symbol s_mu("mu"), s_nu("nu"), s_rho("rho"), s_sigma("sigma"), s_tau("tau");
symbol d("d");
varidx mu(s_mu, 4), nu(s_nu, 4), rho(s_rho, 4), sigma(s_sigma, 4), tau(s_tau, 4);
+ varidx mu_co(s_mu, 4, true), nu_co(s_nu, 4, true), rho_co(s_rho, 4, true), sigma_co(s_sigma, 4, true), tau_co(s_tau, 4, true);
// antisymmetry
result += check_equal(lorentz_eps(mu, nu, rho, sigma) + lorentz_eps(sigma, rho, mu, nu), 0);
// convolution is zero
- result += check_equal(lorentz_eps(mu, nu, rho, nu.toggle_variance()), 0);
- result += check_equal(lorentz_eps(mu, nu, mu.toggle_variance(), nu.toggle_variance()), 0);
- result += check_equal_simplify(lorentz_g(mu.toggle_variance(), nu.toggle_variance()) * lorentz_eps(mu, nu, rho, sigma), 0);
+ result += check_equal(lorentz_eps(mu, nu, rho, nu_co), 0);
+ result += check_equal(lorentz_eps(mu, nu, mu_co, nu_co), 0);
+ result += check_equal_simplify(lorentz_g(mu_co, nu_co) * lorentz_eps(mu, nu, rho, sigma), 0);
// contraction with symmetric tensor is zero
- result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, indexed::symmetric, mu.toggle_variance(), nu.toggle_variance()), 0);
- result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, indexed::symmetric, nu.toggle_variance(), sigma.toggle_variance(), rho.toggle_variance()), 0);
- ex e = lorentz_eps(mu, nu, rho, sigma) * indexed(d, indexed::symmetric, mu.toggle_variance(), tau);
+ result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), mu_co, nu_co), 0);
+ result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), nu_co, sigma_co, rho_co), 0);
+ ex e = lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), mu_co, tau);
result += check_equal_simplify(e, e);
+ // contractions of epsilon tensors
+ result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * lorentz_eps(mu_co, nu_co, rho_co, sigma_co), -24);
+ result += check_equal_simplify(lorentz_eps(tau, nu, rho, sigma) * lorentz_eps(mu_co, nu_co, rho_co, sigma_co), -6 * delta_tensor(tau, mu_co));
+
return result;
}
symbol A("A"), B("B");
ex e;
- result += check_equal(indexed(A, indexed::symmetric, i, j), indexed(A, indexed::symmetric, j, i));
- result += check_equal(indexed(A, indexed::antisymmetric, i, j) + indexed(A, indexed::antisymmetric, j, i), 0);
- result += check_equal(indexed(A, indexed::antisymmetric, i, j, k) - indexed(A, indexed::antisymmetric, j, k, i), 0);
- e = indexed(A, indexed::symmetric, i, j, k) *
- indexed(B, indexed::antisymmetric, l, k, i);
+ result += check_equal(indexed(A, sy_symm(), i, j), indexed(A, sy_symm(), j, i));
+ result += check_equal(indexed(A, sy_anti(), i, j) + indexed(A, sy_anti(), j, i), 0);
+ result += check_equal(indexed(A, sy_anti(), i, j, k) - indexed(A, sy_anti(), j, k, i), 0);
+ e = indexed(A, sy_symm(), i, j, k) *
+ indexed(B, sy_anti(), l, k, i);
result += check_equal_simplify(e, 0);
- e = indexed(A, indexed::symmetric, i, i, j, j) *
- indexed(B, indexed::antisymmetric, k, l); // GiNaC 0.8.0 had a bug here
+ e = indexed(A, sy_symm(), i, i, j, j) *
+ indexed(B, sy_anti(), k, l); // GiNaC 0.8.0 had a bug here
result += check_equal_simplify(e, e);
+ symmetry R = sy_symm(sy_anti(0, 1), sy_anti(2, 3));
+ e = indexed(A, R, i, j, k, l) + indexed(A, R, j, i, k, l);
+ result += check_equal(e, 0);
+ e = indexed(A, R, i, j, k, l) + indexed(A, R, i, j, l, k);
+ result += check_equal(e, 0);
+ e = indexed(A, R, i, j, k, l) - indexed(A, R, j, i, l, k);
+ result += check_equal(e, 0);
+ e = indexed(A, R, i, j, k, l) + indexed(A, R, k, l, j, i);
+ result += check_equal(e, 0);
+
e = indexed(A, i, j);
result += check_equal(symmetrize(e) + antisymmetrize(e), e);
- e = indexed(A, indexed::symmetric, i, j, k, l);
+ e = indexed(A, sy_symm(), i, j, k, l);
result += check_equal(symmetrize(e), e);
result += check_equal(antisymmetrize(e), 0);
- e = indexed(A, indexed::antisymmetric, i, j, k, l);
+ e = indexed(A, sy_anti(), i, j, k, l);
result += check_equal(symmetrize(e), 0);
result += check_equal(antisymmetrize(e), e);