ex e = expand_dummy_sum(normal(simplify_indexed(e1) - e2), true);
for (int j=0; j<4; j++) {
- ex esub = e.subs(lst(is_a<varidx>(mu) ?
- mu == idx(j, mu.get_dim()), ex_to<varidx>(mu).toggle_variance() == idx(j, mu.get_dim())
- : mu == idx(j, mu.get_dim())));
+ ex esub = e.subs(
+ is_a<varidx>(mu)
+ ? lst (
+ mu == idx(j, mu.get_dim()),
+ ex_to<varidx>(mu).toggle_variance() == idx(j, mu.get_dim())
+ )
+ : lst(mu == idx(j, mu.get_dim()))
+ );
if (!(canonicalize_clifford(esub).is_zero())) {
clog << "simplify_indexed(" << e1 << ") - (" << e2 << ") erroneously returned "
<< canonicalize_clifford(esub) << " instead of 0 for mu=" << j << endl;
* the cases when used indexes have or have not variance.
* To this end we recycle the code through the following macros */
-#define CHECK6(IDX,TOGGLE) {IDX v(symbol("v"), 4), nu(symbol("nu"), 4), mu(symbol("mu"), 4), \
- psi(symbol("psi"),4), lam(symbol("lambda"), 4),\
- xi(symbol("xi"), 4), rho(symbol("rho"),4);\
-\
-/* checks general identities and contractions for clifford_unit*/\
- e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2);\
- result += check_equal(e, clifford_unit(mu, A, 2));\
-\
- e = clifford_unit(idx(2, 4), A) * clifford_unit(idx(1, 4), A)\
- * clifford_unit(idx(1, 4), A) * clifford_unit(idx(2, 4), A);\
- result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());\
-\
- e = clifford_unit(IDX(2, 4), A) * clifford_unit(IDX(1, 4), A)\
- * clifford_unit(IDX(1, 4), A) * clifford_unit(IDX(2, 4), A);\
- result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A);\
- result += check_equal_simplify(e, A.trace() * dirac_ONE());\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu, A);\
- result += check_equal_simplify(e, indexed(A_symm, sy_symm(), nu, nu) * dirac_ONE());\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A) * clifford_unit(mu, A);\
- result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));\
-\
- e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu TOGGLE, A);\
- \
- result += check_equal_simplify_term(e, 2 * indexed(A_symm, sy_symm(), nu TOGGLE, mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);\
-\
- e = clifford_unit(nu, A) * clifford_unit(nu TOGGLE, A)\
- * clifford_unit(mu, A) * clifford_unit(mu TOGGLE, A);\
- result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());\
-\
- e = clifford_unit(mu, A) * clifford_unit(nu, A)\
- * clifford_unit(nu TOGGLE, A) * clifford_unit(mu TOGGLE, A);\
- result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());\
-\
- e = clifford_unit(mu, A) * clifford_unit(nu, A)\
- * clifford_unit(mu TOGGLE, A) * clifford_unit(nu TOGGLE, A);\
-\
- result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu TOGGLE, mu TOGGLE) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());\
-\
- e = clifford_unit(mu TOGGLE, A) * clifford_unit(nu, A)\
- * clifford_unit(mu, A) * clifford_unit(nu TOGGLE, A);\
-\
- result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu TOGGLE, A) * clifford_unit(nu TOGGLE, A) - pow(A.trace(), 2)*dirac_ONE());\
-\
- e = clifford_unit(nu TOGGLE, A) * clifford_unit(rho TOGGLE, A)\
- * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);\
- e = e.simplify_indexed().collect(clifford_unit(mu, A));\
- \
