3 * Implementation of GiNaC's products of expressions. */
6 * GiNaC Copyright (C) 1999-2011 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::even:
287 case info_flags::crational_polynomial:
288 case info_flags::rational_function: {
289 epvector::const_iterator i = seq.begin(), end = seq.end();
291 if (!(recombine_pair_to_ex(*i).info(inf)))
295 if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even)
297 return overall_coeff.info(inf);
299 case info_flags::algebraic: {
300 epvector::const_iterator i = seq.begin(), end = seq.end();
302 if ((recombine_pair_to_ex(*i).info(inf)))
308 case info_flags::positive:
309 case info_flags::negative: {
310 if ((inf==info_flags::positive) && (flags & status_flags::is_positive))
312 else if ((inf==info_flags::negative) && (flags & status_flags::is_negative))
314 if (flags & status_flags::purely_indefinite)
318 epvector::const_iterator i = seq.begin(), end = seq.end();
320 const ex& factor = recombine_pair_to_ex(*i++);
321 if (factor.info(info_flags::positive))
323 else if (factor.info(info_flags::negative))
328 if (overall_coeff.info(info_flags::negative))
330 setflag(pos ? status_flags::is_positive : status_flags::is_negative);
331 return (inf == info_flags::positive? pos : !pos);
333 case info_flags::nonnegative: {
334 if (flags & status_flags::is_positive)
337 epvector::const_iterator i = seq.begin(), end = seq.end();
339 const ex& factor = recombine_pair_to_ex(*i++);
340 if (factor.info(info_flags::nonnegative) || factor.info(info_flags::positive))
342 else if (factor.info(info_flags::negative))
347 return (overall_coeff.info(info_flags::negative)? pos : !pos);
349 case info_flags::posint:
350 case info_flags::negint: {
352 epvector::const_iterator i = seq.begin(), end = seq.end();
354 const ex& factor = recombine_pair_to_ex(*i++);
355 if (factor.info(info_flags::posint))
357 else if (factor.info(info_flags::negint))
362 if (overall_coeff.info(info_flags::negint))
364 else if (!overall_coeff.info(info_flags::posint))
366 return (inf ==info_flags::posint? pos : !pos);
368 case info_flags::nonnegint: {
370 epvector::const_iterator i = seq.begin(), end = seq.end();
372 const ex& factor = recombine_pair_to_ex(*i++);
373 if (factor.info(info_flags::nonnegint) || factor.info(info_flags::posint))
375 else if (factor.info(info_flags::negint))
380 if (overall_coeff.info(info_flags::negint))
382 else if (!overall_coeff.info(info_flags::posint))
386 case info_flags::indefinite: {
387 if (flags & status_flags::purely_indefinite)
389 if (flags & (status_flags::is_positive | status_flags::is_negative))
391 epvector::const_iterator i = seq.begin(), end = seq.end();
393 const ex& term = recombine_pair_to_ex(*i);
394 if (term.info(info_flags::positive) || term.info(info_flags::negative))
398 setflag(status_flags::purely_indefinite);
402 return inherited::info(inf);
405 bool mul::is_polynomial(const ex & var) const
407 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
408 if (!i->rest.is_polynomial(var) ||
409 (i->rest.has(var) && !i->coeff.info(info_flags::integer))) {
416 int mul::degree(const ex & s) const
418 // Sum up degrees of factors
420 epvector::const_iterator i = seq.begin(), end = seq.end();
422 if (ex_to<numeric>(i->coeff).is_integer())
423 deg_sum += recombine_pair_to_ex(*i).degree(s);
426 throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
433 int mul::ldegree(const ex & s) const
435 // Sum up degrees of factors
437 epvector::const_iterator i = seq.begin(), end = seq.end();
439 if (ex_to<numeric>(i->coeff).is_integer())
440 deg_sum += recombine_pair_to_ex(*i).ldegree(s);
443 throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
450 ex mul::coeff(const ex & s, int n) const
453 coeffseq.reserve(seq.size()+1);
456 // product of individual coeffs
457 // if a non-zero power of s is found, the resulting product will be 0
458 epvector::const_iterator i = seq.begin(), end = seq.end();
460 coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
463 coeffseq.push_back(overall_coeff);
464 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
467 epvector::const_iterator i = seq.begin(), end = seq.end();
468 bool coeff_found = false;
470 ex t = recombine_pair_to_ex(*i);
471 ex c = t.coeff(s, n);
473 coeffseq.push_back(c);
476 coeffseq.push_back(t);
481 coeffseq.push_back(overall_coeff);
482 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
488 /** Perform automatic term rewriting rules in this class. In the following
489 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
490 * stand for such expressions that contain a plain number.
