* Here we test GiNaC's Clifford algebra objects. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 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
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include "exams.h"
+#include <iostream>
+#include "ginac.h"
+using namespace std;
+using namespace GiNaC;
const numeric half(1, 2);
ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
for (int j=0; j<4; j++) {
- ex esub = e.subs(lst(is_a<varidx>(mu) ?
- mu == idx(j, mu.get_dim()), ex_to<varidx>(mu).toggle_variance() == idx(j, mu.get_dim())
- : mu == idx(j, mu.get_dim())));
+ ex esub = e.subs(
+ is_a<varidx>(mu)
+ ? lst (
+ mu == idx(j, mu.get_dim()),
+ ex_to<varidx>(mu).toggle_variance() == idx(j, mu.get_dim())
+ )
+ : lst(mu == idx(j, mu.get_dim()))
+ );
if (!(canonicalize_clifford(esub).is_zero())) {
clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned "
<< canonicalize_clifford(esub) << " instead of 0 for mu=" << j << endl;
* the cases when used indexes have or have not variance.
* To this end we recycle the code through the following macros */
-#define CHECK6(IDX,TOGGLE) {IDX v(symbol("v"), 4), nu(symbol("nu"), 4), mu(symbol("mu"), 4), \
- psi(symbol("psi"),4), lam(symbol("lambda"), 4),\
- xi(symbol("xi"), 4), rho(symbol("rho"),4);\
-\
-/* checks general identities and contractions for clifford_unit*/\
- e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2);\
- result += check_equal(e, clifford_unit(mu, A, 2));\
-\
- e = clifford_unit(idx(2, 4), A) * clifford_unit(idx(1, 4), A)\
- * clifford_unit(idx(1, 4), A) * clifford_unit(idx(2, 4), A);\
- result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());\
-\
- e = clifford_unit(IDX(2, 4), A) * clifford_unit(IDX(1, 4), A)\
- * clifford_unit(IDX(1, 4), A) * clifford_unit(IDX(2, 4), A);\
- result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A);\
- result += check_equal_simplify(e, A.trace() * dirac_ONE());\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu, A);\
- result += check_equal_simplify(e, indexed(A_symm, sy_symm(), nu, nu) * dirac_ONE());\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A) * clifford_unit(mu, A);\
- result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));\
-\
- e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu TOGGLE, A);\
- \
- result += check_equal_simplify_term(e, 2 * indexed(A_symm, sy_symm(), nu TOGGLE, mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A)\
- * clifford_unit(mu, A) * clifford_unit(mu TOGGLE, A);\
- result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());\
-\
- e = clifford_unit(mu, A) * clifford_unit(nu, A)\
- * clifford_unit(nu TOGGLE, A) * clifford_unit(mu TOGGLE, A);\
- result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());\
-\
- e = clifford_unit(mu, A) * clifford_unit(nu, A)\
- * clifford_unit(mu TOGGLE, A) * clifford_unit(nu TOGGLE, A);\
-\
- result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu TOGGLE, mu TOGGLE) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());\
-\
- e = clifford_unit(mu TOGGLE, A) * clifford_unit(nu, A)\
- * clifford_unit(mu, A) * clifford_unit(nu TOGGLE, A);\
-\
- result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu TOGGLE, A) * clifford_unit(nu TOGGLE, A) - pow(A.trace(), 2)*dirac_ONE());\
-\
- e = clifford_unit(nu TOGGLE, A) * clifford_unit(rho TOGGLE, A)\
- * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);\
- e = e.simplify_indexed().collect(clifford_unit(mu, A));\
- \
- result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu TOGGLE, rho)*indexed(A_symm, sy_symm(), rho TOGGLE, mu) *clifford_unit(nu, A) \
- - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho TOGGLE, mu) \
- + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);\
-\
- e = clifford_unit(nu TOGGLE, A) * clifford_unit(rho, A)\
- * clifford_unit(mu, A) * clifford_unit(rho TOGGLE, A) * clifford_unit(nu, A);\
- e = e.simplify_indexed().collect(clifford_unit(mu, A));\
