{"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$define xc_dimensions_2d\n\n_2d_b86_beta := 0.002105:\n_2d_b86_gamma := 0.000119:\n\n_2d_b86_f := x -> (1 + _2d_b86_beta*x^2)/(1 + _2d_b86_gamma*x^2):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(_2d_b86_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "f4dadfd33f5cede33fffabac992d00e048a87f1c", "size": 486, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_2d_b86.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_2d_b86.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_2d_b86.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": 25.5789473684, "max_line_length": 77, "alphanum_fraction": 0.6790123457, "num_tokens": 183, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9334308073258007, "lm_q2_score": 0.749087201911703, "lm_q1q2_score": 0.6992210716378661}} {"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_c_hl_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_hl_params * )(p->params);\n*)\n\n$ifdef lda_c_vbh_params\nparams_a_r := [30, 75.0]:\nparams_a_c := [0.0252, 0.0127]:\n$endif\n\nxx := (k, rs) -> rs/params_a_r[k]:\nhl := (k, rs) -> -params_a_c[k]*\n ((1 + xx(k, rs)^3)*log(1 + 1/xx(k, rs)) - xx(k, rs)^2 + 1/2*xx(k, rs) - 1/3):\n\nf_hl := (rs, zeta) -> hl(1, rs) + f_zeta(zeta)*(hl(2, rs) - hl(1, rs)):\nf := (rs, zeta) -> f_hl(rs, zeta):", "meta": {"hexsha": "8588d6952f941b8a93a2ae8ddeda7d06db45ed4e", "size": 724, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/lda_c_hl.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_c_hl.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_c_hl.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": 26.8148148148, "max_line_length": 79, "alphanum_fraction": 0.5966850829, "num_tokens": 283, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9294404057671712, "lm_q2_score": 0.7520125682019722, "lm_q1q2_score": 0.6989508665316535}} {"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(* replace: \"my_dilog\\(\" -> \"xc_dilogarithm(\" *)\n\n`diff/my_dilog` := proc(g, x) -log(1 - g)/g * diff(g, x) end proc:\n\ngg99_a := 3^(1/4)/(2*sqrt(2)*Pi^(3/2)):\ngg99_b := 4*sqrt(3)*Pi^3:\n\n(* Equation 22 in the paper, i.e.\n the solution of x = 2*Pi*sinh(r)/(3*cosh(r))^(1/3) *)\n\ngg99_r_branch1 := x -> arcsinh( (gg99_a * x * sqrt(x^2 + (gg99_b + sqrt(gg99_b^2 - x^6))^(2/3))) / (gg99_b + sqrt(gg99_b^2 - x^6))^(1/6) ):\n\n(* The second branch is from Andrew Gilbert via email *)\n\ngg99_r_branch2 := x-> arcsinh(sqrt(x^3*(3/gg99_b)*cos(arctan(sqrt(1/(gg99_b^2)*x^6-1))/3))):\n\n(* Glue the pieces together. The min and max are required\n to avoid float exceptions *)\ngg99_r := x -> my_piecewise3(x < gg99_b^(1/3),\n gg99_r_branch1(m_min(x, gg99_b^(1/3) - 1e-10)),\n gg99_r_branch2(m_max(x, gg99_b^(1/3) + 1e-10))\n ):\n\n(* Equation 21 *)\ngg99_f0 := r -> (Pi^2 - 12*r*log(1 + exp(-2*r)) +\n12*my_dilog(-exp(-2*r))) / (2*3^(1/3)*Pi*r*sech(r)^(2/3)) / X_FACTOR_C:\n\n(* Assemble the function *)\ngg99_f := x -> gg99_f0(gg99_r(x)):\n\nf := (rs, zeta, xt, xs0, xs1) ->\n gga_exchange(gg99_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "6c40fe5f11dd794ae2287bc26d71832273cfd0c1", "size": 1386, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_gg99.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_gg99.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_gg99.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": 32.2325581395, "max_line_length": 139, "alphanum_fraction": 0.6075036075, "num_tokens": 551, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896802383029, "lm_q2_score": 0.7577943767446201, "lm_q1q2_score": 0.6977692418490627}} {"text": "# This checks some formulae in the LaTeX file Out_SL2.tex\n\ncheck_aut_SL2 := proc()\n local i2,alpha,beta,beta0,gamma,mu,sigma,rho,\n m,n,g,h,a,b,c,d,t,u,v,rels,\n is_in_U,is_in_T,is_in_B,err;\n\n i2 := IdentityMatrix(2);\n alpha := (v) -> <<1|v>,<0|1>>;\n mu := (u) -> <,<0|1/u>>;\n \n is_in_U := (g) -> g[2,1] = 0 and g[1,2] = 0 and g[1,1] * g[2,2] = 1;\n is_in_T := (g) -> g[2,1] = 0 and g[1,1] = 1 and g[2,2] = 1;\n is_in_B := (g) -> g[2,1] = 0 and g[1,1] * g[2,2] = 1;\n rho := (u) -> g[1,1];\n sigma := (a) -> <<0|1>,<1|a>>;\n beta := (a,b) -> alpha(b) . sigma(a) . (1/alpha(b)) . (1/sigma(a));\n beta0 := (b) -> <<1+b^2|b>,>;\n gamma := (b,u) -> <<1/u|0>,<(1+b^2)/u|u>>;\n\n _ASSERT(\n Equal(map(modp,simplify(beta(a,b)),2),beta0(b)),\n \"Formula for beta(b)\"\n ):\n \n err := gamma(b,u).beta0(b).(1/gamma(b,u)) - sigma(b^2);\n err := map(modp,simplify(subs(b = u^2,err)),2);\n _ASSERT(\n Equal(err,<<0|0>,<0|0>>),\n \"beta(b) is conjugate to sigma(b^2)\"\n ):\n\n m := <<1/u|0>,<0|u>>;\n n := <,<0|1/u>>;\n _ASSERT(\n Equal(m.n,alpha(1)),\n \"m n = alpha(1)\"\n );\n\n g := <,>;\n g := subs(solve(map(op,convert(g.alpha(1) - alpha(1).g,listlist)),{c,d}),g);\n _ASSERT(\n Equal(g,<,<0|a>>),\n \"Centraliser of alpha(1)\"\n );\n\n g := <,<0|1/u>>;\n h := alpha(v/(1/u-u));\n _ASSERT(\n Equal(simplify(h.mu(u).(1/h)),g),\n \"D_u is conjugate to mu(u) in B\"\n );\n\n g := <,>;\n rels := map(numer,map(op,convert(mu(u).g.mu(u).g - i2,listlist)));\n rels := map(coeffs,expand(rels),u);\n g := subs(solve(rels,{a,c,d}),g);\n _ASSERT(\n Equal(g,<<0|b>,<1/b|0>>),\n \"(mu(u) . g)^2 = 1 only on U\"\n );\n\n _ASSERT(\n Equal(mu(u) . alpha(t) . (1/mu(u)),alpha(u^2*t)),\n \"Conjugate of alpha(t) by mu(u)\"\n );\nend:\n", "meta": {"hexsha": "5d065b95f6c2dfca936fead3e71d0ed009995dcc", "size": 1699, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/groups/Out_SL2.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/Out_SL2.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/Out_SL2.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": 24.9852941176, "max_line_length": 77, "alphanum_fraction": 0.5038257799, "num_tokens": 737, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8872046056466901, "lm_q2_score": 0.7853085859124002, "lm_q1q2_score": 0.6967293942753708}} {"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\n$include \"mgga_x_tm.mpl\"\n\n(* revtm uses the tpss definition of qtilde *)\ntm_b := 0.4:\ntm_qtilde := (x, t) ->\n 9/20 * (tm_alpha(x, t) - 1)/sqrt(1 + tm_b*tm_alpha(x, t)*(tm_alpha(x, t) - 1))\n + 2*tm_p(x)/3:\n", "meta": {"hexsha": "3c72e60af7c315783b8e20ad3dca1b863cf65b77", "size": 507, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_revtm.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_revtm.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_revtm.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": 26.6842105263, "max_line_length": 83, "alphanum_fraction": 0.6252465483, "num_tokens": 179, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9184802440252811, "lm_q2_score": 0.757794360334681, "lm_q1q2_score": 0.6960191490011796}} {"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\nmu1 := 0.042:\nmu2 := 0.26 - mu1:\nnu_MGE4 := -0.195:\nk2 := -mu2^2/nu_MGE4:\nk1 := 0.804 - k2:\n\nf0 := s -> 1 + k1 + k2 \n - k1*(1 - mu1*s^2/k1)/(1 - (mu1*s^2/k1)^5)\n - k2/(1 + mu2*s^2/k2):\n\nf:= x -> f0(X2S*x): ", "meta": {"hexsha": "7fa8be8e2916e49ee3f473121843fbac9f15103e", "size": 491, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_sg4.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_sg4.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_sg4.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": 23.380952381, "max_line_length": 68, "alphanum_fraction": 0.5621181263, "num_tokens": 204, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.951142221377825, "lm_q2_score": 0.7310585727705126, "lm_q1q2_score": 0.6953406748622476}} {"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_dk87_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_dk87_params * )(p->params);\n*)\n\ndk87_betag := 7/(432*Pi*(6*Pi^2)^(1/3))/X_FACTOR_C:\n\ndk87_f := x -> 1 + dk87_betag*x^2*(1 + params_a_a1*x^params_a_alpha)/(1 + params_a_b1*x^2):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(dk87_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "74ed8c05fc6d01a6eecbf486355dfa3d57fbf403", "size": 594, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_dk87.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_dk87.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_dk87.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": 27.0, "max_line_length": 91, "alphanum_fraction": 0.6531986532, "num_tokens": 216, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9504109728022221, "lm_q2_score": 0.7310585669110202, "lm_q1q2_score": 0.6948060837533011}} {"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\nkappa := 0.8040:\n\nden := s -> kappa + 1*MU_GE*s^2 + MU_GE^2*s^4/kappa:\nf0 := s -> 1 + kappa * (1 - kappa/den(s)):\nf := x -> f0(X2S * x):\n", "meta": {"hexsha": "7981ef6c99906fe652c0a27077e0f1463729b0ab", "size": 403, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_rge2.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_rge2.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_rge2.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": 25.1875, "max_line_length": 68, "alphanum_fraction": 0.6203473945, "num_tokens": 143, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8933094060543488, "lm_q2_score": 0.7772998560157665, "lm_q1q2_score": 0.6943692727035752}} {"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(* prefix:\n mgga_k_pgslb_params *params;\n\n assert(p->params != NULL);\n params = (mgga_k_pgslb_params * )(p->params);\n*)\n\n# Equation (4) and (8)\npgslb_f0 := (s, q) -> 5/3*s^2 + exp(-params_a_pgslb_mu * s^2) + params_a_pgslb_beta*q^2:\npgslb_f := (x, u) -> pgslb_f0(X2S*x, X2S^2*u):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_kinetic(pgslb_f, rs, z, xs0, xs1, u0, u1):\n\n", "meta": {"hexsha": "f9c70f3b723a504a2772d027cdc8026a4452c577", "size": 639, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_k_pgslb.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_k_pgslb.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_k_pgslb.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": 26.625, "max_line_length": 88, "alphanum_fraction": 0.641627543, "num_tokens": 251, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947117065459, "lm_q2_score": 0.7341195327172402, "lm_q1q2_score": 0.6937390761782726}} {"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\n$define lda_c_vbh_params\n$include \"lda_c_hl.mpl\"\n\nmalpha := (4*Pi/3)^(1/6):\n\n(* 4.28e-3/2, where the 2 comes from the covertion from Ryd. to Hartree *)\na1 := Pi/(16*(3*Pi^2)^(4/3)):\na2 := -0.262:\na3 := -7/(9*2^(5/3)):\n\nt1 := (rs, z, xt) -> \n + xt^2*exp(a2*xt/(malpha*sqrt(rs))) \n * sqrt(2)/sqrt((1 + z)^(5/3) + (1 - z)^(5/3)):\nt2 := (z, xs0, xs1) -> \n + a3*(xs0^2*(1 + z)^(4/3) + xs1^2*(1 - z)^(4/3)):\n\nf := (rs, z, xt, xs0, xs1) -> \n + f_hl(rs, z)\n + a1/(malpha^2*rs)*(t1(rs, z, xt) + t2(z, xs0, xs1)):\n\n", "meta": {"hexsha": "50f875b60cbfb0fe18009ca2eba88d539ffbc739", "size": 785, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_c_lm.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_lm.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_lm.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": 25.3225806452, "max_line_length": 74, "alphanum_fraction": 0.549044586, "num_tokens": 348, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9407897459384732, "lm_q2_score": 0.7371581741774411, "lm_q1q2_score": 0.6935108514008635}} {"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_pbe_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_pbe_params * )(p->params);\n*)\n\n(* standard PBE *)\n$ifdef gga_x_pbe_params\nparams_a_kappa := 0.8040:\nparams_a_mu := 0.2195149727645171:\n$endif\n\n(* PBE_SOL *)\n$ifdef gga_x_pbe_sol_params\nparams_a_kappa := 0.8040:\nparams_a_mu := MU_GE:\n$endif\n\n$ifdef gga_x_pbe_tca_params\nparams_a_kappa := 1.227:\nparams_a_mu := 0.2195149727645171:\n$endif\n\npbe_f0 := s -> 1 + params_a_kappa*(1 - params_a_kappa/(params_a_kappa + params_a_mu*s^2)):\npbe_f := x -> pbe_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(pbe_f, rs, z, xs0, xs1):\n\n", "meta": {"hexsha": "d878eac4e768b7a2d596faaf4515a0dab141f423", "size": 883, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbe.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_pbe.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_pbe.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": 22.641025641, "max_line_length": 90, "alphanum_fraction": 0.6840317101, "num_tokens": 316, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850110816422, "lm_q2_score": 0.740174367770488, "lm_q1q2_score": 0.6930141661303388}} {"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\na1 := (10/(3*(6*Pi*Pi)^(2/3)))^(4/5): (* (2/C_F)^(4/5) *):\n\nf := (rs, x, t, u) -> a1*t^(4/5): ", "meta": {"hexsha": "eb4b9b598b1a825370f089897e4426f0b1783dc6", "size": 358, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_lta.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_lta.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_lta.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": 27.5384615385, "max_line_length": 68, "alphanum_fraction": 0.6005586592, "num_tokens": 136, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9173026573249612, "lm_q2_score": 0.7549149868676283, "lm_q1q2_score": 0.6924855235081135}} {"text": "######################################################################\n\n# Real numbers\n\n`is_element/RR` := (x) -> type(x,realcons):\n\n`is_equal/RR` := (x,y) -> evalb(simplify(y-x) = 0):\n\n`is_leq/RR` := (x,y) -> is(simplify(y-x) >= 0);\n\n`random_element/RR` := proc() rand(-720..720)()/(360); end:\n\n`list_elements/RR` := NULL;\n`count_elements/RR` := NULL;\n\n`random_element/RR_plus` := proc() rand(1..720)()/(360); end:\n\n######################################################################\n# R(N) is the vector space RR^N\n\n`is_element/R` := (N::posint) -> (x) -> type(x,[realcons$N]);\n\n`is_equal/R` := (N::posint) -> (x,y) -> evalb(simplify(x -~ y) = [0$N]);\n\n`is_leq/R` := (N::posint) -> proc(x,y) local i; `and`(seq(`is_leq/RR`(x[i],y[i]),i=1..N)); end:\n\n`is_leq_lex/R` := (N::posint) -> proc(x,y)\n local i,z;\n for i from 1 to n do\n z := simplify(y[i] - x[i]);\n if is(z > 0) then\n return true;\n elif is(z < 0) then\n return false;\n fi;\n od;\n return true;\nend:\n\n`is_zero/R` := (N::posint) -> (x) -> evalb(simplify(x) = [0$N]);\n\n`norm_2/R` := (N::posint) -> proc(x) local i; sqrt(add(x[i]^2,i=1..N)); end:\n\n`dot/R` := (N::posint) -> proc(x,y) local i; add(x[i]*y[i],i=1..N); end:\n\n`d_2/R` := (N::posint) -> (x,y) -> `norm_2/R`(N)(x -~ y);\n\n`norm_infinity/R` := (N::posint) -> (x) -> max(map(abs,x));\n\n`d_infinity/R` := (N::posint) -> (x,y) -> `norm_infinity/R`(N)(x -~ y);\n \n`random_element/R` := (N::posint) -> proc() local i; [seq(`random_element/RR`(),i=1..N)] end;\n\n`list_elements/R` := NULL;\n`count_elements/R` := NULL;\n\n`cross_product` := proc(x,y)\n [x[2]*y[3] - x[3]*y[2],\n x[3]*y[1] - x[1]*y[3],\n x[1]*y[2] - x[2]*y[1]];\nend:", "meta": {"hexsha": "60a594daa23273c6f462cf290af78447e9e4b658", "size": 1640, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/R.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/R.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/R.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": 26.8852459016, "max_line_length": 95, "alphanum_fraction": 0.487804878, "num_tokens": 631, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8757870046160258, "lm_q2_score": 0.7905303137346446, "lm_q1q2_score": 0.6923361755238314}} {"text": "input := StringTools:-Trim(FileTools:-Text:-ReadFile(\"AoC-2021-15-input.txt\"));\n\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\n out := out, [i+1, j];\n end if;\n if j < gridsize then\n out := out, [i, j+1];\n end if;\n\n if i > 1 then\n out := out, [i-1,j];\n end if;\n if j > 1 then\n out := out, [i, j-1];\n end if;\n\n return [out];\nend proc:\n\nDijkstra := proc(start, theend, grid)\nlocal pq, costsofar, curr, nb, newcost, pt, gridsize; \nuses priqueue;\n\ngridsize := upperbound(grid)[1];\ncostsofar := table(sparse=infinity):\n\ninitialize(pq):\ninsert([0,start], pq):\ncostsofar[start] := 0:\n\nwhile pq[0] <> 0 do\n curr := extract(pq)[2];\n if curr = theend then\n return costsofar[theend];\n end if;\n nb := nbs(curr[], gridsize);\n for pt in nb do\n newcost := costsofar[curr] + grid[pt[]];\n if newcost < costsofar[pt] then\n costsofar[pt] := newcost;\n insert([-newcost,pt], pq);\n end if;\n end do;\nend do:\n\nend proc:\n\nanswer1 := Dijkstra([1,1], [gridl,gridw], grid);\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);\nanswer2 := Dijkstra([1,1], [biggridl,biggridw], biggrid);\n\n\n", "meta": {"hexsha": "b95afc3d62b1fc5690fafd1b13965faaf40f78e9", "size": 1429, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day15/AoC15-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": "Day15/AoC15-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": "Day15/AoC15-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": 23.0483870968, "max_line_length": 87, "alphanum_fraction": 0.5836249125, "num_tokens": 475, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357735451835, "lm_q2_score": 0.7981867801399695, "lm_q1q2_score": 0.6920564923521977}} {"text": "`is_element/total_preord` := (A::set) -> proc(R)\n local AA,a,b,ab,U;\n\n global reason;\n\n AA := [seq(seq([a,b],b in A),a in A)];\n\n if not(`is_element/preord`(A)(R)) then\n reason := [convert(procname,string),\"R is not a preorder\",R,reason];\n return false;\n fi;\n\n if not(`is_total/preord`(A)(R)) then\n reason := [convert(procname,string),\"R is not a total preorder on A\",R,A];\n return false;\n fi;\n\n return true;\nend;\n\n`is_equal/total_preord` := (A::set) -> (R1,R2) -> `is_equal/preord`(A)(R1,R2);\n`is_leq/total_preord` := (A::set) -> (R1,R2) -> `is_leq/preord`(A)(R1,R2);\n\n######################################################################\n\n`build/total_preord` := (A::set) -> proc(pi)\n local m,r,i,a,b,R;\n \n m := nops(pi);\n r := table();\n for i from 1 to m do\n for a in pi[i] do\n r[a] := i;\n od;\n od;\n\n R := NULL;\n for a in A do\n for b in A do\n if r[a] <= r[b] then R := R,[a,b]; fi;\n od;\n od;\n R := {R};\n\n return R;\nend;\n\n######################################################################\n\n`random_element/total_preord` := (A::set) -> proc()\n local pi,pi0,pi1,m,r,i,a,b,R;\n\n pi := `random_element/partitions`(A)();\n pi0 := map(u -> sort([op(u)]),pi);\n pi0 := sort([op(pi0)]);\n pi1 := combinat[randperm](pi0);\n return `build/total_preord`(A)(pi1);\nend;\n\n######################################################################\n\n`list_elements/total_preord` := proc(A::set)\n local PI,pi,pi0,pi1,L;\n\n PI := `list_elements/partitions`(A);\n L := NULL;\n for pi in PI do\n pi0 := map(u -> sort([op(u)]),pi);\n pi0 := sort([op(pi0)]);\n for pi1 in combinat[permute](pi0) do\n L := L,`build/total_preord`(A)(pi1);\n od;\n od;\n L := [L];\n return L;\nend;\n\n######################################################################\n\n`count_elements/total_preord` := proc(A::set)\n local n,k;\n n := nops(A);\n add(k! * Stirling2(n,k),k=1..n);\nend;\n", "meta": {"hexsha": "385dda1b43b247c9a9f0648321e275404bd5e385", "size": 1847, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/total_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/total_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/total_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": 21.7294117647, "max_line_length": 78, "alphanum_fraction": 0.4910665945, "num_tokens": 585, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357598021707, "lm_q2_score": 0.7981867729389246, "lm_q1q2_score": 0.6920564751391433}} {"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: lda_exc *)\n\n$include \"vwn.mpl\"\n\nf_vwn := (rs, z) ->\n + f_aux(A_rpa[1], b_rpa[1], c_rpa[1], x0_rpa[1], rs)*(1 - f_zeta(z))\n + f_aux(A_rpa[2], b_rpa[2], c_rpa[2], x0_rpa[2], rs)*f_zeta(z):\n\nf := (rs, z) -> f_vwn(rs, z):\n", "meta": {"hexsha": "e0c352fb9199f64ab8de9bbaeabdba60fa4a80a2", "size": 468, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_vwn_rpa.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_vwn_rpa.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_vwn_rpa.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": 26.0, "max_line_length": 70, "alphanum_fraction": 0.6239316239, "num_tokens": 182, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9304582593509315, "lm_q2_score": 0.7431680086124811, "lm_q1q2_score": 0.6914868116988673}} {"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: lda_exc *)\n\nAA := -0.655868:\nBB := 4.888270:\nCC := 3.177037:\nDD := 0.897889:\n\nphi := z -> 1/2*(opz_pow_n(z,2/3) + opz_pow_n(-z,2/3)):\n\nf_rc04 := (rs, zeta) -> phi(zeta)^3 * (AA*arctan(BB + CC*rs) + DD)/rs:\n\nf := (rs, zeta) -> f_rc04(rs, zeta):\n", "meta": {"hexsha": "e1282bfd53f065365eaa8f31b9bd112d01e3963c", "size": 500, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_rc04.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_rc04.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_rc04.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": 23.8095238095, "max_line_length": 70, "alphanum_fraction": 0.606, "num_tokens": 195, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9566342012360932, "lm_q2_score": 0.7217432122827968, "lm_q1q2_score": 0.6904442413797254}} {"text": "# Proof by PDF that X <~ standardChiSq(2) == Y <~ exponential(1/2)\n\nPDF_chisq := (n, x) -> x^(1/2*n-1)*exp(-1/2*x)/(2^(1/2*n))/GAMMA(1/2*n); \nsimplify(PDF_chisq(2,x));\n\nPDF_exponential := (l, x) -> l*exp(-l*x);\nsimplify(PDF_exponential(1/2,x));\n\nevalb(PDF_chisq(2,x) = PDF_exponential(1/2,x));\n", "meta": {"hexsha": "b76502db8f84f2d48b6421f0733d63bdaaf0aea7", "size": 294, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip2/t_stdChiSq_to_exponential.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip2/t_stdChiSq_to_exponential.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip2/t_stdChiSq_to_exponential.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 29.4, "max_line_length": 73, "alphanum_fraction": 0.6088435374, "num_tokens": 129, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9136765281148513, "lm_q2_score": 0.7549149813536518, "lm_q1q2_score": 0.6897480991850923}} {"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\nmkappa := 0.4604:\nmmu := 0.354546875:\n\nf0 := s -> 1 + mkappa*(1 - mkappa/(mkappa + mmu*s^2)):\nf := x -> f0(X2S_2D*x):\n", "meta": {"hexsha": "3b17568fa8ebf6181b1d529c5c5d1ee1d0692b16", "size": 385, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_2d_pbe.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_2d_pbe.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_2d_pbe.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": 24.0625, "max_line_length": 68, "alphanum_fraction": 0.638961039, "num_tokens": 137, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8962513842182775, "lm_q2_score": 0.76908023177796, "lm_q1q2_score": 0.6892892223059104}} {"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$include \"mgga_xc_b98.mpl\"\n\n(* Fitted parameters, given below Eq. 50 *)\nedmgga_mu := 0.21:\nedmgga_a := 0.704:\n\n(* Eq. 40: F_x'(0) *)\nedmgga_fp0 := 27*edmgga_mu/50:\n(* Eq. 27: lim_(x -> -infinity) F_x(x) *)\nedmgga_fminf := 1/3 * (4*Pi^2/3)^(1/3):\n(* Eq. 44 *)\nedmgga_b := 2*Pi/9 * sqrt(6/5):\n\n(* Eq. 47 *)\nedmgga_c1 := edmgga_fminf:\n(* Eq. 48 *)\nedmgga_c2 := 1 - edmgga_c1:\n(* Eq. 49 *)\nedmgga_c3 := edmgga_c2*sqrt(2*edmgga_a)/(2*edmgga_b):\n\n(* Eq. 50. There's some problem in the equation, since the first line,\n1/edmgga_c3^3 * (edmgga_c3^2 - edmgga_fp0/(2*edmgga_b^2)) * edmgga_c2,\ndoes not agree with the second line. The first line evaluates to a\nnegative value, which makes the functional blow up. The second line\nyields values that are close to the reported ones, but Tao might have\nused a more accurate numerical value in his implementation since the\nagreement is not perfect. Unfortunately there's no way to check this\nas he has passed away. *)\nedmgga_c4 := 1/edmgga_c3^3 * (edmgga_c3^2 - 0.09834*edmgga_mu):\n\n(* Eq. 46 *)\n(* Apparently, edmgga_x can sometimes be smaller than 0,\n as Qb can be very negative. The expansion for -infinity\n has an error of 1e-13 *)\nedmgga_x_large := y -> -1/(2*y) + 1/(8*y^3):\n\nedmgga_x := Qb -> my_piecewise3(\n Qb < -1e4/edmgga_a,\n edmgga_x_large(m_min(edmgga_a*Qb, -1e-4/edmgga_a)),\n edmgga_a*Qb + sqrt(1 + (edmgga_a*Qb)^2)\n):\n\n(* Eq. 45 *)\nedmgga_f_x := x -> edmgga_c1 + edmgga_c2*x/(1 + edmgga_c3*sqrt(x)*arcsinh(edmgga_c4*(x - 1))):\n\n(* the evalf is absolutely necessary to avoid exceptions *)\nedmgga_f := (x, u, t) -> edmgga_f_x(edmgga_x(b98_q(x, u, t))):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(edmgga_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "6bc81412121b133e566047b6e61554a7426cc1e8", "size": 2011, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_edmgga.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_edmgga.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_edmgga.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": 32.9672131148, "max_line_length": 95, "alphanum_fraction": 0.6658378916, "num_tokens": 783, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632916317103, "lm_q2_score": 0.7431680029241321, "lm_q1q2_score": 0.6891867254270876}} {"text": "#######################################################################\n# This file is part of the crlibm library, and is distributed under\n# the LGPL.\n# To use:\n# restart; read \"sqrt.mpl\";\nDigits := 120:\n\ninterface(quiet=true):\n\nread \"common-procedures.mpl\":\nread \"triple-double.mpl\":\nmkdir(\"TEMPSQRT\"):\n\npolyDegree := 4:\n\nERecSqrtmMin := 0.707:\nERecSqrtmMax := 1.4143:\n\nxErrMin := evalf((1/(ERecSqrtmMax^2))):\nxErrMax := evalf((1/(ERecSqrtmMin^2))):\n\nprintf(\"Using a %d degree polynomial for computing the iteration seed\\n\",polyDegree);\n\npolyExact := numapprox[minimax](1/sqrt(x),x=1/2..2,[polyDegree,0],1,'err'):\npoly := poly_exact(polyExact):\neps := numapprox[infnorm]((poly*sqrt(x))-1,x=xErrMin..xErrMax):\n\nprintf(\"Relative approximation error eps = 2^(%f)\\n\",log[2](abs(eps))):\n\nprintf(\"Writing tables...\\n\");\n\nfilename:=\"TEMPSQRT/sqrt.h\":\nfd:=fopen(filename, WRITE, TEXT):\n\nfprintf(fd, \"\\n/* File generated by maple/sqrt.mpl */\\n\"):\n\nfor i from 0 to polyDegree do\n\tfprintf(fd, \"\\#define SQRTPOLYC%d %1.50e\\n\",i,coeff(poly,x,i)):\nod:\nfprintf(fd, \"\\#define TWO52 %1.50e\\n\",evalf(2^(52))):\n\n\nfclose(fd):\n\nfilename:=\"TEMPSQRT/sqrt.sed\":\nfd:=fopen(filename, WRITE, TEXT):\n\nfprintf(fd, \"s/_epsilonApprox/%1.50e/g\\n\",eps):\nfprintf(fd, \"s/_ERecSqrtmMin/%1.50e/g\\n\",ERecSqrtmMin):\nfprintf(fd, \"s/_ERecSqrtmMax/%1.50e/g\\n\",ERecSqrtmMax):\n\n\nfor i from 0 to polyDegree do\n fprintf(fd, \"s/_SQRTPOLYC%d/%1.50e/g\\n\",i,coeff(poly,x,i)):\nod:\n\nfclose(fd):\n\nprintf(\"... done\\n\");", "meta": {"hexsha": "a681510327052b1fbf974ef9ab87fc801901185a", "size": 1470, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "crlibm/maple/sqrt.mpl", "max_stars_repo_name": "squarePenguin/parvsl", "max_stars_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "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": "crlibm/maple/sqrt.mpl", "max_issues_repo_name": "squarePenguin/parvsl", "max_issues_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2019-03-25T17:02:38.000Z", "max_issues_repo_issues_event_max_datetime": "2019-03-25T17:02:38.000Z", "max_forks_repo_path": "crlibm/maple/sqrt.mpl", "max_forks_repo_name": "squarePenguin/parvsl", "max_forks_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "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": 24.9152542373, "max_line_length": 85, "alphanum_fraction": 0.6462585034, "num_tokens": 498, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8918110540642805, "lm_q2_score": 0.7718435083355187, "lm_q1q2_score": 0.6883385727413712}} {"text": "######################################################################\n# Maps of finite sets\n\n`is_element/maps` := (A::set,B::set) -> proc(p)\n local dom,cod;\n global reason;\n\n if not(type(p,table)) then\n reason := [convert(procname,string),\"not table\"];\n return false;\n fi;\n\n # Note, if p has indices 5, 6 and 7 then indices(p) will return \n # [5],[6],[7] (an unbracketed list with each individual entry in\n # square brackets). The construct map(op,{indices(p)}) gives \n # {5,6,7} instead.\n dom := map(op,{indices(p)});\n if dom <> A then\n reason := [convert(procname,string),\"wrong domain\",dom,A];\n return false;\n fi;\n\n # Similarly, if p[5]=55 and p[6]=66 and p[7]=77 then entries(p)\n # is [55],[66],[77] but map(op,{entries(p)}) is {55,66,77}.\n cod := map(op,{entries(p)});\n if cod minus B <> {} then\n reason := [convert(procname,string),\"wrong codomain\",cod,B];\n return false;\n fi;\n\n return true;\nend;\n\n`is_equal/maps` := (A::set,B::set) -> proc(p,q)\n local a;\n global reason;\n\n for a in A do \n if p[a] <> q[a] then\n reason := [convert(procname,string),\"different value\",a,p[a],q[a]];\n return false;\n fi; \n od;\n\n return true;\nend;\n\n`is_leq/maps` := NULL;\n\n`random_element/maps` := (A::set,B::set) -> proc()\n local p,n,r,a;\n\n p := table();\n if B = {} then\n if A = {} then\n return eval(p);\n else\n return FAIL;\n fi;\n fi;\n\n # nops(B) gives the number of operands in B. Here B is supposed\n # to be a set, so the operands are just the elements.\n n := nops(B);\n\n # Note that the line below defines r to be a function such that each\n # invocation of r() will return a new random number in the range \n # {1,...,n}.\n r := rand(1..n);\n\n for a in A do p[a] := B[r()]; od;\n\n return eval(p);\nend;\n\n# To list the maps from A to B, we let a be the first element in A,\n# and put A0 = A \\ {a}. By induction we can enumerate all the maps\n# p0 : A0 -> B, and we generate all possible extensions of p0 by\n# sending a to each possible element of B.\n\n`list_elements/maps` := proc(A::set,B::set)\n local A0,a,b,M0,M,p0,p;\n\n # The unique map from the empty set to B is represented by a \n # table with no entries; this starts the induction.\n if A = {} then\n return [table()];\n fi;\n\n A0 := sort([op(A)]);\n a := A0[1];\n A0 := {op(2..-1,A0)};\n M0 := `list_elements/maps`(A0,B);\n M := [];\n\n for b in B do\n for p0 in M0 do\n p := copy(p0);\n p[a] := b;\n\n # The next line is the standard way to append an element to the\n # list M. We use op() to strip off the square brackets, and then\n # put them back in with the new element eval(p) inside. The \n # reason for eval(p) instead of p is technical and will not be \n # explained here, except to say that p is a table and it is \n # often good to apply eval() to tables if they are going to be\n # returned as values of functions or otherwise passed around.\n M := [op(M),eval(p)];\n od;\n od;\n\n return M;\nend;\n\n`count_elements/maps` := (A::set,B::set) -> nops(B) ^ nops(A);\n\n# fibres(A,B)(p) assumes that p is a function from A to B, and\n# returns a table indexed by the elements of B, whose entries \n# are the fibres p^{-1}{b}.\n\nfibres := (A::set,B::set) -> proc(p)\n local F,a,b;\n\n F := table();\n for b in B do F[b] := {}; od;\n for a in A do F[p[a]] := {op(F[p[a]]),a}; od;\n for b in B do F[b] := sort(F[b]); od;\n \n return eval(F);\nend;\n\n# `id/maps`(A) is the identity map A -> A\n`id/maps` := proc(A::set) local a; table({seq(a=a,a in A)}); end:\n\n# `compose/maps`(A,B,C)(p,q) assumes that p : A -> B and q : B -> C,\n# and it returns the composite q o p : A -> C.\n`compose/maps` := (A::set,B::set,C::set) -> proc(p,q) local a;\n table({seq(a = q[p[a]],a in A)}); end:\n\n", "meta": {"hexsha": "c9a6adf9ddd5d3a956350d6550535333a79a43dd", "size": 3625, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/maps.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/maps.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/maps.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": 25.8928571429, "max_line_length": 70, "alphanum_fraction": 0.5977931034, "num_tokens": 1120, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127529517043, "lm_q2_score": 0.8056321889812553, "lm_q1q2_score": 0.6879396003594914}} {"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\na1 := 199.81:\na2 := 4.3476:\nc1 := 0.8524:\nc2 := 1.2264:\n\n# This is Eq. (40) of the paper.\nf0 := s -> c1*(1 - exp(-a1*s^2)) + c2*(1 - exp(-a2*s^4)):\n\nf := x -> f0(X2S*x):", "meta": {"hexsha": "3f05ff9560157f2aa3876b140e5b671b5ae6c4ec", "size": 433, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_k_exp4.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_k_exp4.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_k_exp4.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": 22.7894736842, "max_line_length": 68, "alphanum_fraction": 0.6050808314, "num_tokens": 169, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218434359676, "lm_q2_score": 0.7461389930307512, "lm_q1q2_score": 0.6878818359143667}} {"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_am05_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_am05_params * )(p->params);\n*)\n\nam05_d := 28.23705740248932030511071641312341561894: (* POW(CBRT(4/3) * 2*M_PI/3, 4) *)\n\nam05_csi := s -> (3/2 * LambertW(s^(3/2) / (2*sqrt(6))))^(2/3):\nam05_fb := s -> Pi/3 * s/(am05_csi(s) * (am05_d + am05_csi(s)^2)^(1/4)):\nam05_flaa := s -> (1 + params_a_c*s^2)/(1 + params_a_c*s^2/am05_fb(s)):\nam05_XX := s -> 1 - params_a_alpha*s^2/(1 + params_a_alpha*s^2):\n\nam05_f := x -> am05_XX(X2S*x) + (1 - am05_XX(X2S*x))*am05_flaa(X2S*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(am05_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "4975285159d3cb24d8212cd5cc0569962f0c1f9c", "size": 936, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_am05.