added check for contraction of epsilon with symmetric tensor

[ginac.git] / check / exam_indexed.cpp

diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp
index e5a3772f5fc02a25dbccb21b99486209fffbdb3b..2426430c8e4450e27a9614983046827f87e8489c 100644 (file)
--- a/check/exam_indexed.cpp
+++ b/check/exam_indexed.cpp
@@ -109,8 +109,9 @@ static unsigned epsilon_check(void)
 
        unsigned result = 0;
 
-       symbol s_mu("mu"), s_nu("nu"), s_rho("rho"), s_sigma("sigma");
-       varidx mu(s_mu, 4), nu(s_nu, 4), rho(s_rho, 4), sigma(s_sigma, 4);
+       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);
 
        // antisymmetry
        result += check_equal(lorentz_eps(mu, nu, rho, sigma) + lorentz_eps(sigma, rho, mu, nu), 0);
@@ -120,6 +121,12 @@ static unsigned epsilon_check(void)
        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);
 
+       // 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(e, e);
+
        return result;
 }
 
@@ -161,23 +168,15 @@ static unsigned edyn_check(void)
        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.set(2, 2, 1); L.set(3, 3, 1);
 
        // Electromagnetic field tensor
-       matrix F(4, 4);
-       F.set(0, 1, -Ex);
-       F.set(1, 0, Ex);
-       F.set(0, 2, -Ey);
-       F.set(2, 0, Ey);
-       F.set(0, 3, -Ez);
-       F.set(3, 0, Ez);
-       F.set(1, 2, -Bz);
-       F.set(2, 1, Bz);
-       F.set(1, 3, By);
-       F.set(3, 1, -By);
-       F.set(2, 3, -Bx);
-       F.set(3, 2, Bx);
+       matrix F(4, 4, lst(
+                0, -Ex, -Ey, -Ez,
+               Ex,   0, -Bz,  By,
+               Ey,  Bz,   0, -Bx,
+               Ez, -By,  Bx // 0
+       ));
 
        // Indices
        symbol s_mu("mu"), s_nu("nu"), s_rho("rho"), s_sigma("sigma");
@@ -185,8 +184,8 @@ static unsigned edyn_check(void)
 
        // Apply transformation law of second rank tensor
        ex e = (indexed(L, mu, rho.toggle_variance())
-          * indexed(L, nu, sigma.toggle_variance())
-          * indexed(F, rho, sigma)).simplify_indexed();
+             * indexed(L, nu, sigma.toggle_variance())
+             * indexed(F, rho, sigma)).simplify_indexed();
 
        // Extract transformed electric and magnetic fields
        ex Ex_p = e.subs(lst(mu == 1, nu == 0)).normal();
@@ -207,11 +206,7 @@ static unsigned edyn_check(void)
        // Test 2: check energy density and Poynting vector of electromagnetic field
 
        // Minkowski metric
-       matrix eta(4, 4);
-       eta.set(0, 0, 1);
-       eta.set(1, 1, -1);
-       eta.set(2, 2, -1);
-       eta.set(3, 3, -1);
+       ex eta = diag_matrix(lst(1, -1, -1, -1));
 
        // Covariant field tensor
        ex F_mu_nu = (indexed(eta, mu.toggle_variance(), rho.toggle_variance())