- \
- result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu TOGGLE, rho)*indexed(A_symm, sy_symm(), rho TOGGLE, mu) *clifford_unit(nu, A) \
- - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho TOGGLE, mu) \
- + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);\
-\
- e = clifford_unit(mu, A) * clifford_unit(nu, A) + clifford_unit(nu, A) * clifford_unit(mu, A);\
- result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(A_symm, sy_symm(), mu, nu));\
-\
- e = (clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A)\
- + clifford_unit(nu, A) * clifford_unit(lam, A) * clifford_unit(mu, A)\
- + clifford_unit(lam, A) * clifford_unit(mu, A) * clifford_unit(nu, A)\
- - clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(lam, A)\
- - clifford_unit(lam, A) * clifford_unit(nu, A) * clifford_unit(mu, A)\
- - clifford_unit(mu, A) * clifford_unit(lam, A) * clifford_unit(nu, A)) / 6\
- + indexed(A_symm, sy_symm(), mu, nu) * clifford_unit(lam, A)\
- - indexed(A_symm, sy_symm(), mu, lam) * clifford_unit(nu, A)\
- + indexed(A_symm, sy_symm(), nu, lam) * clifford_unit(mu, A)\
- - clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A);\
- result += check_equal(canonicalize_clifford(e), 0);\
-\
-/* lst_to_clifford() and clifford_inverse() check*/\
- realsymbol x("x"), y("y"), t("t"), z("z");\
- \
- ex c = clifford_unit(nu, A, 1);\
- e = lst_to_clifford(lst(t, x, y, z), mu, A, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);\
- e1 = clifford_inverse(e);\
- result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1));\
-\
-/* Moebius map (both forms) checks for symmetric metrics only */\
- matrix M1(2, 2), M2(2, 2);\
- c = clifford_unit(nu, A);\
- \
- e = clifford_moebius_map(0, dirac_ONE(), \
- dirac_ONE(), 0, lst(t, x, y, z), A); \
-/* this is just the inversion*/\
- M1 = 0, dirac_ONE(),\
- dirac_ONE(), 0;\
- e1 = clifford_moebius_map(M1, lst(t, x, y, z), A); \
-/* the inversion again*/\
- result += check_equal_lst(e, e1);\
- \
- e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst(t, x, y, z), mu, A)), c);\
- result += check_equal_lst(e, e1);\
- \
- e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), nu, A), \
- 0, dirac_ONE(), lst(t, x, y, z), A); \
-/*this is just a shift*/\
- M2 = dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), c),\
- 0, dirac_ONE();\
- e1 = clifford_moebius_map(M2, lst(t, x, y, z), c); \
-/* the same shift*/\
- result += check_equal_lst(e, e1);\
- \
- result += check_equal(e, lst(t+1, x+2, y+3, z+4));\
- \
-/* Check the group law for Moebius maps */\
- e = clifford_moebius_map(M1, ex_to<lst>(e1), c); \
-/*composition of M1 and M2*/\
- e1 = clifford_moebius_map(M1.mul(M2), lst(t, x, y, z), c); \
-/* the product M1*M2*/\
- result += check_equal_lst(e, e1);}
-
-static unsigned clifford_check6(const matrix & A)
+template <typename IDX> unsigned clifford_check6(const matrix &A)
{
+ unsigned result = 0;
+
matrix A_symm(4,4), A2(4, 4);
A_symm = A.add(A.transpose()).mul(half);
A2 = A_symm.mul(A_symm);
-
+
+ IDX v(symbol("v"), 4), nu(symbol("nu"), 4), mu(symbol("mu"), 4),
+ psi(symbol("psi"),4), lam(symbol("lambda"), 4),
+ xi(symbol("xi"), 4), rho(symbol("rho"),4);
+ ex mu_TOGGLE = is_a<varidx>(mu) ? ex_to<varidx>(mu).toggle_variance() : mu;
+ ex nu_TOGGLE = is_a<varidx>(nu) ? ex_to<varidx>(nu).toggle_variance() : nu;
+ ex rho_TOGGLE
+ = is_a<varidx>(rho) ? ex_to<varidx>(rho).toggle_variance() : rho;
+
ex e, e1;
- int result = 0;
+
+/* checks general identities and contractions for clifford_unit*/
+ e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2);
+ result += check_equal(e, clifford_unit(mu, A, 2));
+
+ e = clifford_unit(IDX(2, 4), A) * clifford_unit(IDX(1, 4), A)
+ * clifford_unit(IDX(1, 4), A) * clifford_unit(IDX(2, 4), A);
+ result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());
+
+ e = clifford_unit(IDX(2, 4), A) * clifford_unit(IDX(1, 4), A)
