")>0, sigma):\n\t\t\n\t\tstate_eqs := map(x->convert(subs({seq(parse(states[i])=parse(cat(states[i],\"(t)\")), i=1..nops(states))}, parse(x)), string), state_eqs):\n\t\tstate_eqs := map(x->parse(RegSubs(\"d([a-zA-Z0-9]+)/dt(.*)\" = \"diff(\\\\1(t), t)\\\\2\", x)), state_eqs):\n\t\n\t\toutput_eqs := map(x->parse(Subs({seq(outputs[i]=cat(outputs[i],\"(t)\"), i=1..nops(outputs))}, x)), output_eqs):\t\n\t\toutput_eqs := map(x->subs({seq(parse(states[i])=parse(cat(states[i],\"(t)\")), i=1..nops(states))}, x), output_eqs):\n\t\t\n\t\tsigma := [op(state_eqs), op(output_eqs)]:\n\tend if:\n\treturn sigma;\nend proc:\n\n\nDocumentTools:-SetProperty(\"RunningTimeSingle\", value, \"\"):\nDocumentTools:-SetProperty(\"RunningTimeMulti\", value, \"\"):\nDocumentTools:-SetProperty(\"RunningTimeSIAN\", value, \"\"):\n\nDocumentTools:-SetProperty(\"run_system\", enabled, true):\nDocumentTools:-SetProperty(\"Meter_sian\", visible, true):\nDocumentTools:-SetProperty(\"Meter_sian\", value, 0):\nDocumentTools:-SetProperty(\"sigma\", enabled, true):\nDocumentTools:-SetProperty(\"p\", value, \"0.99\"):\nDocumentTools:-SetProperty(\"params\", value, \"\"):\nDocumentTools:-SetProperty(\"replicas\", value, \"1\"):\n\nDocumentTools:-SetProperty(\"p\", enabled, true):\nDocumentTools:-SetProperty(\"params\", enabled, true):\nDocumentTools:-SetProperty(\"replicas\", enabled, true):\nDocumentTools:-SetProperty(\"LogAreaSE\", value, \"\"):\nDocumentTools:-SetProperty(\"LogAreaSIAN\", value, \"\"):\nDocumentTools:-SetProperty(\"LogAreaME\", value, \"\"):\n\nDocumentTools:-SetProperty(\"printSolutions\", enabled, true):\nDocumentTools:-SetProperty(\"printSolutions\", value, true):\n\nDocumentTools:-SetProperty(\"GlobalParams1\", expression, NULL):\nDocumentTools:-SetProperty(\"LocalParams1\", expression, NULL):\nDocumentTools:-SetProperty(\"NoIDParams1\", expression, NULL):\n\nDocumentTools:-SetProperty(\"Parameters\", value, \"\"):\n\nDocumentTools:-SetProperty(\"Bound\", expression, NULL):\nDocumentTools:-SetProperty(\"MultiFunctions\", expression, NULL):\nDocumentTools:-SetProperty(\"SingleFunctions\", expression, NULL):\n\nDocumentTools:-SetProperty(\"use_char\", enabled, true):\nDocumentTools:-SetProperty(\"use_char\", value, false):\nDocumentTools:-SetProperty(\"p_label\", enabled, true):\n\nDocumentTools:-SetProperty(\"ComputeId\", enabled, true):\nDocumentTools:-SetProperty(\"ComputeId\", value, false):\nDocumentTools:-SetProperty(\"bypass\", enabled, false):\n\nDocumentTools:-SetProperty(\"bypass\", value, true):\nDocumentTools:-SetProperty(\"SimplifiedGen\", enabled, false):\nDocumentTools:-SetProperty(\"SimplifiedGen\", value, true):\nDocumentTools:-SetProperty(\"SkipSingle\", enabled, false):\nDocumentTools:-SetProperty(\"SkipSingle\", value, false):\nDocumentTools:-SetProperty(\"Refine\", enabled, false):\nDocumentTools:-SetProperty(\"NoBound\", enabled, false):\nDocumentTools:-SetProperty(\"NoBound\", value, false):\nDocumentTools:-SetProperty(\"UsingUpTo\", enabled, false):\nDocumentTools:-SetProperty(\"MaxPermutations\", enabled, false):\nDocumentTools:-SetProperty(\"Permutations\", enabled, false):\nDocumentTools:-SetProperty(\"RunSIAN\", enabled, true):\nDocumentTools:-SetProperty(\"RunSIAN\", value, true):\nDocumentTools:-SetProperty(\"being_refined\", caption, \"\");\nDocumentTools:-SetProperty(\"sigma\", value, \"dx1/dt = a*x1 + x2*b + u(t);\\ndx2/dt = x2*c + x1;\\ny=x2\"):\nDocumentTools:-SetProperty(\"example_box\", value, \"Custom\"):\nDocumentTools:-SetProperty(reference, value, \"\"):\nDocumentTools:-SetProperty(\"LocalLabel\" , caption, \"Locally Identifiable Paramters\");\nDocumentTools:-SetProperty(TxtOutput, visible, false);\nDocumentTools:-SetProperty(TxtOutput, value, \"\");\nDocumentTools:-SetProperty(SaveOutputLabel, visible, false);\n\nreadyToSave:=false:\ncounter:=0:\nexname:=\"Custom\"", "meta": {"hexsha": "f7e1b4c34b2fed5624c3d62f243e4a3ba1d98a58", "size": 67582, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "src/src.mpl", "max_stars_repo_name": "iliailmer/sian-web-app", "max_stars_repo_head_hexsha": 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"lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8333245787544824, "lm_q2_score": 0.6757645944891558, "lm_q1q2_score": 0.5631312460398694}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(S(t), t) = -b*S(t)*Ninv(t)*A(t)*q - b*S(t)*Ninv(t)*II(t) - b*S(t)*Ninv(t)*J(t),\ndiff(A(t), t) = -E(t)*k*r + E(t)*k - A(t)*g1,\ndiff(E(t), t) = b*S(t)*Ninv(t)*A(t)*q + b*S(t)*Ninv(t)*II(t) + b*S(t)*Ninv(t)*J(t) - E(t)*k,\ndiff(C(t), t) = alpha*II(t),\ndiff(Ninv(t), t) = 0,\ndiff(J(t), t) = alpha*II(t) - g2*J(t),\ndiff(II(t), t) = -alpha*II(t) + E(t)*k*r - g1*II(t),\ny2(t) = Ninv(t),\ny(t) = C(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "5a05570f0f237d1bcd021353897f5f13d3873c64", "size": 507, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/SEAIJRC-Covid-model.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/SEAIJRC-Covid-model.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/SEAIJRC-Covid-model.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 36.2142857143, "max_line_length": 92, "alphanum_fraction": 0.516765286, "num_tokens": 232, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9046505428129514, "lm_q2_score": 0.6224593312018546, "lm_q1q2_score": 0.5631081718507445}} {"text": "`is_element/ICP_alt` := (N::posint) -> (A::set) -> proc(Ru)\n local n,R,u;\n global reason;\n\n n := nops(A);\n if n = 0 then\n reason := [convert(procname,string),\"A is empty\"];\n return false;\n fi;\n\n if not(type(Ru,list) and nops(Ru) = 2) then\n reason := [convert(procname,string),\"Ru is not a list of length two\"];\n return false;\n fi;\n\n R,u := op(Ru);\n\n if not `is_element/ord`(A)(R) then\n reason := [convert(procname,string),\"R is not an order on A\",reason];\n return false;\n fi;\n\n if not(type(u,list(posint)) and\n nops(u) = n-1 and\n max(op(u)) <= N) then\n reason := [convert(procname,string),\"u is not in [1,N]^(n-1)\"];\n return false; \n fi;\n\n return true;\nend:\n\n`is_equal/ICP_alt` := (N::posint) -> (A::set) -> proc(Ru1,Ru2)\n global reason;\n\n if Ru1 <> Ru2 then\n reason := [convert(procname,string),\"Ru1 <> Ru2\",Ru1,Ru2];\n return false;\n fi;\n\n return true;\nend:\n\n`list_elements/ICP_alt` := (N::posint) -> proc(A::set)\n local RR,uu,n,R,u,i;\n\n RR := `list_elements/ord`(A);\n n := nops(A);\n uu := [[]];\n for i from 1 to n-1 do\n uu := [seq(seq([op(u),i],i=1..N),u in uu)];\n od: \n\n return [seq(seq([R,u],u in uu),R in RR)];\nend:\n\n`random_element/ICP_alt` := (N::posint) -> (A::set) -> proc()\n local R,u,i;\n\n R := `random_element/ord`(A)();\n u := [seq(rand(1..N)(),i=1..nops(A)-1)];\n return [R,u];\nend:\n\n`count_elements/ICP_alt` := (N::posint) -> proc(A::set)\n local n;\n\n n := nops(A);\n return n! * N^(n-1);\nend: \n\n\n\n", "meta": {"hexsha": "eaa673e6630b30df9502bccd70975f9844d20540", "size": 1434, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/chains/ICP_alt.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/operads/chains/ICP_alt.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/operads/chains/ICP_alt.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": 19.3783783784, "max_line_length": 72, "alphanum_fraction": 0.5760111576, "num_tokens": 508, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7905303285397349, "lm_q2_score": 0.7122321964553657, "lm_q1q2_score": 0.5630411522604373}} {"text": "\n# Implizite kinematische Zwangsbedingungen für 2D-Picker\n\n# \n# Erklärung des Dateinamens\n# picker2D: 2D-Roboter für Pick&Place\n# m2: Modellierung der geschlossenen Ketten als Parallelogramm\n# IC: Modellierung des Roboters mit impliziten Zwangsbedingungen\n# kinematic_contraints_implizit: Berechnung der kinematischen Zwangsbedingungen (implizite Form)\n# \n# Quelle\n# Aufzeichnungen Schappler, 6.5.2019\n# Ursprüngliche Notizen von Abderahman Bejaoui (Hiwi bei Moritz Schappler)\n# \n# Autor\n# Abderahman Bejaoui\n# Hiwi bei: Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2019-03\n# (C) Institut fuer mechatronische Systeme, Leibniz Universitaet Hannover\n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nkin_constraints_exist := true: # Für Speicherung\n;\nwith(StringTools): # Für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\ncodegen_act := true:\ncodegen_opt := 1: # Geringerer Optimierungsgrad. Sonst zu lange.\ncodegen_debug := 0: # Zur Code-Generierung auch für Nicht-Inert-Ausdrücke\n;\nread \"../helper/proc_MatlabExport\":\nread \"../transformation/proc_rotx\":\nread \"../transformation/proc_roty\":\nread \"../transformation/proc_rotz\":\nread \"../transformation/proc_trotz\":\nread \"../transformation/proc_transl\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\nread \"../helper/proc_intersect_circle\":\nwith(RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env_IC\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name_OL):\n# Ergebnisse der Kinematik laden\nread sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name_OL, base_method_name);\nread \"../robot_codegen_definitions/robot_env_IC\":\nTrf := Trf:\nTrf_c := Trf_c:\n# VGK Gelb 0-7-13-10-4-2-1-0\n# Schleife (0-7)-(7-13)\nT_1_13 := combine( Matrix(Trf(1..4,1..4, 7)) . Matrix(Trf(1..4,1..4,13))):\n# Schleife (0-1)(1-2)-(2-4)-(4-10)\nT_1_10:= combine( Matrix(Trf(1..4,1..4, 1)) . Matrix(Trf(1..4,1..4,2)) . Matrix(Trf(1..4,1..4,4)) . Matrix(Trf(1..4,1..4,10))):\nh1t := T_1_13(1..3,4) - T_1_10(1..3,4):\n\n#tmp := Transpose( Matrix(T_1_13(1..3,1..3)) ) . Matrix(T_1_10(1..3,1..3)); nur anzeigen lassen für h1r\n;\n#combine(tmp);# nur anzeigen lassen für h1r\n;\nh1r := (-qJ7(t)+qJ1(t)+qJ2(t)+qJ4(t)+qJ10(t))+Pi/2:\n# VGK PINK 0-5-14-11-8-1-0\n# Schleife (0-5)-(5-14)\nT_2_14 := combine(Matrix(Trf(1..4,1..4, 5)) . Matrix(Trf(1..4,1..4,14))):\n# Schleife (0-1)-(1-8)-(8-11)\nT_2_11:= combine(Matrix(Trf(1..4,1..4, 1)) . Matrix(Trf(1..4,1..4,8)).Matrix(Trf(1..4,1..4, 11))):\nh2t := T_2_11(1..3,4) - T_2_14(1..3,4):\n#tmp := Transpose( Matrix(T_2_11(1..3,1..3)) ) . Matrix(T_2_14(1..3,1..3)); # nur anzeigen lassen für h1r\n;\n #combine(tmp); # nur anzeigen lassen für h1r\n;\nh2r:=(-qJ1(t)-qJ8(t)-qJ11(t)+phi05+qJ5(t)):\n# VGK GRÜN 2-6-12-15-9-3\n# Schleife (2-6)-(6-12)\nT_2_12 := combine( Matrix(Trf(1..4,1..4, 6)) . Matrix(Trf(1..4,1..4,12))):\n# Schleife (2-3)-(3-9)-(9-15)\nT_2_15:= combine( Matrix(Trf(1..4,1..4, 3)) . Matrix(Trf(1..4,1..4,9)).Matrix(Trf(1..4,1..4,15)) ):\nh3t := T_2_12(1..3,4) - T_2_15(1..3,4):\n#tmp := Transpose( Matrix(T_2_12(1..3,1..3)) ) . Matrix(T_2_15(1..3,1..3)); nur anzeigen lassen für h2r\n;\n#combine(tmp); nur anzeigen lassen für h3r\n;\nh3r:=(qJ6(t)+qJ12(t)-qJ3(t)-qJ9(t)):\n# Zusätzliche Zwangsbedingung (6 und 8 sind gleiche Körper)\n# TODO: In einer neuen Modellierung sollten beide Körper zusammengefasst werden.\nh4:=Pi/2 - qJ8(t) - qJ9(t) + qJ2(t):\n# Zusammenstellen aller Zwangsbedingungen\nimplconstr_t := ; # TODO: In h1r, h2r, h3r muss das richtige drinstehen.\nimplconstr_s := convert_t_s(implconstr_t):\n# Exportiere Code für folgende Skripte\nkin_constraints_exist:=true:\nsave implconstr_t, implconstr_s, kin_constraints_exist, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_implicit_maple.m\", robot_name):\n# Exportieren des vollständigen Ausdruckes\nif codegen_act then\n MatlabExport(implconstr_s, sprintf(\"../codeexport/%s/tmp/kinconstr_impl_matlab.m\", robot_name), 2):\nend if:\n# Liste mit abhängigen konstanten Kinematikparametern erstellen (wichtig für Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\nkc_symbols := Matrix(list_constant_expressions( implconstr_s )):\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_implicit_constraints_symbols_list_maple\", robot_name):\nMatlabExport(Transpose(kc_symbols), sprintf(\"../codeexport/%s/tmp/kinematic_implicit_constraints_symbols_list_matlab.m\", robot_name), 2):\n\n", "meta": {"hexsha": "f7e362af32626b211953f5574ed66c4ebfc11731", "size": 4795, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "systems/picker2Dm2/codegen/picker2Dm2IC_kinematic_constraints_implicit.mpl", "max_stars_repo_name": "SchapplM/robsynth-serhybroblib", "max_stars_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/picker2Dm2/codegen/picker2Dm2IC_kinematic_constraints_implicit.mpl", "max_issues_repo_name": "SchapplM/robsynth-serhybroblib", "max_issues_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/picker2Dm2/codegen/picker2Dm2IC_kinematic_constraints_implicit.mpl", "max_forks_repo_name": "SchapplM/robsynth-serhybroblib", "max_forks_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": 45.6666666667, "max_line_length": 144, "alphanum_fraction": 0.7236704901, "num_tokens": 1790, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.815232489352, "lm_q2_score": 0.689305616785446, "lm_q1q2_score": 0.5619443338963149}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-8-input.txt\" ):\n\nlines := subs(\"\"=NULL,(op@StringTools:-Split)~(StringTools:-Split(input, \"\\n\"),\"|\"));\n\n# part 1, just count the 1, 4, 7, and 8s\ntotal := 0:\nfor i from 2 to nops(lines) by 2 do\n tal := table(sparse=0,Statistics:-Tally(map(length, StringTools:-Split(lines[i]))));\n total := total + tal[2] + tal[3] + tal[4] + tal[7];\nend do:\n\nanswer1 := total;\n\n# part 2\n\nDecode := proc( code, output )\n\n local decode := table();\n # inputs are sets of letters so we can use set operations on everything\n local displays := { ({op@StringTools:-Explode})~(\n StringTools:-Split(StringTools:-Trim(code),\" \"))[] };\n\n # easy cases - unique lengths\n decode[\"1\"] := select(d->nops(d)=2, displays)[1];\n decode[\"4\"] := select(d->nops(d)=4, displays)[1];\n decode[\"7\"] := select(d->nops(d)=3, displays)[1];\n decode[\"8\"] := select(d->nops(d)=7, displays)[1];\n\n local sixes := select(d->nops(d)=6, displays);\n local fives := select(d->nops(d)=5, displays);\n\n # length six 0, 6, 9\n # 6 is disjoint from 1\n decode[\"6\"] := select(d->not decode[\"1\"] subset d, sixes)[1];\n # 9 contains 4\n decode[\"9\"] := select(d->decode[\"4\"] subset d, sixes)[1];\n # otherwise 0 - 0 contains 7 also works\n decode[\"0\"] := op(1,sixes minus {decode[\"6\"], decode[\"9\"]});\n\n # length five 2,3,5\n # 3 contains 1\n decode[\"3\"] := select(d->decode[\"1\"] subset d, fives)[1];\n # 5 is contained in 6\n decode[\"5\"] := select(d->d subset decode[\"6\"], fives)[1];\n # otherwise 2 \n decode[\"2\"] := op(1,fives minus {decode[\"5\"], decode[\"3\"]});\n\n local decodsubs := sort((rhs=lhs)~([entries(decode,pairs)]));\n\n local outs := ({op@StringTools:-Explode})~(\n StringTools:-Split(StringTools:-Trim(output),\" \"));\n\n return parse(StringTools:-Join(subs(decodsubs, outs),\"\"));\n\nend proc: # Decode\n\nanswer2 := add( Decode(lines[i], lines[i+1]), i=1..nops(lines), 2);\n", "meta": {"hexsha": "67505a9977bc2afe22e73cb7ddfa7dbad11f65cd", "size": 1944, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day8/AoC8-Maple-cleaner.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day8/AoC8-Maple-cleaner.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day8/AoC8-Maple-cleaner.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 33.5172413793, "max_line_length": 88, "alphanum_fraction": 0.5905349794, "num_tokens": 632, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581000631541, "lm_q2_score": 0.7057850278370112, "lm_q1q2_score": 0.5615635743018167}} {"text": "PotraShi := module()\n\n description \"linesearch\"\n \"Efficient Line Search Algorithm for Unconstrained Optimization\"\n \"F. A. POTRA AND Y.SHI\"\n \"JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS\"\n \"Vol.85,No.3,pp.677-704,1995\";\n\n # Module defined as a package (i.e.) collection of procedures\n option package, load = ModuleLoad, unload = ModuleUnLoad;\n\n export lines, linesearch_A2, esatta, AB_list, doplot, doplot2;\n \n local ModuleLoad,\n ModuleUnLoad,\n _debug,\n min_quadratic,\n min_cubic,\n sigma, rho, tau1, tau2, tau3, Jbig,\n max_iter, A_list, B_list;\n\n uses LinearAlgebra;\n\n ModuleUnLoad := proc()\n printf(\"PotraShi unload\\n\");\n NULL;\n end proc:\n\n ModuleLoad := proc()\n printf(\"PotraShi load\\n\");\n _debug := true;\n rho := 0.25;\n sigma := 0.75;\n tau1 := 0.1;\n tau2 := 0.49;\n tau3 := 2.5;\n Jbig := 2;\n max_iter := 40;\n NULL;\n end proc;\n \n # Explicitly call ModuleLoad here so the type is registered when this\n # code is cut&pasted in. ModuleLoad gets called when the module is\n # read from the repository, but the code used to define a module\n # (like the command below) is not called at library read time.\n ModuleLoad();\n\n AB_list := proc()\n A_list, B_list;\n end proc;\n\n min_quadratic := proc ( a, fa, Dfa, b, fb )\n local t, delta; # A+B*(x-a)+C*(x-a)^2\n # p = fa + Dfa*(x-a)+t*(x-a)^2\n # p' = Dfa+2*t*(x-a)\n ##t := ((fb-fa)/(b-a)-Dfa)/(b-a);\n ##delta := -Dfa/(2*t);\n t := (fb-fa)/(b-a)-Dfa;\n delta := max(tau1,min(1-tau1,-Dfa/(2*t)));\n a+(b-a)*delta;\n end proc;\n\n lines := proc( f0, df0, L )\n [ [0,f0], [L,f0+L*rho*df0] ], [ [0,f0], [L,f0+L*sigma*df0] ];\n end proc;\n\n linesearch_A2 := proc( f_in, df_in )\n local f, df, a, b, c, alpha,\n fa, dfa, fb, fc,\n r_df0, s_df0,\n f0, df0, df1, t1, t2, delta, k;\n\n f := x->evalf(f_in(x));\n df := x->evalf(df_in(x));\n\n alpha := 1;\n a := 0;\n b := 1;\n fa := f(0);\n fb := f(1);\n df0 := df(0);\n\n if df0 >= 0 then\n error \"[linesearch_A2] df0 = %1 must be < 0!\\n\", df0;\n end;\n\n r_df0 := rho*df0;\n s_df0 := sigma*df0;\n f0 := fa;\n\n A_list := [];\n B_list := [];\n\n # step 1 (check alpha = 1)\n if fb <= f0 + r_df0 then\n if sigma > 0.5 then\n if fb >= f0 + s_df0 then\n if _debug then\n printf(\"[step1] return 1 (a case)\\n\");\n end;\n return 1;\n end;\n else\n df1 := df(1);\n if df1 >= s_df0 then\n if _debug then\n printf(\"[step1] return 1 (b case)\\n\");\n end;\n return 1;\n end;\n end;\n # step 2\n if _debug then\n if sigma > 0.5 then\n printf(\n \"\\n[step2] now\\n\"\n \"f(1) [%g] <= f(0)+rho*f'(0) [%g]\\n\"\n \"and f(1) [%g] < f(0)+sigma*f'(0) [%g]\\n\",\n fb, f0 + r_df0,\n fb, f0 + s_df0\n );\n else\n printf(\n \"\\n[step2] now\\n\"\n \"f(1) [%g] <= f(0)+rho*f'(0) [%g]\\n\"\n \"and f'(1) [%g] < sigma*f'(0) [%g]\\n\",\n fb, f0 + r_df0,\n df1, s_df0\n );\n end;\n end;\n a := 1;\n b := Jbig;\n A_list := [op(A_list), a];\n B_list := [op(B_list), b];\n fa := fb;\n fb := f(b);\n while fb <= fa + (b-a)*r_df0 do\n\n if fb >= fa + (b-a)*s_df0 then\n if _debug then\n printf( \"[step2] return b = %g\\n\", b );\n end;\n return b;\n end;\n\n a := b;\n b := Jbig*b;\n fa := fb;\n fb := f(b);\n\n if _debug then\n printf( \"[step2] a=%g b=%g f(a)=%g f(b)=%g\\n\", a, b, fa, fb );\n end;\n\n A_list := [op(A_list), a];\n B_list := [op(B_list), b];\n\n if a > 1000 then\n error \"a too big\\n\";\n end;\n end;\n else\n printf(\n \"\\n[step2] case\\n\"\n \"f(1) [%g] > f(0)+rho*f'(0) [%g]\\n\",\n fb, f0 + r_df0\n );\n end;\n \n # aggiunta ad algoritmo\n if a > 0 then\n dfa := df(a);\n if dfa >= 0 then\n if _debug then\n printf(\"[step3] return a = %g (added)\\n\", a);\n end;\n return a;\n end;\n else\n dfa := df0;\n end;\n\n # step 3\n if _debug then\n printf(\n \"\\n[step3] a=%g b=%g with f(0)=%g, f(a)=%g, f'(a)=%g\\n\"\n \"f(a) [%g] <= f(0)+a*rho*f'(0) [%g]\\n\"\n \"and f(b) [%g] > f(a)+(b-a)*sigma*f'(0) [%g]\\n\",\n a, b, f0, fa, dfa,\n fa, f0 + a*r_df0,\n fb, fa + (b-a)*s_df0\n );\n end;\n\n for k from 1 to max_iter do\n\n c := min_quadratic( a, fa, dfa, b, fb );\n #c := (a+b)/2;\n fc := f(c);\n\n if fc <= fa + (b-a)*r_df0 and fc >= fa + (b-a)*s_df0 then\n if _debug then\n printf(\"[step3] return c = %g (case a)\\n\", c);\n end;\n return c;\n end;\n\n t1 := (fb-fc)/(b-c);\n t2 := (fc-fa)/(c-a);\n delta := abs( (t1-t2)/(b-a) );\n\n if fc <= fa + (c-a)*r_df0 then\n if (rho-sigma)*df0 >= tau3*(b-a)*delta then\n if _debug then\n printf(\"[step3] return c = %g (case b)\\n\", c);\n end;\n return c;\n end;\n a := c;\n fa := fc;\n dfa := df(c);\n else\n if (rho-sigma)*df0 >= tau3*(b-a)*delta and a > 0 then\n if _debug then\n printf(\"[step3] return a = %g\\n\", a);\n end;\n return a;\n end;\n b := c;\n fb := fc;\n end;\n\n A_list := [op(A_list), a];\n B_list := [op(B_list), b];\n\n if _debug then\n printf(\n \"[step3] a=%.4g b=%.4g f(a)=%.4g f'(a)=%.4g f(b)=%.4g f'(b)=%.4g\\n\",\n a, b, fa, dfa, fb, df(b)\n );\n end;\n\n if a > 1000 then\n error \"a = %1\\n\", a;\n end;\n end;\n\n printf(\"[step3] search failed\\n\");\n return NULL;\n \n end proc;\n\n esatta := proc( fun )\n local res, alpha;\n #res := Optimization[Minimize](\n res := Optimization[NLPSolve](\n fun(alpha),\n {alpha >= 0, alpha <= 3},\n #initialpoint={alpha=1},\n iterationlimit=50\n ):\n subs(res[2],alpha);\n end proc:\n\n doplot := proc( f_in, df_in, alpha, amax)\n local f0, df0, x, AA, BB, CC, DD;\n f0 := evalf(f_in(0));\n df0 := evalf(df_in(0));\n\n AA := plot(f_in(x),x=0..amax);\n BB := plot([[0,f0],[amax,f0+amax*rho*df0]],color=\"LimeGreen\");\n CC := plot([[0,f0],[amax,f0+amax*sigma*df0]],color=\"blue\");\n DD := plot([[alpha,f_in(alpha)]],color=\"red\",style = point);\n display(AA,BB,CC,DD);\n end;\n\n doplot2 := proc( f_in, df_in, alpha, amax, A_list, B_list )\n local i, f0, df0, x, AA, BB, CC, DD, EE;\n f0 := evalf(f_in(0));\n df0 := evalf(df_in(0));\n\n AA := plot(f_in(x),x=0..amax);\n BB := plot([[0,f0],[amax,f0+amax*rho*df0]],color=\"LimeGreen\");\n CC := plot([[0,f0],[amax,f0+amax*sigma*df0]],color=\"blue\");\n DD := plot([[alpha,f_in(alpha)]],color=\"red\",style = point);\n EE := plot([seq([[A_list[i],-i/5],[B_list[i],-i/5]],i=1..nops(A_list))],color=\"black\");\n display(AA,BB,CC,DD,EE);\n end;\n\nend module:\n", "meta": {"hexsha": "e63a42140491f2977157fdfbb44f7d59c10ebc21", "size": 7197, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NL-PotraShi.mpl", "max_stars_repo_name": "ebertolazzi/NLtoolbox", "max_stars_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_stars_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-28T09:12:53.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-28T09:12:53.000Z", "max_issues_repo_path": "maple/NL-PotraShi.mpl", "max_issues_repo_name": "ebertolazzi/NLtoolbox", "max_issues_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_issues_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/NL-PotraShi.mpl", "max_forks_repo_name": "ebertolazzi/NLtoolbox", "max_forks_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_forks_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.647260274, "max_line_length": 91, "alphanum_fraction": 0.4536612477, "num_tokens": 2517, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7577943712746406, "lm_q2_score": 0.7401743620390163, "lm_q1q2_score": 0.5608999653149646}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(N(t), t) = -delta_NE*N(t)*P(t) - mu_N*N(t),\ndiff(S(t), t) = -mu_LE*S(t)*E(t) + delta_EL*S(t) - S(t)^2*mu_LL - S(t)*delta_LM,\ndiff(M(t), t) = S(t)*delta_LM - M(t)*mu_M,\ndiff(P(t), t) = rho_P*P(t)^2 - S(t)*P(t)*mu_PL - E(t)*mu_PE*P(t) - P(t)*mu_P,\ndiff(E(t), t) = -mu_EE*E(t)^2 + delta_NE*N(t)*P(t) - delta_EL*E(t) + E(t)*P(t)*rho_E,\ny1(t) = N(t),\ny3(t) = M(t),\ny2(t) = S(t) + E(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "5f2bfc3d1b37e60a6716f0c728fe0c3d919d2a30", "size": 496, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/CD8-T-cell-differentiation.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/CD8-T-cell-differentiation.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/CD8-T-cell-differentiation.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 38.1538461538, "max_line_length": 85, "alphanum_fraction": 0.5544354839, "num_tokens": 219, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391579526935, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5608969006014168}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2019 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(* Equation 28 squared with Equation 25 built in *)\ntpss_xi2 := (z, xt, xs0, xs1) ->\n (1 - z^2)*(t_total(z, xs0^2, xs1^2) - xt^2)/(2*(3*Pi^2)^(1/3))^2:\n\n(* Equation 33 *)\ntpss_C00 := (cc, z) ->\n + add(cc[i]*z^(2*(i-1)), i=1..4):\n\n(* Equation 34 *)\n(* The series expansion of C0 for z -> +- 1 goes as C + D*(1+-z)^(2/3) + O(1+-z)\n whose first derivative seems to diverge for ferromagnetic densities, leading\n to severe numerical instabilities. I can not correct for the bad design of\n the functional, and this is the possible solution that I found *)\ntpss_C0_den := (z, xt, xs0, xs1) ->\n 1 + tpss_xi2(z, xt, xs0, xs1)*((1 + z)^(-4/3) + (1 - z)^(-4/3))/2:\ntpss_C0 := (cc, z, xt, xs0, xs1) -> my_piecewise3(1 - m_abs(z) <= 1e-12,\n add(cc[i], i=1..4),\n tpss_C00(cc, z) / tpss_C0_den(z_thr(z), xt, xs0, xs1)^4):\n\n(* Equation 11, with tau_W from Equation 12 *)\ntpss_aux := (z, xt, ts0, ts1) ->\n m_min(xt^2/(8*t_total(z, ts0, ts1)), 1):\n\n(* n_sigma/n \\epsilon^sigma in Equation 25 *)\ntpss_par_s0 := (f_gga, rs, z, xt, xs0, xs1) ->\n m_max(f_gga(rs*(2/(1 + z))^(1/3), 1, xs0, xs0, 0), f_gga(rs, z, xt, xs0, xs1))*(1 + z)/2:\ntpss_par_s1 := (f_gga, rs, z, xt, xs0, xs1) ->\n m_max(f_gga(rs*(2/(1 - z))^(1/3), -1, xs1, 0, xs1), f_gga(rs, z, xt, xs0, xs1))*(1 - z)/2:\n\n(* Second line of Equation 25 *)\n(* The screening of the density is important in order to stabilize this functional\n for ferromagnetic densities *)\ntpss_par := (f_gga, rs, z, xt, xs0, xs1, ts0, ts1) ->\n - (1 + tpss_C0(params_a_C0_c, z, xt, xs0, xs1))*tpss_aux(z, xt, ts0, ts1)^2*(\n + my_piecewise3(screen_dens_zeta(rs, z),\n f_gga(rs, z_thr(z), xt, xs0, xs1)*(1 + z)/2,\n tpss_par_s0(f_gga, rs, z_thr(z), xt, xs0, xs1)\n )\n + my_piecewise3(screen_dens_zeta(rs, -z),\n f_gga(rs, z_thr(z), xt, xs0, xs1)*(1 - z)/2,\n tpss_par_s1(f_gga, rs, z_thr(z), xt, xs0, xs1)\n )\n ):\n\n(* First line of Equation 25 *)\ntpss_perp := (f_gga, rs, z, xt, xs0, xs1, ts0, ts1) ->\n (1 + tpss_C0(params_a_C0_c, z, xt, xs0, xs1)*tpss_aux(z, xt, ts0, ts1)^2)\n * f_gga(rs, z, xt, xs0, xs1):\n\n(* Equation in full 25 *)\ntpss_f0 := (f_gga, rs, z, xt, xs0, xs1, ts0, ts1) ->\n + tpss_par (f_gga, rs, z, xt, xs0, xs1, ts0, ts1)\n + tpss_perp(f_gga, rs, z, xt, xs0, xs1, ts0, ts1):\n\n(* Equation 24 *)\ntpss_f := (f_gga, rs, z, xt, xs0, xs1, ts0, ts1) ->\n + tpss_f0(f_gga, rs, z, xt, xs0, xs1, ts0, ts1)\n * (1 + params_a_d*tpss_f0(f_gga, rs, z, xt, xs0, xs1, ts0, ts1)*tpss_aux(z, xt, ts0, ts1)^3):\n", "meta": {"hexsha": "733e1a1d5640a62341d93b68e477d1044dc2308b", "size": 2754, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/tpss_c.