X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_indexed.cpp;h=e8560b54b5dd4214edd7c0613be7885d8c58f208;hp=75a99e513a509410e4fb7c6826bf5d86f451deb9;hb=0160f9ab1da453641e30539abcf0eaa4162582eb;hpb=0117bd6ef4af029934703940d59e1c70866937b0 diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp index 75a99e51..e8560b54 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) 1999-2005 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 @@ -17,7 +17,7 @@ * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #include "exams.h" @@ -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 @@ -123,57 +123,86 @@ 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, indexed::symmetric, mu.toggle_variance(), nu.toggle_variance()), 0); - result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, indexed::symmetric, nu.toggle_variance(), sigma.toggle_variance(), rho.toggle_variance()), 0); - ex e = lorentz_eps(mu, nu, rho, sigma) * indexed(d, indexed::symmetric, 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, indexed::symmetric, i, j), indexed(A, indexed::symmetric, j, i)); - result += check_equal(indexed(A, indexed::antisymmetric, i, j) + indexed(A, indexed::antisymmetric, j, i), 0); - result += check_equal(indexed(A, indexed::antisymmetric, i, j, k) - indexed(A, indexed::antisymmetric, j, k, i), 0); - e = indexed(A, indexed::symmetric, i, j, k) * - indexed(B, indexed::antisymmetric, l, k, i); + result += check_equal(indexed(A, sy_symm(), i, j), indexed(A, sy_symm(), j, i)); + result += check_equal(indexed(A, sy_anti(), i, j) + indexed(A, sy_anti(), j, i), 0); + result += check_equal(indexed(A, sy_anti(), i, j, k) - indexed(A, sy_anti(), j, k, i), 0); + e = indexed(A, sy_symm(), i, j, k) * + indexed(B, sy_anti(), l, k, i); result += check_equal_simplify(e, 0); - e = indexed(A, indexed::symmetric, i, i, j, j) * - indexed(B, indexed::antisymmetric, k, l); // GiNaC 0.8.0 had a bug here + e = indexed(A, sy_symm(), i, i, j, j) * + indexed(B, sy_anti(), k, l); // GiNaC 0.8.0 had a bug here result += check_equal_simplify(e, e); + symmetry R = sy_symm(sy_anti(0, 1), sy_anti(2, 3)); + e = indexed(A, R, i, j, k, l) + indexed(A, R, j, i, k, l); + result += check_equal(e, 0); + e = indexed(A, R, i, j, k, l) + indexed(A, R, i, j, l, k); + result += check_equal(e, 0); + e = indexed(A, R, i, j, k, l) - indexed(A, R, j, i, l, k); + result += check_equal(e, 0); + e = indexed(A, R, i, j, k, l) + indexed(A, R, k, l, j, i); + result += check_equal(e, 0); + e = indexed(A, i, j); result += check_equal(symmetrize(e) + antisymmetrize(e), e); - e = indexed(A, indexed::symmetric, i, j, k, l); + e = indexed(A, sy_symm(), i, j, k, l); result += check_equal(symmetrize(e), e); result += check_equal(antisymmetrize(e), 0); - e = indexed(A, indexed::antisymmetric, i, j, k, l); + e = indexed(A, sy_anti(), i, j, k, l); 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 @@ -196,7 +225,7 @@ static unsigned scalar_product_check(void) return result; } -static unsigned edyn_check(void) +static unsigned edyn_check() { // Relativistic electrodynamics @@ -212,19 +241,17 @@ static unsigned edyn_check(void) // Lorentz transformation matrix (boost along x axis) matrix L(4, 4); - L.set(0, 0, gamma); - L.set(0, 1, -beta*gamma); - L.set(1, 0, -beta*gamma); - L.set(1, 1, gamma); - L.set(2, 2, 1); L.set(3, 3, 1); + L = gamma, -beta*gamma, 0, 0, + -beta*gamma, gamma, 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1; // Electromagnetic field tensor - matrix F(4, 4, lst( - 0, -Ex, -Ey, -Ez, + matrix F(4, 4); + F = 0, -Ex, -Ey, -Ez, Ex, 0, -Bz, By, Ey, Bz, 0, -Bx, - Ez, -By, Bx // 0 - )); + Ez, -By, Bx, 0; // Indices symbol s_mu("mu"), s_nu("nu"), s_rho("rho"), s_sigma("sigma"); @@ -283,14 +310,14 @@ 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; @@ -312,13 +339,15 @@ 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; @@ -337,10 +366,28 @@ 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); + + // GiNaC 1.2.1 had a bug here because p.i*p.i -> (p.i)^2 + e = indexed(p, i) * indexed(p, i) * indexed(p, j) + indexed(p, j); + ex fi = exprseq(e.get_free_indices()); + if (!fi.is_equal(exprseq(j))) { + clog << "get_free_indices(" << e << ") erroneously returned " + << fi << " instead of (.j)" << endl; + ++result; + } + return result; } -unsigned exam_indexed(void) +unsigned exam_indexed() { unsigned result = 0;