+ e = spinor_metric(D, A) * spinor_metric(A_co, B_co) * spinor_metric(B, C) - spinor_metric(D, A_co) * spinor_metric(A, B_co) * spinor_metric(B, C);
+ result += check_equal_simplify(e, 0);
+
+ return result;
+}
+
+static unsigned dummy_check(void)
+{
+ // check dummy index renaming/repositioning
+
+ unsigned result = 0;
+
+ symbol p("p"), q("q");
+ idx i(symbol("i"), 3), j(symbol("j"), 3), n(symbol("n"), 3);
+ varidx mu(symbol("mu"), 4), nu(symbol("nu"), 4);
+ 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);
+
+ e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu, nu.toggle_variance());
+ result += check_equal_simplify(e, 0);
+
+ e = indexed(p, mu.toggle_variance(), nu, mu) * indexed(q, i)
+ - indexed(p, mu, nu, mu.toggle_variance()) * indexed(q, i);
+ result += check_equal_simplify(e, 0);
+
+ e = indexed(p, mu, mu.toggle_variance()) - indexed(p, nu.toggle_variance(), nu);
+ result += check_equal_simplify(e, 0);
+ e = indexed(p, mu.toggle_variance(), mu) - indexed(p, nu, nu.toggle_variance());
+ result += check_equal_simplify(e, 0);