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/tpss_c.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/tpss_c.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": 40.5, "max_line_length": 95, "alphanum_fraction": 0.5922294844, "num_tokens": 1158, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026573249611, "lm_q2_score": 0.611381973294151, "lm_q1q2_score": 0.5608223087433031}} {"text": "######################################################################\n\n`is_element/linord` := (A::set) -> proc(L)\n global reason;\n\n if not type(L,list) then\n reason := [\"is_element/linord\",\"L is not a list\",L];\n return false;\n fi;\n\n if nops(L) <> nops(A) then \n reason := [\"is_element/linord\",\"L does not the same length as A\",L,A];\n return false;\n fi;\n \n if {op(L)} <> A then\n reason := [\"is_element/linord\",\"L is not an enumeration of A\",L,A];\n return false;\n fi;\n \n return true;\nend;\n\n######################################################################\n\n`is_equal/linord` := (A::set) -> proc(L0,L1)\n return evalb(L0 = L1);\nend;\n\n######################################################################\n\n`op/linord` := (A::set) -> proc(L)\n local n,i;\n n := nops(A);\n return [seq(L[n-i],i=0..n-1)];\nend;\n\n`res/linord` := (A::set,B::set) -> proc(L)\n return select(a -> member(a,B),L);\nend:\n\n######################################################################\n\n`flip/linord` := (A::set) -> (L) -> proc(a)\n local n,i;\n n := nops(L);\n if n <= 1 then return L; fi;\n i := 1;\n while i <= n and L[i] <> a do i := i+1; od;\n if i > n then error(\"a is not in L\"); fi;\n return [op(i..n,L),op(1..i-1,L)];\nend:\n\n`loop/linord` := (A::set) -> (L) -> L;\n\n######################################################################\n\n`random_element/linord` := (A::set) -> proc()\n return combinat[randperm](A);\nend:\n\n`list_elements/linord` := proc(A::set)\n return combinat[permute](A);\nend:\n\n`count_elements/linord` := proc(A::set)\n return nops(A) !;\nend:\n\n######################################################################\n\n`linord_is_leq` := (A::set) -> (L) -> proc(a,b)\n local x;\n for x in L do\n if x = a then return true; fi;\n if x = b then return false; fi;\n od;\n error(\"Neither a nor b is in L\");\nend:\n\n`linord_is_less` := (A::set) -> (L) -> proc(a,b)\n return evalb((a <> b) and `linord_is_leq`(A)(L)(a,b));\nend:\n\n\n", "meta": {"hexsha": "1a5c53ab74d57fb571ac4d08fc3bc1cf2f8e3168", "size": 1915, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/linord.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/linord.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/linord.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": 22.2674418605, "max_line_length": 72, "alphanum_fraction": 0.4433420366, "num_tokens": 561, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7662936430859597, "lm_q2_score": 0.7310585727705127, "lm_q1q2_score": 0.5602055370375384}} {"text": "\n# Berechne kinematische Zwangsbedingungen für aufgestellte Viergelenkkette\n# Einleitung\n\n# Die kinematischen Zwangsbedingungen werden als Ersetzungsausdruck für die abhängigen Winkel aufgestellt.\n# \n# fourbar1turnTE -> Viergelenkkette, Modellierung der Zwangsbedingungen mit Ausdrücken für trigonometrische Elimination. Drehbar aufgestellt mit zusätzlichem Gelenk\n# kinematic_constraint -> Kinematische Zwangsbedingungen\n# \n# TODO: Fertige Ergebnisse von Viergelenkkette laden und nicht hier neu berechnen.\n# Quelle\n# SA Bejaoui: Bejaoui2018_S749; \"Modellierung kinematischer Zwangsbedingungen für hybride serielle Roboter mit planaren Parallelmechanismen\"\n# SA Shan: Shan2019_S828, \"Reduktion der Modellkomplexität von seriell-hybriden Palettierrobotern\"\n# Autor\n# Weipu Shan (Studienarbeit), Abderahman Bejaoui (Vorlage fourbar1), Moritz Schappler (Korrekturen)\n# Studienarbeit bei: Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2018-08\n# (C) Institut fuer Mechatronische Systeme, Leibniz Universitaet Hannover\n# \n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nkin_constraints_exist := true: # Für Speicherung\n;\nwith(StringTools): # Für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\n#with(ListTools):\ncodegen_act := true:\ncodegen_opt := 1: # Geringerer Optimierungsgrad. Sonst zu lange.\ncodegen_debug := 0: # Zur Code-Generierung auch für Nicht-Inert-Ausdrücke\n;\nread \"../helper/proc_MatlabExport\":\nread \"../transformation/proc_rotx\":\nread \"../transformation/proc_roty\":\nread \"../transformation/proc_rotz\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\nread \"../helper/proc_intersect_circle\":\nwith(RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\n\n# Variable mit Winkeln der Nebenstruktur nur in Abhängigkeit der verallgemeinerten Koordinaten\nkintmp_qs := Matrix(RowDimension(kintmp_s),1):\nkintmpD_t:=diff~(kintmp_t,t):\nkintmpD_s:=Matrix(< etaD_s, xiD_s, rhoD_s>):\n# Konstante Winkel bereits hineinschreiben ( Keine für Viergelenkkette)\nfor i from 1 to RowDimension(kintmp_s) do\n if diff(kintmp_s(i,1), t) = 0 then\n kintmp_qs(i,1) := kintmp_s(i,1):\n end if:\nend do:\n# Variablen definieren für die Hilfswinkel\n# \n# Ersetzungsausdrücke definieren.\n# Speichere Sinus und Cosinus der Winkel direkt ab, da diese in den Rotationsmatrizen direkt auftreten.\n# Spalte 1: Zu suchender Ausdruck (sin oder cos eines Winkels)\n# Spalte 2: Einzusetzender Ausdruck.\n# Dadurch werden arctan-Ausdrücke in der direkten Kinematik reduziert.\n# Ähnliches Vorgehen wie in [1].\nkintmp_subsexp := Matrix(2*RowDimension(kintmp_s),2):\nfor i from 1 to RowDimension(kintmp_s) do\n kintmp_subsexp(2*i-1, 1) := sin(kintmp_s(i,1)):\n kintmp_subsexp(2*i, 1) := cos(kintmp_s(i,1)):\n # Initialisierung der rechten Spalte mit gleichen Werten. Später nur Ersetzung, wenn Vorteilhaft.\n kintmp_subsexp(2*i-1, 2) := kintmp_subsexp(2*i-1, 1):\n kintmp_subsexp(2*i, 2) := kintmp_subsexp(2*i, 1):\nend do:\nprintf(\"Beginn der Berechnungen. %s\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nst := time():\n# Reihenfolge, in der die Winkel der Parallelstruktur berechnet werden. Hilft beim exportieren von Code, wenn beim Debuggen in der gleichen Reihenfolge ausgegeben wird.\nReihenfolge_kintmp := <1;3;2>:\n# Zwangsbedingung mit Kreisschnittpunkt C zur Bestimmung von rho\nr_p1:= < l1 , 0 >: # Punkt B\n;\nr_p2:= < l2*cos(qJ2s) , l2*sin(qJ2s)> : # Punkt D\n;\nr1:=l4:\nr2:=l3:\nA:=intersect_circle(r_p1, r_p2, r1, r2):\nr_s1x:=simplify(A(1,1),trig):\nr_s1y:=simplify(A(2,1),trig):\nr_acx:=l2*cos(qJ2s) + l3*(-cos(rho_s)*cos(qJ2s)+sin(rho_s)*sin(qJ2s)): # aus Homogener Trafo\n;\nr_acy:=l2*sin(qJ2s)- l3*(cos(rho_s)*sin(qJ2s)+sin(rho_s)*cos(qJ2s)): # aus Homogener Trafo\n;\nf1:=r_s1x-r_acx=0: # GL1\n;\nf2:=r_s1y-r_acy=0: # GL2\n;\n# Zwangsbedingungen für eta , zweiter Weg zum Kreisschnittpunkt C\nr_acx2:=l1-l4*cos(eta_s):\nr_acy2:=l4*sin(eta_s):\nf11:=r_s1x-r_acx2=0: # GL3\n;\nf12:=r_s1y-r_acy2=0: # GL4\n;\n# Zwangsbedingungen für xi , zwei Wege zum Punkt D\nr_adx1:=l2*cos(qJ2s):\nr_ady1:=l2*sin(qJ2s):\nr_adx2:=l1-l4*cos(eta_s)+l3*(cos(eta_s)*cos(xi_s)-sin(eta_s)*sin(xi_s)):\nr_ady2:=l4*sin(eta_s)-l3*(cos(eta_s)*sin(xi_s)+sin(eta_s)*cos(xi_s)): # hier schon einen Fehler erkannt\n;\nf21:=r_adx1-r_adx2=0: # GL5\n;\nf22:=r_ady1-r_ady2=0: # GL6\n;\n# Bestimme Winkel\nsol:=simplify(solve({f1,f2},[cos(rho_s),sin(rho_s)]),trig):\nsol:=op(sol):\ncos(rho_s):=simplify(rhs(sol[1]),trig):\nsin(rho_s):=simplify(rhs(sol[2]),trig):\n# eta bestimmen\nsol1:=solve({f11,f12},{cos(eta_s),sin(eta_s)}): \nassign(sol1):\ncos(eta1_s):=simplify(rhs(sol1[1]),trig): \nsin(eta1_s):=simplify(rhs(sol1[2]),trig):\n# xi bestimmen\nsol2:=solve({f21,f22},{cos(xi_s),sin(xi_s)}):\nsol2:=op(sol2):\ncos(xi_s):=simplify(rhs(sol2[1]),trig):\nconvert_s_t(cos(xi_s)):\nsin(xi_s):=simplify(rhs(sol2[2]),trig):\ncos(eta_s):=-cos(eta1_s):\nsin(eta_s):=sin(eta1_s):\n# kintmp_subsexp\nkintmp_subsexp(1,2):=sin(rho_s):\nkintmp_subsexp(2,2):=cos(rho_s):\nkintmp_subsexp(3,2):=sin(eta_s):\nkintmp_subsexp(4,2):=cos(eta_s):\nkintmp_subsexp(5,2):=sin(xi_s):\nkintmp_subsexp(6,2):=cos(xi_s):\n# Kintmp_qs\nkintmp_qs(1,1):=arctan(sin(rho_s),cos(rho_s)):\nkintmp_qs(2,1):=arctan(sin(eta_s),cos(eta_s)):\nkintmp_qs(3,1):=arctan(sin(xi_s),cos(xi_s)):\n# Exportiere Code für folgende Skripte\nkintmp_qt := convert_s_t(kintmp_qs):\n# Speichere Maple-Ausdruck (Eingabe-Format und internes Format)\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple\", robot_name):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple.m\", robot_name):\nprintf(\"Ausdrücke für kintmp_subsexp gespeichert (Maple). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\nfor i from 1 to RowDimension(kintmp_s) do\n tmp := kintmp_qs(i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d\", robot_name, i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d.m\", robot_name, i):\nend do:\nsave kin_constraints_exist, kintmp_qs, kintmp_qt,kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert\", robot_name):\nsave kin_constraints_exist, kintmp_qs, kintmp_qt, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nsave kintmp_qs, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_qs_maple_inert\", robot_name):\nprintf(\"Ausdrücke mit Inert-Arctan exportiert (Matlab). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Liste mit abhängigen konstanten Kinematikparametern erstellen (wichtig für Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\nkc_symbols := Matrix(list_constant_expressions( kintmp_subsexp ));\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_maple\", robot_name):\nMatlabExport(kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_matlab.m\",robot_name),2);\nprintf(\"Fertig. %s. 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YES\n2. YES", "lm_q1_score": 0.8596637577007393, "lm_q2_score": 0.6513548714339145, "lm_q1q2_score": 0.5599461763735608}} {"text": "# # Computation for the equivariant cohomology of G/B\r\n# # by Shizuo Kaji\r\n\r\n# it requires coxeter and weyl package by J.Stembridge\r\n# http://www.math.lsa.umich.edu/~jrs/maple.html\r\n\r\n# symbols\r\n# e(i), a[i]: elements in H^*(BT) in abstract coordinate and root coordinate\r\n# x[i], z[i]: elements in H^*(G/T) in abstract coordinate and root coordinate\r\n\r\n# look at the demo worksheet \"BGGT_example.mw\" for the details.\r\n\r\nwith(coxeter); with(weyl);with(WeylOps);\r\n\r\n# decompose a word into products of smaller words\r\n# used in \"double\"\r\ndecomp := proc(weyl::list) local L, i, temp;\r\n if nops(weyl)=1 then return {[weyl]}; end if;\r\n temp:={};\r\n for i in descent(weyl) do\r\n for L in procname(weyl.[i]) do\r\n if nops(L)=1 then\r\n\t temp:={op(temp), [op(L),[i]], [L[1].[i]]};\r\n else\r\n temp:={op(temp), [op(L),[i]], [op(1..-2,L),L[-1].[i]]};\r\n end if;\r\n end do;\r\n end do;\r\n return temp;\r\nend proc:\r\n\r\n# Enumerate subwords of \"longweyl\" which is equal to \"weyl\"\r\nsubwords := proc(weyl::list, longweyl::list) local i,L,W; global R;\r\n W := {};\r\n for L in combinat[choose]([seq(i,i=1..nops(longweyl))],nops(weyl)) do\r\n if reduce([seq(longweyl[i],i=L)], R)=weyl then\r\n\t W:=W union {L};\r\n end if;\r\n end do;\r\n return W;\r\nend proc;\r\n\r\n## Utility Functions\r\n# convert between e-poly and z-poly\r\ne2x := proc(f::polynom);\r\n\treturn eval(f,[seq(e(j)=x[j], j = 1 .. dimr(R))]);\r\nend proc:\r\nx2e := proc(f::polynom);\r\n\treturn eval(f,[seq(x[j]=e(j) , j = 1 .. dimr(R))]);\r\nend proc:\r\ne2u := proc(f::polynom);\r\n\treturn eval(f,[seq(e(j)=u[j], j = 1 .. dimr(R))]);\r\nend proc:\r\n\r\n# convert between a-poly and z-poly\r\na2z := proc(f::polynom);\r\n\treturn eval(f,[seq(a[j]=z[j], j = 1 .. rank(R))]);\r\nend proc:\r\n\r\n# BGG operator on GKM poly\r\nBGG_GKM := proc(rt::integer, f::list(polynom), LR::symbol := 'R') local j,k,ff,v,u; global reduw, R, B, optype; option remember;\r\n ff := [seq(0,j=1..nops(reduw))];\r\n if LR='R' then\r\n\tfor j from 1 to nops(reduw) do\r\n\t\tu := reflect(seq(B[reduw[j][k]],k=1..nops(reduw[j])),B[rt]);\r\n\t\tmember(reduw[j].[rt],reduw,'v');\r\n if optype = 'e' then\r\n ff[j] := -simplify((f[j] - f[v])/u);\r\n else\r\n ff[j] := -simplify((f[j] - f[v])/e2a(u));\r\n end if;\r\n\tend do;\r\n elif LR='L' then\r\n\tfor j from 1 to nops(reduw) do\r\n\t\tmember([rt].reduw[j], reduw,'v');\r\n if optype = 'e' then\r\n ff[j]:=simplify((f[j]-subs({seq(e(i)=reflect(B[rt],e(i))\r\n ,i=1..dimr(R))},f[v]))/B[rt]);\r\n else\r\n ff[j]:=simplify((f[j]-subs({seq(a[i]=e2a(reflect(B[rt],B[i]))\r\n ,i=1..nops(B))},f[v]))/a[rt]);\r\n end if;\r\n\tend do;\r\n end if;\r\n return ff;\r\nend proc:\r\n\r\n# BGG on double polynomials\r\nBGGT_e := proc(rt::integer, f::polynom, LR::symbol := 'R')\r\n if LR='R' then\r\n return -simplify((f - act([rt], f))/e2x(B[rt]));\r\n else\r\n return simplify((f - act([rt], f, 'L'))/B[rt]);\r\n end if;\r\n return -infinity;\r\nend proc;\r\n#\r\nBGGT_a := proc(rt::integer, f::polynom, LR::symbol := 'R')\r\n if LR='R' then\r\n return -simplify((f - act([rt], f))/z[rt]);\r\n else\r\n return simplify((f - act([rt], f, 'L'))/a[rt]);\r\n end if;\r\n return -infinity;\r\nend proc;\r\n\r\n# BGG operator for poly in \"X[weyl]\"\r\nBGGT_X := proc(rt::integer, f::polynom, LR::symbol := 'R') local ff,w,term;\r\n if degree(f) < 1 then\r\n return 0;\r\n elif LR = 'L' then\r\n if optype = 'e' then\r\n return (f-act([rt],f,'L'))/B[rt];\r\n else\r\n return (f-act([rt],f,'L'))/a[rt];\r\n end if;\r\n elif LR ='R' then\r\n if type(f, 'indexed') and op(0,f)=`X` then\r\n w:=op(1,f).[rt];\r\n if nops(w)=0 then return 1;\r\n elif nops(w) < nops(op(1,f)) then return(X[w]);\r\n else return 0;\r\n end if;\r\n elif op(0, f) = `+` then\r\n return expand(map2(procname, rt, f));\r\n elif op(0, f) = `*` then\r\n if type(op(1,f), 'rational') then\r\n return op(1,f)*procname(rt, f/op(1,f));\r\n end if;\r\n term[1] := op(1, f);\r\n term[2] := mul(op(i, f), i = 2 .. nops(f));\r\n return expand(procname(rt, term[1])*term[2]\r\n +ref_rt(rt, term[1])*procname(rt, term[2]));\r\n elif op(0, f) = `^` then\r\n term[1] := op(1, f);\r\n return expand(procname(rt, term[1])*add(term[1]^(i-1)*act([rt], term[1])^(op(2,f)-i),i=1..op(2,f)));\r\n end if;\r\n print(\"error in BGGT_X:\",f);\r\n end if;\r\nend proc;\r\n\r\n# BGG operator for weyl words\r\nBGGweylT := proc(weyl::list, f::{list(polynom),polynom}, LR::symbol := 'R')\r\n global optype; local i,temp,func;\r\n\ttemp := f;\r\n\tif type(f, list(polynom)) then\r\n\t func := 'BGG_GKM';\r\n elif has(f,`X`) then\r\n func := 'BGGT_X';\r\n elif type(f, polynom) then\r\n\t func := cat('BGGT_',optype);\r\n else\r\n print(\"error in BGGWeylT:\",f);\r\n return -infinity;\r\n end if;\r\n\tfor i from nops(weyl) to 1 by -1 do\r\n\t\ttemp := func(weyl[i], temp, LR);\r\n\tend do;\r\n\treturn temp;\r\nend proc:\r\n\r\n\r\n# Weyl group action on polynomials\r\nact := proc(weyl::list, f::ratpoly, LR::symbol := 'R') local ff,t,rt; global R,optype;\r\n if nops(weyl)=0 then\r\n return f;\r\n elif nops(weyl)>1 then\r\n return procname(weyl[1..-2],procname([weyl[-1]],f,LR),LR);\r\n elif nops(weyl)=1 then\r\n rt := weyl[-1];\r\n if LR='R' then\r\n ff:=eval(f, [seq(x[i] = subs([seq(e(j) = x[j], j = 1 .. dimr(R))],\r\n reflect(B[rt], e(i))), i = 1 .. dimr(R))]);\r\n ff:=eval(ff, [seq(z[i] = add(root_coords(reflect(B[rt],B[i]),R)[j]*z[j],\r\n j = 1 .. rank(R)), i = 1 .. rank(R))]);\r\n return eval(ff,[seq(t=ref_weyl(rt,op(1,t),'R'), t=indetsX(ff))]);\r\n elif LR='L' then\r\n ff:= eval(f, [seq(e(i)=reflect(B[rt], e(i)),\r\n i = 1 .. dimr(R))]);\r\n ff := eval(ff, [seq(a[i] = add(root_coords(reflect(B[rt], B[i]),R)[j]*a[j],\r\n j = 1 .. rank(R)), i = 1 .. rank(R))]);\r\n return eval(ff,[seq(t=ref_weyl(rt,op(1,t),'L'), t=indetsX(ff))]);\r\n end if;\r\n end if;\r\n print(\"error in act:\",weyl,f);\r\n return -infinity;\r\nend proc;\r\n\r\n# enumerate X in a polynomial\r\nindetsX := proc(f) local t,V;\r\n V:=[];\r\n for t in indets(f) do\r\n if type(t,'indexed') and op(0,t)=`X` then\r\n V:=[op(V),t];\r\n end if;\r\n end do;\r\n return V;\r\nend proc:\r\n\r\n# Weyl group action on X\r\nref_weyl := proc(rt::integer,weyl::list, LR::symbol := 'R') local b,j,v,u,w,temp; global B;\r\n if LR = 'R' then\r\n w := weyl.[rt];\r\n if nops(w) > nops(weyl) then\r\n return X[weyl];\r\n end if;\r\n temp := X[weyl]+act(w,B[rt],'L')*X[w];\r\n for b in pos_roots(B) do\r\n v := reflect(b,interior_pt(B));\r\n v := reflect(seq(B[j],j=w),v);\r\n vec2fc(v,R,'u'); # u = w.s_b\r\n if nops(u)=nops(weyl) then\r\n temp := temp - iprod(2/iprod(b,b)*b,B[rt])*X[u];\r\n end if;\r\n end do;\r\n return temp;\r\n elif LR = 'L' then\r\n w := [rt].weyl;\r\n if nops(w) > nops(weyl) then\r\n return X[weyl]\r\n else\r\n return -B[rt]*X[w]+X[weyl];\r\n end if;\r\n end if;\r\n print(\"error in ref_weyl:\",rt,weyl);\r\n return -infinity;\r\nend proc:\r\n\r\n# evaluate poly at \"w\" by putting x[i]=w^{-1}e[i]\r\nev := proc(weyl::list, f::polynom) local ff; global R,optype;\r\n ff := eval(act(weyl,f), [seq(x[i] = e(i), i = 1 .. dimr(R))]);\r\n return eval(ff, [seq(z[i] = a[i], i = 1 .. rank(R))]);\r\nend proc:\r\n\r\n# orbit sum\r\norbit_sum := proc(f::polynom) global reduw,R;\r\n return expand(add(ev(weyl,f), weyl=reduw)/size(R));\r\nend proc:\r\n\r\n# push-forward in cohomology\r\npush := proc(f::polynom) local d,weyl; global reduw,R,P;\r\n d := mul(e2x(i), i = P);\r\n return expand(ev([],(-1)^(nops(P))*simplify(add(act(weyl,f/d), weyl=reduw)))):\r\nend proc:\r\n\r\n\r\n# convert double polynomials to Schubert basis\r\nP2X := proc(f::polynom) local weyl, temp, i; global R, redu;\r\n temp := ev([],f);\r\n for i to min(degree(f),nops(redu)) do\r\n temp := temp+add(\r\n \t ev([],BGGweylT(weyl, f))*X[weyl], weyl=redu[i]);\r\n end do;\r\n\treturn col(temp);\r\nend proc:\r\n\r\n# Convert GKM polynomials to Schubert basis using upper triangularity\r\nGKM2X := proc (f::list(polynom)) local i, j, it, lc, ff; global reduw;\r\n for it to nops(f) do\r\n if f[it] <> 0 then break; end if;\r\n end do;\r\n if nops(f) < it then return 0; end if;\r\n lc := normal(f[it]/GKM(reduw[it])[it]);\r\n ff := normal(zip(`-`, f, zip(`*`, lc, GKM(reduw[it]))));\r\n return col(lc*X[reduw[it]]+procname(ff));\r\nend proc;\r\n\r\n# Convert GKM polynomials to Schubert basis using right BGG operators\r\nGKM2X2 := proc (f::list(polynom)) local i, deg, temp, weyl; global reduw;\r\n temp := f[1];\r\n deg := max(map(degree,f));\r\n for i to min(deg,nops(redu)) do\r\n temp := temp+add(BGGweylT(weyl, f)[1]*X[weyl], weyl=redu[i]);\r\n end do;\r\n return col(temp);\r\nend proc;\r\n\r\n# convert poly in \"X\" to Schubert basis\r\nX2X := proc(f::polynom);\r\n\treturn GKM2X(X2GKM(f));\r\nend proc:\r\n\r\n# Convert poly in \"X\" into GKM-poly\r\nX2GKM := proc (f::polynom) local i, weyl; global reduw;\r\n return [seq(eval(f, [seq(X[weyl] = GKM(weyl)[i], weyl = reduw)]),i=1..nops(reduw))] ;\r\nend proc;\r\n\r\n# convert double poly into GKM-poly\r\nP2GKM := proc(f::polynom);\r\n return ([seq(simplify(ev(w, f)), w = reduw)])\r\nend proc:\r\n\r\n# GKM polys (Billey's formula)\r\nGKM :=proc(weyl::list, upto:=-1) option remember; global reduw;\r\n return [seq(GKM_internal(weyl,v),v=reduw[1..upto])];\r\nend proc:\r\n\r\nGKM_internal := proc(weyl::list, longweyl::list) local i,j,k,u,L,K,M; global R,B,optype;\r\n K := 0;\r\n for L in subwords(weyl, longweyl) do\r\n M := 1;\r\n for i from 1 to nops(weyl) do\r\n u := reflect(seq(B[longweyl[j]],j=1..L[i]-1), B[longweyl[L[i]]]);\r\n\t if optype = 'e' then\r\n\t \t M := M * u;\r\n\t else\r\n\t\t M := M * e2a(u);\r\n\t end if;\r\n\tend do;\r\n K := K + M;\r\n end do;\r\n return simplify(K);\r\nend proc:\r\n\r\n# initialize for Lie type\r\nsetupT := proc (lie_type, roots::set :={}, upto::integer := 0) local i;\r\n global R, B, P, S, ST, redu, udim, reduw, optype, optypeK, w0;\r\n forget(GKM);\r\n forget(BGG_GKM);\r\n forget(refK); forget(strong_bruhat);\r\n unassign('S','ST');\r\n\r\n R := lie_type;\r\n B := base(R);\r\n P := pos_roots(R);\r\n optype := 'e';\r\n if R = cat('A',rank(R)) then\r\n optypeK := 'x'\r\n else\r\n optypeK := 'u'\r\n end if;\r\n udim := `if`(upto>0,upto,nops(P));\r\n redu := PReducedWd(R, roots, udim);\r\n reduw := [[],seq(op(i),i=redu)];\r\n w0 := longest_elt(R);\r\n return R;\r\nend proc;\r\n\r\n# TopSchubert poly\r\ntop := proc () local k, j, i, temp; global R,P;\r\n temp := 1;\r\n if optype='e' then\r\n\tif R = G2 then\r\n\t return (-3*e2x(w[1])^6+2*e2x(w[1])^5*e2x(w[2]))/6;\r\n elif R = cat('A',rank(R)) then\r\n\t return mul(x[i]^(rank(R)-i+1), i = 1 .. rank(R));\r\n\telif R = cat('B',rank(R)) then\r\n \treturn mul(x[i]^(rank(R)-i), i = 1 .. rank(R))*mul(c(i,`x`)/2, i = 1 .. rank(R));\r\n elif lie_type = cat('C',rank(R)) then\r\n\t\t return mul(x[i]^(2*rank(R)-2*i+1), i = 1 .. rank(R));\r\n elif R = E7 then\r\n\t\ttemp := mul(x[i]-c(1,`x`), i = 1 .. 7);\r\n\t\tfor i to 6 do temp := temp*mul(x[i]-x[j], j = i+1 .. 7) end do;\r\n\t for i to 5 do\r\n\t\t for j from i+1 to 6 do\r\n\t\t\ttemp := temp*mul(x[i]+x[j]+x[k]-c(1,`x`), k = j+1 .. 7);\r\n\t end do;\r\n\t\tend do;\r\n\t\treturn temp;\r\n elif R = E8 then\r\n\t\ttemp := mul(t[i], i = 1 .. 8);\r\n\t\tfor i to 7 do temp := temp*mul(t[i]-t[j], j = i+1 .. 8) end do;\r\n\t\tfor i to 7 do temp := temp*mul(t[i]+t[j]-t[0], j = i+1 .. 8) end do;\r\n\t\tfor i to 6 do\r\n\t\t\tfor j from i+1 to 7 do\r\n\t\t\t\ttemp := temp*mul(t[i]+t[j]+t[k]-t[0], k = j+1 .. 