3 * Implementation of GiNaC's products of expressions. */
6 * GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
31 #include "operators.h"
40 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
41 print_func<print_context>(&mul::do_print).
42 print_func<print_latex>(&mul::do_print_latex).
43 print_func<print_csrc>(&mul::do_print_csrc).
44 print_func<print_tree>(&mul::do_print_tree).
45 print_func<print_python_repr>(&mul::do_print_python_repr))
49 // default constructor
54 tinfo_key = TINFO_mul;
63 mul::mul(const ex & lh, const ex & rh)
65 tinfo_key = TINFO_mul;
67 construct_from_2_ex(lh,rh);
68 GINAC_ASSERT(is_canonical());
71 mul::mul(const exvector & v)
73 tinfo_key = TINFO_mul;
75 construct_from_exvector(v);
76 GINAC_ASSERT(is_canonical());
79 mul::mul(const epvector & v)
81 tinfo_key = TINFO_mul;
83 construct_from_epvector(v);
84 GINAC_ASSERT(is_canonical());
87 mul::mul(const epvector & v, const ex & oc)
89 tinfo_key = TINFO_mul;
91 construct_from_epvector(v);
92 GINAC_ASSERT(is_canonical());
95 mul::mul(std::auto_ptr<epvector> vp, const ex & oc)
97 tinfo_key = TINFO_mul;
98 GINAC_ASSERT(vp.get()!=0);
100 construct_from_epvector(*vp);
101 GINAC_ASSERT(is_canonical());
104 mul::mul(const ex & lh, const ex & mh, const ex & rh)
106 tinfo_key = TINFO_mul;
109 factors.push_back(lh);
110 factors.push_back(mh);
111 factors.push_back(rh);
112 overall_coeff = _ex1;
113 construct_from_exvector(factors);
114 GINAC_ASSERT(is_canonical());
121 DEFAULT_ARCHIVING(mul)
124 // functions overriding virtual functions from base classes
127 void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
129 const numeric &coeff = ex_to<numeric>(overall_coeff);
130 if (coeff.csgn() == -1)
132 if (!coeff.is_equal(*_num1_p) &&
133 !coeff.is_equal(*_num_1_p)) {
134 if (coeff.is_rational()) {
135 if (coeff.is_negative())
140 if (coeff.csgn() == -1)
141 (-coeff).print(c, precedence());
143 coeff.print(c, precedence());
149 void mul::do_print(const print_context & c, unsigned level) const
151 if (precedence() <= level)
154 print_overall_coeff(c, "*");
156 epvector::const_iterator it = seq.begin(), itend = seq.end();
158 while (it != itend) {
163 recombine_pair_to_ex(*it).print(c, precedence());
167 if (precedence() <= level)
171 void mul::do_print_latex(const print_latex & c, unsigned level) const
173 if (precedence() <= level)
176 print_overall_coeff(c, " ");
178 // Separate factors into those with negative numeric exponent
180 epvector::const_iterator it = seq.begin(), itend = seq.end();
181 exvector neg_powers, others;
182 while (it != itend) {
183 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
184 if (ex_to<numeric>(it->coeff).is_negative())
185 neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
187 others.push_back(recombine_pair_to_ex(*it));
191 if (!neg_powers.empty()) {
193 // Factors with negative exponent are printed as a fraction
195 mul(others).eval().print(c);
197 mul(neg_powers).eval().print(c);
202 // All other factors are printed in the ordinary way
203 exvector::const_iterator vit = others.begin(), vitend = others.end();
204 while (vit != vitend) {
206 vit->print(c, precedence());
211 if (precedence() <= level)
215 void mul::do_print_csrc(const print_csrc & c, unsigned level) const
217 if (precedence() <= level)
220 if (!overall_coeff.is_equal(_ex1)) {
221 overall_coeff.print(c, precedence());
225 // Print arguments, separated by "*" or "/"
226 epvector::const_iterator it = seq.begin(), itend = seq.end();
227 while (it != itend) {
229 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
230 bool needclosingparenthesis = false;
231 if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
232 if (is_a<print_csrc_cl_N>(c)) {
234 needclosingparenthesis = true;
239 // If the exponent is 1 or -1, it is left out
240 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
241 it->rest.print(c, precedence());
242 else if (it->coeff.info(info_flags::negint))
243 // Outer parens around ex needed for broken GCC parser:
244 (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
246 // Outer parens around ex needed for broken GCC parser:
247 (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