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_am05.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_am05.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": 33.4285714286, "max_line_length": 91, "alphanum_fraction": 0.6153846154, "num_tokens": 373, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850057480346, "lm_q2_score": 0.7341195385342971, "lm_q1q2_score": 0.6873451163563289}} {"text": "# ClusterComplexRoots.mpl\n#\n# clusteredList := ClusterComplexRoots( rootList, tolerance=s, MaxOrder=M );\n#\n# Take a list rootList of complex numbers and cluster them\n# according to apparent multiplicity.\n#\n# This routine is heuristic (the problem is hard) and is intended\n# to work only up to the given maximum order (default MaxOrder is 3)\n#\n# The routine uses distances and a fuzz factor F[m] and only considers\n# neighbouring points up to about |r[i]-r[j]| <= F[m]*s^(1/m) to be\n# possible candidates for a cluster; it also uses approximate \n# angle symmetry, looking for angles between adjacent roots to be\n# approximately 2*Pi/m .\n#\n# The returned clusteredList will be a list of pairs [r,m] where\n# r is the mean of the original cluster of m roots.\n# -----------------------------------------------------------------------------\n# (c) Robert M. Corless and Leili Rafiee Sevyeri 2020 (MIT Release licence)\n#\n# Permission is hereby granted, free of charge, to any person obtaining a copy\n# of this software and associated documentation files (the \"Software\"), to deal\n# in the Software without restriction, including without limitation the rights\n# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n# copies of the Software, and to permit persons to whom the Software is\n# furnished to do so, subject to the following conditions:\n#\n# The above copyright notice and this permission notice shall be included in all\n# copies or substantial portions of the Software.\n#\n# THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\n# SOFTWARE.\n# -------------------------------------------------------------------------------\n\nClusterComplexRoots := proc( rootList::list, \n {tolerance::numeric := Float(1,2-Digits)}, \n {MaxOrder::nonnegint := 3}, $ )\n local anglesequal, \n c, closeenough, closeNeighbours, clustered, combos, countem, \n DistanceMatrix, exactangle, finished_combos, Fuzz,\n i, j, k, m, max_radius, mean, \n n, neighbours, notInAcluster, nroots, \n phasedifference, phases, phaseorder, \n r, radius, trialcluster, trialindices, unseen_m;\n\n\n # Safety factors for distance computations.\n # They essentially replace the factor m!*B(r)/(D@@m)(f)(r)\n # which connects the root semimetric with the coefficient\n # metric; in this implementation, no account is taken of\n # the problem in this way (but it can be done in a post-\n # processing validation step).\n Fuzz := Array(2..MaxOrder);\n for m from 2 to MaxOrder do\n Fuzz[m] := evalf(2^(1/m));\n od;\n\n # Process small rootlists\n nroots := numelems( rootList );\n if nroots=0 then\n error \"cannot cluster an empty list of roots\";\n elif nroots=1 then\n # Return a cluster of 1\n return [[rootList[1],1]];\n end if;\n\n # nroots>=2 from now on\n # We will need distances between roots\n # -- to identify \"close\" roots\n # -- to ignore \"far\" roots\n DistanceMatrix := Matrix( nroots, nroots, 'shape'='symmetric' );\n for i to nroots do\n for j to nroots do\n DistanceMatrix[i,j] := evalf( abs( rootList[i] - rootList[j]) ) ;\n od;\n od;\n\n # We order neighbours from nearest to farthest\n neighbours := Array(1..nroots);\n for i to nroots do\n neighbours[i] := sort( [seq(DistanceMatrix[i,j],j=1..nroots)], \n 'output'='permutation');\n # neighbours[i] should be a list of integers such that\n # the nearest root to rootList[i] should be \n # rootList[neighbours[i][1]] (itself), the next nearest should be\n # rootList[neighbours[i][2]], and so on\n od;\n\n # Now begin the clustering. We start with no clustered roots at all.\n clustered := NULL;\n # The notInAcluster roots are, at the start, all of them.\n # This states that we *assume* these are not in any m-cluster\n # for m > MaxOrder.\n notInAcluster := seq(k,k=1..nroots); \n for m from MaxOrder by -1 to 2 do\n # The sequence \"notInAcluster\" can shrink inside this loop\n # The list unseen_m tracks which roots we haven't yet\n # considered for any cluster at level m\n unseen_m := [notInAcluster]; # never any duplicates\n notInAcluster := NULL; # means known not to be part of any m-cluster\n # Assert nroots in clustered, notInAcluster,unseen_m +0(i)\n while numelems(unseen_m) >= m do\n # Checking for m-cycles over all elements of unseen_m\n i := unseen_m[1];\n # print(\"considering root\", i, \"or\", rootList[i], \"for cycles of length\", m);\n unseen_m := unseen_m[2..numelems(unseen_m)]; # Assert nroots-1 + 1(i)\n # the root under consideration is rootList[i]\n # we try to find an m-cluster with this in it\n # No need to consider roots farther away than \n # twice the distance to the centre of any m-cluster\n # to this tolerance\n k := nroots;\n while k > 0 and \n DistanceMatrix[i,neighbours[i][k]] > 2*Fuzz[m]*tolerance^(1/m) do\n k := k-1;\n od;\n closeNeighbours := {seq(neighbours[i][j], j=2..k)}; # might be empty\n closeNeighbours := closeNeighbours intersect convert(unseen_m,set);\n closeNeighbours := convert(closeNeighbours,list);\n # examine all sets of m-1 close neighbours\n n := numelems(closeNeighbours); # <= k-1\n if n>=m-1 then\n # Now look at all possible choices of m-clusters\n # from the set of close neighbours\n combos := Iterator:-Combination( n, m-1 ); # at least 1\n finished_combos := false;\n for c in combos do\n # Iterator:-Combination indexes from 0 but lists index from 1\n trialindices := [i,seq(closeNeighbours[c[k]+1],k=1..m-1)];\n trialcluster := seq( rootList[k], k in trialindices );\n mean := evalf( add( r, r in [trialcluster] )/m );\n # Check the distances\n closeenough := true;\n max_radius := 0;\n for r in trialcluster do\n radius := abs(r-mean);\n max_radius := max( max_radius, radius ); \n if radius > Fuzz[m]*tolerance^(1/m) then\n closeenough := false;\n break;\n end if;\n od;\n if closeenough then\n # Now check the angles\n # May be nonsense if max_radius=0\n anglesequal := true;\n if max_radius >= Float(1,1-Digits) then\n phases := [seq( argument( trialcluster[k]-mean), k=1..m) ];\n phaseorder := sort( phases, 'output'='permutation' );\n trialcluster := [seq( trialcluster[phaseorder[k]], k=1..m)];\n phases := [seq( phases[phaseorder[k]], k=1..m)];\n # Now check if all the angles are approximately equal\n exactangle := evalf(2*Pi/m);\n for k from 2 to m do\n phasedifference := phases[k]-phases[k-1];\n # Heuristic: what constitutes approximately equal angle?\n if 0.75*exactangle > phasedifference or\n phasedifference > 1.25*exactangle then\n anglesequal := false;\n break; # no need to consider this trial cluster further\n end if;\n end do; # exit this loop on break for unequal angles\n end if;\n # closeenough is true, remember\n if anglesequal then\n # We have found a cluster of m roots\n clustered := [mean,m,trialcluster],clustered;\n # print([clustered], unseen_m);\n unseen_m := remove( k->member(k,convert(trialindices,set)), \n unseen_m );\n # print(\"removed\",trialindices,\"got\",unseen_m);\n # Assert nroots + 1(i)\n break; # stop considering rootList[i]\n end if;\n # else Not close enough to be a cluster.\n end if; \n finished_combos := Rank(combos)=Number(combos);\n # Go look at the other choices of m-1 elements\n end do; # end for c in combos do; exit this loop via break for found cluster\n # stop looking at rootList[i] but keep looking for m-clusters\n if finished_combos then\n # Loop finished without finding a cluster\n notInAcluster := i,notInAcluster;\n # else We did find a cluster and have seen i\n end if;\n # print(m,\"unseen_m\",unseen_m);\n else\n # Not enough close neighbours to form an m-cycle\n notInAcluster := i, notInAcluster;\n end if;\n end do; # end while unseen_m has more than m elts do\n # Now look at clusters of smaller order\n for k in unseen_m do\n notInAcluster := k,notInAcluster;\n od;\n unseen_m := [];\n end do;\n # Everything left over is a 1-cluster\n notInAcluster := [notInAcluster];\n return [clustered, seq( [rootList[notInAcluster[k]],1], \n k=1..numelems(notInAcluster)) ];\n end proc:\n", "meta": {"hexsha": "ad3c4a0c44d6ce8c79d3c283d23b12db5c133bd1", "size": 9551, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "ClusterComplexRoots.mpl", "max_stars_repo_name": "rcorless/ClusterComplexRootsMaple", "max_stars_repo_head_hexsha": "22483c3c086bcb6f8b7a8274805e3321c742a8eb", "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": "ClusterComplexRoots.mpl", "max_issues_repo_name": "rcorless/ClusterComplexRootsMaple", "max_issues_repo_head_hexsha": "22483c3c086bcb6f8b7a8274805e3321c742a8eb", "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": "ClusterComplexRoots.mpl", "max_forks_repo_name": "rcorless/ClusterComplexRootsMaple", "max_forks_repo_head_hexsha": "22483c3c086bcb6f8b7a8274805e3321c742a8eb", "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": 45.6985645933, "max_line_length": 86, "alphanum_fraction": 0.5997277772, "num_tokens": 2327, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.88720460564669, "lm_q2_score": 0.7745833841649232, "lm_q1q2_score": 0.6872139458885194}} {"text": "# Subspaces of (Z/p)^d are represented as pairs [U,V], where\n# U and V are lists of lists, which correspond to RREF matrices.\n# The rows of U are a basis for the subspace, and the rows\n# of V are a basis for the annihilator.\n\n`dim/subspaces` := (p,d) -> U -> nops(U[1]);\n`codim/subspaces` := (p,d) -> U -> nops(U[2]);\n\n`span/subspaces` := (p,d) -> proc(U)\n local U0,r,c,i;\n\n if U = [] then return [[],convert(IdentityMatrix(d),listlist)]; fi;\n\n U0 := map(modp,U,p);\n if type(U0,list) then U0 := Matrix(U0); fi;\n r,c := Dimension(U0);\n if c <> d then error(\"Dimension mismatch\"); fi;\n r := LinearAlgebra[Modular][MatBasis](p,U0,r,false);\n U0 := Matrix([op(1..r,convert(U0,listlist)),\n seq([0$c],i=1..c-r)]);\n LinearAlgebra[Modular][MatBasis](p,U0,r,true);\n U0 := convert(U0,listlist);\n return [[op(1..r,U0)],[op(r+1..c,U0)]];\nend:\n\n`ann/subspaces` := (p,d) -> proc(U)\n local U0;\n U0 := U;\n if type(U,list(list(integer))) then \n U0 := `span/subspaces`(p,d)(U0);\n fi;\n return `span/subspaces`(p,d)(U0[2]);\nend:\n\n`bot/subspaces` := (p,d) -> [[],convert(IdentityMatrix(d),listlist)];\n\n`top/subspaces` := (p,d) -> [convert(IdentityMatrix(d),listlist),[]];\n\n`sum/subspaces` := (p,d) -> (U,V) -> `span/subspaces`(p,d)([op(U[1]),op(V[1])]);\n\n`inter/subspaces` := (p,d) -> (U,V) -> `ann/subspaces` (p,d)([op(U[2]),op(V[2])]);\n\n`is_member/subspaces` := (p,d) -> proc(u,V)\n if V[2] = [] then return true; fi;\n return is_all_zero(map(modp, Matrix(V[2]) . Vector(u),p));\nend:\n\n`is_le/subspaces` := (p,d) -> proc(U,V)\n if U[1] = [] or V[2] = [] then return true; fi;\n return is_all_zero(map(modp, Matrix(V[2]) . Transpose(Matrix(U[1])),p)); \nend:\n\n`random_element/subspaces` := (p,d) -> proc()\n local r,U,i,j;\n r := rand(0..d)();\n U := [seq([seq(rand(0..p-1)(),j=1..d)],i=1..r)];\n return `span/subspaces`(p,d)(U);\nend:\n\n", "meta": {"hexsha": "b0901f0ab0d7d046e0f56eeeed7c00ec063c4dbd", "size": 1834, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/subspaces.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/subspaces.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/subspaces.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": 30.5666666667, "max_line_length": 82, "alphanum_fraction": 0.5817884406, "num_tokens": 657, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299653388752, "lm_q2_score": 0.7401743620390163, "lm_q1q2_score": 0.6848314993340832}} {"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\nlambda := y -> 1/2*(1 + (1 - y^2)*log((1 + y)/abs(1 - y))/(2*y)):\n\nf := x -> 1 + lambda(X2S*x/6)*x^2/(8*K_FACTOR_C):", "meta": {"hexsha": "8e26d97d84a0af53288aa7f346f24d81f8c214ae", "size": 379, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_k_meyer.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_k_meyer.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_k_meyer.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": 29.1538461538, "max_line_length": 68, "alphanum_fraction": 0.6200527704, "num_tokens": 135, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9173026528034426, "lm_q2_score": 0.7461389817407016, "lm_q1q2_score": 0.684435267310805}} {"text": "Primes:=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59]:\nL:=1000;\nS:=[1,7,11,13,17,19,23,29,31,37,41,43,47,49,53,59];\nW:=[seq(i,i=1..ceil(L/60)-1)]:\n\nfor w in W do\n\tfor s in S do\n\t\tn:=60*w+s;\n\t\ta:=0;\n\n \t\t########3.1\n\t\tif modp(s,4)=1 then \n\t\t\tfor x from 1 to ceil(sqrt(n)/2) do\n\t\t\t\tfor y from 1 to ceil(sqrt(n)) do \n\t\t\t\t\tif 4*x^2+y^2=n then a:=1-a;end if;\n\t\t\t\tend do;\n\t\t\tend do;\n\t\tend if;\n\n\t\t########3.2\n\t\tif modp(s,6)=1 and modp(s,4)<>1 then \n\t\t\tfor x from 1 to ceil(sqrt(n/3)) do\n\t\t\t\tfor y from 1 to ceil(sqrt(n)) do \n\t\t\t\t\tif 3*x^2+y^2=n then a:=1-a;end if;\n\t\t\t\tend do;\n\t\t\tend do;\n\t\tend if;\n\n\t\t########3.3\n\t\tif modp(s,12)=11 and modp(s,6)<>1 and modp(s,4)<>1 then \n\t\t\tfor x from 2 to n do \n\t\t\t\tfor y from 1 to x-1 do\n\t\t\t\t\tif 3*x^2-y^2=n then a:=1-a;end if;\n\t\t\t\tend do;\n\t\t\tend do;\n\t\t end if;\n\n\t\t##### squares\n\t\tif a=1 then \n\t\t\tfor q in Primes while q^2<=n and a=1 do if irem(n,q^2)=0 then a:=0;fi;end do;\n\t\tend if;\n\n\t\tif a=1 then Primes:=[op(Primes),n]; end if; \n\t\tend do;\nend do;", "meta": {"hexsha": "6f031cf8ed3dcab4c2c279f4cfa8e0417c8b3287", "size": 1002, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Atkin.mpl", "max_stars_repo_name": "fylux/SieveOfAtkin", "max_stars_repo_head_hexsha": "609bf980225779de758d2f57c3dcdd8babc29362", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2017-11-19T19:32:35.000Z", "max_stars_repo_stars_event_max_datetime": "2021-08-25T12:04:03.000Z", "max_issues_repo_path": "Atkin.mpl", "max_issues_repo_name": "fylux/SieveOfAtkin", "max_issues_repo_head_hexsha": "609bf980225779de758d2f57c3dcdd8babc29362", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-07-05T00:35:18.000Z", "max_issues_repo_issues_event_max_datetime": "2021-07-05T00:35:18.000Z", "max_forks_repo_path": "Atkin.mpl", "max_forks_repo_name": "fylux/SieveOfAtkin", "max_forks_repo_head_hexsha": "609bf980225779de758d2f57c3dcdd8babc29362", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-08-25T12:07:15.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-25T12:07:15.000Z", "avg_line_length": 22.2666666667, "max_line_length": 80, "alphanum_fraction": 0.5199600798, "num_tokens": 470, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391727723469, "lm_q2_score": 0.7401743563075446, "lm_q1q2_score": 0.6832099255534203}} {"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\npbepow_kappa := KAPPA_PBE:\npbepow_mu := 0.2195149727645171:\n\n(* pbepow_m has to be written in float format otherwise the code is converted to C\n in a numerically unstable way *)\npbepow_m := 100.0:\n\n(* The geometrical series 1 + pbepow_kappa/pbepow_m * add(pbepow_yy(X2S*s)^i, i=1..pbepow_m)\n is summed analytically and simplified *)\npbepow_f0 := s -> 1 - pbepow_mu*s^2 * ( ((pbepow_m * pbepow_mu * s^2) / (pbepow_m * pbepow_mu * s^2 + pbepow_kappa))^pbepow_m - 1):\n\npbepow_f := x -> pbepow_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(pbepow_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "10cee5475f89d182af9cc1337e742f748f69bdfe", "size": 878, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbepow.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_pbepow.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_pbepow.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": 33.7692307692, "max_line_length": 131, "alphanum_fraction": 0.6708428246, "num_tokens": 320, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951680216529, "lm_q2_score": 0.7310585669110203, "lm_q1q2_score": 0.6830975924624916}} {"text": "# Example from Section 5.2 of the paper\n\nread \"../ComputeIdentifiableFunctions.mpl\";\n\nmodel := [\n diff(xa(t), t) = -k1 * xa(t),\n diff(xb(t), t) = k1 * xa(t) - k2 * xb(t),\n diff(xc(t), t) = k2 * xb(t),\n diff(eA(t), t) = 0,\n diff(eC(t), t) = 0,\n y1(t) = eA(t) * xa(t) + eB * xb(t) + eC(t) * xc(t),\n y2(t) = xc(t),\n y3(t) = eA(t), \n y4(t) = eC(t)\n]:\n\n# Computing function identifiable from a single experiment\nprintf(\"Single-experiment identifiable functions: %a\\n\", SingleExperimentIdentifiableFunctions(model)):\n\nme := MultiExperimentIdentifiableFunctions(model, simplified_generators=true):\nprintf(\"The multi-experiment identifiable functions are %a; This is not the same as for a single experiment!\\n\", me[3]):\nprintf(\"The bound from the theorem is %a showing that %a experiments are sufficient to identify these functions\\n\", me[1], me[1]):\n", "meta": {"hexsha": "5e3860d3b4313af8329488b94e82dfba49f54ac1", "size": 879, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/SlowFast.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/SlowFast.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/SlowFast.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": 38.2173913043, "max_line_length": 130, "alphanum_fraction": 0.6416382253, "num_tokens": 265, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8962513731336204, "lm_q2_score": 0.7606506418255927, "lm_q1q2_score": 0.6817341822111571}} {"text": "`is_element/binary_standard_stasheff_trees` := (n::posint) -> proc(TT)\n global reason;\n \n if not(`is_element/standard_stasheff_trees`(n)(TT)) then\n reason := [convert(procname,string),\"TT is not a standard Stasheff tree\",TT,reason];\n return false;\n fi;\n\n if not(`is_binary/standard_stasheff_trees`(n)(TT)) then\n reason := [convert(procname,string),\"TT is not binary\",TT,reason];\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/binary_standard_stasheff_trees` :=\n eval(`is_equal/standard_stasheff_trees`);\n\n`is_leq/binary_standard_stasheff_trees` :=\n eval(`is_leq/standard_stasheff_trees`);\n\n`list_elements/binary_standard_stasheff_trees` := proc(n::posint) \n option remember;\n local L,A,UUU,VVV,UU,VV,p,i;\n\n if n = 0 then\n return [];\n elif n = 1 then \n return [{{1}}];\n fi;\n\n L := NULL;\n A := {seq(i,i=1..n)};\n\n for p from 1 to n-1 do\n UUU := `list_elements/binary_standard_stasheff_trees`(p);\n VVV := `list_elements/binary_standard_stasheff_trees`(n-p);\n VVV := map(VV -> map(V -> map(v -> v+p,V),VV),VVV);\n L := L,seq(seq({op(UU),op(VV),A},VV in VVV),UU in UUU);\n od;\n return [L];\nend:\n\n`random_element/binary_standard_stasheff_trees` := (n::posint) -> proc()\n local L;\n\n L := `list_elements/binary_standard_stasheff_trees`(n);\n L[rand(1..nops(L))()];\nend:\n\n`count_elements/binary_standard_stasheff_trees` :=\n (n::posint) -> binomial(2*(n-1),n-1)/n;\n\n", "meta": {"hexsha": "5d7abe7f6799862b5f70e9f11dc5ea7487c6ad04", "size": 1366, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/binary_standard_stasheff_trees.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/binary_standard_stasheff_trees.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/binary_standard_stasheff_trees.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": 24.8363636364, "max_line_length": 86, "alphanum_fraction": 0.6888726208, "num_tokens": 451, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8615382165412809, "lm_q2_score": 0.7905303285397349, "lm_q1q2_score": 0.6810720893719161}} {"text": "# This is the problem 11914 the American Mathematical Monthly (May 2016)\n# The following sum is zero.\n\nS := Sum(Sum(x^n*y^m*Sum((-4)^(-k)*Binomial(n-k,k-1)*Sum((-2)^(-j)*Binomial(n+1-2*k,j-1)*Binomial(m-k,3*m-j),j=1..3*m), k=1..n), n=1..infinity), m=1..infinity);\n\nR, ord := BinomSums[sumtores](S, u);\n# -> 0, []\n\n\n", "meta": {"hexsha": "f2b9a0a2029e777a17cc18fc875e2c6053434b77", "size": 316, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/AMM-pb11914.mpl", "max_stars_repo_name": "lairez/binomsum", "max_stars_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2015-10-28T00:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2021-05-27T07:47:59.000Z", "max_issues_repo_path": "examples/AMM-pb11914.mpl", "max_issues_repo_name": "lairez/binomsum", "max_issues_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "examples/AMM-pb11914.mpl", "max_forks_repo_name": "lairez/binomsum", "max_forks_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.6, "max_line_length": 160, "alphanum_fraction": 0.6012658228, "num_tokens": 128, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9390248225478307, "lm_q2_score": 0.724870282120402, "lm_q1q2_score": 0.6806711880383065}} {"text": "mobius_complex := proc()\n local T,V,E,F,R,r,v,a,mob,mob_arc,i,e;\n \n V := [seq(seq([i,a],a=0..2),i=0..1)];\n F := [\n seq([[0,a],[0,modp(a+1,3)],[1,a]],a=0..2),\n seq([[0,a],[0,modp(a+1,3)],[1,modp(a+1,3)]],a=0..2),\n seq([[0,a],[1,modp(a+1,3)],[1,modp(a+2,3)]],a=0..2) \n ];\n\n E := map(f -> ([f[1],f[2]],[f[1],f[3]],[f[2],f[3]]),F);\n\n T := table([]);\n\n T[\"vertices\"] := V;\n T[\"edges\"] := E;\n T[\"faces\"] := F;\n T[\"max_simplices\"] := T[\"faces\"];\n \n T[\"all_simplices\"] := [map(v -> [v],V),op(E),op(F)];\n\n v := table():\n for a from 0 to 2 do \n v[0,a] := [a/6,0];\n v[1,a] := [a/3,1];\n od:\n\n R := 1;\n r := 1/3:\n mob := mobius_embedding(R,r);\n \n mob_arc := mobius_arc(R,r);\n\n T[\"plot\"] :=\n display(\n spacecurve(mob(t,1),t=0..1,colour=blue),\n plot3d(mob(t,u),t=0..1,u=0..1,style=wireframe,colour=\"LightGray\"),\n seq(mob_arc(op(v[op(e[1])]),op(v[op(e[2])]),colour=red),e in E),\n axes=none,scaling=constrained\n );\n\n return eval(T);\nend():\n\nflat_mobius_complex := proc(n::posint)\n local f,g,T,V,E,F,r,v,a,i;\n\n f := (i) -> modp(i+1,4*n+2);\n g := (i) -> modp(i+2*n+3/2+(-1)^i/2,4*n+2);\n \n V := [seq(i,i=0..4*n+1)];\n E := [seq([i,f(i)],i=0..4*n+1),seq([i,g(i)],i=0..4*n+1)];\n F := [seq([i,f(i),g(i)],i=0..4*n+1)];\n\n T := table([]);\n\n T[\"vertices\"] := V;\n T[\"edges\"] := E;\n T[\"faces\"] := F;\n T[\"max_simplices\"] := T[\"faces\"];\n T[\"all_simplices\"] := [map(v -> [v],V),op(E),op(F)];\n\n T[\"embedding_dim\"] := 3;\n T[\"embedding\"] := table([seq(i = evalf(mobius_embedding(0.2)(i/(4*n+2),1)),i=0..4*n+1)]);\n\n T[\"plot\"] := `plot/raw_simplicial_complex`(T[\"vertices\"])(T[\"faces\"],3,T[\"embedding\"]);\n\n return eval(T);\n\nend:", "meta": {"hexsha": "d4b1c4ada693caa0fafc472bf4b42e233b3f63d0", "size": 1605, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/mobius_complex.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/mobius_complex.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/mobius_complex.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": 22.9285714286, "max_line_length": 90, "alphanum_fraction": 0.4953271028, "num_tokens": 699, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8976953030553434, "lm_q2_score": 0.757794360334681, "lm_q1q2_score": 0.6802684379542715}} {"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: lda_exc *)\n\nparams_a_alpha := 1:\n$include \"lda_x.mpl\"\n\nbeta := rs -> (9*Pi/4)^(1/3)/(rs*M_C):\nphi := rs -> 1 - 1.5*(sqrt(1 + beta(rs)^2)/beta(rs) - arcsinh(beta(rs))/beta(rs)^2)^2:\n\nf := (rs, z) -> f_lda_x(rs, z)*phi(rs):\n", "meta": {"hexsha": "ddeff2d925c43781d9b3bc33ca035aab4da377e0", "size": 474, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x_rel.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x_rel.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x_rel.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": 26.3333333333, "max_line_length": 87, "alphanum_fraction": 0.6181434599, "num_tokens": 168, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218327098193, "lm_q2_score": 0.7371581568543043, "lm_q1q2_score": 0.6796021989641127}} {"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\nkappa := 0.8040:\nmu := 0.2195149727645171:\nm := 100:\n\ngamm := m*mu/kappa:\nCx := kappa/m:\n\nf0 := s -> 1 + add(Cx * (gamm*s^2/(1 + gamm*s^2))^i, i=1..m):\n\nf := x -> f0(X2S*x):\n", "meta": {"hexsha": "f802e3ce5f694880f282958c627649de273513be", "size": 449, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_pbepow.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_pbepow.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_pbepow.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": 21.380952381, "max_line_length": 68, "alphanum_fraction": 0.6013363029, "num_tokens": 167, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9324533051062238, "lm_q2_score": 0.7279754430043072, "lm_q1q2_score": 0.6788031078655337}} {"text": "program gcd2;\n\nfunction gcd(n1: integer, n2: integer): integer;\nbegin\n if n2 > n1 then\n begin\n var new: integer;\n new := n2 % n1;\n n2 := new;\n end\n else\n begin\n var new: integer;\n new := n1 % n2;\n n1 := n2;\n n2 := new;\n end;\n\n if n2 > 0 then\n begin\n return gcd(n1, n2);\n end\n else\n begin\n return n1;\n end;\nend;\n\nbegin\n var n1, n2: integer;\n read(n1);\n read(n2);\n writeln(gcd(n1, n2));\nend.", "meta": {"hexsha": "e2687fe1823922ffcb51257aa0d8e977b349e205", "size": 500, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "example_programs/gcd2.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/gcd2.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/gcd2.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": 14.7058823529, "max_line_length": 48, "alphanum_fraction": 0.474, "num_tokens": 167, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361557147439, "lm_q2_score": 0.743168019989179, "lm_q1q2_score": 0.6780933712090644}} {"text": "\n# Energy Calculation for the Robot based on MDH frames\n# Introduction\n# Berechnung von potentieller und kinetischer 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# par1 -> Parametersatz 1 (Schwerpunkt als Parameter: SX,SY,SZ)\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 (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\":\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, 2=auch E_kin (einzelne), 3=auch E_kin (komplett)\nif not assigned(simplify_options) or simplify_options(6)=-1 then\n # Die Vereinfachung ist ein Kompromiss aus Laufzeit des Programms und Güte der Ergebnisse\n # Bei zu komplizierten Termen stürzt Maple bei der Vereinfachung unvorhersehbar ab.\n # Die folgenden Regeln sind konservative Einstellungen, damit die Code-Generierung nicht zu lange dauert.\n if not kin_constraints_exist then # ohne Zwangsbedingungen. Annahme: Bringt dann sowieso nicht so viel\n use_simplify := 0:\n else # für Systeme mit Zwangsbedingungen\n if NJ <= 7 then\n use_simplify := 3: # standardmäßig bei einfachen Systemen alle simplify-Befehle anwenden\n elif NJ <= 11 then # das ist nur eine grobe Abschätzung\n use_simplify := 2: # Simplify reduzieren (Annahme: Optimierung Gesamt-Energie dauer länger)\n else\n use_simplify := 1: # simplify-Befehle weiter begrenzen (sonst hängt Maple sich auf)\n end if:\n end if:\nelse\n use_simplify := simplify_options(6): # sechster Eintrag ist für Energie\nend if:\n\n# Ergebnisse der Kinematik laden (Rotationsmatrizen, Schwerpunktskoordinaten, Geschwindigkeiten)\nread sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name, base_method_name):\nTrf := Trf:\nTrf_c := Trf_c:\nread sprintf(\"../codeexport/%s/tmp/kinematics_com_worldframe_floatb_%s_par1_maple.m\", robot_name, base_method_name):\nr_W_W_Si := r_W_W_Si:\nr_W_i_Si := r_W_i_Si:\nread sprintf(\"../codeexport/%s/tmp/velocity_worldframe_floatbase_%s_par1_maple.m\", robot_name, base_method_name):\nomega_W_i := omega_W_i: \nrD_W_i := rD_W_i:\nrD_W_Si := rD_W_Si:\n\n# Potential Energy\nU_b := Matrix(NL, 1):\nU_grav := 0:\nfor i to NL do \n U_b[i] := -M[i, 1]*Multiply(Transpose(g_world), r_W_W_Si(1 .. 3, i)):\n printf(\"%s. Potentielle Energie aus Gravitation für Körper %d berechnet (im Welt-KS, Parametersatz 1).\\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. 1; 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. 1) 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 vereinfachen\n if use_simplify>=1 then\n tmp_t1:=time(): tmp_l1 := length(U_grav):\n printf(\"%s. Beginne Vereinfachung für potentielle Energie (Param. 1; 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 vereinfacht (Param. 1; 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_par1_maple.m\", robot_name, base_method_name):\n# Kinetic Energy\n# Use velocities in base frame and SX,SY,SZ as a parameter\n# Berechne kinetische Energie aller durch Gelenkwinkel bewegter Körper.\nT_b := Matrix(NL, 1):\nT := 0:\nfor i to NL do \n # Trägheitstensor (3x3) um den Körperschwerpunkt in Körper-KS\n I_i_Si_Tensor := Matrix([[I_i_Si[1, i], I_i_Si[2, i], I_i_Si[3, i]], [I_i_Si[2, i], I_i_Si[4, i], I_i_Si[5, i]], [I_i_Si[3, i], I_i_Si[5, i], I_i_Si[6, i]]]):\n # Rotation vom Welt-KS zum jeweiligen Körper-KS (Die Basis ist dabei laufende Nummer 1)\n R_W_i := Matrix(Trf_c(1 .. 3, 1 .. 3, i)):\n # Trägheitstensor (3x3) um den Körperschwerpunkt in Basis-KS\n I_i_W := Multiply(R_W_i, Multiply(I_i_Si_Tensor, Transpose(R_W_i))):\n T_b[i] := (1/2)*M[i, 1]*Multiply(Transpose(rD_W_Si(1 .. 3, i)), rD_W_Si(1 .. 3, i))+(1/2)*Multiply(Transpose(omega_W_i(1 .. 3, i)), Multiply(I_i_W, omega_W_i(1 .. 3, i))):\n printf(\"%s. Kinetische Energie für Körper %d berechnet (im Welt-KS, Parametersatz 1)\\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>=2 then\n tmp_t1:=time(): tmp_l1 := length(T_b[i,1]):\n printf(\"%s. Beginne Vereinfachung für kinetische Energie (Param. 1; Körper %d). Länge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l1):\n T_b[i,1] := simplify2(T_b[i,1]):\n tmp_t2:=time(): tmp_l2 := length(T_b[i,1]):\n printf(\"%s. Terme für kinetische Energie (Param. 1) 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 T := T+T_b[i, 1]:\n\n # Terme vereinfachen (optional, Standardmäßig nur kinetische Energie einzelner Körper optimieren)\n # Für komplizierte Systeme hängt sich Maple hier auf.\n if use_simplify>=3 then\n tmp_t1:=time(): tmp_l1 := length(T):\n printf(\"%s. Beginne Vereinfachung für kinetische Energie (Param. 1; Summe bis Körper %d). Länge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i-1, tmp_l1):\n T := simplify2(T):\n tmp_t2:=time(): tmp_l2 := length(T):\n printf(\"%s. Terme für kinetische Energie (Param. 1; Summe bis Körper %d) vereinfacht. 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 T, sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_worldframe_par1_maple.m\", robot_name, base_method_name):\n# Matlab Export\nprintf(\"%s: Energie (Param. 1) 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_par1_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:\nif codegen_act then\n MatlabExport(U_s_fixb, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_worldframe_par1_matlab.m\", robot_name), codegen_opt):\nend if:\n# Maple Export (Fixed-Base)\nsave U_s_fixb, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_worldframe_par1_maple.m\", robot_name):\n# Kinetic Energy\n# Floating Base\n# Eliminiere die Basis-Position (nicht: Orientierung). Die kinetische Energie kann nicht davon abhängen.\n# Falls die Ausdrücke doch vorkommen, liegt es daran, dass Maple diese nicht wegoptimieren konnte.\nT_s:=convert_t_s(T):\nfor i from 1 to 3 do\n T_s := subs({X_base_s[i,1]=0},T_s):\nend do:\nif codegen_act then\n MatlabExport(T_s, sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_worldframe_par1_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n# Fixed Base\nT_s_fixb:=T_s:\nfor i from 1 to NQB do\n T_s_fixb := subs({X_base_s[i,1]=0},T_s_fixb):\nend do:\nfor i from 1 to 6 do\n T_s_fixb := subs({V_base_s[i,1]=0},T_s_fixb):\nend do:\nif codegen_act then\n MatlabExport(T_s_fixb, sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_worldframe_par1_matlab.m\", robot_name), codegen_opt):\nend if:\n# Maple Export (Fixed-Base)\nsave T_s_fixb, sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_worldframe_par1_maple.m\", robot_name):\n\n", "meta": {"hexsha": "54f4d4f53b0aed338ba07136d37391262218a5a4", "size": 9812, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_energy/robot_tree_floatb_rotmat_energy_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_energy/robot_tree_floatb_rotmat_energy_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_energy/robot_tree_floatb_rotmat_energy_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": 49.06, "max_line_length": 173, "alphanum_fraction": 0.7208520179, "num_tokens": 3327, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361580958427, "lm_q2_score": 0.7431680143008301, "lm_q1q2_score": 0.6780933677883657}} {"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\nexp4_a1 := 199.81:\nexp4_a2 := 4.3476:\nexp4_c1 := 0.8524:\nexp4_c2 := 1.2264:\n\n# This is Eq. (40) of the paper.