+ // 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()
+{
+ // 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()
+{
+ // 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*dirac_ONE()*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);
+