3 * Implementation of GiNaC's products of expressions. */
6 * GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
33 #ifndef NO_NAMESPACE_GINAC
35 #endif // ndef NO_NAMESPACE_GINAC
37 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
40 // default constructor, destructor, copy constructor assignment operator and helpers
47 debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
48 tinfo_key = TINFO_mul;
53 debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
57 mul::mul(const mul & other)
59 debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
63 const mul & mul::operator=(const mul & other)
65 debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
75 void mul::copy(const mul & other)
77 inherited::copy(other);
80 void mul::destroy(bool call_parent)
82 if (call_parent) inherited::destroy(call_parent);
91 mul::mul(const ex & lh, const ex & rh)
93 debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
94 tinfo_key = TINFO_mul;
95 overall_coeff = _ex1();
96 construct_from_2_ex(lh,rh);
97 GINAC_ASSERT(is_canonical());
100 mul::mul(const exvector & v)
102 debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
103 tinfo_key = TINFO_mul;
104 overall_coeff = _ex1();
105 construct_from_exvector(v);
106 GINAC_ASSERT(is_canonical());
109 mul::mul(const epvector & v)
111 debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
112 tinfo_key = TINFO_mul;
113 overall_coeff = _ex1();
114 construct_from_epvector(v);
115 GINAC_ASSERT(is_canonical());
118 mul::mul(const epvector & v, const ex & oc)
120 debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
121 tinfo_key = TINFO_mul;
123 construct_from_epvector(v);
124 GINAC_ASSERT(is_canonical());
127 mul::mul(epvector * vp, const ex & oc)
129 debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
130 tinfo_key = TINFO_mul;
133 construct_from_epvector(*vp);
135 GINAC_ASSERT(is_canonical());
138 mul::mul(const ex & lh, const ex & mh, const ex & rh)
140 debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
141 tinfo_key = TINFO_mul;
144 factors.push_back(lh);
145 factors.push_back(mh);
146 factors.push_back(rh);
147 overall_coeff = _ex1();
148 construct_from_exvector(factors);
149 GINAC_ASSERT(is_canonical());
156 /** Construct object from archive_node. */
157 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
159 debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
162 /** Unarchive the object. */
163 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
165 return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
168 /** Archive the object. */
169 void mul::archive(archive_node &n) const
171 inherited::archive(n);
175 // functions overriding virtual functions from bases classes
180 basic * mul::duplicate() const
182 debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
183 return new mul(*this);
186 void mul::print(std::ostream & os, unsigned upper_precedence) const
188 debugmsg("mul print",LOGLEVEL_PRINT);
189 if (precedence<=upper_precedence) os << "(";
191 // first print the overall numeric coefficient:
192 numeric coeff = ex_to_numeric(overall_coeff);
193 if (coeff.csgn()==-1) os << '-';
194 if (!coeff.is_equal(_num1()) &&
195 !coeff.is_equal(_num_1())) {
196 if (coeff.is_rational()) {
197 if (coeff.is_negative())
202 if (coeff.csgn()==-1)
203 (-coeff).print(os, precedence);
205 coeff.print(os, precedence);
209 // then proceed with the remaining factors:
210 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
216 recombine_pair_to_ex(*cit).print(os,precedence);
218 if (precedence<=upper_precedence) os << ")";
221 void mul::printraw(std::ostream & os) const
223 debugmsg("mul printraw",LOGLEVEL_PRINT);
226 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
228 (*it).rest.bp->printraw(os);
230 (*it).coeff.bp->printraw(os);
233 os << ",hash=" << hashvalue << ",flags=" << flags;
237 void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
239 debugmsg("mul print csrc", LOGLEVEL_PRINT);
240 if (precedence <= upper_precedence)
243 if (!overall_coeff.is_equal(_ex1())) {
244 overall_coeff.bp->printcsrc(os,type,precedence);
248 // Print arguments, separated by "*" or "/"
249 epvector::const_iterator it = seq.begin();
250 epvector::const_iterator itend = seq.end();
251 while (it != itend) {
253 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
254 if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
255 if (type == csrc_types::ctype_cl_N)
261 // If the exponent is 1 or -1, it is left out
262 if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
263 it->rest.bp->printcsrc(os, type, precedence);
265 // outer parens around ex needed for broken gcc-2.95 parser:
266 (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
268 // Separator is "/" for negative integer powers, "*" otherwise
271 if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
277 if (precedence <= upper_precedence)
281 bool mul::info(unsigned inf) const
284 case info_flags::polynomial:
285 case info_flags::integer_polynomial:
286 case info_flags::cinteger_polynomial:
287 case info_flags::rational_polynomial:
288 case info_flags::crational_polynomial:
289 case info_flags::rational_function: {
290 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
291 if (!(recombine_pair_to_ex(*i).info(inf)))
294 return overall_coeff.info(inf);
296 case info_flags::algebraic: {
297 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
298 if ((recombine_pair_to_ex(*i).info(inf)))
304 return inherited::info(inf);
307 typedef std::vector<int> intvector;
309 int mul::degree(const symbol & s) const
312 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
313 if (ex_to_numeric(cit->coeff).is_integer())
