3 * Implementation of GiNaC's products of expressions. */
6 * GiNaC Copyright (C) 1999-2007 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"
41 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
42 print_func<print_context>(&mul::do_print).
43 print_func<print_latex>(&mul::do_print_latex).
44 print_func<print_csrc>(&mul::do_print_csrc).
45 print_func<print_tree>(&mul::do_print_tree).
46 print_func<print_python_repr>(&mul::do_print_python_repr))
50 // default constructor
55 tinfo_key = &mul::tinfo_static;
64 mul::mul(const ex & lh, const ex & rh)
66 tinfo_key = &mul::tinfo_static;
68 construct_from_2_ex(lh,rh);
69 GINAC_ASSERT(is_canonical());
72 mul::mul(const exvector & v)
74 tinfo_key = &mul::tinfo_static;
76 construct_from_exvector(v);
77 GINAC_ASSERT(is_canonical());
80 mul::mul(const epvector & v)
82 tinfo_key = &mul::tinfo_static;
84 construct_from_epvector(v);
85 GINAC_ASSERT(is_canonical());
88 mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
90 tinfo_key = &mul::tinfo_static;
92 construct_from_epvector(v, do_index_renaming);
93 GINAC_ASSERT(is_canonical());
96 mul::mul(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
98 tinfo_key = &mul::tinfo_static;
99 GINAC_ASSERT(vp.get()!=0);
101 construct_from_epvector(*vp, do_index_renaming);
102 GINAC_ASSERT(is_canonical());
105 mul::mul(const ex & lh, const ex & mh, const ex & rh)
107 tinfo_key = &mul::tinfo_static;
110 factors.push_back(lh);
111 factors.push_back(mh);
112 factors.push_back(rh);
113 overall_coeff = _ex1;
114 construct_from_exvector(factors);
115 GINAC_ASSERT(is_canonical());
122 DEFAULT_ARCHIVING(mul)
125 // functions overriding virtual functions from base classes
128 void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
130 const numeric &coeff = ex_to<numeric>(overall_coeff);
131 if (coeff.csgn() == -1)
133 if (!coeff.is_equal(*_num1_p) &&
134 !coeff.is_equal(*_num_1_p)) {
135 if (coeff.is_rational()) {
136 if (coeff.is_negative())
141 if (coeff.csgn() == -1)
142 (-coeff).print(c, precedence());
144 coeff.print(c, precedence());
150 void mul::do_print(const print_context & c, unsigned level) const
152 if (precedence() <= level)
155 print_overall_coeff(c, "*");
157 epvector::const_iterator it = seq.begin(), itend = seq.end();
159 while (it != itend) {
164 recombine_pair_to_ex(*it).print(c, precedence());
168 if (precedence() <= level)
172 void mul::do_print_latex(const print_latex & c, unsigned level) const
174 if (precedence() <= level)
177 print_overall_coeff(c, " ");
179 // Separate factors into those with negative numeric exponent
181 epvector::const_iterator it = seq.begin(), itend = seq.end();
182 exvector neg_powers, others;
183 while (it != itend) {
184 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
185 if (ex_to<numeric>(it->coeff).is_negative())
186 neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
188 others.push_back(recombine_pair_to_ex(*it));
192 if (!neg_powers.empty()) {
194 // Factors with negative exponent are printed as a fraction
196 mul(others).eval().print(c);
198 mul(neg_powers).eval().print(c);
203 // All other factors are printed in the ordinary way
204 exvector::const_iterator vit = others.begin(), vitend = others.end();
205 while (vit != vitend) {
207 vit->print(c, precedence());
212 if (precedence() <= level)
216 void mul::do_print_csrc(const print_csrc & c, unsigned level) const
218 if (precedence() <= level)
221 if (!overall_coeff.is_equal(_ex1)) {
222 if (overall_coeff.is_equal(_ex_1))
225 overall_coeff.print(c, precedence());
230 // Print arguments, separated by "*" or "/"
231 epvector::const_iterator it = seq.begin(), itend = seq.end();
232 while (it != itend) {
234 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
235 bool needclosingparenthesis = false;
236 if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
237 if (is_a<print_csrc_cl_N>(c)) {
239 needclosingparenthesis = true;
244 // If the exponent is 1 or -1, it is left out
245 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
246 it->rest.print(c, precedence());
247 else if (it->coeff.info(info_flags::negint))
248 // Outer parens around ex needed for broken GCC parser:
249 (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
251 // Outer parens around ex needed for broken GCC parser:
