1 /** @file exam_color.cpp
3 * Here we test GiNaC's color objects (su(3) Lie algebra). */
6 * GiNaC Copyright (C) 1999-2014 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
24 using namespace GiNaC;
29 static unsigned check_equal(const ex &e1, const ex &e2)
33 clog << e1 << "-" << e2 << " erroneously returned "
34 << e << " instead of 0" << endl;
40 static unsigned check_equal_simplify(const ex &e1, const ex &e2)
42 ex e = simplify_indexed(e1) - e2;
44 clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned "
45 << e << " instead of 0" << endl;
51 static unsigned color_check1()
53 // checks general identities and contractions of the structure constants
57 idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), d(symbol("d"), 8);
59 result += check_equal(color_d(a, c, a), 0);
60 result += check_equal_simplify(color_d(a, b, c) * color_d(b, d, c), numeric(5,3) * delta_tensor(a, d));
61 result += check_equal_simplify(color_d(idx(5, 8), b, c) * color_d(b, idx(5, 8), c), numeric(5,3));
62 result += check_equal_simplify(color_d(a, b, c) * color_d(b, c, a), numeric(40,3));
63 result += check_equal_simplify(color_d(a, b, c) * color_f(b, d, c), 0);
64 result += check_equal_simplify(color_d(a, b, c) * color_f(b, c, a), 0);
65 result += check_equal_simplify(color_f(a, b, c) * color_f(b, c, a), 24);
66 result += check_equal_simplify(color_f(a, b, c) * color_f(b, d, c), -3 * delta_tensor(a, d));
67 result += check_equal_simplify(color_h(a, b, c) * color_h(a, b, c), numeric(-32,3));
68 result += check_equal_simplify(color_h(a, b, c) * color_h(b, a, c), numeric(112,3));
70 ex e = color_h(a, b, c) * color_h(a, b, c);
72 for (int i=1; i<9; i++)
73 for (int j=1; j<9; j++)
74 for (int k=1; k<9; k++)
75 sum += e.subs(lst(a == i, b == j, c == k));
76 if (!sum.is_equal(numeric(-32,3))) {
77 clog << "numeric contraction of " << e << " erroneously returned "
78 << sum << " instead of -32/3" << endl;
85 static unsigned color_check2()
87 // checks general identities and contractions of the generators
91 idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 8);
94 e = color_T(k) * color_T(k);
95 result += check_equal_simplify(e, 4 * color_ONE() / 3);
96 e = color_T(k) * color_T(a) * color_T(k);
97 result += check_equal_simplify(e, -color_T(a) / 6);
98 e = color_T(k) * color_T(a) * color_T(b) * color_T(k);
99 result += check_equal_simplify(e, delta_tensor(a, b) * color_ONE() / 4 - color_T(a) * color_T(b) / 6);
100 e = color_T(k) * color_T(a) * color_T(b) * color_T(c) * color_T(k);
101 result += check_equal_simplify(e, (color_h(a, b, c) * color_ONE() / 8).expand() - color_T(a) * color_T(b) * color_T(c) / 6);
102 e = color_T(a) * color_T(b) * color_T(a) * color_T(b);
103 result += check_equal_simplify(e, -2 * color_ONE() / 9);
104 e = color_T(a) * color_T(b) * color_T(b) * color_T(a);
105 result += check_equal_simplify(e, 16 * color_ONE() / 9);
106 e = color_T(a) * color_T(b) * color_T(c) * color_T(c) * color_T(b) * color_T(a);
107 result += check_equal_simplify(e, 64 * color_ONE() / 27);
108 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);
109 result += check_equal_simplify(e, -color_ONE() / 162);
114 static unsigned color_check3()
120 idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8);
124 result += check_equal(color_trace(e), 3);
126 result += check_equal(color_trace(e), 0);
127 e = color_T(a) * color_T(b);
128 result += check_equal(color_trace(e), delta_tensor(a, b) / 2);
129 e = color_T(a) * color_T(b) * color_T(c);
130 result += check_equal(color_trace(e), color_h(a, b, c) / 4);
132 e = color_ONE(0) * color_ONE(1) / 9;
133 result += check_equal(color_trace(e, 0), color_ONE(1) / 3);
134 result += check_equal(color_trace(e, 1), color_ONE(0) / 3);
135 result += check_equal(color_trace(e, 2), e);
136 result += check_equal(color_trace(e, lst(0, 1)), 1);
138 e = color_T(a, 0) * color_T(a, 1) * color_T(b, 0) * color_T(b, 1);
139 result += check_equal_simplify(color_trace(e, 0), 2 * color_ONE(1) / 3);
140 result += check_equal_simplify(color_trace(e, 1), 2 * color_ONE(0) / 3);
141 result += check_equal_simplify(color_trace(e, 2), e);
142 result += check_equal_simplify(color_trace(e, lst(0, 1)), 2);
147 unsigned exam_color()
151 cout << "examining color objects" << flush;
153 result += color_check1(); cout << '.' << flush;
154 result += color_check2(); cout << '.' << flush;
155 result += color_check3(); cout << '.' << flush;
160 int main(int argc, char** argv)