\nexp4_f0 := s -> exp4_c1*(1 - exp(-exp4_a1*s^2)) + exp4_c2*(1 - exp(-exp4_a2*s^4)):\nexp4_f := x -> exp4_f0(X2S*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_kinetic(exp4_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "ba63c33c9f7efeef0ecf2616715a552d2ac29711", "size": 560, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_exp4.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_exp4.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_exp4.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": 26.6666666667, "max_line_length": 82, "alphanum_fraction": 0.6392857143, "num_tokens": 226, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422241476943, "lm_q2_score": 0.7122321720225278, "lm_q1q2_score": 0.6774340922070503}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n Copyright (C) 2018 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n(* prefix:\n gga_x_lsrpbe_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_lsrpbe_params * )(p->params);\n*)\n\nlsrpbe_f0 := s -> 1 + params_a_kappa * (\n 1 - exp(-params_a_mu*s^2/params_a_kappa)\n) - (params_a_kappa+1)*(1 - exp(-params_a_alpha*s^2)):\nlsrpbe_f := x -> lsrpbe_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(lsrpbe_f, rs, z, xs0, xs1):\n\n", "meta": {"hexsha": "39875b99170d875e598ff86a50651bc89249c439", "size": 664, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_lsrpbe.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_lsrpbe.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_lsrpbe.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": 26.56, "max_line_length": 70, "alphanum_fraction": 0.6611445783, "num_tokens": 241, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240142763573, "lm_q2_score": 0.7217432122827968, "lm_q1q2_score": 0.6770846395834504}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n Copyright (C) 2018 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n(* prefix:\n gga_x_lspbe_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_lspbe_params * )(p->params);\n*)\n\nlspbe_f0 := s -> 1 + params_a_kappa*(1 - params_a_kappa/(params_a_kappa + params_a_mu*s^2))\n - (params_a_kappa+1)*(1-exp(-params_a_alpha*s^2)):\nlspbe_f := x -> lspbe_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(lspbe_f, rs, z, xs0, xs1):\n\n", "meta": {"hexsha": "e335d40d9435fe16c91ab91571fae3f60d570631", "size": 675, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_lspbe.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_lspbe.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_lspbe.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": 28.125, "max_line_length": 91, "alphanum_fraction": 0.6577777778, "num_tokens": 235, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240108164656, "lm_q2_score": 0.7217432062975979, "lm_q1q2_score": 0.6770846314714383}} {"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: lda_exc *)\n\n(* eq 26 *)\na1 := -0.0357:\na2 := 0.0562:\nb1 := -0.0311:\nb2 := 2.39:\n\n(* eq 25 *)\nf := (rs, zeta) -> a1/(1 + a2*rs/RS_FACTOR)\n + b1*log((rs/RS_FACTOR + b2)/(rs/RS_FACTOR)):\n", "meta": {"hexsha": "f618d8f049eaf20fa8f50c08113c6f5e33145bfc", "size": 435, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_gombas.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_gombas.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_gombas.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": 21.75, "max_line_length": 68, "alphanum_fraction": 0.6114942529, "num_tokens": 163, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9381240125464114, "lm_q2_score": 0.7217432003123989, "lm_q1q2_score": 0.677084627105156}} {"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: lda_exc *)\n\n$include \"vwn.mpl\"\n\nf_vwn := (rs, z) ->\n + f_aux(A_vwn[1], b_vwn[1], c_vwn[1], x0_vwn[1], rs)\n + f_aux(A_rpa[3], b_rpa[3], c_rpa[3], x0_rpa[3], rs)*f_zeta(z)*(1 - z^4)/fpp_vwn\n - DRPA(rs, z)*f_zeta(z)*(1 - z^4)\n + DMC(rs, z)*f_zeta(z):\n\nf := (rs, z) -> f_vwn(rs, z):\n", "meta": {"hexsha": "70154e178e224ce6d2628ca48254c2228e2504fc", "size": 532, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "external/libxc-5.1.6/maple/lda_exc/lda_c_vwn_2.mpl", "max_stars_repo_name": "francoMU/lsms", "max_stars_repo_head_hexsha": "36a77b7855f7cdba5f55fe03df6553a27f4b3cef", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-09-14T23:01:42.000Z", "max_stars_repo_stars_event_max_datetime": "2021-09-14T23:01:42.000Z", "max_issues_repo_path": "external/libxc-5.1.6/maple/lda_exc/lda_c_vwn_2.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/lda_exc/lda_c_vwn_2.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": 26.6, "max_line_length": 82, "alphanum_fraction": 0.6090225564, "num_tokens": 219, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9504109798251322, "lm_q2_score": 0.7122321903471562, "lm_q1q2_score": 0.6769132938908409}} {"text": "######################################################################\n# partitions(A) is the set of all partitions of A\n# (Section sec-partitions)\n\n# Partitions are represented as nonempty sets of nonempty subsets, so \n# {{1,2},{3},{4,5}} is an element of partitions({1,2,3,4,5}).\n\n`is_element/partitions` := (A::set) -> proc(pi)\n local n,T,U;\n global reason;\n\n if not type(pi,set) then\n reason := [convert(procname,string),\"pi is not a set\",pi];\n return false;\n fi;\n\n n := nops(pi);\n if n = 0 then\n reason := [convert(procname,string),\"pi is empty\"];\n return false;\n fi;\n\n T := {};\n\n for U in pi do\n if U = {} then\n reason := [convert(procname,string),\"pi contaisn the empty set\",pi];\n return false;\n fi;\n\n if U minus A <> {} then\n reason := [convert(procname,string),\"U is not contained in A\",U,A];\n return false;\n fi;\n\n if T intersect U <> {} then\n reason := [convert(procname,string),\"sets in pi are not disjoint\",U,T];\n return false;\n fi;\n\n T := T union U;\n od;\n\n if A minus T <> {} then\n reason := [convert(procname,string),\"sets in pi do not cover A\",T,A];\n return false;\n fi;\n\n return true; \nend;\n\n######################################################################\n\n`is_equal/partitions` := (A::set) -> (pi,rho) -> evalb(pi = rho):\n\n######################################################################\n\n`is_leq/partitions` := (A::set) -> proc(pi,rho)\n local T,U,ok;\n global reason;\n\n for T in rho do\n ok := false;\n for U in pi do\n if T minus U = {} then\n ok := true;\n break;\n fi;\n od;\n\n if not ok then\n reason := [convert(procname,string),\"T is not contained in any block of pi\",T,pi];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`random_element/partitions` := (A::set) -> proc()\n local n,m,r,t,i,a,pi;\n\n if A = {} then return FAIL; fi;\n\n n := nops(A);\n m := rand(1..n)();\n r := rand(1..m);\n t := table();\n for i from 1 to m do t[i] := NULL; od;\n for a in A do \n i := r();\n t[i] := t[i],a;\n od:\n\n pi := NULL;\n for i from 1 to m do\n if t[i] <> NULL then pi := pi,{t[i]}; fi;\n od;\n\n pi := {pi};\n\n return pi;\nend;\n\n######################################################################\n\n`list_elements/partitions` := proc(A::set)\n local n,a,A0,B0,B,C,S,P,Q,rho,pi;\n\n n := nops(A);\n if n = 0 then return {}; fi;\n if n = 1 then return {{A}}; fi; \n\n A0 := sort([op(A)]);\n a := A0[1];\n A0 := {op(2..-1,A0)};\n P := {A};\n S := `list_elements/subsets`(A0);\n\n for B0 in S do\n B := {a,op(B0)};\n Q := `list_elements/partitions`(A minus B);\n for rho in Q do\n pi := {B,op(rho)};\n P := P,pi;\n od;\n od;\n\n P := [P];\n return P;\nend;\n\n######################################################################\n\n`count_elements/partitions` := (A::set) -> combinat[bell](nops(A));\n\n`top/partitions` := (A::set) -> `if`(A = {},FAIL,map(a -> {a},A));\n\n`bot/partitions` := (A::set) -> `if`(A = {},FAIL,{A});", "meta": {"hexsha": "4bb0806b9cd767699dc4d0e599ed6e217e8b4f24", "size": 2922, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/partitions.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/partitions.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/partitions.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": 20.7234042553, "max_line_length": 85, "alphanum_fraction": 0.484257358, "num_tokens": 853, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8558511616741041, "lm_q2_score": 0.7905303162021596, "lm_q1q2_score": 0.6765762894602152}} {"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\na2 := 146/2025:\na3 := -73/405:\na4 := 0.131957187845257783631757384393: (* DD + 100/(81*81*kappa) *)\n\nkappa := 0.804:\n\nxx := (p, qt) -> MU_GE*p + a2*qt*qt + a3*qt*p + a4*p*p:\n\nf := (rs, x, t, u) -> 1 + kappa - \\\n kappa^2/(kappa + xx(X2S^2*x^2, 6*X2S^2*t - 9/20 - X2S^2*x^2/12)):\n", "meta": {"hexsha": "e92d5c04ee835c802ef1a7b2d027d886d8701214", "size": 543, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_pkzb.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_pkzb.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_pkzb.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": 25.8571428571, "max_line_length": 68, "alphanum_fraction": 0.6077348066, "num_tokens": 224, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107878954105, "lm_q2_score": 0.7217431943271999, "lm_q1q2_score": 0.6764255078135454}} {"text": "`find_bases/homology` := proc(H)\n local dM,dZM,nC,nZ,nB,nH,d,d_max,i,j,r,LM,ZM,BZM,BM,HZM,HM,\n S,M0,M1,M2,M3,pivots,non_pivots;\n\n dM := H[differential_matrix]:\n nC := eval(H['chain_number']);\n d_max := H['dim'];\n for d from 0 to d_max do\n if d = 0 then\n LM[0] := Matrix(nC[0],0):\n ZM[0] := IdentityMatrix(nC[0]):\n nZ[0] := nC[0];\n else\n ZM[d] := [op(NullSpace(dM[d]))];\n nZ[d] := nops(ZM[d]);\n ZM[d] := Matrix(nC[d],nZ[d],ZM[d]);\n fi;\n\n if d = d_max then\n BZM[d] := Matrix(nZ[d],0);\n BM[d] := Matrix(nC[d],0);\n nB[d] := 0;\n HZM[d] := IdentityMatrix(nZ[d]);\n HM[d] := ZM[d];\n nH[d] := nZ[d];\n else\n dZM[d+1] := LinearSolve(ZM[d],dM[d+1]);\n S := LUDecomposition(Transpose(dZM[d+1]),output=['P','L','U1','R']):\n M0,M1 := Transpose(S[4]),Transpose(S[1].S[2].S[3]):\n pivots := {}:\n j := 1:\n i := 1:\n while i <= nC[d+1] do\n while j <= nZ[d] and M0[j,i] = 0 do j := j+1; od;\n if j <= nZ[d] then pivots := {op(pivots),j}; fi;\n i := i+1;\n od:\n r := nops(pivots);\n nB[d] := r;\n nH[d] := nZ[d]-r;\n\n non_pivots := {seq(j,j=1..nZ[d])} minus pivots;\n\n M2 := Matrix(nZ[d],nZ[d]-r);\n for i from 1 to nZ[d]-r do M2[non_pivots[i],i] := 1; od:\n M3 := SubMatrix(M0,1..nZ[d],1..r);\n HM[d] := ZM[d] . M2;\n BM[d] := ZM[d] . M3;\n ZM[d] := ;\n HZM[d] := ;\n BZM[d] := ;\n LM[d+1] := (1/M1).;\n fi;\n od:\n\n H['cycle_matrix'] := eval(ZM);\n H['boundary_matrix'] := eval(BM);\n H['boundary_cycle_matrix'] := eval(BZM);\n H['boundary_lift_matrix'] := eval(LM);\n H['homology_matrix'] := eval(HM);\n H['homology_cycle_matrix'] := eval(HZM);\n \n H['cycle_number'] := eval(nZ);\n H['boundary_number'] := eval(nB);\n H['homology_number'] := eval(nH);\n\n return NULL;\nend:\n\n######################################################################\n\n`check_bases/homology` := proc(H)\n local dM,dZM,nC,nZ,nB,nH,d,d_max,i,j,r,LM,ZM,BZM,BM,HZM,HM,\n checks;\n\n nC := eval(H['chain_number']);\n nZ := eval(H['cycle_number']);\n nB := eval(H['boundary_number']);\n nH := eval(H['homology_number']);\n ZM := eval(H['cycle_matrix']);\n BM := eval(H['boundary_matrix']);\n BZM := eval(H['boundary_cycle_matrix']);\n LM := eval(H['boundary_lift_matrix']);\n HM := eval(H['homology_matrix']);\n HZM := eval(H['homology_cycle_matrix']);\n d_max := H['dim'];\n dM := eval(H['differential_matrix']):\n\n for d from 0 to d_max do \n checks := [\n [Dimension( ZM[d])] = [nC[d],nZ[d]],\n [Dimension( BM[d])] = [nC[d],nB[d]],\n [Dimension(BZM[d])] = [nZ[d],nB[d]],\n [Dimension( LM[d])] = [nC[d],`if`(d>0,nB[d-1],0)],\n [Dimension( HM[d])] = [nC[d],nH[d]],\n [Dimension(HZM[d])] = [nZ[d],nH[d]],\n nC[d] = nH[d] + nB[d] + `if`(d>0,nB[d-1],0),\n nH[d] = H['betti_number'][d]\n ];\n\n if not(`and`(op(map(evalb,checks)))) then\n print([d,checks]);\n return false;\n fi;\n od:\n\n for d from 1 to d_max do\n checks := [\n Equal(dM[d] . ZM[d],Matrix(nC[d-1],nZ[d])),\n Equal(dM[d] . BM[d],Matrix(nC[d-1],nB[d])),\n Equal(dM[d] . LM[d],BM[d-1]),\n Rank(dM[d]) = nB[d-1],\n Rank(ZM[d]) = nZ[d],\n Rank(BM[d]) = nB[d],\n Rank(HM[d]) = nH[d],\n Rank(BZM[d]) = nB[d],\n Rank(HZM[d]) = nH[d]\n ];\n if not(`and`(op(map(evalb,checks)))) then\n print([d,checks]);\n return false;\n fi;\n od:\n return true;\nend:\n\n######################################################################\n\n`vec/chains` := (H) -> (d::nonnegint) -> proc(u)\n local v,i,uc,uv;\n\n if u = 0 then \n return Vector(H['chain_number'][d]);\n elif type(u,`+`) then\n # Slightly convoluted because of funny behaviour of + on vectors\n return `+`(op(map(`vec/chains`(H)(d),[op(u)])));\n elif type(u,`*`) then\n uc,uv := selectremove(type,u,rational);\n if uc <> 1 then\n return uc * `vec/chains`(H)(d)(uv);\n fi;\n elif type(u,specfunc(chain)) then\n v := Vector(H['chain_number'][d]);\n i := H['chain_index'][d][u];\n v[i] := 1;\n return v;\n fi;\n return 'procname'(args);\nend:\n\n`vec/cycles/vec` := (H) -> (d::nonnegint) -> proc(v)\n LinearSolve(H['cycle_matrix'][d],v);\nend:\n\n`vec/cycles` := (H) -> (d::nonnegint) -> proc(u)\n `vec/cycles/vec`(H)(d)(`vec/chains`(H)(d)(u));\nend:\n\n`vec/homology/vec` := (H) -> (d::nonnegint) -> proc(v)\n SubVector(LinearSolve(H['cycle_matrix'][d],v),1..H['homology_number'][d]);\nend:\n\n`vec/homology` := (H) -> (d::nonnegint) -> proc(u)\n `vec/homology/vec`(H)(d)(`vec/chains`(H)(d)(u));\nend:\n\n`basis/homology` := (H) -> proc(d::nonnegint)\n convert(Transpose(H['homology_matrix'][d]) . Vector(H['chains'][d]),list);\nend:\n\n######################################################################\n\nis_homology_sphere := proc(H,d_)\n local d,d1,b,i;\n d1 := H['dim'];\n if nargs > 1 then \n d := d_;\n else \n d := d1;\n fi;\n b := eval(H['betti_number']);\n \n if d = -1 then # The -1 sphere is empty\n return evalb(d1 = -1);\n fi;\n\n for i from 0 to d1 do \n if i <> 0 and i <> d and b[i] <> 0 then\n return false;\n fi; \n od;\n\n if d = 0 then \n return evalb(b[0] = 2);\n else\n return evalb(b[0] = 1 and b[d] = 1);\n fi;\nend:\n\n######################################################################\n\nis_homology_bouquet := proc(H,d,r)\n local d1,b,i;\n d1 := H['dim'];\n b := eval(H['betti_number']);\n \n for i from 0 to d1 do \n if i <> 0 and i <> d and b[i] <> 0 then\n return false;\n fi; \n od;\n\n if d = 0 then \n return evalb(b[0] = r+1);\n else\n return evalb(b[0] = 1 and b[d] = r);\n fi;\nend:\n\n######################################################################\n\nis_homology_acyclic := proc(H)\n local d1,b,i;\n d1 := H['dim'];\n if d1 = -1 then return false; fi;\n \n b := eval(H['betti_number']);\n if b[0] <> 1 then return false; fi;\n \n for i from 1 to d1 do \n if b[i] <> 0 then\n return false;\n fi; \n od;\n\n return true;\nend:\n\n\n", "meta": {"hexsha": "7a374acddfcfa6713d7d42136c69c6bd7329d02d", "size": 5771, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/homology.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/homology.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/homology.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": 24.0458333333, "max_line_length": 75, "alphanum_fraction": 0.515162017, "num_tokens": 2153, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8757869981319863, "lm_q2_score": 0.7718434925908525, "lm_q1q2_score": 0.6759704954038508}} {"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\nhtbs_s1 := 0.6:\nhtbs_s2 := 2.6:\n\n(* The equations to solve in order to obtain the coeficients cc are\n G(s1) = 0\n G(s2) = 1\n G'(s1) = 0\n G'(s2) = 0\nG''(s1) = 0\nG''(s2) = 0\n*)\n\nhtbs_cc0 := htbs_s1^3*(htbs_s1^2 - 5*htbs_s1*htbs_s2 + 10*htbs_s2^2)/(htbs_s1 - htbs_s2)^5:\nhtbs_cc1 := -30*htbs_s1^2*htbs_s2^2/(htbs_s1 - htbs_s2)^5:\nhtbs_cc2 := 30*htbs_s1*htbs_s2*(htbs_s1 + htbs_s2)/(htbs_s1 - htbs_s2)^5:\nhtbs_cc3 := -10*(htbs_s1^2 + 4*htbs_s1*htbs_s2 + htbs_s2^2)/(htbs_s1 - htbs_s2)^5:\nhtbs_cc4 := 15*(htbs_s1 + htbs_s2)/(htbs_s1 - htbs_s2)^5:\nhtbs_cc5 := -6/(htbs_s1 - htbs_s2)^5:\n\n$define gga_x_rpbe_params\n$include \"gga_x_rpbe.mpl\"\n$include \"gga_x_wc.mpl\"\n\nhtbs_g := s -> htbs_cc0 + htbs_cc1*s + htbs_cc2*s^2 + htbs_cc3*s^3 + htbs_cc4*s^4 + htbs_cc5*s^5:\n\nhtbs_f0 := s -> my_piecewise3(\n s < htbs_s1, wc_f0(s),\n my_piecewise3(s > htbs_s2, rpbe_f0(s), htbs_g(s)*rpbe_f0(s) + (1 - htbs_g(s))*wc_f0(s))\n):\n\nhtbs_f := x -> htbs_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(htbs_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "8dc3fa5640036819376ae6b2b2177e3a9d3244e2", "size": 1275, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_htbs.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_htbs.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_htbs.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": 28.9772727273, "max_line_length": 97, "alphanum_fraction": 0.648627451, "num_tokens": 593, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896693699844, "lm_q2_score": 0.7341195152660687, "lm_q1q2_score": 0.6759696657398966}} {"text": "# Proof by PDF that \n# If R ~ rayleigh(2) then R^2 ~ stdChiSq(2)\n\n\nPDF_rayleigh := (a, x) -> 2*x*exp(-x^2/a)/a;\n\n# Transform on random variable is f(R)=R^2. Inverse function is g(x) = sqrt(x)\nPDF_transform := (x) -> PDF_rayleigh(2,sqrt(x))*diff(sqrt(x),x);\n\nPDF_chisq := (n, x) -> x^(1/2*n-1)*exp(-1/2*x)/(2^(1/2*n))/GAMMA(1/2*n); \nsimplify(PDF_chisq(2,x));\n\n\nevalb(PDF_chisq(2,x) = PDF_transform(x));\n", "meta": {"hexsha": "c949dade5f4fa9bc18e5588d9b1ef1d69de83bcb", "size": 402, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip2/t_rayleigh_to_stdChiSq.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip2/t_rayleigh_to_stdChiSq.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip2/t_rayleigh_to_stdChiSq.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 26.8, "max_line_length": 78, "alphanum_fraction": 0.6069651741, "num_tokens": 166, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9284087965937711, "lm_q2_score": 0.7279754489059774, "lm_q1q2_score": 0.6758588104686087}} {"text": "\n\n\n\n\n#Symetry operators#\n\n#I need Kw, the superN2symetry operator\n\nKzij:= proc(poly, i, j, forceVars:=1)\n local p_poly;\n p_poly:= sort(subs({z||i = z||j, z||j = z||i}, poly));\n return p_poly;\nend proc:\n\nKscrypt_ij:= proc(poly, ijvec)\n local KsijPoly, i,j; \n i:= ijvec[1];\n j:= ijvec[2]; \n\tKsijPoly:= sort(subs({z||i = z||j, z||j = z||i, theta||i = theta||j, theta||j= theta||i, phi||i=phi||j, phi||j = phi||i}, poly)); \n return KsijPoly;\nend proc:\n\nKsigma_j:= proc(poly, someSet)\n local sigma_j, sigma_1, non_fixed_points, permVect, KsigmaPoly, RcycleIndex, theSubSeq, Ksigma_jPoly, table_index;\n sigma_j:= someSet;\n sigma_1:= [seq(i, i=1..nops(someSet))];\n non_fixed_points:= map(x -> if sigma_j[x]=x then NULL; else x; end if, [seq(i, i=1..nops(someSet))]); \n permVect:= [seq( [ z||(sigma_1[k]) = z||(sigma_j[k]), phi||(sigma_1[k]) = phi||(sigma_j[k]), theta||(sigma_1[k]) = theta||(sigma_j[k]) ], k in non_fixed_points )]; \n permVect:= Flatten(permVect);\n KsigmaPoly:= subs(permVect, poly); \n return KsigmaPoly; \nend proc:\nKw:= proc(poly, forceVars:=0) \n # alias K_omega\n\t#Somme sur toutes les permutations de S_N\n#Ajout pour obtenir l 0 then N:= forceVars; else N:=NbVars; end if; \n\tif N < NbVars then print(`Error, not enough variables`); N:= NbVars; end if;\n\tpermutations:= permute(N);\t\n \t#ici\n\tKwPoly:= map(onePerm->sort(expand(Ksigma_j(poly, onePerm))), permutations);\n\t#keeping only distinct permutations\n\t#KwPoly:= map(sort,KwPoly);\n\tKwPoly:= MakeUnique(KwPoly);\n\tKwPoly:= add(k, k in KwPoly);\n\treturn KwPoly;\nend proc:\nkappa_ij:= proc(poly, i,j)\n\tlocal kappaij; \n\tkappaij:= sort(subs({phi||i = phi||j, phi||j=phi||i, theta||i=theta||j, theta||j=theta||i}, poly)); \n\treturn kappaij; \nend proc:\nMakeSubListFromList:= proc( identity_list, permutation_list)\n\treturn [ seq( z||(identity_list[k]) = z||(permutation_list[k]), k=1..nops(identity_list))];\nend proc:\nAntiSymetrize:= proc(poly, variables_indices::list)\n\tlocal Apoly, perms_of_poly, subs_list, omega_sign, omega_perm, identity_perm, nbVars;\n\tif nops(variables_indices) < 2 then return poly; end if;\n\tnbVars:= nops(variables_indices);\n\tidentity_perm:= variables_indices;\n\tomega_perm:= permute(variables_indices);\n\tomega_sign:= map(x-> sign_of_permutation(x), omega_perm);\n\tsubs_list := map(x-> MakeSubListFromList(identity_perm, x), omega_perm);\n\tperms_of_poly:= map(x-> subs(x, poly), subs_list);\n\tApoly:= add( omega_sign[k]*perms_of_poly[k], k=1..nops(omega_perm));\n\treturn Apoly;\nend proc:\n\nVar_Symmetrize:= proc(poly, variables_indices::list)\n\tlocal Spoly, perms_of_poly, subs_list, omega_sign, omega_perm, identity_perm, nbVars;\n\tif nops(variables_indices) < 2 then return poly; end if;\n\tnbVars:= nops(variables_indices);\n\tidentity_perm:= variables_indices;\n\tomega_perm:= permute(variables_indices);\n\tsubs_list := map(x-> MakeSubListFromList(identity_perm, x), omega_perm);\n\tperms_of_poly:= map(x-> subs(x, poly), subs_list);\n\tSpoly:= add(perms_of_poly[k], k=1..nops(omega_perm));\n\treturn Spoly;\nend proc:\n# Dunkl-Cherednik\nDunkl_i_n:= proc(i, n, poly, Nin:=0, parameter:= beta)\n local something, Vars, N, term1, term2, term3, term4, Dpoly, beta;\n option remember;\n\t#The Dunkl-like-Cherednik-... operator, still pretty clear code\n\t# i: the Dunkl index, n: the exponent, Nin: number of variables, parameter : beta, 1/alpha ... \n\tif n = 0 then return poly; end if; \n\tif n < 0 then return 0; end if; \n\tVars:= giveVars(poly);\n\tN:= max(nops(Vars[1]), nops(Vars[2]), nops(Vars[3])); #Number of variables, (particles in CMS)\n \tif Nin > N then N:= Nin; end if;\n\tif parameter <> beta then beta := parameter end if;\n\tterm1:= z||i * diff(poly, z||i);\n\tterm2:= beta*add(z||i/(z||i - z||j)*(poly- Kzij(poly,i,j)), j in seq(k, k=(i-1)..1, -1));\n\tterm3:= beta*add(z||j/(z||i - z||j)*(poly- Kzij(poly,i,j)), j in seq(k, k=(i+1)..N, 1));\n\tterm4:= -1*beta*(i-1)*poly;\n\tDpoly:= factor(term1 + term2+ term3 + term4);\n\n\tif n=1 then return Dpoly; end if;\n\tif n>1 then return Dunkl_i_n(i,n-1, expand(sort(Dpoly)), Nin, beta); end if;\nend proc:\n\nsign_of_permutation:= proc(L::list)\n\tlocal n, N, i, j;\n\t\n\tn:=nops(L);\n\tif nops(convert(L,set))=n then\n\t\tN:=0;\n\t\tfor i to n-1 do\n\t\t\tfor j from i+1 to n do\n\t\t\t\tif L[i]>L[j] then N:=N+1; fi;\n\t\t\tend do; \n\t\tend do;\n\telse print(`Invalid input`); \n\tend if;\n\n\treturn (-1)^N;\nend proc:\n\n\n#Operations regarding the representation of S_N only with the generators s_i\nget_list_perm_rep:= proc(sigma, N)\n\treturn map(x->PermApply(sigma,x), [seq(k, k=1..N)]);\nend proc:\n\ninversion_number:= proc(k, a_list)\n\tlocal inversion_number, chopped_list, inversions;\n\tif k = nops(a_list) then return 0; end if;\n\tif nops(a_list) = 0 then return 0; end if;\n\tchopped_list:= a_list[(k+1)..-1];\n\tinversions:= map(x-> if x < a_list[k] then 1; else 0; end if, chopped_list);\n\treturn add(l, l in inversions); \nend proc:\n\nTotal_inversions:= proc(a_list)\n\tlocal all_inversions;\n\tall_inversions:=map(x->inversion_number(x,a_list), [seq(k, k=1..(nops(a_list)-1))]);\n\treturn add(k, k in all_inversions); \nend proc:\n\ngen_coxeter_rep_of_SN:=proc(N)\n\tlocal all_perms, adj_rep, generators, longest_chain, N_terms, permutations, number_of_inversions, perms_with_numb_of_inv, wanted_perms, choose_from, choices, numb_of_inv, new_elements, stop_it, a_choice, serie_of_perm, effective_perm, permuted, where_is_it; remember;\n\t#Trivial terms [0] is the identity and is not included in the generators;\n\tgenerators:= [ seq([k], k=1..(N-1))];\n\tadj_rep:= [[0],op(generators)];\n\t#This is the chain that reverses completly [1...N], \n\t#The idea is that you carry the 1 up to the end, then carry the 2 up to the 1, and so on and so forth\n\t#We see that this as exactly N(N-1)/2 terms, just like the maximal number of inversions. \n\tlongest_chain:= [ seq(seq( j, j=1..i), i=(N-1)..1,-1)]; \n\tadj_rep:=[op(adj_rep), longest_chain]; \n\tN_terms:= [seq(k, k=1..N)];\n\tpermutations:= permute(N);\n\tnumber_of_inversions:= map(Total_inversions, permutations); \n\t#We start the folling loop at 2 since we have the identity and the generators which have \n\t#total number of inversion of 0 and 1\n\t#We also skip the last length in the number of inversion since we have longest_chain\n\tfor numb_of_inv from 2 to (N*(N-1)/2-1) do\n\t\tperms_with_numb_of_inv := ListTools:-SearchAll(numb_of_inv, number_of_inversions);\n\t\twanted_perms := map(x-> op(x,permutations), [perms_with_numb_of_inv]);\n\t\tchoose_from:= [ seq( op(generators), k=1..ceil(numb_of_inv/2)) ];\t\n\t\tchoices:= permute(choose_from, numb_of_inv); \n\t\tchoices:= map(void_redundant_list, choices); \n\t\tnew_elements:=[];\n\t\tstop_it:= nops(wanted_perms); \n\t\tfor a_choice in choices do\n\t\t\tserie_of_perm:= list_of_index_to_perm(a_choice);\n\t\t\teffective_perm:= prod_of_perm(serie_of_perm);\n\t\t\tpermuted:= get_list_perm_rep(effective_perm, N); \n\t\t\twhere_is_it:=ListTools:-Search(permuted, wanted_perms);\n\t\t\tif where_is_it <> 0 then \n\t\t\t\tnew_elements:= [op(new_elements), a_choice];\n\t\t\t\twanted_perms:= subsop(where_is_it=NULL, wanted_perms);\n\t\t\tend if;\n\t\t\tif nops(new_ele) = stop_it then break; end if; \n\t\tend do:\n\t\tadj_rep:=[op(adj_rep), op(new_elements)];\n\tend do:\n\t\tadj_rep:= map(x-> Flatten(x), adj_rep); \n\treturn adj_rep;\nend proc:\n\nrestricted_coxeter_rep:= proc(n1,n2,N)\n\tlocal SNrep, unallowed, valid_terms;\n\tSNrep:= gen_coxeter_rep_of_SN(N); \n\t#We remove the identity\n\t#SNrep:= SNrep[2..-1];\n\tunallowed:= { seq(k, k=1..(n1-1)), seq(k, k=(n2)..N)};\n\tvalid_terms:=map(x-> if {op(x)} intersect unallowed = {} then x; else NULL; end if, SNrep);\n\treturn valid_terms;\nend proc:\n\nSNcheckCoxeter:= proc(mbarbar, mbar, mubar, N)\n\tlocal S1, S2, S3, S4, Stot, doneS, Scheck;\n\tS1:= restricted_coxeter_rep(1,mbarbar,N);\n\tS2:= restricted_coxeter_rep(1+mbarbar,mbarbar+mbar,N);\n\tS3:= restricted_coxeter_rep(1+mbarbar+mbar,mbarbar+mbar+mubar,N);\n\tS4:= restricted_coxeter_rep(1+mbarbar+mbar+mubar,N,N);\n\tStot:= {op(gen_coxeter_rep_of_SN(N))}; \n\tdoneS:= {op(S1), op(S2), op(S3), op(S4)};\n\tScheck:= Stot minus doneS;\n\tScheck:= [[0], op(Scheck)]; \n\treturn Scheck;\nend proc:\n\nvoid_redundant_list:= proc(list)\n\tlocal k;\n\tfor k from 1 to nops(list)-1 do\n\t\tif list[k] = list[k+1] then return NULL;\n\t\telif k+3 < nops(list) then\n\t\t\tif list[k..k+1] = list[k+2..k+3] then return NULL; end if;\n\t\tend if\n\tend do:\n\treturn list;\nend proc:\n\nindex_coxeter_gen_to_perm:= proc(a_gen)\n\tlocal the_val;\n\tthe_val:= op(a_gen);\n\treturn Perm([[the_val, the_val+1]]); \nend proc:\n\nlist_of_index_to_perm:= proc(a_list)\n\treturn map(index_coxeter_gen_to_perm, a_list); \nend proc:\n\nprod_of_perm:= proc(list_of_perm)\n\tlocal k, out;\n\tout:= Perm([]); \n\tfor k from 1 to nops(list_of_perm) do\n\t\tout:=PermProduct(out,list_of_perm[k]);\n\tend do:\nend proc:\n\n\n#Operators related to nsMacdo\n#T_sigma operation\nopTi:= proc(i, expr_z, N)\n\tlocal expr, out, out1, out2, out2b;\n\tif i = N then return 0; end if;\n\tif i = 0 then return expr_z; end if;\n\texpr:= expr_z;\n\tout1:= t*expr;\n\tout2:= ((t*z||i - z||(i+1))/(z||i-z||(i+1)));\n\tout2b:= Kzij(expr, i, i+1) - expr;\n\tout2:= out2*out2b;\n\tout:= out1 + out2;\n#\tout:= t*expr + ((t*z||i - z||(i+1))/(z||i-z||(i+1)))*(Kzij(expr,i, i+1) - expr);\n\t#out:= simplify(factor(out)); \n\treturn out;\nend proc:\n\ninv_opTi:= proc(i, expr_z, N)\n\tlocal expr, out;\n\treturn simplify(factor((t^(-1) - 1)*expr_z + t^(-1)*opTi(i, expr_z, N))); \nend proc:\n\nopT_sigma:= proc(sigma, expr, N) \n\tlocal out,k;\n\tout:= expr; \n\tfor k from 1 to nops(sigma) do\n\t\tout:= factor(opTi(sigma[-k], out, N)); \n\tend do:\n\treturn out;\nend proc:\n\ntSymmetrize:= proc(expr_z, N, n1:=0, n2:=0)\n\tlocal coxeterSN, out, sigma;\n\tif n1 = 0 then \n\t\tcoxeterSN:= gen_coxeter_rep_of_SN(N); \t\n\telse\n\t\tcoxeterSN:= restricted_coxeter_rep(n1,n2,N);\n\tend if;\n\tout:= 0; \n\tfor sigma in coxeterSN do\n\t\tout:= out + opT_sigma(sigma, expr_z,N);\n\tend do:\n\tout:= factor(out); \n\treturn out;\nend proc:\ntVandermonde:= proc(the_range, remove_t:=0)\n\tlocal N, out;\n\tN:= the_range[2]-the_range[1];\n\tout:= t^(-N*(N-1)/2)*mul(mul( t*z||i - z||j, i=the_range[1]..(j-1)), j=the_range[1]..the_range[2]); \n\tif remove_t <> 0 then out:= subs(t=1, out); end if;\n\treturn out;\nend proc:\ntantiSymmetrize:= proc(expr_z, n1:=0, n2:=0)\n\tlocal coxeterSN, out, sigma;\n\tout:= AntiSymetrize(expr_z, [seq(k,k=n1..n2)]);\n\tout:= tVandermonde([n1,n2])/tVandermonde([n1,n2],1)*out;\n\tout:= factor(out);\n\treturn out;\nend proc:\nbkp_tantiSymmetrize:= proc(expr_z, N, n1:=0, n2:=0)\n\tlocal coxeterSN, out, sigma, permsign;\n\tif n1 = 0 then \n\t\tcoxeterSN:= gen_coxeter_rep_of_SN(N); \t\n\telse\n\t\tcoxeterSN:= restricted_coxeter_rep(n1,n2,N);\n\tend if;\n\tout:= 0; \n\tfor sigma in coxeterSN do\n\t\tpermsign:= nops(sigma); \n\t\tout:= out + (-1*t)^permsign*opT_sigma(sigma, expr_z,N);\n\tend do:\n\tout:= factor(out); \n\treturn out;\nend proc:\napply_sigma_si:= proc(expr, sigma)\n\tlocal out, k,i;\n\tif sigma = [0] then return expr; end if; \n\tout:= expr;\n\tfor k from 1 to nops(sigma) do\n\t\ti := sigma[-k];\n\t\tout:= Kscrypt_ij(out, [i, i+1])\n\tend do:\n\treturn out; \nend proc:\n\nvar_omega:= proc(expr, N)\n\tlocal out, k;\n\tout:= opTaui(1,expr); \n\tfor k from 1 to (N-1) do\n\t\tout:= Kzij(out,k,k+1); \n\tend do:\n\treturn out;\nend proc:\n\nopTaui:= proc(i,expr)\n\treturn factor(subs(z||i = q*z||i, expr)); \nend proc:\n\nopYi:= proc(i, expr, N)\n\tlocal out, k;\n\tout:=expr;\n\tif i > 1 then\n\t\tfor k from (i-1) to 1 by -1 do\n\t\t\tout:= inv_opTi(k, out, N);\n\t\tend do:\n\tend if;\n\tout:= var_omega(out, N); \n\tif i <> N then\n\t\tfor k from (N-1) to i by -1 do\n\t\t\tout:= opTi(k,out, N);\n\t\tend do:\n\tend if;\n\tout:=factor(t^(-N+i)*out); \n\treturn out;\nend proc:\n\neigen_val_opYi:= proc(i, eta)\n\tlocal qexp,leta1,leta2,leta, out;\n\tqexp:= eta[i];\n\tif i >1 then \n\t\tleta1:= map(x-> if x>= eta[i] then 1; else 0; end if, eta[1..(i-1)]);\n\telse\n\t\tleta1:=0; \n\tend if;\n\tif i if x>eta[i] then 1; else 0; end if, eta[(i+1)..-1]); \n\telse\n\t\tleta2:= 0;\n\tend if;\n\tleta:= add(k, k in leta1) + add(k, k in leta2); \n\tout:= q^(qexp)*t^(-leta);\n\treturn out; \nend proc:\n\n\n", "meta": {"hexsha": "a7819ae948ccddbd26738bc94624d2a3f677dce3", "size": 12063, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operators.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/operators.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/operators.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": 32.168, "max_line_length": 268, "alphanum_fraction": 0.6694852027, "num_tokens": 4144, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8723473746782093, "lm_q2_score": 0.7745833841649232, "lm_q1q2_score": 0.6757057816456337}} {"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\ntheta0 := 1.0008:\ntheta1 := 0.1926:\ntheta2 := 1.8962:\n\nf0 := s -> s^2/(1 + s)^2:\nf := x -> theta0 + f0(X2S*x)* (theta1 + f0(X2S*x) * theta2):\n", "meta": {"hexsha": "5c6446a1796123e920f015c157fb5624e6789362", "size": 406, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_bayesian.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_bayesian.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_bayesian.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": 23.8823529412, "max_line_length": 68, "alphanum_fraction": 0.6305418719, "num_tokens": 149, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9149009549929797, "lm_q2_score": 0.7371581568543043, "lm_q1q2_score": 0.6744267016868678}} {"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\ncoeffs_beefvdw := [\n 1.516501714e0, 4.413532099e-1, -9.182135241e-2, -2.352754331e-2,\n 3.418828455e-2, 2.411870076e-3, -1.416381352e-2, 6.975895581e-4,\n 9.859205137e-3, -6.737855051e-3, -1.573330824e-3, 5.036146253e-3,\n -2.569472453e-3, -9.874953976e-4, 2.033722895e-3, -8.018718848e-4,\n -6.688078723e-4, 1.030936331e-3, -3.673838660e-4, -4.213635394e-4,\n 5.761607992e-4, -8.346503735e-5, -4.458447585e-4, 4.601290092e-4,\n -5.231775398e-6, -4.239570471e-4, 3.750190679e-4, 2.114938125e-5,\n -1.904911565e-4, 7.384362421e-5\n]:\n\nk := 4:\nxi := p -> 2*p/(k + p) - 1:\n\nwith(orthopoly):\nf := x -> add(coeffs_beefvdw[i]*P(i-1, xi(X2S^2*x^2)), i=1..30):\n", "meta": {"hexsha": "2cdf08770c2062723daad3c60b3ed478956ddc83", "size": 933, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_beefvdw.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_beefvdw.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_beefvdw.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": 34.5555555556, "max_line_length": 69, "alphanum_fraction": 0.6591639871, "num_tokens": 464, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802440252811, "lm_q2_score": 0.734119521083126, "lm_q1q2_score": 0.674274276868152}} {"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$define xc_dimensions_2d\n\n_2d_b86_mgc_beta := 0.003317:\n_2d_b86_mgc_gamma := 0.008323:\n\n_2d_b86_mgc_f := x -> 1 + _2d_b86_mgc_beta/X_FACTOR_2D_C*x^2/(1 + _2d_b86_mgc_gamma*x^2)^(3/4):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(_2d_b86_mgc_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "7281c6ebf419abccd86d13a75101c8bbdaba54d7", "size": 528, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_2d_b86_mgc.