* Here we test GiNaC's Clifford algebra objects. */
/*
- * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2019 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 "ginac.h"
+using namespace GiNaC;
+
+#include <iostream>
+using namespace std;
const numeric half(1, 2);
return 0;
}
-static unsigned check_equal_simplify_term(const ex & e1, const ex & e2, varidx & mu)
+static unsigned check_equal_simplify_term(const ex & e1, const ex & e2, idx & mu)
{
ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
- for (int j=0; j<4; j++) {
- ex esub = e.subs(lst(mu == idx(j, mu.get_dim()), mu.toggle_variance() == idx(j, mu.get_dim())));
+ for (int j=0; j<4; j++) {
+ 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;
static unsigned check_equal_simplify_term2(const ex & e1, const ex & e2)
{
- ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
+ ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
if (!(canonicalize_clifford(e).is_zero())) {
clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned "
<< canonicalize_clifford(e) << " instead of 0" << endl;
result += check_equal(dirac_trace(e, 0), dirac_ONE(1) / 4);
result += check_equal(dirac_trace(e, 1), dirac_ONE(0) / 4);
result += check_equal(dirac_trace(e, 2), e);
- result += check_equal(dirac_trace(e, lst(0, 1)), 1);
+ result += check_equal(dirac_trace(e, lst{0, 1}), 1);
e = dirac_gamma(mu, 0) * dirac_gamma(mu.toggle_variance(), 1) * dirac_gamma(nu, 0) * dirac_gamma(nu.toggle_variance(), 1);
result += check_equal_simplify(dirac_trace(e, 0), 4 * dim * dirac_ONE(1));
result += check_equal_simplify(dirac_trace(e, 1), 4 * dim * dirac_ONE(0));
- result += check_equal_simplify(dirac_trace(e, 2), canonicalize_clifford(e)); // e will be canonicalized by the calculation of the trace
- result += check_equal_simplify(dirac_trace(e, lst(0, 1)), 16 * dim);
+ // Fails with new tinfo mechanism because the order of gamma matrices with different rl depends on luck.
+ // TODO: better check.
+ //result += check_equal_simplify(dirac_trace(e, 2), canonicalize_clifford(e)); // e will be canonicalized by the calculation of the trace
+ result += check_equal_simplify(dirac_trace(e, lst{0, 1}), 16 * dim);
return result;
}
return result;
}
+/* We make two identical checks with metrics defined through a matrix in
+ * the cases when used indexes have or have not variance.
+ * To this end we recycle the code through the following macros */
-static unsigned clifford_check6(const matrix & A)
+template <typename IDX> unsigned clifford_check6(const matrix &A)
{
- varidx 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);
+ 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;
- bool anticommuting = ex_to<clifford>(clifford_unit(nu, A)).is_anticommuting();
- int result = 0;
- // checks general identities and contractions for clifford_unit
+/* 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);
+ 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(varidx(2, 4), A) * clifford_unit(varidx(1, 4), A)
- * clifford_unit(varidx(1, 4), A) * clifford_unit(varidx(2, 4), A);
+ 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_variance(), A);
+ 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_variance(), A) * clifford_unit(mu, A);
+ 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_variance(), A);
- if (anticommuting)
- result += check_equal_simplify(e, 2*indexed(A_symm, sy_symm(), mu, mu)*clifford_unit(mu, A) - 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_variance(), mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);
+ 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_variance(), A)
- * clifford_unit(mu, A) * clifford_unit(mu.toggle_variance(), A);
+ 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_variance(), A) * clifford_unit(mu.toggle_variance(), 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_variance(), A) * clifford_unit(nu.toggle_variance(), A);
- if (anticommuting)
- result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE());
-
- result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu.toggle_variance(), mu.toggle_variance()) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());
-
- e = clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu, A)
- * clifford_unit(mu, A) * clifford_unit(nu.toggle_variance(), A);
- if (anticommuting) {
- result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE());
- e1 = remove_dirac_ONE(simplify_indexed(e));
- result += check_equal(e1, 2*A2.trace() - pow(A.trace(), 2));
- }
+ * 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());
- result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu.toggle_variance(), 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);
- e = clifford_unit(nu.toggle_variance(), A) * clifford_unit(rho.toggle_variance(), 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));
- if (anticommuting)
- result += check_equal(e, (4*indexed(A2, sy_symm(), mu, mu) - 4 * indexed(A_symm, sy_symm(), mu, mu)*A.trace() +pow(A.trace(), 2)) * clifford_unit(mu, A));
- result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu.toggle_variance(), rho)*indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) *clifford_unit(nu, A)
- - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho.toggle_variance(), mu)
- + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu.toggle_variance(), mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
+ 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_variance(), A) * clifford_unit(rho, A)
- * clifford_unit(mu, A) * clifford_unit(rho.toggle_variance(), A) * clifford_unit(nu, A);
+ 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));
- if (anticommuting)
- result += check_equal(e, (4*indexed(A2, sy_symm(), mu, mu) - 4*indexed(A_symm, sy_symm(), mu, mu)*A.trace() +pow(A.trace(), 2))* clifford_unit(mu, A));
- result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu.toggle_variance(), rho)*indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) *clifford_unit(nu, A)
- - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho.toggle_variance(), mu)
- + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu.toggle_variance(), mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
+ 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));
- 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");
-
+/* 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);
+ 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((e*e1).simplify_indexed(), dirac_ONE(1));
+ 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);
+/* 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 */
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
+ dirac_ONE(), 0, lst{t, x, y, z}, A);
+/* this is just the inversion*/
+ matrix 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
+
+ e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst{t, x, y, z}, mu, A)), c);
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
+
+ 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*/
+ matrix 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;
}
-
static unsigned clifford_check7(const ex & G, const symbol & dim)
{
// checks general identities and contractions
varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim),
psi(symbol("psi"),dim), lam(symbol("lambda"), dim), xi(symbol("xi"), dim);
- ex e, G_base;
-
- if (is_a<indexed>(G))
- G_base = G.op(0);
- else
- G_base = G;
-
+ ex e;
+ clifford unit = ex_to<clifford>(clifford_unit(mu, G));
+ ex scalar = unit.get_metric(varidx(0, dim), varidx(0, dim));
+
e = dirac_ONE() * dirac_ONE();
result += check_equal(e, dirac_ONE());
e = clifford_unit(varidx(2, dim), G) * clifford_unit(varidx(1, dim), G)
* clifford_unit(varidx(1, dim), G) * clifford_unit(varidx(2, dim), G);
- result += check_equal(e, dirac_ONE());
+ result += check_equal(e, dirac_ONE()*pow(scalar, 2));
e = clifford_unit(mu, G) * clifford_unit(nu, G)
* clifford_unit(nu.toggle_variance(), G) * clifford_unit(mu.toggle_variance(), G);
- result += check_equal_simplify(e, pow(dim, 2) * dirac_ONE());
+ result += check_equal_simplify(e, pow(dim*scalar, 2) * dirac_ONE());
e = clifford_unit(mu, G) * clifford_unit(nu, G)
* clifford_unit(mu.toggle_variance(), G) * clifford_unit(nu.toggle_variance(), G);
- result += check_equal_simplify(e, 2*dim*dirac_ONE() - pow(dim, 2)*dirac_ONE());
+ result += check_equal_simplify(e, (2*dim - pow(dim, 2))*pow(scalar,2)*dirac_ONE());
e = clifford_unit(nu.toggle_variance(), G) * clifford_unit(rho.toggle_variance(), G)
* clifford_unit(mu, G) * clifford_unit(rho, G) * clifford_unit(nu, G);
e = e.simplify_indexed().collect(clifford_unit(mu, G));
- result += check_equal(e, pow(2 - dim, 2).expand() * clifford_unit(mu, G));
+ result += check_equal(e, pow(scalar*(dim-2), 2).expand() * clifford_unit(mu, G));
// canonicalize_clifford() checks, only for symmetric metrics
- if (ex_to<symmetry>(ex_to<indexed>(ex_to<clifford>(clifford_unit(mu, G)).get_metric()).get_symmetry()).has_symmetry()) {
+ if (is_a<indexed>(ex_to<clifford>(clifford_unit(mu, G)).get_metric()) &&
+ ex_to<symmetry>(ex_to<indexed>(ex_to<clifford>(clifford_unit(mu, G)).get_metric()).get_symmetry()).has_symmetry()) {
e = clifford_unit(mu, G) * clifford_unit(nu, G) + clifford_unit(nu, G) * clifford_unit(mu, G);
- result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(G_base, sy_symm(), nu, mu));
+ result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*unit.get_metric(nu, mu));
e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G)
+ clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G)
- clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G)
- clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G)
- clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6
- + indexed(G_base, sy_symm(), mu, nu) * clifford_unit(lam, G)
- - indexed(G_base, sy_symm(), mu, lam) * clifford_unit(nu, G)
- + indexed(G_base, sy_symm(), nu, lam) * clifford_unit(mu, G)
+ + unit.get_metric(mu, nu) * clifford_unit(lam, G)
+ - unit.get_metric(mu, lam) * clifford_unit(nu, G)
+ + unit.get_metric(nu, lam) * clifford_unit(mu, G)
- clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G);
result += check_equal(canonicalize_clifford(e), 0);
} else {
e = clifford_unit(mu, G) * clifford_unit(nu, G) + clifford_unit(nu, G) * clifford_unit(mu, G);
- result += check_equal(canonicalize_clifford(e), dirac_ONE()*(indexed(G_base, mu, nu) + indexed(G_base, nu, mu)));
+ result += check_equal(canonicalize_clifford(e), dirac_ONE()*(unit.get_metric(mu, nu) + unit.get_metric(nu, mu)));
