+ ex rp, ip;
+ find_real_imag(rp, ip);
+ return rp;
+}
+
+ex mul::imag_part() const
+{
+ ex rp, ip;
+ find_real_imag(rp, ip);
+ return ip;
+}
+
+ex mul::evalm() const
+{
+ // numeric*matrix
+ if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
+ && is_a<matrix>(seq[0].rest))
+ return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
+
+ // Evaluate children first, look whether there are any matrices at all
+ // (there can be either no matrices or one matrix; if there were more
+ // than one matrix, it would be a non-commutative product)
+ std::auto_ptr<epvector> s(new epvector);
+ s->reserve(seq.size());
+
+ bool have_matrix = false;
+ epvector::iterator the_matrix;
+
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ const ex &m = recombine_pair_to_ex(*i).evalm();
+ s->push_back(split_ex_to_pair(m));
+ if (is_a<matrix>(m)) {
+ have_matrix = true;
+ the_matrix = s->end() - 1;
+ }
+ ++i;
+ }
+
+ if (have_matrix) {
+
+ // The product contained a matrix. We will multiply all other factors
+ // into that matrix.
+ matrix m = ex_to<matrix>(the_matrix->rest);
+ s->erase(the_matrix);
+ ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+ return m.mul_scalar(scalar);
+
+ } else
+ return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+}
+
+ex mul::eval_ncmul(const exvector & v) const
+{
+ if (seq.empty())
+ return inherited::eval_ncmul(v);
+
+ // Find first noncommutative element and call its eval_ncmul()
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ if (i->rest.return_type() == return_types::noncommutative)
+ return i->rest.eval_ncmul(v);
+ ++i;
+ }
+ return inherited::eval_ncmul(v);
+}
+
+bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls)
+{
+ ex origbase;
+ int origexponent;
+ int origexpsign;
+
+ if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
+ origbase = origfactor.op(0);
+ int expon = ex_to<numeric>(origfactor.op(1)).to_int();
+ origexponent = expon > 0 ? expon : -expon;
+ origexpsign = expon > 0 ? 1 : -1;
+ } else {
+ origbase = origfactor;
+ origexponent = 1;
+ origexpsign = 1;
+ }
+
+ ex patternbase;
+ int patternexponent;
+ int patternexpsign;
+
+ if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
+ patternbase = patternfactor.op(0);
+ int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
+ patternexponent = expon > 0 ? expon : -expon;
+ patternexpsign = expon > 0 ? 1 : -1;
+ } else {
+ patternbase = patternfactor;
+ patternexponent = 1;
+ patternexpsign = 1;
+ }
+
+ exmap saverepls = repls;
+ if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
+ return false;
+ repls = saverepls;
+
+ int newnummatches = origexponent / patternexponent;
+ if (newnummatches < nummatches)
+ nummatches = newnummatches;
+ return true;
+}
+
+/** Checks wheter e matches to the pattern pat and the (possibly to be updated)
+ * list of replacements repls. This matching is in the sense of algebraic
+ * substitutions. Matching starts with pat.op(factor) of the pattern because
+ * the factors before this one have already been matched. The (possibly
+ * updated) number of matches is in nummatches. subsed[i] is true for factors
+ * that already have been replaced by previous substitutions and matched[i]
+ * is true for factors that have been matched by the current match.
+ */
+bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls,
+ int factor, int &nummatches, const std::vector<bool> &subsed,
+ std::vector<bool> &matched)
+{
+ GINAC_ASSERT(subsed.size() == e.nops());
+ GINAC_ASSERT(matched.size() == e.nops());
+
+ if (factor == (int)pat.nops())
+ return true;
+
+ for (size_t i=0; i<e.nops(); ++i) {
+ if(subsed[i] || matched[i])
+ continue;
+ exmap newrepls = repls;
+ int newnummatches = nummatches;
+ if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
+ matched[i] = true;
+ if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
+ newnummatches, subsed, matched)) {
+ repls = newrepls;
+ nummatches = newnummatches;
+ return true;
+ }
+ else
+ matched[i] = false;