249 if (needclosingparenthesis)
252 // Separator is "/" for negative integer powers, "*" otherwise
255 if (it->coeff.info(info_flags::negint))
262 if (precedence() <= level)
266 void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
268 c.s << class_name() << '(';
270 for (size_t i=1; i<nops(); ++i) {
277 bool mul::info(unsigned inf) const
280 case info_flags::polynomial:
281 case info_flags::integer_polynomial:
282 case info_flags::cinteger_polynomial:
283 case info_flags::rational_polynomial:
284 case info_flags::crational_polynomial:
285 case info_flags::rational_function: {
286 epvector::const_iterator i = seq.begin(), end = seq.end();
288 if (!(recombine_pair_to_ex(*i).info(inf)))
292 return overall_coeff.info(inf);
294 case info_flags::algebraic: {
295 epvector::const_iterator i = seq.begin(), end = seq.end();
297 if ((recombine_pair_to_ex(*i).info(inf)))
304 return inherited::info(inf);
307 int mul::degree(const ex & s) const
309 // Sum up degrees of factors
311 epvector::const_iterator i = seq.begin(), end = seq.end();
313 if (ex_to<numeric>(i->coeff).is_integer())
314 deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
320 int mul::ldegree(const ex & s) const
322 // Sum up degrees of factors
324 epvector::const_iterator i = seq.begin(), end = seq.end();
326 if (ex_to<numeric>(i->coeff).is_integer())
327 deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
333 ex mul::coeff(const ex & s, int n) const
336 coeffseq.reserve(seq.size()+1);
339 // product of individual coeffs
340 // if a non-zero power of s is found, the resulting product will be 0
341 epvector::const_iterator i = seq.begin(), end = seq.end();
343 coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
346 coeffseq.push_back(overall_coeff);
347 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
350 epvector::const_iterator i = seq.begin(), end = seq.end();
351 bool coeff_found = false;
353 ex t = recombine_pair_to_ex(*i);
354 ex c = t.coeff(s, n);
356 coeffseq.push_back(c);
359 coeffseq.push_back(t);
364 coeffseq.push_back(overall_coeff);
365 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
371 /** Perform automatic term rewriting rules in this class. In the following
372 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
373 * stand for such expressions that contain a plain number.
375 * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
379 * @param level cut-off in recursive evaluation */
380 ex mul::eval(int level) const
382 std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
383 if (evaled_seqp.get()) {
384 // do more evaluation later
385 return (new mul(evaled_seqp, overall_coeff))->
386 setflag(status_flags::dynallocated);
389 #ifdef DO_GINAC_ASSERT
390 epvector::const_iterator i = seq.begin(), end = seq.end();
392 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
393 (!(ex_to<numeric>(i->coeff).is_integer())));
394 GINAC_ASSERT(!(i->is_canonical_numeric()));
395 if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
396 print(print_tree(std::cerr));
397 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
399 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
400 GINAC_ASSERT(p.rest.is_equal(i->rest));
401 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
405 #endif // def DO_GINAC_ASSERT
407 if (flags & status_flags::evaluated) {
408 GINAC_ASSERT(seq.size()>0);
409 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
413 int seq_size = seq.size();
414 if (overall_coeff.is_zero()) {
417 } else if (seq_size==0) {
419 return overall_coeff;
420 } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
422 return recombine_pair_to_ex(*(seq.begin()));
423 } else if ((seq_size==1) &&
424 is_exactly_a<add>((*seq.begin()).rest) &&
425 ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
426 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
427 const add & addref = ex_to<add>((*seq.begin()).rest);
428 std::auto_ptr<epvector> distrseq(new epvector);
429 distrseq->reserve(addref.seq.size());
430 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
432 distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
435 return (new add(distrseq,
436 ex_to<numeric>(addref.overall_coeff).
