* Here we test GiNaC's color objects (su(3) Lie algebra). */
/*
- * 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
*
* 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"
return 0;
}
-static unsigned color_check1(void)
+static unsigned color_check1()
{
- // checks general identities and contractions
+ // 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);
- // structure constants
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));
return result;
}
-unsigned exam_color(void)
+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;
clog << "----------color objects:" << endl;
result += color_check1(); cout << '.' << flush;
+ result += color_check2(); cout << '.' << flush;
+ result += color_check3(); cout << '.' << flush;
if (!result) {
cout << " passed " << endl;