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/** @file exam_color.cpp
*
* Here we test GiNaC's color objects (su(3) Lie algebra). */
/*
* GiNaC Copyright (C) 1999-2002 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 color_check1(void)
{
// 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(void)
{
// 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(void)
{
// checks traces
unsigned result = 0;
idx a(symbol("a"), 8), b(symbol("b"), 8), c(symbol("c"), 8), k(symbol("k"), 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);
return result;
}
unsigned exam_color(void)
{
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;
}
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