added checks for dummy index renaming and canonicalize_clifford()

[ginac.git] / check / exam_indexed.cpp

diff --git a/check/exam_indexed.cpp b/check/exam_indexed.cpp
index e5a3772f5fc02a25dbccb21b99486209fffbdb3b..e1ee1eb1c8977e84c6b269acd632247db6073e41 100644 (file)
--- a/check/exam_indexed.cpp
+++ b/check/exam_indexed.cpp
@@ -44,6 +44,17 @@ static unsigned check_equal_simplify(const ex &e1, const ex &e2)
        return 0;
 }
 
+static unsigned check_equal_simplify(const ex &e1, const ex &e2, const scalar_products &sp)
+{
+       ex e = simplify_indexed(e1, sp) - e2;
+       if (!e.is_zero()) {
+               clog << "simplify_indexed(" << e1 << ")-" << e2 << " erroneously returned "
+                    << e << " instead of 0" << endl;
+               return 1;
+       }
+       return 0;
+}
+
 static unsigned delta_check(void)
 {
        // checks identities of the delta tensor
@@ -109,8 +120,9 @@ 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 +132,12 @@ 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;
 }
 
@@ -129,14 +147,42 @@ static unsigned symmetry_check(void)
 
        unsigned result = 0;
 
-       symbol s_i("i"), s_j("j"), s_k("k");
-       idx i(s_i, 3), j(s_j, 3), k(s_k, 3);
-       symbol A("A");
-       ex e, e1, e2;
+       idx i(symbol("i"), 3), j(symbol("j"), 3), k(symbol("k"), 3), l(symbol("l"), 3);
+       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_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
+       result += check_equal_simplify(e, e);
+
+       return result;
+}
+
+static unsigned scalar_product_check(void)
+{
+       // check scalar product replacement
+
+       unsigned result = 0;
+
+    idx i(symbol("i"), 3), j(symbol("j"), 3);
+    symbol A("A"), B("B"), C("C");
+       ex e;
+
+    scalar_products sp;
+    sp.add(A, B, 0); // A and B are orthogonal
+    sp.add(A, C, 0); // A and C are orthogonal
+    sp.add(A, A, 4); // A^2 = 4 (A has length 2)
+
+    e = (indexed(A + B, i) * indexed(A + C, i)).expand(expand_options::expand_indexed);
+       result += check_equal_simplify(e, indexed(B, i) * indexed(C, i) + 4, sp);
+       e = indexed(A, i, i) * indexed(B, j, j); // GiNaC 0.8.0 had a bug here
+       result += check_equal_simplify(e, e, sp);
 
        return result;
 }
@@ -161,23 +207,15 @@ 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 +223,8 @@ 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 +245,7 @@ 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())
@@ -240,6 +274,59 @@ static unsigned edyn_check(void)
        return result;
 }
 
+static unsigned spinor_check(void)
+{
+       // check identities of the spinor metric
+
+       unsigned result = 0;
+
+       symbol psi("psi");
+       spinidx A(symbol("A"), 2), B(symbol("B"), 2), C(symbol("C"), 2);
+       ex A_co = A.toggle_variance(), B_co = B.toggle_variance();
+       ex e;
+
+       e = spinor_metric(A_co, B_co) * spinor_metric(A, B);
+       result += check_equal_simplify(e, 2);
+       e = spinor_metric(A_co, B_co) * spinor_metric(B, A);
+       result += check_equal_simplify(e, -2);
+       e = spinor_metric(A_co, B_co) * spinor_metric(A, C);
+       result += check_equal_simplify(e, delta_tensor(B_co, C));
+       e = spinor_metric(A_co, B_co) * spinor_metric(B, C);
+       result += check_equal_simplify(e, -delta_tensor(A_co, C));
+       e = spinor_metric(A_co, B_co) * spinor_metric(C, A);
+       result += check_equal_simplify(e, -delta_tensor(B_co, C));
+       e = spinor_metric(A, B) * indexed(psi, B_co);
+       result += check_equal_simplify(e, indexed(psi, A));
+       e = spinor_metric(A, B) * indexed(psi, A_co);
+       result += check_equal_simplify(e, -indexed(psi, B));
+       e = spinor_metric(A_co, B_co) * indexed(psi, B);
+       result += check_equal_simplify(e, -indexed(psi, A_co));
+       e = spinor_metric(A_co, B_co) * indexed(psi, A);
+       result += check_equal_simplify(e, indexed(psi, B_co));
+
+       return result;
+}
+
+static unsigned dummy_check(void)
+{
+       // check dummy index renaming
+
+       unsigned result = 0;
+
+       symbol p("p"), q("q");
+       idx i(symbol("i"), 3), j(symbol("j"), 3), n(symbol("n"), 3);
+       ex e;
+
+       e = indexed(p, i) * indexed(q, i) - indexed(p, j) * indexed(q, j);
+       result += check_equal_simplify(e, 0);
+
+       e = indexed(p, i) * indexed(p, i) * indexed(q, j) * indexed(q, j)
+         - indexed(p, n) * indexed(p, n) * indexed(q, j) * indexed(q, j);
+       result += check_equal_simplify(e, 0);
+
+       return result;
+}
+
 unsigned exam_indexed(void)
 {
        unsigned result = 0;
@@ -251,7 +338,10 @@ unsigned exam_indexed(void)
        result += metric_check();  cout << '.' << flush;
        result += epsilon_check();  cout << '.' << flush;
        result += symmetry_check();  cout << '.' << flush;
+       result += scalar_product_check();  cout << '.' << flush;
        result += edyn_check();  cout << '.' << flush;
+       result += spinor_check(); cout << '.' << flush;
+       result += dummy_check(); cout << '.' << flush;
        
        if (!result) {
                cout << " passed " << endl;