Vladimirs patch for removing the "anti-commuting" branches from Clifford

[ginac.git] / check / exam_clifford.cpp

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index 53b57906557727df751f9bf6b3146f69b4514f9e..e43708f232e409f328b51cf25984734ed72827cf 100644 (file)
--- a/check/exam_clifford.cpp
+++ b/check/exam_clifford.cpp
@@ -318,7 +318,6 @@ static unsigned clifford_check6(const matrix & A)
        A2 = A_symm.mul(A_symm);
        
        ex e, e1;
-       bool anticommuting = ex_to<clifford>(clifford_unit(nu, A)).is_anticommuting();
        int result = 0;
 
        // checks general identities and contractions for clifford_unit
@@ -343,8 +342,6 @@ static unsigned clifford_check6(const matrix & A)
        result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));
 
        e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu.toggle_variance(), A);
-       if (anticommuting)
-               result += check_equal_simplify(e, 2*indexed(A_symm, sy_symm(), mu, mu)*clifford_unit(mu, A) - A.trace()*clifford_unit(mu, A));
        
        result += check_equal_simplify_term(e,  2 * indexed(A_symm, sy_symm(), nu.toggle_variance(), mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);
 
@@ -358,26 +355,17 @@ static unsigned clifford_check6(const matrix & A)
 
        e = clifford_unit(mu, A) * clifford_unit(nu, A)
          * clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu.toggle_variance(), A);
-       if (anticommuting) 
-               result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE());
 
        result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu.toggle_variance(), mu.toggle_variance()) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());
 
        e = clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu, A)
          * clifford_unit(mu, A) * clifford_unit(nu.toggle_variance(), A);
-       if (anticommuting) {
-               result += check_equal_simplify(e, 2*A2.trace()*dirac_ONE() - pow(A.trace(), 2)*dirac_ONE());
-               e1 = remove_dirac_ONE(simplify_indexed(e));
-               result += check_equal(e1, 2*A2.trace() - pow(A.trace(), 2));
-       }
 
        result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu.toggle_variance(), A) * clifford_unit(nu.toggle_variance(), A) - pow(A.trace(), 2)*dirac_ONE());
 
        e = clifford_unit(nu.toggle_variance(), A) * clifford_unit(rho.toggle_variance(), A)
          * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);
        e = e.simplify_indexed().collect(clifford_unit(mu, A));
-       if (anticommuting)
-               result += check_equal(e, (4*indexed(A2, sy_symm(), mu, mu) - 4 * indexed(A_symm, sy_symm(), mu, mu)*A.trace() +pow(A.trace(), 2)) * clifford_unit(mu, A));
        
        result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu.toggle_variance(),  rho)*indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) *clifford_unit(nu, A) 
                                            - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) 
@@ -386,8 +374,6 @@ static unsigned clifford_check6(const matrix & A)
        e = clifford_unit(nu.toggle_variance(), A) * clifford_unit(rho, A)
          * clifford_unit(mu, A) * clifford_unit(rho.toggle_variance(), A) * clifford_unit(nu, A);
        e = e.simplify_indexed().collect(clifford_unit(mu, A));
-       if (anticommuting)
-               result += check_equal(e, (4*indexed(A2, sy_symm(), mu, mu) - 4*indexed(A_symm, sy_symm(), mu, mu)*A.trace() +pow(A.trace(), 2))* clifford_unit(mu, A));
        
        result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu.toggle_variance(),  rho)*indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) *clifford_unit(nu, A) 
                                            - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho.toggle_variance(), mu) 
@@ -457,13 +443,10 @@ static unsigned clifford_check7(const ex & G, const symbol & dim)
        varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim),
               psi(symbol("psi"),dim), lam(symbol("lambda"), dim), xi(symbol("xi"), dim);
 
-       ex e, G_base;
-
-       if (is_a<indexed>(G))
-               G_base = G.op(0);
-       else
-               G_base = G;
-
+       ex e;
+       clifford unit = ex_to<clifford>(clifford_unit(mu, G));
+       ex scalar = unit.get_metric(varidx(0, dim), varidx(0, dim));
+       
        e = dirac_ONE() * dirac_ONE();
        result += check_equal(e, dirac_ONE());
 
