3 * Implementation of GiNaC's products of expressions. */
6 * GiNaC Copyright (C) 1999-2010 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
26 #include "operators.h"
42 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
43 print_func<print_context>(&mul::do_print).
44 print_func<print_latex>(&mul::do_print_latex).
45 print_func<print_csrc>(&mul::do_print_csrc).
46 print_func<print_tree>(&mul::do_print_tree).
47 print_func<print_python_repr>(&mul::do_print_python_repr))
51 // default constructor
64 mul::mul(const ex & lh, const ex & rh)
67 construct_from_2_ex(lh,rh);
68 GINAC_ASSERT(is_canonical());
71 mul::mul(const exvector & v)
74 construct_from_exvector(v);
75 GINAC_ASSERT(is_canonical());
78 mul::mul(const epvector & v)
81 construct_from_epvector(v);
82 GINAC_ASSERT(is_canonical());
85 mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
88 construct_from_epvector(v, do_index_renaming);
89 GINAC_ASSERT(is_canonical());
92 mul::mul(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
94 GINAC_ASSERT(vp.get()!=0);
96 construct_from_epvector(*vp, do_index_renaming);
97 GINAC_ASSERT(is_canonical());
100 mul::mul(const ex & lh, const ex & mh, const ex & rh)
104 factors.push_back(lh);
105 factors.push_back(mh);
106 factors.push_back(rh);
107 overall_coeff = _ex1;
108 construct_from_exvector(factors);
109 GINAC_ASSERT(is_canonical());
117 // functions overriding virtual functions from base classes
120 void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
122 const numeric &coeff = ex_to<numeric>(overall_coeff);
123 if (coeff.csgn() == -1)
125 if (!coeff.is_equal(*_num1_p) &&
126 !coeff.is_equal(*_num_1_p)) {
127 if (coeff.is_rational()) {
128 if (coeff.is_negative())
133 if (coeff.csgn() == -1)
134 (-coeff).print(c, precedence());
136 coeff.print(c, precedence());
142 void mul::do_print(const print_context & c, unsigned level) const
144 if (precedence() <= level)
147 print_overall_coeff(c, "*");
149 epvector::const_iterator it = seq.begin(), itend = seq.end();
151 while (it != itend) {
156 recombine_pair_to_ex(*it).print(c, precedence());
160 if (precedence() <= level)
164 void mul::do_print_latex(const print_latex & c, unsigned level) const
166 if (precedence() <= level)
169 print_overall_coeff(c, " ");
171 // Separate factors into those with negative numeric exponent
173 epvector::const_iterator it = seq.begin(), itend = seq.end();
174 exvector neg_powers, others;
175 while (it != itend) {
176 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
177 if (ex_to<numeric>(it->coeff).is_negative())
178 neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
180 others.push_back(recombine_pair_to_ex(*it));
184 if (!neg_powers.empty()) {
186 // Factors with negative exponent are printed as a fraction
188 mul(others).eval().print(c);
190 mul(neg_powers).eval().print(c);
195 // All other factors are printed in the ordinary way
196 exvector::const_iterator vit = others.begin(), vitend = others.end();
197 while (vit != vitend) {
199 vit->print(c, precedence());
204 if (precedence() <= level)
208 void mul::do_print_csrc(const print_csrc & c, unsigned level) const
210 if (precedence() <= level)
213 if (!overall_coeff.is_equal(_ex1)) {
214 if (overall_coeff.is_equal(_ex_1))
217 overall_coeff.print(c, precedence());
222 // Print arguments, separated by "*" or "/"
223 epvector::const_iterator it = seq.begin(), itend = seq.end();
224 while (it != itend) {
226 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
227 bool needclosingparenthesis = false;
228 if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
229 if (is_a<print_csrc_cl_N>(c)) {
231 needclosingparenthesis = true;
236 // If the exponent is 1 or -1, it is left out
237 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
238 it->rest.print(c, precedence());
239 else if (it->coeff.info(info_flags::negint))
240 // Outer parens around ex needed for broken GCC parser:
241 (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
243 // Outer parens around ex needed for broken GCC parser:
244 (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
246 if (needclosingparenthesis)
249 // Separator is "/" for negative integer powers, "*" otherwise
252 if (it->coeff.info(info_flags::negint))
259 if (precedence() <= level)
263 void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
265 c.s << class_name() << '(';
267 for (size_t i=1; i<nops(); ++i) {
274 bool mul::info(unsigned inf) const
277 case info_flags::polynomial:
278 case info_flags::integer_polynomial:
279 case info_flags::cinteger_polynomial:
280 case info_flags::rational_polynomial:
281 case info_flags::real:
282 case info_flags::rational:
283 case info_flags::integer:
284 case info_flags::crational:
285 case info_flags::cinteger:
