X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=check%2Fexam_clifford.cpp;h=06396e1a0fb5dd8b09011a85ad48c7a587b357b4;hp=dd4b8a24425a7d504bb1f440ca4e962b42212b4b;hb=547db2f0380c03c7d013aa8bda36aa33ff5559e1;hpb=97bcb4160e08260339677cfe800a826f4bcb9a02

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index dd4b8a24..06396e1a 100644
--- a/check/exam_clifford.cpp
+++ b/check/exam_clifford.cpp
@@ -184,6 +184,19 @@ static unsigned clifford_check3()
 	e = dirac_trace(e);
 	result += check_equal(e, 4);
 
+	// traces with multiple representation labels
+	e = dirac_ONE(0) * dirac_ONE(1) / 16;
+	result += check_equal(dirac_trace(e, 0), dirac_ONE(1) / 4);
+	result += check_equal(dirac_trace(e, 1), dirac_ONE(0) / 4);
+	result += check_equal(dirac_trace(e, 2), e);
+	result += check_equal(dirac_trace(e, lst(0, 1)), 1);
+
+	e = dirac_gamma(mu, 0) * dirac_gamma(mu.toggle_variance(), 1) * dirac_gamma(nu, 0) * dirac_gamma(nu.toggle_variance(), 1);
+	result += check_equal_simplify(dirac_trace(e, 0), 4 * dim * dirac_ONE(1));
+	result += check_equal_simplify(dirac_trace(e, 1), 4 * dim * dirac_ONE(0));
+	result += check_equal_simplify(dirac_trace(e, 2), e);
+	result += check_equal_simplify(dirac_trace(e, lst(0, 1)), 16 * dim);
+
 	return result;
 }
 
@@ -255,7 +268,7 @@ static unsigned clifford_check6(const matrix & A)
 	       psi(symbol("psi"),4), lam(symbol("lambda"), 4),
 	       xi(symbol("xi"), 4),  rho(symbol("rho"),4);
 
-	ex G = indexed(A, sy_symm(), psi, xi);
+	ex G = A;
 
 	matrix A2(4, 4);
 	A2 = A.mul(A);
@@ -275,13 +288,13 @@ static unsigned clifford_check6(const matrix & A)
 	result += check_equal_simplify(e, A.trace() * dirac_ONE());
 
 	e = clifford_unit(nu, G) * clifford_unit(nu, G);
-	result += check_equal_simplify(e, G.subs(psi == nu).subs(xi == nu) * dirac_ONE());
+	result += check_equal_simplify(e, indexed(G, sy_symm(), nu, nu) * dirac_ONE());
 
 	e = clifford_unit(nu, G) * clifford_unit(nu.toggle_variance(), G) * clifford_unit(mu, G);
 	result += check_equal_simplify(e, A.trace() * clifford_unit(mu, G));
 
 	e = clifford_unit(nu, G) * clifford_unit(mu, G) * clifford_unit(nu.toggle_variance(), G);
-	result += check_equal_simplify(e, 2*G.subs(psi == mu).subs(xi == mu)*clifford_unit(mu, G) - A.trace()*clifford_unit(mu, G));
+	result += check_equal_simplify(e, 2*indexed(G, sy_symm(), mu, mu)*clifford_unit(mu, G) - A.trace()*clifford_unit(mu, G));
 
 	e = clifford_unit(nu, G) * clifford_unit(nu.toggle_variance(), G)
 	  * clifford_unit(mu, G) * clifford_unit(mu.toggle_variance(), G);
@@ -311,7 +324,7 @@ static unsigned clifford_check6(const matrix & A)
 
 	// canonicalize_clifford() checks
 	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()*G.subs(psi == mu).subs(xi == nu));
+	result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(G, sy_symm(), mu, nu));
 
 	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)
@@ -319,9 +332,9 @@ static unsigned clifford_check6(const matrix & A)
 	   - 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
-	  + G.subs(psi == mu).subs(xi == nu) * clifford_unit(lam, G)
-	  - G.subs(psi == mu).subs(xi == lam) * clifford_unit(nu, G)
-	  + G.subs(psi == nu).subs(xi == lam) * clifford_unit(mu, G)
+	  + indexed(G, sy_symm(), mu, nu) * clifford_unit(lam, G)
+	  - indexed(G, sy_symm(), mu, lam) * clifford_unit(nu, G)
+	  + indexed(G, sy_symm(), 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);
 
@@ -347,7 +360,7 @@ static unsigned clifford_check7()
 
 	ex e;
 
-	ex G = lorentz_g(psi, xi);
+	ex G = minkmetric();
 
 	e = dirac_ONE() * dirac_ONE();
 	result += check_equal(e, dirac_ONE());
@@ -374,7 +387,7 @@ static unsigned clifford_check7()
 
 	// canonicalize_clifford() checks
 	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()*G.subs(psi == mu).subs(xi == nu));
+	result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(G, sy_symm(), mu, nu));
 
 	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)
@@ -382,9 +395,9 @@ static unsigned clifford_check7()
 	   - 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
-	  + G.subs(psi == mu).subs(xi == nu) * clifford_unit(lam, G)
-	  - G.subs(psi == mu).subs(xi == lam) * clifford_unit(nu, G)
-	  + G.subs(psi == nu).subs(xi == lam) * clifford_unit(mu, G)
+	  + indexed(G, sy_symm(), mu, nu) * clifford_unit(lam, G)
+	  - indexed(G, sy_symm(), mu, lam) * clifford_unit(nu, G)
+	  + indexed(G, sy_symm(), 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);