8)\r\n\t\t\tend do;\r\n\t\tend do;\r\n\t\treturn temp;\r\n else\r\n\t\treturn mul(e2x(i), i = P)/mul(i, i=degrees(R));\r\n end if;\r\n else\r\n\tif R = G2 then\r\n \t\treturn z[1]^5*z[2]/2;\r\n\telse\r\n\t\treturn mul(a2z(-e2a(i)), i = P)/mul(i, i=degrees(R));\r\n end if;\r\n end if;\r\nend proc;\r\n\r\n# Top double poly\r\ntopT := proc() global R,optype,S,w0; local u, i, j, k, D, temp;\r\n if optype='e' then\r\n if R = cat('A',rank(R)) then\r\n\t return mul(mul(x[i]-e(j), j = 1 .. rank(R)-i+1), i = 1 .. rank(R)+1);\r\n\t elif R = cat('B',rank(R)) then\r\n\t # D:=Matrix(rank(R));\r\n\t\t# for i from 1 to rank(R) do\r\n\t\t# for j from 1 to rank(R) do\r\n\t\t# k:=rank(R)+1+j-2*i;\r\n\t\t# \t\t if k<=rank(R) and k>=0 then\r\n\t\t# \t\t D[i,j]:=(c(k,`x`)+eval(c(k,`t`),[seq(t[h]=e(h),h=1..rank(R))]))/2;\r\n\t\t# \t\t end if;\r\n\t\t# \tend do;\r\n\t\t# end do;\r\n\t\t# return act(longest_elt(R),mul(mul(x[i]-e(j), j = 1 .. i-1), i = 2 .. rank(R))\r\n\t\t# *LinearAlgebra[Determinant](D));\r\n return mul(mul(x[i]-e(j), j = 1 .. i), i = 1 .. rank(R))\r\n *mul(mul(x[i]+e(j), j = 1 .. i-1), i = 1 .. rank(R))/(-2)^rank(R);\r\n\r\n\t elif R = cat('C',rank(R)) then\r\n\t # D:=Matrix(rank(R));\r\n\t\t# for i from 1 to rank(R) do\r\n\t\t# for j from 1 to rank(R) do\r\n\t\t# k:=rank(R)+1+j-2*i;\r\n\t\t# \t\t if k<=rank(R) and k>=0 then\r\n\t\t# \t\t D[i,j]:=(c(k,`x`)+eval(c(k,`t`),[seq(t[h]=e(h),h=1..rank(R))]));\r\n\t\t# \t\t end if;\r\n\t\t# \tend do;\r\n\t\t# end do;\r\n\t\t# return act(longest_elt(R),mul(mul(x[i]-e(j), j = 1 .. i-1), i = 2 .. rank(R))\r\n\t\t# *LinearAlgebra[Determinant](D));\r\n return mul(mul(x[i]-e(j), j = 1 .. i), i = 1 .. rank(R))\r\n *mul(mul(x[i]+e(j), j = 1 .. i-1), i = 1 .. rank(R));\r\n\t elif R = cat('D',rank(R)) then\r\n\t D:=Matrix(rank(R));\r\n\t\t for i from 1 to rank(R) do\r\n\t\t for j from 1 to rank(R) do\r\n\t\t k:=rank(R)+j-2*i;\r\n\t\t\t\t if k<=rank(R) and k>=0 then\r\n\t\t\t\t D[i,j]:=(c(k,`x`)+eval(c(k,`t`),[seq(t[h]=e(h),h=1..rank(R))]))/2;\r\n\t\t\t\t end if;\r\n\t\t\tend do;\r\n\t\tend do;\r\n\t\treturn act(w0,mul(mul(x[i]-e(j), j = 1 .. i-1), i = 2 .. rank(R))\r\n *LinearAlgebra[Determinant](D));\r\n elif R = G2 then\r\n return ((x[1]-x[2]+e2-e1)/2)*(x[2]-x[1]-e2+e3)*(x[2]-x[1]-e1+e3)\r\n *(x[1]-x[2]-e2+e3)*(x[1]-x[2]-e1+e3)*(-x[1]+2*x[2]-x[3]+e2-2*e1+e3);\r\n#\t return -(x[3]-(2/3)*e3+(1/3)*e1-(2/3)*e2)*((3/2)*x[1]-(3/2)*e1)*(3*x[1]-3*e2)\r\n# *(3*x[1]-3*e3)*(x[2]-(2/3)*e1-(2/3)*e2+(1/3)*e3)*(x[2]-(2/3)*e3+(1/3)*e1-(2/3)*e2);\r\n\t elif type(name_of(R),'indexed') then # type I2\r\n\t D:=[]; temp:=x[2]-e2;\r\n\t for i from 1 to trunc(op(1,name_of(R))/2-1) do\r\n\t\t D:=[1,2,op(D)];\r\n\t\t temp:=temp*(x[2]-act(D,e2,'L'));\r\n\t\t end do;\r\n\t\t D:=[];\r\n\t\t for i from 1 to trunc((op(1,name_of(R))-1)/2) do\r\n\t\t D:=[2,1,op(D)];\r\n\t\t temp:=temp*(x[2]-act(D,e2,'L'));\r\n\t\t end do;\r\n\t return temp*(x[1]+act(w0,e1,'L'));\r\n\t else\r\n\t return double(w0);\r\n\t end if;\r\n elif optype='a' then\r\n if R = G2 then\r\n return ((-z[1]+a[1])/2)*(z[1]+a[1]+a[2])*(z[1]+2*a[1]+a[2])\r\n *(-z[1]+a[1]+a[2])*(-z[1]+2*a[1]+a[2])*(-z[2]+3*a[1]+a[2]);\r\n elif R = cat('A',rank(R)) then\r\n for i from 1 to rank(R)+1 do\r\n\t u[i] := e2a(-add(e(j), j = 1 .. rank(R)+1)/(rank(R)+1) + e(i));\r\n\t end do;\r\n return mul(mul(eval(u[i],[seq(a[k]=z[k],k=1..rank(R))])-u[j], j = 1 .. rank(R)-i+1),\r\n\t i = 1 .. rank(R)+1);\r\n else\r\n\t return double(w0);\r\n\t end if;\r\n end if:\r\nend proc:\r\n\r\n\r\n# enumerate Schubert polynomials\r\nschubertpolys := proc () global S,reduw,w0; local w,f;\r\n f:=top();\r\n for w in reduw do\r\n\t S[w] := simplify(BGGweylT(inv(w).w0,f));\r\n end do;\r\n print(\"The top schubert poly is\",f);\r\nend proc:\r\n\r\n# enumerate Double Schubert polynomials\r\nschubertpolysT := proc () global optype,ST,reduw,w0; local w,f;\r\n f:=topT();\r\n for w in reduw do\r\n\t ST[w] := simplify(BGGweylT(inv(w).w0,f));\r\n end do;\r\n print(\"The top double schubert poly is\",f);\r\nend proc:\r\n\r\n# single to double formula\r\n# compute double Schubert poly \"ST[weyl]\" from single Schubert polys \"S[]\"\r\ndouble:=proc(weyl::list) global S; local temp,L;\r\n if optype = 'e' then\r\n return add((-1)^(nops(L))*mul(x2e(S[L[i]]),i=1..nops(L)-1)\r\n *(x2e(S[L[-1]])-S[L[-1]]),L=decomp(weyl));\r\n else\r\n return add((-1)^(nops(L))*mul(z2a(S[L[i]]),i=1..nops(L)-1)\r\n *(z2a(S[L[-1]])-S[L[-1]]),L=decomp(weyl));\r\n end if;\r\nend proc:\r\n\r\n# double to single\r\nsingle:=proc(f::polynom) local ff; global R;\r\n ff := eval(f,[seq(e(j) = 0, j = 1 .. dimr(R))]);\r\n return eval(ff, [seq(a[j] = 0, j = 1 .. rank(R))]);\r\nend proc:\r\n\r\n# Cauchy formula for type A\r\nCauchy:=proc() global reduw,w0 ;local weyl;\r\n return add((-1)^(nops(weyl))*x2e(S[weyl])*S[weyl.w0],weyl=reduw);\r\nend proc:\r\n\r\n# Chevalley formula computes \"X[weyl]X[rt]\"\r\nChev := proc(weyl::list,rt::integer) local j,v,u,temp; global w,P;\r\n\t temp := 0;\r\n for v in P do\r\n \t vec2fc(reflect(seq(B[j], j = weyl),v,interior_pt(R)),R,'u');\r\n if nops(u)=nops(weyl)+1 then\r\n\t\t temp := temp + iprod(2/iprod(v,v)*v,w[rt])*X[u];\r\n end if;\r\n end do;\r\n return (w[rt]-reflect(seq(B[j], j = weyl),w[rt]))*X[weyl]+temp;\r\nend proc:\r\n\r\n# collect terms in Schubert presentation\r\ncol := proc(f::algebraic) local g; global reduw;\r\n g := collect(simplify(f),[seq(X[weyl],weyl=reduw)]);\r\n return collect(g,[seq(XK[weyl],weyl=reduw)]);\r\nend proc:\r\n\r\n", "meta": {"hexsha": "7087190a8006a8dcdaccdc6b97f010044100bdbc", "size": 17286, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "BGGT.mpl", "max_stars_repo_name": "shizuo-kaji/Maple-flag-cohomology", "max_stars_repo_head_hexsha": "c4e1669cfd228e182a44d291d6b0ffe0f670a8af", "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": "BGGT.mpl", "max_issues_repo_name": "shizuo-kaji/Maple-flag-cohomology", "max_issues_repo_head_hexsha": "c4e1669cfd228e182a44d291d6b0ffe0f670a8af", "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": "BGGT.mpl", "max_forks_repo_name": "shizuo-kaji/Maple-flag-cohomology", "max_forks_repo_head_hexsha": "c4e1669cfd228e182a44d291d6b0ffe0f670a8af", "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": 32.9885496183, "max_line_length": 129, "alphanum_fraction": 0.5070577346, "num_tokens": 6298, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8198933447152498, "lm_q2_score": 0.6825737408694988, "lm_q1q2_score": 0.5596376674162936}} {"text": "read (\"metaMPFR_straightforwardAlgo.mpl\"):\n\nf := AiryAi(x):\ndeq := holexprtodiffeq(f, y(x)):\nrec := diffeqtorec(deq, y(x), a(n)):\nname_of_function := op(0,f):\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nf := erf(x):\ndeq := holexprtodiffeq(f, y(x)):\nrec := diffeqtorec(deq, y(x), a(n)):\nname_of_function := op(0,f):\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = -(6*n+1)*(6*n+2)*(6*n+3)*(6*n+4)*(6*n+5)*(6*n+6)*a(n)/( (n+1)^3*(3*n+1)*(3*n+2)*(3*n+3)*12288000 ), a(0)=1 }:\nname_of_function := alpha:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\n\nrec := { a(n+1) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1 }:\nname_of_function := test0a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=Pi }:\nname_of_function := test1a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=1 }:\nname_of_function := test2a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi }:\nname_of_function := test3a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1, a(1)=2 }:\nname_of_function := test4a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=Pi, a(1)=0}:\nname_of_function := test5a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=1, a(1)=Pi }:\nname_of_function := test6a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi, a(1)=0}:\nname_of_function := test7a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1, a(1)=0, a(2)=0 }:\nname_of_function := test8a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=0, a(1)=Pi, a(2)=2 }:\nname_of_function := test9a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=0, a(1)=0, a(2)=1 }:\nname_of_function := test10a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+7) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi, a(4)=1, a(6)=2 }:\nname_of_function := test11a:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), CONSTANT_SERIES, name_of_function, name_of_file, f):\n\n\nrec := { a(n+1) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1 }:\nname_of_function := test0b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=Pi }:\nname_of_function := test1b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=1 }:\nname_of_function := test2b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi }:\nname_of_function := test3b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1, a(1)=2 }:\nname_of_function := test4b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=Pi, a(1)=0}:\nname_of_function := test5b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=1, a(1)=Pi }:\nname_of_function := test6b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi, a(1)=0}:\nname_of_function := test7b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1, a(1)=0, a(2)=0 }:\nname_of_function := test8b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=0, a(1)=Pi, a(2)=2 }:\nname_of_function := test9b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=0, a(1)=0, a(2)=1 }:\nname_of_function := test10b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\nrec := { a(n+7) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi, a(4)=1, a(6)=2 }:\nname_of_function := test11b:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES, name_of_function, name_of_file, f):\n\n\nrec := { a(n+1) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1 }:\nname_of_function := test0c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=Pi }:\nname_of_function := test1c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=1 }:\nname_of_function := test2c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+1) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi }:\nname_of_function := test3c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1, a(1)=2 }:\nname_of_function := test4c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=Pi, a(1)=0}:\nname_of_function := test5c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=1, a(1)=Pi }:\nname_of_function := test6c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+2) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi, a(1)=0}:\nname_of_function := test7c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=1, a(1)=0, a(2)=0 }:\nname_of_function := test8c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = -(6*n+1)*a(n)/( (n+1)^3 ), a(0)=0, a(1)=Pi, a(2)=2 }:\nname_of_function := test9c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+3) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=0, a(1)=0, a(2)=1 }:\nname_of_function := test10c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\nrec := { a(n+7) = (1/Pi)*(3*n+1)*a(n)/( (n+2) ), a(0)=Pi, a(4)=1, a(6)=2 }:\nname_of_function := test11c:\nname_of_file := sprintf(\"%a.c\", name_of_function):\nprintf(\"\\n\\n\\n/************************** Implémentation de %s ******************************/\\n\", name_of_file):\ngenerateStraightforwardAlgo(rec, a(n), FUNCTION_SERIES_RATIONAL, name_of_function, name_of_file, f):\n\n", "meta": {"hexsha": "0a350804b457873d42e7745a35f0cf6dec1c33ac", "size": 13971, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "LibSource/mpfr/tools/metaMPFR/metaMPFR_tests.mpl", "max_stars_repo_name": "ekzyis/CrypTool-2", "max_stars_repo_head_hexsha": "1af234b4f74486fbfeb3b3c49228cc36533a8c89", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 12, "max_stars_repo_stars_event_min_datetime": "2021-09-29T14:50:06.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-31T15:01:21.000Z", "max_issues_repo_path": "LibSource/mpfr/tools/metaMPFR/metaMPFR_tests.mpl", "max_issues_repo_name": "ekzyis/CrypTool-2", "max_issues_repo_head_hexsha": "1af234b4f74486fbfeb3b3c49228cc36533a8c89", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 15, "max_issues_repo_issues_event_min_datetime": "2021-12-24T22:53:49.000Z", "max_issues_repo_issues_event_max_datetime": "2021-12-25T10:03:13.000Z", "max_forks_repo_path": "LibSource/mpfr/tools/metaMPFR/metaMPFR_tests.mpl", "max_forks_repo_name": "ekzyis/CrypTool-2", "max_forks_repo_head_hexsha": "1af234b4f74486fbfeb3b3c49228cc36533a8c89", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2021-10-17T19:46:51.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-18T02:57:57.000Z", "avg_line_length": 57.2581967213, "max_line_length": 127, "alphanum_fraction": 0.5620929067, "num_tokens": 4227, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8031737963569016, "lm_q2_score": 0.6959583313396339, "lm_q1q2_score": 0.5589754950882682}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_mgga_c *)\n\n$include \"gga_c_gapc.mpl\"\n\n(* override definition of gap_C *)\ngap_G := (rs, z, xt, par) -> RS_FACTOR^2/8 * xt^2/rs^2:\n\nf_kcis := (rs, z, xt, xs0, xs1, ts0, ts1) ->\n + f_gap(rs, z, xt)\n - xs0^2/(8*ts0) * (1 + z)/2 * f_gap(rs, 1, xs0)\n - xs1^2/(8*ts1) * (1 - z)/2 * f_gap(rs, -1, xs1):\n\nf := (rs, z, xt, xs0, xs1, ts0, ts1, us0, us1) ->\n f_kcis(rs, z, xt, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "35ef8428c624a2f8850af3d0b583c75bea196944", "size": 645, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_c_kcis.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_c_kcis.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_c_kcis.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 28.0434782609, "max_line_length": 68, "alphanum_fraction": 0.5937984496, "num_tokens": 269, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8824278788223265, "lm_q2_score": 0.6334102498375401, "lm_q1q2_score": 0.5589388631884604}} {"text": "with(LinearAlgebra):\nwith(Groebner):\n\n# Exterior powers of matrices (implicitly using lexicographic ordering\n# of the standard bases of exterior powers of R^n).\n\nexterior_power := proc(k::nonnegint,A)\n local m,n,S,T,s,t;\n m,n := Dimension(A);\n S := combinat[choose](m,k);\n T := combinat[choose](n,k);\n Matrix([seq([seq(Determinant(SubMatrix(A,s,t)),t in T)],s in S)]);\nend:\n\n# If S is a subset of {1,..,n} then we have an associated shuffle\n# permutation of {1,..,n}. The next function computes the signature.\n\nshuffle_sgn := proc(n,S)\n local k,T,ST;\n k := nops(S);\n T := sort([op({seq(i,i=1..n)} minus S)]);\n ST := [op(S),op(T)];\n return signum(mul(mul(ST[j]-ST[i],j=i+1..n),i=1..n));\nend:\n\n# Given a matrix A we get an induced map of Koszul algebras. Each\n# Koszul algebra has a natural Frobenius form, with using which we\n# get a kind of dual map in the opposite direction, which is computed\n# by the function below. For a square matrix A, the composite of the\n# k'th exterior power and the k'th koszul adjoint (in either order)\n# is multiplication by det(A).\n\nkoszul_adjoint := proc(k::nonnegint,A)\n local m,n,M,N,S,T,Sc,Tc,Se,Te,s,t,i,j;\n m,n := Dimension(A);\n M := {seq(i,i=1..m)};\n N := {seq(j,j=1..n)};\n S := combinat[choose](m,k);\n T := combinat[choose](n,k);\n Sc := map(s -> sort([op(M minus {op(s)})]),S);\n Tc := map(t -> sort([op(N minus {op(t)})]),T);\n Se := [seq([op(S[i]),op(Sc[i])],i=1..nops(S))];\n Se := map(u -> signum(mul(mul(u[j]-u[i],j=i+1..m),i=1..m)),Se);\n Te := [seq([op(T[i]),op(Tc[i])],i=1..nops(T))];\n Te := map(u -> signum(mul(mul(u[j]-u[i],j=i+1..n),i=1..n)),Te);\n\n M := Matrix(nops(T),nops(S));\n for i from 1 to nops(S) do\n for j from 1 to nops(T) do\n M[j,i] := Determinant(SubMatrix(A,Sc[i],Tc[j])) * Se[i] * Te[j];\n od:\n od:\n\n return M;\nend:\n\n# A list u of length n in a ring R gives a differential on the\n# Koszul algebra of R^n. The function below gives the matrix of\n# this differential with respect to the standard bases of the\n# k'th and (k-1)'th exterior powers of R^n.\n\nkoszul_d := proc(k::posint,u)\n local n,S,T,s,t,i,j,MT,M;\n n := nops(convert(u,list));\n S := combinat[choose](n,k);\n T := combinat[choose](n,k-1);\n MT := table():\n for s in S do\n for t in T do\n MT[t,s] := 0;\n od:\n for i from 1 to k do\n t := [seq(s[j],j=1..i-1),seq(s[j],j=i+1..k)];\n MT[t,s] := (-1)^(i-1) * u[s[i]];\n od;\n od: \n M := Matrix([seq([seq(MT[T[i],S[j]],j=1..nops(S))],i=1..nops(T))]);\n return M;\nend:\n\n# koszul_p can be set equal to a prime number if we want to work in that\n# characteristic.\n\nkoszul_p := infinity;\n\nkoszul_pmod := (x) -> `if`(koszul_p=infinity,x,mods(x,koszul_p)):\n\n# The function below sets up a number of global variables. The\n# original v can be supplied as a list. Then v_vec will be the corresponding\n# row vector. Also u_vec will be the vector of variables x[i], and w_vec\n# will be the vector of powers x[i]^h, where h is minimal such that x[i]^h\n# lies in I = (v[1],...,v[n]) for all i. Next, A and B will be matrices with\n# u_vec = v_vec.A and v_vec = w_vec.B, which witnesses the inclusions\n# (x[1]^(h),...,x[n]^(h)) <= I <= (x[1],...,x[n]). These matrices induce\n# morphisms of Koszul complexes alpha : K(u) ->K(v) and beta: K(v)->K(w). It\n# is easy to understand K(u) and K(w) in particular, they only have homology\n# in degree zero. All three complexes can be regarded as commutative\n# Frobenius algebras in the category of chain complexes, so there are adjoint\n# morphisms alpha^! : K(v) -> K(u) and beta^! : K(w) -> K(v). The idea is\n# to use these to show that K(v) also has homology concentrated in degree zero.\n\nkoszul_setup := proc(v)\n global n,u_vec,v_vec,w_vec,x_vec,x_vars,Iv,Mv,Nv,\n soc_u,soc_v,soc_w,A,B,p;\n local a,b,c,i,h,v0,v1,x0,x1,char;\n n := nops(v);\n v_vec := Transpose(Vector(v));\n x_vec := Transpose();\n w_vec := x_vec;\n soc_w := 1;\n x_vars := tdeg(seq(x[i],i=1..n));\n\n a := table();\n v0 := v_vec;\n v1 := v_vec;\n for i from n to 1 by -1 do\n v0 := v1;\n v1 := subs(x[i]=0,v1);\n a[i] := koszul_pmod((v0 - v1)/x[i]); \n od;\n\n B := Matrix([seq(convert(a[i],list),i=1..n)]);\n soc_v := koszul_pmod(Determinant(B));\n char := `if`(koszul_p=infinity,NULL,characteristic = koszul_p);\n\n Iv,Mv := Basis(convert(v,list),x_vars,output=extended,char);\n Mv := Transpose(Matrix(Mv));\n Nv := (z) -> koszul_pmod(NormalForm(z,Iv,x_vars,char));\n\n h := 1;\n x0 := map(Nv,convert(x_vec,list));\n x1 := x0;\n while h < 100 and x1 <> [0$n] do\n h := h+1;\n x1 := map(Nv,x0 *~ x1);\n od;\n\n if h >= 100 then\n error(\"Variables are not nilpotent mod given ideal\");\n fi;\n\n u_vec := Transpose(Vector([seq(x[i]^h,i=1..n)]));\n soc_u := mul(x[i]^(h-1),i=1..n);\n\n a := NULL;\n b := NULL;\n for i from 1 to n do \n unassign('b');\n c := NormalForm(x[i]^h,Iv,x_vars,b,char);\n a := a,b;\n od;\n\n A := map(expand,Mv . Transpose(Matrix([a])));\n NULL;\nend:\n", "meta": {"hexsha": "bf02f4c76e6757607d5202cac0a73050b266a517", "size": 4837, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/koszul_a.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/koszul_a.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/koszul_a.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": 31.0064102564, "max_line_length": 79, "alphanum_fraction": 0.6173247881, "num_tokens": 1698, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8354835207180243, "lm_q2_score": 0.6688802603710086, "lm_q1q2_score": 0.558838434873559}} {"text": "# # Draw weak and strong Bruhat diagram\n# # by Shizuo Kaji\n\n# it requires \"coxeter and weyl\" and \"poset\" packages by J.Stembridge\n\n# http://www.math.lsa.umich.edu/~jrs/maple.html\n\nwith(posets);\nwith(coxeter); with(weyl);\nwith(WeylOps):\n\n# Draw weak (left or right) bruhat diagram\n#\n# Example:\n# H,L := wbruhat(F4, {}, 'L')\n# plot_poset(H, labels = L, stretch = 1)\n\nwbruhat:=proc(R,roots::set:={}, lr::symbol:='L', upto::integer :=0)\n local H,i,j,w,newweyl,oldweyl,p,pos,wlabel,udim;\n udim := `if`(upto>0,upto,nops(pos_roots(R)));\n wlabel:=[[]]; oldweyl:=[[]];\n H:=NULL;\n while nops(wlabel[-1])0 do\n newweyl:=[];\n \tfor i from 1 to nops(oldweyl) do\n\t for j in {$1..rank(R)} minus roots do\n\t \tw:=`if`(lr='L',reduce([j,op(oldweyl[i])],R),reduce([op(oldweyl[i]),j],R));\n\t\t\tif nops(w)=nops(oldweyl[i])+1 then\n\t\t\t\tif not member(w, newweyl, 'pos') then\n\t\t\t\t\tH:=H, [nops(wlabel)-nops(oldweyl)+i, nops(wlabel)+nops(newweyl)+1];\n\t\t\t\t\tnewweyl:=[op(newweyl), w];\n\t\t\t\telse\n\t\t\t\t\tH:=H, [nops(wlabel)-nops(oldweyl)+i, nops(wlabel)+pos];\n\t\t\t\tend if;\n\t\t\tend if;\n\t end do;\n\tend do;\n wlabel:=[op(wlabel), op(newweyl)]; oldweyl:=newweyl;\n end do;\n return {H},table([seq(i = convert(wlabel[i], 'string'), i = 1 .. nops(wlabel))]):\nend proc:\n\n# Draw strong bruhat diagram\n#\n# Example:\n# H,L,E := wbruhat(F4, {}, 3)\n# plot_poset(H, labels = L, stretch = 1)\n# E contains edge labeling\n\nsbruhat := proc (R, roots::set:={}, upto::integer:=0)\nlocal H, w, r, v, i, j, beta, pos, newvects, newreps, vects,\n len, reps, oldvects, oldreps, edge, udim,B,P;\n\n B := base(R); r := nops(B); P:=pos_roots(R);\n udim := `if`(upto>0,upto,nops(P));\n\tnewvects := [add(weights(R)[i], i={$1..r} minus roots)];\n newreps := []; reps := [[]]; vects := newvects;\n\n for len from 1 to udim do;\n\t\toldvects := newvects; oldreps := [newreps];\n\t\tnewvects := []; newreps := NULL;\n\t\tfor j to nops(oldvects) do\n\t\t\tfor i to r do\n\t\t\t\tif 0 < iprod(B[i], oldvects[j]) then\n\t\t\t\t\tv := reflect(B[i], oldvects[j]);\n\t\t\t\t\tif not member(v, newvects) then\n\t\t\t\t\t\tnewvects := [op(newvects), v];\n\t\t\t\t\t\tnewreps := newreps, reduce([i, op(oldreps[j])], R)\n\t\t\t\t\tend if\n\t\t\t\tend if\n\t\t\tend do\n\t\tend do;\n\t\tif newreps=NULL then break; end if;\n reps := [op(reps), newreps];\n vects := [op(vects), op(newvects)];\n end do;\n\n H:= NULL;\n for j from 1 to nops(vects) do\n for beta in P do\n if iprod(beta,vects[j])>0 then\n v:=reflect(beta,vects[j]);\n if member(v,vects,'pos') then\n edge[j,pos]:=root_coords(beta,R);\n H:= H, [j,pos];\n end if;\n end if;\n end do;\n end do;\n return {H},table([seq(i=[i,reps[i]],i=1..nops(reps))]),edge;\nend proc;\n\n\n\n# check if v is minimal w.r.t. a reflection subgroup;\nhas_descent:=proc(w::list,refsub_gen::set,R) local ref;\n for ref in refsub_gen do\n if nops(reduce([op(w),op(ref)],R))0,upto,nops(P));\n\n refsub_gen:={};\n for ref in refsub do;\n vec2fc(reflect(ref,interior_pt(R)),B,'w');\n refsub_gen:={op(refsub_gen),w};\n end do;\n\n # enumerate reduced words\n\tnewvects := {interior_pt(R)};\n reps := [[]]; newreps := reps; vects := newvects;\n\n for len from 1 to udim do;\n\t\toldvects := newvects; oldreps := newreps;\n\t\tnewvects := []; newreps := [];\n\t\tfor j to nops(oldvects) do\n\t\t\tfor i to r do\n\t\t\t\tif 0 < iprod(B[i], oldvects[j]) then\n v := reflect(B[i], oldvects[j]);\n w := reduce([i, op(oldreps[j])], R);\n\t\t\t\t\tif not member(v, newvects) then\n if not has_descent(w,refsub_gen,R) then\n newreps := [op(newreps), w];\n newvects := [op(newvects), v];\n end if;\n\t\t\t\t\tend if\n\t\t\t\tend if\n\t\t\tend do\n\t\tend do;\n\t\tif newreps={} then break; end if;\n reps := [op(reps), op(newreps)];\n vects := [op(vects), op(newvects)];\n end do;\n\n # edges\n H:=NULL;\n for j from 1 to nops(vects) do;\n for ref in P do\n if iprod(ref,vects[j])<0 then next; end if;\n vec2fc(reflect(ref,vects[j]),R,'w');\n w:=ref_reduce(w,refsub_gen,R):\n member(w,reps,'pos');\n if j x[3..4], sparts);\n\treturn sparts;\nend proc:\n\nisSpartValid:= proc(spart, debug:=0) local spartphi, spartthe, spartzed, spartpt;\n\t#tells you wether a spart is valid or not. \n\tif type(spart, list) <> true then \n\t\treturn false; \n\tend if;\n\tif nops(spart) <> 4 then \n\t\t\treturn false; \n\t\tend if; \n\t\t#Some local vars\n\t\tspartpt := spart[1];\n\t\tspartphi:= spart[2];\n\t\tspartthe:= spart[3];\n\t\tspartzed:= spart[4];\n\t\t#Conditions on constituting partitions\n\t\tif MakeUnique(sort(spartphi)) <> sort(spartphi) then return false; end if;\n\t\tif MakeUnique(sort(spartthe)) <> sort(spartthe) then return false; end if;\n\t\tif min(FlattenOnce(spart)) < 0 then return false; end if;\n\t\treturn true;\nend proc:\n\ngiveSpartSector:= proc(spart::pN2spart)\n\t\tlocal n, mbar, mubar, mbarbar;\n\t#Takes a spart and returns the sector\n\t\tn := add(k, k in Flatten(spart));\n\t\tmbarbar:= nops(spart[1]);\n\t\tmbar:= nops(spart[2]);\n\t\tmubar:= nops(spart[3]);\n\t\treturn [n, mbar, mubar, mbarbar];\nend proc:\n\ngenN2spart:= proc(n, mbar, mubar, mbarbar, mode:=[1,2,3])\n\tlocal degreePT, ptSparts, spartPhi, spartThe, spartZed, degreePhi, degreeThe, degreeZed, sparts, newsparts, T, phiSparts, thetaSparts, zedSparts, part_of_n, ones_list;\n\t#Returns all the spart in a given sector\n\t#Initializing the number of boxes in each subpart\n\tsparts:= [];\n\tdegreePT := n -mubar*(mubar-1)/2 - mbar*(mbar-1)/2;\n\tdegreePhi:= n - degreePT;\n\tdegreeThe:= n-degreePhi;\n\tdegreeZed:= 0;\n\tif degreePT < 0 then return [[],[],[],[]]; end if;\n\twhile degreePT >=0 do\n\t\tptSparts:= partition(degreePT+mbarbar);\n\t\tptSparts:= map(x-> if nops(x) <> mbarbar then NULL; else x; end if, ptSparts); \n\t\tones_list:= map(x-> [seq(1, j=1..nops(x))], ptSparts);\n\t\tptSparts:= ptSparts - ones_list;\n\t\tptSparts:= map(x-> Reverse(x), ptSparts); \n\t\n\t\tdegreePhi:= n - degreePT;\n\t\twhile degreePhi >= mbar*(mbar-1)/2 do\n\t\t\t#All the dispart with degreePhi starting High\n\t\t\tphiSparts:=genSpartDist(degreePhi,mbar);\n\n\t\t\tdegreeThe:=n-degreePhi-degreePT;\n\t\t\twhile degreeThe >= mubar*(mubar-1)/2 do\n\t\t\t\tdegreeZed:= n - degreePhi - degreeThe -degreePT;\n\n\t\t\t\tthetaSparts:= genSpartDist(degreeThe,mubar);\n\t\t\t\t#zedSparts:= Reverse(partition(degreeZed));\n\t\t\t\tpart_of_n:= partition(degreeZed);\n\t\t\t\tzedSparts:= map(x-> Reverse(x), part_of_n); \n\t\t\t\t#Update the list of sparts\n\t\t\t\tT:=cartprod([ptSparts, phiSparts, thetaSparts, zedSparts]);\n\t\t\t\tnewsparts:= [];\n\t\t\t\twhile not T[finished] do newsparts:= [op(newsparts),T[nextvalue]()] end do;\n\t\t\t\tsparts:= [op(sparts), op(newsparts)];\n\t\n\t\t\t\tdegreeThe:= degreeThe-1;\n\t\t\tend do:\n\t\t\tdegreePhi:= degreePhi-1;\n\t\tend do:\n\tdegreePT:= degreePT-1; \n\tend do:\nreturn(spart_sort(sparts, mode));\nend proc:\n\nspart_sort:= proc(sparts, mode:=[1,2,3])\n\tlocal scores, k, j, out, perms, dom_score;\n\tscores:=[];\n\tfor k in sparts do\n\t\tdom_score:=add(j, j in map(x->if `<` = sCompareDominance(k, x, mode) then 1; else 0; end if, sparts));\n\t\tscores:=[op(scores), dom_score]; \n\tend do:\n\tperms:=sort(scores, output=permutation);\n\tout:= map(x->sparts[x], perms);\n\treturn out;\nend proc:\n\nsuper_pol_sort:= proc(expr, the_symbol, sector, mode:=[1,2,3])\n\tlocal sort_vec;\n\tsort_vec:= map(x-> the_symbol[op(x)], genN2spart(op(sector), mode)); \n\treturn sort(expr, sort_vec); \nend proc:\n\nlist_sort:= proc(in1, in2)\n\tif sCompareDominance([op(in1)], [op(in2)]) = `>` then return true; else return false; end if;\nend proc:\n\ngenSpartDist:=proc(n,ell, debug:=0)\n\t\tlocal part_list, one_list;\n\t#Generates all the sparts with distinct parts including the zeros\n\tpart_list:= Reverse(partition(n+ell));\n\tif debug <> 0 then print(part_list); end if;\n\t\tpart_list:= map(x-> if nops(x) <> ell then NULL; else x; end if, part_list);\n\tif debug <> 0 then print(part_list); end if;\n\t\tpart_list:= map(x-> if FindRepetitions(x) <> [] then NULL; else Reverse(x); end if, part_list);\n\tif debug <> 0 then print(part_list); end if;\n\tone_list:= map(x-> [seq(1, i=1..(nops(x)))], part_list); \n\t\t#part_list:= map(x-> Reverse(x - [seq(1, i=1..nops(x))]), part_list); \n\tpart_list:= part_list - one_list; \n\t\treturn part_list;\nend proc:\n\nswitch_notation:= proc(spart, numbering:=a, uniquenum:=0, mode:=[1,2,3])\n\tlocal phis, thetas, phithetas, zeds, Lambda, pts, newLambda, counter,k;\n\t# exchange a spart for the other notation ( [] [] [] ) --> ( 4T, 3C, ...)