1 /** @file exam_color.cpp
3 * Here we test GiNaC's color objects (su(3) Lie algebra). */
6 * GiNaC Copyright (C) 1999-2007 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
26 using namespace GiNaC;
28 static unsigned check_equal(const ex &e1, const ex &e2)
32 clog << e1 << "-" << e2 << " erroneously returned "
33 << e << " instead of 0" << endl;
39 static unsigned check_equal_simplify(const ex &e1, const ex &e2)
41 ex e = simplify_indexed(e1) - e2;
43 clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned "
44 << e << " instead of 0" << endl;
50 static unsigned color_check1()
52 // checks general identities and contractions of the structure constants
56 idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), d(symbol("d"), 8);
58 result += check_equal(color_d(a, c, a), 0);
59 result += check_equal_simplify(color_d(a, b, c) * color_d(b, d, c), numeric(5,3) * delta_tensor(a, d));
60 result += check_equal_simplify(color_d(idx(5, 8), b, c) * color_d(b, idx(5, 8), c), numeric(5,3));
61 result += check_equal_simplify(color_d(a, b, c) * color_d(b, c, a), numeric(40,3));
62 result += check_equal_simplify(color_d(a, b, c) * color_f(b, d, c), 0);
63 result += check_equal_simplify(color_d(a, b, c) * color_f(b, c, a), 0);
64 result += check_equal_simplify(color_f(a, b, c) * color_f(b, c, a), 24);
65 result += check_equal_simplify(color_f(a, b, c) * color_f(b, d, c), -3 * delta_tensor(a, d));
66 result += check_equal_simplify(color_h(a, b, c) * color_h(a, b, c), numeric(-32,3));
67 result += check_equal_simplify(color_h(a, b, c) * color_h(b, a, c), numeric(112,3));
69 ex e = color_h(a, b, c) * color_h(a, b, c);
71 for (int i=1; i<9; i++)
72 for (int j=1; j<9; j++)
73 for (int k=1; k<9; k++)
74 sum += e.subs(lst(a == i, b == j, c == k));
75 if (!sum.is_equal(numeric(-32,3))) {
76 clog << "numeric contraction of " << e << " erroneously returned "
77 << sum << " instead of -32/3" << endl;
84 static unsigned color_check2()
86 // checks general identities and contractions of the generators
90 idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8);
93 e = color_T(k) * color_T(k);
94 result += check_equal_simplify(e, 4 * color_ONE() / 3);
95 e = color_T(k) * color_T(a) * color_T(k);
96 result += check_equal_simplify(e, -color_T(a) / 6);
97 e = color_T(k) * color_T(a) * color_T(b) * color_T(k);
98 result += check_equal_simplify(e, delta_tensor(a, b) * color_ONE() / 4 - color_T(a) * color_T(b) / 6);
99 e = color_T(k) * color_T(a) * color_T(b) * color_T(c) * color_T(k);
100 result += check_equal_simplify(e, (color_h(a, b, c) * color_ONE() / 8).expand() - color_T(a) * color_T(b) * color_T(c) / 6);
101 e = color_T(a) * color_T(b) * color_T(a) * color_T(b);
102 result += check_equal_simplify(e, -2 * color_ONE() / 9);
103 e = color_T(a) * color_T(b) * color_T(b) * color_T(a);
104 result += check_equal_simplify(e, 16 * color_ONE() / 9);
105 e = color_T(a) * color_T(b) * color_T(c) * color_T(c) * color_T(b) * color_T(a);
106 result += check_equal_simplify(e, 64 * color_ONE() / 27);
107 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);
108 result += check_equal_simplify(e, -color_ONE() / 162);
113 static unsigned color_check3()
119 idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8);
123 result += check_equal(color_trace(e), 3);
125 result += check_equal(color_trace(e), 0);
126 e = color_T(a) * color_T(b);
127 result += check_equal(color_trace(e), delta_tensor(a, b) / 2);
128 e = color_T(a) * color_T(b) * color_T(c);
129 result += check_equal(color_trace(e), color_h(a, b, c) / 4);
131 e = color_ONE(0) * color_ONE(1) / 9;
132 result += check_equal(color_trace(e, 0), color_ONE(1) / 3);
133 result += check_equal(color_trace(e, 1), color_ONE(0) / 3);
134 result += check_equal(color_trace(e, 2), e);
135 result += check_equal(color_trace(e, lst(0, 1)), 1);
137 e = color_T(a, 0) * color_T(a, 1) * color_T(b, 0) * color_T(b, 1);
138 result += check_equal_simplify(color_trace(e, 0), 2 * color_ONE(1) / 3);
139 result += check_equal_simplify(color_trace(e, 1), 2 * color_ONE(0) / 3);
140 result += check_equal_simplify(color_trace(e, 2), e);
141 result += check_equal_simplify(color_trace(e, lst(0, 1)), 2);
146 unsigned exam_color()
150 cout << "examining color objects" << flush;
152 result += color_check1(); cout << '.' << flush;
153 result += color_check2(); cout << '.' << flush;
154 result += color_check3(); cout << '.' << flush;
159 int main(int argc, char** argv)