492 * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
496 * @param level cut-off in recursive evaluation */
497 ex mul::eval(int level) const
499 std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
500 if (evaled_seqp.get()) {
501 // do more evaluation later
502 return (new mul(evaled_seqp, overall_coeff))->
503 setflag(status_flags::dynallocated);
506 if (flags & status_flags::evaluated) {
507 GINAC_ASSERT(seq.size()>0);
508 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
512 size_t seq_size = seq.size();
513 if (overall_coeff.is_zero()) {
516 } else if (seq_size==0) {
518 return overall_coeff;
519 } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
521 return recombine_pair_to_ex(*(seq.begin()));
522 } else if ((seq_size==1) &&
523 is_exactly_a<add>((*seq.begin()).rest) &&
524 ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
525 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
526 const add & addref = ex_to<add>((*seq.begin()).rest);
527 std::auto_ptr<epvector> distrseq(new epvector);
528 distrseq->reserve(addref.seq.size());
529 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
531 distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
534 return (new add(distrseq,
535 ex_to<numeric>(addref.overall_coeff).
536 mul_dyn(ex_to<numeric>(overall_coeff)))
537 )->setflag(status_flags::dynallocated | status_flags::evaluated);
538 } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
539 // Strip the content and the unit part from each term. Thus
540 // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)^2
542 epvector::const_iterator last = seq.end();
543 epvector::const_iterator i = seq.begin();
544 epvector::const_iterator j = seq.begin();
545 std::auto_ptr<epvector> s(new epvector);
546 numeric oc = *_num1_p;
547 bool something_changed = false;
549 if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
550 // power::eval has such a rule, no need to handle powers here
555 // XXX: What is the best way to check if the polynomial is a primitive?
556 numeric c = i->rest.integer_content();
557 const numeric lead_coeff =
558 ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div(c);
559 const bool canonicalizable = lead_coeff.is_integer();
561 // XXX: The main variable is chosen in a random way, so this code
562 // does NOT transform the term into the canonical form (thus, in some
563 // very unlucky event it can even loop forever). Hopefully the main
564 // variable will be the same for all terms in *this
565 const bool unit_normal = lead_coeff.is_pos_integer();
566 if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
571 if (! something_changed) {
572 s->reserve(seq_size);
573 something_changed = true;
576 while ((j!=i) && (j!=last)) {
582 c = c.mul(*_num_1_p);
586 // divide add by the number in place to save at least 2 .eval() calls
587 const add& addref = ex_to<add>(i->rest);
588 add* primitive = new add(addref);
589 primitive->setflag(status_flags::dynallocated);
590 primitive->clearflag(status_flags::hash_calculated);
591 primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
592 for (epvector::iterator ai = primitive->seq.begin(); ai != primitive->seq.end(); ++ai)
593 ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
595 s->push_back(expair(*primitive, _ex1));
600 if (something_changed) {
605 return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
606 )->setflag(status_flags::dynallocated);
613 ex mul::evalf(int level) const
616 return mul(seq,overall_coeff);
618 if (level==-max_recursion_level)
619 throw(std::runtime_error("max recursion level reached"));
621 std::auto_ptr<epvector> s(new epvector);
622 s->reserve(seq.size());
625 epvector::const_iterator i = seq.begin(), end = seq.end();
627 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
631 return mul(s, overall_coeff.evalf(level));
634 void mul::find_real_imag(ex & rp, ex & ip) const
636 rp = overall_coeff.real_part();
637 ip = overall_coeff.imag_part();
638 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
639 ex factor = recombine_pair_to_ex(*i);
640 ex new_rp = factor.real_part();
641 ex new_ip = factor.imag_part();
642 if(new_ip.is_zero()) {
646 ex temp = rp*new_rp - ip*new_ip;
647 ip = ip*new_rp + rp*new_ip;
655 ex mul::real_part() const
658 find_real_imag(rp, ip);
662 ex mul::imag_part() const
665 find_real_imag(rp, ip);
669 ex mul::evalm() const
672 if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
673 && is_a<matrix>(seq[0].rest))
674 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
676 // Evaluate children first, look whether there are any matrices at all
677 // (there can be either no matrices or one matrix; if there were more
678 // than one matrix, it would be a non-commutative product)
