/** @file exam_clifford.cpp * * Here we test GiNaC's Clifford algebra objects. */ /* * GiNaC Copyright (C) 1999-2001 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 * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * 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 */ #include "exams.h" static unsigned check_equal(const ex &e1, const ex &e2) { ex e = e1 - e2; if (!e.is_zero()) { clog << e1 << "-" << e2 << " erroneously returned " << e << " instead of 0" << endl; return 1; } return 0; } static unsigned check_equal_simplify(const ex &e1, const ex &e2) { ex e = simplify_indexed(e1) - e2; if (!e.is_zero()) { clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned " << e << " instead of 0" << endl; return 1; } return 0; } static unsigned clifford_check1(void) { // checks general identities and contractions unsigned result = 0; symbol dim("D"); varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim); ex e; e = dirac_ONE() * dirac_ONE(); result += check_equal(e, dirac_ONE()); e = dirac_ONE() * dirac_gamma(mu) * dirac_ONE(); result += check_equal(e, dirac_gamma(mu)); e = dirac_gamma(varidx(2, dim)) * dirac_gamma(varidx(1, dim)) * dirac_gamma(varidx(1, dim)) * dirac_gamma(varidx(2, dim)); result += check_equal(e, dirac_ONE()); e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(nu.toggle_variance()) * dirac_gamma(mu.toggle_variance()); result += check_equal_simplify(e, pow(dim, 2) * dirac_ONE()); e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance()); result += check_equal_simplify(e, 2*dim*dirac_ONE()-pow(dim, 2)*dirac_ONE()); return result; } static unsigned clifford_check2(void) { // checks identities relating to gamma5 unsigned result = 0; symbol dim("D"); varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim); ex e; e = dirac_gamma(mu) * dirac_gamma5() + dirac_gamma5() * dirac_gamma(mu); result += check_equal(e, 0); e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma5() + dirac_gamma(mu); result += check_equal(e, 0); return result; } unsigned exam_clifford(void) { unsigned result = 0; cout << "examining clifford objects" << flush; clog << "----------clifford objects:" << endl; result += clifford_check1(); cout << '.' << flush; result += clifford_check2(); cout << '.' << flush; if (!result) { cout << " passed " << endl; clog << "(no output)" << endl; } else { cout << " failed " << endl; } return result; }