252 (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
254 if (needclosingparenthesis)
257 // Separator is "/" for negative integer powers, "*" otherwise
260 if (it->coeff.info(info_flags::negint))
267 if (precedence() <= level)
271 void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
273 c.s << class_name() << '(';
275 for (size_t i=1; i<nops(); ++i) {
282 bool mul::info(unsigned inf) const
285 case info_flags::polynomial:
286 case info_flags::integer_polynomial:
287 case info_flags::cinteger_polynomial:
288 case info_flags::rational_polynomial:
289 case info_flags::crational_polynomial:
290 case info_flags::rational_function: {
291 epvector::const_iterator i = seq.begin(), end = seq.end();
293 if (!(recombine_pair_to_ex(*i).info(inf)))
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)))
309 return inherited::info(inf);
312 int mul::degree(const ex & s) const
314 // Sum up degrees of factors
316 epvector::const_iterator i = seq.begin(), end = seq.end();
318 if (ex_to<numeric>(i->coeff).is_integer())
319 deg_sum += recombine_pair_to_ex(*i).degree(s);
322 throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
329 int mul::ldegree(const ex & s) const
331 // Sum up degrees of factors
333 epvector::const_iterator i = seq.begin(), end = seq.end();
335 if (ex_to<numeric>(i->coeff).is_integer())
336 deg_sum += recombine_pair_to_ex(*i).ldegree(s);
339 throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
346 ex mul::coeff(const ex & s, int n) const
349 coeffseq.reserve(seq.size()+1);
352 // product of individual coeffs
353 // if a non-zero power of s is found, the resulting product will be 0
354 epvector::const_iterator i = seq.begin(), end = seq.end();
356 coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
359 coeffseq.push_back(overall_coeff);
360 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
363 epvector::const_iterator i = seq.begin(), end = seq.end();
364 bool coeff_found = false;
366 ex t = recombine_pair_to_ex(*i);
367 ex c = t.coeff(s, n);
369 coeffseq.push_back(c);
372 coeffseq.push_back(t);
377 coeffseq.push_back(overall_coeff);
378 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
384 /** Perform automatic term rewriting rules in this class. In the following
385 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
386 * stand for such expressions that contain a plain number.
388 * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
392 * @param level cut-off in recursive evaluation */
393 ex mul::eval(int level) const
395 std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
396 if (evaled_seqp.get()) {
397 // do more evaluation later
398 return (new mul(evaled_seqp, overall_coeff))->
399 setflag(status_flags::dynallocated);
402 #ifdef DO_GINAC_ASSERT
403 epvector::const_iterator i = seq.begin(), end = seq.end();
405 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
406 (!(ex_to<numeric>(i->coeff).is_integer())));
407 GINAC_ASSERT(!(i->is_canonical_numeric()));
408 if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
409 print(print_tree(std::cerr));
410 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
412 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
413 GINAC_ASSERT(p.rest.is_equal(i->rest));
414 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
418 #endif // def DO_GINAC_ASSERT
420 if (flags & status_flags::evaluated) {
421 GINAC_ASSERT(seq.size()>0);
422 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
426 size_t seq_size = seq.size();
427 if (overall_coeff.is_zero()) {
430 } else if (seq_size==0) {
432 return overall_coeff;
433 } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
435 return recombine_pair_to_ex(*(seq.begin()));
436 } else if ((seq_size==1) &&
437 is_exactly_a<add>((*seq.begin()).rest) &&
438 ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
439 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
440 const add & addref = ex_to<add>((*seq.begin()).rest);
441 std::auto_ptr<epvector> distrseq(new epvector);
442 distrseq->reserve(addref.seq.size());
443 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
445 distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
448 return (new add(distrseq,
449 ex_to<numeric>(addref.overall_coeff).