286 case info_flags::positive:
287 case info_flags::nonnegative:
288 case info_flags::posint:
289 case info_flags::nonnegint:
290 case info_flags::even:
291 case info_flags::crational_polynomial:
292 case info_flags::rational_function: {
293 epvector::const_iterator i = seq.begin(), end = seq.end();
295 if (!(recombine_pair_to_ex(*i).info(inf)))
299 if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even)
301 return overall_coeff.info(inf);
303 case info_flags::algebraic: {
304 epvector::const_iterator i = seq.begin(), end = seq.end();
306 if ((recombine_pair_to_ex(*i).info(inf)))
313 return inherited::info(inf);
316 int mul::degree(const ex & s) const
318 // Sum up degrees of factors
320 epvector::const_iterator i = seq.begin(), end = seq.end();
322 if (ex_to<numeric>(i->coeff).is_integer())
323 deg_sum += recombine_pair_to_ex(*i).degree(s);
326 throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
333 int mul::ldegree(const ex & s) const
335 // Sum up degrees of factors
337 epvector::const_iterator i = seq.begin(), end = seq.end();
339 if (ex_to<numeric>(i->coeff).is_integer())
340 deg_sum += recombine_pair_to_ex(*i).ldegree(s);
343 throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
350 ex mul::coeff(const ex & s, int n) const
353 coeffseq.reserve(seq.size()+1);
356 // product of individual coeffs
357 // if a non-zero power of s is found, the resulting product will be 0
358 epvector::const_iterator i = seq.begin(), end = seq.end();
360 coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
363 coeffseq.push_back(overall_coeff);
364 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
367 epvector::const_iterator i = seq.begin(), end = seq.end();
368 bool coeff_found = false;
370 ex t = recombine_pair_to_ex(*i);
371 ex c = t.coeff(s, n);
373 coeffseq.push_back(c);
376 coeffseq.push_back(t);
381 coeffseq.push_back(overall_coeff);
382 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
388 /** Perform automatic term rewriting rules in this class. In the following
389 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
390 * stand for such expressions that contain a plain number.
392 * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
396 * @param level cut-off in recursive evaluation */
397 ex mul::eval(int level) const
399 std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
400 if (evaled_seqp.get()) {
401 // do more evaluation later
402 return (new mul(evaled_seqp, overall_coeff))->
403 setflag(status_flags::dynallocated);
406 #ifdef DO_GINAC_ASSERT
407 epvector::const_iterator i = seq.begin(), end = seq.end();
409 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
410 (!(ex_to<numeric>(i->coeff).is_integer())));
411 GINAC_ASSERT(!(i->is_canonical_numeric()));
412 if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
413 print(print_tree(std::cerr));
414 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
416 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
417 GINAC_ASSERT(p.rest.is_equal(i->rest));
418 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
422 #endif // def DO_GINAC_ASSERT
424 if (flags & status_flags::evaluated) {
425 GINAC_ASSERT(seq.size()>0);
426 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
430 size_t seq_size = seq.size();
431 if (overall_coeff.is_zero()) {
434 } else if (seq_size==0) {
436 return overall_coeff;
437 } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
439 return recombine_pair_to_ex(*(seq.begin()));
440 } else if ((seq_size==1) &&
441 is_exactly_a<add>((*seq.begin()).rest) &&
442 ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
443 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
444 const add & addref = ex_to<add>((*seq.begin()).rest);
445 std::auto_ptr<epvector> distrseq(new epvector);
446 distrseq->reserve(addref.seq.size());
447 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
449 distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
452 return (new add(distrseq,
453 ex_to<numeric>(addref.overall_coeff).
454 mul_dyn(ex_to<numeric>(overall_coeff)))
455 )->setflag(status_flags::dynallocated | status_flags::evaluated);
456 } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
457 // Strip the content and the unit part from each term. Thus
458 // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)2
460 epvector::const_iterator last = seq.end();
461 epvector::const_iterator i = seq.begin();
462 epvector::const_iterator j = seq.begin();
463 std::auto_ptr<epvector> s(new epvector);
464 numeric oc = *_num1_p;
465 bool something_changed = false;
467 if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
468 // power::eval has such a rule, no need to handle powers here
473 // XXX: What is the best way to check if the polynomial is a primitive?
