X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_indexed.cpp;h=69816a74bcf81c34160d69fddf6a8b9344163340;hp=546eea78ae0b1b43856e76019400cc667efd7a54;hb=3fb7166724ec9a4e5acac793f42c347da9aa9a87;hpb=83b8438ae031fa9abe70ddaace4d1501c8683551 diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp index 546eea78..69816a74 100644 --- a/check/exam_indexed.cpp +++ b/check/exam_indexed.cpp @@ -3,7 +3,7 @@ * Here we test manipulations on GiNaC's indexed objects. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by @@ -55,7 +55,7 @@ static unsigned check_equal_simplify(const ex &e1, const ex &e2, const scalar_pr return 0; } -static unsigned delta_check(void) +static unsigned delta_check() { // checks identities of the delta tensor @@ -81,7 +81,7 @@ static unsigned delta_check(void) return result; } -static unsigned metric_check(void) +static unsigned metric_check() { // checks identities of the metric tensor @@ -114,7 +114,7 @@ static unsigned metric_check(void) return result; } -static unsigned epsilon_check(void) +static unsigned epsilon_check() { // checks identities of the epsilon tensor @@ -123,32 +123,44 @@ static unsigned epsilon_check(void) symbol s_mu("mu"), s_nu("nu"), s_rho("rho"), s_sigma("sigma"), s_tau("tau"); symbol d("d"); varidx mu(s_mu, 4), nu(s_nu, 4), rho(s_rho, 4), sigma(s_sigma, 4), tau(s_tau, 4); + varidx mu_co(s_mu, 4, true), nu_co(s_nu, 4, true), rho_co(s_rho, 4, true), sigma_co(s_sigma, 4, true), tau_co(s_tau, 4, true); // antisymmetry result += check_equal(lorentz_eps(mu, nu, rho, sigma) + lorentz_eps(sigma, rho, mu, nu), 0); // convolution is zero - result += check_equal(lorentz_eps(mu, nu, rho, nu.toggle_variance()), 0); - result += check_equal(lorentz_eps(mu, nu, mu.toggle_variance(), nu.toggle_variance()), 0); - result += check_equal_simplify(lorentz_g(mu.toggle_variance(), nu.toggle_variance()) * lorentz_eps(mu, nu, rho, sigma), 0); + result += check_equal(lorentz_eps(mu, nu, rho, nu_co), 0); + result += check_equal(lorentz_eps(mu, nu, mu_co, nu_co), 0); + result += check_equal_simplify(lorentz_g(mu_co, nu_co) * lorentz_eps(mu, nu, rho, sigma), 0); // contraction with symmetric tensor is zero - result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), mu.toggle_variance(), nu.toggle_variance()), 0); - result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), nu.toggle_variance(), sigma.toggle_variance(), rho.toggle_variance()), 0); - ex e = lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), mu.toggle_variance(), tau); - result += check_equal_simplify(e, e); + result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), mu_co, nu_co), 0); + result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), nu_co, sigma_co, rho_co), 0); + result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, mu_co) * indexed(d, nu_co), 0); + result += check_equal_simplify(lorentz_eps(mu_co, nu, rho, sigma) * indexed(d, mu) * indexed(d, nu_co), 0); + ex e = lorentz_eps(mu, nu, rho, sigma) * indexed(d, mu_co) - lorentz_eps(mu_co, nu, rho, sigma) * indexed(d, mu); + result += check_equal_simplify(e, 0); + + // contractions of epsilon tensors + result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * lorentz_eps(mu_co, nu_co, rho_co, sigma_co), -24); + result += check_equal_simplify(lorentz_eps(tau, nu, rho, sigma) * lorentz_eps(mu_co, nu_co, rho_co, sigma_co), -6 * delta_tensor(tau, mu_co)); return result; } -static unsigned symmetry_check(void) +DECLARE_FUNCTION_2P(symm_fcn) +REGISTER_FUNCTION(symm_fcn, set_symmetry(sy_symm(0, 1))); +DECLARE_FUNCTION_2P(anti_fcn) +REGISTER_FUNCTION(anti_fcn, set_symmetry(sy_anti(0, 1))); + +static unsigned symmetry_check() { // check symmetric/antisymmetric objects unsigned result = 0; idx i(symbol("i"), 3), j(symbol("j"), 3), k(symbol("k"), 3), l(symbol("l"), 3); - symbol A("A"), B("B"); + symbol A("A"), B("B"), C("C"); ex e; result += check_equal(indexed(A, sy_symm(), i, j), indexed(A, sy_symm(), j, i)); @@ -180,10 +192,17 @@ static unsigned symmetry_check(void) result += check_equal(symmetrize(e), 0); result += check_equal(antisymmetrize(e), e); + e = (indexed(A, sy_anti(), i, j, k, l) * (indexed(B, j) * indexed(C, k) + indexed(B, k) * indexed(C, j)) + indexed(B, i, l)).expand(); + result += check_equal_simplify(e, indexed(B, i, l)); + + result += check_equal(symm_fcn(0, 1) + symm_fcn(1, 0), 2*symm_fcn(0, 1)); + result += check_equal(anti_fcn(0, 1) + anti_fcn(1, 0), 0); + result += check_equal(anti_fcn(0, 0), 0); + return result; } -static unsigned scalar_product_check(void) +static unsigned scalar_product_check() { // check scalar product replacement @@ -206,7 +225,7 @@ static unsigned scalar_product_check(void) return result; } -static unsigned edyn_check(void) +static unsigned edyn_check() { // Relativistic electrodynamics @@ -293,14 +312,14 @@ static unsigned edyn_check(void) return result; } -static unsigned spinor_check(void) +static unsigned spinor_check() { // check identities of the spinor metric unsigned result = 0; symbol psi("psi"); - spinidx A(symbol("A"), 2), B(symbol("B"), 2), C(symbol("C"), 2); + spinidx A(symbol("A")), B(symbol("B")), C(symbol("C")), D(symbol("D")); ex A_co = A.toggle_variance(), B_co = B.toggle_variance(); ex e; @@ -322,13 +341,15 @@ static unsigned spinor_check(void) result += check_equal_simplify(e, -indexed(psi, A_co)); e = spinor_metric(A_co, B_co) * indexed(psi, A); result += check_equal_simplify(e, indexed(psi, B_co)); + e = spinor_metric(D, A) * spinor_metric(A_co, B_co) * spinor_metric(B, C) - spinor_metric(D, A_co) * spinor_metric(A, B_co) * spinor_metric(B, C); + result += check_equal_simplify(e, 0); return result; } -static unsigned dummy_check(void) +static unsigned dummy_check() { - // check dummy index renaming + // check dummy index renaming/repositioning unsigned result = 0; @@ -347,10 +368,19 @@ static unsigned dummy_check(void) e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu, nu.toggle_variance()); result += check_equal_simplify(e, 0); + e = indexed(p, mu.toggle_variance(), nu, mu) * indexed(q, i) + - indexed(p, mu, nu, mu.toggle_variance()) * indexed(q, i); + result += check_equal_simplify(e, 0); + + e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu.toggle_variance(), nu); + result += check_equal_simplify(e, 0); + e = indexed(p, mu.toggle_variance(), mu) - indexed(p, nu, nu.toggle_variance()); + result += check_equal_simplify(e, 0); + return result; } -unsigned exam_indexed(void) +unsigned exam_indexed() { unsigned result = 0;