450 mul_dyn(ex_to<numeric>(overall_coeff)))
451 )->setflag(status_flags::dynallocated | status_flags::evaluated);
452 } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
453 // Strip the content and the unit part from each term. Thus
454 // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)2
456 epvector::const_iterator last = seq.end();
457 epvector::const_iterator i = seq.begin();
458 epvector::const_iterator j = seq.begin();
459 std::auto_ptr<epvector> s(new epvector);
460 numeric oc = *_num1_p;
461 bool something_changed = false;
463 if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
464 // power::eval has such a rule, no need to handle powers here
469 // XXX: What is the best way to check if the polynomial is a primitive?
470 numeric c = i->rest.integer_content();
471 const numeric& lead_coeff =
472 ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div_dyn(c);
473 const bool canonicalizable = lead_coeff.is_integer();
475 // XXX: The main variable is chosen in a random way, so this code
476 // does NOT transform the term into the canonical form (thus, in some
477 // very unlucky event it can even loop forever). Hopefully the main
478 // variable will be the same for all terms in *this
479 const bool unit_normal = lead_coeff.is_pos_integer();
480 if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
485 if (! something_changed) {
486 s->reserve(seq_size);
487 something_changed = true;
490 while ((j!=i) && (j!=last)) {
496 c = c.mul(*_num_1_p);
500 // divide add by the number in place to save at least 2 .eval() calls
501 const add& addref = ex_to<add>(i->rest);
502 add* primitive = new add(addref);
503 primitive->setflag(status_flags::dynallocated);
504 primitive->clearflag(status_flags::hash_calculated);
505 primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
506 for (epvector::iterator ai = primitive->seq.begin();
507 ai != primitive->seq.end(); ++ai)
508 ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
510 s->push_back(expair(*primitive, _ex1));
515 if (something_changed) {
520 return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
521 )->setflag(status_flags::dynallocated);
528 ex mul::evalf(int level) const
531 return mul(seq,overall_coeff);
533 if (level==-max_recursion_level)
534 throw(std::runtime_error("max recursion level reached"));
536 std::auto_ptr<epvector> s(new epvector);
537 s->reserve(seq.size());
540 epvector::const_iterator i = seq.begin(), end = seq.end();
542 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
546 return mul(s, overall_coeff.evalf(level));
549 void mul::find_real_imag(ex & rp, ex & ip) const
551 rp = overall_coeff.real_part();
552 ip = overall_coeff.imag_part();
553 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
554 ex factor = recombine_pair_to_ex(*i);
555 ex new_rp = factor.real_part();
556 ex new_ip = factor.imag_part();
557 if(new_ip.is_zero()) {
561 ex temp = rp*new_rp - ip*new_ip;
562 ip = ip*new_rp + rp*new_ip;
570 ex mul::real_part() const
573 find_real_imag(rp, ip);
577 ex mul::imag_part() const
580 find_real_imag(rp, ip);
584 ex mul::evalm() const
587 if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
588 && is_a<matrix>(seq[0].rest))
589 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
591 // Evaluate children first, look whether there are any matrices at all
592 // (there can be either no matrices or one matrix; if there were more
593 // than one matrix, it would be a non-commutative product)
594 std::auto_ptr<epvector> s(new epvector);
595 s->reserve(seq.size());
597 bool have_matrix = false;
598 epvector::iterator the_matrix;
600 epvector::const_iterator i = seq.begin(), end = seq.end();
602 const ex &m = recombine_pair_to_ex(*i).evalm();
603 s->push_back(split_ex_to_pair(m));
604 if (is_a<matrix>(m)) {
606 the_matrix = s->end() - 1;
613 // The product contained a matrix. We will multiply all other factors
615 matrix m = ex_to<matrix>(the_matrix->rest);
616 s->erase(the_matrix);
617 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
618 return m.mul_scalar(scalar);
621 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
624 ex mul::eval_ncmul(const exvector & v) const
627 return inherited::eval_ncmul(v);
629 // Find first noncommutative element and call its eval_ncmul()
630 epvector::const_iterator i = seq.begin(), end = seq.end();
632 if (i->rest.return_type() == return_types::noncommutative)
633 return i->rest.eval_ncmul(v);
636 return inherited::eval_ncmul(v);
639 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls)
645 if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
646 origbase = origfactor.op(0);
647 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
648 origexponent = expon > 0 ? expon : -expon;
649 origexpsign = expon > 0 ? 1 : -1;
651 origbase = origfactor;
660 if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
661 patternbase = patternfactor.op(0);
662 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
663 patternexponent = expon > 0 ? expon : -expon;
664 patternexpsign = expon > 0 ? 1 : -1;
666 patternbase = patternfactor;
671 lst saverepls = repls;
672 if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
676 int newnummatches = origexponent / patternexponent;
677 if (newnummatches < nummatches)
678 nummatches = newnummatches;
682 /** Checks wheter e matches to the pattern pat and the (possibly to be updated)
683 * list of replacements repls. This matching is in the sense of algebraic
684 * substitutions. Matching starts with pat.op(factor) of the pattern because
685 * the factors before this one have already been matched. The (possibly
686 * updated) number of matches is in nummatches. subsed[i] is true for factors
687 * that already have been replaced by previous substitutions and matched[i]
688 * is true for factors that have been matched by the current match.