+ * clifford_unit(IDX(1, 4), A) * clifford_unit(IDX(2, 4), A);
+ result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());
+
+ e = clifford_unit(nu, A) * clifford_unit(nu_TOGGLE, A);
+ result += check_equal_simplify(e, A.trace() * dirac_ONE());
+
+ e = clifford_unit(nu, A) * clifford_unit(nu, A);
+ result += check_equal_simplify(e, indexed(A_symm, sy_symm(), nu, nu) * dirac_ONE());
+
+ e = clifford_unit(nu, A) * clifford_unit(nu_TOGGLE, A) * clifford_unit(mu, A);
+ result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));
+
+ e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu_TOGGLE, A);
- CHECK6(varidx,.toggle_variance())
+ result += check_equal_simplify_term(e, 2 * indexed(A_symm, sy_symm(), nu_TOGGLE, mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);
- return result;
-}
+ e = clifford_unit(nu, A) * clifford_unit(nu_TOGGLE, A)
+ * clifford_unit(mu, A) * clifford_unit(mu_TOGGLE, A);
+ result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());
-static unsigned clifford_check6a(const matrix & A)
-{
- matrix A_symm(4,4), A2(4, 4);
- A_symm = A.add(A.transpose()).mul(half);
- A2 = A_symm.mul(A_symm);
+ e = clifford_unit(mu, A) * clifford_unit(nu, A)
+ * clifford_unit(nu_TOGGLE, A) * clifford_unit(mu_TOGGLE, A);
+ result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());
+
+ e = clifford_unit(mu, A) * clifford_unit(nu, A)
+ * clifford_unit(mu_TOGGLE, A) * clifford_unit(nu_TOGGLE, A);
+
+ result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu_TOGGLE, mu_TOGGLE) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());
+
+ e = clifford_unit(mu_TOGGLE, A) * clifford_unit(nu, A)
+ * clifford_unit(mu, A) * clifford_unit(nu_TOGGLE, A);
+
+ result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu_TOGGLE, A) * clifford_unit(nu_TOGGLE, A) - pow(A.trace(), 2)*dirac_ONE());
+
+ e = clifford_unit(nu_TOGGLE, A) * clifford_unit(rho_TOGGLE, A)
+ * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);
+ e = e.simplify_indexed().collect(clifford_unit(mu, A));
- ex e, e1;
- int result = 0;
+ result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu_TOGGLE, rho)*indexed(A_symm, sy_symm(), rho_TOGGLE, mu) *clifford_unit(nu, A)
+ - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho_TOGGLE, mu)
+ + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu_TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
- CHECK6(idx,)
+ e = clifford_unit(nu_TOGGLE, A) * clifford_unit(rho, A)
+ * clifford_unit(mu, A) * clifford_unit(rho_TOGGLE, A) * clifford_unit(nu, A);
+ e = e.simplify_indexed().collect(clifford_unit(mu, A));
+
+ result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu_TOGGLE, rho)*indexed(A_symm, sy_symm(), rho_TOGGLE, mu) *clifford_unit(nu, A)
+ - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho_TOGGLE, mu)
+ + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu_TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
+
+ e = clifford_unit(mu, A) * clifford_unit(nu, A) + clifford_unit(nu, A) * clifford_unit(mu, A);
+ result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(A_symm, sy_symm(), mu, nu));
+
+ e = (clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A)
+ + clifford_unit(nu, A) * clifford_unit(lam, A) * clifford_unit(mu, A)
+ + clifford_unit(lam, A) * clifford_unit(mu, A) * clifford_unit(nu, A)
+ - clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(lam, A)
+ - clifford_unit(lam, A) * clifford_unit(nu, A) * clifford_unit(mu, A)
+ - clifford_unit(mu, A) * clifford_unit(lam, A) * clifford_unit(nu, A)) / 6
+ + indexed(A_symm, sy_symm(), mu, nu) * clifford_unit(lam, A)
+ - indexed(A_symm, sy_symm(), mu, lam) * clifford_unit(nu, A)
+ + indexed(A_symm, sy_symm(), nu, lam) * clifford_unit(mu, A)
+ - clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A);
+ result += check_equal(canonicalize_clifford(e), 0);
+/* lst_to_clifford() and clifford_inverse() check*/