437 mul_dyn(ex_to<numeric>(overall_coeff))))
438 ->setflag(status_flags::dynallocated | status_flags::evaluated);
443 ex mul::evalf(int level) const
446 return mul(seq,overall_coeff);
448 if (level==-max_recursion_level)
449 throw(std::runtime_error("max recursion level reached"));
451 std::auto_ptr<epvector> s(new epvector);
452 s->reserve(seq.size());
455 epvector::const_iterator i = seq.begin(), end = seq.end();
457 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
461 return mul(s, overall_coeff.evalf(level));
464 ex mul::evalm() const
467 if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
468 && is_a<matrix>(seq[0].rest))
469 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
471 // Evaluate children first, look whether there are any matrices at all
472 // (there can be either no matrices or one matrix; if there were more
473 // than one matrix, it would be a non-commutative product)
474 std::auto_ptr<epvector> s(new epvector);
475 s->reserve(seq.size());
477 bool have_matrix = false;
478 epvector::iterator the_matrix;
480 epvector::const_iterator i = seq.begin(), end = seq.end();
482 const ex &m = recombine_pair_to_ex(*i).evalm();
483 s->push_back(split_ex_to_pair(m));
484 if (is_a<matrix>(m)) {
486 the_matrix = s->end() - 1;
493 // The product contained a matrix. We will multiply all other factors
495 matrix m = ex_to<matrix>(the_matrix->rest);
496 s->erase(the_matrix);
497 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
498 return m.mul_scalar(scalar);
501 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
504 ex mul::eval_ncmul(const exvector & v) const
507 return inherited::eval_ncmul(v);
509 // Find first noncommutative element and call its eval_ncmul()
510 epvector::const_iterator i = seq.begin(), end = seq.end();
512 if (i->rest.return_type() == return_types::noncommutative)
513 return i->rest.eval_ncmul(v);
516 return inherited::eval_ncmul(v);
519 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls)
525 if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
526 origbase = origfactor.op(0);
527 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
528 origexponent = expon > 0 ? expon : -expon;
529 origexpsign = expon > 0 ? 1 : -1;
531 origbase = origfactor;
540 if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
541 patternbase = patternfactor.op(0);
542 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
543 patternexponent = expon > 0 ? expon : -expon;
544 patternexpsign = expon > 0 ? 1 : -1;
546 patternbase = patternfactor;
551 lst saverepls = repls;
552 if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
556 int newnummatches = origexponent / patternexponent;
557 if (newnummatches < nummatches)
558 nummatches = newnummatches;
562 ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
564 std::vector<bool> subsed(seq.size(), false);
565 exvector subsresult(seq.size());
567 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
569 if (is_exactly_a<mul>(it->first)) {
571 int nummatches = std::numeric_limits<int>::max();
572 std::vector<bool> currsubsed(seq.size(), false);
576 for (size_t j=0; j<it->first.nops(); j++) {
578 for (size_t k=0; k<nops(); k++) {
579 if (currsubsed[k] || subsed[k])
581 if (tryfactsubs(op(k), it->first.op(j), nummatches, repls)) {
582 currsubsed[k] = true;
595 bool foundfirstsubsedfactor = false;
596 for (size_t j=0; j<subsed.size(); j++) {
598 if (foundfirstsubsedfactor)
599 subsresult[j] = op(j);
601 foundfirstsubsedfactor = true;
602 subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches);
610 int nummatches = std::numeric_limits<int>::max();
613 for (size_t j=0; j<this->nops(); j++) {
614 if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) {
616 subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::no_pattern) / it->first.subs(ex(repls), subs_options::no_pattern), nummatches);
622 bool subsfound = false;
623 for (size_t i=0; i<subsed.size(); i++) {
630 return subs_one_level(m, options | subs_options::algebraic);
632 exvector ev; ev.reserve(nops());
633 for (size_t i=0; i<nops(); i++) {
635 ev.push_back(subsresult[i]);
640 return (new mul(ev))->setflag(status_flags::dynallocated);
645 /** Implementation of ex::diff() for a product. It applies the product rule.