474 numeric c = i->rest.integer_content();
475 const numeric lead_coeff =
476 ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div(c);
477 const bool canonicalizable = lead_coeff.is_integer();
479 // XXX: The main variable is chosen in a random way, so this code
480 // does NOT transform the term into the canonical form (thus, in some
481 // very unlucky event it can even loop forever). Hopefully the main
482 // variable will be the same for all terms in *this
483 const bool unit_normal = lead_coeff.is_pos_integer();
484 if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
489 if (! something_changed) {
490 s->reserve(seq_size);
491 something_changed = true;
494 while ((j!=i) && (j!=last)) {
500 c = c.mul(*_num_1_p);
504 // divide add by the number in place to save at least 2 .eval() calls
505 const add& addref = ex_to<add>(i->rest);
506 add* primitive = new add(addref);
507 primitive->setflag(status_flags::dynallocated);
508 primitive->clearflag(status_flags::hash_calculated);
509 primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
510 for (epvector::iterator ai = primitive->seq.begin();
511 ai != primitive->seq.end(); ++ai)
512 ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
514 s->push_back(expair(*primitive, _ex1));
519 if (something_changed) {
524 return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
525 )->setflag(status_flags::dynallocated);
532 ex mul::evalf(int level) const
535 return mul(seq,overall_coeff);
537 if (level==-max_recursion_level)
538 throw(std::runtime_error("max recursion level reached"));
540 std::auto_ptr<epvector> s(new epvector);
541 s->reserve(seq.size());
544 epvector::const_iterator i = seq.begin(), end = seq.end();
546 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
550 return mul(s, overall_coeff.evalf(level));
553 void mul::find_real_imag(ex & rp, ex & ip) const
555 rp = overall_coeff.real_part();
556 ip = overall_coeff.imag_part();
557 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
558 ex factor = recombine_pair_to_ex(*i);
559 ex new_rp = factor.real_part();
560 ex new_ip = factor.imag_part();
561 if(new_ip.is_zero()) {
565 ex temp = rp*new_rp - ip*new_ip;
566 ip = ip*new_rp + rp*new_ip;
574 ex mul::real_part() const
577 find_real_imag(rp, ip);
581 ex mul::imag_part() const
584 find_real_imag(rp, ip);
588 ex mul::evalm() const
591 if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
592 && is_a<matrix>(seq[0].rest))
593 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
595 // Evaluate children first, look whether there are any matrices at all
596 // (there can be either no matrices or one matrix; if there were more
597 // than one matrix, it would be a non-commutative product)
598 std::auto_ptr<epvector> s(new epvector);
599 s->reserve(seq.size());
601 bool have_matrix = false;
602 epvector::iterator the_matrix;
604 epvector::const_iterator i = seq.begin(), end = seq.end();
606 const ex &m = recombine_pair_to_ex(*i).evalm();
607 s->push_back(split_ex_to_pair(m));
608 if (is_a<matrix>(m)) {
610 the_matrix = s->end() - 1;
617 // The product contained a matrix. We will multiply all other factors
619 matrix m = ex_to<matrix>(the_matrix->rest);
620 s->erase(the_matrix);
621 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
622 return m.mul_scalar(scalar);
625 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
628 ex mul::eval_ncmul(const exvector & v) const
631 return inherited::eval_ncmul(v);
633 // Find first noncommutative element and call its eval_ncmul()
634 epvector::const_iterator i = seq.begin(), end = seq.end();
636 if (i->rest.return_type() == return_types::noncommutative)
637 return i->rest.eval_ncmul(v);
640 return inherited::eval_ncmul(v);
643 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls)
649 if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
650 origbase = origfactor.op(0);
651 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
652 origexponent = expon > 0 ? expon : -expon;
653 origexpsign = expon > 0 ? 1 : -1;
655 origbase = origfactor;
664 if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
665 patternbase = patternfactor.op(0);
666 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
667 patternexponent = expon > 0 ? expon : -expon;
668 patternexpsign = expon > 0 ? 1 : -1;
670 patternbase = patternfactor;
675 exmap saverepls = repls;
676 if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
680 int newnummatches = origexponent / patternexponent;
681 if (newnummatches < nummatches)
682 nummatches = newnummatches;
686 /** Checks wheter e matches to the pattern pat and the (possibly to be updated)
687 * list of replacements repls. This matching is in the sense of algebraic
688 * substitutions. Matching starts with pat.op(factor) of the pattern because
689 * the factors before this one have already been matched. The (possibly
690 * updated) number of matches is in nummatches. subsed[i] is true for factors
691 * that already have been replaced by previous substitutions and matched[i]
692 * is true for factors that have been matched by the current match.