679 std::auto_ptr<epvector> s(new epvector);
680 s->reserve(seq.size());
682 bool have_matrix = false;
683 epvector::iterator the_matrix;
685 epvector::const_iterator i = seq.begin(), end = seq.end();
687 const ex &m = recombine_pair_to_ex(*i).evalm();
688 s->push_back(split_ex_to_pair(m));
689 if (is_a<matrix>(m)) {
691 the_matrix = s->end() - 1;
698 // The product contained a matrix. We will multiply all other factors
700 matrix m = ex_to<matrix>(the_matrix->rest);
701 s->erase(the_matrix);
702 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
703 return m.mul_scalar(scalar);
706 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
709 ex mul::eval_ncmul(const exvector & v) const
712 return inherited::eval_ncmul(v);
714 // Find first noncommutative element and call its eval_ncmul()
715 epvector::const_iterator i = seq.begin(), end = seq.end();
717 if (i->rest.return_type() == return_types::noncommutative)
718 return i->rest.eval_ncmul(v);
721 return inherited::eval_ncmul(v);
724 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls)
730 if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
731 origbase = origfactor.op(0);
732 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
733 origexponent = expon > 0 ? expon : -expon;
734 origexpsign = expon > 0 ? 1 : -1;
736 origbase = origfactor;
745 if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
746 patternbase = patternfactor.op(0);
747 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
748 patternexponent = expon > 0 ? expon : -expon;
749 patternexpsign = expon > 0 ? 1 : -1;
751 patternbase = patternfactor;
756 exmap saverepls = repls;
757 if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
761 int newnummatches = origexponent / patternexponent;
762 if (newnummatches < nummatches)
763 nummatches = newnummatches;
767 /** Checks wheter e matches to the pattern pat and the (possibly to be updated)
768 * list of replacements repls. This matching is in the sense of algebraic
769 * substitutions. Matching starts with pat.op(factor) of the pattern because
770 * the factors before this one have already been matched. The (possibly
771 * updated) number of matches is in nummatches. subsed[i] is true for factors
772 * that already have been replaced by previous substitutions and matched[i]
773 * is true for factors that have been matched by the current match.
775 bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls,
776 int factor, int &nummatches, const std::vector<bool> &subsed,
777 std::vector<bool> &matched)
779 GINAC_ASSERT(subsed.size() == e.nops());
780 GINAC_ASSERT(matched.size() == e.nops());
782 if (factor == (int)pat.nops())
785 for (size_t i=0; i<e.nops(); ++i) {
786 if(subsed[i] || matched[i])
788 exmap newrepls = repls;
789 int newnummatches = nummatches;
790 if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
792 if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
793 newnummatches, subsed, matched)) {
795 nummatches = newnummatches;
806 bool mul::has(const ex & pattern, unsigned options) const
808 if(!(options&has_options::algebraic))
809 return basic::has(pattern,options);
810 if(is_a<mul>(pattern)) {
812 int nummatches = std::numeric_limits<int>::max();
813 std::vector<bool> subsed(nops(), false);
814 std::vector<bool> matched(nops(), false);
815 if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
819 return basic::has(pattern, options);
822 ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
824 std::vector<bool> subsed(nops(), false);
828 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
830 if (is_exactly_a<mul>(it->first)) {
832 int nummatches = std::numeric_limits<int>::max();
833 std::vector<bool> currsubsed(nops(), false);
836 if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
839 for (size_t j=0; j<subsed.size(); j++)
843 = it->first.subs(repls, subs_options::no_pattern);
844 divide_by *= power(subsed_pattern, nummatches);
846 = it->second.subs(repls, subs_options::no_pattern);
847 multiply_by *= power(subsed_result, nummatches);
852 for (size_t j=0; j<this->nops(); j++) {
853 int nummatches = std::numeric_limits<int>::max();
855 if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
858 = it->first.subs(repls, subs_options::no_pattern);
859 divide_by *= power(subsed_pattern, nummatches);
861 = it->second.subs(repls, subs_options::no_pattern);
862 multiply_by *= power(subsed_result, nummatches);
868 bool subsfound = false;
869 for (size_t i=0; i<subsed.size(); i++) {
876 return subs_one_level(m, options | subs_options::algebraic);
878 return ((*this)/divide_by)*multiply_by;
881 ex mul::conjugate() const
883 // The base class' method is wrong here because we have to be careful at
884 // branch cuts. power::conjugate takes care of that already, so use it.