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_2d_b86_mgc.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_2d_b86_mgc.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": 27.7894736842, "max_line_length": 95, "alphanum_fraction": 0.6988636364, "num_tokens": 206, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299570920386, "lm_q2_score": 0.7279754489059774, "lm_q1q2_score": 0.6735446933553351}} {"text": "with(Groebner):\nwith(PolynomialIdeals):\n\nJ := PolynomialIdeal({x0^2 - x0 + 2*x1^2 + 2*x2^2 + 2*x3^2 + 2*x4^2 + 2*x5^2 + 2*x6^2 + 2*x7^2 + 2*x8^2,\n2*x0*x1 + 2*x1*x2 - x1 + 2*x2*x3 + 2*x3*x4 + 2*x4*x5 + 2*x5*x6 + 2*x6*x7 + 2*x7*x8, 2*x0*x2 + x1^2 + 2*x1*x3 + 2*x2*x4 - x2 + 2*x3*x5 + 2*x4*x6 + 2*x5*x7 + 2*x6*x8,\n2*x0*x3 + 2*x1*x2 + 2*x1*x4 + 2*x2*x5 + 2*x3*x6 - x3 + 2*x4*x7 + 2*x5*x8,\n2*x0*x4 + 2*x1*x3 + 2*x1*x5 + x2^2 + 2*x2*x6 + 2*x3*x7 + 2*x4*x8 - x4,\n2*x0*x5 + 2*x1*x4 + 2*x1*x6 + 2*x2*x3 + 2*x2*x7 + 2*x3*x8 - x5,\n2*x0*x6 + 2*x1*x5 + 2*x1*x7 + 2*x2*x4 + 2*x2*x8 + x3^2 - x6,\n2*x0*x7 + 2*x1*x6 + 2*x1*x8 + 2*x2*x5 + 2*x3*x4 - x7,\nx0 + 2*x1 + 2*x2 + 2*x3 + 2*x4 + 2*x5 + 2*x6 + 2*x7 + 2*x8 - 1}):\nst := time[real]():\nBasis(J, tdeg(x0,x1,x2,x3,x4,x5,x6)):\ntime[real]() - st;\n", "meta": {"hexsha": "a57915d748b8e7676a428ea73a25d4918e2e5386", "size": 778, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmark/maplescripts/katsura.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/katsura.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/katsura.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": 51.8666666667, "max_line_length": 164, "alphanum_fraction": 0.5128534704, "num_tokens": 501, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107843878721, "lm_q2_score": 0.7185943985973772, "lm_q1q2_score": 0.6734744199661791}} {"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$define gga_x_pbe_tca_params\n$include \"gga_x_pbe.mpl\"\n\n$define gga_x_pw91_params\n$include \"gga_x_pw91.mpl\"\n\nbpccac_malpha := 1:\nbpccac_mbeta := 19:\n\nbpccac_fab := x -> 1/(1 + exp(-bpccac_malpha*(x - bpccac_mbeta))):\nbpccac_f := x -> (1 - bpccac_fab(x))*pbe_f(x) + bpccac_fab(x)*pw91_f(x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(bpccac_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "09b71ed56a5ca8c55578c8305db9213bf9fb6e7d", "size": 625, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_bpccac.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_bpccac.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_bpccac.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": 26.0416666667, "max_line_length": 74, "alphanum_fraction": 0.6784, "num_tokens": 237, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896802383028, "lm_q2_score": 0.7310585727705126, "lm_q1q2_score": 0.6731511894568303}} {"text": "function pascal(n)\n if n < 7 then\n field_width = 4\n else\n field_width = floor((lgamma(n+1) - 2*lgamma((n+1)/2))/log(10) + 1)\n if field_width mod 2 == 1 then\n field_width = field_width + 1\n end\n end\n line_width = (n+1)*field_width\n p = list(n+1)\n for i in 0:n\n p[i] = 1\n\tfor j in i-1:1:-1\n\t p[j] = p[j-1] + p[j]\n\tend\n s = \"\"\n\tfor j in 0:i\n\t s = s + center(ffmt(p[j], 0), field_width)\n\tend\n\tcenter(s, line_width)\t\n end\nend\n\npascal(13)\n", "meta": {"hexsha": "ccacdec46f5ec3332e69ff62cb49446316775c10", "size": 513, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/pascal.mpl", "max_stars_repo_name": "yugyfoog/MPL", "max_stars_repo_head_hexsha": "4159236c621fb823ada3d45b5b05368c60d8cb12", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2020-12-08T22:55:44.000Z", "max_stars_repo_stars_event_max_datetime": "2020-12-08T22:55:44.000Z", "max_issues_repo_path": "examples/pascal.mpl", "max_issues_repo_name": "yugyfoog/MPL", "max_issues_repo_head_hexsha": "4159236c621fb823ada3d45b5b05368c60d8cb12", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "examples/pascal.mpl", "max_forks_repo_name": "yugyfoog/MPL", "max_forks_repo_head_hexsha": "4159236c621fb823ada3d45b5b05368c60d8cb12", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.7307692308, "max_line_length": 74, "alphanum_fraction": 0.5068226121, "num_tokens": 194, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8705972751232808, "lm_q2_score": 0.7718434978390747, "lm_q1q2_score": 0.6719648460403203}} {"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\nparams_a_mu := MU_GE:\nparams_a_b := 0.4:\nparams_a_c := 2.14951:\nparams_a_e := 1.987:\n\nmgamma := 0.000023:\nff := 3:\n\nmkappa := (x, t) ->\n 1/(mgamma/params_a_mu^2 + mgamma/params_a_mu + 1):\n\n$include \"tpss_x.mpl\"\n\n(* Equation (8) *)\n\nf := (rs, x, t, u) -> 1 + fx(x, t)*exp(-mgamma*fx(x, t)/params_a_mu)/(1 + fx(x, t)) \\\n + (1 - exp(-mgamma*fx(x, t)^2/params_a_mu^2))*(params_a_mu/fx(x, t) - 1):\n", "meta": {"hexsha": "a21ad7d2b04d3f64807b9f570e6e6e235c836c19", "size": 680, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_vt84.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_vt84.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_vt84.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": 24.2857142857, "max_line_length": 87, "alphanum_fraction": 0.6044117647, "num_tokens": 258, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037343628702, "lm_q2_score": 0.7248702702332476, "lm_q1q2_score": 0.6714500382456801}} {"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\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\nmalpha := 2.804:\nmgamma := 0.8098:\n\nXX := s -> 1/(1 + malpha*s^2):\nff := s -> XX(s) + mgamma*(1 - XX(s)):\n\nf := (rs, z, xt, xs0, xs1) -> f_pw(rs, z)*(\n + (1 + z)/2 * ff(X2S*xs0)\n + (1 - z)/2 * ff(X2S*xs1)\n):", "meta": {"hexsha": "ddd8fb73f7df06cff444b0b52366054f7978db5d", "size": 554, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_c_am05.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_am05.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_am05.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": 23.0833333333, "max_line_length": 68, "alphanum_fraction": 0.619133574, "num_tokens": 208, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9416541626630937, "lm_q2_score": 0.712232184238947, "lm_q1q2_score": 0.6706764010712318}} {"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: lda_exc *)\n(* prefix:\n lda_c_hl_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_hl_params * )(p->params);\n*)\n\n$ifdef lda_c_vbh_params\nparams_a_hl_r := [30, 75.0]:\nparams_a_hl_c := [0.0252, 0.0127]:\n$endif\n\nhl_xx := (k, rs) -> rs/params_a_hl_r[k]:\nhl_f0 := (k, rs) -> -params_a_hl_c[k]*\n ((1 + hl_xx(k, rs)^3)*log(1 + 1/hl_xx(k, rs)) - hl_xx(k, rs)^2 + 1/2*hl_xx(k, rs) - 1/3):\n\nhl_f := (rs, zeta) -> hl_f0(1, rs) + f_zeta(zeta)*(hl_f0(2, rs) - hl_f0(1, rs)):\nf := (rs, zeta) -> hl_f(rs, zeta):\n", "meta": {"hexsha": "4cddbec7f758d5d1c3f47b4c35a15355b43261c3", "size": 763, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_hl.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_hl.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_hl.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": 27.25, "max_line_length": 91, "alphanum_fraction": 0.6159895151, "num_tokens": 301, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.90192066862062, "lm_q2_score": 0.743168019989179, "lm_q1q2_score": 0.6702785974861026}} {"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\nmkappa := KAPPA_PBE:\nmmu := 0.00361218645365094697:\nmalpha := 0.52:\n\nf := x -> 1 + mkappa*(1 - (1 + mmu*x^2/(malpha*mkappa))^(-malpha)):\n", "meta": {"hexsha": "408047697c8c32195d2488339b7110a567a11b4f", "size": 404, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_pbea.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_pbea.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_pbea.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": 25.25, "max_line_length": 68, "alphanum_fraction": 0.6559405941, "num_tokens": 141, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9241418178895028, "lm_q2_score": 0.7248702761768248, "lm_q1q2_score": 0.6698829347601167}} {"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_pbe_vwn_params *params;\n\n assert(p->params != NULL);\n params = (gga_c_pbe_vwn_params * )(p->params);\n*)\n\n$include \"lda_c_vwn.mpl\"\n$ifdef gga_c_pbe_params\nparams_a_beta := 0.06672455060314922:\nparams_a_gamma := (1 - log(2))/Pi^2:\nparams_a_BB := 1:\n$endif\n\nmgamma := params_a_gamma:\nmbeta := (rs, t) -> params_a_beta:\nBB := params_a_BB:\n\ntp := (rs, z, xt) -> tt(rs, z, xt):\n\n(* Equation (8) *)\nA := (rs, z, t) ->\n mbeta(rs, t)/(mgamma*(exp(-f_vwn(rs, z)/(mgamma*mphi(z)^3)) - 1)):\n\n(* Equation (7) *)\nf1 := (rs, z, t) -> t^2 + BB*A(rs, z, t)*t^4:\nf2 := (rs, z, t) -> mbeta(rs, t)*f1(rs, z, t)/(mgamma*(1 + A(rs, z, t)*f1(rs, z, t))):\n\nfH := (rs, z, t) -> mgamma*mphi(z)^3*log(1 + f2(rs, z, t)):\n\nf_pbe := (rs, z, xt, xs0, xs1) ->\n f_vwn(rs, z) + fH(rs, z, tp(rs, z, xt)):\n\nf := (rs, z, xt, xs0, xs1) -> f_pbe(rs, z, xt, xs0, xs1):\n\n", "meta": {"hexsha": "fccb75a1bb25d0fc10b22a352006eb0229e0ea25", "size": 1158, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_pbe_vwn.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_pbe_vwn.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_pbe_vwn.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": 25.1739130435, "max_line_length": 86, "alphanum_fraction": 0.5725388601, "num_tokens": 466, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361580958426, "lm_q2_score": 0.7341195327172402, "lm_q1q2_score": 0.6698372060156338}} {"text": "with(Groebner):\nwith(PolynomialIdeals):\n\nJ := PolynomialIdeal({x1*x2*x11 + x1*x11 + x2*x3*x11 + x3*x4*x11 + x4*x5*x11 + x5*x6*x11 + x6*x7*x11 + x7*x8*x11 + x8*x9*x11 + x9*x10*x11 - 1, x1*x3*x11 + x2*x4*x11 + x2*x11 + x3*x5*x11 + x4*x6*x11 + x5*x7*x11 + x6*x8*x11 + x7*x9*x11 + x8*x10*x11 - 2, x1*x4*x11 + x2*x5*x11 + x3*x6*x11 + x3*x11 + x4*x7*x11 + x5*x8*x11 + x6*x9*x11 + x7*x10*x11 - 3, x1*x5*x11 + x2*x6*x11 + x3*x7*x11 + x4*x8*x11 + x4*x11 + x5*x9*x11 + x6*x10*x11 - 4, x1*x6*x11 + x2*x7*x11 + x3*x8*x11 + x4*x9*x11 + x5*x10*x11 + x5*x11 - 5, x1*x7*x11 + x2*x8*x11 + x3*x9*x11 + x4*x10*x11 + x6*x11 - 6, x1*x8*x11 + x2*x9*x11 + x3*x10*x11 + x7*x11 - 7, x1*x9*x11 + x2*x10*x11 + x8*x11 - 8, x1*x10*x11 + x9*x11 - 9, x10*x11 - 10, x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + 1}):\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11), characteristic=2^31-1):\ntime[real]() - st;\n\nJ := PolynomialIdeal({x1*x2*x12 + x1*x12 + x2*x3*x12 + x3*x4*x12 + x4*x5*x12 + x5*x6*x12 + x6*x7*x12 + x7*x8*x12 + x8*x9*x12 + x9*x10*x12 + x10*x11*x12 - 1,\nx1*x3*x12 + x2*x4*x12 + x2*x12 + x3*x5*x12 + x4*x6*x12 + x5*x7*x12 + x6*x8*x12 + x7*x9*x12 + x8*x10*x12 + x9*x11*x12 - 2,\nx1*x4*x12 + x2*x5*x12 + x3*x6*x12 + x3*x12 + x4*x7*x12 + x5*x8*x12 + x6*x9*x12 + x7*x10*x12 + x8*x11*x12 - 3,\nx1*x5*x12 + x2*x6*x12 + x3*x7*x12 + x4*x8*x12 + x4*x12 + x5*x9*x12 + x6*x10*x12 + x7*x11*x12 - 4,\nx1*x6*x12 + x2*x7*x12 + x3*x8*x12 + x4*x9*x12 + x5*x10*x12 + x5*x12 + x6*x11*x12 - 5,\nx1*x7*x12 + x2*x8*x12 + x3*x9*x12 + x4*x10*x12 + x5*x11*x12 + x6*x12 - 6,\nx1*x8*x12 + x2*x9*x12 + x3*x10*x12 + x4*x11*x12 + x7*x12 - 7,\nx1*x9*x12 + x2*x10*x12 + x3*x11*x12 + x8*x12 - 8,\nx1*x10*x12 + x2*x11*x12 + x9*x12 - 9, x1*x11*x12 + x10*x12 - 10,\nx11*x12 - 11,\nx1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + 1}):\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12), characteristic=2^31-1):\ntime[real]() - st;\n\nJ := PolynomialIdeal({x1*x2*x13 + x1*x13 + x2*x3*x13 + x3*x4*x13 + x4*x5*x13 + x5*x6*x13 + x6*x7*x13 + x7*x8*x13 + x8*x9*x13 + x9*x10*x13 + x10*x11*x13 + x11*x12*x13 - 1,\nx1*x3*x13 + x2*x4*x13 + x2*x13 + x3*x5*x13 + x4*x6*x13 + x5*x7*x13 + x6*x8*x13 + x7*x9*x13 + x8*x10*x13 + x9*x11*x13 + x10*x12*x13 - 2,\nx1*x4*x13 + x2*x5*x13 + x3*x6*x13 + x3*x13 + x4*x7*x13 + x5*x8*x13 + x6*x9*x13 + x7*x10*x13 + x8*x11*x13 + x9*x12*x13 - 3,\nx1*x5*x13 + x2*x6*x13 + x3*x7*x13 + x4*x8*x13 + x4*x13 + x5*x9*x13 + x6*x10*x13 + x7*x11*x13 + x8*x12*x13 - 4,\nx1*x6*x13 + x2*x7*x13 + x3*x8*x13 + x4*x9*x13 + x5*x10*x13 + x5*x13 + x6*x11*x13 + x7*x12*x13 - 5,\nx1*x7*x13 + x2*x8*x13 + x3*x9*x13 + x4*x10*x13 + x5*x11*x13 + x6*x12*x13 + x6*x13 - 6,\nx1*x8*x13 + x2*x9*x13 + x3*x10*x13 + x4*x11*x13 + x5*x12*x13 + x7*x13 - 7, x1*x9*x13 + x2*x10*x13 + x3*x11*x13 + x4*x12*x13 + x8*x13 - 8,\nx1*x10*x13 + x2*x11*x13 + x3*x12*x13 + x9*x13 - 9,\nx1*x11*x13 + x2*x12*x13 + x10*x13 - 10,\nx1*x12*x13 + x11*x13 - 11, x12*x13 - 12,\nx1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + 1}):\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13), characteristic=2^31-1):\ntime[real]() - st;\n", "meta": {"hexsha": "6fe3394cf01c7c6c6c1259af39b4461c53122565", "size": 3111, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmark/maplescripts/eco.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/eco.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/eco.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": 81.8684210526, "max_line_length": 748, "alphanum_fraction": 0.5830922533, "num_tokens": 1723, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9489172587090975, "lm_q2_score": 0.7057850278370112, "lm_q1q2_score": 0.6697315938530207}} {"text": "\r\n { MultPlan.MPL }\r\n\r\n\r\nTITLE\r\n Multistage_Production_Planning ;\r\n\r\n\r\nINDEX\r\n time = (June,July,August) -> (Jun,Jul,Aug);\r\n tire = (Nylon,Glass) -> (Nyl,Gls);\r\n machine = (Wheel,Regular) -> (W,R);\r\n\r\n\r\nDATA\r\n ProdHours[machine,time] = (( 700, 300,1000),\r\n (1500, 400, 300));\r\n\r\n Delivery[tire,time] = ((4000, 8000, 3000),\r\n (1000, 5000, 5000));\r\n\r\n ProdRates[machine,tire] = ((0.15, 0.12),\r\n (0.16, 0.14));\r\n\r\n Prices[tire] = (7.00, 9.00)\r\n PurchasePrice[tire] = (3.10, 3.90)\r\n\r\n\r\nDECISION\r\n Prod[machine,tire,time] -> P\r\n Invt[tire,time];\r\n\r\n\r\nMACRO\r\n TotalRevenues := SUM(tire,time: Prices * Delivery) ;\r\n ProductionCost := 0.50 SUM(machine,tire,time: ProdRates * Prod) ;\r\n InventoryCost := 0.10 SUM(tire,time: Invt) ;\r\n\r\n RawMaterialCost := SUM(tire,time: PurchasePrice * Delivery);\r\n Post&PackCost := 0.23 SUM(tire,time: Delivery) ;\r\n FixedCost := RawMaterialCost + Post&PackCost ;\r\n\r\n\r\n{----------------------------------------------------------------------------}\r\n\r\n\r\n MAX Profit = TotalRevenues\r\n - ProductionCost\r\n - InventoryCost\r\n - FixedCost ;\r\n\r\nSUBJECT TO\r\n\r\n\r\n ProdCap[machine,time] :\r\n\r\n SUM(tire: ProdRates * Prod) < ProdHours ;\r\n\r\n\r\n Inventory[tire,time] :\r\n\r\n Invt[time-1] + SUM(machine: Prod) = Invt + Delivery ;\r\n\r\n\r\nBOUNDS\r\n CloseInvt[tire,time=August] : Invt = 0 ;\r\nEND\r\n\r\n", "meta": {"hexsha": "78c0f4f5054c4d75693f90a22a6f7b5caa907cb7", "size": 1605, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Multplan.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Multplan.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Multplan.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.2608695652, "max_line_length": 79, "alphanum_fraction": 0.4710280374, "num_tokens": 471, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9399133515091157, "lm_q2_score": 0.712232184238947, "lm_q1q2_score": 0.6694365393406866}} {"text": "`bideg0/Lambda` := proc(u)\n if type(u,specfunc(nonnegint,lambda)) then\n return [nops(u),`+`(op(u)) + nops(u)];\n else\n return [0,0];\n fi;\nend:\n\n`bideg/Lambda` := apply_deg(`bideg0/Lambda`);\n\n`mu0/Lambda` := (u,v) -> `reduce/Lambda`(op(u),op(v));\n\n`mu/Lambda` := apply_linear_assoc_mod(`mu0/Lambda`,lambda(),2);\n\n`is_admissible/Lambda` := proc()\n if nargs = 1 and type(args[1],specfunc(nonnegint,lambda)) then\n return `is_admissible/Lambda`(op(args[1]));\n elif type([args],list(nonnegint)) then\n return evalb(min(op((2 *~ [infinity,args]) -~ [args,0])) >= 0);\n else\n return FAIL;\n fi;\nend:\n\n`reduce/Lambda` := proc()\n local K,t,left,right,i,j,n,u,c;\n \n option remember;\n\n if `is_admissible/Lambda`(args) then\n return lambda(args);\n fi;\n\n K := [args];\n t := 1;\n while t < nargs and K[t+1] <= 2*K[t] do t := t+1; od;\n left := lambda(seq(K[i],i=1..t-1));\n right := `reduce/Lambda`(seq(K[i],i=t+2..nops(K)));\n i := K[t];\n n := K[t+1] - 2*i - 1;\n u := 0;\n for j from 0 to floor((n-1)/2) do\n c := modp(binomial(n-1-j,j),2);\n if c <> 0 then\n u := modp(u + c * `mu/Lambda`(left,`reduce/Lambda`(i+n-j,2*i+1+j),right),2);\n fi;\n od;\n return u;\nend:\n\n`d0/Lambda` := proc(n::nonnegint)\n local u,j,c;\n option remember;\n\n u := 0;\n for j from 1 to floor(n/2) do\n c := modp(binomial(n-j,j),2);\n if c <> 0 then\n u := u + `reduce/Lambda`(n-j,j-1);\n fi;\n od;\n u := modp(u,2);\n return u;\nend:\n\n`d1/Lambda` := proc(u)\n local K,n,v,i,j,x,y,z;\n option remember;\n \n if not(type(u,specfunc(nonnegint,lambda))) then\n return FAIL;\n fi;\n \n K := [op(u)];\n n := nops(K);\n v := 0;\n for i from 1 to n do\n x := lambda(seq(K[j],j=1..i-1));\n y := `d0/Lambda`(K[i]);\n z := lambda(seq(K[j],j=i+1..n));\n v := modp(v + `mu/Lambda`(x,y,z),2);\n od;\n return v;\nend:\n\n`d/Lambda` := apply_linear_mod(`d1/Lambda`,2);\n\n`basis/Lambda` := proc(s::integer,t::integer)\n local B,C,r;\n option remember;\n \n if s < 0 then\n return [];\n elif s = 0 then\n if t = 0 then\n return [lambda()];\n else\n return [];\n fi;\n elif s = 1 then\n if t >= 1 then\n return [lambda(t-1)];\n else\n return [];\n fi;\n else\n B := NULL;\n for r from 0 to t-1 do\n C := `basis/Lambda`(s-1,r);\n C := select(v -> (op(-1,v) >= t-r-1),C);\n C := map(v -> lambda(op(v),t-r-1),C);\n B := B,op(C);\n od;\n return [B];\n fi; \nend:\n\n`vec/Lambda` := (s,t) -> proc(u)\n local m;\n \n [seq(modp(coeff(u,m,1),2),m in `basis/Lambda`(s,t))]; \nend:\n\n`d_matrix/Lambda` := proc(s,t)\n local M;\n option remember;\n\n M := map(m -> `vec/Lambda`(s+1,t)(`d/Lambda`(m)),`basis/Lambda`(s,t));\n M := LinearAlgebra[Modular][Mod](2,Transpose(Matrix(M)),integer[]);\n return M;\nend:", "meta": {"hexsha": "ea53695de4f61fad8a6f299da7a1b34921653334", "size": 2599, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/chromatic/Lambda2.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/chromatic/Lambda2.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/chromatic/Lambda2.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": 19.8396946565, "max_line_length": 79, "alphanum_fraction": 0.5636783378, "num_tokens": 986, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.927363299661721, "lm_q2_score": 0.7217432062975979, "lm_q1q2_score": 0.6693181613005706}} {"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\ntm_lambda := 0.6866:\ntm_beta := 79.873:\n\n(* below Equation (6) *)\ntm_p := x -> (X2S*x)^2:\ntm_y := x -> (2*tm_lambda - 1)^2 * tm_p(x):\n\n(* Equation (7) *)\ntm_f0 := x -> (1 + 10*(70*tm_y(x)/27) + tm_beta*tm_y(x)^2)^(1/10):\n\n(* after Equation (9) *)\ntm_R := (x, t) -> 1 + 595*(2*tm_lambda - 1)^2 * tm_p(x)/54 \\\n - (t - 3*(tm_lambda^2 - tm_lambda + 1/2)*(t - K_FACTOR_C - x^2/72))/K_FACTOR_C:\n\ntm_fx_DME := (x, t) -> 1/tm_f0(x)^2 + 7*tm_R(x, t)/(9*tm_f0(x)^4):\n\ntm_alpha := (x, t) -> (t - x^2/8)/K_FACTOR_C:\n\n(* after Equation (11) *)\ntm_qtilde := (x, t) -> 9/20*(tm_alpha(x, t) - 1) + 2*tm_p(x)/3:\n\n(* Ratio tW/t; we have to make sure it's 1 at maximum *)\ntm_tratio := (x, t) -> m_min(1.0, x^2/(8*t)):\n\ntm_fx_SC := (x, t) -> (1 + 10*( \\\n + (MU_GE + 50*tm_p(x)/729)*tm_p(x) + 146*tm_qtilde(x, t)^2/2025 \\\n - 73*tm_qtilde(x,t)/405*(3/5*tm_tratio(x,t))*(1 - tm_tratio(x,t)))\n )^(1/10):\n\n(* Equation 10 and below *)\ntm_w := (x,t)-> (tm_tratio(x,t)^2 + 3*tm_tratio(x,t)^3)/(1 + tm_tratio(x,t)^3)^2:\n\ntm_f := (x, u, t) -> tm_w(x,t)*tm_fx_DME(x, t) + (1 - tm_w(x,t))*tm_fx_SC(x, t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) -> mgga_exchange(tm_f, rs, z, xs0, xs1, u0, u1, t0, t1):", "meta": {"hexsha": "799e7ae4d64f8cab0487d8e62f6a071edcdb0f3e", "size": 1492, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_tm.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_tm.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_tm.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": 32.4347826087, "max_line_length": 99, "alphanum_fraction": 0.5495978552, "num_tokens": 644, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122238669025, "lm_q2_score": 0.7371581510799252, "lm_q1q2_score": 0.668832601397941}} {"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$define gga_x_pbe_sol_params\n$include \"gga_x_pbe.mpl\"\n\nq2d_cc := 100:\nq2d_c1 := 0.5217:\n\nq2d_f1 := s -> pbe_f0(s)*(q2d_cc - s^4) + q2d_c1*s^3.5*(1 + s^2):\nq2d_f2 := s -> q2d_cc + s^6:\nq2d_f := x -> q2d_f1(X2S*x)/q2d_f2(X2S*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(q2d_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "38b6f3907e6690a4503e77b2ba319638eee099f2", "size": 563, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_q2d.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_q2d.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_q2d.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": 25.5909090909, "max_line_length": 73, "alphanum_fraction": 0.6465364121, "num_tokens": 239, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.934395157060208, "lm_q2_score": 0.7154239897159439, "lm_q1q2_score": 0.6684887112352701}} {"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 \"mgga_c_kcis.mpl\"\n\nkcisk_p := 0.193:\nkcisk_gcnst := 20/(3*Pi*(6*Pi^2)^(1/3)):\n\n(* Eqs. (27) *)\n(* There was a \"bug\" in the reference implementation of Stefan Kurth. The\n f_pw was calculated for an unpolarized density instead of a polarized one.\n Here, we follow the original code. *)\nkcisk_gamma0 := rs -> m_max(0, kcis_beta + 2^(1/3)*kcisk_gcnst*f_pw(2^(1/3)*rs, 0)/n_total(rs)^(1/3)):\n\nkcisk_gamma1 := rs -> m_max(0, kcis_beta + kcisk_gcnst*f_pw(rs, 0)/n_total(rs)^(1/3)):\n\n(* Eq. (19) and (22) *)\n(* There seems to be a misspel in Eq. (22) regarding the \"1 +\". This follows the\n reference implementation of Stefan Kurth *)\nkcis_gga0 := (rs, xt) -> f_pw(rs, 0) /\n (1 + kcisk_p*log(1 + kcisk_gamma0(rs)*kcis_t(rs, xt)^2/(kcisk_p*m_abs(f_pw(rs, 0))) )):\n\nkcis_gga1 := (rs, xt) -> f_pw(rs, 1) /\n (1 + kcisk_p*log(1 + 2^(-1/3)*kcisk_gamma1(rs)*kcis_t(rs, xt)^2/(kcisk_p*m_abs(f_pw(rs, 1))) )):\n", "meta": {"hexsha": "96a0d4d2b5df0d96f9cc46010f01555a412af757", "size": 1170, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_kcisk.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_kcisk.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_kcisk.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": 36.5625, "max_line_length": 102, "alphanum_fraction": 0.6512820513, "num_tokens": 436, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.93812402119614, "lm_q2_score": 0.7122321720225278, "lm_q1q2_score": 0.6681621092430347}} {"text": "`is_element/sphere` := (N::nonnegint) -> proc(x)\n local err,i;\n\n if not `is_element/R`(N+1)(x) then\n return false;\n fi;\n\n err := simplify(add(x[i]^2,i=1..N+1) - 1);\n return evalb(err = 0);\nend:\n\n`is_equal/sphere` := (N::nonnegint) -> (x,y) -> evalb(simplify(x -~ y) = [0$(N+1)]);\n\n`is_leq/sphere` := NULL;\n`list_elements/sphere` := NULL;\n`count_elements/sphere` := NULL;\n\n`random_element/sphere` := (N::nonnegint) -> proc(d::posint := 5)\n local r,x,n,k,e,i;\n\n r := rand(-d..d);\n x := [seq(r(),i=1..N)];\n n := add(x[i]^2,i=1..N);\n x := x *~ (2/(1+n));\n k := rand(0..N)();\n e := (-1) ^ rand(0..1)(); # only really needed for N = 0\n x := e *~ [op(1..k,x),(1-n)/(1+n),op(k+1..N,x)];\n return x;\nend: ", "meta": {"hexsha": "1f80c7dbb8ffc56cc5347be5db2caa0bf015bc86", "size": 696, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/sphere.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/sphere.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/sphere.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": 24.0, "max_line_length": 84, "alphanum_fraction": 0.5301724138, "num_tokens": 279, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8918110569397306, "lm_q2_score": 0.7490872075132153, "lm_q1q2_score": 0.6680442542723919}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2021 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n\n$include \"lda_x_yukawa.mpl\"\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\nbn05_A := 3.4602:\nbn05_C0 := 3.2:\nbn05_C1 := -0.9:\n\nf := (rs, z) ->\n f_lda_x_yukawa(rs, z) + f_pw(rs, z)*bn05_A/(bn05_C0 + bn05_C1*rs + rs^2):\n", "meta": {"hexsha": "8e37a618092797ed5867ead23b284a914c23ff0d", "size": 548, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/hyb_lda_xc_bn05.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/hyb_lda_xc_bn05.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/hyb_lda_xc_bn05.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": 23.8260869565, "max_line_length": 75, "alphanum_fraction": 0.6715328467, "num_tokens": 198, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9416541643004809, "lm_q2_score": 0.7090191276365462, "lm_q1q2_score": 0.6676508141076479}} {"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$define xc_dimensions_2d\n\n_2d_b88_beta := 0.007:\n_2d_b88_csi := 8: (* for harmonic potentials *)\n\n_2d_b88_f := x -> 1 + _2d_b88_beta/X_FACTOR_2D_C*x^2/(1 + _2d_b88_csi*_2d_b88_beta*x*arcsinh(x)):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(_2d_b88_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "0d9a21499a3fa6e652c88bbfab7f76d0ad772e91", "size": 536, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_2d_b88.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_2d_b88.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_2d_b88.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": 28.2105263158, "max_line_length": 97, "alphanum_fraction": 0.6902985075, "num_tokens": 202, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9407897442783527, "lm_q2_score": 0.7090191214879991, "lm_q1q2_score": 0.6670379179931569}} {"text": "program GCMLCM;\t\t/* sample17 */\r\nvar m, n, a, b, r : integer;\r\n\tgcm, lcm : integer;\r\nbegin\r\n\twriteln('Input two integers');\r\n\treadln(m, n);\r\n\ta := m;\r\n\tb := n;\r\n\twhile b <> 0 do begin\r\n\t\tr := a - (a div b) * b;\r\n\t\ta := b;\r\n\t\tb := r\r\n\tend;\r\n\tgcm := a;\r\n\tlcm := (m div gcm) * n;\r\n\twriteln('GCM = ', gcm, ' LCM = ', lcm)\r\nend.\r\n", "meta": {"hexsha": "a4d67c0fd2b0886a81496b57c28fb022d8bf6ead", "size": 327, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "data/sample17.mpl", "max_stars_repo_name": "naru380/SoftwareExperience5", "max_stars_repo_head_hexsha": "89020bf73d9fc6b58f8d564c7aaed52a0e02f371", "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": "data/sample17.mpl", "max_issues_repo_name": "naru380/SoftwareExperience5", "max_issues_repo_head_hexsha": "89020bf73d9fc6b58f8d564c7aaed52a0e02f371", "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": "data/sample17.mpl", "max_forks_repo_name": "naru380/SoftwareExperience5", "max_forks_repo_head_hexsha": "89020bf73d9fc6b58f8d564c7aaed52a0e02f371", "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": 18.1666666667, "max_line_length": 42, "alphanum_fraction": 0.4740061162, "num_tokens": 124, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9196425267730008, "lm_q2_score": 0.7248702702332476, "lm_q1q2_score": 0.6666215268999317}} {"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\nm_min := (x1, x2) -> x1 + (x2 - x1)*Heaviside(x1 - x2):\nm_max := (x1, x2) -> x1 + (x2 - x1)*Heaviside(x2 - x1):\nm_abs := (x) -> m_max(x, -x):\n\n# a series of useful definitions\n\nM_C := 137.0359996287515: (* speed of light *)\n\nRS_FACTOR := (3/(4*Pi))^(1/3):\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\nn_total := rs -> (RS_FACTOR/rs)^3:\nn_spin := (rs, z) -> (1 + z)*n_total(rs)/2:\nsigma_spin := (rs, z, xs) -> 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# See Eq. (9) of Perdew1992_13244\nf_zeta := z -> ((1 + z)^(4/3) + (1 - z)^(4/3) - 2)/(2^(4/3) - 2):\nf_zeta_2d := z -> 1/2*((1 + z)^(3/2) + (1 - z)^(3/2)):\n\n# used in several correlation functionals\nmphi := z -> ((1 + z)^(2/3) + (1 - 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# This is the Stoll decomposition in our language\nlda_stoll_par := (lda_func, rs, z, spin) ->\n lda_func(rs*(2/(1 + z))^(1/3), spin)*(1 + z)/2:\n\nlda_stoll_perp := (lda_func, rs, z) ->\n + lda_func(rs, z)\n - lda_stoll_par(lda_func, rs, z, 1)\n - lda_stoll_par(lda_func, rs, -z, -1):\n\ngga_stoll_par := (gga_func, rs, z, xs, spin) ->\n + gga_func(rs*(2/(1 + z))^(1/3), spin, xs, xs*(1 + spin)/2, xs*(1 - spin)/2)\n * (1 + z)/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 in JCP 127, 214103 (2007); doi: http://dx.doi.org/10.1063/1.2800011\nFermi_D_a := 1e-4:\nFermi_D_corrected := (xs, ts) -> (1 - xs^2/(8*ts)) * (1 - exp(-ts^2/a^2)):\n\n# Becke function used in several correlation functionals\nb88_R_F := (f_x, rs, z, xs) ->\n 1/(2*X_FACTOR_C*n_spin(rs, z)^(1/3)*f_x(xs)):\n\nb88_zss := (css, f_x, rs, z, xs) ->\n 2*css*b88_R_F(f_x, rs, z, xs):\nb88_zab := (cab, f_x, rs, z, xs0, xs1) ->\n cab*(b88_R_F(f_x, rs, z, xs0) + b88_R_F(f_x, rs, -z, xs1)):\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 + z))^(1/3) * RS_FACTOR/rs:\nnu := (rs, z) -> params_a_omega/kF(rs, z):\n", "meta": {"hexsha": "529f290a0c3dfce03937d099e3ea231c4dd454c0", "size": 3020, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/util.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/util.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/util.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": 33.5555555556, "max_line_length": 91, "alphanum_fraction": 0.5715231788, "num_tokens": 1303, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8962513703624558, "lm_q2_score": 0.7431680143008301, "lm_q1q2_score": 0.6660653512266642}} {"text": "(*\n 不变量化简的算法如下：\n +\t对于每个不变量，\n + 尝试使用其它不变量来进行表示，为了防止循环替代，以及出于化简的目的，只允许表示之后项数变少的替换。\n + 先尝试按照乘法规则进行化简，因式分解之后，删去能够成为不变量的因子。\n + 再尝试按照加法规则进行化简，展开之后，删去能够成为不变量的项。\n +\t将无法化简的不变量整体替换回其表达式形式。\n +\t消除不变量的系数。\n +\t调整不变量的阶数为正整数。\n +\t对于能够调整次数的不变量，调整其次数，例如把a[1]^3变成a[1]，把a[1]^4变成a[1]^2。\n\n 重复执行上述算法，直到不能再化简为止。\n*)\n\n$ifndef _INVSIMPLIFY_\n$define _INVSIMPLIFY_\n\n$include \"InvOrder.mpl\"\n\n# 化简不变量,不改变不变量的顺序。\nsimplifyInvariants:=proc(iinvs)\n local x,nx;\n x:=iinvs;\n while true do\n nx:=simplifyInvs(x);\n if (x=nx) then\n break;\n end if;\n x:=nx;\n end do;\n return x;\nend proc:\n\n# 内部化简函数\nsimplifyInvs:=proc(iinvs)\n local invs,tmp,ttmp,i,j,n,vars,vset,vv,v1,v2;\n invs:=iinvs;\n n:=numelems(invs);\n vars:=[seq(_Delta[i],i=1..n)];\n vset:={vars[]};\n # 尝试将不变量进行整体代换并进行化简\n for i from 1 to n do\n # 尝试把每个不变量用其它不变量进行表示\n tmp:=invs[i];\n for j from 1 to n do\n if (i<>j) then\n # 替换时用简单替换复杂的，不用复杂的替换简单的。\n try \n ttmp:=myAlgsubs(invs[j]=vars[j],tmp);\n if ( nops(expand(ttmp)) <= nops(expand(tmp)) ) then\n tmp:=ttmp;\n end if;\n catch:\n end try;\n end if;\n end do;\n invs[i]:=spAdd(spMul(tmp));\n if type(invs[i],numeric) then\n invs[i]:=0;\n end if:\n end do;\n vv:=[seq(vars[i]=invs[i],i=1..n)];\n # 将不能化简掉的整体代回原表达式\n while true do\n (v1,v2):=selectremove(e->(indets(rhs(e),name) intersect vset <> {}),vv);\n if (v1=[]) then\n break;\n end if;\n v1:=subs(v2[],v1);\n vv:=[v1[],v2[]];\n end do;\n vv:={vv[]};# 为了按照Delta排序\n vv:=rhs~([vv[]]);# 返回list才能保持顺序不变\n vv:=simpleSimplify~(vv);# 消去整体的倍数\n vv:=invOrd~(vv);# 调整阶数为正整数\n vv:=rmOrd~(vv);# 降次\n vv:=simplify(vv);# 默认化简\n return vv;\nend proc:\n\n# 自定义algsubs，解决algsubs对于分式替换的不足\nmyAlgsubs:=proc(_s::seq(equation),v)\n local s;\n s:=dealsubs~(_s);\n return algsubs(s,numer(v))/algsubs(s,denom(v));\nend proc:\n\n# 处理替换等式\ndealsubs:=proc(e)\n local l,r;\n l:=lhs(e);\n r:=rhs(e);\n if type(numer(l),numeric) then\n return denom(l)=numer(l)/r;\n elif not type(denom(l),numeric) then\n return numer(l)=denom(l)*r;\n else\n return e;\n end if;\nend proc:\n\n# 调整不变量的阶数为正整数\ninvOrd:=proc(v)\n local ord;\n if type(v,numeric) then \n return v;\n end if;\n ord:=findInvariantsOrder(v);\n if type(ord,fraction) then\n return v^denom(ord);\n elif (ord<0) then\n return v^(-1);\n else\n return v;\n end if;\nend proc:\n\n# 不变量降次\nrmOrd:=proc(_v)\n local v,ks,k;\n v:=expand(_v);\n if type(v,`*`) then\n v:=remove(type,v,numeric);\n ks:=map(getOrd,[op(v)]);\n k:=myGcd(ks);\n # 保证偶次不能变奇次\n if type(k,even) then\n k:=k/2;\n end if;\n v:=map(setOrd,v,k);\n return v;\n elif type(v,`^`) then\n if type(op(2,v),even) then\n return op(1,v)^2;\n else\n return op(1,v);\n end if;\n else \n return v;\n end if;\nend proc:\n\n# 获取次数\ngetOrd:=proc(e)\n if type(e,`^`) then\n return op(2,e);\n else\n return 1;\n end if;\nend proc:\n\n# 设置次数\nsetOrd:=proc(e,k)\n if type(e,`^`) then\n return subsop(2=op(2,e)/k,e);\n else\n return e^(1/k);\n end if;\nend proc:\n\n(*\n * 若不变量\n * D[i]=f(D[j1],D[j2],...,D[jn])+g(a[1],...,a[m]), j1,j2,...,jn!=i\n * 则化简为\n * D[i]=g(a[1],...,a[m])\n*)\nspAdd:=proc(ee)\n local e,r;\n e:=expand(ee);\n if type(e,`+`) then\n r:=remove(isInv,e);\n if (r=NULL) then\n r:=0;\n end if;\n return r;\n else\n return e;\n end if;\nend proc:\n\n(*\n * 若不变量\n * D[i]=f(D[j1],D[j2],...,D[jn])*g(a[1],...,a[m]), j1,j2,...,jn!