\n\tpts := spart[1];\n\tif nops(spart[1])<>0 then pts := map(x-> [x, \"TC\", numbering^(x+1)], pts); end if;\n\tphis:= spart[2];\n\tif nops(spart[2])<>0 then phis:= map( x-> [x,\"T\",numbering^(x)], phis); end if;\n\tthetas:= spart[3];\n\tif nops(spart[3])<>0 then thetas:= map(x-> [x,\"C\", numbering^(x)], thetas); end if;\n\tzeds:= spart[4];\n\tif nops(spart[4])<>0 then zeds:= map(x-> [x,\"\", numbering^(x)], zeds); end if;\n\tLambda:= Reverse(sort([op(pts),op(phis), op(thetas), op(zeds)]));\n\tif uniquenum=0 then\n\t\tnewLambda:=[];\n\t\tcounter:=1;\n\t\tfor k from 1 to nops(Lambda) do\n\t\t\tif (op(2,Lambda[k]) = \"T\") or (op(2,Lambda[k]) = \"C\") then\n\t\t\t\tnewLambda:=[op(newLambda), [op(Lambda[k]), numbering[counter]]];\n\t\t\t\tcounter:= counter + 1;\n\t\t\telse\n\t\t\t\tnewLambda:= [op(newLambda), [op(Lambda[k]), numbering]]; \n\t\t\tend if;\n\t\tend do:\n\t\tLambda:=newLambda;\n\t\t#Lambda:= map(x-> \n\t\t#if (op(2,Lambda[x]) = \"T\") or (op(2,Lambda[x]) = \"C\") then\n\t\t#[op(Lambda[x]), numbering[x]];\n\t\t#else\n\t\t#[op(Lambda[x]), numbering]; end if, [seq(k, k=1..nops(Lambda))]); \n\telse\n\t\tLambda:= map(x-> \n\t\t[op(Lambda[x]), numbering[x]]\n\t\t, [seq(k, k=1..nops(Lambda))]); \n\tend if;\n\tif mode <> [1,2,3] then\n\t\tLambda:= sort_switch(Lambda, mode);\t\n\tend if;\n\treturn Lambda;\nend proc:\n\nsort_switch:= proc(sw_spart, mode:=[1,2,3])\n\tlocal orig, perm, sublist, switched;\n\torig:= [\"TC\", \"T\", \"C\"];\n\tperm:= subs({1=\"TC\", 2=\"T\", 3=\"C\"}, mode);\n\tsublist:= {perm[1]=\"C0\", perm[2]=\"B0\", perm[3]=\"A0\"};\n\tswitched:= subs(sublist, sw_spart);\n\tswitched:= Reverse(sort(switched)); \n\tsublist:= {\"C0\"=perm[1], \"B0\"=perm[2], \"A0\"=perm[3]};\n\tswitched:= subs(sublist, switched); \n\treturn switched;\nend proc:\n\nreverse_notation:= proc(spart)\n\tlocal phis, thetas, phithetas, zeds, Lambda;\n\tphis:= \t\tReverse(sort(map(x-> if x[2] = \"T\" then x[1]; else NULL; end if, spart)));\n\tthetas:= \tReverse(sort(map(x-> if x[2] = \"C\" then x[1]; else NULL; end if, spart)));\n\tphithetas:= \tReverse(sort(map(x-> if x[2] = \"TC\" then x[1]; else NULL; end if, spart)));\n\tzeds:= \t\tReverse(sort(map(x-> if x[2] = \"\" then x[1]; else NULL; end if, spart)));\n\tLambda:=\t[phithetas,phis,thetas,zeds];\n\treturn Lambda;\nend proc:\n\n#n-tupple aka compositions \n#compositions\ncompare_bruhat:= proc(composition1, composition2)\n\tlocal compart, cumul_part1, cumul_part2, max_length, is1greater2, is1smaller2; \n\t# compare the weight of two composition, not really the bruhat order, it's the order defined in Baker, T. H., & Forrester, P. J. (1996). Non-Symmetric Jack Polynomials and Integral Kernels, 33. Quantum Algebra. Retrieved from http://arxiv.org/abs/q-alg/9612003\n\tcompart:= compare_dominance(Reverse(sort(composition1)), Reverse(sort(composition2))); \n\tif composition1 = composition2 then return `=`; end if;\n\tif compart = `>` then \n\t\treturn compart; \n\telif compart = `<` then \n\t\treturn compart; \n\telif compart = `Non-comparable` then\n\t\treturn compart; \n\telif compart= `=` then \n\t\tcumul_part1:= PartialSums(composition1);\n\t\tcumul_part2:= PartialSums(composition2);\n\t\tmax_length:= min(nops(cumul_part1), nops(cumul_part2));\n\t\tis1greater2 := map(x-> if op(x, cumul_part1) >= op(x, cumul_part2) then true; else false; end if, [seq(i, i=1..max_length)]);\n\t\tis1smaller2 := map(x-> if op(x, cumul_part1) <= op(x, cumul_part2) then true; else false; end if, [seq(i, i=1..max_length)]);\n\t\n\t\tif false in is1greater2 then \n\t\t\tif false in is1smaller2 then \n\t\t\t\t\t\treturn `Non-comparable`;\n\t\t\t\telse \n\t\t\t\t\t\treturn `<`;\n\t\t\tend if;\n\t\telse\n\t\t\t\treturn `>`;\n\t\t\tend if; \n\tend if; \nreturn `ErrorInBruhat`; \nend proc:\n\ngenCompositions:=proc(weight, complength)\n\tlocal allcomp;\n\tallcomp:= [seq(op(composition(weight,k)),k=1..complength)]; \n\tallcomp:= map(x-> if nops(x) < complength then [op(x),seq(0, k=1..(complength-nops(x)))]; else x; end if, allcomp); \n\tallcomp:= map(x-> permute(x), allcomp); \n\tallcomp:= FlattenOnce(allcomp); \n\tallcomp:= MakeUnique(allcomp); \n\treturn allcomp;\nend proc:\n\ngive_smallerComps:= proc(composition)\n\tlocal weight, allcomp, smallercomp;\n\tweight:= add(k, k in composition); \n\tallcomp:= genCompositions(weight, nops(composition)); \n\tsmallercomp:= map(x-> if compare_bruhat(composition, x) = `>` then x; else NULL; end if, allcomp); \n\treturn smallercomp;\nend proc:\n\ncompare_dominance:= proc(part1, part2, TEST:=NULL)\n\tlocal cumul_part1, cumul_part2, max_length, is1greater2, is1smaller2;\n\t#Normal dominance ordering comparision \n\tif part1=part2 then return `=`; end if;\n\tif add(i,i in part1) <> add(i,i in part2) then return `Non-comparable`; end if;\n\tcumul_part1:= PartialSums(part1);\n\tcumul_part2:= PartialSums(part2);\n\tif TEST <> NULL then \n\t\tif nops(part1) > nops(part2) then\n\t\t\treturn `>`; \n\t\telse\n\t\t\treturn `<`; \n\t\tend if;\n\tend if;\n\tmax_length:= min(nops(cumul_part1), nops(cumul_part2));\n\tis1greater2 := map(x-> if op(x, cumul_part1) >= op(x, cumul_part2) then true; else false; end if, [seq(i, i=1..max_length)]);\n\tis1smaller2 := map(x-> if op(x, cumul_part1) <= op(x, cumul_part2) then true; else false; end if, [seq(i, i=1..max_length)]);\n#debug\n\n\tif false in is1greater2 then \n\t\tif false in is1smaller2 then \n\t\t\treturn `Non-comparable`;\n\t\telse \n\t\t\treturn `<`;\n\t\tend if;\n\telse\n\t\treturn `>`;\n\tend if;\nend proc:\n\nell:= proc(spart)\n\tlocal ell_out;\n\t#Returns the length of a spart\n\tell_out:= nops(Flatten(spart)); \n\treturn ell_out; \nend proc:\n\nlambda_box:= proc(spart)\n\t#removes circles from diagram\n\treturn eliminate_zeros(sort(Flatten(spart), `>`)); \nend proc:\n\nlambda_phitheta:= proc(spart)\n\tlocal phis, thetas, zeds, pts, ones;\n\t#removes h-circle, convert v-circle into boxes\n\tpts:= spart[1];\n\tones:= [seq(1, k=1..nops(pts))];\n\tpts:= pts+ones;\n\tphis:= eliminate_zeros(spart[2]);\n\tthetas:= eliminate_zeros(spart[3]);\n\tzeds:= spart[4];\n\treturn sort(Flatten([pts, phis, thetas, zeds]), `>`);\nend proc:\n\nlambda_phitheta_phi:= proc(spart)\n\tlocal pts, phis, thetas, zeds, ones;\n\t#removes h-circle, convert v-circle into boxes\n\tpts:= spart[1];\n\tones:= [seq(1, k=1..nops(pts))];\n\tpts:= pts+ones;\n\tphis:= spart[2];\n\tones:= [seq(1, k=1..nops(phis))];\n\tphis:= phis+ones;\n\tthetas:= eliminate_zeros(spart[3]);\n\tzeds:= spart[4];\n\treturn sort(Flatten([pts, phis, thetas, zeds]), `>`);\nend proc:\n\nlambda_phitheta_phi_theta:= proc(spart)\n\tlocal pts, phis, thetas, zeds, ones;\n\t#removes h-circle, convert v-circle into boxes\n\tpts:= spart[1];\n\tones:= [seq(1, k=1..nops(pts))];\n\tpts:= pts+ones;\n\tphis:= spart[2];\n\tones:= [seq(1, k=1..nops(phis))];\n\tphis:= phis+ones;\n\tthetas:= spart[3];\n\tones:= [seq(1, k=1..nops(thetas))]; \n\tthetas:= thetas+ones;\n\tzeds:= spart[4];\n\treturn sort(Flatten([pts, phis, thetas, zeds]), `>`);\nend proc:\n\nlambda_circle:= proc(spart, circs)\n\tlocal sector, pts, phis, thetas, zeds, partition, theseq;\n\tsector:= giveSpartSector(spart);\n\tpts:= spart[1];\n\tphis:= spart[2];\n\tthetas:= spart[3]; \n\tzeds := spart[4];\n\tif 1 in circs then\n\t\ttheseq:= [seq(1, k=1..sector[-1])];\n\t\tpts:= pts+theseq;\n\tend if:\n\tif 2 in circs then\n\t\ttheseq:= [seq(1, k=1..sector[2])];\n\t\tphis:= phis+theseq;\n\tend if:\n\tif 3 in circs then\n\t\ttheseq:= [seq(1, k=1..sector[3])];\n\t\tthetas:= thetas+theseq;\n\tend if:\n\tpartition:= Flatten([pts, phis, thetas, zeds]); \n\tpartition:= Reverse(sort(partition)); \n\treturn eliminate_zeros(partition); \nend proc:\n\nstar_quatuor:= proc(spart, mode:=[1,2,3])\n\tlocal gradation, quatuor;\n\t#Self explanatory\n\t#Allowed modes: \n\t# [TC, T, C]=[1,2,3](Normal), [TC, C, T]=[1,3,2], [T, C, TC]=2,3,1, [T, TC, C]=[2,1,3]...\n\tgradation:= [ seq(mode[1..k], k=0..3) ]; \n\tquatuor:= map(x-> lambda_circle(spart,x), gradation);\n\treturn quatuor; \n\t#return [ lambda_box(spart), lambda_phitheta(spart), lambda_phitheta_phi(spart), lambda_phitheta_phi_theta(spart)];\nend proc:\n\neliminate_zeros:= proc(a_list)\n\t#Removes 0's from a list\n\treturn map(x-> if x = 0 then NULL; else x; end if, a_list);\nend proc:\n\nconjugate_part:= proc(part)\n\tlocal eat_part, new_part, len, ones;\n\teat_part:= part;\n\tnew_part:= [];\n\tlen := nops(part);\n\twhile len <> 0 do\n\t\tlen := nops(eat_part);\n\t\tones := [seq(1,j=1..len)];\n\t\teat_part := eliminate_zeros(eat_part - ones);\n\t\tif len <> 0 then new_part := [op(new_part), len]; end if;\n\tend do:\n\treturn new_part; \nend proc:\n\nsCompareDominance:= proc(spart1, spart2, mode:=[1,2,3])\n\tlocal quatuor1, quatuor2, quatuor_dom; option remember;\n\t#Compares the dominance of two sparts\n\tif spart1 = spart2 then return `=`; end if;\n\tquatuor1:= star_quatuor(spart1, mode);\n\tquatuor2:= star_quatuor(spart2, mode);\n\tquatuor_dom:=map(x-> compare_dominance(quatuor1[x], quatuor2[x]), [1,2,3,4]);\n\tif \t`Non-comparable` in quatuor_dom then return `Non-comparable`;\n\telif \t`>` in quatuor_dom and `<` in quatuor_dom then return `Non-comparable`;\n\telif\t`>` in quatuor_dom then return `>`;\n\telif\t`<` in quatuor_dom then return `<`;\n\telse\treturn \"This should not happen, error in sCompareDominance\"; \n\tend if;\nend proc:\n\nsKeep_smaller_sparts:= proc(spart, sparts, mode:=[1,2,3]) local compared_dominance, list_indices, smaller_sparts;\n\t#Given a spart and a list of sparts, returns all the sparts within the set that are smaller than then one given\n\tcompared_dominance:= map(x-> sCompareDominance(spart, x, mode), sparts);\n\tlist_indices:= [seq(k, k=1..nops(sparts))]; \n\tsmaller_sparts:= map(x-> if compared_dominance[x] = `>` then sparts[x]; else NULL; end if, list_indices); \n\treturn smaller_sparts;\nend proc:\n\ngive_greatest_spart:= proc(sparts, mode:=[1,2,3]) local k, dominance_of_spart;\n\t#Given a set of sparts, returns the highest one in the dominance ordering\n\tfor k in sparts do\n\t\tdominance_of_spart:=map(x-> if x <> k then sCompareDominance(k, x, mode); else NULL; end if, sparts);\n\t\tif MakeUnique(dominance_of_spart) = [`>`] then return k; end if;\n\tend do:\nend proc:\n\n\ngive_smallest_spart:= proc(sparts, mode:=[1,2,3]) local k, dominance_of_spart;\n\t#Given a set of sparts, returns the lowest one in the dominance ordering\n\tfor k in sparts do\n\t\tdominance_of_spart:=map(x-> if x <> k then sCompareDominance(k, x, mode); else NULL; end if, sparts);\n\t\tif MakeUnique(dominance_of_spart) = [`<`] then return k; end if;\n\tend do:\nend proc:\n\narm_part:= proc(i,j,part)\n\t#i is the row\n\t#j is the column\n\treturn part[i]-j;\nend proc:\nco_arm_part:= proc(i,j,part)\n\treturn j-1;\nend proc:\nco_leg_part:= proc(i,j,part)\n\treturn i-1;\nend proc:\nleg_part:= proc(i,j,part)\n\t#i is the row\n\t#j is the column\n\treturn conjugate_part(part)[j] - i;\nend proc:\nJack_norm:= proc(spart, mode:=[1,2,3])\n\tlocal quatuor, spart0, spart1, spart2, spart3, spart_sector, M3, switched, nb_parts, B0, Btc, Bt, Bc, B1,B2,B3, ncoeff0, ncoeff1, ncoeff2, ncoeff3, the_coeff, pt_part, pt_distPart, zeta1;\n\tspart_sector:= giveSpartSector(spart); \n\tquatuor := star_quatuor(spart, mode);\n\tM3:= spart_sector[2] + spart_sector[3] + spart_sector[4]; \n\tspart0:= quatuor[1];\n\tspart1:= quatuor[2];\n\tspart2:= quatuor[3];\n\tspart3:= quatuor[4];\n\tswitched := switch_notation(spart, a, 0, mode);\n\tnb_parts := nops(switched); \n\tB0 := map(x-> if switched[x][2] = \"\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBtc := map(x-> if switched[x][2] = \"TC\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBt := map(x-> if switched[x][2] = \"T\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBt := map(x-> if x[2]-1 in spart[2] then NULL; else x; end if, Bt); \n\tBc := map(x-> if switched[x][2] = \"C\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBc := map(x-> if x[2]-1 in spart[3] then NULL; else x; end if, Bc); \n\tif mode[1] = 1 then\n\t\tB1:= Btc;\n\telif mode[1] = 2 then\n\t\tB1:= Bt;\n\telif mode[1] = 3 then\n\t\tB1:= Bc;\n\tend if;\n\tif mode[2] = 1 then\n\t\tB2:= Btc;\n\telif mode[2] = 2 then\n\t\tB2:= Bt;\n\telif mode[2] = 3 then\n\t\tB2:= Bc;\n\tend if;\n\tif mode[3] = 1 then\n\t\tB3:= Btc;\n\telif mode[3] = 2 then\n\t\tB3:= Bt;\n\telif mode[3] = 3 then\n\t\tB3:= Bc;\n\tend if;\n\tncoeff0:= map(x->(leg_part(op(x),spart3) + alpha*(arm_part(op(x), spart0) + 1))/(leg_part(op(x),spart0) + 1 + alpha*arm_part(op(x), spart3)), B0); \n\tncoeff1:= map(x->(leg_part(op(x),spart0) + alpha*(arm_part(op(x), spart0) + 1))/(leg_part(op(x),spart1) + 1 + alpha*arm_part(op(x), spart3)), B1); \n\tncoeff2:= map(x->(leg_part(op(x),spart1) + alpha*(arm_part(op(x), spart0) + 1))/(leg_part(op(x),spart2) + 1 + alpha*arm_part(op(x), spart3)), B2); \n\tncoeff3:= map(x->(leg_part(op(x),spart2) + alpha*(arm_part(op(x), spart0) + 1))/(leg_part(op(x),spart3) + 1 + alpha*arm_part(op(x), spart3)), B3); \n\tthe_coeff:= mul(x, x in ncoeff0);\n\tthe_coeff:= the_coeff*mul(x, x in ncoeff1);\n\tthe_coeff:= the_coeff*mul(x, x in ncoeff2);\n\tthe_coeff:= the_coeff*mul(x, x in ncoeff3);\n\tpt_part:= spart[1];\n\tpt_distPart:= {op(pt_part)}; \n\tzeta1:= mul(factorial(Occurrences(i,pt_part)), i in pt_distPart);\n\treturn factor(1/zeta1*alpha^(M3)*the_coeff); \nend proc:\n\n\ndown_hook:= proc(spart, mode:=[1,2,3])\n\tlocal quatuor, spart0, spart1, spart2, spart3, spart_sector, M3, switched, nb_parts, B0, Btc, Bt, Bc, B1,B2,B3, ncoeff0, ncoeff1, ncoeff2, ncoeff3, the_coeff, pt_part, pt_distPart, zeta1;\n\tspart_sector:= giveSpartSector(spart); \n\tquatuor := star_quatuor(spart, mode);\n\tM3:= spart_sector[2] + spart_sector[3] + spart_sector[4]; \n\tspart0:= quatuor[1];\n\tspart1:= quatuor[2];\n\tspart2:= quatuor[3];\n\tspart3:= quatuor[4];\n\tswitched := switch_notation(spart, a, 0, mode);\n\tnb_parts := nops(switched); \n\tB0 := map(x-> if switched[x][2] = \"\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBtc := map(x-> if switched[x][2] = \"TC\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBt := map(x-> if switched[x][2] = \"T\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBt := map(x-> if x[2]-1 in spart[2] then NULL; else x; end if, Bt); \n\tBc := map(x-> if switched[x][2] = \"C\" then seq([x,j], j=1..switched[x][1]); else NULL; end if, [seq(k, k=1..nb_parts)]);\n\tBc := map(x-> if x[2]-1 in spart[3] then NULL; else x; end if, Bc); \n\tif mode[1] = 1 then\n\t\tB1:= Btc;\n\telif mode[1] = 2 then\n\t\tB1:= Bt;\n\telif mode[1] = 3 then\n\t\tB1:= Bc;\n\tend if;\n\tif mode[2] = 1 then\n\t\tB2:= Btc;\n\telif mode[2] = 2 then\n\t\tB2:= Bt;\n\telif mode[2] = 3 then\n\t\tB2:= Bc;\n\tend if;\n\tif mode[3] = 1 then\n\t\tB3:= Btc;\n\telif mode[3] = 2 then\n\t\tB3:= Bt;\n\telif mode[3] = 3 then\n\t\tB3:= Bc;\n\tend if;\n\tncoeff0:= map(x->(leg_part(op(x),spart0) + 1 + alpha*arm_part(op(x), spart3)), B0); \n\tncoeff1:= map(x->(leg_part(op(x),spart1) + 1 + alpha*arm_part(op(x), spart3)), B1); \n\tncoeff2:= map(x->(leg_part(op(x),spart2) + 1 + alpha*arm_part(op(x), spart3)), B2); \n\tncoeff3:= map(x->(leg_part(op(x),spart3) + 1 + alpha*arm_part(op(x), spart3)), B3); \n\tthe_coeff:= mul(x, x in ncoeff0);\n\tthe_coeff:= the_coeff*mul(x, x in ncoeff1);\n\tthe_coeff:= the_coeff*mul(x, x in ncoeff2);\n\tthe_coeff:= the_coeff*mul(x, x in ncoeff3);\n\tpt_part:= spart[1];\n\tpt_distPart:= {op(pt_part)}; \n\tzeta1:= mul(factorial(Occurrences(i,pt_part)), i in pt_distPart);\n\treturn factor(zeta1*the_coeff); \n\t#return the_coeff;\nend proc:\n", "meta": {"hexsha": "74c8231f5644ff915379afa354e62cb444223662", "size": 19480, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/sparts.mpl", "max_stars_repo_name": "LAV42/N2-Superpolynomials", "max_stars_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "max_stars_repo_licenses": ["BSD-3-Clause"], "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/sparts.mpl", "max_issues_repo_name": "LAV42/N2-Superpolynomials", "max_issues_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "max_issues_repo_licenses": ["BSD-3-Clause"], "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/sparts.mpl", "max_forks_repo_name": "LAV42/N2-Superpolynomials", "max_forks_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.8747697974, "max_line_length": 261, "alphanum_fraction": 0.6566735113, "num_tokens": 6953, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7154239836484143, "lm_q2_score": 0.7799928900257126, "lm_q1q2_score": 0.5580256205996348}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_mgga_c *)\n\npar_n := 5:\n\ngamma_x := 0.004:\npar_x := [\n [ 1.000, 0, 0],\n [ 1.308, 0, 1],\n [ 1.901, 0, 2],\n [ 0.416, 1, 0],\n [ 3.070, 1, 1]\n]:\n\ngamma_ss := 0.2:\npar_ss := [\n [ 1.000, 0, 0],\n [ -1.855, 0, 2],\n [ -5.668, 1, 0],\n [-20.497, 3, 2],\n [-20.364, 4, 2]\n]:\n\ngamma_os := 0.006:\npar_os := [\n [ 1.000, 0, 0],\n [ 1.573, 0, 1],\n [ -6.298, 0, 3],\n [ 2.535, 1, 0],\n [ -6.427, 3, 2]\n]:\n\n$define lda_x_params\n$include \"lda_x.mpl\"\n$include \"b97mv.mpl\"\n\nf := (rs, z, xt, xs0, xs1, ts0, ts1, us0, us1) ->\n f_b97mv(f_lda_x, rs, z, xt, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "4b8a99cd59fb7a67e4f16718869383af3d42cc4e", "size": 856, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_xc_b97mv.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_xc_b97mv.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_xc_b97mv.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 18.6086956522, "max_line_length": 68, "alphanum_fraction": 0.5081775701, "num_tokens": 405, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.870597271765821, "lm_q2_score": 0.6406358479787609, "lm_q1q2_score": 0.5577358214456926}} {"text": "inputfile := \"AOC4-input.txt\":\ninput := StringTools:-Split(FileTools:-Text:-ReadFile(inputfile), \"\\n\"):\nnumbers := [parse(input[1])]:\ninput := map(StringTools:-Trim@StringTools:-Squeeze,input[3..-1]):\nnumboards := ceil( nops(input) / 6 );\ntheboards := [seq(1..numboards)]:\n\n# create board and mark arrays for each bingo board\nfor i to numboards do\n tmp := map(s->map(parse, StringTools:-Split(s)),input[1..5]);\n boards[i] := Array(tmp,datatype=integer);\n marks[i] := Array(1..5, 1..5, 0, datatype=integer[1]);\n if i <> numboards then\n input := input[7..-1];\n else\n input := [];\n end if;\nend do:\n\n# find the location of n on each board and mark it\ndrawnumber := proc(n)\nglobal boards, marks, theboards;\nlocal i, loc;\n for i in theboards do\n if member(n, boards[i], 'loc') then\n marks[i][loc] := 1;\n end if;\n end do;\n return NULL;\nend proc:\n\n# check if board i has a bingo marked\ncheckbingo :=proc(i)\nglobal marks;\n if max(ArrayTools:-AddAlongDimension(marks[i], 1)) = 5 then\n return true;\n elif max(ArrayTools:-AddAlongDimension(marks[i], 2)) = 5 then\n return true;\n else\n return false;\n end if;\nend proc:\n\n# first problem - find the board that will win FIRST\nanswer1 := FAIL:\nfor j to nops(numbers) while answer1 = FAIL do\n n := numbers[j];\n drawnumber(n);\n for i to numboards do\n if checkbingo(i) then\n answer1 := add(boards[i]-boards[i]*marks[i])*n;\n break;\n end if;\n end do;\nend do:\nanswer1;\n\n# second problem - find the board that will win LAST\nanswer2 := FAIL:\nnumbingos := 0:\nfor j to nops(numbers) while answer2 = FAIL do\n n := numbers[j];\n drawnumber(n);\n for i in theboards do\n if checkbingo(i) then\n if nops(theboards) = 1 then\n answer2 := add(boards[i]-boards[i]*marks[i])*n;\n end if;\n theboards := subs(i=NULL, theboards); \n end if;\n end do;\nend do:\nanswer2;\n", "meta": {"hexsha": "6eb4e2ce76c1ad05f8343528dccd803f7f1da1a8", "size": 1992, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day4/AdventOfCode2021-Day4.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day4/AdventOfCode2021-Day4.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day4/AdventOfCode2021-Day4.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.9189189189, "max_line_length": 72, "alphanum_fraction": 0.6019076305, "num_tokens": 571, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8376199714402813, "lm_q2_score": 0.6654105521116445, "lm_q1q2_score": 0.5573611676558174}} {"text": "myseries := series(sin(x), x = 0, 10);\npoly := convert(myseries, polynom);\n\nplotsetup(gif,plotoutput=\"plot.gif\"):\nplot(poly, x = -2*Pi .. 2*Pi, y = -3 .. 3);\n", "meta": {"hexsha": "1d100cc866d07e1a4e6acf1ef413d01f8dcbf180", "size": 158, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "assets/maple/hpc2/series_example_fixedplot.mpl", "max_stars_repo_name": "frb-yousefi/RSE-Sheffield.github.io", "max_stars_repo_head_hexsha": "28b03284ba6a0234ea1e304144f9df55364f3c57", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 12, "max_stars_repo_stars_event_min_datetime": "2015-12-19T00:32:38.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-28T14:25:20.000Z", "max_issues_repo_path": "assets/maple/hpc2/series_example_fixedplot.mpl", "max_issues_repo_name": "frb-yousefi/RSE-Sheffield.github.io", "max_issues_repo_head_hexsha": "28b03284ba6a0234ea1e304144f9df55364f3c57", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": 352, "max_issues_repo_issues_event_min_datetime": "2016-01-21T12:29:46.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-24T15:51:44.000Z", "max_forks_repo_path": "assets/maple/hpc2/series_example_fixedplot.mpl", "max_forks_repo_name": "frb-yousefi/RSE-Sheffield.github.io", "max_forks_repo_head_hexsha": "28b03284ba6a0234ea1e304144f9df55364f3c57", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": 51, "max_forks_repo_forks_event_min_datetime": "2016-01-21T11:08:30.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-23T10:47:57.000Z", "avg_line_length": 26.3333333333, "max_line_length": 43, "alphanum_fraction": 0.6012658228, "num_tokens": 58, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8289388083214156, "lm_q2_score": 0.6723317057447908, "lm_q1q2_score": 0.5573218429567915}} {"text": "######################################################################\n\n`is_element/SEM` := (N::posint) -> (A::set) -> proc(eta)\n local AA,a,b,c,ok;\n global reason;\n\n if not(type(eta,table)) then\n reason := [convert(procname,string),\"eta is not a table\",eta];\n return false;\n fi;\n\n AA := [seq(seq([a,b],b in A),a in A)];\n if {indices(eta)} <> {op(AA)} then\n reason := [convert(procname,string),\"eta is not indexed by A^2\",eta,AA];\n return false;\n fi; \n\n for a in A do\n for b in A do\n if eta[a,b] = 0 and a <> b then\n reason := [convert(procname,string),\"eta does not separate a and b\",a,b,eta];\n return false;\n fi;\n\n if eta[a,b] + eta[b,a] <> 0 then\n reason := [convert(procname,string),\"eta is not antisymmetric at [a,b]\",a,b,eta];\n return false;\n fi;\n\n for c in A do\n ok := `is_leq/E`(N)(0,eta[a,c]) or \n `is_leq/E`(N)(eta[a,b],eta[a,c]) or \n `is_leq/E`(N)(eta[b,c],eta[a,c]);\n if not(ok) then\n reason := [convert(procname,string),\"min(0,eta[a,b],eta[a,c]) > eta[a,c]\",a,b,c,eta];\n return false;\n fi;\n\n ok := `is_leq/E`(N)(eta[a,c],0) or \n `is_leq/E`(N)(eta[a,c],eta[a,b]) or \n `is_leq/E`(N)(eta[a,c],eta[b,c]);\n if not(ok) then\n reason := [convert(procname,string),\"eta[a,c] > max(0,eta[a,b],eta[a,c])\",a,b,c,eta];\n return false;\n fi;\n od;\n od;\n od;\n\n return true;\nend;\n\n`is_equal/SEM` := (N::posint) -> (A::set) -> proc(eta,zeta)\n local a,b;\n global reason;\n\n for a in A do\n for b in A do\n if eta[a,b] <> zeta[a,b] then\n reason := [convert(procname,string),\"eta[a,b] <> zeta[a,b]\",a,b,eta[a,b],zeta[a,b]];\n return false;\n fi;\n od;\n od;\n\n return true;\nend:\n\n`is_leq/SEM` := (N::posint) -> (A::set) -> proc(eta,zeta)\n local a,b;\n\n for a in A do\n for b in A do\n if not(`preceq/E`(N)(A)(eta[a,b],zeta[a,b])) then\n return false;\n fi;\n od;\n od;\n\n return true;\nend:\n\n`build/SEM` := (N::posint) -> (A::set) -> proc(s::list,u::list) \n local n,L,i,j,k,m,eta,a,b;\n\n n := nops(A);\n if nops(s) <> n or nops(u) <> n-1 then return FAIL; fi;\n if {op(s)} <> A then return FAIL; fi;\n\n L := table();\n for i from 1 to n do\n L[s[i]] := i;\n od:\n\n eta := table;\n\n for a in A do\n eta[a,a] := 0;\n for b in A do\n i := L[a];\n j := L[b];\n if i < j then\n m := min(seq(u[k],k=i..j-1));\n eta[a,b] := epsilon^m;\n eta[b,a] := -epsilon^m;\n fi;\n od;\n od;\n\n return eval(eta);\nend:\n\n`random_element/SEM` := (N::posint) -> (A::set) -> proc()\n local s,m,u,i;\n \n s := `random_element/ord`(A)();\n m := nops(A);\n u := [seq(rand(0..N-1)(),i=1..m-1)];\n return `build/SEM`(N)(A)(s,u);\nend:\n\n`list_elements/SEM` := (N::posint) -> proc(A::set)\n option remember;\n local S,U,s,u,m,i,j;\n\n S := `list_elements/ord`(A);\n U := [[]];\n m := nops(A);\n for i from 1 to m-1 do\n U := map(u -> seq([op(u),j],j=0..N-1),U);\n od: \n\n return [seq(seq(`build/SEM`(N)(A)(s,u),u in U),s in S)];\nend:\n\n`count_elements/SEM` := (N::posint) -> (A::set) ->\n nops(A)! * N^(nops(A) - 1);\n \n`mu/F/SEM` := (N::posint) -> (A::set) -> proc(x)\n local eta,a,b,u,v,i;\n\n eta := table();\n for a in A do\n for b in A do\n u := x[b] -~ x[a];\n v := add(u[i] * epsilon^(i-1),i = 1..N);\n eta[a,b] := `lambda/P/E`(N)(v);\n od;\n od;\n\n return eval(eta);\nend:\n\n`sigma/SEM/F` := (N::posint) -> (A::set) -> proc(eta)\n local n,m,a,b,A1,x,u,i;\n\n n := table():\n\n for a in A do\n for b in A do\n n[a,b] := `is_leq/E`(N)(0,eta[a,b]);\n od;\n od;\n\n A1 := sort([op(A)],(a,b) -> n[a,b]);\n\n x := table():\n u := 0;\n m := nops(A1);\n x[A1[1]] := [0$N];\n\n for i from 2 to m do\n u := u + eta[A1[i-1],A1[i]];\n x[A1[i]] := [seq(coeff(u,epsilon,i),i=0..N-1)];\n od;\n\n return(eval(x));\nend:\n", "meta": {"hexsha": "a21a106c8b13ec7fab5d96787dbbc94ab12cf20a", "size": 3634, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/chains/SEM.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/operads/chains/SEM.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/operads/chains/SEM.