314 deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
319 int mul::ldegree(const symbol & s) const
322 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
323 if (ex_to_numeric(cit->coeff).is_integer())
324 deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
329 ex mul::coeff(const symbol & s, int n) const
332 coeffseq.reserve(seq.size()+1);
335 // product of individual coeffs
336 // if a non-zero power of s is found, the resulting product will be 0
337 epvector::const_iterator it=seq.begin();
338 while (it!=seq.end()) {
339 coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
342 coeffseq.push_back(overall_coeff);
343 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
346 epvector::const_iterator it=seq.begin();
348 while (it!=seq.end()) {
349 ex t=recombine_pair_to_ex(*it);
352 coeffseq.push_back(c);
355 coeffseq.push_back(t);
360 coeffseq.push_back(overall_coeff);
361 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
367 ex mul::eval(int level) const
369 // simplifications *(...,x;0) -> 0
370 // *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
374 debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
376 epvector * evaled_seqp=evalchildren(level);
377 if (evaled_seqp!=0) {
378 // do more evaluation later
379 return (new mul(evaled_seqp,overall_coeff))->
380 setflag(status_flags::dynallocated);
383 #ifdef DO_GINAC_ASSERT
384 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
385 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
386 (!(ex_to_numeric((*cit).coeff).is_integer())));
387 GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
388 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
391 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
393 expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
394 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
395 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
398 #endif // def DO_GINAC_ASSERT
400 if (flags & status_flags::evaluated) {
401 GINAC_ASSERT(seq.size()>0);
402 GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
406 int seq_size=seq.size();
407 if (overall_coeff.is_equal(_ex0())) {
410 } else if (seq_size==0) {
412 return overall_coeff;
413 } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
415 return recombine_pair_to_ex(*(seq.begin()));
416 } else if ((seq_size==1) &&
417 is_ex_exactly_of_type((*seq.begin()).rest,add) &&
418 ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
419 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
420 const add & addref=ex_to_add((*seq.begin()).rest);
422 distrseq.reserve(addref.seq.size());
423 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
424 distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
426 return (new add(distrseq,
427 ex_to_numeric(addref.overall_coeff).
428 mul_dyn(ex_to_numeric(overall_coeff))))
429 ->setflag(status_flags::dynallocated | status_flags::evaluated);
434 ex mul::evalf(int level) const
437 return mul(seq,overall_coeff);
439 if (level==-max_recursion_level)
440 throw(std::runtime_error("max recursion level reached"));
443 s.reserve(seq.size());
446 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
447 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
450 return mul(s,overall_coeff.evalf(level));
453 exvector mul::get_indices(void) const
455 // return union of indices of factors
457 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
458 exvector subiv=(*cit).rest.get_indices();
459 iv.reserve(iv.size()+subiv.size());
460 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
467 ex mul::simplify_ncmul(const exvector & v) const
469 throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
474 /** Implementation of ex::diff() for a product. It applies the product rule.
476 ex mul::derivative(const symbol & s) const
479 addseq.reserve(seq.size());
481 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
482 for (unsigned i=0; i!=seq.size(); ++i) {
483 epvector mulseq = seq;
484 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
485 seq[i].rest.diff(s));
486 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
488 return (new add(addseq))->setflag(status_flags::dynallocated);
491 int mul::compare_same_type(const basic & other) const
493 return inherited::compare_same_type(other);
496 bool mul::is_equal_same_type(const basic & other) const
498 return inherited::is_equal_same_type(other);
501 unsigned mul::return_type(void) const
504 // mul without factors: should not happen, but commutes
505 return return_types::commutative;
508 bool all_commutative = 1;
510 epvector::const_iterator cit_noncommutative_element; // point to first found nc element
512 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
513 rt=(*cit).rest.return_type();
514 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
515 if ((rt==return_types::noncommutative)&&(all_commutative)) {
516 // first nc element found, remember position
517 cit_noncommutative_element = cit;
520 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
521 // another nc element found, compare type_infos
522 if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
523 // diffent types -> mul is ncc
524 return return_types::noncommutative_composite;
528 // all factors checked
529 return all_commutative ? return_types::commutative : return_types::noncommutative;
532 unsigned mul::return_type_tinfo(void) const
535 // mul without factors: should not happen
538 // return type_info of first noncommutative element
539 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
540 if ((*cit).rest.return_type()==return_types::noncommutative) {
541 return (*cit).rest.return_type_tinfo();
