- result += check_equal(indexed(A, indexed::symmetric, i, j), indexed(A, indexed::symmetric, j, i));
- result += check_equal(indexed(A, indexed::antisymmetric, i, j) + indexed(A, indexed::antisymmetric, j, i), 0);
- result += check_equal(indexed(A, indexed::antisymmetric, i, j, k) - indexed(A, indexed::antisymmetric, j, k, i), 0);
+ symmetry R = sy_symm(sy_anti(0, 1), sy_anti(2, 3));
+ e = indexed(A, R, i, j, k, l) + indexed(A, R, j, i, k, l);
+ result += check_equal(e, 0);
+ e = indexed(A, R, i, j, k, l) + indexed(A, R, i, j, l, k);
+ result += check_equal(e, 0);
+ e = indexed(A, R, i, j, k, l) - indexed(A, R, j, i, l, k);
+ result += check_equal(e, 0);
+ e = indexed(A, R, i, j, k, l) + indexed(A, R, k, l, j, i);
+ result += check_equal(e, 0);
+
+ e = indexed(A, i, j);
+ result += check_equal(symmetrize(e) + antisymmetrize(e), e);
+ e = indexed(A, sy_symm(), i, j, k, l);
+ result += check_equal(symmetrize(e), e);
+ result += check_equal(antisymmetrize(e), 0);
+ e = indexed(A, sy_anti(), i, j, k, l);
+ result += check_equal(symmetrize(e), 0);
+ result += check_equal(antisymmetrize(e), e);
+
+ return result;
+}
+
+static unsigned scalar_product_check(void)
+{
+ // check scalar product replacement
+
+ unsigned result = 0;
+
+ idx i(symbol("i"), 3), j(symbol("j"), 3);
+ symbol A("A"), B("B"), C("C");
+ ex e;
+
+ scalar_products sp;
+ sp.add(A, B, 0); // A and B are orthogonal
+ sp.add(A, C, 0); // A and C are orthogonal
+ sp.add(A, A, 4); // A^2 = 4 (A has length 2)
+
+ e = (indexed(A + B, i) * indexed(A + C, i)).expand(expand_options::expand_indexed);
+ result += check_equal_simplify(e, indexed(B, i) * indexed(C, i) + 4, sp);
+ e = indexed(A, i, i) * indexed(B, j, j); // GiNaC 0.8.0 had a bug here
+ result += check_equal_simplify(e, e, sp);