694 bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls,
695 int factor, int &nummatches, const std::vector<bool> &subsed,
696 std::vector<bool> &matched)
698 if (factor == (int)pat.nops())
701 for (size_t i=0; i<e.nops(); ++i) {
702 if(subsed[i] || matched[i])
704 exmap newrepls = repls;
705 int newnummatches = nummatches;
706 if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
708 if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
709 newnummatches, subsed, matched)) {
711 nummatches = newnummatches;
722 bool mul::has(const ex & pattern, unsigned options) const
724 if(!(options&has_options::algebraic))
725 return basic::has(pattern,options);
726 if(is_a<mul>(pattern)) {
728 int nummatches = std::numeric_limits<int>::max();
729 std::vector<bool> subsed(seq.size(), false);
730 std::vector<bool> matched(seq.size(), false);
731 if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
735 return basic::has(pattern, options);
738 ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
740 std::vector<bool> subsed(seq.size(), false);
741 exvector subsresult(seq.size());
745 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
747 if (is_exactly_a<mul>(it->first)) {
749 int nummatches = std::numeric_limits<int>::max();
750 std::vector<bool> currsubsed(seq.size(), false);
753 if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
756 for (size_t j=0; j<subsed.size(); j++)
760 = it->first.subs(repls, subs_options::no_pattern);
761 divide_by *= power(subsed_pattern, nummatches);
763 = it->second.subs(repls, subs_options::no_pattern);
764 multiply_by *= power(subsed_result, nummatches);
769 for (size_t j=0; j<this->nops(); j++) {
770 int nummatches = std::numeric_limits<int>::max();
772 if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
775 = it->first.subs(repls, subs_options::no_pattern);
776 divide_by *= power(subsed_pattern, nummatches);
778 = it->second.subs(repls, subs_options::no_pattern);
779 multiply_by *= power(subsed_result, nummatches);
785 bool subsfound = false;
786 for (size_t i=0; i<subsed.size(); i++) {
793 return subs_one_level(m, options | subs_options::algebraic);
795 return ((*this)/divide_by)*multiply_by;
800 /** Implementation of ex::diff() for a product. It applies the product rule.
802 ex mul::derivative(const symbol & s) const
804 size_t num = seq.size();
808 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
809 epvector mulseq = seq;
810 epvector::const_iterator i = seq.begin(), end = seq.end();
811 epvector::iterator i2 = mulseq.begin();
813 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
816 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
820 return (new add(addseq))->setflag(status_flags::dynallocated);
823 int mul::compare_same_type(const basic & other) const
825 return inherited::compare_same_type(other);
828 unsigned mul::return_type() const
831 // mul without factors: should not happen, but commutates
832 return return_types::commutative;
835 bool all_commutative = true;
836 epvector::const_iterator noncommutative_element; // point to first found nc element
838 epvector::const_iterator i = seq.begin(), end = seq.end();
840 unsigned rt = i->rest.return_type();
841 if (rt == return_types::noncommutative_composite)
842 return rt; // one ncc -> mul also ncc
843 if ((rt == return_types::noncommutative) && (all_commutative)) {
844 // first nc element found, remember position
845 noncommutative_element = i;
846 all_commutative = false;
848 if ((rt == return_types::noncommutative) && (!all_commutative)) {
849 // another nc element found, compare type_infos
850 if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
851 // different types -> mul is ncc
852 return return_types::noncommutative_composite;
857 // all factors checked
858 return all_commutative ? return_types::commutative : return_types::noncommutative;
861 return_type_t mul::return_type_tinfo() const
864 return make_return_type_t<mul>(); // mul without factors: should not happen
866 // return type_info of first noncommutative element
867 epvector::const_iterator i = seq.begin(), end = seq.end();
869 if (i->rest.return_type() == return_types::noncommutative)
870 return i->rest.return_type_tinfo();
873 // no noncommutative element found, should not happen
874 return make_return_type_t<mul>();
877 ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
879 return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
