+/** Given a set of indices, extract those of class varidx. */
+static void find_variant_indices(const exvector & v, exvector & variant_indices)
+{
+ exvector::const_iterator it1, itend;
+ for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+ if (is_exactly_a<varidx>(*it1))
+ variant_indices.push_back(*it1);
+ }
+}
+
+/** Raise/lower dummy indices in a single indexed objects to canonicalize their
+ * variance.
+ *
+ * @param e Object to work on
+ * @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function)
+ * @param moved_indices The set of indices that have been repositioned (will be changed by this function)
+ * @return true if 'e' was changed */
+bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices)
+{
+ bool something_changed = false;
+
+ // 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) {
+ if (!is_exactly_a<varidx>(*it2))
+ continue;
+
+ exvector::iterator vit, vitend;
+ 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
+ ));
+ 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);
+ goto next_index;
+ }
+ }
+
+ 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());
+ 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: ;
+ }
+
+ return something_changed;
+}
+