-// 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;
-
- // Transform object vector to a list
- exlist iv_lst;
- iv_lst.insert(iv_lst.begin(), first, last);
- lst orig_lst(iv_lst, true);
-
- // Create index vectors for permutation
- unsigned *iv = new unsigned[num], *iv2;
- for (unsigned i=0; i<num; i++)
- iv[i] = i;
- iv2 = (asymmetric ? new unsigned[num] : NULL);
-
- // Loop over all permutations (the first permutation, which is the
- // identity, is unrolled)
- ex sum = e;
- while (std::next_permutation(iv, iv + num)) {
- lst new_lst;
- for (unsigned i=0; i<num; i++)
- new_lst.append(orig_lst.op(iv[i]));
- ex term = e.subs(orig_lst, new_lst);
- if (asymmetric) {
- memcpy(iv2, iv, num * sizeof(unsigned));
- term *= permutation_sign(iv2, iv2 + num);
- }
- sum += term;
- }
-
- delete[] iv;
- delete[] iv2;
-
- return sum / factorial(numeric(num));
-}
-
-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_cyclic(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
-{
- // Need at least 2 objects for this operation
- int num = last - first;
- if (num < 2)
- return e;
-
- // Transform object vector to a list
- exlist iv_lst;
- iv_lst.insert(iv_lst.begin(), first, last);
- lst orig_lst(iv_lst, true);
- lst new_lst = orig_lst;
-
- // Loop over all cyclic permutations (the first permutation, which is
- // the identity, is unrolled)
- ex sum = e;
- for (unsigned i=0; i<num-1; i++) {
- ex perm = new_lst.op(0);
- new_lst.remove_first().append(perm);
- sum += e.subs(orig_lst, new_lst);
- }
- return sum / num;
-}
-
-/** Symmetrize expression over a list of objects (symbols, indices). */
-ex ex::symmetrize(const lst & l) const
-{
- exvector v;
- v.reserve(l.nops());
- for (unsigned i=0; i<l.nops(); i++)
- v.push_back(l.op(i));
- return symm(*this, v.begin(), v.end(), false);
-}
-
-/** Antisymmetrize expression over a list of objects (symbols, indices). */
-ex ex::antisymmetrize(const lst & l) const
-{
- exvector v;
- v.reserve(l.nops());
- for (unsigned i=0; i<l.nops(); i++)
- v.push_back(l.op(i));
- return symm(*this, v.begin(), v.end(), true);
-}
-
-/** Symmetrize expression by cyclic permutation over a list of objects
- * (symbols, indices). */
-ex ex::symmetrize_cyclic(const lst & l) const
-{
- exvector v;
- v.reserve(l.nops());
- for (unsigned i=0; i<l.nops(); i++)
- v.push_back(l.op(i));
- return GiNaC::symmetrize_cyclic(*this, v.begin(), v.end());
-}
-
-/** Force inclusion of functions from initcns_gamma and inifcns_zeta
- * for static lib (so ginsh will see them). */
-unsigned force_include_tgamma = function_index_tgamma;
-unsigned force_include_zeta1 = function_index_zeta1;