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": 20.3016759777, "max_line_length": 90, "alphanum_fraction": 0.5071546505, "num_tokens": 1369, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.82446190912407, "lm_q2_score": 0.6757645944891558, "lm_q1q2_score": 0.5571421676909825}} {"text": "\n# Definitions for Robot Dynamics Code Generation\n# Init\n# Erstelle Definitionen für die Maple-Skripte zur Berechnung von Kinematik und Dynamik des Roboters\n# Nutze Euler-Winkel (RPY-Konvention) zur Darstellung der Basisorientierung\n# \n# Quellen:\n# [1] Sousa, C. D. and Cortesao, R.: Physical feasibility of robot base inertial parameter identification: A linear matrix inequality approach (2014)\n# [2] Ayusawa, K. and Venture, G. and Nakamura, Y.: Identifiability and identification of inertial parameters using the underactuated base-link dynamics for legged multibody systems (2013)\n# [3] Fujimoto, Y. and Obata, S. and Kawamura, A.: Robust biped walking with active interaction control between foot and ground (1998)\n# [4] Khalil, W. and Kleinfinger, J.-F.: Minimum operations and minimum parameters of the dynamic models of tree structure robots (1987)\n# [5] Ortmaier: Robotik I Vorlesungsskript\n# \n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-04\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\n# Funktion für Euler-Transformation aus Robotik-Repo laden (Pfad muss bekannt sein)\nread(\"../robotics_repo_path\"):\nread(sprintf(\"%s/transformation/maple/proc_eulxyzjac\", robotics_repo_path)):\n# Lese Umgebungsvariable für Codegenerierung.\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"Generiere Parameter für %s\\n\",robot_name):\n# Lese allgemeine Definitionen für Floating-Base\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_twist_definitions\", robot_name):\n# Robotics Definitions\n# Position und Orientierung der Basis (pelvis). Die Orientierung ist mit XYZ-Euler-Winkeln definiert.\n# Eine Invertierung der Orientierungsdarstellung sollte nicht notwendig werden, von daher kein Problem mit Orientierungsrepräsentationssingularität.\n# gem. [2], S. 4 X_base_t SE(3): Position und Orientierung.\nNQB := 6:\nX_base_t:=Matrix(6, 1, [rx_base(t),ry_base(t),rz_base(t),alphax_base(t), betay_base(t), gammaz_base(t)]):\nX_base_s:=Matrix(6, 1, [rxs_base,rys_base,rzs_base,alphaxs_base, betays_base, gammazs_base]):\n# Geschwindigkeit der Basis\n# Twist: Verallgemeinerte Geschwindigkeit\nV_base_t:=diff~(X_base_t, t):\nV_base_s:=Matrix(6, 1, [vxs_base,vys_base,vzs_base,alphaDx_base, betaDy_base, gammaDz_base]):\n# Zeitableitung davon\nVD_base_t:=diff~(V_base_t, t):\nVD_base_s:=Matrix(6, 1, [vDxs_base,vDys_base,vDzs_base,alphaDDx_base, betaDDy_base, gammaDDz_base]):\n# Name der Methode für die Orientierungsdarstellung der Basis\nbase_method_name := \"eulxyz\":\n# Umrechnung von der Ableitung der Basis-Orientierung zu Winkelgeschwindigkeiten:\n# Nutze die Euler-XYZ-Konvention (\"RPY\").\n# Siehe [5], Gl. (4.23)\nT_basevel := eulxyzjac(X_base_t(4..6,1)):\n# Verallgemeinerte Koordinaten, gem [2], S. 4, [3], S.1\nNQ:=NQJ+NQB:\nq_t := Matrix(NQ,1, ):\nq_s := Matrix(NQ,1, ):\nqD_t:= Matrix(NQ,1, ):\nqD_s:= Matrix(NQ,1, ):\nqDD_t:= Matrix(NQ,1, ):\nqDD_s:= Matrix(NQ,1, ):\n# MDH-Gelenkwinkel neu speichern (Definition der verallg. Koordinaten war dort noch nicht bekannt\ntheta := value(theta):\n# Export\nsave q_t, q_s, qD_t, qD_s, qDD_t, qDD_s, qJ_t, qJ_s, qJD_t, qJD_s, qJDD_t, qJDD_s, g_world, X_base_t, X_base_s, V_base_t, V_base_s, VD_base_t, VD_base_s, qoffset, theta, alpha, d, a,v,b,beta, sigma,mu, M, r_i_i_Si, mr_i_i_Si, I_i_i, I_i_Si, PV2_vec, PV2_mat, robot_name, NQ,NQB,NQJ,NJ,NL, base_method_name, T_basevel, kintmp_t, kintmp_s, sprintf(\"../codeexport/%s/tmp/tree_floatb_eulxyz_definitions\", robot_name):\nsave q_t, q_s, qD_t, qD_s, qDD_t, qDD_s, qJ_t, qJ_s, qJD_t, qJD_s, qJDD_t, qJDD_s, g_world, X_base_t, X_base_s, V_base_t, V_base_s, VD_base_t, VD_base_s, qoffset, theta, alpha, d, a,v,b,beta, sigma,mu, M, r_i_i_Si, mr_i_i_Si, I_i_i, I_i_Si, PV2_vec, PV2_mat, robot_name, NQ,NQB,NQJ,NJ,NL, base_method_name, T_basevel, kintmp_t, kintmp_s, sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\n\n", "meta": {"hexsha": "b887c5dba016262aa5cb420373e5feda24d50b42", "size": 4099, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_definitions/robot_tree_floatb_eulxyz_definitions.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_definitions/robot_tree_floatb_eulxyz_definitions.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_definitions/robot_tree_floatb_eulxyz_definitions.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 67.1967213115, "max_line_length": 413, "alphanum_fraction": 0.7684801171, "num_tokens": 1378, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8688267728417087, "lm_q2_score": 0.6406358479787609, "lm_q1q2_score": 0.5566015763660984}} {"text": "# This code sets up a toy model of the nonstandard product structure\n# on the HKR character ring for V x V, where V is the groupoid of\n# finite-dimensional F-vector spaces.\n\n# We fix a number d > 0 (which should really be infinity).\n# We consider the set A1 of tables indexed by natural numbers u < d,\n# and the set A2 indexed by pairs (u,v) with u+v < d. These sets\n# have products called `star/A1` and `star/A2`. The first is given by\n# the following rule: `star/A1`(f,g)[u] is the sum of all terms\n# c1[u0,u1] * f[u0] * g[u1], where u0+u1 = u, and c1[u0,u1] is the\n# number of splittings of F^u as a direct sum of subspaces of\n# dimensions u0 and u1.\n#\n# Similarly, `star/A2`(f,g)[u,v] is a sum of terms\n# c2[u0,v0,u1,v1] * f[u0,v0] * g[u1,v1] where\n# (u0,v0) + (u1,v1) = (u,v) and\n# c2[u0,v0,u1,v1] is c1[u0,u1] times c1[v0,v1] times\n# q^(u0*v1+2*u1*v0). This final factor is inserted to ensure that\n# the coproduct map psi : A1 -> A2 (given by psi(f)[u,v]=f[u+v])\n# is a ring map.\n\nd := 10;\n\ngrassmann_count := (q) -> (n,d) ->\n mul(q^(n-i)-1,i=0..d-1)/mul(q^(d-i)-1,i=0..d-1);\n\nsplitting_count := (q) -> (n,m) ->\n grassmann_count(q)(n+m,n) * q^(n*m);\n\n######################################################################\n\n`is_element/A1` := proc(f)\n local u,L;\n \n if not(type(f,table)) then\n return false;\n fi;\n\n L := [seq([u],u=0..d-1)];\n\n if [indices(f)] <> L then\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/A1` := proc(f,g)\n local u;\n \n for u from 0 to d-1 do\n if simplify(f[u]-g[u]) <> 0 then\n return false;\n fi;\n od;\n return true;\nend:\n\n`to_list/A1` := (f) -> [seq(f[u],u=0..d-1)]:\n`from_symbol/A1` := (f) -> table([seq(u=f[u],u=0..d-1)]);\n\n`zero/A1` := table([seq(u=0,u=0..d-1)]):\n`one/A1` := table([seq(u=1,u=0..d-1)]):\n`delta/A1` := table([seq(u=`if`(u=0,1,0),u=0..d-1)]):\n\n`plus/A1` := proc(f,g)\n table([seq(u = f[u]+g[u],u=0..d-1)]);\nend:\n\n`minus/A1` := proc(f,g)\n table([seq(u = f[u]-g[u],u=0..d-1)]);\nend:\n\n`dot/A1` := proc(f,g)\n table([seq(u = f[u]*g[u],u=0..d-1)]);\nend:\n\n`scalar_times/A1` := proc(c,f)\n table([seq(u = c*f[u],u=0..d-1)]);\nend:\n\n`star/A1` := proc(f,g)\n local h,u,u0,u1;\n h := table();\n for u from 0 to d-1 do\n h[u] := 0;\n od;\n\n for u0 from 0 to d-1 do \n for u1 from 0 to d-1-u0 do\n h[u0+u1] := h[u0+u1] + splitting_count(q)(u0,u1)*f[u0]*g[u1];\n od;\n od:\n\n return eval(h);\nend:\n\n######################################################################\n\n`is_element/A2` := proc(f)\n local u,L;\n \n if not(type(f,table)) then\n return false;\n fi;\n\n L := [seq(seq([u,v],v=0..d-1-u),u=0..d-1)];\n\n if [indices(f)] <> L then\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/A2` := proc(f,g)\n local u,v;\n \n for u from 0 to d-1 do\n for v from 0 to d-1-u do\n if simplify(f[u,v]-g[u,v]) <> 0 then\n return false;\n fi;\n od;\n od;\n return true;\nend:\n\n`to_list/A2` := (f) -> [seq(seq(f[u,v],v=0..d-1-u),u=0..d-1)]:\n`from_symbol/A2` := (f) -> table([seq(seq((u,v)=f[u,v],v=0..d-1-u),u=0..d-1)]);\n\n`zero/A2` := table([seq(seq((u,v)=0,v=0..d-1-u),u=0..d-1)]):\n`one/A2` := table([seq(seq((u,v)=1,v=0..d-1-u),u=0..d-1)]):\n`delta/A2` := table([seq(seq((u,v)=`if`(u=0 and v = 0,1,0),v=0..d-1-u),u=0..d-1)]):\n\n`plus/A2` := proc(f,g)\n table([seq(seq((u,v) = f[u,v]+g[u,v],v=0..d-1-u),u=0..d-1)]);\nend:\n\n`minus/A2` := proc(f,g)\n table([seq(seq((u,v) = f[u,v]-g[u,v],v=0..d-1-u),u=0..d-1)]);\nend:\n\n`dot/A2` := proc(f,g)\n table([seq(seq((u,v) = f[u,v]*g[u,v],v=0..d-1-u),u=0..d-1)]);\nend:\n\n`scalar_times/A2` := proc(c,f)\n table([seq(seq((u,v) = c*f[u,v],v=0..d-1-u),u=0..d-1)]);\nend:\n\n`mu/A2` := (u0,v0,u1,v1) -> q^(u0*v1+2*u1*v0);\n\n`star/A2` := proc(f,g)\n local h,u,v,u0,u1,v0,v1;\n h := table();\n\n for u from 0 to d-1 do \n for v from 0 to d-1-u do\n h[u,v] := 0;\n od;\n od:\n\n for u0 from 0 to d-1 do\n for u1 from 0 to d-1-u0 do\n for v0 from 0 to d-1-u0-u1 do\n for v1 from 0 to d-1-u0-u1-v0 do\n h[u0+u1,v0+v1] :=\n h[u0+u1,v0+v1] + \n splitting_count(q)(u0,u1) * \n splitting_count(q)(v0,v1) * \n `mu/A2`(u0,v0,u1,v1) * \n f[u0,v0] * g[u1,v1];\n od;\n od;\n od;\n od;\n\n return eval(h);\nend:\n\n######################################################################\n\n`is_element/A3` := proc(f)\n local u,L;\n \n if not(type(f,table)) then\n return false;\n fi;\n\n L := [seq(seq(seq([u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)];\n\n if [indices(f)] <> L then\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/A3` := proc(f,g)\n local u,v,w;\n \n for u from 0 to d-1 do\n for v from 0 to d-1-u do\n for w from 0 to d-1-u-v do\n if simplify(f[u,v,w]-g[u,v,w]) <> 0 then\n return false;\n fi;\n od;\n od;\n od;\n return true;\nend:\n\n`to_list/A3` := (f) -> [seq(seq(seq(f[u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]:\n`from_symbol/A3` := (f) -> table([seq(seq(seq((u,v,w)=f[u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]);\n\n`zero/A3` := table([seq(seq(seq((u,v,w)=0,w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]):\n`one/A3` := table([seq(seq(seq((u,v,w)=1,w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]):\n`delta/A3` := table([seq(seq(seq((u,v,w)=`if`([u,v,w]=[0,0,0],1,0),w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]):\n\n`plus/A3` := proc(f,g)\n table([seq(seq(seq((u,v,w) = f[u,v,w]+g[u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]);\nend:\n\n`minus/A3` := proc(f,g)\n table([seq(seq(seq((u,v,w) = f[u,v,w]-g[u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]);\nend:\n\n`dot/A3` := proc(f,g)\n table([seq(seq(seq((u,v,w) = f[u,v,w]*g[u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]);\nend:\n\n`scalar_times/A3` := proc(c,f)\n table([seq(seq(seq((u,v,w) = c*f[u,v,w],w=0..d-1-u-v),v=0..d-1-u),u=0..d-1)]);\nend:\n\n`mu/A3` := (u0,v0,w0,u1,v1,w1) -> q^(u0*v1+u0*w1+v0*w1+2*u1*v0+2*u1*w0+2*v1*w0);\n\n`star/A3` := proc(f,g)\n local h,u,v,w,u0,u1,v0,v1,w0,w1;\n h := table();\n\n for u from 0 to d-1 do \n for v from 0 to d-1-u do\n for w from 0 to d-1-u-v do\n h[u,v,w] := 0;\n od;\n od;\n od:\n\n for u0 from 0 to d-1 do\n for u1 from 0 to d-1-u0 do\n for v0 from 0 to d-1-u0-u1 do\n for v1 from 0 to d-1-u0-u1-v0 do\n for w0 from 0 to d-1-u0-u1-v0-v1 do\n for w1 from 0 to d-1-u0-u1-v0-v1-w0 do\n h[u0+u1,v0+v1,w0+w1] :=\n\th[u0+u1,v0+v1,w0+w1] + \n\t splitting_count(q)(u0,u1) * \n\t splitting_count(q)(v0,v1) * \n\t splitting_count(q)(w0,w1) * \n\t `mu/A3`(u0,v0,w0,u1,v1,w1) * \n\t f[u0,v0,w0] * g[u1,v1,w1];\n od;\n od;\n od;\n od;\n od;\n od;\n\n return eval(h);\nend:\n\n######################################################################\n\npsi := proc(f)\n local h,u,v;\n\n h := table();\n\n for u from 0 to d-1 do \n for v from 0 to d-1-u do\n h[u,v] := f[u+v];\n od;\n od:\n \n return eval(h);\nend:\n\npsi_L := proc(f)\n local h,u,v,w;\n\n h := table();\n\n for u from 0 to d-1 do \n for v from 0 to d-1-u do\n for w from 0 to d-1-u-v do\n h[u,v,w] := f[u+v,w];\n od;\n od;\n od:\n \n return eval(h);\nend:\n\npsi_R := proc(f)\n local h,u,v,w;\n\n h := table();\n\n for u from 0 to d-1 do \n for v from 0 to d-1-u do\n for w from 0 to d-1-u-v do\n h[u,v,w] := f[u,v+w];\n od;\n od;\n od:\n \n return eval(h);\nend:\n\ntensor11 := proc(f,g)\n table([seq(seq((u,v)=f[u]*g[v],v=0..d-1-u),u=0..d-1)]);\nend: \n\ntwisted_tensor11 := proc(f,g)\n table([seq(seq((u,v)=q^(u*v)*f[u]*g[v],v=0..d-1-u),u=0..d-1)]);\nend: \n\neta_L := (f) -> tensor11(`delta/A1`,f):\n\neta_R := (f) -> tensor11(f,`delta/A1`):\n\nepsilon_L := proc(f)\n local h,u;\n\n h := table;\n\n for u from 0 to d-1 do\n h[u] := f[0,u];\n od;\n\n return eval(h):\nend:\n\nepsilon_R := proc(f)\n local h,u;\n\n h := table;\n\n for u from 0 to d-1 do\n h[u] := f[u,0];\n od;\n\n return eval(h):\nend:\n\n######################################################################\n\ncheck_A1 := proc()\n local f,g,h,ff,gg,hh;\n\n ff := `from_symbol/A1`(f);\n gg := `from_symbol/A1`(g);\n hh := `from_symbol/A1`(h);\n \n printf(\"%a()\\n\",procname);\n\n _ASSERT(\n `is_equal/A1`(`star/A1`(`delta/A1`,ff),ff),\"Left unit law\"\n );\n\n _ASSERT(\n `is_equal/A1`(`star/A1`(ff,`delta/A1`),ff),\"Right unit law\"\n );\n\n _ASSERT(\n `is_equal/A1`(`star/A1`(ff,`star/A1`(gg,hh)),\n `star/A1`(`star/A1`(ff,gg),hh)),\n \"Associativity law\"\n );\nend:\n\ncheck_A2 := proc()\n local f,g,h,ff,gg,hh;\n\n ff := `from_symbol/A2`(f);\n gg := `from_symbol/A2`(g);\n hh := `from_symbol/A2`(h);\n \n printf(\"%a()\\n\",procname);\n\n _ASSERT(\n `is_equal/A2`(`star/A2`(`delta/A2`,ff),ff),\"Left unit law\"\n );\n\n _ASSERT(\n `is_equal/A2`(`star/A2`(ff,`delta/A2`),ff),\"Right unit law\"\n );\n\n _ASSERT(\n `is_equal/A2`(`star/A2`(ff,`star/A2`(gg,hh)),\n `star/A2`(`star/A2`(ff,gg),hh)),\n \"Associativity law\"\n );\nend:\n\ncheck_A3 := proc()\n local f,g,h,ff,gg,hh;\n\n ff := `from_symbol/A3`(f);\n gg := `from_symbol/A3`(g);\n hh := `from_symbol/A3`(h);\n \n printf(\"%a()\\n\",procname);\n\n _ASSERT(\n `is_equal/A3`(`star/A3`(`delta/A3`,ff),ff),\"Left unit law\"\n );\n\n _ASSERT(\n `is_equal/A3`(`star/A3`(ff,`delta/A3`),ff),\"Right unit law\"\n );\n\n _ASSERT(\n `is_equal/A3`(`star/A3`(ff,`star/A3`(gg,hh)),\n `star/A3`(`star/A3`(ff,gg),hh)),\n \"Associativity law\"\n );\nend:\n\ncheck_A_maps := proc()\n local f1,g1,h1,ff1,gg1,hh1,f2,g2,h2,ff2,gg2,hh2;\n\n ff1 := `from_symbol/A1`(f1);\n gg1 := `from_symbol/A1`(g1);\n hh1 := `from_symbol/A1`(h1);\n\n ff2 := `from_symbol/A2`(f2);\n gg2 := `from_symbol/A2`(g2);\n hh2 := `from_symbol/A2`(h2);\n\n _ASSERT(\n `is_equal/A2`(eta_L(`delta/A1`),`delta/A2`) and\n `is_equal/A2`(eta_L(`star/A1`(ff1,gg1)),`star/A2`(eta_L(ff1),eta_L(gg1))),\n \"eta_L is a ring map\"\n );\n\n _ASSERT(\n `is_equal/A2`(eta_R(`delta/A1`),`delta/A2`) and\n `is_equal/A2`(eta_R(`star/A1`(ff1,gg1)),`star/A2`(eta_R(ff1),eta_R(gg1))),\n \"eta_R is a ring map\"\n );\n\n _ASSERT(\n `is_equal/A2`(psi(`delta/A1`),`delta/A2`) and\n `is_equal/A2`(psi(`star/A1`(ff1,gg1)),`star/A2`(psi(ff1),psi(gg1))),\n \"psi is a ring map\"\n );\n\n _ASSERT(\n `is_equal/A1`(epsilon_L(`delta/A2`),`delta/A1`) and\n `is_equal/A1`(epsilon_L(`star/A2`(ff2,gg2)),`star/A1`(epsilon_L(ff2),epsilon_L(gg2))),\n \"epsilon_L is a ring map\"\n );\n\n _ASSERT(\n `is_equal/A1`(epsilon_R(`delta/A2`),`delta/A1`) and\n `is_equal/A1`(epsilon_R(`star/A2`(ff2,gg2)),`star/A1`(epsilon_R(ff2),epsilon_R(gg2))),\n \"epsilon_R is a ring map\"\n );\n\n _ASSERT(\n `is_equal/A1`(epsilon_L(psi(ff1)),ff1),\n \"epsilon_L o psi = 1\"\n );\n\n _ASSERT(\n `is_equal/A1`(epsilon_R(psi(ff1)),ff1),\n \"epsilon_R o psi = 1\"\n );\n\n _ASSERT(\n `is_equal/A2`(`star/A2`(eta_R(ff1),eta_L(gg1)),twisted_tensor11(ff1,gg1)),\n \"eta_R * eta_L\"\n );\nend;\n\n", "meta": {"hexsha": "df5a3c3c20d4c261e543237027fdca6d0610d913", "size": 10245, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/tanabe/old/twisted_product.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", 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"alphanum_fraction": 0.5305026842, "num_tokens": 4276, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127641048444, "lm_q2_score": 0.651354857898194, "lm_q1q2_score": 0.556200227120965}} {"text": "# This file sets up the letters of the alphabet as one-dimensional simplicial\n# complexes. \n\nletters := table():\n\nalphabet_list := [[\"A\",\"B\",\"C\",\"D\",\"E\"],\n [\"F\",\"G\",\"H\",\"I\",\"J\"],\n [\"K\",\"L\",\"M\",\"N\",\"O\"],\n [\"P\",\"Q\",\"R\",\"S\",\"T\"],\n [\"U\",\"V\",\"W\",\"X\",\"Y\"]]:\n\nalphabet_type_list := [\n [\"C\",\"G\",\"L\",\"M\",\"N\",\"S\",\"U\",\"V\",\"W\"],\n [\"E\",\"F\",\"J\",\"T\",\"Y\"],\n [\"H\",\"I\"],\n [\"K\",\"X\"],\n [\"O\",\"D\",\"A\",\"Q\"],\n [\"B\"]\n]:\n \nset_map := proc(T)\n local P,e,s,t;\n T[\"map\"] := table():\n P := T[\"embedding\"]:\n for e in T[\"max_simplices\"] do \n T[\"map\"][e] := unapply((1-t) *~ P[e[1]] +~ t *~ P[e[2]],t);\n od:\nend:\n\nset_alt_map := proc(T)\n local P,e,s,t;\n T[\"alt_map\"] := table():\n P := T[\"alt_embedding\"]:\n for e in T[\"max_simplices\"] do \n T[\"alt_map\"][e] := unapply((1-t) *~ P[e[1]] +~ t *~ P[e[2]],t);\n od:\nend:\n\nset_isotopy := proc(T)\n local P,Q,e,s,t;\n T[\"isotopy\"] := table():\n for e in T[\"max_simplices\"] do \n T[\"isotopy\"][e] := \n unapply((1-s) *~ T[\"map\"][e](t) +~ s *~ T[\"alt_map\"][e](t),s,t);\n od:\nend:\n\nrotate_isotopy := proc(T,a)\n local P0,P1,P2,e,v,s,t;\n P0 := eval(T[\"alt_embedding\"]):\n P1 := eval(T[\"alt_map\"]):\n P2 := eval(T[\"isotopy\"]):\n T[\"alt_embedding\"] := table():\n T[\"alt_map\"] := table():\n T[\"isotopy\"] := table():\n for v in T[\"vertices\"] do\n T[\"alt_embedding\"][v] := rot(a,P0[v]):\n od:\n for e in T[\"max_simplices\"] do \n T[\"alt_map\"][e] := unapply(rot(a,P1[e](t)),t):\n T[\"isotopy\"][e] := unapply(rot(a*s,P2[e](s,t)),s,t):\n od:\nend:\n\ntranslate_letter := proc(T,a)\n local P0,P1,P2,P3,P4,e,v,s,t;\n P0 := eval(T[\"embedding\"]):\n P1 := eval(T[\"map\"]):\n P2 := eval(T[\"alt_embedding\"]):\n P3 := eval(T[\"alt_map\"]):\n P4 := eval(T[\"isotopy\"]):\n T[\"embedding\"] := table():\n T[\"map\"] := table():\n T[\"alt_embedding\"] := table():\n T[\"alt_map\"] := table():\n T[\"isotopy\"] := table():\n for v in T[\"vertices\"] do\n T[\"embedding\"][v] := P0[v] +~ a:\n T[\"alt_embedding\"][v] := P3[v] +~ a:\n od:\n for e in T[\"max_simplices\"] do \n T[\"map\"][e] := unapply(P1[e](t) +~ a,t):\n T[\"alt_map\"][e] := unapply(P3[e](t) +~ a,t):\n T[\"isotopy\"][e] := unapply(P2[e](s,t) +~ a,s,t):\n od:\nend:\n\npol := (r,t) -> evalf([r * cos(Pi*t),r * sin(Pi*t)]):\nrot := (t,x) -> evalf([cos(Pi*t)*x[1]-sin(Pi*t)*x[2],sin(Pi*t)*x[1] + cos(Pi*t)*x[2]]):\n\nshow_map := (T,s) -> \n display(seq(plot([op(T[\"map\"][e](t)),t=0..1]),e in T[\"max_simplices\"]),axes=none,scaling=constrained):\n\nshow_alt_map := (T,s) -> \n display(seq(plot([op(T[\"alt_map\"][e](t)),t=0..1]),e in T[\"max_simplices\"]),axes=none,scaling=constrained):\n\nshow_isotopy := (T,s) -> \n display(seq(plot([op(T[\"isotopy\"][e](s,t)),t=0..1]),e in T[\"max_simplices\"]),axes=none,scaling=constrained):\n\nshow_movie := (T) -> \n display([seq(show_isotopy(T,s),s=0..1,0.02)],insequence=true,view=[-1.5..1.5,-1.5..1.5]):\n\nshow_list_map := proc(L)\n display(seq(seq(\n translate(show_map(letters[L[i][j]]),2*j,-3*i),\n j=1..nops(L[i])),i=1..nops(L)),scaling=constrained);\nend:\n\nshow_list_alt_map := proc(L)\n display(seq(seq(\n translate(show_alt_map(letters[L[i][j]]),3*j,-3*i),\n j=1..nops(L[i])),i=1..nops(L)),scaling=constrained);\nend:\n\nshow_list_isotopy := proc(L,s)\n display(seq(seq(\n translate(show_isotopy(letters[L[i][j]],s),3*j,-3*i),\n j=1..nops(L[i])),i=1..nops(L)),scaling=constrained);\nend:\n\nshow_list_movie := proc(L)\n display([seq(show_list_isotopy(L,s),s=0..1,0.02)],insequence=true):\nend:\n\ntikz_map := proc(T)\n local s,e,u,n;\n s := \"\";\n for e in T[\"max_simplices\"] do\n u := T[\"map\"][e];\n if type(u(t),list(polynom(realcons,t))) and\n max(map(degree,u,t)) <= 1 then\n n := 1;\n else\n n := 16;\n fi;\n s := cat(s,\" \\\\draw \",\n StringTools[Join]([seq(sprintf(\"(%.3f,%.3f)\",op(u(i/n))),i=0..n)],\" -- \"),\n \";\\n\");\n od:\n return s;\nend:\n\ntikz_alt_map := proc(T)\n local s,e,u,n;\n s := \"\";\n for e in T[\"max_simplices\"] do\n u := T[\"alt_map\"][e];\n if type(u(t),list(polynom(realcons,t))) and\n max(map(degree,u,t)) <= 1 then\n n := 1;\n else\n n := 16;\n fi;\n s := cat(s,\" \\\\draw \",\n StringTools[Join]([seq(sprintf(\"(%.3f,%.3f)\",op(u(i/n))),i=0..n)],\" -- \"),\n \";\\n\");\n od:\n return s;\nend:\n\ntikz_list_map := proc(L,{width::numeric := 2},{height::numeric := 3})\n cat(seq(seq(\n cat(\n sprintf(\"\\\\begin{scope}[shift={(%f,%f)}]\\n\",width*j,-height*i),\n tikz_map(letters[L[i][j]]),\n \"\\\\end{scope}\\n\"),\n j=1..nops(L[i])),i=1..nops(L)));\nend:\n\ntikz_list_alt_map := proc(L,{width::numeric := 3.2},{height::numeric := 3})\n cat(seq(seq(\n cat(\n sprintf(\"\\\\begin{scope}[shift={(%f,%f)}]\\n\",width*j,-height*i),\n tikz_alt_map(letters[L[i][j]]),\n \"\\\\end{scope}\\n\"),\n j=1..nops(L[i])),i=1..nops(L)));\nend:\n\n######################################################################\n# A\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[4,5],[2,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([\n 1 = [-1,-1], 2 = [-0.5,0], 3 = [0,1], 4 = [0.5,0], 5 = [1,-1]\n]):\nT[\"alt_embedding\"] := table([\n 1 = [-1.5,0], 2 = [-1,0], 3 = [0,1], 4 = [1,0], 5 = [1.5,0]\n]):\nset_map(T): \nset_alt_map(T):\nT[\"alt_map\"][[2,3]] := (t) -> [-cos(Pi/2*t),sin(Pi/2*t)]:\nT[\"alt_map\"][[3,4]] := (t) -> [ sin(Pi/2*t),cos(Pi/2*t)]:\nT[\"alt_map\"][[2,4]] := (t) -> [-cos(Pi*t),-sin(Pi*t)]:\nset_isotopy(T):\nletters[\"A\"] := eval(T):\n\n######################################################################\n# B\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5,6]:\nT[\"max_simplices\"] := [[1,2],[1,4],[2,3],[2,5],[3,6],[4,5],[5,6]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([\n 1 = [-0.5,-1],2=[-0.5,0],3=[-0.5,1],4=[0,-1],5=[0,0],6=[0,1]\n]):\nT[\"alt_embedding\"] := table([\n 1 = pol(1,-2/3), 2 = pol(1,1), 3 = pol(1,2/3), 4 = pol(1,-1/3), 5 = pol(1,0), 6 = pol(1,1/3)\n]):\nset_map(T): \nset_alt_map(T):\nT[\"map\"][[4,5]] := (t) -> [0,-0.5] +~ pol(0.5,t-0.5):\nT[\"map\"][[5,6]] := (t) -> [0, 0.5] +~ pol(0.5,t-0.5):\nT[\"alt_map\"][[1,2]] := (t) -> pol(1,(-2-t)/3):\nT[\"alt_map\"][[1,4]] := (t) -> pol(1,(-2+t)/3):\nT[\"alt_map\"][[2,3]] := (t) -> pol(1,(-3-t)/3):\nT[\"alt_map\"][[3,6]] := (t) -> pol(1,( 2-t)/3):\nT[\"alt_map\"][[4,5]] := (t) -> pol(1,(-1+t)/3):\nT[\"alt_map\"][[5,6]] := (t) -> pol(1,( t)/3):\nset_isotopy(T):\nletters[\"B\"] := eval(T):\n\n######################################################################\n# C\n\nT := table():\nT[\"vertices\"] := [1,2]:\nT[\"max_simplices\"] := [[1,2]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1 = pol(1,0.4) *~ [0.8,1], 2 = pol(1,-0.4) *~ [0.8,1]]):\nT[\"alt_embedding\"] := table([1 = [0,1], 2=[0,-1]]):\nT[\"map\"] := table([[1,2] = ((t) -> pol(1,0.4 + 1.2*t) *~ [0.8,1])]):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"C\"] := eval(T):\n\n######################################################################\n# D\n\nT := table():\nT[\"vertices\"] := [1,2,3]:\nT[\"max_simplices\"] := [[1,2],[1,3],[2,3]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1 = [-0.5,-1], 2=[-0.5,1], 3 = [0.5,0]]):\nT[\"alt_embedding\"] := table([1 = [0,-1], 2=[0,1], 3 = [1,0]]):\nset_map(T):\nT[\"map\"][[1,3]] := (t) -> [-0.5,0] +~ pol(1,-0.5 + 0.5*t):\nT[\"map\"][[2,3]] := (t) -> [-0.5,0] +~ pol(1, 0.5 - 0.5*t):\nT[\"alt_map\"] := table():\nT[\"alt_map\"][[1,2]] := (t) -> pol(1,-0.5 - t):\nT[\"alt_map\"][[1,3]] := (t) -> pol(1,-0.5 + 0.5*t):\nT[\"alt_map\"][[2,3]] := (t) -> pol(1, 0.5 - 0.5*t):\nset_isotopy(T):\nletters[\"D\"] := eval(T):\n\n######################################################################\n# E\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5,6]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[4,5],[3,6]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([\n 1 = [0.5,-1], 2 = [-0.5,-1], 3 = [-0.5,0], 4 = [-0.5,1], 5 = [0.5,1], 6 = [0,0]\n]):\nT[\"alt_embedding\"] := table([\n 1 = [-1,-1], 2 = [-1,-0.5], 3 = [-1,0], 4 = [-1,0.5], 5 = [-1,1], 6 = [1,0]\n]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nT[\"isotopy\"][[1,2]] := (s,t) -> (1-s) *~ [-0.5,-1] +~ s *~ [-1,-0.5] +~ pol((1-0.5*s)*(1-t),-s/2):\nT[\"isotopy\"][[4,5]] := (s,t) -> (1-s) *~ [-0.5, 1] +~ s *~ [-1, 0.5] +~ pol((1-0.5*s)*(1-t), s/2):\nrotate_isotopy(T,-0.5):\nletters[\"E\"] := eval(T):\n\n######################################################################\n# F\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[2,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([\n 1 = [-0.5,-1], 2 = [-0.5,0], 3 = [-0.5,1], 4 = [0.5,1], 5 = [0,0]\n]):\nT[\"alt_embedding\"] := table([\n 1 = [-1,-1], 2 = [-1,0], 3 = [-1,0.5], 4 = [-1,1], 5 = [1,0]\n]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nT[\"isotopy\"][[3,4]] := (s,t) -> (1-s) *~ [-0.5, 1] +~ s *~ [-1, 0.5] +~ pol((1-0.5*s)*(1-t), s/2):\nrotate_isotopy(T,-0.5):\nletters[\"F\"] := eval(T):\n\n######################################################################\n# G\n\nT := table():\nT[\"vertices\"] := [1,2,3]:\nT[\"max_simplices\"] := [[1,2],[2,3]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1 = pol(1,0.4) *~ [0.8,1], 2 = pol(1,-0.4) *~ [0.8,1],\n 3 = pol(1,-0.4) *~ [0.8,1] +~ [0,-0.4]\n ]):\nT[\"alt_embedding\"] := table([1 = [0,1], 2=[0,0], 3=[0,-1]]):\nset_map(T):\nT[\"map\"][[1,2]] := ((t) -> pol(1,0.4 + 1.2*t) *~ [0.8,1]):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"G\"] := eval(T):\n\n######################################################################\n# H\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5,6]:\nT[\"max_simplices\"] := [[1,2],[2,3],[2,5],[4,5],[5,6]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.5,-1],2=[-0.5,0],3=[-0.5,1],\n 