-/** non-commutative power. */
-ex ncpow(const ex & basis, unsigned exponent)
-{
- if (exponent == 0)
- return _ex1();
-
- exvector v;
- v.reserve(exponent);
- for (unsigned i=0; i<exponent; ++i)
- v.push_back(basis);
-
- return ncmul(v, true);
-}
-
-// 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
- exlist iv_lst;
- iv_lst.insert(iv_lst.begin(), first, last);
- shaker_sort(iv_lst.begin(), iv_lst.end(), ex_is_less());
- 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);
-}
-
-/** Force inclusion of functions from initcns_gamma and inifcns_zeta
- * for static lib (so ginsh will see them). */