/** @file exam_color.cpp * * Here we test GiNaC's color objects (su(3) Lie algebra). */ /* * 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 * 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 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 color_check1() { // checks general identities and contractions of the structure constants unsigned result = 0; idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), d(symbol("d"), 8); result += check_equal(color_d(a, c, a), 0); result += check_equal_simplify(color_d(a, b, c) * color_d(b, d, c), numeric(5,3) * delta_tensor(a, d)); result += check_equal_simplify(color_d(idx(5, 8), b, c) * color_d(b, idx(5, 8), c), numeric(5,3)); result += check_equal_simplify(color_d(a, b, c) * color_d(b, c, a), numeric(40,3)); result += check_equal_simplify(color_d(a, b, c) * color_f(b, d, c), 0); result += check_equal_simplify(color_d(a, b, c) * color_f(b, c, a), 0); result += check_equal_simplify(color_f(a, b, c) * color_f(b, c, a), 24); result += check_equal_simplify(color_f(a, b, c) * color_f(b, d, c), -3 * delta_tensor(a, d)); result += check_equal_simplify(color_h(a, b, c) * color_h(a, b, c), numeric(-32,3)); result += check_equal_simplify(color_h(a, b, c) * color_h(b, a, c), numeric(112,3)); ex e = color_h(a, b, c) * color_h(a, b, c); ex sum = 0; for (int i=1; i<9; i++) for (int j=1; j<9; j++) for (int k=1; k<9; k++) sum += e.subs(lst(a == i, b == j, c == k)); if (!sum.is_equal(numeric(-32,3))) { clog << "numeric contraction of " << e << " erroneously returned " << sum << " instead of -32/3" << endl; result++; } return result; } static unsigned color_check2() { // checks general identities and contractions of the generators unsigned result = 0; idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8); ex e; e = color_T(k) * color_T(k); result += check_equal_simplify(e, 4 * color_ONE() / 3); e = color_T(k) * color_T(a) * color_T(k); result += check_equal_simplify(e, -color_T(a) / 6); e = color_T(k) * color_T(a) * color_T(b) * color_T(k); result += check_equal_simplify(e, delta_tensor(a, b) * color_ONE() / 4 - color_T(a) * color_T(b) / 6); e = color_T(k) * color_T(a) * color_T(b) * color_T(c) * color_T(k); result += check_equal_simplify(e, (color_h(a, b, c) * color_ONE() / 8).expand() - color_T(a) * color_T(b) * color_T(c) / 6); e = color_T(a) * color_T(b) * color_T(a) * color_T(b); result += check_equal_simplify(e, -2 * color_ONE() / 9); e = color_T(a) * color_T(b) * color_T(b) * color_T(a); result += check_equal_simplify(e, 16 * color_ONE() / 9); e = color_T(a) * color_T(b) * color_T(c) * color_T(c) * color_T(b) * color_T(a); result += check_equal_simplify(e, 64 * color_ONE() / 27); e = color_T(a) * color_T(b) * color_T(c) * color_T(k) * color_T(a) * color_T(k) * color_T(c) * color_T(b); result += check_equal_simplify(e, -color_ONE() / 162); return result; } static unsigned color_check3() { // checks traces unsigned result = 0; idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8); ex e; e = color_ONE(); result += check_equal(color_trace(e), 3); e = color_T(a); result += check_equal(color_trace(e), 0); e = color_T(a) * color_T(b); result += check_equal(color_trace(e), delta_tensor(a, b) / 2); e = color_T(a) * color_T(b) * color_T(c); result += check_equal(color_trace(e), color_h(a, b, c) / 4); e = color_ONE(0) * color_ONE(1) / 9; result += check_equal(color_trace(e, 0), color_ONE(1) / 3); result += check_equal(color_trace(e, 1), color_ONE(0) / 3); result += check_equal(color_trace(e, 2), e); result += check_equal(color_trace(e, lst(0, 1)), 1); e = color_T(a, 0) * color_T(a, 1) * color_T(b, 0) * color_T(b, 1); result += check_equal_simplify(color_trace(e, 0), 2 * color_ONE(1) / 3); result += check_equal_simplify(color_trace(e, 1), 2 * color_ONE(0) / 3); result += check_equal_simplify(color_trace(e, 2), e); result += check_equal_simplify(color_trace(e, lst(0, 1)), 2); return result; } unsigned exam_color() { unsigned result = 0; cout << "examining color objects" << flush; clog << "----------color objects:" << endl; result += color_check1(); cout << '.' << flush; result += color_check2(); cout << '.' << flush; result += color_check3(); cout << '.' << flush; if (!result) { cout << " passed " << endl; clog << "(no output)" << endl; } else { cout << " failed " << endl; } return result; }