4=[ 0.5,-1],5=[ 0.5,0],6=[ 0.5,1]\n ]):\nT[\"alt_embedding\"] := table([1 = [-1,-1], 2=[-1,0], 3=[-1,1],\n 4=[1,-1],5=[1,0],6=[1,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nrotate_isotopy(T,-0.5):\nletters[\"H\"] := eval(T):\n\n######################################################################\n# I\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5,6]:\nT[\"max_simplices\"] := [[1,2],[2,3],[2,5],[4,5],[5,6]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.2,-1],2=[0,-1],3=[0.2,-1],\n 4=[-0.2,1],5=[0,1],6=[0.2,1]\n ]):\nT[\"alt_embedding\"] := table([1 = [-1,-1], 2=[0,-1], 3=[1,-1],\n 4=[-1,1],5=[0,1],6=[1,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"I\"] := eval(T):\n\n######################################################################\n# J\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,4],[3,4],[4,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.6,-0.7],2=[0,-0.7],3=[-0.5,1],\n 4=[0,1],5=[0.5,1]\n ]):\nT[\"alt_embedding\"] := table([1 = [0,-1], 2=[0,0], 3=[-1,1],\n 4=[0,1],5=[1,1]]):\nset_map(T):\nT[\"map\"][[1,2]] := (t) -> [-0.3,-0.7] +~ pol(0.3,-1+t):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"J\"] := eval(T):\n\n######################################################################\n# K\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[2,4],[2,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.5,-1],2=[-0.5,0],3=[-0.5,1],\n 4=[0.5,-1],5=[0.5,1]\n ]):\nT[\"alt_embedding\"] := table([1 = [-1,-1], 2=[0,0], 3=[-1,1],\n 4=[1,-1],5=[1,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"K\"] := eval(T):\n\n######################################################################\n# L\n\nT := table():\nT[\"vertices\"] := [1,2,3]:\nT[\"max_simplices\"] := [[1,2],[2,3]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[0.5,-1],2=[-0.5,-1],3=[-0.5,1]]):\nT[\"alt_embedding\"] := table([1 = [0,-1], 2=[0,0], 3=[0,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"L\"] := eval(T):\n\n######################################################################\n# M\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[4,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.6,-1],2=[-0.3,1],3=[0,-1],4=[0.3,1],5=[0.6,-1]]):\nT[\"alt_embedding\"] := table([1 = [-1,0], 2=[-0.5,0], 3=[0,0],4=[0.4,0],5=[1,0]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nrotate_isotopy(T,-0.5):\nletters[\"M\"] := eval(T):\n\n######################################################################\n# N\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.5,-1],2=[-0.5,1],3=[0.5,-1],4=[0.5,1]]):\nT[\"alt_embedding\"] := table([1 = [-1,0], 2=[-0.33,0], 3=[0.33,0],4=[1,0]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nrotate_isotopy(T,-0.5):\nletters[\"N\"] := eval(T):\n\n######################################################################\n# O\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[1,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=pol(1,0) *~ [0.6,1], 2=pol(1,0.5) *~ [0.6,1],\n 3=pol(1,1) *~ [0.6,1], 4=pol(1,1.5) *~ [0.6,1]]):\nT[\"alt_embedding\"] := table([1 = pol(1,0),2=pol(1,0.5),3=pol(1,1),4=pol(1,1.5)]):\nset_map(T):\nset_alt_map(T):\nT[\"map\"][[1,2]] := (t) -> pol(1,0.5* t ) *~ [0.6,1]:\nT[\"map\"][[2,3]] := (t) -> pol(1,0.5*(t+1)) *~ [0.6,1]:\nT[\"map\"][[3,4]] := (t) -> pol(1,0.5*(t+2)) *~ [0.6,1]:\nT[\"map\"][[1,4]] := (t) -> pol(1,0.5*(4-t)) *~ [0.6,1]:\nT[\"alt_map\"][[1,2]] := (t) -> pol(1,0.5* t ):\nT[\"alt_map\"][[2,3]] := (t) -> pol(1,0.5*(t+1)):\nT[\"alt_map\"][[3,4]] := (t) -> pol(1,0.5*(t+2)):\nT[\"alt_map\"][[1,4]] := (t) -> pol(1,0.5*(4-t)):\nset_isotopy(T):\nletters[\"O\"] := eval(T):\n\n######################################################################\n# P\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[2,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.25,-1],2=[-0.25,0],3=[-0.25,1],4=[0.5,0.5]]):\nT[\"alt_embedding\"] := table([1=[0,-1.5],2=[0,-1],3=pol(1,2/3),4=pol(1,1/3)]):\nset_map(T):\nset_alt_map(T):\nT[\"map\"][[2,4]] := (t) -> pol(0.5,0.5*(t-1)) *~ [1.5,1] +~ [-0.25,0.5]:\nT[\"map\"][[3,4]] := (t) -> pol(0.5,0.5*(1-t)) *~ [1.5,1] +~ [-0.25,0.5]:\nT[\"alt_map\"][[2,3]] := (t) -> pol(1,-1/2-2/3*t):\nT[\"alt_map\"][[2,4]] := (t) -> pol(1,-1/2+2/3*t):\nT[\"alt_map\"][[3,4]] := (t) -> pol(1,5/6-2/3*t):\nset_isotopy(T):\nrotate_isotopy(T,0.5):\nletters[\"P\"] := eval(T):\n\n######################################################################\n# Q\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[1,3],[1,4],[1,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([\n 1= pol(1,-1/4) *~ [0.6,1],\n 2= pol(1,5/12) *~ [0.6,1],\n 3= pol(1,13/12) *~ [0.6,1],\n 4= pol(1.3,-1/4) *~ [0.6,1],\n 5= pol(0.7,-1/4) *~ [0.6,1]\n]):\nT[\"alt_embedding\"] := \ntable([\n 1= pol(1,-1/4),\n 2= pol(1,5/12),\n 3= pol(1,13/12),\n 4= pol(1.5,-1/4),\n 5= pol(0.5,-1/4)\n]):\nset_map(T):\nset_alt_map(T):\nT[\"map\"][[1,2]] := (t) -> pol(1,-1/4+2/3*t) *~ [0.6,1]:\nT[\"map\"][[1,3]] := (t) -> pol(1,-1/4-2/3*t) *~ [0.6,1]:\nT[\"map\"][[2,3]] := (t) -> pol(1,5/12+2/3*t) *~ [0.6,1]:\nT[\"alt_map\"][[1,2]] := (t) -> pol(1,-1/4+2/3*t):\nT[\"alt_map\"][[1,3]] := (t) -> pol(1,-1/4-2/3*t):\nT[\"alt_map\"][[2,3]] := (t) -> pol(1,5/12+2/3*t):\nset_isotopy(T):\nrotate_isotopy(T,0.25):\nletters[\"Q\"] := eval(T):\n\n######################################################################\n# R\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[2,4],[2,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.25,-1],2=[-0.25,0],3=[-0.25,1],4=[0.5,0.5],5=[0.5,-1]]):\nT[\"alt_embedding\"] := table([1=[-0.5,-1.5],2=[0,-1],3=pol(1,2/3),4=pol(1,1/3),5=[0.5,-1.5]]):\nset_map(T):\nset_alt_map(T):\nT[\"map\"][[2,4]] := (t) -> pol(0.5,0.5*(t-1)) *~ [1.5,1] +~ [-0.25,0.5]:\nT[\"map\"][[3,4]] := (t) -> pol(0.5,0.5*(1-t)) *~ [1.5,1] +~ [-0.25,0.5]:\nT[\"alt_map\"][[2,3]] := (t) -> pol(1,-1/2-2/3*t):\nT[\"alt_map\"][[2,4]] := (t) -> pol(1,-1/2+2/3*t):\nT[\"alt_map\"][[3,4]] := (t) -> pol(1,5/6-2/3*t):\nset_isotopy(T):\nrotate_isotopy(T,0.5):\nletters[\"R\"] := eval(T):\n\n######################################################################\n# S\n\nT := table():\nT[\"vertices\"] := [1,2,3]:\nT[\"max_simplices\"] := [[1,2],[2,3]]:\nT[\"embedding_dim\"] := 2:\ntheta := -0.05;\nT[\"embedding\"] := table([\n 1=rot(theta,[0,-0.5] +~ pol(0.5,-0.7)),\n 2=rot(theta,[0,0],3=[0,0.5] +~ pol(0.5,0.3))\n ]):\nT[\"alt_embedding\"] := table([1=[0,-1],2=[0,0],3=[0,1]]):\nset_map(T):\nset_alt_map(T):\nT[\"map\"][[1,2]] := (t) -> rot(theta,[0,-0.5] +~ pol(0.5,-0.7+1.2*t)):\nT[\"map\"][[2,3]] := (t) -> rot(theta,[0, 0.5] +~ pol(0.5,-0.5-1.2*t)):\nset_isotopy(T):\nletters[\"S\"] := eval(T):\n\n######################################################################\n# T\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[2,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[0,-1],2=[0,1],3=[-0.7,1],4=[0.7,1]]):\nT[\"alt_embedding\"] := table([1 = [0,-1], 2=[0,1], 3=[-1,1],4=[1,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"T\"] := eval(T):\n\n######################################################################\n# U\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.6,1],2=[-0.6,-0.4],3=[0.6,-0.4],4=[0.6,1]]):\nT[\"alt_embedding\"] := table([1 = [-1,0], 2=[-0.33,0], 3=[0.33,0],4=[1,0]]):\nset_map(T):\nset_alt_map(T):\nT[\"map\"][[2,3]] := (t) -> [0,-0.4] +~ pol(0.6,t-1):\nset_isotopy(T):\nrotate_isotopy(T,-0.5):\nletters[\"U\"] := eval(T):\n\n######################################################################\n# V\n\nT := table():\nT[\"vertices\"] := [1,2,3]:\nT[\"max_simplices\"] := [[1,2],[2,3]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.6,1],2=[0,-1],3=[0.6,1]]):\nT[\"alt_embedding\"] := table([1 = [-1,0], 2=[0,0], 3=[1,0]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nrotate_isotopy(T,-0.5):\nletters[\"V\"] := eval(T):\n\n######################################################################\n# W\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4],[4,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.6,1],2=[-0.3,-1],3=[0,1],4=[0.3,-1],5=[0.6,1]]):\nT[\"alt_embedding\"] := table([1 = [-1,0], 2=[-0.5,0], 3=[0,0],4=[0.4,0],5=[1,0]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nrotate_isotopy(T,-0.5):\nletters[\"W\"] := eval(T):\n\n######################################################################\n# X\n\nT := table():\nT[\"vertices\"] := [1,2,3,4,5]:\nT[\"max_simplices\"] := [[1,2],[2,3],[2,4],[2,5]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[-0.5,-1],2=[0,0],3=[-0.5,1],\n 4=[0.5,-1],5=[0.5,1]\n ]):\nT[\"alt_embedding\"] := table([1 = [-1,-1], 2=[0,0], 3=[-1,1],\n 4=[1,-1],5=[1,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"X\"] := eval(T):\n\n######################################################################\n# Y\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[2,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[0,-1],2=[0,0],3=[-0.7,1],4=[0.7,1]]):\nT[\"alt_embedding\"] := table([1 = [0,-1], 2=[0,1], 3=[-1,1],4=[1,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"Y\"] := eval(T):\n\n######################################################################\n# Z\n\nT := table():\nT[\"vertices\"] := [1,2,3,4]:\nT[\"max_simplices\"] := [[1,2],[2,3],[3,4]]:\nT[\"embedding_dim\"] := 2:\nT[\"embedding\"] := table([1=[0.5,-1],2=[-0.5,-1],3=[0.5,1],4=[-0.5,1]]):\nT[\"alt_embedding\"] := table([1 = [0,-1], 2=[0,-0.33], 3=[0,0.33],4=[0,1]]):\nset_map(T):\nset_alt_map(T):\nset_isotopy(T):\nletters[\"Z\"] := eval(T):\n", "meta": {"hexsha": "adf8610cfae493be3f215ccc531833d2bc071813", "size": 19375, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/letters.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/simplicial_complexes/letters.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/simplicial_complexes/letters.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": 29.7162576687, "max_line_length": 109, "alphanum_fraction": 0.4232258065, "num_tokens": 8133, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7879311956428947, "lm_q2_score": 0.7057850278370112, "lm_q1q2_score": 0.55611004085047}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: work_mgga_x *)\n(* prefix:\n mgga_x_tpss_params *params;\n \n assert(pt->params != NULL);\n params = (mgga_x_tpss_params * ) (pt->params);\n*)\n\nff := z -> params_a_BLOC_a + params_a_BLOC_b*z:\nmkappa := (x, t) -> params_a_kappa:\n\n$include \"tpss_x.mpl\"\n\n(* Equation (5) *)\n\na1 := (x, t) -> mkappa(x, t)/(mkappa(x, t) + fx(x, t)):\nf := (rs, x, t, u) -> 1 + mkappa(x, t)*(1 - a1(x, t)):\n", "meta": {"hexsha": "0b9bb86c737c03fec0e27e7bc1b99a012b91a915", "size": 635, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_tpss.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_x_tpss.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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-4.2.3/maple/mgga_x_tpss.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "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": 24.4230769231, "max_line_length": 68, "alphanum_fraction": 0.6125984252, "num_tokens": 223, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8577681195338729, "lm_q2_score": 0.6477982043529715, "lm_q1q2_score": 0.5556606475852679}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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(* prefix:\n gga_x_n12_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_n12_params * )(p->params);\n*)\n\nn12_omega_x := 2.5:\nn12_gamma_x := 0.004:\n\nn12_rss := (rs, z) -> rs * 2^(1/3) * opz_pow_n(z,-1/3):\n\nn12_vx := rs -> 1/(1 + (1/(RS_FACTOR*n12_omega_x))*rs):\nn12_ux := x -> n12_gamma_x*x^2/(1 + n12_gamma_x*x^2):\n\nn12_FN12 := (rs, z, x) ->\n + add(params_a_CC_0_[i+1]*n12_ux(x)^i, i=0..3)\n + add(params_a_CC_1_[i+1]*n12_ux(x)^i, i=0..3) * n12_vx(n12_rss(rs, z))\n + add(params_a_CC_2_[i+1]*n12_ux(x)^i, i=0..3) * n12_vx(n12_rss(rs, z))^2\n + add(params_a_CC_3_[i+1]*n12_ux(x)^i, i=0..3) * n12_vx(n12_rss(rs, z))^3:\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange_nsp(n12_FN12, rs, z, xs0, xs1):\n", "meta": {"hexsha": "0bef384a21807449b2c095def9ae7201ae87bde6", "size": 967, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_n12.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_n12.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_n12.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": 30.21875, "max_line_length": 76, "alphanum_fraction": 0.6235780765, "num_tokens": 417, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8872045817875224, "lm_q2_score": 0.6261241772283034, "lm_q1q2_score": 0.5555002388048934}} {"text": "with(ListTools):\n\n####################\nf1 := 2*x^2-x*y+4:\nf2 := x*y-2*y^2+4:\nsub := [x=x1+I*x2, y=y1+I*y2]:\nf1 := expand(subs( sub, f1)):\nf2 := expand(subs( sub, f2)):\np1 := Re(f1) assuming real:\np2 := Im(f1) assuming real:\np3 := Re(f2) assuming real:\np4 := Im(f2) assuming real:\n\n################\nnld := proc(d, nb_vars)\nlocal l, i, j, p, x, vars;\nl := [];\nvars := [];\nfor i from 1 to nb_vars do\n p := -1;\n for j from 1 to nb_vars do\n if i=j then\n p := p+x||j^d;\n else\n p := p+x||j;\n end if;\n end do;\n l := [op(l), p];\n vars := [op(vars), x||i];\nend do;\nreturn l, vars;\nend proc:\n\n################\nnqleven := proc(nb_vars, even_d)\nlocal x, vars, eqs, i;\nvars := [ x||1 ];\neqs := [ x||1^even_d-2 ];\nfor i from 2 to nb_vars do\n vars := [ x||i, op(vars)];\n eqs := [op(eqs), x||i^even_d + x||i^(even_d/2)- x||(i-1)];\nod;\nreturn eqs, vars;\nend proc:\n\n################\nsimplenql := proc(nbvar, d)\nlocal x, eqs, i, vars;\nvars := [ x||1 ];\neqs := [ x||1^d-2 ];\nfor i from 2 to nbvar do\n vars := [ x||i, op(vars) ];\n eqs := [op(eqs), x||i^d - x||(i-1)];\nend do;\nreturn eqs, vars;\nend proc:\n\n####################\ncm :=\n[\n [ #(1) 4-body-homog ((1)-(47) are from changbo's folder BCLM-cm14)\n [-2*p^3+2*p^3*phi^3-4*phi^3*s*p^2+5*phi^3*s^3*p-phi^3*s^5,\n -2*s*p^3-2*phi^3*s^2+phi^3*s^4-3*phi^3*s^2*p+2*phi^3*p,\n -2*s^2+s^4-4*s^2*p+phi^2+1+4*p\n ],\n [phi,s,p]\n ],\n [\n #(2) 5-body-homog\n [-6*p^3+4*p^3*phi^3+15*phi^3*s^3*p-3*phi^3*s^5-12*phi^3*s*p^2-3*phi^3*s*p+phi^3*s^3,\n -9*phi^3*s^2*p-5*phi^3*s^2-6*s*p^3+3*phi^3*s^4+5*phi^3*p,\n -12*s^2*p-6*s^2+3*s^4+4*phi^2+3+12*p\n ],\n [phi,s,p]\n ],\n [\n #(3) Arnborg-Lazard\n [x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z,\n x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z,\n x^2*y^2*z^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1\n ],\n [z,y,x]\n ],\n [\n #(4) Arnborg-Lazard-rev\n [x^2*y*z + x*y^2*z + x*y*z^2 + x*y*z + x*y + x*z + y*z,\n x^2*y^2*z + x*y^2*z^2 + x^2*y*z + x*y*z + y*z + x + z,\n x^2*y^2*z ^2 + x^2*y^2*z + x*y^2*z + x*y*z + x*z + z + 1\n ],\n [x,y,z]\n ],\n [\n #(5) Barry\n [-x^5+y^5-3*y-1,\n 5*y^4-3,\n -20*x+y-z \n ],\n [z,y,x]\n ],\n [\n #(6) Caprasse\n [y^2*z+2*x*y*t-2*x-z,\n -x^3*z+4*x*y^2*z+4*x^2*y*t+2*y^3*t+4*x^2-10*y^2+4*x*z-10*y*t+2,\n 2*y*z*t+x*t^2-x-2*z,\n -x*z^3+4*y*z^2*t+4*x*z*t^2+2*y*t^3+4*x*z+4*z^2-10*y*t-10*t^2+2\n ],\n [t,z,y,x]\n ],\n [\n #(7) Caprasse-Li\n [y^2*z+2*x*y*t-2*x-z,\n -x^3*z+4*x*y^2*z+4*x^2*y*t+2*y^3*t+4*x^2-10*y^2+4*x*z-10*y*t+2,\n 2*y*z*t+x*t^2-x-2*z,\n -x*z^3+4*y*z^2*t+4*x*z*t^2+2*y*t^3+4*x*z+4*z^2-10*y*t-10*t^2+2\n ],\n [x,y,z,t]\n ],\n [\n #(8) chemical-reaction\n [2 - 7*x1 + x1^2*x2 - 1/2*(x3 - x1), \n 6*x1 - x1^2*x2 - 5*(x4 - x2 ),\n 2 - 7*x3 + x3^2*x4 - 1/2*(x1 - x3 ),\n 6*x3 - x3^2*x4 + 1 + 1/2*(x2 - x4 )\n ],\n [x1,x2,x3,x4]\n ],\n [\n #(9) circles\n [product( (x-'i'), 'i'=1..10) +1/100,\n product ( (x-'i')^2+(y-'i')^2-2, 'i'=1..5)+1/1000\n ],\n [x,y]\n ],\n [\n #(10) cyclic-5\n [a + b + c + d + e,\n a*b + b*c + c*d + d*e + e*a,\n a*b*c + b*c*d + c*d*e + d*e*a + e*a*b,\n a*b*c*d + b*c*d*e + c*d*e*a + d*e*a*b + e*a*b*c,\n a*b*c*d*e - 1\n ],\n [e,d,c,b,a]\n ],\n [\n #(11) Czapor-Geddes-Wang\n [b-2,\n c*c*q*q-2*d*c*q*q+d*d*q*q-2*c*c*q+2*d*p*c*q+2*b*p*c*q+2*d*c*q-2*d*d*p*q+2*b*p*q-2*p*q-2*b*d*d*q-2*b*q+2*q+c*c-2*d*p*c-2*b*d*c+b*b*d*d*p*p-2*b*d*d*p*p+d*d*p*p+2*b*b*p*p+2*p*p-2*b*b*d*d*p+4*b*d*d*p-4*b*b*p+4*b*p+b*b*d*d+2*b*b-4*b+2,\n -b*p*c*q-p*c*q+b*c*q-2*c*q+2*d*p*q+d*q+p*c+b*b*c-b*c+2*c+b*b*d*p*p+b*d*p*p-2*d*p*p-2*b*b*d*p+b*d*p-d*p+b*b*d-2*b*d,\n -2*p*q-2*q-b*b*p*p+2*p*p+2*b*b*p-b*b+2,\n 3*c*c*q*q-3*d*d*q*q-4*q*q-6*c*c*q+6*b*d*p*c*q+6*b*d*c*q+6*d*d*p*q+3*c*c+6*b*d*p*c-6*b*d*c+3*b*b*d*d*p*p-3*d*d*p*p+b*b*p*p-6*b*b*d*d*p-2*b*b*p+4*p+3*b*b*d*d+b*b\n ],\n [b,d,p,c,q]\n ],\n [\n #(12) fabfaux\n [30752*x^3 + 46128*y*x^2 - 216256*x + 46128*x*y^2 + 141980 + 30752*y^3- 216256*y,\n 30752*x^3 + 46128*z*x^2 - 216256*x + 46128*x*z^2 + 141980 + 30752*z^3+ 216256*z,\n 46128*y^3 + 46128*x*y^2 + 46128*z*y^2 + 46128*y*x^2 - 432512*y +46128*x*z*y + 46128*z^2*y + 46128*x^3 - 432512*x + 425940 +46128*z*x^2 - 432512*z + 46128*x*z^2 + 46128*z^3\n ],\n [z,y,x]\n ],\n [\n #(13) geometric-constraints\n [1/100 - 4*s*(s - 1)*(s - b)*(s - c),\n 1/5 - b*c, \n 2*s - 1 - b - c\n ],\n [s,b,c]\n ],\n [\n #(14) GonzalezGonzalez\n [x^3 + y*x^2 + x + z,\n x^2*y +3*x +2,\n x^2-y*x+z\n ],\n [z,y,x]\n ],\n [\n #(15) Katsura-4\n [2*x^2 + 2*y^2 + 2*z^2 + 2*t^2 + u^2 - u ,\n 2*x*y + 2*y*z + 2*z*t + 2*t*u - t ,\n 2*x*z + 2*y*t + t^2 + 2*z*u - z ,\n 2*x*t + 2*z*t + 2*y*u - y ,\n 2*x + 2*y + 2*z + 2*t + u - 1\n ],\n [u,t,z,y,x]\n ],\n [\n #(16) lhlp1\n [2*x^7+2-3*x^2-x^4,\n x^2+2*y^2-5,\n x*z-1\n ],\n [x,y,z]\n ],\n [\n #(17) lhlp2\n [y*(320+1600*y^4-240*y^5-471*y^6+36*y^7-48*y^2+36*y^8),\n -40*y^2+3*y^3+6*y^4+8*x,\n -8*y*z-8-40*y^4+3*y^5+6*y^6\n ],\n [x,y,z]\n ],\n [\n #(18) lhlp3\n [2450*x^6-1241*x^4+196*x^2-49,\n 86*x^2+35*y*x^2-77*y-14,\n 175*x^4+70*x^2*z-76*x^2-154*z+21\n ],\n [x,y,z]\n ],\n [\n #(19) lhlp4\n [x^4+y^4-1,\n x^5*y^2-4*x^3*y^3+x^2*y^5-1\n ],\n [x,y]\n ],\n [\n #(20) lhlp5\n [-7*x*y*z+6*y*z-14*x*z+9*z-3*x*y-12*y-x+1,\n 2*x*y*z-y*z+14*z+15*x*y+14*y-15*x,\n -8*x*y*z+11*y*z-12*x*z-5*z+15*x*y+2*y+10*x-14\n ],\n [x,y,z]\n ],\n [\n #(21) lhlp6\n [p1,p2,p3,p4\n ],\n [y1,x1,y2,x2]\n ],\n [\n #(22) neural-network\n [1 - c*x - x*y^2 - x*z^2,\n 1 - c*y - y*x^2 - y*z^2,\n 1 - c*z - z*x^2 - z*y^2, \n 8*c^6 + 378*c^3 - 27\n ],\n [z,c,y,x]\n ],\n [\n #(23) nld-3-4\n [x^3 + y + z + t- 1,\n x + y^3 + z + t -1,\n x + y + z^3 + t-1,\n x + y + z + t^3 -1\n ],\n [t,z,y,x]\n ],\n [\n #(24) nld-3-5\n [x^3 + y + z + t + u- 1,\n x + y^3 + z + t + u-1,\n x + y + z^3 + t + u-1,\n x + y + z + t^3 + u-1,\n x + y + z + t + u^3 -1\n ],\n [u,t,z,y,x]\n ],\n [\n #(25) nld-4-5\n [x^4 + y + z + t + u- 1,\n x + y^4 + z + t + u-1,\n x + y + z^4 + t + u-1,\n x + y + z + t^4 + u-1,\n x + y + z + t + u^4 -1\n ],\n [x,y,z,t,u]\n ],\n [\n #(26) nld-7-3\n [x^7 + y + z - 1,\n x + y^7 + z - 1,\n x + y + z^7 - 1\n ],\n [z,y,x]\n ],\n [\n #(27) nld-8-3\n [x^8 + y + z - 1,\n x + y^8 + z - 1,\n x + y + z^8 - 1\n ],\n [z,y,x]\n ],\n [\n #(28) nld-9-3\n [x^9 + y + z - 1,\n x + y^9 + z - 1,\n x + y + z^9 - 1\n ],\n [z,y,x]\n ],\n [\n #(29) nld-10-3\n [x^10 + y + z - 1,\n x + y^10 + z - 1,\n x + y + z^10 - 1\n ],\n [z,y,x]\n ],\n [\n #(30) nql-5-4\n nqleven(5,4)\n ],\n [\n #(31) nql-10-2\n nqleven(10,2)\n ],\n [\n #(32) nql-10-4\n nqleven(10,4)\n ],\n [\n #(33) nql-15-2\n nqleven(15,2)\n ],\n [\n #(34) p3p-special\n [x^2 + y^2 - x*y - 1,\n y^2 + z^2 - y*z - a^2,\n z^2 + x^2 - z*x - b^2,\n a^2 - 1 + b - b^2,\n 3*b^6 + 56*b^4 - 122*b^3 + 56*b^2 + 3\n ],\n [b,a,x,y,z]\n ],\n [\n #(35) PlateForme2d-easy\n [(x1+5)^2+ (y1-0)^2 - 1,\n (x2-5)^2+ (y2-0)^2 - 1,\n (x3)^2 + (y3-5)^2 - 1,\n (x1-x2)^2 + (y1-y2)^2 - 3,\n (x1-x3)^2 + (y1-y3)^2 - 3,\n (x2-x3)^2 + (y2-y3)^2 - 3\n ],\n [y3,x3,y2,x2,y1,x1]\n ],\n [\n #(36) r-5\n [a^2 + a,\n a*b + b + a*b^2 +a,\n b^2*c + c + b*c^3 + b,\n c^3*d + d + c*d^4 + c,\n d^4*e + e + d*e^5 + d\n ],\n [e,d,c,b,a]\n ],\n [\n #(37) r-6\n [a^2 + a,\n a*b + b + a*b^2 +a,\n b^2*c + c + b*c^3 + b,\n c^3*d + d + c*d^4 + c,\n d^4*e + e + d*e^5 + d,\n e^5*f + f + e*f^6 + e\n ],\n [f,e,d,c,b,a]\n ],\n [\n #(38) Reif\n [x4*x13+x5*x14+x6*(1-x13-x14),\n x4*x15+x5*x16-x6*(x15+x16) ,\n x7*x13+x8*x14+x9*(1-x13-x14) ,\n x7*x15+x8*x16-x9*(x15+x16)-1 ,\n x10*x13+x11*x14+x12*(1-x13-x14) ,\n x10*x15+x11*x16-x12*(x15+x16) ,\n x1*x13+x2*x14+x3*(1-x13-x14) ,\n x1*x15+x2*x16-x3*(x15+x16) ,\n x1*x4*x13+x2*x5*x14+x3*x6*(1-x13-x14)-1 ,\n x1*x4*x15+x2*x5*x16-x3*x6*(x15+x16) ,\n x1*x7*x13+x2*x8*x14+x3*x9*(1-x13-x14) ,\n x1*x7*x15+x2*x8*x16-x3*x9*(x15+x16) ,\n x1*x10*x13+x2*x11*x14+x3*x12*(1-x13-x14) ,\n x1*x10*x15+x2*x11*x16-x3*x12*(x15+x16)-1\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16]\n ],\n [\n #(39) Rose\n [7*y^4 - 20*x^2,\n 2160*x*x*z^4+1512*x*z^4+315*z^4-4000*x*x-2800*x-490,\n -10080000*x^4*z^3-28224000*x^3*z^3-15288000*x*x*z^3-1978032*x*z^3-180075*z^3-23520000*x^4*y*z*z-41395200*x^3*y*z*z-26726560*x*x*y*z*z-7727104*x*y*z*z-852355*y*z*z+40320000*x^6*y*y*z+28800000*x^5*y*y*z+21168000*x^3*y*y*z+4939200*x*x*y*y*z+347508*x*y*y*z+67200000*x^5*y^3+94080000*x^4*y^3+40924800*x^3*y^3+2634240*x*x*y^3-2300844*x*y^3-432180*y^3\n ],\n [x,y,z]\n ],\n [\n #(40) simple-nql-20-30\n simplenql(20, 30)\n ],\n [\n #(41) Takeuchi-Lu\n [2*x1*(2 - x1 - y1 ) + x2 - x1,\n 2*x2*(2 - x2 - y2 ) + x1 - x2,\n 2*y1*(5 - x1 - 2*y1 ) + y2 - y1,\n y2*(3 - 2*x2 - 4*y2 ) + y1 - y2\n ],\n [x1,x2,y1,y2]\n ],\n [\n #(42) Themos-net\n [10000*d - 323536,\n (x-48)^2+(y-89)^2+(28)^2-(48*a+89*b+28*c)^2-d^2,\n (x-77)^2+(y-3)^2+(37)^2-(77*a+3*b+37*c)^2-d^2,\n (x-49)^2+(y-23)^2+(57)^2-(49*a+23*b+57*c)^2-d^2,\n a*x+b*y,\n a^2+b^2+c^2-1\n ],\n [d,c,b,a,y,x]\n ],\n [\n #(43) Trinks-2\n [45*y+35*u-165*v-36 ,\n 35*y+25*z+40*t-27*u ,\n 25*y*u-165*v^2+15*x-18*z+30*t ,\n 15*y*z+20*t*u-9*x ,\n -11*v^3+x*y+2*z*t ,\n -11*u*v+3*v^2+99*x ,\n 10000*v^3+6600*v+2673\n ],\n [v,u,z,t,y,x]\n ],\n [\n #(44) Trinks-difficult\n [45*y+35*u-165*v-36 ,\n 35*y+25*z+40*t-27*u ,\n 25*y*u-165*v^2+15*x-18*z+30*t ,\n 15*y*z+20*t*u-9*x ,\n -11*v^3+x*y+2*z*t ,\n -11*u*v+3*v^2+99*x\n ],\n [v,u,z,t,y,x]\n ],\n [\n #(45) Uteshev-Bikker\n [x^2+x*y+y^2-2*x*z-4*y*z+3*z^2-3*x*t+2*y*t+t^2-3*x-2*y+3*z-2*t-2 ,\n 2*x^2-x*y+y^2-x*z-y*z-6*z^2-x*t+y*t-5*z*t-3*t^2-5*x+y+5*z+2*t+5 ,\n -3-3*x*y+2*x*z+x*t^2-5*x*z^2-5*z^2*t-3*x*t-2*z*t+x*y*z+x*y*t-x^2*z+x^2-y^2+2*z^2+11*z-2*t-x+y+x^3+y^3-3*z^3+2*t^3-3*t^2-5*y^2*z+7*y*z^2 ,\n -15+2*x*y+11*x*t^2+5*x*z^2-z*t-4*x*y*z+6*x*y*t-x^2*z+3*x^2+2*y^2-z^2+4*z-10*t-35*x-14*y-x^3+6*y^3+15*z^3+4*t^3+5*t^2+6*y^2*z+4*y*z^2-x*z*t+6*x^2*y-12*x*y^2-7*y^2*t+2*y*t \n ],\n [t,z,y,x]\n ],\n [\n #(46) wilkinson20\n [mul( (x-i),i=0..20 )+1/100],\n [x]\n ],\n [\n #(47) wilkinsonxy\n [mul( (x-i),i=1..5 )+1/100,\n\t mul( (y-x-i),i=1..5)\n ],\n [x,y]\n ],\n [\n #(48) trivial-5 ((48) is from changbo's folder RCtest-zerodim)\n [x^2 -1,\n y^2 - 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YES\n2. YES", "lm_q1_score": 0.8519527869325346, "lm_q2_score": 0.6513548646660543, "lm_q1q2_score": 0.5549235922343089}} {"text": "#@ Not autoload\n\np := 3; # the ambient prime\nn := 2; # height\nd := 243; # degree of approximate FGL \n\n# find the FGL\nT := make_fgl_Morava(p,n,d):\nF_E := eval(T[\"sum\"]);\nF_K := eval(T[\"sum0\"]);\n\n# Generators and relations for O_Y, where Y is the scheme defined in \n# Section sec_Y. Note that the quantities called a,b and c in the \n# main document are aa,bb and cc here. Note also that we build up \n# the relations in two stages: we first do a preliminary version\n# without the condition \\psi^4(D) = D, then we add that condition\n# as a second step.\n\nvars_Y := plex(aa,bb,cc,c[1],c[3],c[2]):\nrels_Y := {\n c[1] - (aa+bb+cc),\n c[2] - (aa*bb+bb*cc+cc*aa),\n c[3] - (aa*bb*cc),\n c[1]^9,c[2]^9,c[3]^9,\n aa + F_K(bb,cc)\n}:\nbasis_Y := Basis(rels_Y,vars_Y,characteristic=p); # Preliminary version\n\n# aa4 = [4](aa), bb4 = [4](bb), cc4 = [4](cc)\naa4 := mods(NormalForm(F_K(aa,aa^(p^n)),basis_Y,vars_Y,characteristic=p),p);\nbb4 := mods(NormalForm(F_K(bb,bb^(p^n)),basis_Y,vars_Y,characteristic=p),p);\ncc4 := mods(NormalForm(F_K(cc,cc^(p^n)),basis_Y,vars_Y,characteristic=p),p);\n\n# To impose the condition psi^4(D) = D, the elementary symmetric functions\n# in aa4, bb4, cc4 must be the same as for aa, bb and cc.\nrels_Y := {\n op(basis_Y),\n c[1] - (aa4+bb4+cc4),\n c[2] - (aa4*bb4+bb4*cc4+cc4*aa4),\n c[3] - (aa4*bb4*cc4)\n}:\n\nbasis_Y := Basis(rels_Y,vars_Y,characteristic=p);\nNF_Y := (u) -> mods(NormalForm(u,basis_Y,vars_Y,characteristic=p),p):\n\n# The above Groebner basis includes the variables aa, bb and cc which were\n# adjoined to O_Y for convenience. Because these were placed first in a pure\n# lexicographic order, we can obtaina Groebner basis for O_Y itself by simply\n# omitting any relations that involve aa, bb or cc.\nvars_Y1 := plex(c[1],c[3],c[2]):\nbasis_Y1 := remove(has,basis_Y,{aa,bb,cc});\ncobasis_Y1 := cobasis(basis_Y1,vars_Y1);\nnops(cobasis_Y1);\n\n# Definitions of some auxiliary elements\n\n# gamma is used by default for the Euler-Mascheroni constant; we need\n# to cancel this.