+ // First, expand the children
+ exvector v = expandchildren(options);
+ const exvector &expanded_seq = v.empty() ? this->seq : v;
+
+ // Now, look for all the factors that are sums and remember their
+ // position and number of terms.
+ uintvector positions_of_adds(expanded_seq.size());
+ uintvector number_of_add_operands(expanded_seq.size());
+
+ size_t number_of_adds = 0;
+ size_t number_of_expanded_terms = 1;
+
+ size_t current_position = 0;
+ for (auto & it : expanded_seq) {
+ if (is_exactly_a<add>(it)) {
+ positions_of_adds[number_of_adds] = current_position;
+ size_t num_ops = it.nops();
+ number_of_add_operands[number_of_adds] = num_ops;
+ number_of_expanded_terms *= num_ops;
+ number_of_adds++;
+ }
+ ++current_position;
+ }
+
+ // If there are no sums, we are done
+ if (number_of_adds == 0) {
+ if (!v.empty())
+ return dynallocate<ncmul>(std::move(v)).setflag(options == 0 ? status_flags::expanded : 0);
+ else
+ return *this;
+ }
+
+ // Now, form all possible products of the terms of the sums with the
+ // remaining factors, and add them together
+ exvector distrseq;
+ distrseq.reserve(number_of_expanded_terms);
+
+ uintvector k(number_of_adds);
+
+ /* Rename indices in the static members of the product */
+ exvector expanded_seq_mod;
+ size_t j = 0;
+ exvector va;
+
+ for (size_t i=0; i<expanded_seq.size(); i++) {
+ if (i == positions_of_adds[j]) {
+ expanded_seq_mod.push_back(_ex1);
+ j++;
+ } else {
+ expanded_seq_mod.push_back(rename_dummy_indices_uniquely(va, expanded_seq[i], true));
+ }
+ }
+
+ while (true) {
+ exvector term = expanded_seq_mod;
+ for (size_t i=0; i<number_of_adds; i++) {
+ term[positions_of_adds[i]] = rename_dummy_indices_uniquely(va, expanded_seq[positions_of_adds[i]].op(k[i]), true);
+ }
+
+ distrseq.push_back(dynallocate<ncmul>(std::move(term)).setflag(options == 0 ? status_flags::expanded : 0));
+
+ // increment k[]
+ int l = number_of_adds-1;
+ while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
+ k[l] = 0;
+ l--;
+ }
+ if (l<0)
+ break;
+ }
+
+ return dynallocate<add>(distrseq).setflag(options == 0 ? status_flags::expanded : 0);
+}
+
+int ncmul::degree(const ex & s) const
+{
+ if (is_equal(ex_to<basic>(s)))
+ return 1;
+
+ // Sum up degrees of factors
+ int deg_sum = 0;
+ for (auto & i : seq)
+ deg_sum += i.degree(s);
+ return deg_sum;
+}
+
+int ncmul::ldegree(const ex & s) const
+{
+ if (is_equal(ex_to<basic>(s)))
+ return 1;
+
+ // Sum up degrees of factors
+ int deg_sum = 0;
+ for (auto & i : seq)
+ deg_sum += i.degree(s);
+ return deg_sum;
+}
+
+ex ncmul::coeff(const ex & s, int n) const
+{
+ if (is_equal(ex_to<basic>(s)))
+ return n==1 ? _ex1 : _ex0;
+
+ exvector coeffseq;
+ coeffseq.reserve(seq.size());
+
+ if (n == 0) {
+ // product of individual coeffs
+ // if a non-zero power of s is found, the resulting product will be 0
+ for (auto & it : seq)
+ coeffseq.push_back(it.coeff(s,n));
+ return dynallocate<ncmul>(std::move(coeffseq));
+ }
+
+ bool coeff_found = false;
+ for (auto & i : seq) {
+ ex c = i.coeff(s,n);
+ if (c.is_zero()) {
+ coeffseq.push_back(i);
+ } else {
+ coeffseq.push_back(c);
+ coeff_found = true;
+ }
+ }
+
+ if (coeff_found)
+ return dynallocate<ncmul>(std::move(coeffseq));
+
+ return _ex0;
+}
+
+size_t ncmul::count_factors(const ex & e) const
+{
+ if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
+ (is_exactly_a<ncmul>(e))) {
+ size_t factors=0;
+ for (size_t i=0; i<e.nops(); i++)
+ factors += count_factors(e.op(i));
+
+ return factors;
+ }
+ return 1;
+}
+
+void ncmul::append_factors(exvector & v, const ex & e) const
+{
+ if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
+ (is_exactly_a<ncmul>(e))) {
+ for (size_t i=0; i<e.nops(); i++)
+ append_factors(v, e.op(i));
+ } else
+ v.push_back(e);
+}
+
+typedef std::vector<unsigned> unsignedvector;
+typedef std::vector<exvector> exvectorvector;
+
+/** Perform automatic term rewriting rules in this class. In the following
+ * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ * stand for such expressions that contain a plain number.
+ * - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...) (associativity)
+ * - ncmul(x) -> x
+ * - ncmul() -> 1
+ * - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...)) (pull out commutative elements)
+ * - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2)) (collect elements of same type)
+ * - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
+ */
+ex ncmul::eval() const
+{
+ // The following additional rule would be nice, but produces a recursion,
+ // which must be trapped by introducing a flag that the sub-ncmuls()
+ // are already evaluated (maybe later...)
+ // ncmul(x1,x2,...,X,y1,y2,...) ->
+ // ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
+ // (X noncommutative_composite)
+
+ if (flags & status_flags::evaluated) {
+ return *this;
+ }
+
+ // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
+ // ncmul(...,x1,x2,...,x3,x4,...) (associativity)
+ size_t factors = 0;
+ for (auto & it : seq)
+ factors += count_factors(it);
+
+ exvector assocseq;
+ assocseq.reserve(factors);
+ make_flat_inserter mf(seq, true);
+ for (auto & it : seq) {
+ ex factor = mf.handle_factor(it, 1);
+ append_factors(assocseq, factor);
+ }
+
+ // ncmul(x) -> x
+ if (assocseq.size()==1) return *(seq.begin());
+
+ // ncmul() -> 1
+ if (assocseq.empty()) return _ex1;
+
+ // determine return types
+ unsignedvector rettypes(assocseq.size());
+ size_t i = 0;
+ size_t count_commutative=0;
+ size_t count_noncommutative=0;
+ size_t count_noncommutative_composite=0;
+ for (auto & it : assocseq) {
+ rettypes[i] = it.return_type();
+ switch (rettypes[i]) {
+ case return_types::commutative:
+ count_commutative++;
+ break;
+ case return_types::noncommutative:
+ count_noncommutative++;
+ break;
+ case return_types::noncommutative_composite:
+ count_noncommutative_composite++;
+ break;
+ default:
+ throw(std::logic_error("ncmul::eval(): invalid return type"));
+ }
+ ++i;
+ }
+ GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
+
+ // ncmul(...,c1,...,c2,...) ->
+ // *(c1,c2,ncmul(...)) (pull out commutative elements)
+ if (count_commutative!=0) {
+ exvector commutativeseq;
+ commutativeseq.reserve(count_commutative+1);
+ exvector noncommutativeseq;
+ noncommutativeseq.reserve(assocseq.size()-count_commutative);
+ size_t num = assocseq.size();
+ for (size_t i=0; i<num; ++i) {
+ if (rettypes[i]==return_types::commutative)
+ commutativeseq.push_back(assocseq[i]);
+ else
+ noncommutativeseq.push_back(assocseq[i]);
+ }
+ commutativeseq.push_back(dynallocate<ncmul>(std::move(noncommutativeseq)));
+ return dynallocate<mul>(std::move(commutativeseq));
+ }
+
+ // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
+ // (collect elements of same type)
+
+ if (count_noncommutative_composite==0) {
+ // there are neither commutative nor noncommutative_composite
+ // elements in assocseq
+ GINAC_ASSERT(count_commutative==0);
+
+ size_t assoc_num = assocseq.size();
+ exvectorvector evv;
+ std::vector<return_type_t> rttinfos;
+ evv.reserve(assoc_num);
+ rttinfos.reserve(assoc_num);
+
+ for (auto & it : assocseq) {
+ return_type_t ti = it.return_type_tinfo();
+ size_t rtt_num = rttinfos.size();
+ // search type in vector of known types
+ for (i=0; i<rtt_num; ++i) {
+ if(ti == rttinfos[i]) {
+ evv[i].push_back(it);
+ break;
+ }
+ }
+ if (i >= rtt_num) {
+ // new type
+ rttinfos.push_back(ti);
+ evv.push_back(exvector());
+ (evv.end()-1)->reserve(assoc_num);
+ (evv.end()-1)->push_back(it);
+ }
+ }
+
+ size_t evv_num = evv.size();
+#ifdef DO_GINAC_ASSERT
+ GINAC_ASSERT(evv_num == rttinfos.size());
+ GINAC_ASSERT(evv_num > 0);
+ size_t s=0;
+ for (i=0; i<evv_num; ++i)
+ s += evv[i].size();
+ GINAC_ASSERT(s == assoc_num);
+#endif // def DO_GINAC_ASSERT
+
+ // if all elements are of same type, simplify the string
+ if (evv_num == 1) {
+ return evv[0][0].eval_ncmul(evv[0]);
+ }
+
+ exvector splitseq;
+ splitseq.reserve(evv_num);
+ for (i=0; i<evv_num; ++i)
+ splitseq.push_back(dynallocate<ncmul>(evv[i]));
+
+ return dynallocate<mul>(splitseq);
+ }
+
+ return dynallocate<ncmul>(assocseq).setflag(status_flags::evaluated);