647 ex mul::derivative(const symbol & s) const
649 size_t num = seq.size();
653 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
654 epvector mulseq = seq;
655 epvector::const_iterator i = seq.begin(), end = seq.end();
656 epvector::iterator i2 = mulseq.begin();
658 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
661 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
665 return (new add(addseq))->setflag(status_flags::dynallocated);
668 int mul::compare_same_type(const basic & other) const
670 return inherited::compare_same_type(other);
673 unsigned mul::return_type() const
676 // mul without factors: should not happen, but commutates
677 return return_types::commutative;
680 bool all_commutative = true;
681 epvector::const_iterator noncommutative_element; // point to first found nc element
683 epvector::const_iterator i = seq.begin(), end = seq.end();
685 unsigned rt = i->rest.return_type();
686 if (rt == return_types::noncommutative_composite)
687 return rt; // one ncc -> mul also ncc
688 if ((rt == return_types::noncommutative) && (all_commutative)) {
689 // first nc element found, remember position
690 noncommutative_element = i;
691 all_commutative = false;
693 if ((rt == return_types::noncommutative) && (!all_commutative)) {
694 // another nc element found, compare type_infos
695 if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
696 // diffent types -> mul is ncc
697 return return_types::noncommutative_composite;
702 // all factors checked
703 return all_commutative ? return_types::commutative : return_types::noncommutative;
706 unsigned mul::return_type_tinfo() const
709 return tinfo_key; // mul without factors: should not happen
711 // return type_info of first noncommutative element
712 epvector::const_iterator i = seq.begin(), end = seq.end();
714 if (i->rest.return_type() == return_types::noncommutative)
715 return i->rest.return_type_tinfo();
718 // no noncommutative element found, should not happen
722 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
724 return (new mul(v, oc))->setflag(status_flags::dynallocated);
727 ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc) const
729 return (new mul(vp, oc))->setflag(status_flags::dynallocated);
732 expair mul::split_ex_to_pair(const ex & e) const
734 if (is_exactly_a<power>(e)) {
735 const power & powerref = ex_to<power>(e);
736 if (is_exactly_a<numeric>(powerref.exponent))
737 return expair(powerref.basis,powerref.exponent);
739 return expair(e,_ex1);
742 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
745 // to avoid duplication of power simplification rules,
746 // we create a temporary power object
747 // otherwise it would be hard to correctly evaluate
748 // expression like (4^(1/3))^(3/2)
749 if (c.is_equal(_ex1))
750 return split_ex_to_pair(e);
752 return split_ex_to_pair(power(e,c));
755 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
758 // to avoid duplication of power simplification rules,
759 // we create a temporary power object
760 // otherwise it would be hard to correctly evaluate
761 // expression like (4^(1/3))^(3/2)
762 if (c.is_equal(_ex1))
765 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
768 ex mul::recombine_pair_to_ex(const expair & p) const
770 if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
773 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
776 bool mul::expair_needs_further_processing(epp it)
778 if (is_exactly_a<mul>(it->rest) &&
779 ex_to<numeric>(it->coeff).is_integer()) {
780 // combined pair is product with integer power -> expand it
781 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
784 if (is_exactly_a<numeric>(it->rest)) {
785 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
786 if (!ep.is_equal(*it)) {
787 // combined pair is a numeric power which can be simplified
791 if (it->coeff.is_equal(_ex1)) {
792 // combined pair has coeff 1 and must be moved to the end
799 ex mul::default_overall_coeff() const
804 void mul::combine_overall_coeff(const ex & c)
806 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
807 GINAC_ASSERT(is_exactly_a<numeric>(c));
808 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
811 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
813 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
814 GINAC_ASSERT(is_exactly_a<numeric>(c1));
815 GINAC_ASSERT(is_exactly_a<numeric>(c2));
816 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
819 bool mul::can_make_flat(const expair & p) const
821 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
822 // this assertion will probably fail somewhere
823 // it would require a more careful make_flat, obeying the power laws
824 // probably should return true only if p.coeff is integer
825 return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
828 bool mul::can_be_further_expanded(const ex & e)
830 if (is_exactly_a<mul>(e)) {
831 for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
832 if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
835 } else if (is_exactly_a<power>(e)) {
836 if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
842 ex mul::expand(unsigned options) const
844 // First, expand the children
845 std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
846 const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
848 // Now, look for all the factors that are sums and multiply each one out
849 // with the next one that is found while collecting the factors which are
851 ex last_expanded = _ex1;
852 bool need_reexpand = false;
855 non_adds.reserve(expanded_seq.size());
857 for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
858 if (is_exactly_a<add>(cit->rest) &&
859 (cit->coeff.is_equal(_ex1))) {
860 if (is_exactly_a<add>(last_expanded)) {
862 // Expand a product of two sums, aggressive version.