\nunprotect('gamma'):\n\nalpha := c[3]^3-c[2]^3*c[3];\nbeta := 1 + c[2]^4;\ngamma := c[2]^3*c[3]^3;\ndd := NF_Y(F_K(aa,-bb));\nmm := aa^5*bb^5 + bb^5*cc^5 + cc^5*aa^5;\nuu := c[2] + c[2]^2*c[3]^2;\nfor i from 0 to 18 do \n s[i] := NF_Y(aa^i + bb^i + cc^i);\nod:\n\n# Formulae in the Claim labelled claim-A\n_ASSERT(\n map(NF_Y,{\n c[1]+c[3]^3,\n c[1]^3\n }) = {0},\n \"claim-A\"\n):\n\n# Formulae in the Claim labelled claim-B and its proof\n_ASSERT(\n map(NF_Y,{\n c[2]^6,\n s[1]-c[1],\n s[2]-(c[1]^2+c[2]),\n s[3],\n s[4]-c[1]*s[3]+c[2]*s[2]-c[3]*s[1],\n s[12]-s[4]^3,\n aa^27,bb^27,cc^27,\n aa4 - (aa + aa^9),\n bb4 - (bb + bb^9),\n cc4 - (cc + cc^9),\n aa4^4 - (aa^4 + aa^12),\n bb4^4 - (bb^4 + bb^12),\n cc4^4 - (cc^4 + cc^12)\n }) = {0},\n \"claim-B\"\n):\n\n# Formulae in the Claim labelled claim-C and its proof\n_ASSERT(\n map(NF_Y,{\n c[1]*c[2] - c[2]^3 * (-c[2]*c[3]),\n c[3]^3*c[2] - c[2]^3 * ( c[2]*c[3]),\n aa^3-c[1]*aa^2+c[2]*aa-c[3],\n aa^9 - c[3]^3 - c[2]^3 * (-aa^3),\n aa^9 + c[1] - c[2]^3 * (-aa^3),\n aa4 - (aa - c[1]) - c[2]^3 * (-aa^3),\n aa4*bb4*cc4 - (aa-c[1])*(bb-c[1])*(cc-c[1]) - c[2]^3*(-c[2]*c[3]),\n aa4*bb4*cc4 - (c[3]-c[2]*c[1]) - c[2]^3*(-c[2]*c[3]),\n aa4*bb4*cc4 - c[3]\n }) = {0},\n \"claim-C\"\n):\n\n# Formulae in Corollary cor-C and its proof\n_ASSERT(\n map(NF_Y,{\n c[3]^6*c[2]^2,\n c[3]^3*c[2]^4,\n c[3]^3*c[2]-c[2]^3*(c[2]*c[3]),\n c[2]^6\n }) = {0},\n \"cor-C\"\n):\n\n# Formulae in the Claim labelled claim-D and its proof\n_ASSERT(\n map(NF_Y,{\n c[3]^3*c[2]-c[3]*c[2]^4,\n aa^3-c[1]*aa^2+c[2]*aa-c[3],\n aa^9+c[2]^3*aa^3-c[3]^3,\n aa^9+c[2]^3*aa^3-c[3]^3,\n aa^9-c[2]^3*c[3]^3*aa^2-c[2]^4*aa+c[2]^3*c[3]-c[3]^3,\n F_K(aa,aa^9) - (aa+aa^9),\n F_K(aa,aa^9) - (alpha + beta*aa + gamma*aa^2),\n alpha*beta - alpha,\n beta*gamma - gamma,\n gamma^2,\n alpha^3,\n alpha^2*gamma,\n beta^3 - 1,\n alpha^2*c[1],\n alpha*gamma*c[1]*c[2],\n gamma*c[1]*c[3],\n aa4*bb4*cc4 -\n ((alpha+beta*aa+gamma*aa^2) *\n (alpha+beta*bb+gamma*bb^2) *\n (alpha+beta*cc+gamma*cc^2)),\n aa4*bb4*cc4 - (alpha^2*c[1]+alpha*c[2]+alpha*gama*c[1]*c[2]+c[3]+gamma*c[1]*c[3]),\n alpha^2*c[1],\n -(c[3]^3-c[2]^3*c[3])^2*c[3]^3,\n alpha*gamma*c[1]*c[2],\n gamma*c[1]*c[3],\n aa4*bb4*cc4 - (c[3]+alpha*c[2]),\n alpha*c[2]\n }) = {0},\n \"claim-D\"\n):\n\n# Formulae in the Claim labelled claim-E and its proof\n_ASSERT(\n map(NF_Y,{\n c[3]^6-c[2]^5,\n aa4^2 - (aa^2-aa^10+aa^18),\n aa4^2+bb4^2+cc4^2 - (s[2]-s[10]+s[18]),\n s[18],\n s[10],\n aa^9-(alpha+(beta-1)*aa+gamma*aa^2),\n gamma,\n aa^10 - (alpha*aa + (beta-1)*aa^2),\n s[10] - (alpha*s[1] + (beta-1)*s[2]),\n s[10] - (-c[3]^6+c[2]^5)\n }) = {0},\n \"claim-E\"\n):\n\n# Groebner basis for O_Y\n_ASSERT(\n mods(basis_Y1,3) = [c[2]^6,c[3]^3*c[2]-c[3]*c[2]^4,c[3]^6-c[2]^5,c[1]+c[3]^3],\n \"prop-Y\"\n):\n\n# Formulae in the Claim labelled claim-F and its proof\n_ASSERT(\n map(NF_Y,{\n dd - (aa-bb+aa^6*bb^3-aa^3*bb^6),\n aa^9+c[2]^3*aa^3-c[3]^3,\n bb^9+c[2]^3*bb^3-c[3]^3,\n (c[2]^3)^2,\n c[2]^3*c[3]^3,\n (c[3]^3)^2-c[2]^5,\n aa^9*bb^9 - c[2]^5,\n aa^3-(-c[3]^3*aa^2-c[2]*aa+c[3]),\n aa^12 * bb^9 - c[2]^5*c[3],\n aa^9 * bb^12 - c[2]^5*c[3],\n aa^9 * bb^9 * (bb^3 - aa^3)\n }) = {0},\n \"claim-F\"\n):\n\n# Formulae in the Claim labelled claim-G and its proof\n_ASSERT(\n map(NF_Y,{\n c[2] - (-(aa^2+aa*bb+bb^2)-(aa+bb)*c[3]^3),\n c[3] - (-aa*bb*(aa+bb)-aa*bb*c[3]^3),\n aa+bb - (-c[3]^3-cc),\n aa*bb - (cc^2+c[3]^3*cc+c[2]),\n aa^9*bb^9 - c[2]^5,\n (aa-bb)^2 - (-c[2]-(aa+bb)*c[3]^3),\n aa^3-bb^3 - (-c[2]*(aa-bb)-c[3]^3*(aa^2-bb^2)),\n aa^9-bb^9 - c[2]^4*(aa-bb),\n aa+bb+cc-c[1],\n aa+bb+cc+c[3]^3,\n c[2] - (-(aa^2+aa*bb+bb^2)-(aa+bb)*c[3]^3),\n c[3] - (-aa*bb*(aa+bb)-aa*bb*c[3]^3),\n cc^2 + cc * c[3]^3 + c[2] - aa * bb,\n - aa^18 - aa^9 * bb^9 - bb^18,\n aa^18 + bb^18 + c[2]^5\n }) = {0},\n \"claim-G\"\n):\n\n# Formulae in the Claim labelled claim-H\n_ASSERT(\n map(NF_Y,{\n s[ 1] - (-c[3]^3),\n s[ 2] - (c[2]+c[2]^5),\n s[ 3],\n s[ 4] - (-c[3]^4-c[2]^2),\n s[ 5] - (c[3]*c[2]),\n s[ 6] - (c[2]^3),\n s[ 7] - (-c[3]^5+c[3]*c[2]^2),\n s[ 8] - (-c[2]^4+c[3]^2*c[2]),\n seq(s[i],i=9..18)\n }) = {0},\n \"claim-H\"\n);\n\n# Formula in the Claim labelled claim-I\n_ASSERT(\n NF_Y(\n dd - (aa-bb)*(1-c[3]^2*c[2]+c[3]^2*c[2]^5-c[2]^4-(c[3]*c[2]^2-c[3]^5)*cc-c[2]^3*cc^2)\n ) = 0,\n \"claim-I\"\n);\n\n# Formulae in the Claim labelled claim-J and its proof\n_ASSERT(\n map(NF_Y,{\n dd^3 - (aa-bb)^3,\n dd^3 - (-c[3]^3*(aa^2-bb^2)-c[2]*(aa-bb)),\n c[2]^4*dd - c[2]^4*(aa-bb)*(1-c[2]*c[3]^2),\n c[2]^4*dd^4,\n c[2]^4*(aa-bb)^4,\n c[2]^5*dd - c[2]^5*(aa-bb),\n c[2]^5*dd^2,\n dd-(aa-bb) - aa^3*bb^3*(aa^3-bb^3),\n aa^9*bb^9*(aa^9-bb^9),\n c[2]^4*c[3]^3,\n aa^3-bb^3+c[3]^3*(aa^2-bb^2)+c[2]*(aa-bb),\n c[2]^4*(aa^3-bb^3)+c[2]^5*(aa-bb),\n (c[3]^3) * c[2]^5,\n (c[2]) * c[2]^5,\n (aa*bb-cc^2) * c[2]^5,\n ((aa*bb)^3-cc^6) * c[2]^5,\n (cc^3-c[3]) * c[2]^5,\n (cc^6-c[3]^2) * c[2]^5,\n c[2]^4*(aa^3-bb^3)*(aa*bb)^3 + c[2]^5*c[3]^2*(aa-bb),\n (aa-bb)^2+c[2]+(aa+bb)*c[3]^3\n }) = {0},\n \"claim-J\"\n);\n\npoints_E := map(NF_Y,[\n F_K(aa,-bb), F_K(bb,-cc), F_K(cc,-aa),\n F_K(bb,-aa), F_K(cc,-bb), F_K(aa,-cc)\n]):\nf_E := NF_Y(expand(mul(t - u,u in points_E)));\n\nvars_Z := plex(aa,bb,cc,c[1],z,c[3],c[2]):\n\naz := rem(NF_Y(F_K(aa,z)),z^9,z);\nbz := rem(NF_Y(F_K(bb,z)),z^9,z);\ncz := rem(NF_Y(F_K(cc,z)),z^9,z);\n\nrels_Z := {\n op(basis_Y),\n z^9,\n c[1] - (az+bz+cz),\n c[2] - (az*bz+bz*cz+cz*az),\n c[3] - (az*bz*cz)\n}:\nbasis_Z := Basis(rels_Z,vars_Z,characteristic=p):\nNF_Z := (u) -> mods(NormalForm(u,basis_Z,vars_Z,characteristic=p),p):\n\nvars_Z1 := plex(c[1],z,c[3],c[2]):\nbasis_Z1 := remove(has,basis_Z,{aa,bb,cc});\ncobasis_Z1 := cobasis(basis_Z1,vars_Z1);\n\n# Formulae in the Claim labelled claim-K and its proof \n_ASSERT(\n map(NF_Z,{\n t^3 * f_E - (t^9 - c[2]^5*t^7 + c[2]^3 * t^3),\n F_K(aa,-bb) - dd,\n F_K(bb,-aa) - (-dd),\n F_K(aa,-cc) - (-dd+aa^9),\n F_K(cc,-aa) - ( dd-aa^9),\n F_K(cc,-bb) - (-dd-bb^9),\n F_K(bb,-cc) - ( dd+bb^9),\n f_E - (t^2-dd^2)*(t^2-(dd-aa^9)^2)*(t^2-(dd+bb^9)^2),\n (dd-aa^9)^2*(dd+bb^9)^2 - dd^4,\n coeff(f_E,t,4) - (-dd^2-(dd-aa^9)^2-(dd+bb^9)^2),\n coeff(f_E,t,4) - (-c[2]^4*(aa-bb)*dd+c[2]^5),\n c[2]^4*dd-c[2]^4*(aa-bb)*(1-c[2]*c[3]^2),\n (aa-bb)^2+c[2]+(aa+bb)*c[3]^3,\n coeff(f_E,t,4) + c[2]^5,\n coeff(f_E,t,2) - (dd^2*(dd-aa^9)^2+dd^2*(dd+bb^9)^2+(dd-aa^9)^2*(dd+bb^9)^2),\n coeff(f_E,t,2),\n coeff(f_E,t,0) + dd^6\n }) = {0},\n \"claim-K\"\n);\n\n# Formulae in the Claim labelled claim-L and its proof \n_ASSERT(\n map(NF_Z,{\n z^9,\n z^3+(c[2]+c[2]^2*c[3]^2)*z,\n (c[3]^3-c[3]*c[2]^3)*z,\n az - z - aa*(1 - z^3*aa^5 - z^6*aa^2),\n (aa-z)*(bb-z)*(cc-z) -\n c[3]*(1-z^3*aa^5-z^6*aa^2)*\n (1-z^3*bb^5-z^6*bb^2)*\n (1-z^3*cc^5-z^6*cc^2),\n c[2]^3*z^3,\n c[3]-c[2]*z+c[1]*z^2-z^3-(c[3]-c[3]*s[5]*z^3-c[3]*s[2]*z^6-c[3]*mm*z^6),\n s[5]-c[3]*c[2],\n c[2]*z+z^3*(1-c[3]^2*c[2]),\n c[3]^4*c[2]^2*z^3,\n c[3]^2*c[2]^5*z^3,\n (c[2]+c[3]^2*c[2]^2)*z+z^3,\n az^2 - (aa^2-z*aa+z^2+z^3*aa^7+z^4*aa^6+z^6*(aa^12+aa^4)+z^7*aa^3),\n az^2 + bz^2 + cz^2 - (s[2]-z*s[1]+z^3*s[7]+z^6*(s[12]+s[4])+z^7*s[3]),\n -z*s[1]+z^3*s[7]+z^4*s[6]+z^6*(s[12]+s[4])+z^7*s[3],\n -z*s[1]+z^3*s[7]+z^7*s[3],\n s[1]+c[3]^3,\n s[3],\n s[7]-(-c[3]^5+c[3]*c[2]^2),\n z^3+(c[3]^2*c[2]^2+c[2])*z,\n (c[3]^3-c[3]*c[2]^3)*z\n }) = {0},\n \"claim-L\"\n):\n\nvars_ZW := plex(aa,bb,cc,c[1],z,w,c[3],c[2]):\nrels_ZW := {\n op(basis_Z),\n op(subs(z = w,basis_Z))\n}:\nbasis_ZW := Basis(rels_ZW,vars_ZW,characteristic=p):\nNF_ZW := (u) -> mods(NormalForm(u,basis_ZW,vars_ZW,characteristic=p),p):\n\nvars_ZW1 := plex(c[1],z,w,c[3],c[2]):\nbasis_ZW1 := remove(has,basis_ZW,{aa,bb,cc});\ncobasis_ZW1 := cobasis(basis_ZW1,vars_ZW1);\n\npoints_ZW := map(NF_ZW,[\n 0,z,-z,w,-w,F_K(z,w),F_K(z,-w),F_K(-z,w),F_K(-z,-w)\n]):\n\nf_ZW := t^9 + uu^3*z^2*w^2*t^7 - (uu*z^2*w^2+uu^2*(z^2+w^2))*t^3;\n\n# Formulae in the Claim labelled claim-M and its proof \n\n### UNFINISHED\n_ASSERT(\n map(NF_ZW,{\n f_ZW - mul(t-m,m in points_ZW),\n z^3 + uu*z,\n z^9,\n uu^4*z,\n F_K(z, w) - (z+w)*(1+uu^3*z*w),\n F_K(z,-w) - (z-w)*(1-uu^3*z*w),\n F_K(z, w)^2 - (z+w)^2 - uu^3*z^2*w^2,\n F_K(z,-w)^2 - (z-w)^2 - uu^3*z^2*w^2,\n uu * z^2*w^2*uu^3,\n z * z^2*w^2*uu^3,\n w * z^2*w^2*uu^3\n }) = {0},\n \"claim-M\"\n):\n\nvars_C := vars_ZW:\nrels_C := {op(basis_ZW),coeffs(mods(expand(f_ZW - t^3*f_E),p),t)}:\nbasis_C := Basis(rels_C,vars_C,characteristic=p);\nNF_C := (u) -> mods(NormalForm(u,basis_C,vars_C,characteristic=p),p);\n\nvars_C1 := plex(c[1],z,w,c[3],c[2]);\nbasis_C1 := mods(remove(has,basis_C,{aa,bb,cc}),p);\ncobasis_C1 := cobasis(basis_C1,vars_C1);\n\n_ASSERT(nops(cobasis_C1) = 108,\"C(K,G) has rank 108\");\n\nrels_C1_alt := [\nc[3]^6-c[2]^5,\nc[3]^3*c[2]-c[3]*c[2]^4,\nc[2]^6,\nc[3]^3*z-c[3]*c[2]^3*z,\nc[2]^4*z,\nz^3+c[2]*z+c[3]^2*c[2]^2*z,\nc[3]^3*w-c[3]*c[2]^3*w,\nc[2]^4*w,\nw^3+c[2]*w+c[3]^2*c[2]^2*w,\nuu*z^2*w^2+uu^3+uu^2*(z^2+w^2)\n]:\n\nmap(NF_C,rels_C1_alt);\n\ncza[1] := mods(expand(rem(expand(a + F_E(a,z) + F_E(a,-z)),z^8+3,z)),p^6):\ncza[2] := mods(expand(rem(expand(a * F_E(a,z) + a * F_E(a,-z) + F_E(a,z)*F_E(a,-z)),z^8+3,z)),p^6):\ncza[3] := mods(expand(rem(expand(a * F_E(a,z) * F_E(a,-z)),z^8+3,z)),p^6):\n\n# Series for [3](x) in terms of y = x(x+_Fz)(x-_Fz) assuming <3>(z)=0\nnn := (z,y) -> \n z^6*y+\n28 *y^3-\n27*z^2*y^5-\n39*z^4*y^7+\n 9*z^2*y^13-\n27 *y^19+\n27*z^4*y^23-\n 9*z^6*y^25+\n27*z^4*y^31-\n27*z^6*y^49-\n27*z^6*y^73;\n\n# Series for c_2({x,x+_Fz,x-_Fz}) in terms of y = x(x+_Fz)(x-_Fz) assuming <3>(z)=0\nmm := (z,y) -> \n-z^2+\n38*z^4*y^2+\n35*z^6*y^4+\n27 *y^6-\n21*z^2*y^8-\n 6*z^4*y^10+\n 9*z^6*y^12+\n18*z^2*y^16+\n18*z^6*y^20+\n 9 *y^22-\n24*z^2*y^24-\n15*z^4*y^26+\n39*z^6*y^28+\n36*z^2*y^32-\n 9*z^4*y^34-\n27*z^6*y^36+\n27*z^2*y^40-\n27*z^4*y^42+\n27*z^6*y^44+\n27 *y^46+\n18*z^2*y^48-\n36*z^4*y^50+\n18*z^6*y^52-\n27*z^2*y^56+\n27*z^4*y^58;\n\n_ASSERT(\n mods(expand(rem(T[\"p_series\"](a)-nn(z,cza[3]),z^8+3,z)),p^4) = 0,\n \"Defining property of nn\"\n);\n\n# The assertion below actually works mod (p^4,p^3z^6) but for simplicity\n# we just check mod p^3.\n_ASSERT(\n mods(expand(rem(cza[2]-mm(z,cza[3]),z^8+3,z)),p^3) = 0,\n \"Defining property of nn\"\n);\n\nmu := 1+3^8+3^16+3^18;\n\n# 3-adic square root of -2\nrr := 5-3^3+3^5-3^6-3^7+3^11+3^12-3^14-3^15-3^17-3^18+3^20-3^22-3^23-3^24;\nnu := mods((rr-2)/(3*mu),p^25);\nlm := 1 + 3 * mu * nu;\n\n_ASSERT(\n modp(rem(T[\"p_series\"](x),x^9+3*mu*x,x),p^25) = 0,\n \"Defining property of mu\"\n);\n\n_ASSERT(\n modp(rr^2+2,p^25) = 0,\n \"Defining property of rr = sqrt(-2)\"\n);\n\n_ASSERT(\n mods(rem(rem(nn(z,y),y^3+y*z^6,y),z^8+3,z),p^4) = 0,\n \"Consistency check for nn\"\n);\n\n_ASSERT(\n mods(rem(rem(mm(z,y)+z^2+nu*z^4*y^2,y^3+y*z^6,y),z^8+3,z),p^4) = 0,\n \"Consistency check for mm\"\n);\n\nchar0 := proc(t)\n local u,v;\n u := subs(LL = 1+3*MU*NU,t);\n v := \n [rem(subs({z=0,w=0,c[2]=3*a^2,c[3]=a^3},u),a^9+3*MU*a,a),\n rem(rem(subs({w= 0,c[2]=-NU*z^4*y^2-z^2,c[3]=y},u),y^3+y*z^6,y),z^8+3*MU,z),\n rem(rem(subs({w= z,c[2]=-NU*z^4*y^2-z^2,c[3]=y},u),y^3+y*z^6,y),z^8+3*MU,z),\n rem(rem(subs({w=-z,c[2]=-NU*z^4*y^2-z^2,c[3]=y},u),y^3+y*z^6,y),z^8+3*MU,z),\n rem(rem(subs({z= 0,c[2]=-NU*w^4*y^2-w^2,c[3]=y},u),y^3+y*w^6,y),w^8+3*MU,w)\n ];\n v := simplify(subs(NU = (sqrt(-2)-2)/(3*MU),v));\n return v;\nend:\n\nchar := proc(t)\n local u;\n u := char0(t);\n [seq(coeff(u[1],a,i),i=0..8),\n seq(seq(seq(coeff(coeff(u[i],y,k),z,j),k=0..2),j=0..7),i=2..4),\n seq(seq(coeff(coeff(u[5],y,k),w,j),k=0..2),j=0..7)];\nend:\n\nSS :=\n (3*MU^2*NU^2+2*MU*NU-3)/MU/((1+3*MU*NU)^3-27) * c[3]^2*(c[2]^3-27*c[3]^2) + \n (3/MU) * c[3]^4 + \n c[2]^2 +\n w^2*z^2 + \n (w^2+z^2)*c[2] +\n (NU/(1+3*MU*NU)^2) * (z^2+w^2)*c[2]^2*c[3]^2;\n\nrels_E_lift := [\n (LL+6)*c[2]^6+(-36*LL-192)*c[3]^2*c[2]^3+(3*LL*MU+18*MU)*c[2]^2+(252*LL+864)*c[3]^4,\n (-LL*MU-3*MU)*c[2]^5+(16*LL*MU+68*MU)*c[3]^2*c[2]^2+(-3*LL*MU^2-9*MU^2)*c[2]+(-32*LL-36)*c[3]^6,\n -c[2]^4*c[3]+(4*LL+24)*c[3]^3*c[2]+(36*LL*MU-27*MU)*c[3],\n z*c[3]*(-c[2]^3+(LL+6)*c[3]^2),\n w*c[3]*(-c[2]^3+(LL+6)*c[3]^2),\n z*((c[2]^4+3*MU)-(4*LL+20)/3*c[2]*c[3]^2),\n w*((c[2]^4+3*MU)-(4*LL+20)/3*c[2]*c[3]^2),\n (LL^2*(c[2]+z^2) + (LL-1)/(3*MU)*c[2]^2*c[3]^2)*z,\n (LL^2*(c[2]+w^2) + (LL-1)/(3*MU)*c[2]^2*c[3]^2)*w,\n SS\n];\n\nss := mods(subs({MU = mu,NU = nu},SS),p^25);\n\n_ASSERT(\n {rem(subs({z=0,w=0,c[2]=3*a^2,c[3]=a^3},SS),a^8+3*MU,a),\n rem(rem(subs({w= 0,c[2]=-NU*z^4*y^2-z^2,c[3]=y},SS),y^3+y*z^6,y),z^8+3*MU,z),\n rem(rem(subs({w= z,c[2]=-NU*z^4*y^2-z^2,c[3]=y},SS),y^3+y*z^6,y),z^8+3*MU,z),\n rem(rem(subs({w=-z,c[2]=-NU*z^4*y^2-z^2,c[3]=y},SS),y^3+y*z^6,y),z^8+3*MU,z),\n rem(rem(subs({z= 0,c[2]=-NU*w^4*y^2-w^2,c[3]=y},SS),y^3+y*w^6,y),w^8+3*MU,w)\n } = {0},\n \"Character theory relation\"\n);\n\nvars_E := vars_C1:\nrels_E := {op(basis_C1),mods(ss,p)}:\nbasis_E := Basis(rels_E,vars_E,characteristic=p);\nNF_E := (u) -> mods(NormalForm(u,basis_E,vars_E,characteristic=p),p);\ncobasis_E := cobasis(basis_E,vars_E);\n\n_ASSERT(nops(cobasis_E) = 105,\"E^0(BG) has rank 105\");\n\n", "meta": {"hexsha": "6e8398a5673b1b5353c386ec9db197146e432d0d", "size": 14816, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/morava/p3.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/morava/p3.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/morava/p3.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": 26.0845070423, "max_line_length": 99, "alphanum_fraction": 0.5149838013, "num_tokens": 7464, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8198933359135361, "lm_q2_score": 0.6757646010190476, "lm_q1q2_score": 0.5540548930217867}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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: mgga_exc *)\n\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\nrmggac_gamma1 := 0.08:\nrmggac_gamma2 := 0.3:\nrmggac_g := (alpha, s) ->\n (1 + rmggac_gamma1)*alpha/(rmggac_gamma1 + alpha + rmggac_gamma2*s^2):\n\nrmggac_f2 := (alpha, s) ->\n 3*rmggac_g(alpha, s)^3/(1 + rmggac_g(alpha, s)^3 + rmggac_g(alpha, s)^6):\nrmggac_f1 := (alpha, s) ->\n 1 - rmggac_f2(alpha, s):\n\nrmggac_gamma := 0.031091:\n\n(* from gga_c_regtpss *)\nbeta_a := 0.066724550603149220:\nbeta_b := 0.1:\nbeta_c := 0.1778:\nmbeta := (rs, t) -> beta_a*(1 + beta_b*rs)/(1 + beta_c*rs):\n(* from mgga_c_r2scan *)\nrmggac_w1 := (rs, z) -> exp(-f_pw(rs, z)/(rmggac_gamma*mphi(z)^3)) - 1:\n(* from gga_c_pbe *)\nA := (rs, z, t) -> mbeta(rs, t)/(rmggac_gamma * rmggac_w1(rs, z)):\n(* from gga_c_scan_e0 *)\nscan_e0_g := (rs, z, t) -> (1 + 4*A(rs, z, t)*t^2)^(-1/4):\n(* from mgga_c_r2scan *)\nrmggac_H1 := (rs, z, t) -> rmggac_gamma*mphi(z)^3*log(1 + rmggac_w1(rs, z) * (1 - scan_e0_g(rs, z, t))):\n\n(* from mgga_c_scan *)\nscan_alpha := (z, xt, ts0, ts1) ->\n (t_total(z, ts0, ts1) - xt^2/8)/(K_FACTOR_C*t_total(z, 1, 1)):\nscan_b1c := 0.0285764:\nscan_b2c := 0.0889:\nscan_b3c := 0.125541:\nscan_eclda0 := rs -> -scan_b1c/(1 + scan_b2c*sqrt(rs) + scan_b3c*rs):\n\nscan_chi_infty := 0.12802585262625815:\nscan_g_infty := s -> 1/(1 + 4*scan_chi_infty*s^2)^(1/4):\nscan_G_cnst := 2.3631:\nscan_Gc := z -> (1 - scan_G_cnst*(2^(1/3) - 1)*f_zeta(z))*(1 - z^12):\n\nscan_H0 := (rs, s) ->\n scan_b1c*log(1 + (exp(-scan_eclda0(rs)/scan_b1c) - 1)*(1 - scan_g_infty(s))):\nscan_e0 := (rs, z, s) ->\n (scan_eclda0(rs) + scan_H0(rs, s))*scan_Gc(z):\n\n(* define the functional *)\nrmggac_eps1 := (rs, z, t) ->\n (f_pw(rs, z) + rmggac_H1(rs, z, t)):\n\nrmggac_f := (rs, z, xt, xs0, xs1, ts0, ts1) ->\n + scan_e0(rs, z, X2S*2^(1/3)*xt)\n * rmggac_f1(scan_alpha(z, xt, ts0, ts1), X2S*2^(1/3)*xt) \n + rmggac_eps1(rs, z, tt(rs, z, xt))\n * rmggac_f2(scan_alpha(z, xt, ts0, ts1), X2S*2^(1/3)*xt):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n rmggac_f(rs, z, xt, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "054ed33c4be22a42b391b1486d03615d475757a4", "size": 2289, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "external/libxc-5.1.6/maple/mgga_exc/mgga_c_rmggac_test.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/mgga_exc/mgga_c_rmggac_test.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/mgga_exc/mgga_c_rmggac_test.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": 32.2394366197, "max_line_length": 104, "alphanum_fraction": 0.6116207951, "num_tokens": 1013, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797148356995, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5536903538044914}} {"text": "######################################################################\n# SW(N)(A) is the sphere associated to the vector space W(N)(A).\n# In the main LaTeX document this is called S(NWA).\n#\n# Elements are represented as nonzero elements of the space W(N)(A),\n# with an appropriate equivalence relation built into the definition\n# the function `is_equal/SW`.\n\n`is_element/SW` := (N::posint) -> (A::set) -> proc(x)\n local x0,a;\n global reason;\n\n if not(`is_element/W`(N)(A)(x)) then\n reason := [convert(procname,string),\"x is not in W(N)(A)\",x,N,A,reason];\n return false;\n fi;\n\n x0 := `normalise/W`(N)(A)(x);\n\n for a in A do\n if x0[a] <> [0$N] then return true; fi;\n od;\n\n reason := [convert(procname,string),\"x is zero\",x];\n return false;\nend;\n\n`normalise/SW` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,r,a;\n\n x0 := `normalise/W`(N)(A)(x);\n r := max(0,seq(op(map(abs,x0[a])),a in A));\n for a in A do\n x0[a] := x0[a] /~ r;\n od;\n\n return(eval(x0));\nend;\n\n`bottom_normalise/SW` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,r,a;\n\n x0 := `bottom_normalise/W`(N)(A)(x);\n r := max(0,seq(op(map(abs,x0[a])),a in A));\n for a in A do\n x0[a] := x0[a] /~ r;\n od;\n\n return(eval(x0));\nend;\n\n`is_equal/SW` := (N::posint) -> (A::set) -> proc(x,y) \n local x0,y0,a;\n\n x0 := `normalise/SW`(N)(A)(x);\n y0 := `normalise/SW`(N)(A)(y);\n\n for a in A do\n if not(`is_equal/R`(N)(x0[a],y0[a])) then\n return false;\n fi;\n od;\n\n return true;\nend;\n\n`dist/SW` := (N::posint) -> (A::set) -> proc(x,y) \n local x0,y0,a,d;\n\n x0 := `normalise/SW`(N)(A)(x);\n y0 := `normalise/SW`(N)(A)(y);\n\n d := 0;\n for a in A do\n d := d + `d_infinity/R`(N)(x0[a],y0[a]);\n od;\n\n return d;\nend;\n\n`normalise_2/SW` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,r2,r,a;\n\n x0 := table();\n u := [0$N];\n\n for a in A do\n x0[a] := x[a];\n u := u +~ x[a];\n od;\n u := u /~ nops(A);\n r2 := 0;\n for a in A do\n x0[a] := x0[a] -~ u;\n r2 := r2 + `norm_2/R`(N)(x0[a])^2;\n od;\n r := sqrt(r2);\n\n for a in A do\n x0[a] := x0[a] /~ r;\n od;\n\n return(eval(x0));\nend;\n\n`dist_2/SW` := (N::posint) -> (A::set) -> proc(x,y) \n local x0,y0,a,d;\n\n x0 := `normalise_2/SW`(N)(A)(x);\n y0 := `normalise_2/SW`(N)(A)(y);\n\n d := 0;\n for a in A do\n d := d + `d_2/R`(N)(x0[a],y0[a])^2;\n od;\n\n d := combine(simplify(expand(d)));\n d := combine(simplify(expand(sqrt(d))));\n return d;\nend;\n\n`is_leq/SW` := NULL;\n\n`random_element/SW` := (N::posint) -> (A::set) -> proc()\n local x,ok;\n\n ok := false;\n\n while not(ok) do\n x := `random_element/W`(N)(A)();\n ok := `is_element/SW`(N)(A)(x);\n od:\n\n return eval(x);\nend;\n\n`list_elements/SW` := NULL;\n`count_elements/SW` := NULL;\n", "meta": {"hexsha": "aa914d71c6b4c11f6d0ac59686de951c04332ddb", "size": 2605, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/SW.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/SW.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/SW.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": 18.7410071942, "max_line_length": 74, "alphanum_fraction": 0.5320537428, "num_tokens": 987, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8311430645886584, "lm_q2_score": 0.6654105587468141, "lm_q1q2_score": 0.5530513710064786}} {"text": "######################################################################\n\n`is_element/cycord` := (A::set) -> proc(C)\n global reason;\n\n if not type(C,list) then\n reason := [\"is_element/cycord\",\"C is not a list\",C];\n return false;\n fi;\n\n if nops(C) <> nops(A) then \n reason := [\"is_element/cycord\",\"C does not the same length as A\",C,A];\n return false;\n fi;\n \n if {op(C)} <> A then\n reason := [\"is_element/cycord\",\"C is not an enumeration of A\",C,A];\n return false;\n fi;\n \n return true;\nend;\n\n######################################################################\n\n`is_equal/cycord` := (A::set) -> proc(C0,C1)\n local n,a,i,C2;\n\n n := nops(A);\n if n <= 2 then\n return true;\n fi;\n\n a := C0[1];\n i := 1;\n while i < n and C1[i] <> a do i := i+1; od;\n\n C2 := [op(i..n,C1),op(1..i-1,C1)];\n return evalb(C0 = C2);\nend;\n\n`is_leq/cycord` := NULL;\n\n######################################################################\n\n`op/cycord` := (A::set) -> proc(C)\n local n,i;\n n := nops(A);\n return [seq(C[n-i],i=0..n-1)];\nend;\n\n`res/cycord` := (A::set,B::set) -> proc(C)\n return select(a -> member(a,B),C);\nend:\n\n######################################################################\n\n`random_element/cycord` := (A::set) -> proc()\n return combinat[randperm](A);\nend:\n\n`list_elements/cycord` := proc(A::set)\n local a,B;\n\n a := A[1];\n B := A minus {a};\n return map(C -> [a,op(C)],combinat[permute](B));\nend:\n\n`count_elements/cycord` := proc(A::set)\n return max(0,nops(A) - 1) !;\nend:\n\n######################################################################\n\n`cut/cycord` := (A::set) -> (C) -> proc(a)\n local n,i;\n n := nops(C);\n if n <= 1 then return C; fi;\n i := 1;\n while i <= n and C[i] <> a do i := i+1; od;\n if i > n then error(\"a is not in C\"); fi;\n return [op(i..n,C),op(1..i-1,C)];\nend:\n\n######################################################################\n\n`cycord_is_strictly_cyclic` := (A::set) -> (C) -> proc(x::list)\n local n,S,a,i,y;\n \n n := nops(x);\n S := {op(x)};\n if n < 2 then return true; fi;\n if nops(S) < n then return false; fi;\n if S minus A <> {} then return false; fi;\n y := `cut/cycord`(A)(C)(x[1]);\n y := select(i -> member(i,S),y);\n return evalb(x = y);\nend:\n\n######################################################################\n\n`cycord_is_cyclic` := (A::set) -> (C) -> proc(x)\n local n,y,i;\n n := nops(x);\n y := NULL;\n for i from 1 to n do\n if (i = n and x[n] <> x[1]) or (i < n and x[i] <> x[i+1]) then\n y := y,x[i];\n fi;\n od;\n y := [y];\n return `cycord_is_strictly_cyclic`(A)(C)(y);\nend:\n\n######################################################################\n\n`open_interval/cycord` := (A::set) -> (C) -> proc(a,b)\n local n,i,J,C0;\n if a = b then return []; fi;\n C0 := `cut/cycord`(A)(C)(a);\n J := NULL;\n i := 2;\n n := nops(C0);\n while i <= n and C0[i] <> b do i := i+1; od;\n return [op(2..i-1,C0)];\nend:\n\n`half_open_interval/cycord` := (A::set) -> (C) -> proc(a,b)\n return [a,op(`open_interval/cycord`(A)(C)(a,b))];\nend:\n\n`closed_interval/cycord` := (A::set) -> (C) -> proc(a,b)\n return [a,op(`open_interval/cycord`(A)(C)(a,b)),b];\nend:\n\n`are_crossed/cycord` := (A::set) -> (C) -> proc(U,V)\n local C0,n,i,j,k;\n if U intersect V <> {} then return true; fi;\n if U = {} or V = {} then return false; fi;\n C0 := `cut/cycord`(A)(C)(U[1]);\n n := nops(C0);\n i := 2;\n while i <= n and not(member(C0[i],V)) do i := i+1; od;\n if i > n then return false; fi;\n j := i+1;\n while j <= n and not(member(C0[j],U)) do j := j+1; od;\n if j > n then return false; fi;\n k := j+1;\n while k <= n and not(member(C0[k],V)) do k := k+1; od;\n if k > n then return false; fi;\n return true;\nend:\n\n`is_convex/cycord` := (A::set) -> (C) -> proc(W)\n return not(`are_crossed/cycord`(A)(C)(W,A minus W));\nend;", "meta": {"hexsha": "04af284d1b0dd1d62c8abef3b56ce99d9450408d", "size": 3699, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/cycord.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/cycord.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/cycord.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": 23.5605095541, "max_line_length": 72, "alphanum_fraction": 0.4620167613, "num_tokens": 1227, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.743168019989179, "lm_q2_score": 0.743168019989179, "lm_q1q2_score": 0.5522987059346368}} {"text": "bar := proc()\n local n,m,i,j,u,a,v,ac,av,x,y;\n n := nargs;\n for i from 1 to n do\n u := seq(args[j],j=1..i-1);\n a := args[i];\n v := seq(args[j],j=i+1..n);\n if type(a,`+`) then\n return map(t -> bar(u,t,v),a);\n elif type(a,`*`) then\n ac,av := selectremove(type,a,rational);\n if ac <> 1 then\n return ac * bar(u,av,v);\n fi;\n elif type(a,specfunc(bar)) then\n return bar(u,op(a),v);\n elif type(a,specfunc(bracket)) then\n m := nops(a);\n if m = 0 then\n return FAIL;\n elif m = 1 then\n return bar(u,op(a),v);\n else\n x := op(1,a);\n y := bracket(op(2..-1,a));\n return bar(u,x,y,v) - bar(u,y,x,v);\n fi; \n fi;\n od;\n return 'procname'(args);\nend:\n\n`mult/free_algebra` := () -> bar(args);\n\n`commutator/free_algebra` := () -> bar(bracket(args));\n\n`basis/free_algebra` := (A::set) -> proc(d::nonnegint)\n local i,B,a,b;\n B := [bar()];\n for i from 1 to d do \n B := [seq(seq(bar(op(b),a),a in A),b in B)];\n od:\n return B;\nend:\n\n`vec/free_algebra` := (A::set) -> (d::nonnegint) -> proc(u)\n local n,ub,uc,T,B,i;\n global `vec_table/free_algebra`;\n n := nops(A);\n if u = 0 then\n return [0$(n^d)];\n elif type(u,`+`) then\n return map(`vec/free_algebra`(A)(d),u); \n else\n if type(u,specfunc(bar)) then\n ub := u;\n uc := 1;\n elif type(u,`*`) then\n ub,uc := selectremove(type,u,specfunc(bar));\n ub := map(op,bar(ub));\n else\n return FAIL;\n fi;\n if not(type(`vec_table/free_algebra`[A,d],table)) then\n T := table():\n B := `basis/free_algebra`(A)(d);\n for i from 1 to n^d do\n T[B[i]] := [0$(i-1),1,0$(n!-i)];\n od:\n `vec_table/free_algebra`[A,d] := eval(T);\n fi;\n return uc *~ `vec_table/free_algebra`[A,d][ub];\n fi;\nend:\n\n", "meta": {"hexsha": "26370dbef92377528293998b9475ca2d80bc303e", "size": 1666, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/free_algebra.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/free_algebra.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/free_algebra.