=i\n * 则化简为\n * D[i]=g(a[1],...,a[m])\n*)\nspMul:=proc(ee)\n local e,r;\n e:=factor(ee);\n if type(e,`*`) then\n r:=remove(isInv,e);\n if (r=NULL) then\n r:=0;\n end if;\n return r;\n elif type(e,`^`) then\n r:=remove(isInv,op(1,e));\n if (r=NULL) then\n r:=0;\n end if;\n return r^op(2,e);\n else\n return e;\n end if;\nend proc:\n\n(*\n * 不变量的简单化简\n * 消去分子分母中的倍数\n*)\nsimpleSimplify:=proc(ee)\n local n,d;\n n:=rmK(numer(ee));\n d:=rmK(denom(ee));\n return simplify(expand(n/d));\nend proc:\n\n# 删除多项式的倍数\nrmK:=proc(_e)\n local e,r;\n if (_e=0) then\n return 0;\n end if:\n e:=expand(_e);\n if type(e,`+`) then\n # 消除多项式中各项系数的倍数\n r:=e/myGcd(map(x->select(type,x,numeric),[op(e)]));\n elif type(e,`*`) then\n # 消除单项多项式的系数\n r:=remove(type,e,numeric);\n else\n # 不处理无系数单项多项式\n r:=e;\n end if;\n if (r=NULL) or type(r,numeric) then\n r:=1;\n end if; \n return r;\nend proc:\n\n# 多个数的gcd\nmyGcd:=proc(ks)\n local k,i,n;\n if (ks=[]) then\n return 1;\n end if;\n k:=ks[1];\n n:=numelems(ks);\n for i from 2 to n do\n k:=gcd(k,ks[i]);\n end do;\n return k;\nend proc:\n\n# 是否是不变量\nisInv:=proc(e)\n return andmap(type,indets(e,name),specindex(_Delta));\nend proc:\n\n$endif", "meta": {"hexsha": "1a2f0c22dd46c265fb5d385cd41288cbb5d85599", "size": 5242, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "InvClassify/InvSimplify.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/InvSimplify.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/InvSimplify.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": 20.1615384615, "max_line_length": 80, "alphanum_fraction": 0.4954215948, "num_tokens": 2161, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8740772286044095, "lm_q2_score": 0.7606506581031359, "lm_q1q2_score": 0.6648674191709093}} {"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\nc := 0.7168:\nalpha := 2.804:\nd := 28.23705740248932030511071641312341561894: (* POW(CBRT(4/3) * 2*M_PI/3, 4) *)\n\ncsi := s -> (3/2 * LambertW(s^(3/2) / (2*sqrt(6))))^(2/3):\nfb := s -> Pi/3 * s/(csi(s) * (d + csi(s)^2)^(1/4)):\nflaa := s -> (1 + c*s^2)/(1 + c*s^2/fb(s)):\nXX := s -> 1 - alpha*s^2/(1 + alpha*s^2):\n\nf := x -> XX(X2S*x) + (1 - XX(X2S*x))*flaa(X2S*x):\n", "meta": {"hexsha": "eeb80025a4b72b9a02c3f23be4471bc39f17dde2", "size": 645, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_am05.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_am05.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_am05.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": 30.7142857143, "max_line_length": 86, "alphanum_fraction": 0.5534883721, "num_tokens": 269, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107878954106, "lm_q2_score": 0.7090191399336402, "lm_q1q2_score": 0.6645003867701332}} {"text": "var t1 : int := 0;\nvar t2 : int := 1;\nvar t3 : int := t1 + t2;\nvar nTimes : int := 0;\nprint \"nth term? \";\nread nTimes;\nvar x : int;\nfor x in 2..nTimes-1 do\n t1:=t2;\n t2:=t3;\n t3:=t1+t2;\nend for;\nprint t3;\nprint \"\\n\";\n", "meta": {"hexsha": "102bb0ea5995860cff45c112a189f07adac7e080", "size": 220, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/fibonacci.mpl", "max_stars_repo_name": "nicohi/mini-pl-interpreter", "max_stars_repo_head_hexsha": "432cd0713046fba10fdf3668b9ce8d04f0412cc6", "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": "test/fibonacci.mpl", "max_issues_repo_name": "nicohi/mini-pl-interpreter", "max_issues_repo_head_hexsha": "432cd0713046fba10fdf3668b9ce8d04f0412cc6", "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": "test/fibonacci.mpl", "max_forks_repo_name": "nicohi/mini-pl-interpreter", "max_forks_repo_head_hexsha": "432cd0713046fba10fdf3668b9ce8d04f0412cc6", "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": 14.6666666667, "max_line_length": 24, "alphanum_fraction": 0.55, "num_tokens": 100, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8577681049901037, "lm_q2_score": 0.7745833737577158, "lm_q1q2_score": 0.6644129126649971}} {"text": "######################################################################\n# proper_nonempty_subsets(A) is the set of all proper nonempty subsets of A\n\n`is_element/proper_nonempty_subsets` := (A::set) -> proc(B)\n type(B,set) and B minus A = {} and nops(B) > 0 and nops(B) < nops(A);\nend;\n\n`is_equal/proper_nonempty_subsets` := (A::set) -> (B,C) -> evalb(B = C):\n\n`is_leq/proper_nonempty_subsets` := (A::set) -> (B,C) -> evalb(B minus C = {}):\n\n`random_element/proper_nonempty_subsets` := (A::set) -> proc()\n local n,r,B;\n\n n := nops(A);\n\n if n < 2 then return FAIL; fi;\n\n r := rand(2);\n B := {};\n\n while nops(B) = 0 or nops(B) = n do\n B := select(a -> (r() = 1),A);\n od;\n\n return B;\nend;\n\n`list_elements/proper_nonempty_subsets` := (A::set) -> \n sort(map(sort,[op(combinat[powerset](A) minus {{},A})])):\n\n`count_elements/proper_nonempty_subsets` := (A::set) -> 2^nops(A) - 2;\n", "meta": {"hexsha": "bbf059877ad03c2554963473a1551071c6e10c24", "size": 873, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/proper_nonempty_subsets.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/proper_nonempty_subsets.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/proper_nonempty_subsets.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": 26.4545454545, "max_line_length": 79, "alphanum_fraction": 0.5624284078, "num_tokens": 286, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8459424373085146, "lm_q2_score": 0.7853085708384736, "lm_q1q2_score": 0.6643258464543647}} {"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_pbeint_params *params;\n \n assert(p->params != NULL);\n params = (gga_x_pbeint_params * )(p->params);\n*)\n\nmu := s -> params_a_muGE + (params_a_muPBE - params_a_muGE)* \\\n params_a_alpha*s^2/(1 + params_a_alpha * s^2):\n\n(* this is the gga_x_pbe expression *)\nf0 := s -> 1 + params_a_kappa * (1 - params_a_kappa/(params_a_kappa + mu(s)*s^2)):\nf := x -> f0(X2S * x):\n", "meta": {"hexsha": "2466a5eb4593aebf1754ed7867df7549b00bf5d6", "size": 647, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_pbeint.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_pbeint.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_pbeint.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": 28.1304347826, "max_line_length": 82, "alphanum_fraction": 0.6599690881, "num_tokens": 215, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9161096181702032, "lm_q2_score": 0.7248702761768248, "lm_q1q2_score": 0.6640606319312806}} {"text": "######################################################################\n\n`is_element/stasheff_trees` := (A::set) -> proc(RTT)\n local R,TT,r,rf,TT1,T,T1,i;\n global reason;\n\n if not(type(RTT,list) and nops(RTT) = 2) then\n reason := [convert(procname,string),\"RTT cannot be split as [R,TT]\",RTT]; \n return false;\n fi;\n\n R,TT := op(RTT);\n\n if not(`is_element/ord`(A)(R)) then\n reason := [convert(procname,string),\"R is not an ordering\",R,reason];\n return false;\n fi;\n\n if not(`is_element/full_trees`(A)(TT)) then\n reason := [convert(procname,string),\"TT is not a full tree\",TT,reason];\n return false;\n fi;\n\n r := table();\n for i from 1 to nops(R) do r[R[i]] := i; od;\n rf := (a) -> r[a];\n\n for T in TT do\n T1 := map(rf,T);\n if nops(T1) <> (max(T1) - min(T1) + 1) then\n reason := [convert(procname,string),\"T is not an R-interval\",T,R,T1];\n return false; \n fi;\n od;\n\n return true;\nend;\n\n`is_equal/stasheff_trees` := (A::set) -> proc(RTT1,RTT2)\n local R1,TT1,R2,TT2;\n\n R1,TT1 := op(RTT1);\n R2,TT2 := op(RTT2);\n return `is_equal/ord`(A)(R1,R2) and `is_equal/trees`(A)(TT1,TT2);\nend:\n\n`is_leq/stasheff_trees` := (A::set) -> proc(RTT1,RTT2)\n local R1,TT1,R2,TT2;\n\n R1,TT1 := op(RTT1);\n R2,TT2 := op(RTT2);\n return `is_equal/ord`(A)(R1,R2) and `is_leq/trees`(A)(TT1,TT2);\nend:\n\n`random_element/stasheff_trees` := (A::set) -> proc()\n local n,R,TT;\n\n n := nops(A);\n\n if n = 0 then return FAIL; fi;\n\n R := `random_element/ord`(A)(); \n TT := `random_element/standard_stasheff_trees`(n)();\n TT := map(U -> map(u -> R[u],U),TT);\n\n return([R,TT]);\nend;\n\n`list_elements/stasheff_trees` := proc(A::set)\n local n,RR,R,TTT0,TT0,TT,XX;\n\n n := nops(A);\n\n RR := `list_elements/ord`(A);\n TTT0 := `list_elements/standard_stasheff_trees`(n);\n\n XX := NULL;\n for R in RR do\n for TT0 in TTT0 do\n TT := map(U -> map(u -> R[u],U),TT0);\n XX := XX,[R,TT];\n od;\n od;\n return([XX]);\nend;\n\n`count_elements/stasheff_trees` := proc(A::set)\n local n,m;\n n := nops(A);\n m := `count_elements/standard_stasheff_trees`(n);\n return n! * m;\nend;\n\n\n", "meta": {"hexsha": "1630850785f1706eaa5a8fe928d102c653942d59", "size": 2021, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/stasheff_trees.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/stasheff_trees.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/stasheff_trees.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": 21.2736842105, "max_line_length": 77, "alphanum_fraction": 0.5888174171, "num_tokens": 729, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8267117940706734, "lm_q2_score": 0.803173791645582, "lm_q1q2_score": 0.6639932462418643}} {"text": " \r\n { Plan.mpl }\r\n\r\n { Aggregate production planning for 6 months }\r\n\r\n { COPYRIGHT (C) 1987-1989, Maximal Software }\r\n\r\nTITLE\r\n Plan_for_x_years ;\r\n\r\nDATA\r\n NrOfYears = 5?;\r\n Dec = 12;\r\n\r\nINDEX\r\n i = 1..NrOfYears ;\r\n j = 1..Dec ;\r\n\r\nDATA\r\n Demand[j] := 1000 (90,81,102,100,140,141,180,170,140,110,90,90);\r\n\r\n\r\nDECISION\r\n Invt[i,j] \r\n Prod[i,j]\r\n Work[i,j]\r\n OvrTm[i,j]\r\n Hired[i,j] -> Hir\r\n Fired[i,j] -> Fir\r\n\r\n\r\nMODEL\r\n\r\n MIN ProductionCost -> ProdCost =\r\n\r\n SUM(i,j: 8.80 Invt\r\n + 64.33 Prod\r\n + 17600 Work\r\n + 160 OvrTm\r\n + 8800 Hired\r\n + 52800 Fired) ;\r\n\r\nSUBJECT TO\r\n\r\n ProdInvt[i=1,j=1] -> PrIn : Invt = 20000 + Prod - Demand ;\r\n ProdInvt[i>1,j=1] -> PrIn : Invt = Invt[i-1,Dec] + Prod - Demand ;\r\n ProdInvt[i,j>1] -> PrIn : Invt = Invt[j-1] + Prod - Demand ;\r\n\r\n HiredFired[i=1,j=1] -> HiFi : Work - 45 = Hired - Fired ;\r\n HiredFired[i>1,j=1] -> HiFi : Work - Work[i-1,Dec] = Hired - Fired ;\r\n HiredFired[i,j>1] -> HiFi : Work - Work[j-1] = Hired - Fired ;\r\n\r\n ProdHours[i,j] -> PrHo : 170 Work + OvrTm > 0.07 Prod ;\r\n OvrTmWork[i,j] -> OvWo : OvrTm < 50% * 170 Work ;\r\n\r\n\r\nBOUNDS\r\n\r\n MaxInvt : Invt[j amgb_aa[i]\n + (amgb_bb[i]*rs + amgb_cc[i]*rs^2 + amgb_dd[i]*rs^3)\n * log(1 + 1/(amgb_ee[i]*rs + amgb_ff[i]*rs^1.5 + amgb_gg[i]*rs^2 + amgb_hh[i]*rs^3)):\n\namgb_ex6 := (rs, z) -> -4*sqrt(2)/(3*Pi*rs)\n * (f_zeta_2d(z) - 1 - 3/8*z^2 - 3/128*z^4):\n\nf_amgb := (rs, z) ->\n amgb_alpha(1, rs) + amgb_alpha(2, rs)*z^2 + amgb_alpha(3, rs)*z^4 + (exp(-amgb_beta*rs) - 1)*amgb_ex6(rs, z):\n\nf := (rs, z) -> f_amgb(rs, z):\n", "meta": {"hexsha": "1eddde4eeb67dbcc6e0ac70b601073f2de83162a", "size": 1184, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_2d_amgb.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_2d_amgb.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_2d_amgb.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": 32.0, "max_line_length": 111, "alphanum_fraction": 0.5658783784, "num_tokens": 560, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.936285002192296, "lm_q2_score": 0.7090191399336402, "lm_q1q2_score": 0.6638439869871482}} {"text": "# An n-simplex in R^d is represented as a length (n+1) list of\n# length d lists of real numbers.\n\n`is_element/simplices` := (d::posint) -> (n::nonnegint) -> proc(a)\n global reason;\n local i,A,indep;\n \n if not (type(a,list) and nops(a) = n+1) then\n reason := [\"is_element/simplices\",\"a is not a list of length n+1\",a,n];\n return false;\n fi;\n\n for i from 1 to n+1 do\n if not `is_element/R`(d)(a[i]) then\n reason := [\"is_element/simplices\",\"a[i] is not in R^d\",a,i,d];\n return false;\n fi;\n od;\n \n A := Matrix([seq(a[i] -~ a[n+1],i=1..n)]);\n indep := evalb(NullSpace(Transpose(A)) = {});\n if not indep then\n reason := [\"is_element/simplices\",\"a is not affinely independent\",a];\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/simplices` := (d::posint) -> (n::nonnegint) -> proc(a,b)\n return evalb(simplify(a -~ b) = [[0$d]$(n+1)]);\nend:\n\n`is_leq/simplices` := NULL;\n`list_elements/simplices` := NULL;\n`count_elements/simplices` := NULL;\n\n`random_element/simplices` := (d::posint) -> (n::nonnegint) -> proc(m := 100)\n local indep,a,A,i,j;\n\n if n > d then\n error \"n cannot be bigger than d\";\n fi;\n \n indep := false;\n while not(indep) do\n a := [seq([seq(rand(-m..m)(),j=1..d)],i = 1..n+1)];\n A := Matrix([seq(a[i] -~ a[n+1],i=1..n)]);\n indep := evalb(NullSpace(Transpose(A)) = {});\n od:\n\n return a;\nend:\n\n`barycentre/simplex` := (d::posint) -> proc(a)\n local n,u,i;\n\n n := nops(a) - 1;\n u := a[n+1];\n for i from 1 to n do u := u +~ a[i]; od;\n u := u /~ (n+1);\n return u;\nend:\n\n`radius/simplex` := (d::posint) -> proc(a)\n local u,r,i;\n \n u := `barycentre/simplex`(d)(a);\n r := max(map(v -> add((v[i]-u[i])^2,i=1..d),a));\n return sqrt(r);\nend:\n\n# The primal matrix has the vertex vectors as its columns,\n# but with an extra row of 1's at the bottom.\n\n`primal_matrix/simplex` := (d::posint) -> proc(a)\n local n,u,i;\n\n n := nops(a) - 1;\n return Transpose(Matrix([seq([op(a[i]),1],i=1..n+1)]));\nend:\n\n# For a d-simplex in R^d, the dual matrix is the inverse \n# of the primal matrix.\n\n`dual_matrix/simplex` := (d::posint) -> proc(a)\n if nops(a) <> d+1 then return FAIL; fi;\n \n return 1/`primal_matrix/simplex`(d)(a);\nend:\n\n# With two arguments, this returns true iff the intersection \n# of the simplices spanned by a and b is the simplex spanned\n# by some subset c of a intersect b. With a third argument c_,\n# we require in addition that c = c_.\n\n`intersect_nicely/simplices` := (d::posint) -> proc(a,b,c_)\n local c,aa,bb,cc,ab,n,m,p,q,e,W_cand,W_new,W_inc,W,WA,WB,A,B,r,C,w,z,i,k;\n\n c := {op(a)} intersect {op(b)};\n if nargs > 2 and c <> {op(c_)} then\n return false;\n fi;\n \n aa := [seq([op(z),1,1],z in {op(a)} minus c)];\n bb := [seq([op(-~z),-1,1],z in {op(b)} minus c)];\n cc := [seq([op(z),1,0],z in c)];\n ab := [op(aa),op(bb)];\n n := nops(aa);\n m := nops(bb);\n p := nops(cc);\n e := Vector([0$d,0,1]);\n W_cand := combinat[choose](n+m,min(d+2-p,n+m));\n W_cand := {seq({op(W)},W in W_cand)};\n W_cand := select(\n W -> W <> {} and min(op(W)) <= n and max(op(W)) > n,\n W_cand\n );\n\n while W_cand <> {} do\n W_new := NULL;\n W_inc := NULL;\n for W in W_cand do \n q := nops(W);\n A := Transpose(Matrix([seq(ab[w],w in W),\n op(cc)]));\n B := ReducedRowEchelonForm();\n if Equal(SubMatrix(B,1..d+2,1..p+q),\n ) then\n r := [seq(B[i,p+q+1],i=1..p+q)];\n if (p+q=d+2 or B[p+q+1,p+q+1] = 0) then \n if min(seq(r[k],k=1..q)) >= 0 then\n return false;\n fi;\n else\n W_inc := W_inc,W;\n fi;\n else\n WA,WB := selectremove(w -> w <= n,W);\n if nops(WA) > 1 then\n W_new := W_new,seq({op(W)} minus {w},w in WA);\n fi;\n if nops(WB) > 1 then\n W_new := W_new,seq({op(W)} minus {w},w in WB);\n fi;\n fi;\n od;\n W_cand := {W_new};\n for W in W_inc do\n W_cand := remove(U -> U minus W = {},W_cand);\n od:\n od;\n return true;\nend:\n\n", "meta": {"hexsha": "e8afdea8f6c905056800d30af299eb9b59568d25", "size": 3853, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplices.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/simplices.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/simplices.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": 24.6987179487, "max_line_length": 77, "alphanum_fraction": 0.5670905788, "num_tokens": 1417, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8791467548438124, "lm_q2_score": 0.7549149758396752, "lm_q1q2_score": 0.6636810511924455}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-3-input.txt\" ):\nbins := map(b->[seq(ifelse(b[i]=\"0\",0,1), i=1..length(b))],\n StringTools:-Split(StringTools:-Trim(input)) ):\n\nmostcommon := proc(L)\n map(b->ifelse(b>=nops(L)/2, 1, 0),\n [seq(add(L[j][i], j=1..nops(L)), i=1..nops(L[1]))] );\nend proc:\nleastcommon := proc(L) map(b->ifelse(b=0, 1, 0), mostcommon(L)); end proc:\nbin2dec := proc(L) add(L[-i]*2^(i-1), i=1..nops(L)); end proc:\n\nbin2dec(mostcommon(bins)) * bin2dec(leastcommon(bins)); # part 1 answer\n\no2gen_bins := bins:\nfor i to nops(bins[1]) while nops(o2gen_bins)<>1 do\n mc := mostcommon(o2gen_bins);\n o2gen_bins := select(r->r[i]=mc[i], o2gen_bins);\nend do:\n\nco2scrub_bins := bins:\nfor i to nops(bins[1]) while nops(co2scrub_bins)<>1 do\n mc := leastcommon(co2scrub_bins);\n co2scrub_bins := select(r->r[i]=mc[i], co2scrub_bins);\nend do:\n\nbin2dec( o2gen_bins[] ) * bin2dec( co2scrub_bins[] ); # part 2 answer\n\n", "meta": {"hexsha": "ac58c63156524345eb8cbe57537cdbcc1ff3331a", "size": 946, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day3/AoC3-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": "Day3/AoC3-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": "Day3/AoC3-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": 33.7857142857, "max_line_length": 74, "alphanum_fraction": 0.6279069767, "num_tokens": 355, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8596637648915617, "lm_q2_score": 0.7718435030872968, "lm_q1q2_score": 0.6635258917711173}} {"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_pw86_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_pw86_params * )(p->params);\n*)\n\n$ifdef gga_x_rpw86_params\nparams_a_aa := 15*0.1234:\nparams_a_bb := 17.33:\nparams_a_cc := 0.163:\n$endif\n\npw86_f0 := s -> (1 + params_a_aa*s^2 + params_a_bb*s^4 + params_a_cc*s^6)^(1/15):\npw86_f := x -> pw86_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(pw86_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "c3de712619d5e6ad83bc3b7b00ae0183bf5dcbdb", "size": 667, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pw86.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_pw86.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_pw86.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": 24.7037037037, "max_line_length": 81, "alphanum_fraction": 0.6596701649, "num_tokens": 243, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218262741297, "lm_q2_score": 0.7185943985973772, "lm_q1q2_score": 0.6624878603052539}} {"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_n12_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_n12_params * )(p->params);\n*)\n\nomega_x := 2.5:\ngamma_x := 0.004:\n\nrss := (rs, z) -> rs * (2/(1 + z))^(1/3):\n\nvx := rs -> 1/(1 + (1/(RS_FACTOR*omega_x))*rs):\nux := x -> gamma_x*x^2/(1 + gamma_x*x^2):\n\nFN12 := (rs, x) -> \n + add(1*params_a_CC_0_[i+1]*ux(x)^i, i=0..3)\n + add(1*params_a_CC_1_[i+1]*ux(x)^i, i=0..3) * vx(rs)\n + add(1*params_a_CC_2_[i+1]*ux(x)^i, i=0..3) * vx(rs)^2\n + add(1*params_a_CC_3_[i+1]*ux(x)^i, i=0..3) * vx(rs)^3:\n\nf_n12 := (rs, z, xt, xs0, xs1) -> -X_FACTOR_C*RS_FACTOR*(\n + (1 + z)*FN12(rss(rs, z), xs0)/(2*rss(rs, z))\n + (1 - z)*FN12(rss(rs, -z), xs1)/(2*rss(rs, -z))\n):\n\nf := (rs, z, xt, xs0, xs1) -> f_n12(rs, z, xt, xs0, xs1):", "meta": {"hexsha": "08cec1259f4a14282815dbab0ca861c4261ed2fc", "size": 1012, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_n12.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_n12.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_n12.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": 28.1111111111, "max_line_length": 68, "alphanum_fraction": 0.5662055336, "num_tokens": 439, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.933430812881347, "lm_q2_score": 0.7090191337850932, "lm_q1q2_score": 0.661820306397448}} {"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\ntpss_csi2 := (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\ntpss_C0 := (cc, z, xt, xs0, xs1) ->\n + add(cc[i]*z^(2*(i-1)), i=1..4)\n / (1 + tpss_csi2(z, xt, xs0, xs1)*((1 + z)^(-4/3) + (1 - z)^(-4/3))/2)^4:\n\ntpss_aux := (z, xt, ts0, ts1) ->\n xt^2/(8*t_total(z, ts0, ts1)):\n\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\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 + m_max(gga_stoll_par(f_gga, rs, z, xs0, 1), f_gga(rs, z, xt, xs0, xs1))\n + m_max(gga_stoll_par(f_gga, rs, -z, xs1, -1), f_gga(rs, z, xt, xs0, xs1))\n ):\n\nf_tpss0 := (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\nf_tpss := (f_gga, rs, z, xt, xs0, xs1, ts0, ts1) ->\n + f_tpss0(f_gga, rs, z, xt, xs0, xs1, ts0, ts1)\n * (1 + params_a_d*f_tpss0(f_gga, rs, z, xt, xs0, xs1, ts0, ts1)*tpss_aux(z, xt, ts0, ts1)^3)\n:\n", "meta": {"hexsha": "7d2e0bb3641ad149431e6217b028c4c0413c8dc2", "size": 1378, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/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/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/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": 37.2432432432, "max_line_length": 94, "alphanum_fraction": 0.5674891147, "num_tokens": 673, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896693699845, "lm_q2_score": 0.7185943925708561, "lm_q1q2_score": 0.6616742931464434}} {"text": "is_left_unit := (A::set) -> proc(m,e) local a;\n `and`(seq(evalb(m(e,a)=a),a in A)); end:\n\nis_right_unit := (A::set) -> proc(m,e) local a; \n `and`(seq(evalb(m(a,e)=a),a in A)); end:\n\nis_left_absorbing := (A::set) -> proc(m,z) local a;\n `and`(seq(evalb(m(z,a)=z),a in A)); end:\n\nis_right_absorbing := (A::set) -> proc(m,z) local a;\n `and`(seq(evalb(m(a,z)=z),a in A)); end:\n\nis_idempotent := (A::set) -> proc(m) local a;\n `and`(seq(evalb(m(a,a)=a),a in A)); end:\n\nis_commutative := (A::set) -> proc(m) local a,b;\n `and`(seq(seq(evalb(m(a,b) = m(b,a)),b in A),a in A)); end:\n\nis_associative := (A::set) -> proc(m) local a,b,c;\n `and`(seq(seq(seq(evalb(m(a,m(b,c))=m(m(a,b),c)),c in A),b in A),a in A)); end:\n\nis_left_distributive := (A::set) -> proc(m,p) local a,b,c;\n `and`(seq(seq(seq(evalb(m(a,p(b,c))=p(m(a,b),m(a,c))),c in A),b in A),a in A)); end:\n\nis_right_distributive := (A::set) -> proc(m,p) local a,b,c;\n `and`(seq(seq(seq(evalb(m(p(a,b),c)=p(m(a,c),m(b,c))),c in A),b in A),a in A)); end:\n\nis_monoid := (A::set) -> proc(m,e) \n is_left_unit(A)(m,e) and is_right_unit(A)(m,e) and is_associative(A)(m); end:\n\nis_semiring := (A::set) -> (m,p,e,z) -> \n is_monoid(A)(m,e) and\n is_monoid(A)(p,z) and\n is_left_absorbing(A)(m,z) and\n is_right_absorbing(A)(m,z) and\n is_left_distributive(A)(m,p) and\n is_right_distributive(A)(m,p);\n", "meta": {"hexsha": "858f2efca680edd9e08f6879826f7276bef24e17", "size": 1331, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/op_props.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/op_props.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/op_props.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": 35.0263157895, "max_line_length": 85, "alphanum_fraction": 0.5875281743, "num_tokens": 522, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361604769413, "lm_q2_score": 0.72487026428967, "lm_q1q2_score": 0.6613978407923723}} {"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_vt84f_params *params;\n\n assert(p->params != NULL);\n params = (gga_k_vt84f_params * ) (p->params);\n*)\n\n(* Equation (5) *)\nvt84f_f0_orig := s -> 1 - params_a_mu*s^2*exp(-params_a_alpha*s^2)/(1+params_a_mu*s^2) + (1-exp(-params_a_alpha*s^4)) * (s^(-2) - 1) + 5*s^2/3:\n(* Since there's a term that looks hairy at small s, do a series expansion up to s^4 *)\nvt84f_f0_series := s -> eval(convert(taylor(vt84f_f0_orig(st), st = 0, 5), polynom), st=s):\n(* Glue the functions together *)\nvt84f_f0 := s-> my_piecewise3(s <= sqrt(DBL_EPSILON), vt84f_f0_series(s), vt84f_f0_orig(m_max(s, sqrt(DBL_EPSILON)))):\n\n(* Convert from x to s *)\nvt84f_f := x -> vt84f_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) ->\n gga_kinetic(vt84f_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "54b0bce7b3e8bc175c3b15639c8abc02a1135f0c", "size": 1008, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_vt84f.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_vt84f.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_vt84f.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": 34.7586206897, "max_line_length": 143, "alphanum_fraction": 0.6607142857, "num_tokens": 366, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.91610961358942, "lm_q2_score": 0.7217432122827968, "lm_q1q2_score": 0.6611958953151797}} {"text": "#######################################################################\n# This file is part of the crlibm library, and is distributed under\n# the LGPL.\n# To use:\n# restart; read \"log-de.mpl\";\n#TODO output scripts for the Gappa proof out for Paterson/Stockmayer\nDigits := 100:\n\ninterface(quiet=true):\n\nread \"common-procedures.mpl\":\nread \"double-extended.mpl\":\nmkdir(\"TEMPLOG\"):\n\n\nlog2h,log2l := hiloExt(log(2)):\n\n\nL := 7: # number of bits used to address the table\n\nMAXINDEX := round(2^L * (sqrt(2)-1)):\n\nfor i from 0 to MAXINDEX-1 do\n center[i] := 1 + i*2^(-L): # center[i] in [1, 2[\n # We want it to fit on 11 bits of mantissa\n r[i] := round(evalf( (1/center[i]) * 2^(11)) ) / 2^(11) ;\n\nod:\nfor i from MAXINDEX to 2^L do\n # y has been divided by two, center[i] in [0.5, 1[\n center[i]:=(1 + i*2^(-L)) / 2:\n # We want it to fit on 11 bits of mantissa,\n r[i] := round(evalf( (1/center[i]) * 2^(10)) ) / 2^(10) ;\nod:\n\n# Note that we go up to 2^L although the case 2^L is wrapped to zero\n# in the C code. It could be important for zmax (but it turns out not).\n\nfor i from 0 to 2^L do\n (logirh[i], logirl[i]) := hiloExt(-log(r[i])):\nod:\n\n#Computation of ZMax.\nfor i from 0 to MAXINDEX-1 do\n t_x := center[i] + 2^(-L-1) :\n zmax[i] := (t_x*r[i]-1) :\n t_x := center[i] - 2^(-L-1) :\n zmin[i] := (t_x*r[i]-1) :\n zabsmax[i] := max(abs(zmin[i]), abs(zmax[i])):\nod:\nfor i from MAXINDEX to 2^L do\n t_x := center[i] + 2^(-L-2) :\n zmax[i] := (t_x*r[i]-1) :\n t_x := center[i] - 2^(-L-2) :\n zmin[i] := (t_x*r[i]-1) :\n zabsmax[i] := max(abs(zmin[i]), abs(zmax[i])):\nod:\n\nzmaxmax:=0:\nzminmin:=0:\nfor i from 0 to 2^L do\n if zmax[i] > zmaxmax then zmaxmax := zmax[i]: fi:\n if zmin[i] < zminmin then zminmin := zmin[i]: fi:\nod:\nprintf(\"zminmin = -2^(%2f) zmaxmax = 2^(%2f)\\n\", log2(-zminmin), log2(zmaxmax) ) :\n\n\nPolyDegreeQuick:=7:\n\n#Keep -zmaxmax..zmaxmax to keep c1=1, which is useful in the proof\n\nif(1+1=3) then # The polynomial used to be computed here,\npolyQuick:= polyExact2Ext(x * numapprox[minimax]( log(1+x)/x, x=-zmaxmax..zmaxmax, [PolyDegreeQuick-1,0], 1 , 'deltaApprox'), 0):\n\nepsilonApproxQuick := numapprox[infnorm]( 1-polyQuick/log(1+x), x=zminmin..zmaxmax):\ndeltaApproxQuick := numapprox[infnorm]( polyQuick-log(1+x), x=zminmin..zmaxmax):\nelse\n# magical polynomial given by Sylvain's tool\npolyQuick := x * (1 + (x * ((-0.50000000000000000000000000000000000000000000000000000000000000e0) + (x * (0.33333333333333342585191871876304503530263900756835937500000000e0 + (x * ((-0.24999999998423708125194764306797878816723823547363281250000000e0) + (x * (0.19999999996748479835773082413652446120977401733398437500000000e0 + (x * ((-0.16666957260954737285452154083031928166747093200683593750000000e0) + (x * 0.14286056338555042088955815415829420089721679687500000000000000e0)))))))))))):\n\n# validated infinite norms given by Christoph's tool\nepsilonApproxQuick := 2^(-64.119667587221):\ndeltaApproxQuick := 2^(-72.230387592107):\nfi:\nprintf(\" rel approximation error for the quick phase is 2^(%2f)\\n\", log2(epsilonApproxQuick) ) :\nprintf(\" abs approximation error for the quick phase is 2^(%2f)\\n\", log2(deltaApproxQuick) ) :\n\n# For the Paterson/Stockmayer method\npolyQuick0:= x * numapprox[minimax]( log(1+x)/x, x=-zmaxmax..zmaxmax, [PolyDegreeQuick-1,0], 1 , 'deltaApprox'):\n\n## Création des nouveaux coefficients\npolyQuick0:= x * numapprox[minimax]( log(1+x)/x, x=-zmaxmax..zmaxmax, [PolyDegreeQuick-1,0], 1 , 'deltaApprox'):\n\n## Création des nouveaux coefficients\na7 := convert(coeff(polyQuick0,x,7),rational):\na6 := convert(coeff(polyQuick0,x,6)/a7,rational):\na5 := convert(coeff(polyQuick0,x,5)/a7,rational):\na4 := convert(coeff(polyQuick0,x,4)/a7,rational):\n\na3 := convert(coeff(polyQuick0,x,3),rational):\na2 := convert(coeff(polyQuick0,x,2),rational):\na1 := convert(coeff(polyQuick0,x,1),rational):\na0 := convert(coeff(polyQuick0,x,0),rational):\n\nalpha0 := a5 - 1:\nalpha1 := a6:\nalpha2 := a4 - alpha0 * a6:\n\n##\na7_hi,a7_lo := hiloExt(a7):\na3_hi,a3_lo := hiloExt(a3):\na2_hi,a2_lo := hiloExt(a2):\na0_hi,a0_lo := hiloExt(a0):\n\nc_hi,c_lo := hiloExt(alpha0):\nalpha_hi,alpha_lo := hiloExt(alpha1):\nbeta_hi,beta_lo := hiloExt(alpha2):\n\n#coef_c := c_hi + c_lo:\n#coef_alpha := alpha_hi + alpha_lo:\n#coef_beta := beta_hi + beta_lo:\n#coef_c7 := a7_hi + a7_lo:\n#coef_c3 := a3_hi + a3_lo:\n#coef_c2 := a2_hi + a2_lo:\n#coef_c0 := a0_hi + a0_lo:\n\ncoef_c := c_hi:\ncoef_alpha := alpha_hi:\ncoef_beta := beta_hi:\ncoef_c7 := a7_hi:\ncoef_c3 := a3_hi:\ncoef_c2 := a2_hi:\ncoef_c0 := a0_hi:\n\npolyQuickPat := ((x^2 + coef_c)*(x + coef_alpha) + (x + coef_beta)) * (coef_c7*x^4) + ((coef_c3 * x + coef_c2)*x^2 + (x)):\n\nepsilonApproxQuickPat := numapprox[infnorm]( 1-polyQuickPat/log(1+x), x=zminmin..zmaxmax):\nprintf(\" approximation rel error for Paterson/Stockmayer in the quick phase is 2^(%2f)\\n\", log2(epsilonApproxQuickPat) ) :\ndeltaApproxQuickPat := numapprox[infnorm]( polyQuickPat-log(1+x), x=zminmin..zmaxmax):\nprintf(\" approximation abs error for Paterson/Stockmayer in the quick phase is 2^(%2f)\\n\", log2(deltaApproxQuickPat) ) :\n\n\n\nPolyDegreeAccurate:=14:\n\nprintf(\"Computing the polynomial for accurate phase (this may take some time...)\\n\"):\npe:= x * numapprox[minimax]( log(1+x)/x, x=-zmaxmax..zmaxmax, [PolyDegreeAccurate-1,0], 1 , 'deltaApprox'):\n\n\nMaxDegreeDDE:=8: #\n\npolyAccurate := polyExact2Ext(pe, MaxDegreeDDE):\ndeltaApproxAccurate := numapprox[infnorm](polyAccurate-log(1+x), x=-zmaxmax..zmaxmax):\nepsilonApproxAccurate := numapprox[infnorm]( 1-polyAccurate/log(1+x), x=-zmaxmax..zmaxmax):\nprintf(\" approximation error for the accurate phase is 2^(%2f)\\n\", log2(epsilonApproxAccurate) ) :\n\n\n\n\nfilename:=\"TEMPLOG/log-de.h\":\nfd:=fopen(filename, WRITE, TEXT):\n\nfprintf(fd, \"/*File generated by maple/log-de.mpl*/\\n\\n\"):\n# some constants\nfprintf(fd, \"#define L %d\\n\", L):\nfprintf(fd, \"#define MAXINDEX %d\\n\", MAXINDEX):\nfprintf(fd, \"#define INDEXMASK %d\\n\", 2^L-1):\nfprintf(fd, \"static const double two64 = %1.25e ;\\n\", evalf(2^64)):\n\nfprintf(fd, \"#if 1\\n#define ESTRIN\\n#else\\n#define PATERSON\\n#endif\\n\"):\n\nfprintf(fd, \"#if defined(CRLIBM_TYPECPU_X86) || defined(CRLIBM_TYPECPU_AMD64)\\n\\n\"):\n\nfprintf(fd, \"#ifdef PATERSON\\n\"):\n # polynomial for quick phase\n fprintf(fd,\"static const long double c7 = %1.50e;\\n\",coef_c7):\n fprintf(fd,\"static const long double c3 = %1.50e;\\n\",coef_c3):\n fprintf(fd,\"static const long double c2 = %1.50e;\\n\",coef_c2):\n fprintf(fd,\"static const long double ps_alpha = %1.50e;\\n\",coef_alpha):\n fprintf(fd,\"static const long double ps_beta = %1.50e;\\n\",coef_beta):\n fprintf(fd,\"static const long double ps_c = %1.50e;\\n\",coef_c):\nfprintf(fd, \"#endif/* PATERSON*/\\n\\n\"):\n\nfprintf(fd, \"#ifdef ESTRIN\\n\"):\n fprintf(fd, \" /* Coefficients are read directly from the array thanks to the following macros */ \\n\"):\n for i from PolyDegreeQuick to 2 by -1 do\n fprintf(fd, \"#define c%d c[%d]\\n\", i, PolyDegreeQuick-i):\n od:\n fprintf(fd, \"static const double c[%d] = {\\n\",PolyDegreeQuick):\n for i from PolyDegreeQuick to 2 by -1 do\n fprintf(fd, \" /* c%d = */ %1.50eL, \\n\", i, coeff(polyQuick,x,i)):\n od:\n fprintf(fd, \"}; \\n \\n\"):\nfprintf(fd, \"#endif/* ESTRIN */\\n\\n\"):\n\n\n\n for i from PolyDegreeAccurate to 1 by -1 do\n fprintf(fd, \"#define c%dh ch[%d]\\n\", i, PolyDegreeAccurate-i):\n od:\n\n for i from MaxDegreeDDE-1 to 1 by -1 do\n fprintf(fd, \"#define c%dl cl[%d]\\n\", i, MaxDegreeDDE-1-i):\n od:\n fprintf(fd, \"#define PREFETCH_POLY_ACCURATE \\n\"):\n fprintf(fd, \"\\n#else /* not(defined(CRLIBM_TYPECPU_X86) || defined(CRLIBM_TYPECPU_AMD64)),\\n assuming Itanium, otherwise we shouldn't be there */ \\n\\n\"):\n fprintf(fd, \"#define PREFETCH_POLY_QUICK \"):\n for i from PolyDegreeQuick to 2 by -1 do\n fprintf(fd, \"c%d=c[%d]; \", i, PolyDegreeQuick-i):\n od:\n fprintf(fd, \"\\n#define PREFETCH_POLY_ACCURATE \"):\n for i from PolyDegreeAccurate to 1 by -1 do\n fprintf(fd, \"c%dh=ch[%d]; \", i, PolyDegreeAccurate-i):\n if i mod 4 =0 then fprintf(fd, \"\\\\\\n \"): fi:\n od:\n fprintf(fd, \"\\\\\\n \"):\n for i from MaxDegreeDDE-1 to 1 by -1 do\n fprintf(fd, \"c%dl=cl[%d]; \", i, MaxDegreeDDE-1-i):\n od:\n\n fprintf(fd, \"\\n#endif /* defined(CRLIBM_TYPECPU_X86) || defined(CRLIBM_TYPECPU_AMD64) */ \\n\\n\"):\n\n # Various constants\n fprintf(fd, \"static const long double log2H = %1.50eL ;\\n\", log2h):\n fprintf(fd, \"static const long double log2L = %1.50eL ;\\n\", log2l):\n\n # The polynomials\n # polynomial for quick phase\n# for i from PolyDegreeQuick to 1 by -1 do\n# fprintf(fd, \"static const long double c%d = %1.50eL ;\\n\", i, coeff(polyQuick,x,i)):\n# od:\n\n # polynomial for accurate phase\n fprintf(fd, \"static const long double ch[%d] = {\\n\",PolyDegreeAccurate):\n for i from PolyDegreeAccurate to 1 by -1 do\n (ch, cl) := hiloExt(coeff(polyAccurate,x,i)):\n fprintf(fd, \" /* ch%d = */ %1.50eL, \\n\", i, ch):\n od:\n fprintf(fd, \"}; \\n \\n\"):\n\n fprintf(fd, \"static const long double cl[%d] = {\\n\", MaxDegreeDDE):\n for i from MaxDegreeDDE-1 to 1 by -1 do\n (ch, cl) := hiloExt(coeff(polyAccurate,x,i)):\n fprintf(fd, \" /* cl%d = */ %1.50eL, \\n\", i, cl):\n od:\n fprintf(fd, \"}; \\n \\n\"):\n\n\n # The tables\n\n\n fprintf(fd, \"typedef struct rri_tag {float r; long double logirh; long double logirl; } rri ; \\n\"):\n fprintf(fd, \"static const rri argredtable[%d] = {\\n\", 2^L):\n for i from 0 to 2^L-1 do\n fprintf(fd, \" { \\n\"):\n fprintf(fd, \" %1.50eL, /* r[%d] */ \\n\", r[i], i):\n fprintf(fd, \" %1.50eL, /* logirh[%d] */ \\n\", logirh[i], i):\n fprintf(fd, \" %1.50eL, /* logirl[%d] */ \\n\", logirl[i], i):\n fprintf(fd, \" } \"):\n if(i<2^L-1) then fprintf(fd, \", \\n\"): fi\n od:\nfprintf(fd, \"}; \\n \\n\"):\n\nfclose(fd):\n\nprintf(\"\\n************ DONE TEMPLOG/log-de.h ************\\n\");\n\n\n\n\nfilename:=\"TEMPLOG/polynomials.sed\":\nfd:=fopen(filename, WRITE, TEXT):\nfor i from PolyDegreeAccurate to 1 by -1 do\n (ch, cl) := hiloExt(coeff(polyAccurate,x,i)):\n fprintf(fd, \" s/_c%dh/%1.40e/g\\n\", i, ch):\n if(i&2\\n\"):\nfprintf(fd, \"sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_0.sed $CRLIBMDIR/gappa/log-de/log-de-acc-index0-E0.gappa | $GAPPA \\n\"):\n\nfprintf(fd, \"echo Accurate phase, case E!