+// Symmetrize/antisymmetrize over a vector of objects
+static ex symm(const ex & e, exvector::const_iterator first, exvector::const_iterator last, bool asymmetric)
+{
+ // Need at least 2 objects for this operation
+ int num = last - first;
+ if (num < 2)
+ return e;
+
+ // Sort object vector, transform it into a list, and make a copy so we
+ // will know which objects get substituted for which
+ exvector iv(first, last);
+ sort(iv.begin(), iv.end(), ex_is_less());
+ exlist iv_lst;
+ iv_lst.insert(iv_lst.begin(), iv.begin(), iv.end());
+ lst orig_lst(iv_lst);
+
+ // With n objects there are n! possible permutations
+ int num_perms = factorial(numeric(num)).to_int();
+
+ // Loop over all permutations (the first permutation, which is the
+ // identity, is unrolled)
+ ex sum = e;
+ int i = 1;
+ do {
+ next_permutation(iv_lst.begin(), iv_lst.end(), ex_is_less());
+ ex term = e.subs(orig_lst, lst(iv_lst));
+ if (asymmetric) {
+ exlist test_lst = iv_lst;
+ term *= permutation_sign(test_lst.begin(), test_lst.end(), ex_is_less());
+ }
+ sum += term;
+ i++;
+ } while (i < num_perms);
+
+ return sum / num_perms;
+}
+
+ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
+{
+ return symm(e, first, last, false);
+}
+
+ex antisymmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
+{
+ return symm(e, first, last, true);
+}
+
+ex symmetrize(const ex & e, const lst & l)
+{
+ exvector v;
+ v.reserve(l.nops());
+ for (unsigned i=0; i<l.nops(); i++)
+ v.push_back(l.op(i));
+ return symm(e, v.begin(), v.end(), false);
+}
+
+ex antisymmetrize(const ex & e, const lst & l)
+{
+ exvector v;
+ v.reserve(l.nops());
+ for (unsigned i=0; i<l.nops(); i++)
+ v.push_back(l.op(i));
+ return symm(e, v.begin(), v.end(), true);
+}
+