885 epvector *newepv = 0;
886 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
888 newepv->push_back(split_ex_to_pair(recombine_pair_to_ex(*i).conjugate()));
891 ex x = recombine_pair_to_ex(*i);
892 ex c = x.conjugate();
896 newepv = new epvector;
897 newepv->reserve(seq.size());
898 for (epvector::const_iterator j=seq.begin(); j!=i; ++j) {
899 newepv->push_back(*j);
901 newepv->push_back(split_ex_to_pair(c));
903 ex x = overall_coeff.conjugate();
904 if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
907 ex result = thisexpairseq(newepv ? *newepv : seq, x);
915 /** Implementation of ex::diff() for a product. It applies the product rule.
917 ex mul::derivative(const symbol & s) const
919 size_t num = seq.size();
923 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
924 epvector mulseq = seq;
925 epvector::const_iterator i = seq.begin(), end = seq.end();
926 epvector::iterator i2 = mulseq.begin();
928 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
931 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
935 return (new add(addseq))->setflag(status_flags::dynallocated);
938 int mul::compare_same_type(const basic & other) const
940 return inherited::compare_same_type(other);
943 unsigned mul::return_type() const
946 // mul without factors: should not happen, but commutates
947 return return_types::commutative;
950 bool all_commutative = true;
951 epvector::const_iterator noncommutative_element; // point to first found nc element
953 epvector::const_iterator i = seq.begin(), end = seq.end();
955 unsigned rt = i->rest.return_type();
956 if (rt == return_types::noncommutative_composite)
957 return rt; // one ncc -> mul also ncc
958 if ((rt == return_types::noncommutative) && (all_commutative)) {
959 // first nc element found, remember position
960 noncommutative_element = i;
961 all_commutative = false;
963 if ((rt == return_types::noncommutative) && (!all_commutative)) {
964 // another nc element found, compare type_infos
965 if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
966 // different types -> mul is ncc
967 return return_types::noncommutative_composite;
972 // all factors checked
973 return all_commutative ? return_types::commutative : return_types::noncommutative;
976 return_type_t mul::return_type_tinfo() const
979 return make_return_type_t<mul>(); // mul without factors: should not happen
981 // return type_info of first noncommutative element
982 epvector::const_iterator i = seq.begin(), end = seq.end();
984 if (i->rest.return_type() == return_types::noncommutative)
985 return i->rest.return_type_tinfo();
988 // no noncommutative element found, should not happen
989 return make_return_type_t<mul>();
992 ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
994 return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
997 ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
999 return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated);
1002 expair mul::split_ex_to_pair(const ex & e) const
1004 if (is_exactly_a<power>(e)) {
1005 const power & powerref = ex_to<power>(e);
1006 if (is_exactly_a<numeric>(powerref.exponent))
1007 return expair(powerref.basis,powerref.exponent);
1009 return expair(e,_ex1);
1012 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
1015 // to avoid duplication of power simplification rules,
1016 // we create a temporary power object
1017 // otherwise it would be hard to correctly evaluate
1018 // expression like (4^(1/3))^(3/2)
1019 if (c.is_equal(_ex1))
1020 return split_ex_to_pair(e);
1022 return split_ex_to_pair(power(e,c));
1025 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
1028 // to avoid duplication of power simplification rules,
1029 // we create a temporary power object
1030 // otherwise it would be hard to correctly evaluate
1031 // expression like (4^(1/3))^(3/2)
1032 if (c.is_equal(_ex1))
1035 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
1038 ex mul::recombine_pair_to_ex(const expair & p) const
1040 if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
1043 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
1046 bool mul::expair_needs_further_processing(epp it)
1048 if (is_exactly_a<mul>(it->rest) &&
1049 ex_to<numeric>(it->coeff).is_integer()) {
1050 // combined pair is product with integer power -> expand it
1051 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
1054 if (is_exactly_a<numeric>(it->rest)) {
1055 if (it->coeff.is_equal(_ex1)) {
1056 // pair has coeff 1 and must be moved to the end
1059 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
1060 if (!ep.is_equal(*it)) {
1061 // combined pair is a numeric power which can be simplified
1069 ex mul::default_overall_coeff() const
1074 void mul::combine_overall_coeff(const ex & c)