863 // Caring for the overall coefficients in separate loops can
864 // sometimes give a performance gain of up to 15%!
866 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
867 // add2 is for the inner loop and should be the bigger of the two sums
868 // in the presence of asymptotically good sorting:
869 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
870 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
871 const epvector::const_iterator add1begin = add1.seq.begin();
872 const epvector::const_iterator add1end = add1.seq.end();
873 const epvector::const_iterator add2begin = add2.seq.begin();
874 const epvector::const_iterator add2end = add2.seq.end();
876 distrseq.reserve(add1.seq.size()+add2.seq.size());
878 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
879 if (!add1.overall_coeff.is_zero()) {
880 if (add1.overall_coeff.is_equal(_ex1))
881 distrseq.insert(distrseq.end(),add2begin,add2end);
883 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
884 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
887 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
888 if (!add2.overall_coeff.is_zero()) {
889 if (add2.overall_coeff.is_equal(_ex1))
890 distrseq.insert(distrseq.end(),add1begin,add1end);
892 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
893 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
896 // Compute the new overall coefficient and put it together:
897 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
899 // Multiply explicitly all non-numeric terms of add1 and add2:
900 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
901 // We really have to combine terms here in order to compactify
902 // the result. Otherwise it would become waayy tooo bigg.
905 for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
906 // Don't push_back expairs which might have a rest that evaluates to a numeric,
907 // since that would violate an invariant of expairseq:
908 const ex rest = (new mul(i1->rest, rename_dummy_indices_uniquely(i1->rest, i2->rest)))->setflag(status_flags::dynallocated);
909 if (is_exactly_a<numeric>(rest)) {
910 oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
912 distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
915 tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
917 last_expanded = tmp_accu;
920 if (!last_expanded.is_equal(_ex1))
921 non_adds.push_back(split_ex_to_pair(last_expanded));
922 last_expanded = cit->rest;
926 non_adds.push_back(*cit);
930 // Now the only remaining thing to do is to multiply the factors which
931 // were not sums into the "last_expanded" sum
932 if (is_exactly_a<add>(last_expanded)) {
933 size_t n = last_expanded.nops();
937 for (size_t i=0; i<n; ++i) {
938 epvector factors = non_adds;
939 factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(mul(non_adds), last_expanded.op(i))));
940 ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
941 if (can_be_further_expanded(term)) {
942 distrseq.push_back(term.expand());
945 ex_to<basic>(term).setflag(status_flags::expanded);
946 distrseq.push_back(term);
950 return ((new add(distrseq))->
951 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
954 non_adds.push_back(split_ex_to_pair(last_expanded));
955 ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
956 if (can_be_further_expanded(result)) {
957 return result.expand();
960 ex_to<basic>(result).setflag(status_flags::expanded);
967 // new virtual functions which can be overridden by derived classes
973 // non-virtual functions in this class
977 /** Member-wise expand the expairs representing this sequence. This must be
978 * overridden from expairseq::expandchildren() and done iteratively in order
979 * to allow for early cancallations and thus safe memory.
982 * @return pointer to epvector containing expanded representation or zero
983 * pointer, if sequence is unchanged. */
984 std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
986 const epvector::const_iterator last = seq.end();
987 epvector::const_iterator cit = seq.begin();
989 const ex & factor = recombine_pair_to_ex(*cit);
990 const ex & expanded_factor = factor.expand(options);
991 if (!are_ex_trivially_equal(factor,expanded_factor)) {
993 // something changed, copy seq, eval and return it
994 std::auto_ptr<epvector> s(new epvector);
995 s->reserve(seq.size());
997 // copy parts of seq which are known not to have changed
998 epvector::const_iterator cit2 = seq.begin();
1000 s->push_back(*cit2);
1004 // copy first changed element
1005 s->push_back(split_ex_to_pair(expanded_factor));
1009 while (cit2!=last) {
1010 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
1018 return std::auto_ptr<epvector>(0); // nothing has changed
1021 } // namespace GiNaC