882 ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
884 return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated);
887 expair mul::split_ex_to_pair(const ex & e) const
889 if (is_exactly_a<power>(e)) {
890 const power & powerref = ex_to<power>(e);
891 if (is_exactly_a<numeric>(powerref.exponent))
892 return expair(powerref.basis,powerref.exponent);
894 return expair(e,_ex1);
897 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
900 // to avoid duplication of power simplification rules,
901 // we create a temporary power object
902 // otherwise it would be hard to correctly evaluate
903 // expression like (4^(1/3))^(3/2)
904 if (c.is_equal(_ex1))
905 return split_ex_to_pair(e);
907 return split_ex_to_pair(power(e,c));
910 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
913 // to avoid duplication of power simplification rules,
914 // we create a temporary power object
915 // otherwise it would be hard to correctly evaluate
916 // expression like (4^(1/3))^(3/2)
917 if (c.is_equal(_ex1))
920 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
923 ex mul::recombine_pair_to_ex(const expair & p) const
925 if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
928 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
931 bool mul::expair_needs_further_processing(epp it)
933 if (is_exactly_a<mul>(it->rest) &&
934 ex_to<numeric>(it->coeff).is_integer()) {
935 // combined pair is product with integer power -> expand it
936 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
939 if (is_exactly_a<numeric>(it->rest)) {
940 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
941 if (!ep.is_equal(*it)) {
942 // combined pair is a numeric power which can be simplified
946 if (it->coeff.is_equal(_ex1)) {
947 // combined pair has coeff 1 and must be moved to the end
954 ex mul::default_overall_coeff() const
959 void mul::combine_overall_coeff(const ex & c)
961 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
962 GINAC_ASSERT(is_exactly_a<numeric>(c));
963 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
966 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
968 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
969 GINAC_ASSERT(is_exactly_a<numeric>(c1));
970 GINAC_ASSERT(is_exactly_a<numeric>(c2));
971 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
974 bool mul::can_make_flat(const expair & p) const
976 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
977 // this assertion will probably fail somewhere
978 // it would require a more careful make_flat, obeying the power laws
979 // probably should return true only if p.coeff is integer
980 return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
983 bool mul::can_be_further_expanded(const ex & e)
985 if (is_exactly_a<mul>(e)) {
986 for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
987 if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
990 } else if (is_exactly_a<power>(e)) {
991 if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
997 ex mul::expand(unsigned options) const
1000 // trivial case: expanding the monomial (~ 30% of all calls)
1001 epvector::const_iterator i = seq.begin(), seq_end = seq.end();
1002 while ((i != seq.end()) && is_a<symbol>(i->rest) && i->coeff.info(info_flags::integer))
1005 setflag(status_flags::expanded);
1010 // do not rename indices if the object has no indices at all
1011 if ((!(options & expand_options::expand_rename_idx)) &&
1012 this->info(info_flags::has_indices))
1013 options |= expand_options::expand_rename_idx;
1015 const bool skip_idx_rename = !(options & expand_options::expand_rename_idx);
1017 // First, expand the children
1018 std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
1019 const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
1021 // Now, look for all the factors that are sums and multiply each one out
1022 // with the next one that is found while collecting the factors which are
1024 ex last_expanded = _ex1;
1027 non_adds.reserve(expanded_seq.size());
1029 for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
1030 if (is_exactly_a<add>(cit->rest) &&
1031 (cit->coeff.is_equal(_ex1))) {
1032 if (is_exactly_a<add>(last_expanded)) {
1034 // Expand a product of two sums, aggressive version.
1035 // Caring for the overall coefficients in separate loops can
1036 // sometimes give a performance gain of up to 15%!