- result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu TOGGLE, rho)*indexed(A_symm, sy_symm(), rho TOGGLE, mu) *clifford_unit(nu, A) \
- - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho TOGGLE, mu) \
- + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);\
-\
- e = clifford_unit(nu TOGGLE, A) * clifford_unit(rho, A)\
- * clifford_unit(mu, A) * clifford_unit(rho TOGGLE, A) * clifford_unit(nu, A);\
- e = e.simplify_indexed().collect(clifford_unit(mu, A));\
- \
- result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu TOGGLE, rho)*indexed(A_symm, sy_symm(), rho TOGGLE, mu) *clifford_unit(nu, A) \
- - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho TOGGLE, mu) \
- + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);\
-\
- e = clifford_unit(mu, A) * clifford_unit(nu, A) + clifford_unit(nu, A) * clifford_unit(mu, A);\
- result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(A_symm, sy_symm(), mu, nu));\
-\
- e = (clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A)\
- + clifford_unit(nu, A) * clifford_unit(lam, A) * clifford_unit(mu, A)\
- + clifford_unit(lam, A) * clifford_unit(mu, A) * clifford_unit(nu, A)\
- - clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(lam, A)\
- - clifford_unit(lam, A) * clifford_unit(nu, A) * clifford_unit(mu, A)\
- - clifford_unit(mu, A) * clifford_unit(lam, A) * clifford_unit(nu, A)) / 6\
- + indexed(A_symm, sy_symm(), mu, nu) * clifford_unit(lam, A)\
- - indexed(A_symm, sy_symm(), mu, lam) * clifford_unit(nu, A)\
- + indexed(A_symm, sy_symm(), nu, lam) * clifford_unit(mu, A)\
- - clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A);\
- result += check_equal(canonicalize_clifford(e), 0);\
-\
-/* lst_to_clifford() and clifford_inverse() check*/\
- realsymbol x("x"), y("y"), t("t"), z("z");\
- \
- ex c = clifford_unit(nu, A, 1);\
- e = lst_to_clifford(lst(t, x, y, z), mu, A, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);\
- e1 = clifford_inverse(e);\
- result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1));\
-\
-/* Moebius map (both forms) checks for symmetric metrics only */\
- matrix M1(2, 2), M2(2, 2);\
- c = clifford_unit(nu, A);\
- \
- e = clifford_moebius_map(0, dirac_ONE(), \
- dirac_ONE(), 0, lst(t, x, y, z), A); \
-/* this is just the inversion*/\
- M1 = 0, dirac_ONE(),\
- dirac_ONE(), 0;\
- e1 = clifford_moebius_map(M1, lst(t, x, y, z), A); \
-/* the inversion again*/\
- result += check_equal_lst(e, e1);\
- \
- e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst(t, x, y, z), mu, A)), c);\
- result += check_equal_lst(e, e1);\
- \
- e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), nu, A), \
- 0, dirac_ONE(), lst(t, x, y, z), A); \
-/*this is just a shift*/\
- M2 = dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), c),\
- 0, dirac_ONE();\
- e1 = clifford_moebius_map(M2, lst(t, x, y, z), c); \
-/* the same shift*/\
- result += check_equal_lst(e, e1);\
- \
- result += check_equal(e, lst(t+1, x+2, y+3, z+4));\
- \
-/* Check the group law for Moebius maps */\
- e = clifford_moebius_map(M1, ex_to<lst>(e1), c); \
-/*composition of M1 and M2*/\
- e1 = clifford_moebius_map(M1.mul(M2), lst(t, x, y, z), c); \
-/* the product M1*M2*/\
- result += check_equal_lst(e, e1);}
-
-static unsigned clifford_check6(const matrix & A)