e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G)
+ clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G)
- clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G)
- clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G)
- clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6
- + half * (indexed(G_base, mu, nu) + indexed(G_base, nu, mu)) * clifford_unit(lam, G)
- - half * (indexed(G_base, mu, lam) + indexed(G_base, lam, mu)) * clifford_unit(nu, G)
- + half * (indexed(G_base, nu, lam) + indexed(G_base, lam, nu)) * clifford_unit(mu, G)
+ + half * (unit.get_metric(mu, nu) + unit.get_metric(nu, mu)) * clifford_unit(lam, G)
+ - half * (unit.get_metric(mu, lam) + unit.get_metric(lam, mu)) * clifford_unit(nu, G)
+ + half * (unit.get_metric(nu, lam) + unit.get_metric(lam, nu)) * clifford_unit(mu, G)
- clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G);
result += check_equal(canonicalize_clifford(e), 0);
}
return result;
}
+static unsigned clifford_check8()
+{
+ unsigned result = 0;
+
+ realsymbol a("a"), b("b"), x("x");
+ varidx mu(symbol("mu", "\\mu"), 1);
+
+ ex e = clifford_unit(mu, diag_matrix({-1})), e0 = e.subs(mu==0);
+ result += ( exp(a*e0)*e0*e0 == -exp(e0*a) ) ? 0 : 1;
+
+ ex P = color_T(idx(a,8))*color_T(idx(b,8))*(x*dirac_ONE()+sqrt(x-1)*e0);
+ ex P_prime = color_T(idx(a,8))*color_T(idx(b,8))*(x*dirac_ONE()-sqrt(x-1)*e0);
+
+ result += check_equal(clifford_prime(P), P_prime);
+ result += check_equal(clifford_star(P), P);
+ result += check_equal(clifford_bar(P), P_prime);
+
+ return result;
+}
+
+static unsigned clifford_check9()
+{
+ unsigned result = 0;
+
+ realsymbol a("a"), b("b"), x("x");;
+ varidx mu(symbol("mu", "\\mu"), 4), nu(symbol("nu", "\\nu"), 4);
+
+ ex e = clifford_unit(mu, lorentz_g(mu, nu));
+ ex e0 = e.subs(mu==0);
+ ex e1 = e.subs(mu==1);
+ ex e2 = e.subs(mu==2);
+ ex e3 = e.subs(mu==3);
+ ex one = dirac_ONE();
+
+ ex P = color_T(idx(a,8))*color_T(idx(b,8))
+ *(x*one+sqrt(x-1)*e0+sqrt(x-2)*e0*e1 +sqrt(x-3)*e0*e1*e2 +sqrt(x-4)*e0*e1*e2*e3);
+ ex P_prime = color_T(idx(a,8))*color_T(idx(b,8))
+ *(x*one-sqrt(x-1)*e0+sqrt(x-2)*e0*e1 -sqrt(x-3)*e0*e1*e2 +sqrt(x-4)*e0*e1*e2*e3);
+ ex P_star = color_T(idx(a,8))*color_T(idx(b,8))
+ *(x*one+sqrt(x-1)*e0+sqrt(x-2)*e1*e0 +sqrt(x-3)*e2*e1*e0 +sqrt(x-4)*e3*e2*e1*e0);
+ ex P_bar = color_T(idx(a,8))*color_T(idx(b,8))
+ *(x*one-sqrt(x-1)*e0+sqrt(x-2)*e1*e0 -sqrt(x-3)*e2*e1*e0 +sqrt(x-4)*e3*e2*e1*e0);
+
+ result += check_equal(clifford_prime(P), P_prime);
+ result += check_equal(clifford_star(P), P_star);
+ result += check_equal(clifford_bar(P), P_bar);
+
+ 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)))); cout << '.' << flush;
- result += clifford_check6(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)))); cout << '.' << flush;
- result += clifford_check6(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)))); cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, 1, 1, 1})));
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, 1, 1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, -1, -1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, -1, -1, -1})));; cout << '.' << flush;
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, 1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, 1, -1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, 0, 1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 0, 1, -1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-3, 0, 2, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-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)))); cout << '.' << flush;
+ realsymbol s("s"), t("t"); // symbolic entries in matrix
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, 1, s, t})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-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); 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); 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); 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); 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); cout << '.' << flush;
+ 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<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<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<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<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<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
symbol dim("D");
result += clifford_check7(minkmetric(), dim); cout << '.' << flush;
varidx chi(symbol("chi"), dim), xi(symbol("xi"), dim);
+ result += clifford_check7(delta_tensor(xi, chi), dim); cout << '.' << flush;
+
result += clifford_check7(lorentz_g(xi, chi), dim); cout << '.' << flush;
- if (!result) {
- cout << " passed " << endl;
- clog << "(no output)" << endl;
- } else {
- cout << " failed " << endl;
- }
+ result += clifford_check7(indexed(-2*minkmetric(), sy_symm(), xi, chi), dim); cout << '.' << flush;
+ result += clifford_check7(-2*delta_tensor(xi, chi), dim); cout << '.' << flush;
+
+ result += clifford_check8(); cout << '.' << flush;
+
+ result += clifford_check9(); cout << '.' << flush;
return result;
}
+
+int main(int argc, char** argv)
+{
+ return exam_clifford();
+}
git://www.ginac.de / ginac.git / blobdiff