1038 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
1039 // add2 is for the inner loop and should be the bigger of the two sums
1040 // in the presence of asymptotically good sorting:
1041 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
1042 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
1043 const epvector::const_iterator add1begin = add1.seq.begin();
1044 const epvector::const_iterator add1end = add1.seq.end();
1045 const epvector::const_iterator add2begin = add2.seq.begin();
1046 const epvector::const_iterator add2end = add2.seq.end();
1048 distrseq.reserve(add1.seq.size()+add2.seq.size());
1050 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
1051 if (!add1.overall_coeff.is_zero()) {
1052 if (add1.overall_coeff.is_equal(_ex1))
1053 distrseq.insert(distrseq.end(),add2begin,add2end);
1055 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
1056 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
1059 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
1060 if (!add2.overall_coeff.is_zero()) {
1061 if (add2.overall_coeff.is_equal(_ex1))
1062 distrseq.insert(distrseq.end(),add1begin,add1end);
1064 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
1065 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
1068 // Compute the new overall coefficient and put it together:
1069 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
1071 exvector add1_dummy_indices, add2_dummy_indices, add_indices;
1074 if (!skip_idx_rename) {
1075 for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
1076 add_indices = get_all_dummy_indices_safely(i->rest);
1077 add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
1079 for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
1080 add_indices = get_all_dummy_indices_safely(i->rest);
1081 add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
1084 sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
1085 sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
1086 dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
1089 // Multiply explicitly all non-numeric terms of add1 and add2:
1090 for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
1091 // We really have to combine terms here in order to compactify
1092 // the result. Otherwise it would become waayy tooo bigg.
1093 numeric oc(*_num0_p);
1095 distrseq2.reserve(add1.seq.size());
1096 const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ?
1098 i2->rest.subs(ex_to<lst>(dummy_subs.op(0)),
1099 ex_to<lst>(dummy_subs.op(1)), subs_options::no_pattern));
1100 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
1101 // Don't push_back expairs which might have a rest that evaluates to a numeric,
1102 // since that would violate an invariant of expairseq:
1103 const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated);
1104 if (is_exactly_a<numeric>(rest)) {
1105 oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
1107 distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
1110 tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated);
1112 last_expanded = tmp_accu;
1114 if (!last_expanded.is_equal(_ex1))
1115 non_adds.push_back(split_ex_to_pair(last_expanded));
1116 last_expanded = cit->rest;
1120 non_adds.push_back(*cit);
1124 // Now the only remaining thing to do is to multiply the factors which
1125 // were not sums into the "last_expanded" sum
1126 if (is_exactly_a<add>(last_expanded)) {
1127 size_t n = last_expanded.nops();
1129 distrseq.reserve(n);
1131 if (! skip_idx_rename) {
1132 va = get_all_dummy_indices_safely(mul(non_adds));
1133 sort(va.begin(), va.end(), ex_is_less());
1136 for (size_t i=0; i<n; ++i) {
1137 epvector factors = non_adds;
1138 if (skip_idx_rename)
1139 factors.push_back(split_ex_to_pair(last_expanded.op(i)));
1141 factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
1142 ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
1143 if (can_be_further_expanded(term)) {
1144 distrseq.push_back(term.expand());
1147 ex_to<basic>(term).setflag(status_flags::expanded);
1148 distrseq.push_back(term);
1152 return ((new add(distrseq))->
1153 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
1156 non_adds.push_back(split_ex_to_pair(last_expanded));
1157 ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
1158 if (can_be_further_expanded(result)) {
1159 return result.expand();
1162 ex_to<basic>(result).setflag(status_flags::expanded);
1169 // new virtual functions which can be overridden by derived classes
1175 // non-virtual functions in this class
1179 /** Member-wise expand the expairs representing this sequence. This must be
1180 * overridden from expairseq::expandchildren() and done iteratively in order
1181 * to allow for early cancallations and thus safe memory.
1183 * @see mul::expand()
1184 * @return pointer to epvector containing expanded representation or zero
1185 * pointer, if sequence is unchanged. */
1186 std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
1188 const epvector::const_iterator last = seq.end();
1189 epvector::const_iterator cit = seq.begin();
1191 const ex & factor = recombine_pair_to_ex(*cit);
1192 const ex & expanded_factor = factor.expand(options);
1193 if (!are_ex_trivially_equal(factor,expanded_factor)) {
1195 // something changed, copy seq, eval and return it
1196 std::auto_ptr<epvector> s(new epvector);
1197 s->reserve(seq.size());
1199 // copy parts of seq which are known not to have changed
1200 epvector::const_iterator cit2 = seq.begin();
1202 s->push_back(*cit2);
1206 // copy first changed element
1207 s->push_back(split_ex_to_pair(expanded_factor));
1211 while (cit2!=last) {
1212 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
1220 return std::auto_ptr<epvector>(0); // nothing has changed
1223 GINAC_BIND_UNARCHIVER(mul);
1225 } // namespace GiNaC