+template <typename IDX> unsigned clifford_check6(const matrix &A)
{
+ unsigned result = 0;
+
matrix A_symm(4,4), A2(4, 4);
A_symm = A.add(A.transpose()).mul(half);
A2 = A_symm.mul(A_symm);
-
+
+ IDX v(symbol("v"), 4), nu(symbol("nu"), 4), mu(symbol("mu"), 4),
+ psi(symbol("psi"),4), lam(symbol("lambda"), 4),
+ xi(symbol("xi"), 4), rho(symbol("rho"),4);
+ ex mu_TOGGLE = is_a<varidx>(mu) ? ex_to<varidx>(mu).toggle_variance() : mu;
+ ex nu_TOGGLE = is_a<varidx>(nu) ? ex_to<varidx>(nu).toggle_variance() : nu;
+ ex rho_TOGGLE
+ = is_a<varidx>(rho) ? ex_to<varidx>(rho).toggle_variance() : rho;
+
ex e, e1;
- int result = 0;
+
+/* checks general identities and contractions for clifford_unit*/
+ e = dirac_ONE(2) * clifford_unit(mu, A, 2) * dirac_ONE(2);
+ result += check_equal(e, clifford_unit(mu, A, 2));
+
+ e = clifford_unit(idx(2, 4), A) * clifford_unit(idx(1, 4), A)
+ * clifford_unit(idx(1, 4), A) * clifford_unit(idx(2, 4), A);
+ result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());
+
+ e = clifford_unit(IDX(2, 4), A) * clifford_unit(IDX(1, 4), A)
+ * clifford_unit(IDX(1, 4), A) * clifford_unit(IDX(2, 4), A);
+ result += check_equal(e, A(1, 1) * A(2, 2) * dirac_ONE());
+
+ e = clifford_unit(nu, A) * clifford_unit(nu_TOGGLE, A);
+ result += check_equal_simplify(e, A.trace() * dirac_ONE());
+
+ e = clifford_unit(nu, A) * clifford_unit(nu, A);
+ result += check_equal_simplify(e, indexed(A_symm, sy_symm(), nu, nu) * dirac_ONE());
+
+ e = clifford_unit(nu, A) * clifford_unit(nu_TOGGLE, A) * clifford_unit(mu, A);
+ result += check_equal_simplify(e, A.trace() * clifford_unit(mu, A));
+
+ e = clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(nu_TOGGLE, A);
- CHECK6(varidx,.toggle_variance())
+ result += check_equal_simplify_term(e, 2 * indexed(A_symm, sy_symm(), nu_TOGGLE, mu) *clifford_unit(nu, A)-A.trace()*clifford_unit(mu, A), mu);
- return result;
-}
+ e = clifford_unit(nu, A) * clifford_unit(nu_TOGGLE, A)
+ * clifford_unit(mu, A) * clifford_unit(mu_TOGGLE, A);
+ result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());
-static unsigned clifford_check6a(const matrix & A)
-{
- matrix A_symm(4,4), A2(4, 4);
- A_symm = A.add(A.transpose()).mul(half);
- A2 = A_symm.mul(A_symm);
+ e = clifford_unit(mu, A) * clifford_unit(nu, A)
+ * clifford_unit(nu_TOGGLE, A) * clifford_unit(mu_TOGGLE, A);
+ result += check_equal_simplify(e, pow(A.trace(), 2) * dirac_ONE());
+
+ e = clifford_unit(mu, A) * clifford_unit(nu, A)
+ * clifford_unit(mu_TOGGLE, A) * clifford_unit(nu_TOGGLE, A);
+
+ result += check_equal_simplify_term2(e, 2*indexed(A_symm, sy_symm(), nu_TOGGLE, mu_TOGGLE) * clifford_unit(mu, A) * clifford_unit(nu, A) - pow(A.trace(), 2)*dirac_ONE());
+
+ e = clifford_unit(mu_TOGGLE, A) * clifford_unit(nu, A)
+ * clifford_unit(mu, A) * clifford_unit(nu_TOGGLE, A);
+
+ result += check_equal_simplify_term2(e, 2*indexed(A_symm, nu, mu) * clifford_unit(mu_TOGGLE, A) * clifford_unit(nu_TOGGLE, A) - pow(A.trace(), 2)*dirac_ONE());
+
+ e = clifford_unit(nu_TOGGLE, A) * clifford_unit(rho_TOGGLE, A)
+ * clifford_unit(mu, A) * clifford_unit(rho, A) * clifford_unit(nu, A);
+ e = e.simplify_indexed().collect(clifford_unit(mu, A));
- ex e, e1;
- int result = 0;