=0, index=0 1>&2\\n\"):\nfprintf(fd, \"sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_0.sed $CRLIBMDIR/gappa/log-de/log-de-acc-index0-E1N.gappa | $GAPPA \\n\"):\n\nfprintf(fd, \"for num in `seq 1 %d`; do\\n\", 2^L-1):\nfprintf(fd, \" echo Accurate phase, case E=0, index=$num 1>&2\\n\"):\nfprintf(fd, \" sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_$num.sed $CRLIBMDIR/gappa/log-de/log-de-acc-index1N-E0.gappa | $GAPPA \\n\"):\nfprintf(fd, \" echo 1>&2\\n\"):\nfprintf(fd, \"done\\n\"):\n\nfprintf(fd, \"for num in `seq 1 %d`; do\\n\", 2^L-1):\nfprintf(fd, \" echo Accurate phase, case E!=0, index = $num 1>&2 \\n\"):\nfprintf(fd, \" sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_$num.sed $CRLIBMDIR/gappa/log-de/log-de-acc-index1N-E1N.gappa | $GAPPA \\n\"):\nfprintf(fd, \" echo 1>&2\\n\"):\nfprintf(fd, \"done\\n\\n\"):\n\n\nfprintf(fd, \"echo Quick phase, case E=0, index=0 1>&2\\n\"):\nfprintf(fd, \"sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_0.sed $CRLIBMDIR/gappa/log-de/log-de-index0-E0.gappa | $GAPPA \\n\"):\nfprintf(fd, \" echo 1>&2\\n\"):\n\nfprintf(fd, \"echo Quick phase, case E!=0, index=0 1>&2 \\n\"):\nfprintf(fd, \"sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_0.sed $CRLIBMDIR/gappa/log-de/log-de-index0-E1N.gappa | $GAPPA \\n\"):\nfprintf(fd, \" echo 1>&2\\n\"):\n\n\nfprintf(fd, \"for num in `seq 1 %d`; do\\n\", 2^L-1):\nfprintf(fd, \" echo Quick phase, for all E, index=$num 1>&2\\n\"):\nfprintf(fd, \" sed -f $CRLIBMDIR/maple/TEMPLOG/polynomials.sed -f $CRLIBMDIR/maple/TEMPLOG/log-de_$num.sed $CRLIBMDIR/gappa/log-de/log-de-index1N-E0N.gappa | $GAPPA \\n\"):\nfprintf(fd, \" echo 1>&2\\n\"):\nfprintf(fd, \"done\\n\"):\n\nfclose(fd):\n\nprintf(\"\\n************ DONE TEMPLOG/run-log-de-proof.sh ************\\n\"):\nprintf(\"Now you should run \\n\"):\nprintf(\" sh ../../gappa/log-de/run-log-de-proof.sh 2> ../../maple/TEMPLOG/Gappa.out\\n\"):\nprintf(\" (You probably need to edit the path to the gappa executable within run-log-de-proof.sh)\\n\"):\nprintf(\"Then look at TEMPLOG/Gappa.out. It shouldn't contain 'some enclosures were not satisfied'.\\n If it does, report it !\\n\"):\n\n\nprintf(\"----DONE---\\n\") :\n\n", "meta": {"hexsha": "9704e23847a17e479311153fa24451e19b210943", "size": 13932, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "crlibm/maple/log-de.mpl", "max_stars_repo_name": "squarePenguin/parvsl", "max_stars_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "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": "crlibm/maple/log-de.mpl", "max_issues_repo_name": "squarePenguin/parvsl", "max_issues_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2019-03-25T17:02:38.000Z", "max_issues_repo_issues_event_max_datetime": "2019-03-25T17:02:38.000Z", "max_forks_repo_path": "crlibm/maple/log-de.mpl", "max_forks_repo_name": "squarePenguin/parvsl", "max_forks_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "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": 38.7, "max_line_length": 490, "alphanum_fraction": 0.6448463968, "num_tokens": 4998, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8596637505099168, "lm_q2_score": 0.7690802370707281, "lm_q1q2_score": 0.6611504010432782}} {"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\nf0 := x -> 1 + 0.0055*x^2/(1 + 0.0253*x*arcsinh(x)):\nf1 := x -> -0.072*x/(1 + 2*4^(1/3)*x):\n\nf := x -> f0(x) + f1(x):\n", "meta": {"hexsha": "2cd1b2dc37b4ed9cde3776471c933f6bb795019f", "size": 381, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_k_thakkar.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_k_thakkar.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_k_thakkar.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": 25.4, "max_line_length": 68, "alphanum_fraction": 0.6062992126, "num_tokens": 145, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9073122163480666, "lm_q2_score": 0.727975443004307, "lm_q1q2_score": 0.6605010126392035}} {"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_ev93_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_ev93_params * )(p->params);\n*)\n\nev93_f0 := s -> (1 + params_a_a1*s^2 + params_a_a2*s^4 + params_a_a3*s^6)/(1 + params_a_b1*s^2 + params_a_b2*s^4 + params_a_b3*s^6):\nev93_f := x -> ev93_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(ev93_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "fbea4785f37cadcde466deb1d2957852d6a5f672", "size": 647, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_ev93.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_ev93.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_ev93.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": 29.4090909091, "max_line_length": 132, "alphanum_fraction": 0.6429675425, "num_tokens": 233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391621868805, "lm_q2_score": 0.7154240018510026, "lm_q1q2_score": 0.6603643712769347}} {"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$define gga_x_rpw86_params\n$include \"gga_x_pw86.mpl\"\n\nlv_alpha := 0.02178:\nlv_beta := 1.15:\nlv_muLV := 0.8491/9:\n\nlv_f0 := s ->\n + (1 + lv_muLV*s^2)/(1 + lv_alpha*s^6)\n + lv_alpha*s^6*pw86_f0(s)/(lv_beta + lv_alpha*s^6):\n\nlv_f := x -> lv_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(lv_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "a20f20b3af15f6b52bd9b72e83ecd1733295799d", "size": 585, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_lv_rpw86.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_lv_rpw86.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_lv_rpw86.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": 23.4, "max_line_length": 68, "alphanum_fraction": 0.6393162393, "num_tokens": 224, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9441768588653855, "lm_q2_score": 0.6992544210587586, "lm_q1q2_score": 0.6602198428229923}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n Copyright (C) 2018 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_x_ms_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_ms_params * ) (p->params);\n*)\n\nms_fa := a -> (1 - a^2)^3 / (1 + a^3 + params_a_b*a^6):\nms_f0 := (p, c) -> 1 + params_a_kappa*(1 - params_a_kappa/(params_a_kappa + MU_GE*p + c)):\n\nms_alpha := (t,x) -> (t - x^2/8)/K_FACTOR_C:\n\nms_f := (x, u, t) -> ms_f0(X2S^2*x^2, 0) + \\\n ms_fa(ms_alpha(t,x))*(ms_f0(X2S^2*x^2, params_a_c) - ms_f0(X2S^2*x^2, 0)):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(ms_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "1347d204054dd3776d0d0fdd25229d9f7a4b84d2", "size": 831, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_ms.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_ms.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_ms.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": 29.6785714286, "max_line_length": 90, "alphanum_fraction": 0.6113116727, "num_tokens": 338, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9390248157222395, "lm_q2_score": 0.7025300636233416, "lm_q1q2_score": 0.6596931635332415}} {"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\nmbeta := 0.0042:\nmgamma := 6:\nc0 := 1.09878:\nc1 := -2.51173:\nc2 := 0.0156233:\n\nf_aux := x -> 1 + mgamma*mbeta*x*arcsinh(x):\n\nf := x -> c0 + mbeta/X_FACTOR_C*x^2*(c1/f_aux(x) + c2/(mbeta*f_aux(x)^2)):", "meta": {"hexsha": "a88b880b3dc8f7e272980673729f3718b347aa9b", "size": 476, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_hcth_a.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_hcth_a.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_hcth_a.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": 25.0526315789, "max_line_length": 74, "alphanum_fraction": 0.6218487395, "num_tokens": 182, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9219218391455085, "lm_q2_score": 0.7154239897159438, "lm_q1q2_score": 0.6595650003677402}} {"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\nmbeta := 0.018641:\nmcsi := 8: (* for harmonic potentials *)\n\nf := x -> 1 + mbeta/X_FACTOR_2D_C*x^2/(1 + mcsi*mbeta*x*arcsinh(x)):", "meta": {"hexsha": "948eece1bb68023f34a319866e169480c46a79e0", "size": 393, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_2d_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/gga_x_2d_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/gga_x_2d_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": 28.0714285714, "max_line_length": 68, "alphanum_fraction": 0.6692111959, "num_tokens": 131, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.90192067652954, "lm_q2_score": 0.7310585844894971, "lm_q1q2_score": 0.6593568531054951}} {"text": "# Taken from\n# N. Tuncer, T. Le\n# \"Structural and practical identifiability analysis of outbreak models\"\n# https://doi.org/10.1016/j.mbs.2018.02.004\n# Equation (2.2) with cumulative incidence observations\nread \"../ComputeIdentifiableFunctions.mpl\";\n\n# Prevalence observations\nmodel := [\n diff(S(t), t) = b * S(t) * In(t) / N,\n diff(E(t), t) = b * S(t) * In(t) / N - nu * E(t),\n diff(In(t), t) = nu * E(t) - a * In(t),\n y(t) = In(t),\n y2(t) = N\n]:\n\nme := MultiExperimentIdentifiableFunctions(model, simplified_generators=true):\nprintf(\"The bound for the number of experiments is %a, this means that the fields of single-experiment and multi-experiment identifiable functions coincide, and they are equal to: %a\\n\", me[1], me[3]):\n\n# Cummulative incidence observations\n# using change of variables Ninv := 1 / N to simplify the computation\nmodel := [\n diff(S(t), t) = b * S(t) * In(t) * Ninv,\n diff(E(t), t) = b * S(t) * In(t) * Ninv - nu * E(t),\n diff(In(t), t) = nu * E(t) - a * In(t),\n diff(Cu(t), t) = nu * E(t),\n y(t) = Cu(t),\n y2(t) = Ninv\n]:\n\nme := MultiExperimentIdentifiableFunctions(model, simplified_generators=true, infolevel=1):\nprintf(\"The bound for the number of experiments is %a, this means that the field of multi-experiment identifiable functions is the same, %a\\n\", me[1], me[3]):\n", "meta": {"hexsha": "2c0471beddef5d37764c5d6788e7b4c63a8e4821", "size": 1309, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/SEIR.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/SEIR.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/SEIR.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": 39.6666666667, "max_line_length": 201, "alphanum_fraction": 0.6562261268, "num_tokens": 408, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8976952866333484, "lm_q2_score": 0.7341195327172402, "lm_q1q2_score": 0.6590156443457427}} {"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_vxc *)\n(* prefix:\n gga_x_lb_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_lb_params * )(p->params);\n*)\n\nlb_f0 := (rs, z, x) -> -my_piecewise3(x < 300,\n params_a_beta*x^2/(1 + 3*params_a_beta*x*arcsinh(params_a_gamma*x)),\n x/(3*log(2*params_a_gamma*x))):\n\nlb_f := (rs, z, x) -> (params_a_alpha*(4/3)*LDA_X_FACTOR + lb_f0(rs, z, x))*n_spin(rs, z)^(1/3):\n\nf := (rs, z, xt, xs0, xs1) -> lb_f(rs, z, xs0):\n", "meta": {"hexsha": "2a3aff00c8fb43e03d328f6c468e0cebe30b129c", "size": 688, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_vxc/gga_x_lb.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_vxc/gga_x_lb.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_vxc/gga_x_lb.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": 28.6666666667, "max_line_length": 96, "alphanum_fraction": 0.625, "num_tokens": 245, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299570920387, "lm_q2_score": 0.7122321903471563, "lm_q1q2_score": 0.6589785589144682}} {"text": "######################################################################\n# prime_simplex_boundary(A) is the set of maps x : A -> [0,1] with \n# min = 0 and max = 1.\n\n`is_element/prime_simplex_boundary` := (A::set) -> proc(x)\n local a,u,v,w;\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 w := 1;\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 w := min(u,w);\n od;\n\n if simplify(v - 1) <> 0 then\n reason := [convert(procname,string),\"max(x[a] : a in A) <> 1\",v];\n return false;\n fi;\n\n if simplify(w) <> 0 then\n reason := [convert(procname,string),\"min(x[a] : a in A) <> 0\",w];\n return false;\n fi;\n\n return true;\nend;\n\n######################################################################\n\n`is_equal/prime_simplex_boundary` := (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######################################################################\n\n`is_leq/prime_simplex_boundary` := NULL;\n\n######################################################################\n\n`random_element/prime_simplex_boundary` := (A::set) -> proc(d::posint := 5)\n local x,a,r1,r2,u,v;\n\n if nops(A) < 2 then return FAIL; fi;\n\n r1 := rand(0..d); \n r2 := rand(1..d);\n x := table();\n u := 0;\n v := 0;\n\n while u = v do\n u := 0;\n v := infinity;\n for a in A do \n x[a] := r1()/r2();\n u := max(u,x[a]);\n v := min(v,x[a]);\n od;\n od;\n\n for a in A do x[a] := (x[a]-v)/(u-v); od;\n\n return eval(x);\nend;\n\n######################################################################\n\n`list_elements/prime_simplex_boundary` := NULL;\n`count_elements/prime_simplex_boundary` := NULL;\n\n######################################################################\n\n`phi/proper_nonempty_subsets/prime_simplex_boundary` := (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\n", "meta": {"hexsha": "9dc2564ac6d756ba2fcda38528ff83b7adc0e5fb", "size": 2353, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/prime_simplex_boundary.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_boundary.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_boundary.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": 20.8230088496, "max_line_length": 79, "alphanum_fraction": 0.4747131322, "num_tokens": 675, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8333245787544825, "lm_q2_score": 0.7905303137346446, "lm_q1q2_score": 0.6587683406855716}} {"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: lda_exc *)\n(* prefix:\n lda_c_pw_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_pw_params * )(p->params);\n*)\n\n$ifdef lda_c_pw_params\nparams_a_pp := [1, 1, 1]:\nparams_a_a := [0.031091, 0.015545, 0.016887]:\nparams_a_alpha1 := [0.21370, 0.20548, 0.11125]:\nparams_a_beta1 := [7.5957, 14.1189, 10.357]:\nparams_a_beta2 := [3.5876, 6.1977, 3.6231]:\nparams_a_beta3 := [1.6382, 3.3662, 0.88026]:\nparams_a_beta4 := [0.49294, 0.62517, 0.49671]:\nparams_a_fz20 := 1.709921:\n$endif\n\n$ifdef lda_c_pw_modified_params\nparams_a_a := [0.0310907, 0.01554535, 0.0168869]:\nparams_a_fz20 := 1.709920934161365617563962776245:\n$endif\n\n(* Equation (10) *)\ng_aux := (k, rs) -> params_a_beta1[k]*sqrt(rs) + params_a_beta2[k]*rs\n + params_a_beta3[k]*rs^1.5 + params_a_beta4[k]*rs^(params_a_pp[k] + 1):\ng := (k, rs) -> -2*params_a_a[k]*(1 + params_a_alpha1[k]*rs)\n * log(1 + 1/(2*params_a_a[k]*g_aux(k, rs))):\n\n(* Equation (8) *)\n(* Attention, the function g parametrizes -alpha *)\nf_pw := (rs, zeta) ->\n g(1, rs) + zeta^4*f_zeta(zeta)*(g(2, rs) - g(1, rs) + g(3, rs)/params_a_fz20)\n - f_zeta(zeta)*g(3, rs)/params_a_fz20:\n\nf := (rs, zeta) -> f_pw(rs, zeta):\n", "meta": {"hexsha": "2a8607c2d1dffc7c14e4d5cd52d68810fc69ef53", "size": 1430, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pw.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pw.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pw.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": 31.0869565217, "max_line_length": 79, "alphanum_fraction": 0.6426573427, "num_tokens": 573, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8791467738423874, "lm_q2_score": 0.7490872075132153, "lm_q1q2_score": 0.6585576018118462}} {"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\nthakkar_f0 := x -> 1 + 0.0055*x^2/(1 + 0.0253*x*arcsinh(x)):\nthakkar_f1 := x -> -0.072*x/(1 + 2*4^(1/3)*x):\n\nthakkar_f := x -> thakkar_f0(x) + thakkar_f1(x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_kinetic(thakkar_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "e53601102f317caf00a21f7f8ae61938fb45a6d2", "size": 496, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_thakkar.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_thakkar.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_thakkar.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": 29.1764705882, "max_line_length": 76, "alphanum_fraction": 0.6350806452, "num_tokens": 197, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9372107861416413, "lm_q2_score": 0.7025300698514778, "lm_q1q2_score": 0.6584187590536457}} {"text": "is_numerical_poly := proc(g,u)\n local m,h;\n\n if not(type(g,polynom(rational,u))) then\n return false;\n fi;\n \n m := degree(g,u);\n h := g;\n while m >= 0 do\n if not(type(subs(u=0,h),integer)) then\n return(false);\n fi;\n h := expand(subs(u=u+1,h)-h);\n m := m-1;\n od:\n return(true);\nend:\n\n`b/numerical_poly` := (k::nonnegint,u) -> expand(binomial(u,k));\n\n`alpha/numerical_poly` := proc(i::nonnegint,j::nonnegint,k::nonnegint)\n if i <= k and j <= k and k <= i+j then\n return k!/((k-i)!*(k-j)!*(i+j-k)!);\n else\n return 0;\n fi;\nend:\n\n`beta/numerical_poly` := proc(i::nonnegint,j::nonnegint,k::nonnegint)\n local m,n;\n \n add(add(\n (-1)^(m+n)*binomial(i,m)*binomial(j,n)*binomial((i-m)*(j-n),k),\n n=0..j),m=0..i);\n \nend:\n\n`Delta/numerical_poly` := proc(f,u)\n subs(u = u+1,f) - f;\nend:\n\n`gamma/numerical_poly` := proc(p,n)\n local N;\n N := floor(n/(p-1));\n N + padic_val(N!,p);\nend:\n\n`Gamma/numerical_poly` := proc(n::posint)\n local g,i,p;\n g := 1;\n i := 1;\n p := ithprime(i);\n while p <= 2*n do\n g := g * p^`gamma/numerical_poly`(p,n);\n i := i+1;\n p := ithprime(i);\n od;\n return(g);\nend:\n\n`Gamma_alt/numerical_poly` := proc(n::posint)\n local k;\n \n if modp(n,2) <> 0 then return FAIL; fi;\n\n return mul(2*denom(bernoulli(2*k)/(2*k)),k=1..n/2);\nend:\n\n\n# There is a canonical basis for the ring of stably numerical\n# polynomials, as discussed in the document ImJ.tex.\n# The first few basis elements are as follows:\n\n`f/stably_numerical_poly` := table([\n 0 = ((u) -> 1),\n 1 = ((u) -> (u+1)/2),\n 2 = ((u) -> (u^2-1)/24),\n 3 = ((u) -> (u^3+u^2-u-1)/48),\n 4 = ((u) -> (u^4+70*u^2-71)/5760),\n 5 = ((u) -> (u^5+u^4+70*u^3+70*u^2-71*u-71)/11520)\n]);\n\n`f_witness/stably_numerical_poly` := table([\n \"max_deg\" = 5,\n \"u_shift\" = table([0 = 0,1 = 1,2 = 3,3 = 4,4 = 7,5 = 8]),\n \"eval_points\" = [1,-1,7,11,13,17,23,37],\n \"split_matrix\" =\n [[0, 1, 0, 0, 0, 0, 0, 0],\n [1, -1, 0, 0, 0, 0, 0, 0],\n [-2497, 1127, 5994, -13853, 10734, -1511, 2, 4],\n [-628, 283, 1513, -3505, 2720, -385, 1, 1],\n [-4976, 2245, 11943, -27574, 21348, -2996, 2, 8],\n [-4334, 1955, 10406, -24026, 18599, -2608, 1, 7]]\n]):\n\n`find_split_matrix/stably_numerical_poly` := proc()\n local f,W,d,A,m,B,eqs,sol,i,j;\n \n f := `f/stably_numerical_poly`;\n W := `f_witness/stably_numerical_poly`;\n d := W[\"max_deg\"];\n\n A := Transpose(Matrix(\n [seq(map(f[i],W[\"eval_points\"]),i=0..d)]));\n\n m := nops(W[\"eval_points\"]);\n \n B := Matrix([seq([seq(b[i,j],j=1..m)],i=0..d)]):\n\n eqs := {op(map(r -> r = 0,map(op,convert(B.A - IdentityMatrix(d+1),listlist))))}:\n sol := isolve(eqs);\n\n if sol = NULL then return FAIL; fi;\n\n B := subs(sol,B);\n B := subs(map(u -> u=0,indets(B)),B);\n\n return B;\nend:\n\n######################################################################\n\n`check_witness/stably_numerical_poly` := proc()\n global Z;\n local f,W,d,s,i,j,M,A,B,p;\n \n f := `f/stably_numerical_poly`;\n W := `f_witness/stably_numerical_poly`;\n d := W[\"max_deg\"];\n\n _ASSERT(type(d,posint),\"max_deg is a positive integer\");\n\n for i from 0 to d do\n s := W[\"u_shift\"][i];\n _ASSERT(is_numerical_poly(u^s*f[i](u),u),\n sprintf(\"f_%d(u) is stably numerical\",i));\n od:\n\n for i from 0 to d do\n M[i] := 1/coeff(f[i](u),u,i);\n _ASSERT(type(M[i],posint),sprintf(\"Leading coefficient of f_%d(u) is egyptian\",i));\n _ASSERT(\n `and`(seq(-1/(2*M[i]) < coeff(f[j](u),u,i) and\n coeff(f[j](u),u,i) <= 1/(2*M[i]),j=i+1..d)),\n sprintf(\"Coefficient bounds for f_%d(u)\",i));\n od:\n \n _ASSERT(type(W[\"eval_points\"],list(integer)),\"eval_points is a list of integers\");\n\n for p in W[\"eval_points\"] do\n _ASSERT(p = 1 or p = -1 or (p > d and isprime(p)),\n sprintf(\"evaluation point %d is +/- 1 or prime and greater than max_deg\",p));\n od:\n\n A := Transpose(Matrix(\n [seq(map(f[i],W[\"eval_points\"]),i=0..d)]));\n\n B := Matrix(W[\"split_matrix\"]);\n Z := [A,B];\n\n _ASSERT(Equal(B.A,IdentityMatrix(d+1)),\"split_matrix splits\");\n\nend:\n\n######################################################################\n\ncheck_numerical_poly := proc()\n local u,v,i,j,k,n,ok,err;\n \n _ASSERT(\n `b/numerical_poly`(0,u) = 1,\n \"b_0(u) = 1\"\n );\n \n _ASSERT(\n `b/numerical_poly`(1,u) = u,\n \"b_1(u) = u\"\n );\n\n ok := true;\n for k from 0 to 10 do\n err :=\n `b/numerical_poly`(k,u+v) -\n add(`b/numerical_poly`(i,u) * `b/numerical_poly`(k-i,v),i=0..k);\n\n err := expand(err);\n if err <> 0 then ok := false; break; fi;\n od:\n _ASSERT(ok,\"Formula for b_k(u+v)\");\n\n ok := true;\n for k from 0 to 10 do\n err :=\n `b/numerical_poly`(k,u*v) -\n add(add(\n `beta/numerical_poly`(i,j,k) *\n `b/numerical_poly`(i,u) *\n `b/numerical_poly`(j,v),\n j=0..k),i=0..k);\n\n err := expand(err);\n if err <> 0 then ok := false; break; fi;\n od:\n _ASSERT(ok,\"Formula for b_k(uv)\");\n\n ok := true;\n for i from 0 to 10 do\n for j from 0 to 10 do\n err := `b/numerical_poly`(i,u) * `b/numerical_poly`(j,u) -\n add(\n `alpha/numerical_poly`(i,j,k) * `b/numerical_poly`(k,u),\n k = 0 .. i+j);\n err := expand(err);\n\n if err <> 0 then ok := false; break; fi;\n od:\n\n if not(ok) then break; fi;\n od:\n _ASSERT(ok,\"Formula for b_i(u) b_j(u)\");\n\n _ASSERT(`Delta/numerical_poly`(`b/numerical_poly`(0,u),u) = 0,\"Delta(b_0) = 0\");\n\n _ASSERT(\n `and`(seq(\n expand(`Delta/numerical_poly`(`b/numerical_poly`(i+1,u),u) - `b/numerical_poly`(i,u))=0,\n i=0..10)),\n \"Delta(b_{i+1}(u)) = b_i(u)\"\n );\n \n _ASSERT(\n `and`(seq(`Gamma_alt/numerical_poly`(2*n) =\n `Gamma/numerical_poly`(2*n),n=1..10)),\n \"Gamma in terms of Bernoulli numbers\"\n );\nend:", "meta": {"hexsha": "4a4346d44921dd8e231c46ae4a28d7de6e8191ba", "size": 5476, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/numerical_poly.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/numerical_poly.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/numerical_poly.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": 23.1054852321, "max_line_length": 91, "alphanum_fraction": 0.5584368152, "num_tokens": 2061, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8962513675912912, "lm_q2_score": 0.7341195269001831, "lm_q1q2_score": 0.6579556299597608}} {"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\nc09x_mu := 0.0617:\nc09x_kappa := 1.245:\nc09x_alpha := 0.0483:\n\nc09x_f0 := s -> 1 + c09x_mu*s^2*exp(-c09x_alpha*s^2) + c09x_kappa*(1 - exp(-1/2*c09x_alpha*s^2)):\nc09x_f := x -> c09x_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(c09x_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "98e7f5d1033eb3b3a54b1015dfd1c2cb2a2bb525", "size": 526, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_c09x.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_c09x.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_c09x.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": 27.6842105263, "max_line_length": 97, "alphanum_fraction": 0.644486692, "num_tokens": 213, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9496693674025232, "lm_q2_score": 0.6926419894793246, "lm_q1q2_score": 0.6577808799852554}} {"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\n$define gga_c_pbe_params\n$include \"gga_c_pbe.mpl\"\n\n$include \"lda_c_2d_amgb.mpl\"\n\nrs2D_factor := 1.704:\nq2d_dd := 1e6:\n\nq2d_rs2D := (rs, xt) -> rs2D_factor*rs*sqrt(X2S*xt)/RS_FACTOR:\n\nfac := t -> t^4*(1 + t^2)/(q2d_dd + t^6):\n\nf_q2d := (rs, z, xt, xs0, xs1) ->\n (1 - fac(tt(rs, z, xt)))*f_pbe(rs, z, xt, xs0, xs1) + fac(tt(rs, z, xt))*f_amgb(q2d_rs2D(rs, xt), z):\n\nf := (rs, z, xt, xs0, xs1) -> f_q2d(rs, z, xt, xs0, xs1):\n", "meta": {"hexsha": "2b79dd60e50d0809ca14960e3b61843c4a2dc38f", "size": 686, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_c_q2d.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_q2d.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_q2d.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": 25.4074074074, "max_line_length": 103, "alphanum_fraction": 0.6282798834, "num_tokens": 286, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632916317102, "lm_q2_score": 0.7090191337850932, "lm_q1q2_score": 0.6575183177368079}} {"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: lda_exc *)\n(* prefix:\n lda_c_pz_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_pz_params * )(p->params);\n*)\n\n$ifdef lda_c_pz_params\nparams_a_gamma := [-0.1423, -0.0843]:\nparams_a_beta1 := [ 1.0529, 1.3981]:\nparams_a_beta2 := [ 0.3334, 0.2611]:\nparams_a_a := [ 0.0311, 0.01555]:\nparams_a_b := [-0.048, -0.0269]:\nparams_a_c := [ 0.0020, 0.0007]:\nparams_a_d := [-0.0116, -0.0048]:\n$endif\n\n(* Equation C3 *)\nec_low := (i, rs) -> params_a_gamma[i] / \\\n (1 + params_a_beta1[i]*sqrt(rs) + params_a_beta2[i]*rs):\n\n(* Equation [1].C5 *)\nec_high := (i, rs) -> params_a_a[i]*log(rs) + params_a_b[i] \\\n + params_a_c[i]*rs*log(rs) + params_a_d[i]*rs:\n\nec := (i, x) -> my_piecewise3(x >= 1, ec_low(i, x), ec_high(i, x)):\n\nf_pz := (rs, zeta) -> \\\n ec(1, rs) + (ec(2, rs) - ec(1, rs))*f_zeta(zeta):\n\nf := (rs, zeta) -> f_pz(rs, zeta):\n", "meta": {"hexsha": "0fa5067566b10b3d8259784278a908a082b93183", "size": 1121, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pz.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pz.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pz.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": 27.3414634146, "max_line_length": 68, "alphanum_fraction": 0.5967885816, "num_tokens": 429, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767874818408, "lm_q2_score": 0.749087201911703, "lm_q1q2_score": 0.6573066314772421}} {"text": "######################################################################\n\n# Complex numbers\n\n`is_element/CC` := (x) -> type(x,constant):\n\n`is_equal/CC` := (x,y) -> evalb(simplify(y-x) = 0):\n\n`is_leq/CC` := NULL;\n\n`is_leq_lex/CC` := proc(x,y)\n local z;\n z := simplify(y - x);\n if is(Re(z) > 0) then\n return true;\n elif is(Re(z) < 0) then\n return false;\n elif is(Im(z) > 0) then\n return true;\n elif is(Im(z) < 0) then\n return false;\n fi;\n return true;\nend:\n\n`random_element/CC` := proc()\n rand(-720..720)()/(360) + rand(-720..720)()/(360) * I;\nend:\n\n`list_elements/CC` := NULL;\n`count_elements/CC` := NULL;\n\n######################################################################\n# C(N) is the vector space CC^N\n\n`is_element/C` := (N::posint) -> (x) -> type(x,[constant$N]);\n\n`is_equal/C` := (N::posint) -> (x,y) -> evalb(simplify(x -~ y) = [0$N]);\n\n`is_leq/C` := NULL;\n\n`is_leq_lex/C` := (N::posint) -> proc(x,y)\n local i,z;\n for i from 1 to n do\n z := simplify(y[i] - x[i]);\n if is(Re(z) > 0) then\n return true;\n elif is(Re(z) < 0) then\n return false;\n elif is(Im(z) > 0) then\n return true;\n elif is(Im(z) < 0) then\n return false;\n fi;\n od;\n return true;\nend:\n\n`is_zero/C` := (N::posint) -> (x) -> evalb(simplify(x) = [0$N]);\n\n`norm_2/C` := (N::posint) -> proc(x) local i; sqrt(add(abs(x[i])^2,i=1..N)); end:\n\n`dot/C` := (N::posint) -> proc(x,y) local i; add(x[i]*conjugate(y[i]),i=1..N); end:\n\n`d_2/C` := (N::posint) -> (x,y) -> `norm_2/C`(N)(x -~ y);\n\n`random_element/C` := (N::posint) -> proc() local i; [seq(`random_element/CC`(),i=1..N)] end;\n\n`list_elements/C` := NULL;\n`count_elements/C` := NULL;", "meta": {"hexsha": "7ec361d9e3c2f4233ba53df8fc1d11ace4c1f7e7", "size": 1618, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/C.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/C.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/C.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": 23.1142857143, "max_line_length": 93, "alphanum_fraction": 0.5092707046, "num_tokens": 589, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127529517043, "lm_q2_score": 0.7690802423634961, "lm_q1q2_score": 0.656727426997377}} {"text": "#@ Not autoload\n\n# This gives a two-parameter family of embeddings of the trefoil in R^3\n\ntrefoil0 := proc(t,a,b)\n [(1 + a * cos(3 * t)) * cos(2 * t),\n (1 + a * cos(3 * t)) * sin(2 * t),\n b * sin(3 * t)]\nend:\n\n# This is a particular embedding from the above family for which the\n# speed is just sqrt(8)*(1 + 2/3 * cos(3*t)). For a typical element\n# of the above family, the speed is a much more complicated function.\n\ntrefoil := (t) -> trefoil0(t,2/3,2/9*sqrt(7));\n\nTrefoil := table():\n\nTrefoil[\"x\"] := trefoil(t,2/3,2*sqrt(7)/9);\nTrefoil[\"t\"] := t;\nTrefoil[\"v\"] := combine(simplify(expand(map(diff,Trefoil[\"x\"],t)))) assuming t > 0;\nTrefoil[\"speed\"] := combine(simplify(factor(expand(`norm_2/R`(3)(Trefoil[\"v\"]))))) assuming t > 0;\nTrefoil[\"s\"] := int(Trefoil[\"speed\"],t);\nTrefoil[\"v_hat\"] := combine(factor(expand(Trefoil[\"v\"] /~ Trefoil[\"speed\"]))) assuming t > 0;\nTrefoil[\"T\"] := Trefoil[\"v_hat\"];\nTrefoil[\"a\"] := map(diff,Trefoil[\"v\"],t);\nTrefoil[\"v_hat_dot\"] := combine(factor(expand(map(diff,Trefoil[\"v_hat\"],t)))) assuming t > 0;\nTrefoil[\"curvature\"] := combine(simplify(factor(expand(`norm_2/R`(3)(Trefoil[\"v_hat_dot\"]))))) assuming t > 0;\nTrefoil[\"radius_of_curvature\"] := simplify(1/Trefoil[\"curvature\"]);\nTrefoil[\"N\"] := factor(combine(factor(expand(rationalize(Trefoil[\"v_hat_dot\"] /~ Trefoil[\"curvature\"]))))) assuming t > 0;\nTrefoil[\"B\"] := factor(combine(factor(expand(`cross_product`(Trefoil[\"T\"],Trefoil[\"N\"]))))) assuming t > 0;\n\n\n\n", "meta": {"hexsha": "7e81857d13aa0c141658c54a26c4e142a7170ce9", "size": 1454, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/knots/trefoil.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/knots/trefoil.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/knots/trefoil.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": 41.5428571429, "max_line_length": 122, "alphanum_fraction": 0.6451169188, "num_tokens": 480, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8872045996818986, "lm_q2_score": 0.7401743620390163, "lm_q1q2_score": 0.6566860985676302}} {"text": "kernelopts(assertlevel=2): # be strict on all assertions while testing\nkernelopts(opaquemodules=false): # allow testing of internal routines\nif not (NewSLO :: `module`) then\n WARNING(\"loading NewSLO failed\");\n `quit`(3);\nend if;\n\nwith(Hakaru):\nwith(NewSLO):\nwith(Partition):\n\n# covers primitive constructs\nmodel1 :=\n Bind(Gaussian(0,1), x,\n Bind(Msum(Ret(0),Weight(1,Lebesgue(-infinity,infinity))), y,\n Ret(1/exp(x^2+y^2)))):\n\n# simplifies to\nmodel1s :=\n Bind(Gaussian(0,1), x,\n Msum(Ret(exp(-x^2)),\n Bind(Lebesgue(-infinity,infinity), y,\n Ret(exp(-(x^2+y^2)))))):\n\nCodeTools[Test](value(integrate(model1,z->z)), (sqrt(Pi)+1)/sqrt(3), equal,\n label=\"primitive constructs + integrate + value\");\n\nTestHakaru(model1, model1s, label = \"primitive constructs simplification\");\n\n# Unknown measures -- no changes\nu1 := Bind(m, x, Ret(x^2)):\nu2 := Bind(Gaussian(0,1), x, m(x)):\n\nTestHakaru(u1, label = \"binding unknown m\");\nTestHakaru(u2, u2, label = \"sending to unknown m\");\n\n# hygiene for Bind\nTestHakaru(Bind(Bind(Uniform(0,1),x,Ret(x^2)),y,Ret(x^3)),\n Ret(x^3),\n label = \"hygiene for Bind\");\n\n# example with an elaborate simplifier to do reordering of\n# integration, which in turn integrates out a variable\nmodel3 := Bind(Gaussian(0,1),x,Gaussian(x,1)):\n\nTestHakaru(model3, Gaussian(0,sqrt(2)),\n simp = (lo -> subsindets(lo, 'specfunc(Int)',\n i -> subsindets(IntegrationTools[CollapseNested](\n IntegrationTools[Combine](i)), 'Int(anything,list)',\n i -> subsop(0=int, applyop(ListTools[Reverse], 2, i))))),\n label = \"use simplifier to integrate out variable\");\n\nTestHakaru(Bind(GammaD(1,1),lambda,PoissonD(lambda)), NegativeBinomial(1,1/2),\n label = \"integrate out GammaD with PoissonD likelihood to Geometric\");\nTestHakaru(Bind(GammaD(r,1/(1/p-1)),lambda,PoissonD(lambda)), NegativeBinomial(r,p),\n ctx = [04,Ret(4),Ret(x)),y,\n Ret(y^2))):\nmodel4s := { Bind(Gaussian(0,1),x,piecewise(x<0,Ret(0),40]);\nmodule()\n local d, m, uMax, kb, result;\n for d in [Gaussian(0,1), GammaD(1,1)] do\n m := Bind(d, x,\n piecewise(And(0=y,Ret(false)))),\n Bind(Uniform(0,1),x,\n Bind(Uniform(0,1),y,\n piecewise(x x), label = \"2 uniform - no change\");\nTestHakaru(introLO, introLOs, simp = ((x,y) -> value(x)), label = \"2 uniform + value = elimination\");\nTestHakaru(introLO, introLOs, label = \"2 uniform + simplifier elimination\");\n\n# a variety of other tests\nTestHakaru(LO(h,(x*applyintegrand(h,5)+applyintegrand(h,3))/x), Weight(1/x, Msum(Weight(x, Ret(5)), Ret(3))));\nTestHakaru(Bind(Gaussian(0,1),x,Weight(x,Msum())), Msum());\nTestHakaru(Bind(Uniform(0,1),x,Weight(x^alpha,Ret(x))), Weight(1/(1+alpha),BetaD(1+alpha,1)));\nTestHakaru(Bind(Uniform(0,1),x,Weight(x^alpha*(1-x)^beta,Ret(x))), Weight(Beta(1+alpha,1+beta),BetaD(1+alpha,1+beta)));\nTestHakaru(Bind(Uniform(0,1),x,Weight((1-x)^beta,Ret(x))), Weight(1/(1+beta),BetaD(1,1+beta)));\n\n# tests that basic densities are properly recognized\n# continuous\nTestHakaru(Bind(Uniform(0,1),x,Weight(x*2,Ret(x))), BetaD(2,1),\n label=\"BetaD(2,1) recog\");\nTestHakaru(BetaD(alpha,beta), label=\"BetaD recog.