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": 21.9210526316, "max_line_length": 59, "alphanum_fraction": 0.5492196879, "num_tokens": 625, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7853085708384735, "lm_q2_score": 0.7025300573952054, "lm_q1q2_score": 0.5517028753440995}} {"text": "\n# Center of Mass Calculation for the Robot based on MDH frames\n# Introduction\n# Berechnung der Schwerpunkts-Kinematik (Positionen)\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# tree -> Berechnung für eine beliebige Baumstruktur (ohne Schleifen)\n# floatb -> floating base wird durch base twist (Geschwindigkeit der Basis) oder vollständige Orientierung (Euler-Winkel) berücksichtigt\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# kinematics_com -> Kinematik der Körperschwerpunkte\n# worldframe -> Berechnung der Geschwindigkeit im Welt-KS (KSW)\n# par1 -> Parametersatz 1 (Schwerpunkt als Parameter: SX,SY,SZ)\n# Testergebnisse\n# Test des exportierten Matlab-Codes erfolgreich (kinetische Energie)\n# Authors\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2014-11\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Sources\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I (WS 2014/15)\n# [Ott2008] Cartesian Impedance Control of Redundant and Flexible-Joint Robots\n# Initialization\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../transformation/proc_rotx\": \nread \"../transformation/proc_roty\": \nread \"../transformation/proc_rotz\": \nread \"../transformation/proc_trotx\": \nread \"../transformation/proc_troty\": \nread \"../transformation/proc_trotz\": \nread \"../transformation/proc_transl\": \nread \"../transformation/proc_trafo_mdh\": \nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"%s. Generiere Schwerpunktskinematik für %s\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name): \nkin_constraints_exist := kin_constraints_exist: # nur zum Abschätzen der Komplexität\n;\nif not assigned(simplify_options) or simplify_options(3)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardmäßig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 1: # standardmäßig simplify-Befehle anwenden\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(3): # dritter Eintrag ist für CoM-Kinematik\nend if:\n\n# Ergebnisse der Kinematik laden\nread sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name, base_method_name):\nTrf := Trf:\nTrf_c := Trf_c:\n\n# Positions of Center of Mass\nr_W_i_Si := Matrix(3, NL):\nr_W_W_Si := Matrix(3, NL):\nmr_W_i_Si := Matrix(3, NL):\n# Es gibt NL Körper (Basis und NJ bewegliche Körper).\n# r_i_i_Si(1 .. 3, i) ist der Vektor vom Ursprung des Körper-KS i zum Schwerpunkt des Körpers i ausgedrückt im Körper-KS i\n# r_W_i_Si(1 .. 3, i) ist der Vektor vom Ursprung des Körper-KS i zum Schwerpunkt des Körpers i ausgedrückt im Basis-KS\n# mr_W_i_Si(1 .. 3, i) ist der Vektor vom Ursprung des Körper-KS i zum Schwerpunkt des Körpers i ausgedrückt im Basis-KS multipliziert mit der Masse des Segments i \n# r_W_W_Si(1 .. 3, i) ist der Vektor vom Ursprung des Basis-KS zum Schwerpunkt des Körpers i ausgedrückt im Basis-KS\n# Trf_c(1 .. 3, 1 .. 3, i) ist das Körperkoordinatensystem zu Körper i im Basis KS.\nfor i to NL do\n r_W_i_Si(1 .. 3, i) := Multiply(Matrix(Trf_c(1 .. 3, 1 .. 3, i)), r_i_i_Si(1 .. 3, i)):\n if use_simplify>=1 then\n tmp_t11:=time():\n tmp_l11 := length(r_W_i_Si(1 .. 3, i)):\n printf(\"%s. Vereinfache Schwerpunktskoordinaten. Länge: %d (r_i_i_Si).\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l11):\n r_W_i_Si(1 .. 3, i) := simplify2(r_W_i_Si(1 .. 3, i)):\n tmp_l21 := length(r_W_i_Si(1 .. 3, i)):\n tmp_t21:=time():\n end if:\n mr_W_i_Si(1 .. 3, i) := Multiply(Matrix(Trf_c(1 .. 3, 1 .. 3, i)), mr_i_i_Si(1 .. 3, i)):\n r_W_W_Si(1 .. 3, i) := Matrix(Trf_c(1 .. 3, 4, i)) + Matrix(r_W_i_Si(1 .. 3, i)):\n printf(\"%s. Schwerpunktsposition in Weltkoordinaten für Körper %d aufgestellt.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1):#0=Basis\n if use_simplify>=1 then\n tmp_t12:=time():\n tmp_l12 := length(mr_W_i_Si(1 .. 3, i)):\n tmp_l13 := length(r_W_W_Si(1 .. 3, i)):\n printf(\"%s. Vereinfache Schwerpunktskoordinaten. Länge: %d/%d (r_W_W_Si/mr_W_i_Si).\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l13, tmp_l12):\n mr_W_i_Si(1 .. 3, i) := simplify2(mr_W_i_Si(1 .. 3, i)):\n r_W_W_Si(1 .. 3, i) := simplify2(r_W_W_Si(1 .. 3, i)):\n tmp_l22 := length(mr_W_i_Si(1 .. 3, i)):\n tmp_l23 := length(r_W_W_Si(1 .. 3, i)):\n tmp_t22:=time():\n printf(\"%s. Terme für Schwerpunktskoord. vereinfacht. Länge: %d->%d / %d->%d / %d->%d (r_W_i_Si / mr_W_i_Si / r_W_W_Si). Rechenzeit %1.1fs und %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l11, tmp_l21, tmp_l12, tmp_l22, tmp_l13, tmp_l23, tmp_t21-tmp_t11, tmp_t22-tmp_t12):\n end if:\nend do:\n# Maple Export\nsave mr_W_i_Si, r_W_W_Si, r_W_i_Si, sprintf(\"../codeexport/%s/tmp/kinematics_com_worldframe_floatb_%s_par1_maple.m\", robot_name, base_method_name):\nprintf(\"Maple-Ausdrücke exportiert.\\n\"):\n# Matlab-Export\nif codegen_act then\n MatlabExport(convert_t_s(r_W_W_Si), sprintf(\"../codeexport/%s/tmp/fkine_com_floatb_%s_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n# Calculate CoM of the whole robot\nc:=Vector(3):\nM_ges:=0:\nfor i from 1 to NL do\n c:=c + r_W_W_Si(1 .. 3,i)*M[i,1]:\n M_ges:=M_ges + M[i,1]:\nend do:\nc:=c/M_ges:\n# Maple-Export\nsave c, sprintf(\"../codeexport/%s/tmp/kinematics_com_total_worldframe_floatb_%s_par1_maple.m\", robot_name, base_method_name):\n# Matlab-Export\nif codegen_act then\n MatlabExport(convert_t_s(c), sprintf(\"../codeexport/%s/tmp/com_total_worldframe_floatb_%s_par1_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n\n", "meta": {"hexsha": "73c1e107ac1f63b623b99730fbafd8bd129e4fae", "size": 6216, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_kinematics/robot_tree_floatb_rotmat_kinematics_com_worldframe_par1.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_kinematics/robot_tree_floatb_rotmat_kinematics_com_worldframe_par1.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_kinematics/robot_tree_floatb_rotmat_kinematics_com_worldframe_par1.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 48.1860465116, "max_line_length": 164, "alphanum_fraction": 0.7226512227, "num_tokens": 2143, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206712569268, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5514180397478452}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\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\nXX := (z, xs) -> xs*opz_pow_n(z,4/3)*2^(-4/3):\nYY := (z, xt, xs0, xs1) -> 2*(XX(z, xs0)^2 + XX(-z, xs1)^2) - xt^2:\n\nf_th := (rs, z, xt, xs0, xs1) -> add(params_a_omega[i]\n * (n_spin(rs, z)^params_a_a[i] + n_spin(rs, -z)^params_a_a[i])\n * z^(2*params_a_b[i])\n * 1/2*(XX(z, xs0)^params_a_c[i] + XX(-z, xs1)^params_a_c[i])\n * YY(z, xt, xs0, xs1)^params_a_d[i], i=1..params_a_n)/n_total(rs):\n", "meta": {"hexsha": "265ad769d5a8a7c8e5555a6d0829c67de2f0282d", "size": 631, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/th.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/th.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/th.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": 37.1176470588, "max_line_length": 68, "alphanum_fraction": 0.6101426307, "num_tokens": 258, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122188543454, "lm_q2_score": 0.6076631698328917, "lm_q1q2_score": 0.5513402189371459}} {"text": "\n# Berechne kinematische Zwangsbedingungen für den Palettierroboter MPL800-YASKAWA aus 3 Viergelenkketten\n# Einleitung\n\n# Die kinematischen Zwangsbedingungen werden als Ersetzungsausdruck für die abhängigen Winkel aufgestellt.\n# \n# palh1m1TE -> MPL800 II-Yaskawa, modellierung der Zwangsbedingungen mit Ausdrücken für trigonometrische Elimination\n# kinematic_constraint -> Kinematische Zwangsbedingungen\n# Datenblatt des Roboters unter : https://www.motoman.com/industrial-robots/mpl800-ii\n# Voraussetzung\n# Viergelenkkette muss mit der Toolbox berechnet worden sein (Arbeitsblatt \"fourbar1TE_kinematic_constraints.mw\")\n# Quelle\n# SA Bejaoui: Bejaoui2018_S749; \"Modellierung kinematischer Zwangsbedingungen für hybride serielle Roboter mit planaren Parallelmechanismen\"\n# Autor\n# Abderahman Bejaoui\n# Studienarbeit bei: Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2018-08\n# (C) Institut fuer mechatronische Systeme, Leibniz Universitaet Hannover\n# Initialisierung\n# Import \ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nkin_constraints_exist := true: # Für Speicherung\n;\nwith(StringTools): # Für Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\n#with(ListTools):\ncodegen_act := true:\ncodegen_opt := 1: # Geringerer Optimierungsgrad. Sonst zu lange.\ncodegen_debug := 0: # Zur Code-Generierung auch für Nicht-Inert-Ausdrücke\n;\nread \"../helper/proc_MatlabExport\":\nread \"../transformation/proc_rotx\":\nread \"../transformation/proc_roty\":\nread \"../transformation/proc_rotz\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\nwith(RealDomain): # Schränkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\",robot_name):\n# Variable mit Winkeln der Nebenstruktur nur in Abhängigkeit der verallgemeinerten Koordinaten\nkintmp_qs := Matrix(RowDimension(kintmp_s),1):\n# Konstante Winkel bereits hineinschreiben \nfor i from 1 to RowDimension(kintmp_s) do\n if diff(kintmp_s(i,1), t) = 0 then\n kintmp_qs(i,1) := kintmp_s(i,1):\n end if:\nend do:\n# Variablen definieren für die Hilfswinkel\n# \n# Ersetzungsausdrücke definieren.\n# Speichere Sinus und Cosinus der Winkel direkt ab, da diese in den Rotationsmatrizen direkt auftreten.\n# Spalte 1: Zu suchender Ausdruck (sin oder cos eines Winkels)\n# Spalte 2: Einzusetzender Ausdruck.\n# Dadurch werden arctan-Ausdrücke in der direkten Kinematik reduziert.\n# Ähnliches Vorgehen wie in [1].\nkintmp_subsexp := Matrix(2*RowDimension(kintmp_s),2):\nfor i from 1 to RowDimension(kintmp_s) do\n kintmp_subsexp(2*i-1, 1) := sin(kintmp_s(i,1)):\n kintmp_subsexp(2*i, 1) := cos(kintmp_s(i,1)):\n # Initialisierung der rechten Spalte mit gleichen Werten. Später nur Ersetzung, wenn Vorteilhaft.\n kintmp_subsexp(2*i-1, 2) := kintmp_subsexp(2*i-1, 1):\n kintmp_subsexp(2*i, 2) := kintmp_subsexp(2*i, 1):\nend do:\n\n# Sicherung der aktuellen Daten\nbackup_kintmp_qs := kintmp_qs:\nbackup_kintmp_qt := kintmp_qt:\nbackup_kintmp_subsexp := kintmp_subsexp:\n\nread sprintf(\"../codeexport/fourbar1TE/tmp/kinematic_constraints_maple_inert.m\"): # mit .m datei wird es schneller\n;\nkintmp_subsexp_fourbar := kintmp_subsexp:\nkintmp_qs_fourbar := kintmp_qs:\nkintmp_qt_fourbar := kintmp_qt:\nkintmp_subsexp_fourbar:\nwinkel(6,2):\nkintmp_subsexp_fourbar(6,2):\nkintmp_subsexp_fourbar(3,2):\nwinkel_neu := Matrix(6,2):\nwinkel_neu(1,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(3,2)):\nwinkel_neu(2,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(4,2)):\nwinkel_neu(3,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(1,2)):\nwinkel_neu(4,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(2,2)):\nwinkel_neu(5,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(5,2)):\nwinkel_neu(6,2) := subs({qJ1s=phi_s}, kintmp_subsexp_fourbar(6,2)):\n# Vorherige Werte für dieses System wieder herstellen\nkintmp_qs := backup_kintmp_qs:\nkintmp_qt := backup_kintmp_qt:\nkintmp_subsexp := backup_kintmp_subsexp:\nwinkel_neu(1..6,1):\n# Viergelenkkette 1: A-M-L-B\nwinkel1:=<;;;;;>:\nfor i from 1 to 6 do\n\twinkel1(i,2):=kintmp_subsexp_fourbar(i,2): \n cos_phi_s :=-(sin(qJ3s)*cos(phi312)+cos(qJ3s)*sin(phi312)):\n\tsin_phi_s := -(cos(qJ3s)*cos(phi312)-sin(qJ3s)*sin(phi312)):\n\twinkel1(i,2):=subs({sin(qJ1s)=sin_phi_s},winkel1(i,2)): \n\twinkel1(i,2):=subs({cos(qJ1s)=cos_phi_s},winkel1(i,2)):\n winkel1(i,2) := subs({l1=BL}, winkel1(i,2)):\n winkel1(i,2) := subs({l2=AB}, winkel1(i,2)):\n winkel1(i,2) := subs({l3=AM}, winkel1(i,2)):\n winkel1(i,2) := subs({l4=ML}, winkel1(i,2)):\nend do:\nwinkel1:\n# Umrechnung aus Zwangsbedingugen für Winkel aus MDH-Tabelle\nsin_rho28_s:=winkel1(1,2): # schon in MDH\n;\ncos_rho28_s:=winkel1(2,2): # schon in MDH\n;\nsin_rho312_s:=winkel1(3,2): # schon in MDH\n;\ncos_rho312_s:=winkel1(4,2): # schon in MDH \n;\nsin_rho89_s:=winkel1(5,2): # für MDH , am 20.11 der neuen fourbar1 angepasst\n;\ncos_rho89_s:=winkel1(6,2): # für MDH , am 20.11 der neuen fourbar1 angepasst\n;\n#sin_rho312_s:=sin_rho3_s: # schon in MDH\n;\n#cos_rho312_s:=-cos_rho3_s: # schon in MDH\n;\n# Viergelenkkette 2: A-B-C-D\nwinkel2:=<;;;;;>:\nfor i from 1 to 6 do\n\twinkel2(i,2):=kintmp_subsexp_fourbar(i,2): #\n\tcos_phi_s :=sin(qJ2s)*cos(phi2)-cos(qJ2s)*sin(phi2):\n\tsin_phi_s :=cos(qJ2s)*cos(phi2)+sin(qJ2s)*sin(phi2):\n\twinkel2(i,2):=subs({sin(qJ1s)=sin_phi_s},winkel2(i,2)): \n\twinkel2(i,2):=subs({cos(qJ1s)=cos_phi_s},winkel2(i,2)):\n winkel2(i,2) := subs({l1=AB}, winkel2(i,2)):\n winkel2(i,2) := subs({l2=DA}, winkel2(i,2)):\n winkel2(i,2) := subs({l3=DC}, winkel2(i,2)):\n winkel2(i,2) := subs({l4=BC}, winkel2(i,2)):\n end do:\nwinkel2(1..6,1):\nsin_eta1_s:=winkel2(1,2):\ncos_eta1_s:=winkel2(2,2):\nsin_eta3_s:=winkel2(3,2):\ncos_eta3_s:=winkel2(4,2):\nsin_eta4_s:=winkel2(5,2): \ncos_eta4_s:=winkel2(6,2):\ncos_eta16_s:=cos(phi1)*cos_eta1_s-sin(phi1)*sin_eta1_s:\nsin_eta16_s:=cos(phi1)*sin_eta1_s+cos_eta1_s*sin(phi1):\ncos_eta711_s:=-cos_eta4_s:\nsin_eta711_s:=sin_eta4_s:\ncos_eta27_s:=cos(phi711)*cos_eta3_s+sin(phi711)*sin_eta3_s: # am 20.11 der neuen fourbar1 angepasst\n;\nsin_eta27_s:=cos(phi711)*sin_eta3_s-cos_eta3_s*sin(phi711): # am 20.11 der neuen fourbar1 angepasst\n;\n# Viergelenkkette 3: B-E-P-G \nwinkel3:=<;;;;;>:\nfor i from 1 to 6 do\n\twinkel3(i,2):=kintmp_subsexp_fourbar(i,2): \n\tcos_phi_s :=(cos(phi711+phi710)*(sin(qJ3s)*cos_eta3_s-cos(qJ3s)*sin_eta3_s)+sin(phi711+phi710)*(cos(qJ3s)*cos_eta3_s+sin(qJ3s)*sin_eta3_s)):\n\tsin_phi_s := (cos(phi711+phi710)*(cos(qJ3s)*cos_eta3_s+sin(qJ3s)*sin_eta3_s)-sin(phi711+phi710)*(sin(qJ3s)*cos_eta3_s-cos(qJ3s)*sin_eta3_s)):\n\twinkel3(i,2):=subs({sin(qJ1s)=sin_phi_s},winkel3(i,2)): \n\twinkel3(i,2):=subs({cos(qJ1s)=cos_phi_s},winkel3(i,2)):\n winkel3(i,2) := subs({l1=BG}, winkel3(i,2)):\n winkel3(i,2) := subs({l2=BE}, winkel3(i,2)):\n winkel3(i,2) := subs({l3=EP}, winkel3(i,2)):\n winkel3(i,2) := subs({l4=GP}, winkel3(i,2)):\n end do:\nwinkel3(1..6,1):\nsin_xi1016_s:=winkel3(1,2):\ncos_xi1016_s:=winkel3(2,2):\nsin_xi3_s:=winkel3(3,2): # schon in MDH\n;\ncos_xi3_s:=winkel3(4,2): # schon in MDH\n;\nsin_xi2_s:=winkel3(5,2):\ncos_xi2_s:=winkel3(6,2):\ncos_xi34_s:=cos_xi3_s*cos(phi413)+sin_xi3_s*sin(phi413): # am 20.11 der neuen fourbar1 angepasst\n;\nsin_xi34_s:=-cos_xi3_s*sin(phi413)+sin_xi3_s*cos(phi413): # am 20.11 der neuen fourbar1 angepasst\n;\ncos_xi413_s:=-cos_xi2_s:\nsin_xi413_s:=sin_xi2_s:\n# Kintmp_subsexp\nkintmp_subsexp(1,2):=sin_xi34_s:\nkintmp_subsexp(2,2):=cos_xi34_s:\nkintmp_subsexp(3,2):=sin_eta16_s:\nkintmp_subsexp(4,2):=cos_eta16_s:\nkintmp_subsexp(5,2):=sin_eta27_s:\nkintmp_subsexp(6,2):=cos_eta27_s:\nkintmp_subsexp(7,2):=sin_rho28_s:\nkintmp_subsexp(8,2):=cos_rho28_s:\nkintmp_subsexp(9,2):=sin_rho89_s:\nkintmp_subsexp(10,2):=cos_rho89_s:\nkintmp_subsexp(11,2):=sin_xi1016_s:\nkintmp_subsexp(12,2):=cos_xi1016_s:\nkintmp_subsexp(13,2):=sin_eta711_s:\nkintmp_subsexp(14,2):=cos_eta711_s:\nkintmp_subsexp(15,2):=sin_rho312_s:\nkintmp_subsexp(16,2):=cos_rho312_s:\nkintmp_subsexp(17,2):=sin_xi413_s:\nkintmp_subsexp(18,2):=cos_xi413_s:\nkintmp_subsexp(11..18,1):\n# Kintmp_qs\nkintmp_qs(1,1):=%arctan(sin_xi34_s,cos_xi34_s):\nkintmp_qs(2,1):=%arctan(sin_eta16_s,cos_eta16_s):\nkintmp_qs(3,1):=%arctan(sin_eta27_s,cos_eta27_s):\nkintmp_qs(4,1):=%arctan(sin_rho28_s,cos_rho28_s):\nkintmp_qs(5,1):=%arctan(sin_rho89_s,cos_rho89_s):\nkintmp_qs(6,1):=%arctan(sin_xi1016_s,cos_xi1016_s):\nkintmp_qs(7,1):=%arctan(sin_eta711_s,cos_eta711_s):\nkintmp_qs(8,1):=%arctan(sin_rho312_s,cos_rho312_s):\nkintmp_qs(9,1):=%arctan(sin_xi413_s,cos_xi413_s):\n# Export\nkintmp_qt := convert_s_t(kintmp_qs):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple\", robot_name):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple.m\", robot_name):\n#printf(\"Ausdrücke für kintmp_subsexp gespeichert (Maple). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\nfor i from 1 to RowDimension(kintmp_s) do\n tmp := kintmp_qs(i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d\",robot_name, i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d.m\", robot_name, i):\nend do:\nsave kin_constraints_exist, kintmp_qs, kintmp_qt,kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert\" ,robot_name):\nsave kin_constraints_exist, kintmp_qs, kintmp_qt, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nsave kintmp_qs, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_qs_maple_inert\", robot_name):\n#printf(\"Ausdrücke mit Inert-Arctan exportiert (Matlab). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Liste mit abhängigen konstanten Kinematikparametern erstellen (wichtig für Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\nkc_symbols := Matrix(list_constant_expressions( kintmp_subsexp ));\n#kc_symbols :=Transpose(kc_symbols);\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_maple\", robot_name):\nMatlabExport(kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_matlab.m\",robot_name),2);\n#printf(\"Fertig. %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n", "meta": {"hexsha": "e1b83364957634f19243b462c467c47999c662fb", "size": 10892, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "systems/palh1m1/codegen/palh1m1TE_kinematic_constraints.mpl", "max_stars_repo_name": "SchapplM/robsynth-serhybroblib", "max_stars_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/palh1m1/codegen/palh1m1TE_kinematic_constraints.mpl", "max_issues_repo_name": "SchapplM/robsynth-serhybroblib", "max_issues_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/palh1m1/codegen/palh1m1TE_kinematic_constraints.mpl", "max_forks_repo_name": "SchapplM/robsynth-serhybroblib", "max_forks_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": 46.547008547, "max_line_length": 165, "alphanum_fraction": 0.7493573265, "num_tokens": 4253, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127641048443, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5501120413855136}} {"text": "grassmann_count := (q) -> proc(n::nonnegint,d::nonnegint)\n local i;\n return factor(mul(q^(n-i)-1,i=0..d-1)/mul(q^(d-i)-1,i=0..d-1));\nend:\n\nsplitting_count := (q) -> (n::nonnegint,m::nonnegint) ->\n grassmann_count(q)(n+m,n) * q^(n*m);\n\n`indices/twisted_product/A` := proc(r::nonnegint)\n option remember;\n local U,V,u,v,e;\n \n if r = 0 then return [[]]; fi;\n if not(type(r,posint)) then return FAIL; fi;\n \n U := `indices/twisted_product/A`(r-1);\n V := NULL;\n for u in U do\n e := d-1-`+`(op(u));\n V := V,seq([op(u),v],v=0..e);\n od;\n return [V];\nend:\n\n`is_element/twisted_product/A` := (r::nonnegint) -> proc(f)\n if not(type(f,table)) then\n return false;\n fi;\n\n return evalb({indices(f)} = {op(`indices/twisted_product/A`(r))});\nend:\n\n`is_equal/twisted_product/A` := (r::nonnegint) -> proc(f,g)\n local U,u;\n \n U := `indices/twisted_product/A`(r);\n\n for u in U do\n if simplify(f[op(u)]-g[op(u)]) <> 0 then\n return false;\n fi;\n od;\n\n return true;\nend:\n\n`to_list/twisted_product/A` := (r::nonnegint) -> proc(f)\n local u;\n return [seq(f[op(u)],u in `indices/twisted_product/A`(r))];\nend:\n\n`from_symbol/twisted_product/A` := (r::nonnegint) -> proc(f)\n local u;\n return table([seq(op(u)=f[op(u)],u in `indices/twisted_product/A`(r))]);\nend:\n\n`zero/twisted_product/A` := proc(r::nonnegint)\n option remember;\n local u;\n return table([seq(op(u)=0,u in `indices/twisted_product/A`(r))]);\nend:\n\n`one/twisted_product/A` := proc(r::nonnegint)\n option remember;\n local u;\n return table([seq(op(u)=1,u in `indices/twisted_product/A`(r))]);\nend:\n\n`delta/twisted_product/A` := proc(r::nonnegint)\n option remember;\n local u;\n return table([seq(op(u)=`if`(u=[0$r],1,0),u in `indices/twisted_product/A`(r))]);\nend:\n\n`plus/twisted_product/A` := (r::nonnegint) -> proc(f,g)\n local u;\n return table([seq(op(u) = f[op(u)] + g[op(u)],u in `indices/twisted_product/A`(r))]);\nend:\n\n`minus/twisted_product/A` := (r::nonnegint) -> proc(f,g)\n local u;\n return table([seq(op(u) = f[op(u)] - g[op(u)],u in `indices/twisted_product/A`(r))]);\nend:\n\n`dot/twisted_product/A` := (r::nonnegint) -> proc(f,g)\n local u;\n return table([seq(op(u) = f[op(u)] * g[op(u)],u in `indices/twisted_product/A`(r))]);\nend:\n\n`scalar_times/twisted_product/A` := (r::nonnegint) -> proc(c,f)\n local u;\n return table([seq(op(u) = c * f[op(u)],u in `indices/twisted_product/A`(r))]);\nend:\n\n`mu/twisted_product/A` := (r::nonnegint) -> proc(u,v)\n option remember;\n local i,j;\n mul(splitting_count(q)(u[i],v[i]),i=1..r) *\n q^add(add(u[i]*v[j]+2*u[j]*v[i],j=i+1..r),i=1..r-1);\nend:\n\n`star/twisted_product/A` := (r::nonnegint) -> proc(f,g)\n local h,X,u,v,w,x;\n \n h := table([seq(op(u)=0,u in `indices/twisted_product/A`(r))]);\n \n X := `indices/twisted_product/A`(2*r);\n for x in X do\n u := [op(1..r,x)];\n v := [op(r+1..2*r,x)];\n w := u +~ v;\n h[op(w)] := h[op(w)] + `mu/twisted_product/A`(r)(u,v) * f[op(u)] * g[op(v)];\n od;\n\n return eval(h);\nend:\n\n", "meta": {"hexsha": "14437d027d4ec609869f90f71065408d31ce46ac", "size": 2893, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/tanabe/twisted_product.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/tanabe/twisted_product.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/tanabe/twisted_product.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": 24.5169491525, "max_line_length": 86, "alphanum_fraction": 0.6097476668, "num_tokens": 1034, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127529517044, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5501120342003809}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-16-input.txt\" ):\n\nbinstr2dec := proc(b) convert(parse(b),decimal,2) end proc:\nhex2bits := proc(input) uses StringTools; local tmp := Explode(input); Join(subs([\n \"0\" = \"0000\", \"1\" = \"0001\", \"2\" = \"0010\", \"3\" = \"0011\", \"4\" = \"0100\",\n \"5\" = \"0101\", \"6\" = \"0110\", \"7\" = \"0111\", \"8\" = \"1000\", \"9\" = \"1001\",\n \"A\" = \"1010\", \"B\" = \"1011\", \"C\" = \"1100\", \"D\" = \"1101\", \"E\" = \"1110\", \"F\" = \"1111\"],\n tmp),\"\"); end proc:\n\nprocesspacket := proc( bitinput )\nlocal vertotal, ver, pid, rest, parts, lofbits, subpak, numpaks,\n n, val, theops, thevalue;\n\n if length(bitinput) < 6 then\n error \"error %1 is too short to be valid\", bininput;\n end if;\n\n PRINT(\"Processing %d bits\", length(bitinput));\n\n ver := binstr2dec(bitinput[1..3]);\n pid := binstr2dec(bitinput[4..6]);\n rest := bitinput[7..];\n vertotal := ver;\n\n if pid = 4 then # literal\n PRINT(\"processing literal\");\n parts := NULL;\n while rest[1] <> \"0\" do\n parts := parts, rest[2..5];\n rest := rest[6..];\n end do;\n parts := parts, rest[2..5];\n\n thevalue := binstr2dec(cat(parts));\n PRINT(\"literal had %d parts with value=%d\", nops([parts]), thevalue);\n rest := rest[6..];\n PRINT(\"after literal %d bits left\", length(rest));\n else\n PRINT(\"processing operator ID=%d\", pid);\n theops := NULL;\n if rest[1] = \"0\" then\n \n lofbits := binstr2dec(rest[2..16]);\n PRINT(\"type-0 operator with %d bits of subpackets\", lofbits);\n rest := rest[17..];\n subpak := rest[1..lofbits];\n while length(subpak) > 6 do\n (n, val, subpak) := thisproc(subpak);\n vertotal += n;\n theops := theops, val;\n end do;\n rest := rest[lofbits+1..];\n PRINT(\"after type-0 %d bits left\", length(rest));\n else \n numpaks := binstr2dec(rest[2..12]);\n PRINT(\"type-1 operator with %d subpackets\",numpaks);\n rest := rest[13..];\n to numpaks do\n (n, val, rest) := thisproc(rest);\n theops := theops, val;\n vertotal += n; \n end do;\n PRINT(\"after type-1 %d bits left\", length(rest));\n end if;\n if pid = 0 then thevalue := `+`(theops);\n elif pid = 1 then thevalue := `*`(theops);\n elif pid = 2 then thevalue := min(theops);\n elif pid = 3 then thevalue := max(theops);\n elif pid = 5 then thevalue := ifelse( theops[1] > theops[2], 1, 0);\n elif pid = 6 then thevalue := ifelse( theops[1] < theops[2], 1, 0);\n elif pid = 7 then thevalue := ifelse( theops[1] = theops[2], 1, 0);\n else error \"bad operator pid\";\n end if;\n end if;\n\n PRINT(\"returning with %d bits left\", length(rest));\n return vertotal, thevalue, rest;\n\nend proc:\n\n# uncomment for verbose output\n#PRINT := s->printf(cat(s,\"\\n\"), _rest);\n\n(*\n# unit tests\nprocesspacket( hex2bits(\"C200B40A82\") )[2]=3;\nprocesspacket( hex2bits(\"04005AC33890\") )[2]=54;\nprocesspacket( hex2bits(\"880086C3E88112\"))[2]=7;\nprocesspacket( hex2bits( \"CE00C43D881120\" ) )[2]=9;\nprocesspacket( hex2bits( \"D8005AC2A8F0\" ))[2]=1;\nprocesspacket( hex2bits(\"F600BC2D8F\") )[2]=0;\nprocesspacket( hex2bits(\"9C005AC2F8F0\") )[2] = 0;\nprocesspacket( hex2bits(\"9C0141080250320F1802104A08\"))[2] = 1;\n*)\n\n# answers\n(answer1, answer2, fluff) := processpacket( hex2bits( input ) ):\nanswer1;\nanswer2;", "meta": {"hexsha": "d561777e385bfaef7f64cfa984a5146d0fdb35a9", "size": 3549, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day16/AoC16-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day16/AoC16-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day16/AoC16-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.8484848485, "max_line_length": 88, "alphanum_fraction": 0.5432516202, "num_tokens": 1134, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8267117940706734, "lm_q2_score": 0.6654105521116443, "lm_q1q2_score": 0.5501027513297748}}