- exvector sub_expanded_seq;
- intvector positions_of_adds;
- intvector number_of_add_operands;
-
- exvector expanded_seq=expandchildren(options);
-
- positions_of_adds.resize(expanded_seq.size());
- number_of_add_operands.resize(expanded_seq.size());
-
- int number_of_adds=0;
- int number_of_expanded_terms=1;
-
- unsigned current_position=0;
- exvector::const_iterator last=expanded_seq.end();
- for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
- if (is_ex_exactly_of_type((*cit),add)) {
- positions_of_adds[number_of_adds]=current_position;
- add const & expanded_addref=ex_to_add(*cit);
- number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
- number_of_expanded_terms *= expanded_addref.seq.size();
- number_of_adds++;
- }
- current_position++;
- }
-
- if (number_of_adds==0) {
- return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
- status_flags::expanded);
- }
-
- exvector distrseq;
- distrseq.reserve(number_of_expanded_terms);
-
- intvector k;
- k.resize(number_of_adds);
-
- int l;
- for (l=0; l<number_of_adds; l++) {
- k[l]=0;
- }
-
- while (1) {
- exvector term;
- term=expanded_seq;
- for (l=0; l<number_of_adds; l++) {
- GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
- add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
- term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
- }
- distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
- status_flags::expanded));
-
- // increment k[]
- l=number_of_adds-1;
- while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
- k[l]=0;
- l--;
- }
- if (l<0) break;
- }
-
- return (new add(distrseq))->setflag(status_flags::dynallocated |
- status_flags::expanded);
-}
-
-int ncmul::degree(symbol const & s) const
-{
- int deg_sum=0;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).degree(s);
- }
- return deg_sum;
-}
-
-int ncmul::ldegree(symbol const & s) const
-{
- int deg_sum=0;
- for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
- deg_sum+=(*cit).ldegree(s);
- }
- return deg_sum;
-}
-
-ex ncmul::coeff(symbol const & s, int const n) const
-{
- 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
- exvector::const_iterator it=seq.begin();
- while (it!=seq.end()) {
- coeffseq.push_back((*it).coeff(s,n));
- ++it;
- }
- return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
- }
-
- exvector::const_iterator it=seq.begin();
- bool coeff_found=0;
- while (it!=seq.end()) {
- ex c=(*it).coeff(s,n);
- if (!c.is_zero()) {
- coeffseq.push_back(c);
- coeff_found=1;
- } else {
- coeffseq.push_back(*it);
- }
- ++it;
- }
-
- if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
-
- return _ex0();
-}
-
-unsigned ncmul::count_factors(ex const & e) const
-{
- if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
- (is_ex_exactly_of_type(e,ncmul))) {
- unsigned factors=0;
- for (unsigned i=0; i<e.nops(); i++)
- factors += count_factors(e.op(i));
-
- return factors;
- }
- return 1;
-}
-
-void ncmul::append_factors(exvector & v, ex const & e) const
-{
- if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
- (is_ex_exactly_of_type(e,ncmul))) {
- for (unsigned i=0; i<e.nops(); i++)
- append_factors(v,e.op(i));
-
- return;
- }
- v.push_back(e);
-}
-
-typedef vector<unsigned> unsignedvector;
-typedef vector<exvector> exvectorvector;
-
+ // First, expand the children
+ std::auto_ptr<exvector> vp = expandchildren(options);
+ const exvector &expanded_seq = vp.get() ? *vp : this->seq;
+
+ // Now, look for all the factors that are sums and remember their
+ // position and number of terms.
+ intvector positions_of_adds(expanded_seq.size());
+ intvector 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;
+ exvector::const_iterator last = expanded_seq.end();
+ for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
+ if (is_exactly_a<add>(*cit)) {
+ positions_of_adds[number_of_adds] = current_position;
+ size_t num_ops = cit->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 (vp.get())
+ return (new ncmul(vp))->
+ setflag(status_flags::dynallocated | (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);
+
+ intvector 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((new ncmul(term, true))->
+ setflag(status_flags::dynallocated | (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 (new add(distrseq))->
+ setflag(status_flags::dynallocated | (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;
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ deg_sum += i->degree(s);
+ ++i;
+ }
+ 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;
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ deg_sum += i->degree(s);
+ ++i;
+ }
+ 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
+ exvector::const_iterator it=seq.begin();
+ while (it!=seq.end()) {
+ coeffseq.push_back((*it).coeff(s,n));
+ ++it;
+ }
+ return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
+ }
+
+ exvector::const_iterator i = seq.begin(), end = seq.end();
+ bool coeff_found = false;
+ while (i != end) {
+ ex c = i->coeff(s,n);
+ if (c.is_zero()) {
+ coeffseq.push_back(*i);
+ } else {
+ coeffseq.push_back(c);
+ coeff_found = true;
+ }
+ ++i;
+ }
+
+ if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
+
+ 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,...)
+ *
+ * @param level cut-off in recursive evaluation */