1 /** @file exam_clifford.cpp
3 * Here we test GiNaC's Clifford algebra objects. */
6 * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
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20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
25 static unsigned check_equal(const ex &e1, const ex &e2)
29 clog << e1 << "-" << e2 << " erroneously returned "
30 << e << " instead of 0" << endl;
36 static unsigned check_equal_simplify(const ex &e1, const ex &e2)
38 ex e = simplify_indexed(e1) - e2;
40 clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned "
41 << e << " instead of 0" << endl;
47 static unsigned clifford_check1(void)
49 // checks general identities and contractions
54 varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
57 e = dirac_ONE() * dirac_ONE();
58 result += check_equal(e, dirac_ONE());
60 e = dirac_ONE() * dirac_gamma(mu) * dirac_ONE();
61 result += check_equal(e, dirac_gamma(mu));
63 e = dirac_gamma(varidx(2, dim)) * dirac_gamma(varidx(1, dim)) *
64 dirac_gamma(varidx(1, dim)) * dirac_gamma(varidx(2, dim));
65 result += check_equal(e, dirac_ONE());
67 e = dirac_gamma(mu) * dirac_gamma(nu) *
68 dirac_gamma(nu.toggle_variance()) * dirac_gamma(mu.toggle_variance());
69 result += check_equal_simplify(e, pow(dim, 2) * dirac_ONE());
71 e = dirac_gamma(mu) * dirac_gamma(nu) *
72 dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
73 result += check_equal_simplify(e, 2*dim*dirac_ONE()-pow(dim, 2)*dirac_ONE());
78 static unsigned clifford_check2(void)
80 // checks identities relating to gamma5
85 varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
88 e = dirac_gamma(mu) * dirac_gamma5() + dirac_gamma5() * dirac_gamma(mu);
89 result += check_equal(e, 0);
91 e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma5() + dirac_gamma(mu);
92 result += check_equal(e, 0);
97 unsigned exam_clifford(void)
101 cout << "examining clifford objects" << flush;
102 clog << "----------clifford objects:" << endl;
104 result += clifford_check1(); cout << '.' << flush;
105 result += clifford_check2(); cout << '.' << flush;
108 cout << " passed " << endl;
109 clog << "(no output)" << endl;
111 cout << " failed " << endl;