690 bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, lst &repls,
691 int factor, int &nummatches, const std::vector<bool> &subsed,
692 std::vector<bool> &matched)
694 if (factor == pat.nops())
697 for (size_t i=0; i<e.nops(); ++i) {
698 if(subsed[i] || matched[i])
700 lst newrepls = repls;
701 int newnummatches = nummatches;
702 if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
704 if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
705 newnummatches, subsed, matched)) {
707 nummatches = newnummatches;
718 bool mul::has(const ex & pattern, unsigned options) const
720 if(!(options&has_options::algebraic))
721 return basic::has(pattern,options);
722 if(is_a<mul>(pattern)) {
724 int nummatches = std::numeric_limits<int>::max();
725 std::vector<bool> subsed(seq.size(), false);
726 std::vector<bool> matched(seq.size(), false);
727 if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
731 return basic::has(pattern, options);
734 ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
736 std::vector<bool> subsed(seq.size(), false);
737 exvector subsresult(seq.size());
741 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
743 if (is_exactly_a<mul>(it->first)) {
745 int nummatches = std::numeric_limits<int>::max();
746 std::vector<bool> currsubsed(seq.size(), false);
749 if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
752 for (size_t j=0; j<subsed.size(); j++)
756 = it->first.subs(ex(repls), subs_options::no_pattern);
757 divide_by *= power(subsed_pattern, nummatches);
759 = it->second.subs(ex(repls), subs_options::no_pattern);
760 multiply_by *= power(subsed_result, nummatches);
765 for (size_t j=0; j<this->nops(); j++) {
766 int nummatches = std::numeric_limits<int>::max();
768 if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
771 = it->first.subs(ex(repls), subs_options::no_pattern);
772 divide_by *= power(subsed_pattern, nummatches);
774 = it->second.subs(ex(repls), subs_options::no_pattern);
775 multiply_by *= power(subsed_result, nummatches);
781 bool subsfound = false;
782 for (size_t i=0; i<subsed.size(); i++) {
789 return subs_one_level(m, options | subs_options::algebraic);
791 return ((*this)/divide_by)*multiply_by;
796 /** Implementation of ex::diff() for a product. It applies the product rule.