+ result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu_TOGGLE, rho)*indexed(A_symm, sy_symm(), rho_TOGGLE, mu) *clifford_unit(nu, A)
+ - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho_TOGGLE, mu)
+ + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu_TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
- CHECK6(idx,)
+ e = clifford_unit(nu_TOGGLE, A) * clifford_unit(rho, A)
+ * clifford_unit(mu, A) * clifford_unit(rho_TOGGLE, A) * clifford_unit(nu, A);
+ e = e.simplify_indexed().collect(clifford_unit(mu, A));
+
+ result += check_equal_simplify_term(e, 4* indexed(A_symm, sy_symm(), nu_TOGGLE, rho)*indexed(A_symm, sy_symm(), rho_TOGGLE, mu) *clifford_unit(nu, A)
+ - 2*A.trace() * (clifford_unit(rho, A) * indexed(A_symm, sy_symm(), rho_TOGGLE, mu)
+ + clifford_unit(nu, A) * indexed(A_symm, sy_symm(), nu_TOGGLE, mu)) + pow(A.trace(),2)* clifford_unit(mu, A), mu);
+
+ e = clifford_unit(mu, A) * clifford_unit(nu, A) + clifford_unit(nu, A) * clifford_unit(mu, A);
+ result += check_equal(canonicalize_clifford(e), 2*dirac_ONE()*indexed(A_symm, sy_symm(), mu, nu));
+
+ e = (clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A)
+ + clifford_unit(nu, A) * clifford_unit(lam, A) * clifford_unit(mu, A)
+ + clifford_unit(lam, A) * clifford_unit(mu, A) * clifford_unit(nu, A)
+ - clifford_unit(nu, A) * clifford_unit(mu, A) * clifford_unit(lam, A)
+ - clifford_unit(lam, A) * clifford_unit(nu, A) * clifford_unit(mu, A)
+ - clifford_unit(mu, A) * clifford_unit(lam, A) * clifford_unit(nu, A)) / 6
+ + indexed(A_symm, sy_symm(), mu, nu) * clifford_unit(lam, A)
+ - indexed(A_symm, sy_symm(), mu, lam) * clifford_unit(nu, A)
+ + indexed(A_symm, sy_symm(), nu, lam) * clifford_unit(mu, A)
+ - clifford_unit(mu, A) * clifford_unit(nu, A) * clifford_unit(lam, A);
+ result += check_equal(canonicalize_clifford(e), 0);
+/* lst_to_clifford() and clifford_inverse() check*/
+ realsymbol x("x"), y("y"), t("t"), z("z");
+
+ ex c = clifford_unit(nu, A, 1);
+ e = lst_to_clifford(lst(t, x, y, z), mu, A, 1) * lst_to_clifford(lst(1, 2, 3, 4), c);
+ e1 = clifford_inverse(e);
+ result += check_equal_simplify_term2((e*e1).simplify_indexed(), dirac_ONE(1));
+
+/* Moebius map (both forms) checks for symmetric metrics only */
+ matrix M1(2, 2), M2(2, 2);
+ c = clifford_unit(nu, A);
+
+ e = clifford_moebius_map(0, dirac_ONE(),
+ dirac_ONE(), 0, lst(t, x, y, z), A);
+/* this is just the inversion*/
+ M1 = 0, dirac_ONE(),
+ dirac_ONE(), 0;
+ e1 = clifford_moebius_map(M1, lst(t, x, y, z), A);
+/* the inversion again*/
+ result += check_equal_lst(e, e1);
+
+ e1 = clifford_to_lst(clifford_inverse(lst_to_clifford(lst(t, x, y, z), mu, A)), c);
+ result += check_equal_lst(e, e1);
+
+ e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), nu, A),
+ 0, dirac_ONE(), lst(t, x, y, z), A);
+/*this is just a shift*/
+ M2 = dirac_ONE(), lst_to_clifford(lst(1, 2, 3, 4), c),
+ 0, dirac_ONE();
+ e1 = clifford_moebius_map(M2, lst(t, x, y, z), c);
+/* the same shift*/
+ result += check_equal_lst(e, e1);
+
+ result += check_equal(e, lst(t+1, x+2, y+3, z+4));
+
+/* Check the group law for Moebius maps */
+ e = clifford_moebius_map(M1, ex_to<lst>(e1), c);
+/*composition of M1 and M2*/
+ e1 = clifford_moebius_map(M1.mul(M2), lst(t, x, y, z), c);
