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 void mul::copy(const mul & other)
55 inherited::copy(other);
58 void mul::destroy(bool call_parent)
60 if (call_parent) inherited::destroy(call_parent);
69 mul::mul(const ex & lh, const ex & rh)
71 debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
72 tinfo_key = TINFO_mul;
73 overall_coeff = _ex1();
74 construct_from_2_ex(lh,rh);
75 GINAC_ASSERT(is_canonical());
78 mul::mul(const exvector & v)
80 debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
81 tinfo_key = TINFO_mul;
82 overall_coeff = _ex1();
83 construct_from_exvector(v);
84 GINAC_ASSERT(is_canonical());
87 mul::mul(const epvector & v)
89 debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
90 tinfo_key = TINFO_mul;
91 overall_coeff = _ex1();
92 construct_from_epvector(v);
93 GINAC_ASSERT(is_canonical());
96 mul::mul(const epvector & v, const ex & oc)
98 debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
99 tinfo_key = TINFO_mul;
101 construct_from_epvector(v);
102 GINAC_ASSERT(is_canonical());
105 mul::mul(epvector * vp, const ex & oc)
107 debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
108 tinfo_key = TINFO_mul;
111 construct_from_epvector(*vp);
113 GINAC_ASSERT(is_canonical());
116 mul::mul(const ex & lh, const ex & mh, const ex & rh)
118 debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
119 tinfo_key = TINFO_mul;
122 factors.push_back(lh);
123 factors.push_back(mh);
124 factors.push_back(rh);
125 overall_coeff = _ex1();
126 construct_from_exvector(factors);
127 GINAC_ASSERT(is_canonical());
134 /** Construct object from archive_node. */
135 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
137 debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
140 /** Unarchive the object. */
141 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
143 return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
146 /** Archive the object. */
147 void mul::archive(archive_node &n) const
149 inherited::archive(n);
153 // functions overriding virtual functions from bases classes
158 void mul::print(std::ostream & os, unsigned upper_precedence) const
160 debugmsg("mul print",LOGLEVEL_PRINT);
161 if (precedence<=upper_precedence) os << "(";
163 // first print the overall numeric coefficient:
164 numeric coeff = ex_to_numeric(overall_coeff);
165 if (coeff.csgn()==-1) os << '-';
166 if (!coeff.is_equal(_num1()) &&
167 !coeff.is_equal(_num_1())) {
168 if (coeff.is_rational()) {
169 if (coeff.is_negative())
174 if (coeff.csgn()==-1)
175 (-coeff).print(os, precedence);
177 coeff.print(os, precedence);
181 // then proceed with the remaining factors:
182 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
188 recombine_pair_to_ex(*cit).print(os,precedence);
190 if (precedence<=upper_precedence) os << ")";
193 void mul::printraw(std::ostream & os) const
195 debugmsg("mul printraw",LOGLEVEL_PRINT);
198 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
200 (*it).rest.bp->printraw(os);
202 (*it).coeff.bp->printraw(os);
205 os << ",hash=" << hashvalue << ",flags=" << flags;
209 void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
211 debugmsg("mul print csrc", LOGLEVEL_PRINT);
212 if (precedence <= upper_precedence)
215 if (!overall_coeff.is_equal(_ex1())) {
216 overall_coeff.bp->printcsrc(os,type,precedence);
220 // Print arguments, separated by "*" or "/"
221 epvector::const_iterator it = seq.begin();
222 epvector::const_iterator itend = seq.end();
223 while (it != itend) {
225 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
226 if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
227 if (type == csrc_types::ctype_cl_N)
233 // If the exponent is 1 or -1, it is left out
234 if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
235 it->rest.bp->printcsrc(os, type, precedence);
237 // outer parens around ex needed for broken gcc-2.95 parser:
238 (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
240 // Separator is "/" for negative integer powers, "*" otherwise
243 if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
249 if (precedence <= upper_precedence)
253 bool mul::info(unsigned inf) const
256 case info_flags::polynomial:
257 case info_flags::integer_polynomial:
258 case info_flags::cinteger_polynomial:
259 case info_flags::rational_polynomial:
260 case info_flags::crational_polynomial:
261 case info_flags::rational_function: {
262 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
263 if (!(recombine_pair_to_ex(*i).info(inf)))
266 return overall_coeff.info(inf);
268 case info_flags::algebraic: {
269 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
270 if ((recombine_pair_to_ex(*i).info(inf)))
276 return inherited::info(inf);
279 typedef std::vector<int> intvector;
281 int mul::degree(const symbol & s) const
284 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
285 if (ex_to_numeric(cit->coeff).is_integer())
286 deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
291 int mul::ldegree(const symbol & s) const
294 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
295 if (ex_to_numeric(cit->coeff).is_integer())
296 deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
301 ex mul::coeff(const symbol & s, int n) const
304 coeffseq.reserve(seq.size()+1);
307 // product of individual coeffs
308 // if a non-zero power of s is found, the resulting product will be 0
309 epvector::const_iterator it=seq.begin();