@@ -472,25 +455,25 @@ static unsigned clifford_check7(const ex & G, const symbol & dim)
 
        e = clifford_unit(varidx(2, dim), G) * clifford_unit(varidx(1, dim), G)
          * clifford_unit(varidx(1, dim), G) * clifford_unit(varidx(2, dim), G);
-       result += check_equal(e, dirac_ONE());
+       result += check_equal(e, dirac_ONE()*pow(scalar, 2));
 
        e = clifford_unit(mu, G) * clifford_unit(nu, G)
          * clifford_unit(nu.toggle_variance(), G) * clifford_unit(mu.toggle_variance(), G);
-       result += check_equal_simplify(e, pow(dim, 2) * dirac_ONE());
+       result += check_equal_simplify(e, pow(dim*scalar, 2) * dirac_ONE());
 
        e = clifford_unit(mu, G) * clifford_unit(nu, G)
          * clifford_unit(mu.toggle_variance(), G) * clifford_unit(nu.toggle_variance(), G);
-       result += check_equal_simplify(e, 2*dim*dirac_ONE() - pow(dim, 2)*dirac_ONE());
+       result += check_equal_simplify(e, (2*dim - pow(dim, 2))*pow(scalar,2)*dirac_ONE());
 
        e = clifford_unit(nu.toggle_variance(), G) * clifford_unit(rho.toggle_variance(), G)
          * clifford_unit(mu, G) * clifford_unit(rho, G) * clifford_unit(nu, G);
        e = e.simplify_indexed().collect(clifford_unit(mu, G));
-       result += check_equal(e, pow(2 - dim, 2).expand() * clifford_unit(mu, G));
+       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()) {
                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()*indexed(G_base, sy_symm(), nu, mu));
+               result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*unit.get_metric(nu, mu));
                
                e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G)
                         + clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G)
@@ -498,14 +481,14 @@ static unsigned clifford_check7(const ex & G, const symbol & dim)
                         - clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G)
                         - clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G)
                         - clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6
-                       + indexed(G_base, sy_symm(), mu, nu) * clifford_unit(lam, G)
-                       - indexed(G_base, sy_symm(), mu, lam) * clifford_unit(nu, G)
-                       + indexed(G_base, sy_symm(), nu, lam) * clifford_unit(mu, G)
+                       + unit.get_metric(mu, nu) * clifford_unit(lam, G)
+                       - unit.get_metric(mu, lam) * clifford_unit(nu, G)
+                       + unit.get_metric(nu, lam) * clifford_unit(mu, G)
                        - clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G);
                result += check_equal(canonicalize_clifford(e), 0);
        } else {
                e = clifford_unit(mu, G) * clifford_unit(nu, G) + clifford_unit(nu, G) * clifford_unit(mu, G);
-               result += check_equal(canonicalize_clifford(e), dirac_ONE()*(indexed(G_base, mu, nu) + indexed(G_base, nu, mu)));
+               result += check_equal(canonicalize_clifford(e), dirac_ONE()*(unit.get_metric(mu, nu) + unit.get_metric(nu, mu)));
                
                e = (clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G)
                         + clifford_unit(nu, G) * clifford_unit(lam, G) * clifford_unit(mu, G)
@@ -513,9 +496,9 @@ static unsigned clifford_check7(const ex & G, const symbol & dim)
                         - clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(lam, G)
                         - clifford_unit(lam, G) * clifford_unit(nu, G) * clifford_unit(mu, G)
                         - clifford_unit(mu, G) * clifford_unit(lam, G) * clifford_unit(nu, G)) / 6
-                       + half * (indexed(G_base,  mu, nu) + indexed(G_base,  nu, mu)) * clifford_unit(lam, G)
-                       - half * (indexed(G_base, mu, lam) + indexed(G_base, lam, mu)) * clifford_unit(nu, G)
-                       + half * (indexed(G_base, nu, lam) + indexed(G_base, lam, nu)) * clifford_unit(mu, G)
+                       + half * (unit.get_metric(mu, nu) + unit.get_metric(nu, mu)) * clifford_unit(lam, G)
+                       - half * (unit.get_metric(mu, lam) + unit.get_metric(lam, mu)) * clifford_unit(nu, G)
+                       + half * (unit.get_metric(nu, lam) + unit.get_metric(lam, nu)) * clifford_unit(mu, G)
                        - clifford_unit(mu, G) * clifford_unit(nu, G) * clifford_unit(lam, G);
                result += check_equal(canonicalize_clifford(e), 0);
        }
@@ -580,8 +563,13 @@ unsigned exam_clifford()
        result += clifford_check7(minkmetric(), dim); cout << '.' << flush;
 
        varidx chi(symbol("chi"), dim), xi(symbol("xi"), dim);
+       result += clifford_check7(delta_tensor(xi, chi), dim); cout << '.' << flush;
+
        result += clifford_check7(lorentz_g(xi, chi), dim); cout << '.' << flush;
 
+       result += clifford_check7(indexed(-2*minkmetric(), sy_symm(), xi, chi), dim); cout << '.' << flush;
+       result += clifford_check7(-2*delta_tensor(xi, chi), dim); cout << '.' << flush;
+
        if (!result) {
                cout << " passed " << endl;
                clog << "(no output)" << endl;