+/* the product M1*M2*/
+ result += check_equal_lst(e, e1);
return result;
}
result += clifford_check5(); cout << '.' << flush;
// anticommuting, symmetric examples
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush;
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, 1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, -1, -1, -1))));; cout << '.' << flush;
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, 1, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 0, 1, -1))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-3, 0, 2, -1))));; cout << '.' << flush;
realsymbol s("s"), t("t"); // symbolic entries in matric
- result += clifford_check6(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))))+clifford_check6a(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst(-1, 1, s, t))));; cout << '.' << flush;
matrix A(4, 4);
A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=0
0, -1, 0, 0,
0, 0, 0, -1,
0, 0, 1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=2
0, 1, 0, 0,
0, 0, 0, -1,
0, 0, 1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=0
0, -1, 0, 0,
0, 0, 0, -1,
0, 0, -1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=2
0, 1, 0, 0,
0, 0, 0, -1,
0, 0, -1, 0;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
A = 1, 1, 0, 0, // not anticommuting, not symmetric, Tr=4
0, 1, 1, 0,
0, 0, 1, 1,
0, 0, 0, 1;
- result += clifford_check6(A)+clifford_check6a(A);; cout << '.' << flush;
+ result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
symbol dim("D");
result += clifford_check7(minkmetric(), dim); cout << '.' << flush;
{
bool something_changed = false;
- // Canonicalize wrt indices that are dummies within e. I.e., their
- // symbol occurs twice in an index of e. This is only done if there
- // is a cyclic symmetry because in that case it may happen that after
- // raising/lowering an index the indices get reshuffled by ::eval in
- // such a way that the iterators no longer point to the right objects.
- if (ex_to<symmetry>(ex_to<indexed>(e).get_symmetry()).has_cyclic()) {
- // Get dummy pairs of varidxes within the indexed object in e.
- exvector local_var_dummies;
- local_var_dummies.reserve(e.nops()/2);
- for (size_t i=1; i<e.nops(); ++i) {
- if (!is_a<varidx>(e.op(i)))
- continue;
- for (size_t j=i+1; j<e.nops(); ++j) {
- if (is_dummy_pair(e.op(i), e.op(j))) {
- local_var_dummies.push_back(e.op(i));
- for (exvector::iterator k = variant_dummy_indices.begin();
- k!=variant_dummy_indices.end(); ++k) {
- if (e.op(i).op(0) == k->op(0)) {
- variant_dummy_indices.erase(k);
- break;
- }
+ // Find dummy symbols that occur twice in the same indexed object.
+ exvector local_var_dummies;
+ local_var_dummies.reserve(e.nops()/2);
+ for (size_t i=1; i<e.nops(); ++i) {
+ if (!is_a<varidx>(e.op(i)))
+ continue;
+ for (size_t j=i+1; j<e.nops(); ++j) {
+ if (is_dummy_pair(e.op(i), e.op(j))) {
+ local_var_dummies.push_back(e.op(i));
+ for (exvector::iterator k = variant_dummy_indices.begin();
+ k!=variant_dummy_indices.end(); ++k) {
+ if (e.op(i).op(0) == k->op(0)) {
+ variant_dummy_indices.erase(k);
+ break;
}
- break;
}
+ break;
}
}
- // Try all posibilities of raising/lowering and keep the least one in
- // the sense of ex_is_less.