310 while (it!=seq.end()) {
311 coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
314 coeffseq.push_back(overall_coeff);
315 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
318 epvector::const_iterator it=seq.begin();
320 while (it!=seq.end()) {
321 ex t=recombine_pair_to_ex(*it);
324 coeffseq.push_back(c);
327 coeffseq.push_back(t);
332 coeffseq.push_back(overall_coeff);
333 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
339 ex mul::eval(int level) const
341 // simplifications *(...,x;0) -> 0
342 // *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
346 debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
348 epvector * evaled_seqp=evalchildren(level);
349 if (evaled_seqp!=0) {
350 // do more evaluation later
351 return (new mul(evaled_seqp,overall_coeff))->
352 setflag(status_flags::dynallocated);
355 #ifdef DO_GINAC_ASSERT
356 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
357 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
358 (!(ex_to_numeric((*cit).coeff).is_integer())));
359 GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
360 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
363 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
365 expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
366 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
367 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
370 #endif // def DO_GINAC_ASSERT
372 if (flags & status_flags::evaluated) {
373 GINAC_ASSERT(seq.size()>0);
374 GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
378 int seq_size=seq.size();
379 if (overall_coeff.is_equal(_ex0())) {
382 } else if (seq_size==0) {
384 return overall_coeff;
385 } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
387 return recombine_pair_to_ex(*(seq.begin()));
388 } else if ((seq_size==1) &&
389 is_ex_exactly_of_type((*seq.begin()).rest,add) &&
390 ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
391 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
392 const add & addref=ex_to_add((*seq.begin()).rest);
394 distrseq.reserve(addref.seq.size());
395 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
396 distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
398 return (new add(distrseq,
399 ex_to_numeric(addref.overall_coeff).
400 mul_dyn(ex_to_numeric(overall_coeff))))
401 ->setflag(status_flags::dynallocated | status_flags::evaluated);
406 ex mul::evalf(int level) const
409 return mul(seq,overall_coeff);
411 if (level==-max_recursion_level)
412 throw(std::runtime_error("max recursion level reached"));
415 s.reserve(seq.size());
418 for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
419 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
422 return mul(s,overall_coeff.evalf(level));
425 exvector mul::get_indices(void) const
427 // return union of indices of factors
429 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
430 exvector subiv=(*cit).rest.get_indices();
431 iv.reserve(iv.size()+subiv.size());
432 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
439 ex mul::simplify_ncmul(const exvector & v) const
441 throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
446 /** Implementation of ex::diff() for a product. It applies the product rule.
448 ex mul::derivative(const symbol & s) const
451 addseq.reserve(seq.size());
453 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
454 for (unsigned i=0; i!=seq.size(); ++i) {
455 epvector mulseq = seq;
456 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
457 seq[i].rest.diff(s));
458 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
460 return (new add(addseq))->setflag(status_flags::dynallocated);
463 int mul::compare_same_type(const basic & other) const
465 return inherited::compare_same_type(other);
468 bool mul::is_equal_same_type(const basic & other) const
470 return inherited::is_equal_same_type(other);
473 unsigned mul::return_type(void) const
476 // mul without factors: should not happen, but commutes
477 return return_types::commutative;
480 bool all_commutative = 1;
482 epvector::const_iterator cit_noncommutative_element; // point to first found nc element
484 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
485 rt=(*cit).rest.return_type();
486 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
487 if ((rt==return_types::noncommutative)&&(all_commutative)) {
488 // first nc element found, remember position
489 cit_noncommutative_element = cit;
492 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
493 // another nc element found, compare type_infos
494 if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
495 // diffent types -> mul is ncc
496 return return_types::noncommutative_composite;
500 // all factors checked
501 return all_commutative ? return_types::commutative : return_types::noncommutative;
504 unsigned mul::return_type_tinfo(void) const
507 // mul without factors: should not happen
510 // return type_info of first noncommutative element
511 for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
512 if ((*cit).rest.return_type()==return_types::noncommutative) {
513 return (*cit).rest.return_type_tinfo();
516 // no noncommutative element found, should not happen
520 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
522 return (new mul(v,oc))->setflag(status_flags::dynallocated);
525 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