\");\nTestHakaru(GammaD(a,b), label=\"GammaD recog.\", ctx = [a>0,b>0]);\nTestHakaru(GammaD(1/2,2), label=\"GammaD(1/2,2) recog.\");\nTestHakaru(LO(h, int(exp(-x/2)*applyintegrand(h,x),x=0..infinity)), Weight(2,GammaD(1,2)), label=\"GammaD(1,2) recog.\");\nTestHakaru(LO(h, int(x*exp(-x/2)*applyintegrand(h,x),x=0..infinity)), Weight(4,GammaD(2,2)), label=\"GammaD(2,2) recog.\");\nTestHakaru(Bind(Lebesgue(-infinity,infinity), x, Weight(1/x^2, Ret(x))));\nTestHakaru(Cauchy(loc,scale), ctx = [scale>0], label=\"Cauchy recog.\");\nTestHakaru(StudentT(nu,loc,scale), ctx=[nu>0,scale>0], label = \"StudentT recog.\");\nTestHakaru(StudentT(1,loc,scale),Cauchy(loc,scale), ctx = [scale>0],\n label = \"StudentT(1,loc,scale) recog.\");\n# discrete\nTestHakaru(Weight(1/26,Counting(17,43)), label=\"Discrete uniform recog.\");\nTestHakaru(NegativeBinomial(r,1-p-q), label=\"NegativeBinomial recog.\");\nTestHakaru(Poisson(foo/exp(bar)), label=\"Poisson recog.\");\n\n# how far does myint get us?\nTestHakaru(\n Bind(Uniform(0,1),x,Weight(x,Ret(Unit))),\n Weight(1/2,Ret(Unit)),\n label = \"eliminate Uniform\");\n\n# just the front-end is already enough to get this\nTestHakaru(\n Bind(Weight(1/2,Ret(Unit)),x,Ret(Unit)),\n Weight(1/2, Ret(Unit)),\n label = \"integrate at work\");\n\n# and more various\nmodel_exp := Bind(Uniform(-1,1),x,Ret(exp(x))):\nTestHakaru(model_exp, model_exp, label = \"uniform -1..1 into exp\");\nTestHakaru(LO(h, IntegrationTools[Expand](Int((1+y)*applyintegrand(h,y),y=0..1))), Msum(Uniform(0,1), Weight(1/2,BetaD(2,1))));\nTestHakaru(Bind(Uniform(0,1),x,Bind(LO(h, IntegrationTools[Expand](Int((1+y)*applyintegrand(h,y),y=0..1))),y,Ret([x,y]))), Weight(3/2,Bind(Uniform(0,1),x,Msum(Weight(2/3,Bind(Uniform(0,1),y,Ret([x,y]))),Weight(1/3,Bind(BetaD(2,1),y,Ret([x,y])))))));\n\n# easy-easy-HMM\neeHMM := Bind(GammaD(1,1),t,\n Weight(NewSLO:-density[Gaussian](0,1/sqrt(t))(a),\n Ret(t))):\nees := Weight(1/(a^2+2)^(3/2), GammaD(3/2, 1/((1/2)*a^2+1))):\n\n\nTestHakaru(eeHMM, ees, ctx = [a::real], label = \"easy-easy-HMM\");\n\n# from an email conversation on Sept. 11\nmodel6 := Bind(Gaussian(0,1),x, piecewise(x>4,Ret(4),Ret(x))):\nTestHakaru(model6, model6, label = \"clamped Gaussian\");\n\n# and now models (then tests) taken from Tests.RoundTrip\nt1 := Bind(Uniform(0, 1), a0, Msum(Weight(a0, Ret(Unit)))):\nt2 := BetaD(1,1):\nt2s := Uniform(0, 1):\nt3 := Gaussian(0,10):\nt4 := Bind(BetaD(1, 1), a0,\n Bind(Msum(Weight(a0, Ret(true)),\n Weight((1-a0), Ret(false))), a1,\n Ret(Pair(a0, a1)))):\nt4s := Bind(Uniform(0, 1), a0,\n Msum(Weight(a0, Ret(Pair(a0, true))),\n Weight((1+(a0*(-1))), Ret(Pair(a0, false))))):\nt5 := Bind(Msum(Weight((1/2), Ret(Unit))), a0, Ret(Unit)):\nt5s := Weight((1/2), Ret(Unit)):\nt6 := Ret(5):\nt7 := Bind(Uniform(0, 1), a0,\n Bind(Msum(Weight((a0+1), Ret(Unit))), a1, Ret((a0*a0)))):\nt7s := Bind(Uniform(0,1),a3,Weight(a3+1,Ret(a3^2))):\nt7n := Bind(Uniform((-1), 0), a0,\n Bind(Msum(Weight((a0+1), Ret(Unit))), a1, Ret((a0*a0)))):\nt7ns := Bind(Uniform(-1,0),a3,Weight(a3+1,Ret(a3^2))):\nt8 := Bind(Gaussian(0, 10), a0, Bind(Gaussian(a0, 20), a1, Ret(Pair(a0, a1)))):\nt9 := Bind(Lebesgue(-infinity,infinity), a0,\n Bind(Msum(Weight(piecewise(And((3=a0, Msum(), a0>=7, Msum(), Weight(1/2, Ret(a0)))):\nt9s := Weight(2, Uniform(3,7)):\n\n#t23, \"bayesNet\", to show exact inference. Original used bern, which\n# is here expanded in terms of MSum.\nt23 :=\n Bind(Msum(Weight((1/2), Ret(true)), Weight((1-(1/2)), Ret(false))), a0,\n Bind(Msum(Weight(piecewise(a0 = true, (9/10), (1/10)), Ret(true)),\n Weight((1-piecewise(a0 = true, (9/10), (1/10))), Ret(false))), a1,\n Bind(Msum(Weight(piecewise(a0 = true, (9/10), (1/10)), Ret(true)),\n Weight((1-piecewise(a0 = true, (9/10), (1/10))), Ret(false))), a2,\n Ret(Pair(a1, a2))))):\nt23s := Msum(Weight(41/100,Ret(Pair(true,true))),\n Weight(9/100,Ret(Pair(true,false))),\n Weight(9/100,Ret(Pair(false,true))),\n Weight(41/100,Ret(Pair(false,false)))):\n\n# to exercise myint_pw\nmodel_pw := Bind(Uniform(0,4), x,\n piecewise(x<1, Ret(x), x<2, Ret(2*x), x<3, Ret(3*x), Ret(5*x))):\nmodel_pw1 := { Bind(Uniform(0,4), x,\n piecewise(x<1, Ret(x), x<2, Ret(2*x), x<3, Ret(3*x), 3=3, Weight(5,Ret(x)))):\nmodel_pw3_r := { Bind(Uniform(0,4), x,\n piecewise(x<1, Ret(x), x<2, Weight(2,Ret(x)), x<3, Weight(3,Ret(x)), x>=3, Weight(5,Ret(x)))) ,\n Bind(Uniform(0,4),x,\n piecewise(x < 1,Ret(x),1 <= x and x < 2,Weight(2,Ret(x)),2 <= x and x < 3,Weight(3,Ret(x)),3 <= x,Weight(5,Ret(x))))\n}:\nmodel_pw5 := Bind(Uniform(0,4), x, Weight(piecewise(x<1, 1, x<2, 2, x<3, 3, x>=3, 5),Ret(x))):\nTestHakaru(model_pw , model_pw1, label = \"multi-branch choice\");\nTestHakaru(model_pw3, model_pw3_r, label = \"fake multi-branch weight\");\nTestHakaru(model_pw2, model_pw5, label = \"proper multi-branch weight\");\n\nfake_pw1 := Bind(Uniform(1,3),x, piecewise(0 < x, Msum(), Ret(x))):\nfake_pw2 := Bind(Uniform(1,3),x, piecewise(x < 0, Ret(x), Msum())):\nTestHakaru(fake_pw1, Msum(), label = \"fake piecewise 1\"):\nTestHakaru(fake_pw2, Msum(), label = \"fake piecewise 2\"):\n\n# t43 without the explicit lam\nt43 := piecewise(x0=true, Uniform(0, 1), Bind(BetaD(1, 1), a1, Ret(a1))):\nt43s := Uniform(0, 1):\n\nt80 := Bind(GammaD(1, 1), a0, Gaussian(0, a0)):\n\nTestHakaru(t1, t5s, label = \"t1\");\nTestHakaru(t2, t2s, label = \"t2\");\nTestHakaru(t3, t3, label = \"t3\");\nTestHakaru(t4, t4s, label = \"t4\");\nTestHakaru(t5, t5s, label = \"t5\");\nTestHakaru(t6, t6, label = \"t6\");\nTestHakaru(t7, t7s, label = \"t7\");\nTestHakaru(t7n, t7ns, label = \"t7n\");\nTestHakaru(t8, t8, label = \"t8\");\nTestHakaru(t9, t9s, label = \"t9\");\nTestHakaru(t9a, t9s, label = \"t9a\");\nTestHakaru(t23, t23s, label = \"t23\");\nTestHakaru(t43, t43s, label = \"t43\"):\n\nTestHakaru(t80, t80, label = \"t80\");\n\n## based on https://github.com/hakaru-dev/hakaru/issues/60\nmodule()\n local kb, clamp_t, clamp_r;\n kb := [y::real]:\n clamp_t :=\n Bind(Gaussian(0,1),x,\n Partition(And(00,1,0), Weight(piecewise(x>1/2,0,1), Weight(piecewise(00,ind1,ind2), piecewise(c>0,ind1s,ind2s), label=\"simplify under piecewise\");\n\n# test how banish handles piecewise\nm1 := Uniform(0,1):\nm2 := BetaD(2,1):\nm3 := BetaD(1,2):\nbp := proc() Bind(Gaussian(0,1), x,\n Bind(Gaussian(0,1), y,\n piecewise(_passed))) end proc:\nTestHakaru(bp(x>y, m1, m2 ), Msum(Weight(1/2, m1), Weight(1/2, m2) ), label=\"banish piecewise 1\");\nTestHakaru(bp(x>0, m1, m2 ), Msum(Weight(1/2, m1), Weight(1/2, m2) ), label=\"banish piecewise 2\");\nTestHakaru(bp(y>0, m1, m2 ), Msum(Weight(1/2, m1), Weight(1/2, m2) ), label=\"banish piecewise 3\");\nTestHakaru(bp(x>y, m1, x>0, m2, m3), Msum(Weight(1/2, m1), Weight(1/8, m2), Weight(3/8, m3)), label=\"banish piecewise 4\");\nTestHakaru(bp(x>0, m1, x>y, m2, m3), Msum(Weight(1/2, m1), Weight(1/8, m2), Weight(3/8, m3)), label=\"banish piecewise 5\");\nTestHakaru(bp(y>x, m1, y>0, m2, m3), Msum(Weight(1/2, m1), Weight(1/8, m2), Weight(3/8, m3)), label=\"banish piecewise 6\");\nTestHakaru(bp(y>0, m1, y>x, m2, m3), Msum(Weight(1/2, m1), Weight(1/8, m2), Weight(3/8, m3)), label=\"banish piecewise 7\");\n\n# Simplify is not yet idempotent\nTestHakaru(Bind(Uniform(0,1), x, Weight(x, Uniform(0,x))), Weight(1/2, BetaD(1, 2)));\n\n# Test for change of variables; see Tests/Relationships.hs\n# t1\n# cv1 := Bind(Gaussian(mu, sigma), x, Ret((x-mu)/sigma)):\n# cv1s := Gaussian(0,1):\n# TestHakaru(cv1, cv1s, ctx = [sigma>0], label = \"renormalize Gaussian\");\n\n# t28\n# cv2 := Bind(BetaD(a,b), x, Ret(1-x)):\n# cv2s := BetaD(b,a):\n# TestHakaru(cv2, cv2s, ctx=[a>0,b>0], label = \"swap BetaD\");\n\nunk_pw := Bind(m, y, Bind(Gaussian(0,1), x, piecewise(x<0, Ret(-x), Ret(x)))):\nunk1 := Bind(Gaussian(0,1), x, Bind(m, y, Bind(Gaussian(x,1), z, Ret([y,z])))):\nunk1s := Bind(m, y, Bind(Gaussian(0,sqrt(2)), z, Ret([y,z]))):\nunk2 := Bind(Gaussian(0,1), x, Bind(Gaussian(x,1), z, Bind(m, y, Ret([y,z])))):\nunk2s := Bind(Gaussian(0,sqrt(2)), z, Bind(m, y, Ret([y,z]))):\nunk3 := Bind(Gaussian(0,1), x, Bind(m(x), y, Bind(Gaussian(x,1), z, Ret([y,z])))):\nunk4 := Bind(Gaussian(0,1), x, Bind(Gaussian(x,1), z, Bind(m(x), y, Ret([y,z])))):\nTestHakaru(unk_pw, unk_pw, label=\"Don't simplify Integrand willy-nilly\");\nTestHakaru(unk1, unk1s, label=\"Banish into Integrand 1\");\nTestHakaru(unk2, unk2s, label=\"Banish into Integrand 2\");\nTestHakaru(unk3, unk3, label=\"Banish into Integrand 3\");\nTestHakaru(unk4, unk4, label=\"Banish into Integrand 4\");\n\n# Disintegration of easierRoadmapProg1 -- variables to be integrated out\nrmProg1 := Msum(Weight(1, Msum(Weight(1, Msum(Weight(1, Msum(Weight(1, Bind(Lebesgue(-infinity,infinity), a4, Msum(Weight(1, Msum(Weight(1, Bind(Lebesgue(-infinity,infinity), a5, Msum(Weight(1, Bind(Lebesgue(-infinity,infinity), a6, Msum(Weight(((exp((-(((p3-a6)*(p3-a6))*(1/(2*exp((ln(a5)*2)))))))*(1/a5))*(1/exp((ln((2*Pi))*(1/2))))), Msum(Weight(1, Bind(Lebesgue(-infinity,infinity), a7, Msum(Weight(((exp((-(((a6-a7)*(a6-a7))*(1/(2*exp((ln(a4)*2)))))))*(1/a4))*(1/exp((ln((2*Pi))*(1/2))))), Msum(Weight(((exp((-(((p2-a7)*(p2-a7))*(1/(2*exp((ln(a5)*2)))))))*(1/a5))*(1/exp((ln((2*Pi))*(1/2))))), Msum(Weight(((exp((-((a7*a7)*(1/(2*exp((ln(a4)*2)))))))*(1/a4))*(1/exp((ln((2*Pi))*(1/2))))), Msum(Weight((1/3), Msum(Weight(1, piecewise((a5<4), piecewise((1 Msum(Weight((1/2), Bind(Uniform(3, 8), a5, Ret(Pair(a5, p4)))), Weight((1/2), Bind(Uniform(1, 4), a6, Ret(Pair(p3, a6)))))), x2), a7, Ret(Pair(a7, (app(x1,a7)/app(x1,x2))))))),lam(x8,blah, unpair(( (p151 , p152) -> app(p152,lam(x153,blah, 1))), app(app(lam(x9,blah, lam(x10,blah, unpair(( (p11 , p12) -> app(lam(x13,blah, app(lam(x14,blah, Pair(Msum(Weight(x13, unpair(( (p15 , p16) -> p15), x14))), lam(x17,blah, (0+(x13*app(unpair(( (p18 , p19) -> p19), x14),x17)))))),app(lam(x20,blah, app(lam(x21,blah, Pair(Msum(Weight(x20, unpair(( (p22 , p23) -> p22), x21))), lam(x24,blah, (0+(x20*app(unpair(( (p25 , p26) -> p26), x21),x24)))))),app(lam(x27,blah, app(lam(x28,blah, app(lam(x29,blah, app(lam(x30,blah, Pair(Msum(Weight(x27, unpair(( (p31 , p32) -> p31), x28)), Weight(x29, unpair(( (p33 , p34) -> p33), x30))), lam(x35,blah, ((0+(x27*app(unpair(( (p36 , p37) -> p37), x28),x35)))+(x29*app(unpair(( (p38 , p39) -> p39), x30),x35)))))),Pair(Msum(), lam(x40,blah, 0)))),1)),app(lam(x41,blah, app(lam(x42,blah, Pair(Msum(Weight(x41, unpair(( (p43 , p44) -> p43), x42))), lam(x45,blah, (0+(x41*app(unpair(( (p46 , p47) -> p47), x42),x45)))))),app(lam(x48,blah, app(lam(x49,blah, app(lam(x50,blah, app(lam(x51,blah, Pair(Msum(Weight(x48, unpair(( (p52 , p53) -> p52), x49)), Weight(x50, unpair(( (p54 , p55) -> p54), x51))), lam(x56,blah, ((0+(x48*app(unpair(( (p57 , p58) -> p58), x49),x56)))+(x50*app(unpair(( (p59 , p60) -> p60), x51),x56)))))),Pair(Msum(), lam(x61,blah, 0)))),1)),app(lam(x62,blah, app(lam(x63,blah, Pair(Msum(Weight(x62, unpair(( (p64 , p65) -> p64), x63))), lam(x66,blah, (0+(x62*app(unpair(( (p67 , p68) -> p68), x63),x66)))))),unpair(( (p69 , p70) -> unpair(( (p71 , p72) -> unpair(( (p73 , p74) -> unpair(( (p75 , p76) -> unpair(( (p77 , p78) -> unpair(( (p79 , p80) -> unpair(( (p81 , p82) -> unpair(( (p83 , p84) -> unpair(( (p85 , p86) -> unpair(( (p87 , p88) -> app(lam(x89,blah, app(lam(x90,blah, Pair(Msum(Weight(x89, unpair(( (p91 , p92) -> p91), x90))), lam(x93,blah, (0+(x89*app(unpair(( (p94 , p95) -> p95), x90),x93)))))),app(lam(x96,blah, app(lam(x97,blah, Pair(Msum(Weight(x96, unpair(( (p98 , p99) -> p98), x97))), lam(x100,blah, (0+(x96*app(unpair(( (p101 , p102) -> p102), x97),x100)))))),app(lam(x103,blah, app(lam(x104,blah, app(lam(x105,blah, app(lam(x106,blah, Pair(Msum(Weight(x103, unpair(( (p107 , p108) -> p107), x104)), Weight(x105, unpair(( (p109 , p110) -> p109), x106))), lam(x111,blah, ((0+(x103*app(unpair(( (p112 , p113) -> p113), x104),x111)))+(x105*app(unpair(( (p114 , p115) -> p115), x106),x111)))))),Pair(Msum(), lam(x116,blah, 0)))),1)),piecewise((p12<4), piecewise((1 p119), x118))), lam(x121,blah, (0+(x117*app(unpair(( (p122 , p123) -> p123), x118),x121)))))),app(lam(x124,blah, app(lam(x125,blah, app(lam(x126,blah, app(lam(x127,blah, Pair(Msum(Weight(x124, unpair(( (p128 , p129) -> p128), x125)), Weight(x126, unpair(( (p130 , p131) -> p130), x127))), lam(x132,blah, ((0+(x124*app(unpair(( (p133 , p134) -> p134), x125),x132)))+(x126*app(unpair(( (p135 , p136) -> p136), x127),x132)))))),Pair(Msum(), lam(x137,blah, 0)))),1)),piecewise((p11<8), piecewise((3 p140), x139))), lam(x142,blah, (0+(x138*app(unpair(( (p143 , p144) -> p144), x139),x142)))))),app(lam(x145,blah, Pair(Ret(x145), lam(x146,blah, app(x146,x145)))),Pair(p11, p12)))),5), Pair(Msum(), lam(x147,blah, 0))), Pair(Msum(), lam(x148,blah, 0))))),1))),(1/5)), Pair(Msum(), lam(x149,blah, 0))), Pair(Msum(), lam(x150,blah, 0))))),1))),(1/3)))),((((1/Pi)*exp((((((((((p69*p71)*(p11*p11))*2)+((((p11*p11)*p73)*p76)*(-2)))+((p78*p80)*(p11*p11)))+((p12*p12)*(p81*p83)))+((p12*p12)*(p86*p88)))*(1/((((p11*p11)*(p11*p11))+(((p12*p12)*(p11*p11))*3))+((p12*p12)*(p12*p12)))))*(-(1/2)))))*exp((ln(((exp(((x -> piecewise(x<0, -337, ln(x)))(p11)*4))+((exp(((x -> piecewise(x<0, -337, ln(x)))(p12)*2))*exp(((x -> piecewise(x<0, -337, ln(x)))(p11)*2)))*3))+exp(((x -> piecewise(x<0, -337, ln(x)))(p12)*4))))*(-(1/2)))))*(1/10)))), x9)), x9)), x9)), x9)), x9)), x9)), x9)), x9)), x9)), x9))),1))),1))),1))),1))),1))),1)), x10))),x0),x8))))):\n TestHakaru(app(app(rmProg4,Pair(r1,r2)),Pair(p1,p2)), Msum(Weight(1/2, Bind(Uniform(3, 8), a5, Ret(Pair(Pair(a5, p2), exp((1/2)*(-p1+a5)*(a5+p1)*(p1^2*p2^2*r1^2+p1^2*p2^2*r2^2+2*p1^2*r1^2*a5^2-2*p1^2*r1*r2*a5^2+p1^2*r2^2*a5^2+p2^4*r1^2+2*p2^4*r1*r2+2*p2^4*r2^2+p2^2*r1^2*a5^2+p2^2*r2^2*a5^2)/((p2^4+3*p2^2*a5^2+a5^4)*(p1^4+3*p1^2*p2^2+p2^4)))*sqrt(p1^4+3*p1^2*p2^2+p2^4)/sqrt(p2^4+3*p2^2*a5^2+a5^4))))), Weight(1/2, Bind(Uniform(1, 4), a6, Ret(Pair(Pair(p1, a6), exp((1/2)*(-p2+a6)*(a6+p2)*(5*p1^4*r1^2-6*p1^4*r1*r2+2*p1^4*r2^2+2*p1^2*p2^2*r1^2-2*p1^2*p2^2*r1*r2+p1^2*p2^2*r2^2+2*p1^2*r1^2*a6^2-2*p1^2*r1*r2*a6^2+p1^2*r2^2*a6^2+p2^2*r1^2*a6^2+p2^2*r2^2*a6^2)/((p1^4+3*p1^2*a6^2+a6^4)*(p1^4+3*p1^2*p2^2+p2^4)))*sqrt(p1^4+3*p1^2*p2^2+p2^4)/sqrt(p1^4+3*p1^2*a6^2+a6^4)))))),\n label=\"rmProg4\",\n ctx= [30, sigma1>0, x::real]);\ninvgamma_gaussian := Bind(GammaD(shape,scale),lambda, Weight(NewSLO:-density[Gaussian](mu,lambda^(-1/2))(x), Ret(lambda))):\ninvgamma_gaussian_s := Weight(GAMMA(1/2+shape)*sqrt(scale)*((1/2)*scale*mu^2-scale*mu*x+(1/2)*scale*x^2+1)^(-shape)/(GAMMA(shape)*sqrt(scale*mu^2-2*scale*mu*x+scale*x^2+2)*sqrt(Pi)), GammaD(1/2+shape, 2*scale/(scale*mu^2-2*scale*mu*x+scale*x^2+2))):\nTestHakaru(invgamma_gaussian, invgamma_gaussian_s,\n label=\"invgamma_gaussian conjugacy\",\n ctx = [mu::real, shape>0, scale>0, x::real]);\ngaussian_invgamma_gaussian := Bind(GammaD(shape,scale),tau, Bind(Gaussian(mu0*sqrt(tau),1/sqrt(nu)),mu, Weight(NewSLO:-density[Gaussian](mu*tau^(-1/2),tau^(-1/2))(x), Ret([mu,tau])))):\ngaussian_invgamma_gaussian_s := Weight(GAMMA(1/2+shape)*sqrt(nu)*sqrt(scale)*(scale*mu0^2*nu-2*scale*mu0*nu*x+scale*nu*x^2+2*nu+2)^(-1/2-shape)*(2*nu+2)^shape/(GAMMA(shape)*sqrt(Pi)), Bind(GammaD(1/2+shape, 2*scale*(nu+1)/(scale*mu0^2*nu-2*scale*mu0*nu*x+scale*nu*x^2+2*nu+2)),tau, Bind(Gaussian(sqrt(tau)*(mu0*nu+x)/(nu+1), 1/sqrt(nu+1)),mu, Ret([mu,tau])))):\nTestHakaru(gaussian_invgamma_gaussian, gaussian_invgamma_gaussian_s,\n label=\"gaussian_invgamma_gaussian conjugacy\",\n ctx = [mu0::real, nu>0, shape>0, scale>0, x::real]);\ngamma_gamma := Bind(GammaD(alpha0,1/beta0),beta, Weight(NewSLO:-density[GammaD](alpha,1/beta)(x), Ret(beta))):\ngamma_gamma_s := Weight(beta0^alpha0*x^(alpha-1)*GAMMA(alpha+alpha0)*(beta0+x)^(-alpha-alpha0)/(GAMMA(alpha0)*GAMMA(alpha)), GammaD(alpha+alpha0, 1/(beta0+x))):\nTestHakaru(gamma_gamma, gamma_gamma_s, label=\"gamma_gamma conjugacy\",\n ctx = [alpha0>0, beta0>0, alpha>0, x>0]);\ngamma_poisson := Bind(GammaD(shape,scale),lambda, Weight(NewSLO:-density[PoissonD](lambda)(k), Ret(lambda))):\ngamma_poisson_s := Weight(scale^k*(scale+1)^(-k-shape)*GAMMA(k+shape)/(GAMMA(shape)*GAMMA(k+1)), GammaD(k+shape, scale/(scale+1))):\nTestHakaru(gamma_poisson, gamma_poisson_s, label=\"gamma_poisson conjugacy\",\n ctx=[shape>0, scale>0, k::nonnegint]);\n\n# For the following test, banishing fails because Maple currently evaluates\n# int(piecewise(x < y, 1/(1-x), 0), x = 0 .. 1) assuming y<1\n# to \"undefined\". (See ppaml-l discussion \"NewSLO giving weird output\"\n# around 2015-12-10.) The test is that we handle the failure gracefully.\nTestHakaru(Bind(Uniform(0,1), x, Uniform(x,1)),\n {Bind(Uniform(0,1), x, Uniform(x,1)),\n Bind(Uniform(0,1), x, Weight(ln(1/(1-x)), Ret(x)))},\n label=\"roundtrip despite banishing failure\");\n\nTestHakaru(Bind(Ret(ary(n,i,i*2)), v, Ret(idx(v,42))), Ret(84), label=\"basic array indexing\");\n\n#####################################################################\n#\n# Tests for type-directed simplification\n#\n#####################################################################\n\nmodule()\n local hpair, hbool, heither, hreal, hprob,\n ppair, ptrue, pfalse, pleft, pright,\n dpair, dtrue, dfalse, dleft, dright,\n unpair;\n uses CodeTools;\n hpair := (t1,t2) -> HData(DatumStruct(pair,[Konst(t1),Konst(t2)])):\n hbool := HData(DatumStruct(true,[]),DatumStruct(false,[])):\n heither := (t1,t2) -> HData(DatumStruct(left,[Konst(t1)]),DatumStruct(right,[Konst(t2)])):\n hreal := HReal():\n hprob := HReal(Bound(`>=`,0)):\n ppair := (p1,p2) -> PDatum(pair,PInl(PEt(p1,PEt(p2,PDone)))):\n ptrue := PDatum(true,PInl(PDone)):\n pfalse := PDatum(false,PInr(PInl(PDone))):\n pleft := p -> PDatum(left,PInl(PEt(p,PDone))):\n pright := p -> PDatum(right,PInr(PInl(PEt(p,PDone)))):\n dpair := (d1,d2) -> Datum(pair,Inl(Et(d1,Et(d2,Done)))):\n dtrue := Datum(true,Inl(Done)):\n dfalse := Datum(false,Inr(Inl(Done))):\n dleft := d -> Datum(left,Inl(Et(d,Done))):\n dright := d -> Datum(right,Inr(Inl(Et(d,Done)))):\n unpair := (e1,x,y,e0) -> case(e1,Branches(Branch(ppair(PVar(x),PVar(y)),e0))):\n TestSimplify(lam(pr,hpair(hprob,hreal),unpair(pr,x,y,sqrt(x^2)+y)),\n HFunction(hpair(hprob,hreal),hreal),\n lam(pr,hpair(hprob,hreal),unpair(pr,x,y,x+y)),\n label=\"Transfer function argument type to KB\");\n TestSimplify(lam(b,hbool,case(b,Branches(Branch(pfalse,3),Branch(ptrue,4)))),\n HFunction(hbool,HInt()),\n lam(b,hbool,case(b,Branches(Branch(ptrue,4),Branch(pfalse,3)))),\n label=\"Eta-expand pure function from boolean\");\n TestSimplify(lam(pr,hpair(hbool,hbool),unpair(pr,x,y,dpair(y,x))),\n HFunction(hpair(hbool,hbool), hpair(hbool,hbool)),\n lam(pr,hpair(hbool,hbool),case(pr,Branches(\n Branch(ppair(ptrue ,ptrue ), dpair(dtrue ,dtrue )),\n Branch(ppair(ptrue ,pfalse), dpair(dfalse,dtrue )),\n Branch(ppair(pfalse,ptrue ), dpair(dtrue ,dfalse)),\n Branch(ppair(pfalse,pfalse), dpair(dfalse,dfalse))))),\n label=\"Eta-expand pure function from pair of booleans\");\n TestSimplify(lam(b,hbool,\n Bind(Uniform(0,1),p,\n Weight(case(b,Branches(Branch(pfalse,1-p),\n Branch(ptrue,p))),\n Ret(p)))),\n HFunction(hbool,HMeasure(hreal)),\n lam(b,hbool,\n case(b,Branches(Branch(ptrue , Weight(1/2,BetaD(2,1))),\n Branch(pfalse, Weight(1/2,BetaD(1,2)))))),\n label=\"Eta-expand function from boolean to measure\");\nend module:\n\n###########\n#\n# RoundTrip tests; due to bug in CodeTest, use lower-level function directly\n\nTestTools:-SetRecord(false):\nmodule()\n local kb, rt1, rt1r;\n kb := [x::real]:\n rt1 := Context(kb, Bind(Gaussian(0,1), x, Ret(0))):\n rt1r := sprintf(\"%a\", eval(ToInert(Context(kb, Ret(0))), _Inert_ATTRIBUTE=NULL)):\n TestTools:-Try(\"simple case of RoundTrip\", RoundTrip(rt1), rt1r);\nend module:\n\n# Categorical distribution\nTestHakaru(Counting(0,11),\n label=\"Counting roundtrip\");\nTestHakaru(Bind(Counting(0,2),x,Weight(p^x*(1-p)^(1-x),Ret(x))),\n Categorical([1-p,p]),\n label=\"Categorical introduction\",\n ctx=[0<=p, p<=1]);\nTestHakaru(Bind(Categorical([p,1-p]),x,Weight(p^x*(1-p)^(1-x),Ret(x))),\n Weight(p*(1-p),Counting(0,2)),\n label=\"Categorical elimination\",\n ctx=[0<=p, p<=1]);\nmodule()\n local bern, burglary;\n bern := p -> Bind(Categorical(ary(2,i,piecewise(i=0,p,1-p))), i, Ret(i=0)):\n burglary := Bind(bern(1/10000), b,\n Bind(bern(piecewise(b=true,19/20,1/100)), a,\n Ret(a))):\n TestHakaru(burglary, bern(5047/500000), label=\"burglary\");\n TestHakaru(Bind(BetaD(alpha,beta), p, bern(p)),\n Weight(1/(alpha+beta), Bind(Categorical([alpha,beta]), i, Ret(i=0))),\n label=\"integrate BetaD out of BetaD-Bernoulli\"):\nend module:\n", "meta": {"hexsha": "bb5fc9426f234f5c23bd9123a987c1ab9b200b38", "size": 29807, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLOTests.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/NewSLOTests.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/NewSLOTests.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": 58.6751968504, "max_line_length": 4330, "alphanum_fraction": 0.6077095984, "num_tokens": 11445, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8596637505099167, "lm_q2_score": 0.7634837689358857, "lm_q1q2_score": 0.6563393202568701}} {"text": "######################################################################\n# W(N)(A) is Map(A,R^N)/Const(A,R^N). \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/W` rather\n# than the representation of the elements.\n\n`is_element/W` := (N::posint) -> (A::set) -> proc(x)\n `is_element/vector_functions`(N)(A)(x);\nend;\n\n######################################################################\n\n`normalise/W` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,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 for a in A do\n x0[a] := x0[a] -~ u;\n od;\n return(eval(x0));\nend;\n\n######################################################################\n\n`bottom_normalise/W` := (N::posint) -> (A::set) -> proc(x)\n local x0,u,a,i;\n\n u := [seq(min(seq(x[a][i],a in A)),i=1..N)];\n x0 := table():\n for a in A do \n x0[a] := x[a] -~ u;\n od:\n return(eval(x0));\nend;\n\n######################################################################\n\n`is_equal/W` := (N::posint) -> (A::set) -> proc(x,y) \n local x0,y0,a;\n\n x0 := `normalise/W`(N)(A)(x);\n y0 := `normalise/W`(N)(A)(y);\n\n return `is_equal/vector_functions`(N)(A)(x0,y0);\nend;\n\n######################################################################\n\n`is_leq/W` := NULL;\n\n######################################################################\n\n`is_zero/W` := (N::posint) -> (A::set) -> proc(x) \n local x0,a;\n\n x0 := `normalise/W`(N)(A)(x);\n return `is_zero/vector_functions`(N)(A)(x0);\nend;\n\n######################################################################\n\n`norm/W` := (N::posint) -> (A::set) -> proc(x) \n local x0,a;\n\n x0 := `normalise/W`(N)(A)(x);\n return `norm/vector_functions`(N)(A)(x0);\nend;\n\n######################################################################\n\n`width/W` := (N::posint) -> (A::set) -> proc(x)\n local i,a;\n max(seq(max(seq(x[a][i],a in A)) - min(seq(x[a][i],a in A)),i=1..N));\nend;\n\n######################################################################\n\n`random_element/W` := (N::posint) -> (A::set) -> proc()\n local x,a,u;\n\n u := [0$N];\n x := table();\n for a in A do\n x[a] := `random_element/R`(N)();\n u := u +~ x[a];\n od:\n u := u /~ nops(A);\n for a in A do \n x[a] := x[a] -~ u;\n od;\n\n return eval(x);\nend;\n\n`list_elements/W` := NULL;\n`count_elements/W` := NULL;\n\n######################################################################\n# Here C is assumed to be a subset of B, and rho is the usual map \n# from W(N,B) to W(N,C).\n\n`rho/W` := (B,C) -> proc(x)\n local y,c;\n\n y := table();\n for c in C do y[c] := x[c]; od;\n return eval(y);\nend;\n", "meta": {"hexsha": "c534754620d23b9ce87ee94abf04d60b8cac3b37", "size": 2708, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/W.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/W.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/W.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": 22.9491525424, "max_line_length": 71, "alphanum_fraction": 0.3999261448, "num_tokens": 772, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8723473614033683, "lm_q2_score": 0.7520125848754472, "lm_q1q2_score": 0.656016194158223}} {"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\na := -1:\nb := 11.8:\nc := 0.150670:\nd := 11.02e-3/RS_FACTOR:\n\n(* I added an abs() to this equation, as otherwise the f_num is\n complex for negative values of z. Of course it is not clear at all\n what was the original intential of Wilson, or if he even considered\n this problem. *)\nif evalb(Polarization = \"unpol\") then\n f_num := z -> a:\nelse\n (* without the max function we get a float exception for derivatives > 2 *)\n f_num := z -> a*sqrt(1 - m_max(m_abs(z), 1e-10)^(5/3)):\nend if:\nf_den := (rs, xt) -> b + c*xt^(51/16) + d*xt^2*rs + rs:\n\n(* Equation (25) *)\nf := (rs, z, xt, xs0, xs1) ->\n f_num(z)/f_den(rs, xt):\n\n", "meta": {"hexsha": "309ae9f6f613b73853c4f45c480c7a9efc8661e7", "size": 894, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_w94.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_w94.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_w94.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": 27.9375, "max_line_length": 79, "alphanum_fraction": 0.6319910515, "num_tokens": 301, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9252299653388754, "lm_q2_score": 0.7090191399336402, "lm_q1q2_score": 0.6560057542654011}} {"text": "(* type: lda_exc *)\n\na := 0.0311:\nb := -0.048:\nc := 0.009:\nd := -0.017:\n\nf_ls := (rs, zeta) -> a*log(rs) + b + c*rs*log(rs) + d*rs:\nf_ms := (rs, zeta) -> -0.06156 + 0.01898*log(rs):\nf_hs := (rs, zeta) -> 0.438/rs + 1.325/rs^(3/2) - 1.47/rs^2 - 0.4/rs^(5/2):\n\nf := (rs, zeta) -> my_piecewise3(\n rs < 0.7, f_ls(rs, zeta), my_piecewise3(rs < 10, f_ms(rs, zeta), f_hs(rs, zeta))):\n\n", "meta": {"hexsha": "dbe5c73adea77bc40f5f8b0260953db0d530d3bf", "size": 383, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_gk72.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_gk72.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_gk72.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": 25.5333333333, "max_line_length": 86, "alphanum_fraction": 0.5065274151, "num_tokens": 189, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9553191284552529, "lm_q2_score": 0.6859494485880928, "lm_q1q2_score": 0.6553006293895381}} {"text": "# Proof by PDF that X <~ rayleigh(1/sqrt(2*lambda)) == X^2 <~ exponential(lambda)\n\nPDF_rayleigh := (a, x) -> 2*x*exp(-x^2/a)/a;\n\nPDF_transform := (x) -> PDF_rayleigh(1,sqrt(x))*diff(sqrt(x),x);\nsimplify(PDF_transform(x));\n\nPDF_exponential := (l, x) -> l*exp(-l*x);\nsimplify(PDF_exponential(1, x));\n\nevalb(PDF_exponential(1, x) = PDF_transform(x));", "meta": {"hexsha": "2b5894d6bbf1873427fa505edfd0021d5dfd78de", "size": 347, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip2/t_exponential_to_rayleigh.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip2/t_exponential_to_rayleigh.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip2/t_exponential_to_rayleigh.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 31.5454545455, "max_line_length": 81, "alphanum_fraction": 0.6484149856, "num_tokens": 124, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9241418199787564, "lm_q2_score": 0.7090191399336402, "lm_q1q2_score": 0.6552342383780468}} {"text": "\n# Berechne kinematische Zwangsbedingungen für Viergelenkkette\n# Einleitung\n\n# Die impliziten kinematischen Zwangsbedingungen werden aufgestellt: Annahme : Alle MDH-Winkel seien unabhängig und die Kette sei offen\n# \n# fivebar1_OL -> Fünfgelenkkette, modellierung impliziten der Zwangsbedingungen mit Ausdrücken einer offenen Kette und basierend auf der MDH-Tabelle. \n# Bei Matlab: Abhängige Winkel durch die Ausdrücke von TE aus der Datei \"fourbar1TE_kinconstr_expl_mdh_sym_varpar\" ersetzen.\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, schappler@irt.uni-hannover.de, 2018-08\n# (C) Institut fuer Mechatronische Systeme, Leibniz Universitaet Hannover\n# \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:\nTrf\n;\n# Fourbar1 0-3-4-5-6-2-1-0\n# Schleife 0-1-2-4\nT_0_5 := combine(Matrix(Trf(1..4,1..4, 3)) . Matrix(Trf(1..4,1..4,4)). Matrix(Trf(1..4,1..4, 5)));\n# Schleife 0-3-5\nT_0_6:= combine(Matrix(Trf(1..4,1..4, 1)) . Matrix(Trf(1..4,1..4,2)) . Matrix(Trf(1..4,1..4,6)));\nh1t := T_0_6(1..3,4) - T_0_5(1..3,4);\ntmp := Transpose( Matrix(T_0_6(1..3,1..3)) ) . Matrix(T_0_5(1..3,1..3)); # nur anzeigen lassen für h1r\n;\n combine(tmp); # nur anzeigen lassen für h1r\n;\nh1r:=qJ1(t) + qJ2(t) - qJ3(t) - qJ4(t) - qJ5(t);\n# Zusammenstellen aller Zwangsbedingungen\nimplconstr_t := ; \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\n", "meta": {"hexsha": "76b916501219bba82505cce17683807389fb4e37", "size": 3521, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "systems/fivebar1/codegen/fivebar1IC_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/fivebar1/codegen/fivebar1IC_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/fivebar1/codegen/fivebar1IC_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": 45.7272727273, "max_line_length": 151, "alphanum_fraction": 0.7713717694, "num_tokens": 1132, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9073122163480667, "lm_q2_score": 0.721743200312399, "lm_q1q2_score": 0.6548464227095894}} {"text": "flat_torus_complex := proc(n::posint,m::posint)\n local f,g,T,V,E,F,R,r;\n\n f := (i) -> modp(i+1,n);\n g := (j) -> modp(j+1,m);\n \n V := [seq(seq([i,j],j=0..m-1),i=0..n-1)];\n E := [seq(seq([[i,j],[f(i),j]],j=0..m-1),i=0..n-1),\n seq(seq([[i,j],[i,g(j)]],j=0..m-1),i=0..n-1),\n seq(seq([[i,j],[f(i),g(j)]],j=0..m-1),i=0..n-1)];\n F := [seq(seq([[i,j],[f(i),j],[f(i),g(j)]],j=0..m-1),i=0..n-1),\n seq(seq([[i,j],[i,g(j)],[f(i),g(j)]],j=0..m-1),i=0..n-1)];\n\n T := table([]);\n\n T[\"vertices\"] := V;\n T[\"edges\"] := E;\n T[\"faces\"] := F;\n T[\"max_simplices\"] := F;\n T[\"simplices\"] := [map(v -> [v],V),op(E),op(F)];\n\n R := 3;\n r := 1;\n\n T[\"embedding_dim\"] := 3;\n T[\"embedding\"] :=\n table([seq(seq([i,j] = evalf(torus_embedding(R,r)(i/n,j/m)),j=0..m-1),i=0..n-1)]);\n\n T[\"plot\"] := `plot/simplicial_complex`(T[\"vertices\"])(T[\"faces\"],3,T[\"embedding\"]);\n\n return eval(T);\n\nend:", "meta": {"hexsha": "baa130728509e0fc136ab2e474261fe81aa86898", "size": 875, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/torus_complex.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/torus_complex.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/torus_complex.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": 26.5151515152, "max_line_length": 84, "alphanum_fraction": 0.4571428571, "num_tokens": 390, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894717137996, "lm_q2_score": 0.7310585727705126, "lm_q1q2_score": 0.6541435141211713}} {"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\nmalpha := (x, t) -> (t - x^2/8)/K_FACTOR_C:\n\ngx_cx0 := 4/3*(2/Pi)^(1/3):\ngx_cx1 := X_FACTOR_C:\n\ngx_c0 := 0.827411:\ngx_c1 := -0.643560:\n\ngx_gx0 := a ->\n + gx_cx0/gx_cx1\n + a*(gx_c0 + gx_c1*a)/(1.0 + (gx_c0 + gx_c1 - 1)*a) * (1 - gx_cx0/gx_cx1):\n\ngx_alphainf := 0.852:\ngx_gx1 := a ->\n 1 + (1 - gx_alphainf)*(1 - a)/(1 + a):\n\nf_gx_a := a->\n + gx_gx0(a)*Heaviside(1 - a)\n + gx_gx1(a)*Heaviside(a - 1):\n\nf := (rs, x, t, u) ->\n f_gx_a(malpha(x, t)):\n", "meta": {"hexsha": "0111c86190b333681d0263face961e5c27e55715", "size": 715, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_gx.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_gx.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_gx.