result += check_equal_simplify(lorentz_g(mu.toggle_variance(), nu.toggle_variance()) * 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.toggle_variance(), nu.toggle_variance()), 0);
+ result += check_equal_simplify(lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), nu.toggle_variance(), sigma.toggle_variance(), rho.toggle_variance()), 0);
+ ex e = lorentz_eps(mu, nu, rho, sigma) * indexed(d, sy_symm(), mu.toggle_variance(), tau);
result += check_equal_simplify(e, e);
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);
+ e = indexed(A, i, j);
+ result += check_equal(symmetrize(e) + antisymmetrize(e), e);
+ e = indexed(A, sy_symm(), i, j, k, l);
+ result += check_equal(symmetrize(e), e);
+ result += check_equal(antisymmetrize(e), 0);
+ e = indexed(A, sy_anti(), i, j, k, l);
+ result += check_equal(symmetrize(e), 0);
+ result += check_equal(antisymmetrize(e), e);
+
return result;
}
// Lorentz transformation matrix (boost along x axis)
matrix L(4, 4);
- L.set(0, 0, gamma);
- L.set(0, 1, -beta*gamma);
- L.set(1, 0, -beta*gamma);
- L.set(1, 1, gamma);
- L.set(2, 2, 1); L.set(3, 3, 1);
+ L(0, 0) = gamma;
+ L(0, 1) = -beta*gamma;
+ L(1, 0) = -beta*gamma;
+ L(1, 1) = gamma;
+ L(2, 2) = 1; L(3, 3) = 1;
// Electromagnetic field tensor
matrix F(4, 4, lst(
0, -Ex, -Ey, -Ez,
Ex, 0, -Bz, By,
Ey, Bz, 0, -Bx,
- Ez, -By, Bx // 0
+ Ez, -By, Bx, 0
));
// Indices
symbol p("p"), q("q");
idx i(symbol("i"), 3), j(symbol("j"), 3), n(symbol("n"), 3);
+ varidx mu(symbol("mu"), 4), nu(symbol("nu"), 4);
ex e;
e = indexed(p, i) * indexed(q, i) - indexed(p, j) * indexed(q, j);
- indexed(p, n) * indexed(p, n) * indexed(q, j) * indexed(q, j);
result += check_equal_simplify(e, 0);
+ e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu, nu.toggle_variance());
+ result += check_equal_simplify(e, 0);
+
return result;
}