798 ex mul::derivative(const symbol & s) const
800 size_t num = seq.size();
804 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
805 epvector mulseq = seq;
806 epvector::const_iterator i = seq.begin(), end = seq.end();
807 epvector::iterator i2 = mulseq.begin();
809 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
812 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
816 return (new add(addseq))->setflag(status_flags::dynallocated);
819 int mul::compare_same_type(const basic & other) const
821 return inherited::compare_same_type(other);
824 unsigned mul::return_type() const
827 // mul without factors: should not happen, but commutates
828 return return_types::commutative;
831 bool all_commutative = true;
832 epvector::const_iterator noncommutative_element; // point to first found nc element
834 epvector::const_iterator i = seq.begin(), end = seq.end();
836 unsigned rt = i->rest.return_type();
837 if (rt == return_types::noncommutative_composite)
838 return rt; // one ncc -> mul also ncc
839 if ((rt == return_types::noncommutative) && (all_commutative)) {
840 // first nc element found, remember position
841 noncommutative_element = i;
842 all_commutative = false;
844 if ((rt == return_types::noncommutative) && (!all_commutative)) {
845 // another nc element found, compare type_infos
846 if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
847 // different types -> mul is ncc
848 return return_types::noncommutative_composite;
853 // all factors checked
854 return all_commutative ? return_types::commutative : return_types::noncommutative;
857 tinfo_t mul::return_type_tinfo() const
860 return this; // mul without factors: should not happen
862 // return type_info of first noncommutative element
863 epvector::const_iterator i = seq.begin(), end = seq.end();
865 if (i->rest.return_type() == return_types::noncommutative)
866 return i->rest.return_type_tinfo();
869 // no noncommutative element found, should not happen
873 ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
875 return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
878 ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
880 return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated);
883 expair mul::split_ex_to_pair(const ex & e) const
885 if (is_exactly_a<power>(e)) {
886 const power & powerref = ex_to<power>(e);
887 if (is_exactly_a<numeric>(powerref.exponent))
888 return expair(powerref.basis,powerref.exponent);
890 return expair(e,_ex1);
893 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
896 // to avoid duplication of power simplification rules,
897 // we create a temporary power object
898 // otherwise it would be hard to correctly evaluate
899 // expression like (4^(1/3))^(3/2)
900 if (c.is_equal(_ex1))
901 return split_ex_to_pair(e);
903 return split_ex_to_pair(power(e,c));
906 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
909 // to avoid duplication of power simplification rules,
910 // we create a temporary power object
911 // otherwise it would be hard to correctly evaluate
912 // expression like (4^(1/3))^(3/2)
913 if (c.is_equal(_ex1))
916 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
919 ex mul::recombine_pair_to_ex(const expair & p) const
921 if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
924 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
927 bool mul::expair_needs_further_processing(epp it)
929 if (is_exactly_a<mul>(it->rest) &&
930 ex_to<numeric>(it->coeff).is_integer()) {
931 // combined pair is product with integer power -> expand it
932 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
935 if (is_exactly_a<numeric>(it->rest)) {
936 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
937 if (!ep.is_equal(*it)) {
938 // combined pair is a numeric power which can be simplified
942 if (it->coeff.is_equal(_ex1)) {
943 // combined pair has coeff 1 and must be moved to the end
950 ex mul::default_overall_coeff() const
955 void mul::combine_overall_coeff(const ex & c)
957 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
958 GINAC_ASSERT(is_exactly_a<numeric>(c));
959 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
962 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
964 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
965 GINAC_ASSERT(is_exactly_a<numeric>(c1));
966 GINAC_ASSERT(is_exactly_a<numeric>(c2));
967 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
970 bool mul::can_make_flat(const expair & p) const
972 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
973 // this assertion will probably fail somewhere
974 // it would require a more careful make_flat, obeying the power laws
975 // probably should return true only if p.coeff is integer
976 return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
979 bool mul::can_be_further_expanded(const ex & e)
981 if (is_exactly_a<mul>(e)) {
982 for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
983 if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
986 } else if (is_exactly_a<power>(e)) {
987 if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
993 ex mul::expand(unsigned options) const
995 // First, expand the children
996 std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
997 const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
999 // Now, look for all the factors that are sums and multiply each one out
1000 // with the next one that is found while collecting the factors which are
1002 ex last_expanded = _ex1;
1005 non_adds.reserve(expanded_seq.size());
1007 for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
1008 if (is_exactly_a<add>(cit->rest) &&
1009 (cit->coeff.is_equal(_ex1))) {
1010 if (is_exactly_a<add>(last_expanded)) {
1012 // Expand a product of two sums, aggressive version.
1013 // Caring for the overall coefficients in separate loops can
1014 // sometimes give a performance gain of up to 15%!