1076 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
1077 GINAC_ASSERT(is_exactly_a<numeric>(c));
1078 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
1081 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
1083 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
1084 GINAC_ASSERT(is_exactly_a<numeric>(c1));
1085 GINAC_ASSERT(is_exactly_a<numeric>(c2));
1086 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
1089 bool mul::can_make_flat(const expair & p) const
1091 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
1092 // this assertion will probably fail somewhere
1093 // it would require a more careful make_flat, obeying the power laws
1094 // probably should return true only if p.coeff is integer
1095 return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
1098 bool mul::can_be_further_expanded(const ex & e)
1100 if (is_exactly_a<mul>(e)) {
1101 for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
1102 if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
1105 } else if (is_exactly_a<power>(e)) {
1106 if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
1112 ex mul::expand(unsigned options) const
1115 // trivial case: expanding the monomial (~ 30% of all calls)
1116 epvector::const_iterator i = seq.begin(), seq_end = seq.end();
1117 while ((i != seq.end()) && is_a<symbol>(i->rest) && i->coeff.info(info_flags::integer))
1120 setflag(status_flags::expanded);
1125 // do not rename indices if the object has no indices at all
1126 if ((!(options & expand_options::expand_rename_idx)) &&
1127 this->info(info_flags::has_indices))
1128 options |= expand_options::expand_rename_idx;
1130 const bool skip_idx_rename = !(options & expand_options::expand_rename_idx);
1132 // First, expand the children
1133 std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
1134 const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
1136 // Now, look for all the factors that are sums and multiply each one out
1137 // with the next one that is found while collecting the factors which are
1139 ex last_expanded = _ex1;
1142 non_adds.reserve(expanded_seq.size());
1144 for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
1145 if (is_exactly_a<add>(cit->rest) &&
1146 (cit->coeff.is_equal(_ex1))) {
1147 if (is_exactly_a<add>(last_expanded)) {
1149 // Expand a product of two sums, aggressive version.
1150 // Caring for the overall coefficients in separate loops can
1151 // sometimes give a performance gain of up to 15%!
1153 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
1154 // add2 is for the inner loop and should be the bigger of the two sums
1155 // in the presence of asymptotically good sorting:
1156 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
1157 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
1158 const epvector::const_iterator add1begin = add1.seq.begin();
1159 const epvector::const_iterator add1end = add1.seq.end();
1160 const epvector::const_iterator add2begin = add2.seq.begin();
1161 const epvector::const_iterator add2end = add2.seq.end();
1163 distrseq.reserve(add1.seq.size()+add2.seq.size());
1165 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
1166 if (!add1.overall_coeff.is_zero()) {
1167 if (add1.overall_coeff.is_equal(_ex1))
1168 distrseq.insert(distrseq.end(),add2begin,add2end);
1170 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
1171 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
1174 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
1175 if (!add2.overall_coeff.is_zero()) {
1176 if (add2.overall_coeff.is_equal(_ex1))
1177 distrseq.insert(distrseq.end(),add1begin,add1end);
1179 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
1180 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
1183 // Compute the new overall coefficient and put it together:
1184 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
1186 exvector add1_dummy_indices, add2_dummy_indices, add_indices;
1189 if (!skip_idx_rename) {
1190 for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
1191 add_indices = get_all_dummy_indices_safely(i->rest);
1192 add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
1194 for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
1195 add_indices = get_all_dummy_indices_safely(i->rest);
1196 add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
1199 sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
1200 sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
1201 dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
1204 // Multiply explicitly all non-numeric terms of add1 and add2:
1205 for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
1206 // We really have to combine terms here in order to compactify
1207 // the result. Otherwise it would become waayy tooo bigg.
