* Here we test GiNaC's Clifford algebra objects. */
/*
- * GiNaC Copyright (C) 1999-2009 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
{
ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
- for (int j=0; j<4; j++) {
+ for (int j=0; j<4; j++) {
ex esub = e.subs(
is_a<varidx>(mu)
- ? lst (
+ ? 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()))
+ }
+ : lst{mu == idx(j, mu.get_dim())}
);
if (!(canonicalize_clifford(esub).is_zero())) {
clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned "
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));
- // Fails with new tinfo mechanism because the order of gamme matrices with different rl depends on luck.
+ // 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);
+ result += check_equal_simplify(dirac_trace(e, lst{0, 1}), 16 * dim);
return result;
}
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_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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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);
+ 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));
+ 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);
+ 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;
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()*unit.get_metric(nu, mu));
{
unsigned result = 0;
- realsymbol a("a");
+ realsymbol a("a"), b("b"), x("x");
varidx mu(symbol("mu", "\\mu"), 1);
- ex e = clifford_unit(mu, diag_matrix(lst(-1))), e0 = e.subs(mu==0);
+ 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;
}
result += clifford_check5(); cout << '.' << flush;
// anticommuting, symmetric examples
- 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;
+ 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<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;
+ 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;
+ 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;
+ 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;
+ 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;
+ 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;
+ 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_check8(); cout << '.' << flush;
+ result += clifford_check9(); cout << '.' << flush;
+
return result;
}
git://www.ginac.de / ginac.git / blobdiff