1016 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
1017 // add2 is for the inner loop and should be the bigger of the two sums
1018 // in the presence of asymptotically good sorting:
1019 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
1020 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
1021 const epvector::const_iterator add1begin = add1.seq.begin();
1022 const epvector::const_iterator add1end = add1.seq.end();
1023 const epvector::const_iterator add2begin = add2.seq.begin();
1024 const epvector::const_iterator add2end = add2.seq.end();
1026 distrseq.reserve(add1.seq.size()+add2.seq.size());
1028 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
1029 if (!add1.overall_coeff.is_zero()) {
1030 if (add1.overall_coeff.is_equal(_ex1))
1031 distrseq.insert(distrseq.end(),add2begin,add2end);
1033 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
1034 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
1037 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
1038 if (!add2.overall_coeff.is_zero()) {
1039 if (add2.overall_coeff.is_equal(_ex1))
1040 distrseq.insert(distrseq.end(),add1begin,add1end);
1042 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
1043 distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
1046 // Compute the new overall coefficient and put it together:
1047 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
1049 exvector add1_dummy_indices, add2_dummy_indices, add_indices;
1051 for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
1052 add_indices = get_all_dummy_indices_safely(i->rest);
1053 add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
1055 for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
1056 add_indices = get_all_dummy_indices_safely(i->rest);
1057 add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
1060 sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
1061 sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
1062 lst dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
1064 // Multiply explicitly all non-numeric terms of add1 and add2:
1065 for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
1066 // We really have to combine terms here in order to compactify
1067 // the result. Otherwise it would become waayy tooo bigg.
1070 ex i2_new = (dummy_subs.op(0).nops()>0?
1071 i2->rest.subs((lst)dummy_subs.op(0), (lst)dummy_subs.op(1), subs_options::no_pattern) : i2->rest);
1072 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
1073 // Don't push_back expairs which might have a rest that evaluates to a numeric,
1074 // since that would violate an invariant of expairseq:
1075 const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated);
1076 if (is_exactly_a<numeric>(rest)) {
1077 oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
1079 distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
1082 tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
1084 last_expanded = tmp_accu;
1087 if (!last_expanded.is_equal(_ex1))
1088 non_adds.push_back(split_ex_to_pair(last_expanded));
1089 last_expanded = cit->rest;
1093 non_adds.push_back(*cit);
1097 // Now the only remaining thing to do is to multiply the factors which
1098 // were not sums into the "last_expanded" sum
1099 if (is_exactly_a<add>(last_expanded)) {
1100 size_t n = last_expanded.nops();
1102 distrseq.reserve(n);
1103 exvector va = get_all_dummy_indices_safely(mul(non_adds));
1104 sort(va.begin(), va.end(), ex_is_less());
1106 for (size_t i=0; i<n; ++i) {
1107 epvector factors = non_adds;
1108 factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
1109 ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
1110 if (can_be_further_expanded(term)) {
1111 distrseq.push_back(term.expand());
1114 ex_to<basic>(term).setflag(status_flags::expanded);
1115 distrseq.push_back(term);
1119 return ((new add(distrseq))->
1120 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
1123 non_adds.push_back(split_ex_to_pair(last_expanded));
1124 ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
1125 if (can_be_further_expanded(result)) {
1126 return result.expand();
1129 ex_to<basic>(result).setflag(status_flags::expanded);
1136 // new virtual functions which can be overridden by derived classes
1142 // non-virtual functions in this class
1146 /** Member-wise expand the expairs representing this sequence. This must be
1147 * overridden from expairseq::expandchildren() and done iteratively in order
1148 * to allow for early cancallations and thus safe memory.
1150 * @see mul::expand()
1151 * @return pointer to epvector containing expanded representation or zero
1152 * pointer, if sequence is unchanged. */
1153 std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
1155 const epvector::const_iterator last = seq.end();
1156 epvector::const_iterator cit = seq.begin();
1158 const ex & factor = recombine_pair_to_ex(*cit);
1159 const ex & expanded_factor = factor.expand(options);
1160 if (!are_ex_trivially_equal(factor,expanded_factor)) {
1162 // something changed, copy seq, eval and return it
1163 std::auto_ptr<epvector> s(new epvector);
1164 s->reserve(seq.size());
1166 // copy parts of seq which are known not to have changed
1167 epvector::const_iterator cit2 = seq.begin();
1169 s->push_back(*cit2);
1173 // copy first changed element
1174 s->push_back(split_ex_to_pair(expanded_factor));
1178 while (cit2!=last) {
1179 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
1187 return std::auto_ptr<epvector>(0); // nothing has changed
1190 } // namespace GiNaC