544 // no noncommutative element found, should not happen
548 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
550 return (new mul(v,oc))->setflag(status_flags::dynallocated);
553 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
555 return (new mul(vp,oc))->setflag(status_flags::dynallocated);
558 expair mul::split_ex_to_pair(const ex & e) const
560 if (is_ex_exactly_of_type(e,power)) {
561 const power & powerref=ex_to_power(e);
562 if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
563 return expair(powerref.basis,powerref.exponent);
566 return expair(e,_ex1());
569 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
572 // to avoid duplication of power simplification rules,
573 // we create a temporary power object
574 // otherwise it would be hard to correctly simplify
575 // expression like (4^(1/3))^(3/2)
576 if (are_ex_trivially_equal(c,_ex1()))
577 return split_ex_to_pair(e);
579 return split_ex_to_pair(power(e,c));
582 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
585 // to avoid duplication of power simplification rules,
586 // we create a temporary power object
587 // otherwise it would be hard to correctly simplify
588 // expression like (4^(1/3))^(3/2)
589 if (are_ex_trivially_equal(c,_ex1()))
592 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
595 ex mul::recombine_pair_to_ex(const expair & p) const
597 if (ex_to_numeric(p.coeff).is_equal(_num1()))
600 return power(p.rest,p.coeff);
603 bool mul::expair_needs_further_processing(epp it)
605 if (is_ex_exactly_of_type((*it).rest,mul) &&
606 ex_to_numeric((*it).coeff).is_integer()) {
607 // combined pair is product with integer power -> expand it
608 *it=split_ex_to_pair(recombine_pair_to_ex(*it));
611 if (is_ex_exactly_of_type((*it).rest,numeric)) {
612 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
613 if (!ep.is_equal(*it)) {
614 // combined pair is a numeric power which can be simplified
618 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
619 // combined pair has coeff 1 and must be moved to the end
626 ex mul::default_overall_coeff(void) const
631 void mul::combine_overall_coeff(const ex & c)
633 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
634 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
635 overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
638 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
640 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
641 GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
642 GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
643 overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
646 bool mul::can_make_flat(const expair & p) const
648 GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
649 // this assertion will probably fail somewhere
650 // it would require a more careful make_flat, obeying the power laws
651 // probably should return true only if p.coeff is integer
652 return ex_to_numeric(p.coeff).is_equal(_num1());
655 ex mul::expand(unsigned options) const
657 if (flags & status_flags::expanded)
660 exvector sub_expanded_seq;
661 intvector positions_of_adds;
663 epvector * expanded_seqp = expandchildren(options);
665 const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
667 int number_of_adds = 0;
669 non_adds.reserve(expanded_seq.size());
670 epvector::const_iterator cit = expanded_seq.begin();
671 epvector::const_iterator last = expanded_seq.end();
672 ex last_expanded=_ex1();
674 if (is_ex_exactly_of_type((*cit).rest,add) &&
675 ((*cit).coeff.is_equal(_ex1()))) {
677 if (is_ex_exactly_of_type(last_expanded,add)) {
679 const add & add1 = ex_to_add(last_expanded);
680 const add & add2 = ex_to_add((*cit).rest);
681 int n1 = add1.nops();
682 int n2 = add2.nops();
684 distrseq.reserve(n1*n2);
685 for (int i1=0; i1<n1; ++i1) {
686 for (int i2=0; i2<n2; ++i2) {
687 distrseq.push_back(add1.op(i1)*add2.op(i2));
690 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
692 non_adds.push_back(split_ex_to_pair(last_expanded));
693 last_expanded = (*cit).rest;
696 non_adds.push_back(*cit);
701 if (is_ex_exactly_of_type(last_expanded,add)) {
702 add const & finaladd = ex_to_add(last_expanded);
704 int n = finaladd.nops();
706 for (int i=0; i<n; ++i) {
707 epvector factors = non_adds;
708 factors.push_back(split_ex_to_pair(finaladd.op(i)));
709 distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
711 return ((new add(distrseq))->
712 setflag(status_flags::dynallocated | status_flags::expanded));
714 non_adds.push_back(split_ex_to_pair(last_expanded));
715 return (new mul(non_adds,overall_coeff))->
716 setflag(status_flags::dynallocated | status_flags::expanded);
721 // new virtual functions which can be overridden by derived classes
727 // non-virtual functions in this class
730 epvector * mul::expandchildren(unsigned options) const
732 epvector::const_iterator last = seq.end();
733 epvector::const_iterator cit = seq.begin();
735 const ex & factor = recombine_pair_to_ex(*cit);
736 const ex & expanded_factor = factor.expand(options);
737 if (!are_ex_trivially_equal(factor,expanded_factor)) {
739 // something changed, copy seq, eval and return it
740 epvector *s=new epvector;
741 s->reserve(seq.size());
743 // copy parts of seq which are known not to have changed
744 epvector::const_iterator cit2 = seq.begin();
749 // copy first changed element
750 s->push_back(split_ex_to_pair(expanded_factor));
754 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
762 return 0; // nothing has changed
766 // static member variables
771 unsigned mul::precedence = 50;
779 const std::type_info & typeid_mul = typeid(some_mul);
781 #ifndef NO_NAMESPACE_GINAC
783 #endif // ndef NO_NAMESPACE_GINAC