X-Git-Url: https://ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=check%2Fexam_clifford.cpp;h=25c815af507399178cc11fe434339f3a37c0c57c;hb=fc15782d51037f2432129a153c47b7d7697c129b;hp=8eee701337931fd94fab5e3f79c4d77812f0d034;hpb=d81773c9ebc817764485203f4892607a98667d48;p=ginac.git

diff --git a/check/exam_clifford.cpp b/check/exam_clifford.cpp
index 8eee7013..25c815af 100644
--- a/check/exam_clifford.cpp
+++ b/check/exam_clifford.cpp
@@ -3,7 +3,7 @@
  *  Here we test GiNaC's Clifford algebra objects. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -51,7 +51,7 @@ static unsigned clifford_check1(void)
 	unsigned result = 0;
 
 	symbol dim("D");
-	varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim);
+	varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim);
 	ex e;
 
 	e = dirac_ONE() * dirac_ONE();
@@ -72,6 +72,11 @@ static unsigned clifford_check1(void)
 	    dirac_gamma(mu.toggle_variance()) * dirac_gamma(nu.toggle_variance());
 	result += check_equal_simplify(e, 2*dim*dirac_ONE()-pow(dim, 2)*dirac_ONE());
 
+	e = dirac_gamma(nu.toggle_variance()) * dirac_gamma(rho.toggle_variance()) *
+	    dirac_gamma(mu) * dirac_gamma(rho) * dirac_gamma(nu);
+	e = e.simplify_indexed().collect(dirac_gamma(mu));
+	result += check_equal(e, pow(2 - dim, 2).expand() * dirac_gamma(mu));
+
 	return result;
 }
 
@@ -102,7 +107,7 @@ static unsigned clifford_check3(void)
 
 	symbol dim("D"), m("m"), q("q"), l("l"), ldotq("ldotq");
 	varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim),
-	       sig(symbol("sig"), dim), kap(symbol("kap"), dim), lam(symbol("lam"), 4);
+	       sig(symbol("sig"), dim), kap(symbol("kap"), dim), lam(symbol("lam"), dim);
 	ex e;
 
 	e = dirac_gamma(mu);
@@ -149,25 +154,98 @@ static unsigned clifford_check3(void)
 	// non-cyclicity of order D-4 of gamma5 * S_6
 	e = dirac_gamma5() * dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap) * dirac_gamma(mu.toggle_variance())
 	  + dim * dirac_gamma5() * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(kap);
-	e = dirac_trace(e);
+	e = dirac_trace(e).simplify_indexed();
 	e = (e / (dim - 4)).normal();
-	result += check_equal(e, 8 * eps0123(nu, rho, sig, kap));
+	result += check_equal(e, 8 * I * lorentz_eps(nu.replace_dim(4), rho.replace_dim(4), sig.replace_dim(4), kap.replace_dim(4)));
 
 	// one-loop vacuum polarization in QED
 	e = dirac_gamma(mu) *
-	    (dirac_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) *
+	    (dirac_slash(l, dim) + dirac_slash(q, 4) + m * dirac_ONE()) *
 	    dirac_gamma(mu.toggle_variance()) *
 	    (dirac_slash(l, dim) + m * dirac_ONE());
 	e = dirac_trace(e).simplify_indexed(sp);
 	result += check_equal(e, 4*((2-dim)*l*l + (2-dim)*ldotq + dim*m*m).expand());
 
-	e = dirac_slash(q, dim) *
-	    (dirac_slash(l, dim) + dirac_slash(q, dim) + m * dirac_ONE()) *
-	    dirac_slash(q, dim) *
+	e = dirac_slash(q, 4) *
+	    (dirac_slash(l, dim) + dirac_slash(q, 4) + m * dirac_ONE()) *
+	    dirac_slash(q, 4) *
 	    (dirac_slash(l, dim) + m * dirac_ONE());
 	e = dirac_trace(e).simplify_indexed(sp);
 	result += check_equal(e, 4*(2*ldotq*ldotq + q*q*ldotq - q*q*l*l + q*q*m*m).expand());
 
