--- /dev/null
+/** @file exam_noncommut.cpp
+ *
+ * Here we test manipulations on GiNaC's lortensors. */
+
+/*
+ * GiNaC Copyright (C) 1999-2000 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 lortensor_check1(void)
+{
+ // checks simple identities of the metric tensor!
+
+ unsigned result = 0;
+ lorentzidx mu("mu"), nu("nu");
+ ex e1, e2, e3, e4, e5, e6;
+ e1 = lortensor_g(mu,nu);
+ e2 = lortensor_g(nu,mu);
+ e3 = e1 - e2; // g(~mu,~nu) - g(~nu,~mu) = 0 !
+ e4 = lortensor_g(mu,mu.toggle_covariant());
+ e5 = lortensor_g(mu.toggle_covariant(),mu);
+ e6 = e4 - e5; // g(~mu,_mu) - g(_mu,~mu) = 0!
+ if (!e3.is_zero()) {
+ clog << e1 << "-" << e2 << " erroneously returned "
+ << e3 << " instead of 0" << endl;
+ ++result;
+ }
+ if (!e6.is_zero()) {
+ clog << e4 << "-" << e5 << " erroneously returned "
+ << e6 << " instead of 0" << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+static unsigned lortensor_check2(void)
+{
+ // checks simple contraction properties of an arbitrary (symmetric!) rankn lortensor!
+
+ unsigned result = 0;
+ lorentzidx mu("mu"), nu("nu"), rho("rho");
+ ex e1, e2, e3, e4, e5, e6, e7, e8, e9, e10;
+ e1 = lortensor_g(mu,nu);
+ e2 = lortensor_g(nu,mu);
+ e3 = lortensor_rank1("p",mu.toggle_covariant());
+ e4 = lortensor_rank1("p",nu);
+ e5 = e3 * e1 - e3 * e2; // p_mu g(~mu,~nu) - p_mu g(~nu,~mu) = 0!
+ e6 = simplify_lortensor(e3 * e1) - e4; // p~nu - p~nu = 0!
+ e7 = lortensor_g(nu,rho);
+ e8 = lortensor_rank2("F",mu.toggle_covariant(),nu.toggle_covariant());
+ e9 = lortensor_rank2("F",mu.toggle_covariant(),rho);
+ e10 = simplify_lortensor(e8 * e7) - e9; // F(_mu,_nu) g(~nu,~rho) - F(_mu,~rho) = 0!
+ if (!e5.is_zero()) {
+ clog << e3 << "*" << e1 << "-" << e3 << "*" << e2 << " erroneously returned "
+ << e5 << " instead of 0" << endl;
+ ++result;
+ }
+ if (!e6.is_zero()) {
+ clog << " simplify_lortensor(e3 * e1)" << "-" << e4 << " erroneously returned"
+ << e6 << " instead of 0" << endl;
+ ++result;
+ }
+ if (!e10.is_zero()) {
+ clog << " simplify_lortensor(e8 * e7)" << "-" << e9 << " erroneously returned"
+ << e10 << " instead of 0" << endl;
+ ++result;
+ }
+
+ return result;
+}
+
+unsigned exam_noncommut(void)
+{
+ unsigned result = 0;
+
+ cout << "examining behaviour of noncommutative objects" << flush;
+ clog << "----------behaviour of noncommutative objects:" << endl;
+
+ result += lortensor_check1(); cout << '.' << flush;
+ result += lortensor_check2(); cout << '.' << flush;
+
+ if (!result) {
+ cout << " passed " << endl;
+ clog << "(no output)" << endl;
+ } else {
+ cout << " failed " << endl;
+ }
+
+ return result;
+}