+/** Bring a vector of indices into a canonic order. Dummy indices will lie
+ * next to each other after the sorting. */
+static void sort_index_vector(exvector &v)
+{
+ // Nothing to sort if less than 2 elements
+ if (v.size() < 2)
+ return;
+
+ // Simple bubble sort algorithm should be sufficient for the small
+ // number of indices expected
+ exvector::iterator it1 = v.begin(), itend = v.end(), next_to_last_idx = itend - 1;
+ while (it1 != next_to_last_idx) {
+ exvector::iterator it2 = it1 + 1;
+ while (it2 != itend) {
+ if (it1->compare(*it2) > 0)
+ it1->swap(*it2);
+ it2++;
+ }
+ it1++;
+ }
+}
+
+
+void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
+{
+ out_free.clear();
+ out_dummy.clear();
+
+ // No indices? Then do nothing
+ if (it == itend)
+ return;
+
+ // Only one index? Then it is a free one if it's not numeric
+ if (itend - it == 1) {
+ if (ex_to_idx(*it).is_symbolic())
+ out_free.push_back(*it);
+ return;
+ }
+
+ // Sort index vector. This will cause dummy indices come to lie next
+ // to each other (because the sort order is defined to guarantee this).
+ exvector v(it, itend);
+ sort_index_vector(v);
+
+ // Find dummy pairs and free indices
+ it = v.begin(); itend = v.end();
+ exvector::const_iterator last = it++;
+ while (it != itend) {
+ if (is_dummy_pair(*it, *last)) {
+ out_dummy.push_back(*last);
+ it++;
+ if (it == itend)
+ return;
+ } else {
+ if (!it->is_equal(*last) && ex_to_idx(*last).is_symbolic())
+ out_free.push_back(*last);
+ }
+ last = it++;
+ }
+ if (ex_to_idx(*last).is_symbolic())
+ out_free.push_back(*last);
+}
+
+exvector index_set_difference(const exvector & set1, const exvector & set2)
+{
+ exvector ret;
+
+ exvector::const_iterator ait = set1.begin(), aitend = set1.end();
+ while (ait != aitend) {
+ exvector::const_iterator bit = set2.begin(), bitend = set2.end();
+ bool found = false;
+ while (bit != bitend) {
+ if (ait->is_equal(*bit)) {
+ found = true;
+ break;
+ }
+ bit++;
+ }
+ if (!found)
+ ret.push_back(*ait);
+ ait++;
+ }
+
+ return ret;
+}
+