527 return (new mul(vp,oc))->setflag(status_flags::dynallocated);
530 expair mul::split_ex_to_pair(const ex & e) const
532 if (is_ex_exactly_of_type(e,power)) {
533 const power & powerref=ex_to_power(e);
534 if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
535 return expair(powerref.basis,powerref.exponent);
538 return expair(e,_ex1());
541 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
544 // to avoid duplication of power simplification rules,
545 // we create a temporary power object
546 // otherwise it would be hard to correctly simplify
547 // expression like (4^(1/3))^(3/2)
548 if (are_ex_trivially_equal(c,_ex1()))
549 return split_ex_to_pair(e);
551 return split_ex_to_pair(power(e,c));
554 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
557 // to avoid duplication of power simplification rules,
558 // we create a temporary power object
559 // otherwise it would be hard to correctly simplify
560 // expression like (4^(1/3))^(3/2)
561 if (are_ex_trivially_equal(c,_ex1()))
564 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
567 ex mul::recombine_pair_to_ex(const expair & p) const
569 if (ex_to_numeric(p.coeff).is_equal(_num1()))
572 return power(p.rest,p.coeff);
575 bool mul::expair_needs_further_processing(epp it)
577 if (is_ex_exactly_of_type((*it).rest,mul) &&
578 ex_to_numeric((*it).coeff).is_integer()) {
579 // combined pair is product with integer power -> expand it
580 *it=split_ex_to_pair(recombine_pair_to_ex(*it));
583 if (is_ex_exactly_of_type((*it).rest,numeric)) {
584 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
585 if (!ep.is_equal(*it)) {
586 // combined pair is a numeric power which can be simplified
590 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
591 // combined pair has coeff 1 and must be moved to the end
598 ex mul::default_overall_coeff(void) const
603 void mul::combine_overall_coeff(const ex & c)
605 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
606 GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
607 overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
610 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
612 GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
613 GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
614 GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
615 overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
618 bool mul::can_make_flat(const expair & p) const
620 GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
621 // this assertion will probably fail somewhere
622 // it would require a more careful make_flat, obeying the power laws
623 // probably should return true only if p.coeff is integer
624 return ex_to_numeric(p.coeff).is_equal(_num1());
627 ex mul::expand(unsigned options) const
629 if (flags & status_flags::expanded)
632 exvector sub_expanded_seq;
633 intvector positions_of_adds;
635 epvector * expanded_seqp = expandchildren(options);
637 const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
639 int number_of_adds = 0;
641 non_adds.reserve(expanded_seq.size());
642 epvector::const_iterator cit = expanded_seq.begin();
643 epvector::const_iterator last = expanded_seq.end();
644 ex last_expanded=_ex1();
646 if (is_ex_exactly_of_type((*cit).rest,add) &&
647 ((*cit).coeff.is_equal(_ex1()))) {
649 if (is_ex_exactly_of_type(last_expanded,add)) {
651 const add & add1 = ex_to_add(last_expanded);
652 const add & add2 = ex_to_add((*cit).rest);
653 int n1 = add1.nops();
654 int n2 = add2.nops();
656 distrseq.reserve(n1*n2);
657 for (int i1=0; i1<n1; ++i1) {
658 for (int i2=0; i2<n2; ++i2) {
659 distrseq.push_back(add1.op(i1)*add2.op(i2));
662 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
664 non_adds.push_back(split_ex_to_pair(last_expanded));
665 last_expanded = (*cit).rest;
668 non_adds.push_back(*cit);
673 if (is_ex_exactly_of_type(last_expanded,add)) {
674 add const & finaladd = ex_to_add(last_expanded);
676 int n = finaladd.nops();
678 for (int i=0; i<n; ++i) {
679 epvector factors = non_adds;
680 factors.push_back(split_ex_to_pair(finaladd.op(i)));
681 distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
683 return ((new add(distrseq))->
684 setflag(status_flags::dynallocated | status_flags::expanded));
686 non_adds.push_back(split_ex_to_pair(last_expanded));
687 return (new mul(non_adds,overall_coeff))->
688 setflag(status_flags::dynallocated | status_flags::expanded);
693 // new virtual functions which can be overridden by derived classes
699 // non-virtual functions in this class
702 epvector * mul::expandchildren(unsigned options) const
704 epvector::const_iterator last = seq.end();
705 epvector::const_iterator cit = seq.begin();
707 const ex & factor = recombine_pair_to_ex(*cit);
708 const ex & expanded_factor = factor.expand(options);
709 if (!are_ex_trivially_equal(factor,expanded_factor)) {
711 // something changed, copy seq, eval and return it
712 epvector *s=new epvector;
713 s->reserve(seq.size());
715 // copy parts of seq which are known not to have changed
716 epvector::const_iterator cit2 = seq.begin();
721 // copy first changed element
722 s->push_back(split_ex_to_pair(expanded_factor));
726 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
734 return 0; // nothing has changed
738 // static member variables
743 unsigned mul::precedence = 50;
745 #ifndef NO_NAMESPACE_GINAC
747 #endif // ndef NO_NAMESPACE_GINAC