- ex optimal_e = e;
- size_t numpossibs = 1 << local_var_dummies.size();
- for (size_t i=0; i<numpossibs; ++i) {
- ex try_e = e;
- for (size_t j=0; j<local_var_dummies.size(); ++j) {
- exmap m;
- if (1<<j & i) {
- ex curr_idx = local_var_dummies[j];
- ex curr_toggle = ex_to<varidx>(curr_idx).toggle_variance();
- m[curr_idx] = curr_toggle;
- m[curr_toggle] = curr_idx;
- }
- try_e = e.subs(m, subs_options::no_pattern);
- }
- if(ex_is_less()(try_e, optimal_e))
- { optimal_e = try_e;
- something_changed = true;
+ }
+
+ // In the case where a dummy symbol occurs twice in the same indexed object
+ // we try all posibilities of raising/lowering and keep the least one in
+ // the sense of ex_is_less.
+ ex optimal_e = e;
+ size_t numpossibs = 1 << local_var_dummies.size();
+ for (size_t i=0; i<numpossibs; ++i) {
+ ex try_e = e;
+ for (size_t j=0; j<local_var_dummies.size(); ++j) {
+ exmap m;
+ if (1<<j & i) {
+ ex curr_idx = local_var_dummies[j];
+ ex curr_toggle = ex_to<varidx>(curr_idx).toggle_variance();
+ m[curr_idx] = curr_toggle;
+ m[curr_toggle] = curr_idx;
}
+ try_e = e.subs(m, subs_options::no_pattern);
+ }
+ if(ex_is_less()(try_e, optimal_e))
+ { optimal_e = try_e;
+ something_changed = true;
}
- e = optimal_e;
}
+ e = optimal_e;
+
+ if (!is_a<indexed>(e))
+ return true;
+
+ exvector seq = ex_to<indexed>(e).seq;
// If a dummy index is encountered for the first time in the
// product, pull it up, otherwise, pull it down
- exvector::const_iterator it2, it2start, it2end;
- for (it2start = ex_to<indexed>(e).seq.begin(), it2end = ex_to<indexed>(e).seq.end(), it2 = it2start + 1; it2 != it2end; ++it2) {
+ for (exvector::iterator it2 = seq.begin()+1, it2end = seq.end();
+ it2 != it2end; ++it2) {
if (!is_exactly_a<varidx>(*it2))
continue;
for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) {
if (it2->op(0).is_equal(vit->op(0))) {
if (ex_to<varidx>(*it2).is_covariant()) {
- e = e.subs(lst(
- *it2 == ex_to<varidx>(*it2).toggle_variance(),
- ex_to<varidx>(*it2).toggle_variance() == *it2
- ), subs_options::no_pattern);
+ /*
+ * N.B. we don't want to use
+ *
+ * e = e.subs(lst(
+ * *it2 == ex_to<varidx>(*it2).toggle_variance(),
+ * ex_to<varidx>(*it2).toggle_variance() == *it2
+ * ), subs_options::no_pattern);
+ *
+ * since this can trigger non-trivial repositioning of indices,
+ * e.g. due to non-trivial symmetry properties of e, thus
+ * invalidating iterators
+ */
+ *it2 = ex_to<varidx>(*it2).toggle_variance();
something_changed = true;
- it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
- it2start = ex_to<indexed>(e).seq.begin();
- it2end = ex_to<indexed>(e).seq.end();
}
moved_indices.push_back(*vit);
variant_dummy_indices.erase(vit);
for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) {
if (it2->op(0).is_equal(vit->op(0))) {
if (ex_to<varidx>(*it2).is_contravariant()) {
- e = e.subs(*it2 == ex_to<varidx>(*it2).toggle_variance(), subs_options::no_pattern);
+ *it2 = ex_to<varidx>(*it2).toggle_variance();
something_changed = true;
- it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
- it2start = ex_to<indexed>(e).seq.begin();
- it2end = ex_to<indexed>(e).seq.end();
}
goto next_index;
}
next_index: ;
}
+ if (something_changed)
+ e = ex_to<indexed>(e).thiscontainer(seq);
+
return something_changed;
}