+	// stuff that had problems in the past
+	ex prop = dirac_slash(q, dim) - m * dirac_ONE();
+	e = dirac_slash(l, dim) * dirac_gamma5() * dirac_slash(l, dim) * prop;
+	e = dirac_trace(dirac_slash(q, dim) * e) - dirac_trace(m * e)
+	  - dirac_trace(prop * e);
+	result += check_equal(e, 0);
+
+	e = (dirac_gamma5() + dirac_ONE()) * dirac_gamma5();
+	e = dirac_trace(e);
+	result += check_equal(e, 4);
+
+	return result;
+}
+
+static unsigned clifford_check4(void)
+{
+	// simplify_indexed()/dirac_trace() cross-checks
+
+	unsigned result = 0;
+
+	symbol dim("D");
+	varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), rho(symbol("rho"), dim),
+	       sig(symbol("sig"), dim), lam(symbol("lam"), dim);
+	ex e, t1, t2;
+
+	e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(mu.toggle_variance());
+	t1 = dirac_trace(e).simplify_indexed();
+	t2 = dirac_trace(e.simplify_indexed());
+	result += check_equal((t1 - t2).expand(), 0);
+
+	e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(sig) * dirac_gamma(mu.toggle_variance()) * dirac_gamma(lam);
+	t1 = dirac_trace(e).simplify_indexed();
+	t2 = dirac_trace(e.simplify_indexed());
+	result += check_equal((t1 - t2).expand(), 0);
+
+	e = dirac_gamma(sig) * dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(nu.toggle_variance()) * dirac_gamma(mu.toggle_variance());
+	t1 = dirac_trace(e).simplify_indexed();
+	t2 = dirac_trace(e.simplify_indexed());
+	result += check_equal((t1 - t2).expand(), 0);
+
+	e = dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(rho) * dirac_gamma(mu.toggle_variance()) * dirac_gamma(sig) * dirac_gamma(nu.toggle_variance());
+	t1 = dirac_trace(e).simplify_indexed();
+	t2 = dirac_trace(e.simplify_indexed());
+	result += check_equal((t1 - t2).expand(), 0);
+
+	return result;
+}
+
+static unsigned clifford_check5(void)
+{
+	// canonicalize_clifford() checks
+
+	unsigned result = 0;
+
+	symbol dim("D");
+	varidx mu(symbol("mu"), dim), nu(symbol("nu"), dim), lam(symbol("lam"), dim);
+	ex e;
+
+	e = dirac_gamma(mu) * dirac_gamma(nu) + dirac_gamma(nu) * dirac_gamma(mu);
+	result += check_equal(canonicalize_clifford(e), 2*lorentz_g(mu, nu));
+
+	e = (dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(lam)
+	   + dirac_gamma(nu) * dirac_gamma(lam) * dirac_gamma(mu)
+	   + dirac_gamma(lam) * dirac_gamma(mu) * dirac_gamma(nu)
+	   - dirac_gamma(nu) * dirac_gamma(mu) * dirac_gamma(lam)
+	   - dirac_gamma(lam) * dirac_gamma(nu) * dirac_gamma(mu)
+	   - dirac_gamma(mu) * dirac_gamma(lam) * dirac_gamma(nu)) / 6
+	  + lorentz_g(mu, nu) * dirac_gamma(lam)
+	  - lorentz_g(mu, lam) * dirac_gamma(nu)
+	  + lorentz_g(nu, lam) * dirac_gamma(mu)
+	  - dirac_gamma(mu) * dirac_gamma(nu) * dirac_gamma(lam);
+	result += check_equal(canonicalize_clifford(e), 0);
+
 	return result;
 }
 
@@ -181,7 +259,9 @@ unsigned exam_clifford(void)
 	result += clifford_check1();  cout << '.' << flush;
 	result += clifford_check2();  cout << '.' << flush;
 	result += clifford_check3();  cout << '.' << flush;
-	
+	result += clifford_check4();  cout << '.' << flush;
+	result += clifford_check5();  cout << '.' << flush;
+
 	if (!result) {
 		cout << " passed " << endl;
 		clog << "(no output)" << endl;