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": 21.6666666667, "max_line_length": 76, "alphanum_fraction": 0.586013986, "num_tokens": 314, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9304582554941719, "lm_q2_score": 0.7025300449389326, "lm_q1q2_score": 0.6536748800461214}} {"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(* prefix:\n mgga_k_lk_params *params;\n\n assert(p->params != NULL);\n params = (mgga_k_lk_params * ) (p->params);\n*)\n\nlk_p := x -> X2S^2*x^2:\nlk_q := u -> X2S^2*u:\n\n(* Equation (10) *)\nlk_delta := (p, q) -> 8/81*q^2 - 1/9*p*q + 8/243*p^2:\n(* Equation (15) *)\nlk_f0 := (x1, x2) -> 1 + params_a_kappa*(2 - 1/(1+x1/params_a_kappa) - 1/(1+x2/params_a_kappa)):\n(* Equation (16) *)\nlk_x1 := (p, q) -> 5/27*p + lk_delta(p,q) + (5/27*p)^2/params_a_kappa:\n(* Equation (17) *)\nlk_x2 := (p, q) -> 2*(5/27*p)*lk_delta(p,q)/params_a_kappa + (5/27*p)^3/params_a_kappa^2:\n\n(* Full functional *)\nlk_f := (x, u) ->\n lk_f0(lk_x1(lk_p(x),lk_q(u)), lk_x2(lk_p(x),lk_q(u))):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_kinetic(lk_f, rs, z, xs0, xs1, u0, u1):\n", "meta": {"hexsha": "170e5f15c1af5eb8bdb6f0489e821e59e1359f88", "size": 1008, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_k_lk.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_k_lk.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_k_lk.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": 28.8, "max_line_length": 96, "alphanum_fraction": 0.5982142857, "num_tokens": 418, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951698485603, "lm_q2_score": 0.6992544210587585, "lm_q1q2_score": 0.6533799535325553}} {"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_k_pc07_params *params;\n\n assert(p->params != NULL);\n params = (mgga_k_pc07_params * ) (p->params);\n*)\n\npc07_p := x -> X2S^2*x^2:\npc07_q := u -> X2S^2*u:\n\n(* Equation (15) redefined with decaying exponentials to avoid inf/inf situations *)\npc07_fab0 := z -> exp(-params_a_a*params_a_b/z) * (1+exp(-params_a_a/(params_a_a-z)))^params_a_b/(exp(-params_a_a/z) + exp(-params_a_a/(params_a_a-z)))^params_a_b:\n(* The function is ill-behaving at z=0 and z=a.\n However, it also goes to 0 and 1 very quickly near these points.\n pc07_fab0(params_a_a/40) is ~ 1.6e-17, which is smaller than machine epsilon.\n*)\npc07_thr := 1/40:\npc07_zlo := pc07_thr*params_a_a:\npc07_zhi := (1-pc07_thr)*params_a_a:\npc07_fab := z -> my_piecewise5(z<=pc07_zlo, 0, z>=pc07_zhi, 1, pc07_fab0( m_min(pc07_zhi, m_max(pc07_zlo, z)) ) ):\n\n(* Equation (7) *)\npc07_Delta := (x, u) ->\n 8*pc07_q(u)^2/81 - pc07_p(x)*pc07_q(u)/9 + 8*pc07_p(x)^2/243:\n\npc07_f_W := x -> 5*pc07_p(x)/3:\n\n(* Equation (8) *)\npc07_GE4 := (x, u) ->\n 1 + 5*pc07_p(x)/27 + 20*pc07_q(u)/9 + pc07_Delta(x, u):\n\n(* Equation (11) *)\npc07_GE4_M := (x, u) ->\n pc07_GE4(x, u)/sqrt(1 + pc07_Delta(x, u)^2/(1 + pc07_f_W(x))^2):\n\n(* Equation (17) *)\npc07_f := (x, u) ->\n pc07_f_W(x) + (pc07_GE4_M(x, u) - pc07_f_W(x))*pc07_fab(pc07_GE4_M(x, u) - pc07_f_W(x)):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_kinetic(pc07_f, rs, z, xs0, xs1, u0, u1):\n", "meta": {"hexsha": "0a5680616591ad21a809dfbe8fb74c3918d0c05b", "size": 1671, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_k_pc07.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_k_pc07.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_k_pc07.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": 32.7647058824, "max_line_length": 163, "alphanum_fraction": 0.6403351287, "num_tokens": 670, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9173026505426832, "lm_q2_score": 0.712232184238947, "lm_q1q2_score": 0.6533324704041907}} {"text": "######################################################################\n\n`is_element/partord` := (A::set) -> proc(R)\n global reason;\n\n if not `is_element/autorel`(A)(R) then\n reason := [\"is_element/partord\",\"R is not a relation on A\",R,A,reason];\n return false;\n fi;\n\n if not(`is_reflexive/autorel`(A)(R)) then\n reason := [\"is_element/partord\",\"R is not reflexive\",R];\n return false;\n fi;\n \n if not(`is_transitive/autorel`(A)(R)) then\n reason := [\"is_element/partord\",\"R is not transitive\",R];\n return false;\n fi;\n \n if not(`is_separated/autorel`(A)(R)) then\n reason := [\"is_element/partord\",\"R is not separated\",R];\n return false;\n fi;\n \n return true;\nend;\n\n######################################################################\n\n`is_equal/partord` := eval(`is_equal/autorel`);\n`is_leq/partord` := eval(`is_leq/autorel`);\n`is_separated/partord` := eval(`is_separated/autorel`);\n\n######################################################################\n\n`op/partord` := eval(`op/autorel`);\n\n######################################################################\n\n`random_element/partord` := (A::set) -> proc()\n local M,B,E,RB,RA,DS,xy,x,y,d,m,a,e;\n if nops(A) <= 1 then return {seq([a,a],a in A)}; fi;\n\n M := `random_element/nonempty_subsets`(A)();\n B := A minus M;\n RB := `random_element/partord`(B)();\n DS := `list_elements/subsets`(B);\n for xy in RB do\n x,y := op(xy);\n if x <> y then \n DS := select(S -> (member(x,S) or not(member(y,S))),DS);\n fi;\n od;\n d := nops(DS);\n RA := RB union {seq([m,m],m in M)};\n for m in M do\n E := DS[rand(1..d)()];\n RA := RA union {seq([e,m],e in E)};\n od;\n\n return RA;\nend:\n\n######################################################################\n\n`top_element/partord` := (A) -> proc(R)\n local n,a,U;\n n := nops(A);\n for a in A do\n U := select(e -> e[2] = a,R);\n if nops(U) = n then \n return a;\n fi;\n od:\n\n return FAIL;\nend:\n\n######################################################################\n\n`bottom_element/partord` := (A) -> proc(R)\n local n,a,U;\n n := nops(A);\n for a in A do\n U := select(e -> e[1] = a,R);\n if nops(U) = n then \n return a;\n fi;\n od:\n\n return FAIL;\nend:\n\n######################################################################\n\n`rank_table/partord` := (A::set) -> proc(R)\n local pi,pi0,a,b,r,k,B;\n \n r := table():\n for a in A do\n r[a] := nops(select(x -> member([x,a],R),A)) - 1;\n od;\n\n return eval(r);\nend;\n\n######################################################################\n\n`hasse_diagram/partord` := (A::set) -> proc(R)\n local R1,R2;\n R1 := R minus `id/autorel`(A);\n R2 := `o/autorel`(A)(R1,R1);\n return R1 minus R2;\nend:\n\n######################################################################\n\n`maximal_chains/partord` := (A::set) -> proc(R)\n local H,LC,UC,a,C,C0,extra,c,u;\n\n H := `hasse_diagram/partord`(A)(R);\n LC := table():\n UC := table():\n for a in A do\n LC[a] := map(e -> e[1],select(e -> e[2] = a,H));\n UC[a] := map(e -> e[2],select(e -> e[1] = a,H));\n od:\n \n C := map(a -> [a],select(a -> LC[a] = {},A));\n extra := true;\n while extra do\n extra := false;\n C0 := C;\n C := NULL;\n for c in C0 do\n u := UC[c[-1]];\n if u = {} then\n C := C,c;\n else\n C := C,seq([op(c),a],a in u);\n extra := true;\n fi;\n od:\n C := {C};\n od;\n\n return C;\nend:\n\n######################################################################\n\n`partord_is_leq` := (A::set) -> (R) -> (a,b) -> member([a,b],R);\n\n######################################################################\n\n`partord_is_equiv` := (A::set) -> (R) -> (a,b) ->\n member([a,b],R) and member([b,a],R);\n\n######################################################################\n\n`partord_is_less` := (A::set) -> (R) -> (a,b) ->\n member([a,b],R) and not(member([b,a],R));\n\n######################################################################\n# Returns [A0,R0] where A0 is of the form {1,...,n} and\n# (A0,R0) is isomorphic to (A,R).\n\n`skeleton/partord` := (A::set) -> proc(R)\n local n,i,A0,Ai,R0;\n n := nops(A);\n A0 := {seq(i,i=1..n)};\n Ai := table():\n for i from 1 to n do Ai[A[i]] := i; od;\n R0 := map(u -> [Ai[u[1]],Ai[u[2]]],R);\n return [A0,R0];\nend:\n\n######################################################################\n\n`partord/from_comparator` := (A::set) -> proc(C)\n local R,a,b;\n \n R := {seq(seq([a,b],b in A),a in A)};\n R := select(ab -> C(op(ab)),R);\n\n return [A,R];\nend:\n\n######################################################################\n\n`skeleton/partord/from_comparator` := (A::{set,list}) -> proc(C)\n local n,i,j,A0,R0;\n\n n := nops(A);\n A0 := {seq(i,i=1..n)};\n R0 := {seq(seq([i,j],j = 1..n),i = 1..n)};\n R0 := select(ij -> C(A[ij[1]],A[ij[2]]),R0);\n\n return [A0,R0];\nend:\n\n######################################################################\n\n`homology/partord` := (A::set) -> proc(R,p::nonnegint := 0)\n local U,C,Cn,Ci,dM,rdM,BN,H,c,c1,d,d_max,a,i,i1,j,k,t;\n\n U := table():\n for a in A do\n U[a] := select(b -> (b <> a and member([a,b],R)),A):\n od:\n C[0] := [seq(chain(a),a in A)]:\n d := 0;\n while C[d] <> [] do\n d := d+1;\n C[d] := [seq(seq(chain(op(c),a),a in U[op(d,c)]),c in C[d-1])]:\n od:\n d_max := d - 1;\n for d from 0 to d_max do \n Cn[d] := nops(C[d]):\n Ci[d] := table():\n for i from 1 to nops(C[d]) do\n Ci[d][C[d][i]] := i;\n od:\n od:\n\n dM := table():\n rdM := table():\n rdM[0] := 0;\n rdM[d_max+1] := 0;\n \n for d from 1 to d_max do\n dM[d] := Matrix(Cn[d-1],Cn[d]);\n for i from 1 to Cn[d] do\n c := [op(C[d][i])];\n for j from 0 to d do\n c1 := chain(seq(c[k+1],k=0..j-1),seq(c[k+1],k=j+1..d));\n i1 := Ci[d-1][c1];\n dM[d][i1,i] := (-1)^j;\n od:\n od:\n if p = 0 then \n rdM[d] := LinearAlgebra[Rank](dM[d]);\n else\n rdM[d] := LinearAlgebra[Modular][Rank](p,dM[d]);\n fi;\n od:\n\n BN := table():\n for d from 0 to d_max do\n BN[d] := Cn[d] - rdM[d] - rdM[d+1]; \n od:\n \n H := table():\n H[\"characteristic\"] := p;\n H[\"dim\"] := d_max;\n H[\"chains\"] := eval(C);\n H[\"chain_index\"] := eval(Ci);\n H[\"differential_matrix\"] := eval(dM);\n H[\"chain_number\"] := eval(Cn);\n H[\"betti_number\"] := eval(BN):\n H[\"poincare_series\"] := unapply(add(BN[i]*t^i,i=0..d_max),t);\n H[\"euler_characteristic\"] := add((-1)^d * BN[d],d = 0..d_max):\n \n return eval(H):\nend:\n\n######################################################################\n\n`simplex/partord` := proc(n)\n local i,j;\n return [{seq(i,i=0..n)},{seq(seq([i,j],j=i..n),i=0..n)}];\nend:\n\n`crown/partord` := proc(n)\n local A,R,i;\n A := {seq(i,i=1..2*n)};\n R := {seq([i,i],i=1..2*n),\n seq([2*i-1,2*i],i=1..n),\n seq([2*i+1,2*i],i=1..n-1),\n [1,2*n]};\n return [A,R];\nend:\n\n`saw/partord` := proc(n)\n local A,R,i;\n A := {seq(i,i=1..n)};\n R := {seq([i,i],i=1..n),\n seq([2*i-1,2*i],i=1..floor(n/2)),\n seq([2*i+1,2*i],i=1..floor((n-1)/2))};\n return [A,R];\nend:\n\n`diamond/partord` := proc(n)\n local A,R,i,j;\n\n A := {seq(i,i=1..2*n)};\n R := {seq([i,i],i=1..2*n),\n seq(seq([2*i-1,j],j=2*i+1..2*n),i=1..n),\n seq(seq([2*i ,j],j=2*i+1..2*n),i=1..n)};\n return [A,R];\nend:", "meta": {"hexsha": "4860e9034034b338442f1b7017d994caab475ae5", "size": 6943, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/partord.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/partord.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/partord.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": 22.9900662252, "max_line_length": 73, "alphanum_fraction": 0.4296413654, "num_tokens": 2328, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8652240825770432, "lm_q2_score": 0.7549149923816048, "lm_q1q2_score": 0.6531706317070295}} {"text": "restart;\nkernelopts(printbytes=false):\npartitions := proc(c::list(integer),subtotal::integer) :: integer:\n local i,m,total,cards;\n cards := c;\n m := 0;\n # Hit\n for i from 1 to 10 do\n if (cards[i]>0) then\n total := subtotal+i;\n if (total < 21) then\n # Stand\n m := m+1;\n\t# Hit again\n cards[i] := cards[i]-1;\n m := m+partitions(cards, total);\n cards[i] := cards[i]+1;\n elif (total=21) then\n # Stand; hit again is an automatic bust\n m := m+1;\n end if;\n end if;\n end do;\n return m;\nend proc:\n\ndeck := [4,4,4,4,4,4,4,4,4,16]:\nd := 0:\n\nfor i from 1 to 10 do\n # Dealer showing\n p := 0:\n deck[i] := deck[i]-1:\n for j from 1 to 10 do\n deck[j] := deck[j]-1:\n p := p+partitions(deck,j):\n deck[j] := deck[j]+1:\n end do:\n deck[i] := deck[i]+1:\n printf(\"Dealer showing %d partitions = %d\\n\",i-1,p):\n d := d+p:\nend do:\nprintf(\"Total partitions = %d\\n\",d):\n", "meta": {"hexsha": "cf96b6a28e97a1fc3333701a48b675d22f0f5e79", "size": 939, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/outcomes.mpl", "max_stars_repo_name": "octonion/recursion", "max_stars_repo_head_hexsha": "0c2516e67faa5b60f5286fb2d7e66abb2d50e113", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2018-10-03T21:04:24.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-14T20:32:21.000Z", "max_issues_repo_path": "maple/outcomes.mpl", "max_issues_repo_name": "octonion/recursion", "max_issues_repo_head_hexsha": "0c2516e67faa5b60f5286fb2d7e66abb2d50e113", "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": "maple/outcomes.mpl", "max_forks_repo_name": "octonion/recursion", "max_forks_repo_head_hexsha": "0c2516e67faa5b60f5286fb2d7e66abb2d50e113", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2019-08-20T23:54:55.000Z", "max_forks_repo_forks_event_max_datetime": "2020-01-03T17:52:11.000Z", "avg_line_length": 21.3409090909, "max_line_length": 66, "alphanum_fraction": 0.5314164004, "num_tokens": 329, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9086178895092414, "lm_q2_score": 0.7185943925708562, "lm_q1q2_score": 0.6529277203909066}} {"text": "check_koszul := proc()\n local A,n,dA,u,J,i;\n \n printf(\"%a()\\n\",procname);\n\n A := <<1|5|4|9>,<2|2|7|5>,<3|9|9|6>,<4|3|2|1>>;\n n := Dimension(A)[1];\n dA := Determinant(A);\n u := [4,5,6,11];\n\n J := Matrix(n,n);\n for i from 1 to n do J[i,n+1-i] := (-1)^(i-1); od;\n \n _ASSERT(\n Equal(koszul_adjoint(0,A), <>),\n \"koszul adjoint(0,A) = det(A)\"\n );\n \n _ASSERT(\n Equal(koszul_adjoint(1,A), Adjoint(A)),\n \"koszul_adjoint(1,A) = adj(A)\"\n );\n \n _ASSERT(\n Equal(koszul_adjoint(n-1,A), Transpose((-1)^(n-1) * J . A . J)),\n \"koszul_adjoint(n-1,A) is conjugate to A^T\"\n );\n \n _ASSERT(\n Equal(koszul_adjoint(n,A), <<1>>),\n \"koszul_adjoint(n,A) = 1\"\n );\n\n _ASSERT(\n `and`(seq(Equal(exterior_power(k,A) . koszul_adjoint(k,A),\n dA * IdentityMatrix(binomial(n,k))),k=0..n)),\n \"exterior_power(k,A) o koszul_adjoint(k,A) = det(A) in all degrees\"\n );\n\n _ASSERT(\n `and`(seq(Equal(koszul_d(k,u) . koszul_d(k+1,u),\n Matrix(binomial(n,k-1),binomial(n,k+1))),k=1..n-1)),\n \"koszul_d ^ 2 = 0\"\n );\nend:\n\n\ncheck_koszul_comparison := proc()\n global v,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 \n v := [x[1]^2+x[2]^3,x[1]*x[2]+x[3],x[1]^4-x[3]^2*x[2],x[4]-x[2]^3];\n koszul_setup(v);\n\n _ASSERT(\n Equal(map(koszul_pmod,map(expand,u_vec)),\n map(koszul_pmod,map(expand,v_vec . A))),\n \"u = v . A\"\n );\n \n _ASSERT(\n Equal(map(koszul_pmod,map(expand,v_vec)),\n map(koszul_pmod,map(expand,w_vec . B))),\n \"v = w . B\"\n );\n \n _ASSERT(\n Equal(map(koszul_pmod,map(Nv,soc_v * x_vec)),Transpose(Vector(n))),\n \"soc_v is in the socle\"\n );\n\n _ASSERT(\n not(koszul_pmod(Nv(soc_v)) = 0),\n \"soc_v is nonzero\"\n );\n\n _ASSERT(\n `and`(seq(\n Equal(map(expand,koszul_d(k,v_vec) . exterior_power(k,A)), \n\t map(expand,exterior_power(k-1,A) . koszul_d(k,u_vec))),\n k=1..n\n )),\n \"exterior_power(*,A) is a chain map\"\n );\n\n _ASSERT(\n `and`(seq(\n Equal(map(expand,koszul_d(k,w_vec) . exterior_power(k,B)), \n\t map(expand,exterior_power(k-1,B) . koszul_d(k,v_vec))),\n k=1..n\n )),\n \"exterior_power(*,B) is a chain map\"\n );\n\n _ASSERT(\n `and`(seq(\n Equal(map(expand,koszul_d(k,u_vec) . koszul_adjoint(k,A)), \n\t map(expand,koszul_adjoint(k-1,A) . koszul_d(k,v_vec))),\n k=1..n\n )),\n \"koszul_adjoint(*,A) is a chain map\"\n );\n\n _ASSERT(\n `and`(seq(\n Equal(map(expand,koszul_d(k,v_vec) . koszul_adjoint(k,B)), \n\t map(expand,koszul_adjoint(k-1,B) . koszul_d(k,w_vec))),\n k=1..n\n )),\n \"koszul_adjoint(*,B) is a chain map\"\n );\n\nend:\n", "meta": {"hexsha": "1dcb1e83e967ec57e09d25dec94782c981962b08", "size": 2498, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib_checks/check_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_checks/check_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_checks/check_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": 21.9122807018, "max_line_length": 70, "alphanum_fraction": 0.5872698159, "num_tokens": 991, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8519527869325345, "lm_q2_score": 0.7662936377487305, "lm_q1q2_score": 0.652846000288701}} {"text": "######################################################################\n# simplex(A) is the set of maps x : A -> [0,1] with sum = 1.\n\n`is_element/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 for a in A do\n u := x[a];\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 := v + u;\n od;\n\n if simplify(v - 1) <> 0 then\n reason := [convert(procname,string),\"entries in x do not sum to 1\",x,v];\n return false;\n fi;\n\n return true;\nend;\n\n`is_equal/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 return true;\nend;\n\n`is_leq/simplex` := NULL;\n\n`random_element/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 := 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/simplex` := NULL;\n`count_elements/simplex` := NULL;\n", "meta": {"hexsha": "6ca1f465fa0d508cc2ad56713aaeca7b2305b7dc", "size": 1463, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/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/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/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": 19.7702702703, "max_line_length": 79, "alphanum_fraction": 0.5434039645, "num_tokens": 480, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8221891392358015, "lm_q2_score": 0.793105941403651, "lm_q1q2_score": 0.6520830912854678}} {"text": "######################################################################\n\n`is_element/height_functions` := (A::set) -> proc(h)\n local P,U,V,a,u;\n global reason;\n\n if not(type(h,table)) then\n reason := [convert(procname,string),\"h is not a table\",h];\n return false;\n fi;\n\n P := {op(`list_elements/nonempty_subsets`(A))};\n if map(op,{indices(h)}) <> P then\n reason := [convert(procname,string),\"h is not indexed by the nonempty subsets of A\",h,A];\n return false;\n fi;\n\n for a in A do if h[{a}] <> 0 then\n reason := [convert(procname,string),\"h({a}) <> 0\",h,a];\n return false;\n fi; od;\n\n for U in P do \n u := h[U];\n if not (`is_element/RR`(u) and u >= 0 and u <= 1) then\n reason := [convert(procname,string),\"h(U) is not in the unit interval\",U,u];\n return false;\n fi;\n od;\n\n for U in P do\n for V in P do\n if U intersect V <> {} and \n h[U union V] <> max(h[U],h[V]) then\n reason := [convert(procname,string),\"h(U u V) <> max(h(U),h(V))\",U,V,h[U],h[V],h[U union V]];\n return false;\n fi;\n od;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_equal/height_functions` := (A::set) -> proc(h1,h2)\n local P,U;\n P := `list_elements/nonempty_subsets`(A);\n for U in P do\n if h1[U] <> h2[U] then return false; fi;\n od;\n return true;\nend;\n\n######################################################################\n\n`is_leq/height_functions` := NULL;\n\n`list_elements/height_functions` := NULL;\n`count_elements/height_functions` := NULL;\n\n######################################################################\n\n`is_critical/height_functions` := (A::set) -> proc(h,U)\n local V,a;\n\n V := A minus U;\n\n if V = {} then return evalb(h[A] < 1); fi;\n\n for a in V do\n if h[U union {a}] = h[U] then return false; fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`critical_tree/height_functions` := (A::set) -> proc(h)\n local P;\n\n P := `list_elements/nonempty_subsets`(A);\n\n return {op(select(U ->`is_critical/height_functions`(A)(h,U),P))};\nend;\n\n######################################################################\n\n`theta/partitions/height_functions` := (A::set) -> proc(pi)\n local h,P,T,B,Q;\n\n h := table();\n P := `list_elements/nonempty_subsets`(A);\n for T in P do h[T] := 1; od;\n for B in pi do\n Q := `list_elements/nonempty_subsets`(B);\n for T in Q do h[T] := 0; od;\n od;\n\n return eval(h);\nend;\n\n######################################################################\n\n`theta/realisation/partitions/height_functions` := (A::set) -> proc(x)\n local P,T,C,pi,t,k,h;\n\n h := table();\n P := `list_elements/nonempty_subsets`(A);\n for T in P do h[T] := 0; od;\n\n C := map(op,[indices(x)]);\n\n for pi in C do\n t := x[pi];\n k := `theta/partitions`(A)(pi);\n for T in P do\n h[T] := h[T] + t * k[T];\n od;\n od;\n\n return eval(h);\nend:\n\n######################################################################\n\n`theta_inv/realisation/partitions/height_functions` := (A::set) -> proc(h)\n local TT,TTT,S,r,s,t,x,U,X,Y,pi,a,m,i;\n \n TT := `critical_tree/height_functions`(A)(h);\n S := map(T -> h[T],TT) minus {1};\n r := nops(S) - 1;\n s := table();\n s[-1] := 1;\n for i from 0 to r do s[i] := S[r+1-i]; od;\n TTT := table();\n x := table();\n for i from 0 to r do\n TTT[i] := select(U -> h[U] <= s[i],TT);\n X := TTT[i];\n pi[i] := {};\n while X <> {} do\n a := X[1][1];\n Y := select(T -> member(a,T),X);\n m := max(map(nops,Y));\n U := select(T -> nops(T) = m,Y)[1];\n pi[i] := {op(pi[i]),U};\n X := X minus Y;\n od;\n x[pi[i]] := s[i-1] - s[i]; \n od;\n\n return eval(x);\nend:\n", "meta": {"hexsha": "882800a87a9a9cb22f76b3cce1be6308bc8a410c", "size": 3575, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/height_functions.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/height_functions.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/height_functions.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": 22.9166666667, "max_line_length": 97, "alphanum_fraction": 0.4830769231, "num_tokens": 1052, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213718636752, "lm_q2_score": 0.7248702880639791, "lm_q1q2_score": 0.6517463678273023}} {"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\nad := 1e-8:\nb := 0.024974:\na2 := (ad + 0.1234)/b:\na4 := 29.790:\na6 := 22.417:\na8 := 12.119:\na10 := 1570.1:\na12 := 55.944:\n\nf0 := s-> 1 + a2*s^2 + a4*s^4 + a6*s^6 + a8*s^8 + a10*s^10 + a12*s^12:\nf1 := s-> f0(s)^b/(1 + ad*s^2):\n\nf := x->f1(X2S*x): ", "meta": {"hexsha": "72f92c2b8101f9be486028d34789b84b95d62ab6", "size": 517, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_lg93.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_lg93.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_lg93.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": 22.4782608696, "max_line_length": 70, "alphanum_fraction": 0.5705996132, "num_tokens": 229, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9362850093037731, "lm_q2_score": 0.6959583187272711, "lm_q1q2_score": 0.6516153409246013}} {"text": "DV := NumberTheory[Divisors]:\n\nghost_coeff := (n) -> proc(x)\n local d;\n return add(d * x[d]^(n/d), d in DV(n));\nend:\n\nghost_vector := (n::posint) -> proc(x)\n local m;\n return [seq(ghost_coeff(m)(x),m=1..n)];\nend:\n\nunghost_vector := (n::posint) -> proc(w)\n local x,m,d;\n x := []:\n for m from 1 to n do \n x := [op(x),expand((w[m] - add(d*x[d]^(m/d),d in DV(m) minus {m}))/m)];\n od:\n return x;\nend:\n\nwitt_add_term := proc(n::posint) \n option remember;\n local x,y,u,d,rel;\n \n for d in DV(n) minus {n} do\n u[d] := witt_add_term(d)(x,y);\n od:\n\n rel := ghost_coeff(n)(u) - ghost_coeff(n)(x) - ghost_coeff(n)(y);\n u[n] := expand(solve(rel,u[n]));\n return unapply(u[n],x,y);\nend:\n\nwitt_add := (n::posint) -> proc(x,y)\n local m;\n return [seq(witt_add_term(m)(x,y),m=1..n)];\nend:\n\nwitt_mult_term := proc(n::posint) \n option remember;\n local x,y,u,d,rel;\n \n for d in DV(n) minus {n} do\n u[d] := witt_mult_term(d)(x,y);\n od:\n\n rel := ghost_coeff(n)(u) - ghost_coeff(n)(x) * ghost_coeff(n)(y);\n u[n] := expand(solve(rel,u[n]));\n return unapply(u[n],x,y);\nend:\n\nwitt_mult := (n::posint) -> proc(x,y)\n local m;\n return [seq(witt_mult_term(m)(x,y),m=1..n)];\nend:\n\nwitt_series := (n::posint) -> proc(x)\n local m;\n return expand(rem(mul(1 - x[m]*t^m,m=1..n),t^(n+1),t));\nend:\n\nwitt_unseries := (n::posint) -> proc(f)\n local c,g,d;\n c := []:\n g := f;\n for d from 1 to n do\n c := [op(c),-coeff(g,t,d)];\n g := expand(convert(series(g/(1-c[d]*t^d),t=0,n+1),polynom,t));\n od:\n return c; \nend:\n\nghost_p_coeff := (n) -> proc(x)\n local i;\n return add(p^i * x[i]^(p^(n-i)), i=0..n);\nend:\n\nghost_p_vector := (n::nonnegint) -> proc(x)\n local i;\n return table([seq(i = ghost_p_coeff(i)(x),i=0..n-1)]);\nend:\n\nghost_p_add := (n::nonnegint) -> proc(a,b)\n local i;\n return table([seq(i=expand(a[i]+b[i]),i=0..n-1)]);\nend:\n\nghost_p_sub := (n::nonnegint) -> proc(a,b)\n local i;\n return table([seq(i=expand(a[i]-b[i]),i=0..n-1)]);\nend:\n\nghost_p_mult := (n::nonnegint) -> proc(a,b)\n local i;\n return table([seq(i=expand(a[i]*b[i]),i=0..n-1)]);\nend:\n\nghost_p_is_equal := (n::nonnegint) -> proc(a,b)\n local i;\n return `and`(seq(evalb(simplify(a[i]-b[i])=0),i=0..n-1));\nend:\n\nunghost_p_vector := (n::nonnegint) -> proc(w)\n local x,m,k;\n x := table:\n for m from 0 to n-1 do \n x[m] := expand((w[m] - add(p^k*x[k]^(p^(m-k)),k=0..m-1))/p^m);\n od:\n return eval(x);\nend:\n\nwitt_p_add_term := proc(n::nonnegint) \n option remember;\n local x,y,u,m,rel;\n u := table():\n for m from 0 to n-1 do\n u[m] := witt_p_add_term(m)(x,y);\n od:\n\n rel := ghost_p_coeff(n)(u) - ghost_p_coeff(n)(x) - ghost_p_coeff(n)(y);\n u[n] := expand(solve(rel,u[n]));\n return unapply(u[n],x,y);\nend:\n\nwitt_p_add := (n::posint) -> proc(x,y)\n local m;\n return table([seq(m=witt_p_add_term(m)(x,y),m=0..n-1)]);\nend:\n\nwitt_p_mult_term := proc(n::nonnegint) \n option remember;\n local x,y,u,m,rel;\n u := table():\n for m from 0 to n-1 do\n u[m] := witt_p_mult_term(m)(x,y);\n od:\n\n rel := ghost_p_coeff(n)(u) - ghost_p_coeff(n)(x) * ghost_p_coeff(n)(y);\n u[n] := expand(solve(rel,u[n]));\n return unapply(u[n],x,y);\nend:\n\nwitt_p_mult := (n::posint) -> proc(x,y)\n local m;\n return table([seq(m=witt_p_mult_term(m)(x,y),m=0..n-1)]);\nend:", "meta": {"hexsha": "95cda18d44914741ace985079aa6c3d7c19ed280", "size": 3152, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/witt.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/witt.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/witt.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": 21.4421768707, "max_line_length": 73, "alphanum_fraction": 0.586928934, "num_tokens": 1173, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894717137996, "lm_q2_score": 0.7279754371026368, "lm_q1q2_score": 0.6513847567856907}} {"text": "program sample29;\nvar unused1 : integer;\n UnusedArrayForTest : array[200] of char;\nprocedure gcmlcm(m, n, gc, lc : integer);\nvar a, b, r : integer;\n begin\n a := m;\n b := n;\n while b <> 0 do begin\n r := a - (a div b) * b;\n a := b;\n b := r\n end;\n gc := a;\n lc := (m div gc) * n\n end;\nprocedure abs(a, b : integer);\n if a < 0 then\n b := -a\n else\n b := a\n end;\nprocedure gcm(a, b, gc : integer);\nvar lc, aa, bb : integer;\n if (a = 0) or (b = 0) then\n gc := 1\n else\n call abs(a, aa);\n call abs(b, bb);\n call gcmlcm(aa, bb, gc, lc)\n end\n end;\nprocedure lcm(a, b, lc : integer);\nvar gc, aa, bb : integer;\n if (a = 0) or (b = 0) then\n lc := 1\n else\n call abs(a, aa);\n call abs(b, bb);\n call gcmlcm(aa, bb, gc, lc)\n end\n end;\nvar unusedchar : char;\nprocedure reduce(a1, a2 : integer);\nvar gc : integer;\n if a1 = 0 then\n a2 := 1;\n return\n end;\n if a2 = 0 then\n a1 := 1;\n return\n end;\n if a2 < 0 then\n a1 := -a1;\n a2 := -a2\n end;\n call gcm(a1, a2, gc);\n a1 := a1 div gc;\n a2 := a2 div gc\n end;\nprocedure sum(x1, x2, y1, y2 : integer);\nvar lc, y11 : integer;\n call lcm(x2, y2, lc);\n x1 := x1 * (lc div x2);\n y11 := y1 * (lc div y2);\n x1 := x1 + y11;\n x2 := lc;\n call reduce(x1, x2)\n end;\nprocedure sub(x1, x2, y1, y2 : integer);\nvar lc, y11 : integer;\n call sum(x1, x2, -y1, y2)\n end;\nprocedure mult(x1, x2, y1, y2 : integer);\nvar gc, y22, y11 : integer;\n call gcm(x1, y2, gc);\n x1 := x1 div gc;\n y22 := y2 div gc;\n call gcm(x2, y1, gc);\n x2 := x2 div gc;\n y11 := y1 div gc;\n x1 := x1 * y11;\n x2 := x2 * y22;\n call reduce(x1, x2)\n end;\nprocedure divide(x1, x2, y1, y2 : integer);\n call mult(x1, x2, y2, y1)\n end;\nvar unusedarray : array[100] of char;\nprocedure printfinal(a, b : integer);\n if a = 0 then\n writeln('Final Result =', a)\n else if b = 1 then\n writeln('Final Result =', a)\n else\n writeln('Final Result =', a, '/', b)\n end;\nprocedure printtemp(a, b : integer);\n if a = 0 then\n writeln('Temporary Result =', a)\n else if b = 1 then\n writeln('Temporary Result =', a)\n else\n writeln('Temporary Result =', a, '/', b)\n end;\nvar x1, x2, y1, y2 : integer;\nvar com : char;\n endflag : boolean;\n writeln(' *** Calculator -- h for help ***');\n x1 := 0;\n x2 := 1;\n endflag := false;\n while notendflag do begin\n writeln(' Please input command :');\n readln(com,y1);\n y2 := 1;\n if (com = 'c') or (com = 'C') then\n x1 := y1;\n x2 := y2\n end\n else if com = '+' then\n call sum(x1, x2, y1, y2)\n else if com = '-' then\n call sub(x1, x2, y1, y2)\n else if com = '*' then\n call mult(x1, x2, y1, y2)\n else if com = '/' then\n call divide(x1, x2, y1, y2)\n else if (com = 'o') or (com = 'O') then\n endflag := true\n else\n writeln;\n writeln('Calculator Usage:');\n writeln(' c number : clear & set it');\n writeln(' + number : add it');\n writeln(' - number : subtract it');\n writeln(' * number : multiply it');\n writeln(' / number : divide by it');\n writeln(' o : off(terminate execution)');\n writeln\n end;\n if endflag then\n call printfinal(x1, x2)\n else\n call printtemp(x1, x2)\n end\nend.", "meta": {"hexsha": "691d268c5e3bad8bc1532c523dafb5c2cde90bd7", "size": 4041, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "program2/answers/sample29p.mpl", "max_stars_repo_name": "Hiroya-W/lang-processing", "max_stars_repo_head_hexsha": "c93ef2d5757e560c4df2335f07ac25552750140c", "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": "program2/answers/sample29p.mpl", "max_issues_repo_name": "Hiroya-W/lang-processing", "max_issues_repo_head_hexsha": "c93ef2d5757e560c4df2335f07ac25552750140c", "max_issues_repo_licenses": ["MIT"], "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": "program2/answers/sample29p.mpl", "max_forks_repo_name": "Hiroya-W/lang-processing", "max_forks_repo_head_hexsha": "c93ef2d5757e560c4df2335f07ac25552750140c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 27.3040540541, "max_line_length": 65, "alphanum_fraction": 0.429349171, "num_tokens": 1204, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894632969137, "lm_q2_score": 0.7279754371026367, "lm_q1q2_score": 0.6513847506584044}} {"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_tca.mpl\"\n\nmsinc := x -> my_piecewise3(x = 0, 1, sin(x)/x):\nrevtca_aa := Pi*(9*Pi/4)^(1/3):\n\nrevtca_fD := (rs, z, s) -> 1 - z^4*(1 - msinc(revtca_aa*s/rs)^2):\n\nf := (rs, z, xt, xs0, xs1) ->\n f_tcs(rs, z, xt)*revtca_fD(rs, z, X2S*2^(1/3)*xt):\n", "meta": {"hexsha": "486e7db6b9f3f5c4518f991b7f193e50df8480d9", "size": 518, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_revtca.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_revtca.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_revtca.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": 25.9, "max_line_length": 68, "alphanum_fraction": 0.6177606178, "num_tokens": 208, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037241905732, "lm_q2_score": 0.702530051167069, "lm_q1q2_score": 0.65075620275185}} {"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\nhcth_a_beta := 0.0042:\nhcth_a_gamma := 6:\nhcth_a_c0 := 1.09878:\nhcth_a_c1 := -2.51173:\nhcth_a_c2 := 0.0156233:\n\nhcth_a_aux := x -> 1 + hcth_a_gamma*hcth_a_beta*x*arcsinh(x):\n\nhcth_a_f := x -> hcth_a_c0 + hcth_a_beta/X_FACTOR_C*x^2*(hcth_a_c1/hcth_a_aux(x)\n + hcth_a_c2/(hcth_a_beta*hcth_a_aux(x)^2)):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(hcth_a_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "422b49c1849967d68145b283dbe40d505a166232", "size": 651, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_hcth_a.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_hcth_a.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_hcth_a.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": 28.3043478261, "max_line_length": 80, "alphanum_fraction": 0.6666666667, "num_tokens": 255, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9219218305645894, "lm_q2_score": 0.7057850216484838, "lm_q1q2_score": 0.6506786191432385}} {"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: lda_exc *)\n\n$define xc_dimensions_1d\n\neta0 := -log(sqrt(2*Pi)) - 3/4:\neta1 := 0.359933:\neps0 := -Pi^2/360:\neps1 := 0.00714:\n\nkappa := 0.3083:\n\nc0 := kappa*eta0:\nc1 := 4*kappa*eta0 + kappa*sqrt(kappa)*eta1:\nc2 := 5*eps0 + eps1/kappa:\nc3 := eps1:\n\nt := rs -> (sqrt(1 + 4*kappa*rs) - 1)/(2*kappa*rs):\n\nf := (rs, z) ->\n t(rs)^2*(c0*(1 - t(rs))^3 + c1*t(rs)*(1 - t(rs))^2 + c2*t(rs)^2*(1 - t(rs)) + c3*t(rs)^3):\n", "meta": {"hexsha": "fe7559e4b3448462655fc08938908b4e8831d6c3", "size": 656, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_1d_loos.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_1d_loos.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_1d_loos.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": 22.6206896552, "max_line_length": 92, "alphanum_fraction": 0.5914634146, "num_tokens": 267, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.939024820841433, "lm_q2_score": 0.6926419831347361, "lm_q1q2_score": 0.6504080141203504}}