+ realsymbol s("s"), t("t"), x("x"), y("y"), z("z");
+
+ ex c = clifford_unit(nu, A, 1);
+ e = lst_to_clifford(lst(t, x, y, z), mu, A, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);
+ e1 = clifford_inverse(e);
+ result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1));
+
+/* lst_to_clifford() and clifford_to_lst() check for vectors*/
+ e = lst(t, x, y, z);
+ result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, false), e);
+ result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, true), e);
+
+/* lst_to_clifford() and clifford_to_lst() check for pseudovectors*/
+ e = lst(s, t, x, y, z);
+ result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, false), e);
+ result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, true), e);
+
+/* Moebius map (both forms) checks for symmetric metrics only */
+ matrix M1(2, 2), M2(2, 2);
+ c = clifford_unit(nu, A);
+
+ e = clifford_moebius_map(0, dirac_ONE(),
+ dirac_ONE(), 0, lst(t, x, y, z), A);
+/* this is just the inversion*/
+ M1 = 0, dirac_ONE(),
+ dirac_ONE(), 0;
+ e1 = clifford_moebius_map(M1, lst(t, x, y, z), A);
+/* the inversion again*/
+ result += check_equal_lst(e, e1);
+
+ e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst(t, x, y, z), mu, A)), c);
+ result += check_equal_lst(e, e1);
+
+ e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), nu, A),
+ 0, dirac_ONE(), lst(t, x, y, z), A);
+/*this is just a shift*/
+ M2 = dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), c),
+ 0, dirac_ONE();
+ e1 = clifford_moebius_map(M2, lst(t, x, y, z), c);
+/* the same shift*/
+ result += check_equal_lst(e, e1);
+
+ result += check_equal(e, lst(t+1, x+2, y+3, z+4));
+
+/* Check the group law for Moebius maps */
+ e = clifford_moebius_map(M1, ex_to<lst>(e1), c);
+/*composition of M1 and M2*/
+ e1 = clifford_moebius_map(M1.mul(M2), lst(t, x, y, z), c);
+/* the product M1*M2*/
+ result += check_equal_lst(e, e1);
return result;
}
return result;
}
+static unsigned clifford_check8()
+{
+ unsigned result = 0;
+
+ realsymbol a("a");
+ varidx mu(symbol("mu", "\\mu"), 1);
+
+ ex e = clifford_unit(mu, diag_matrix(lst(-1))), e0 = e.subs(mu==0);
+ result += ( exp(a*e0)*e0*e0 == -exp(e0*a) ) ? 0 : 1;
+
+ return result;
+}
+
unsigned exam_clifford()
{
unsigned result = 0;
cout << "examining clifford objects" << flush;
- clog << "----------clifford objects:" << endl;
result += clifford_check1(); cout << '.' << flush;
result += clifford_check2(); cout << '.' << flush;
result += clifford_check5(); cout << '.' << flush;
// anticommuting, symmetric examples
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush;
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))));; cout << '.' << flush;
realsymbol s("s"), t("t"); // symbolic entries in matric
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))));; cout << '.' << flush;
matrix A(4, 4);
A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=0
0, -1, 0, 0,
0, 0, 0, -1,
0, 0, 1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=2
0, 1, 0, 0,
0, 0, 0, -1,
0, 0, 1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=0
0, -1, 0, 0,
0, 0, 0, -1,
0, 0, -1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=2
0, 1, 0, 0,
0, 0, 0, -1,
0, 0, -1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 1, 0, 0, // not anticommuting, not symmetric, Tr=4
0, 1, 1, 0,
0, 0, 1, 1,
0, 0, 0, 1;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
symbol dim("D");
result += clifford_check7(minkmetric(), dim); cout << '.' << flush;
result += clifford_check7(indexed(-2*minkmetric(), sy_symm(), xi, chi), dim); cout << '.' << flush;
result += clifford_check7(-2*delta_tensor(xi, chi), dim); cout << '.' << flush;
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
+ result += clifford_check8(); cout << '.' << flush;
return result;
}
+
+int main(int argc, char** argv)
+{
+ return exam_clifford();
+}
git://www.ginac.de / ginac.git / blobdiff