1208 numeric oc(*_num0_p);
1210 distrseq2.reserve(add1.seq.size());
1211 const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ?
1213 i2->rest.subs(ex_to<lst>(dummy_subs.op(0)),
1214 ex_to<lst>(dummy_subs.op(1)), subs_options::no_pattern));
1215 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
1216 // Don't push_back expairs which might have a rest that evaluates to a numeric,
1217 // since that would violate an invariant of expairseq:
1218 const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated);
1219 if (is_exactly_a<numeric>(rest)) {
1220 oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
1222 distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
1225 tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated);
1227 last_expanded = tmp_accu;
1229 if (!last_expanded.is_equal(_ex1))
1230 non_adds.push_back(split_ex_to_pair(last_expanded));
1231 last_expanded = cit->rest;
1235 non_adds.push_back(*cit);
1239 // Now the only remaining thing to do is to multiply the factors which
1240 // were not sums into the "last_expanded" sum
1241 if (is_exactly_a<add>(last_expanded)) {
1242 size_t n = last_expanded.nops();
1244 distrseq.reserve(n);
1246 if (! skip_idx_rename) {
1247 va = get_all_dummy_indices_safely(mul(non_adds));
1248 sort(va.begin(), va.end(), ex_is_less());
1251 for (size_t i=0; i<n; ++i) {
1252 epvector factors = non_adds;
1253 if (skip_idx_rename)
1254 factors.push_back(split_ex_to_pair(last_expanded.op(i)));
1256 factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
1257 ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
1258 if (can_be_further_expanded(term)) {
1259 distrseq.push_back(term.expand());
1262 ex_to<basic>(term).setflag(status_flags::expanded);
1263 distrseq.push_back(term);
1267 return ((new add(distrseq))->
1268 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
1271 non_adds.push_back(split_ex_to_pair(last_expanded));
1272 ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
1273 if (can_be_further_expanded(result)) {
1274 return result.expand();
1277 ex_to<basic>(result).setflag(status_flags::expanded);
1284 // new virtual functions which can be overridden by derived classes
1290 // non-virtual functions in this class
1294 /** Member-wise expand the expairs representing this sequence. This must be
1295 * overridden from expairseq::expandchildren() and done iteratively in order
1296 * to allow for early cancallations and thus safe memory.
1298 * @see mul::expand()
1299 * @return pointer to epvector containing expanded representation or zero
1300 * pointer, if sequence is unchanged. */
1301 std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
1303 const epvector::const_iterator last = seq.end();
1304 epvector::const_iterator cit = seq.begin();
1306 const ex & factor = recombine_pair_to_ex(*cit);
1307 const ex & expanded_factor = factor.expand(options);
1308 if (!are_ex_trivially_equal(factor,expanded_factor)) {
1310 // something changed, copy seq, eval and return it
1311 std::auto_ptr<epvector> s(new epvector);
1312 s->reserve(seq.size());
1314 // copy parts of seq which are known not to have changed
1315 epvector::const_iterator cit2 = seq.begin();
1317 s->push_back(*cit2);
1321 // copy first changed element
1322 s->push_back(split_ex_to_pair(expanded_factor));
1326 while (cit2!=last) {
1327 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
1335 return std::auto_ptr<epvector>(0); // nothing has changed
1338 GINAC_BIND_UNARCHIVER(mul);
1340 } // namespace GiNaC