}
/** non-commutative power. */
-ex ncpower(const ex &basis, unsigned exponent)
+ex ncpow(const ex & basis, unsigned exponent)
{
- if (exponent==0) {
+ if (exponent == 0)
return _ex1();
- }
exvector v;
v.reserve(exponent);
- for (unsigned i=0; i<exponent; ++i) {
+ 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);
+
+ // Loop over all permutations (the first permutation, which is the
+ // identity, is unrolled)
+ ex sum = e;
+ while (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;
}
+ return sum / factorial(numeric(num));
+}
+
+ex symmetrize(const ex & e, exvector::const_iterator first, exvector::const_iterator last)
+{
+ return symm(e, first, last, false);
+}
- return ncmul(v,1);
+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