- bugfix: 2^(3/2) does not throw any more. This was now secured in...
[ginac.git] / ginac / mul.cpp
1 /** @file mul.cpp
2  *
3  *  Implementation of GiNaC's products of expressions. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
7  *
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.
12  *
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.
17  *
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
21  */
22
23 #include <vector>
24 #include <stdexcept>
25
26 #include "mul.h"
27 #include "add.h"
28 #include "power.h"
29 #include "archive.h"
30 #include "debugmsg.h"
31 #include "utils.h"
32
33 #ifndef NO_NAMESPACE_GINAC
34 namespace GiNaC {
35 #endif // ndef NO_NAMESPACE_GINAC
36
37 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
38
39 //////////
40 // default constructor, destructor, copy constructor assignment operator and helpers
41 //////////
42
43 // public
44
45 mul::mul()
46 {
47     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
48     tinfo_key = TINFO_mul;
49 }
50
51 mul::~mul()
52 {
53     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
54     destroy(0);
55 }
56
57 mul::mul(const mul & other)
58 {
59     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
60     copy(other);
61 }
62
63 const mul & mul::operator=(const mul & other)
64 {
65     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
66     if (this != &other) {
67         destroy(1);
68         copy(other);
69     }
70     return *this;
71 }
72
73 // protected
74
75 void mul::copy(const mul & other)
76 {
77     inherited::copy(other);
78 }
79
80 void mul::destroy(bool call_parent)
81 {
82     if (call_parent) inherited::destroy(call_parent);
83 }
84
85 //////////
86 // other constructors
87 //////////
88
89 // public
90
91 mul::mul(const ex & lh, const ex & rh)
92 {
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());
98 }
99
100 mul::mul(const exvector & v)
101 {
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());
107 }
108
109 mul::mul(const epvector & v)
110 {
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());
116 }
117
118 mul::mul(const epvector & v, const ex & oc)
119 {
120     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
121     tinfo_key = TINFO_mul;
122     overall_coeff = oc;
123     construct_from_epvector(v);
124     GINAC_ASSERT(is_canonical());
125 }
126
127 mul::mul(epvector * vp, const ex & oc)
128 {
129     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
130     tinfo_key = TINFO_mul;
131     GINAC_ASSERT(vp!=0);
132     overall_coeff = oc;
133     construct_from_epvector(*vp);
134     delete vp;
135     GINAC_ASSERT(is_canonical());
136 }
137
138 mul::mul(const ex & lh, const ex & mh, const ex & rh)
139 {
140     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
141     tinfo_key = TINFO_mul;
142     exvector factors;
143     factors.reserve(3);
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());
150 }
151
152 //////////
153 // archiving
154 //////////
155
156 /** Construct object from archive_node. */
157 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
158 {
159     debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
160 }
161
162 /** Unarchive the object. */
163 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
164 {
165     return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
166 }
167
168 /** Archive the object. */
169 void mul::archive(archive_node &n) const
170 {
171     inherited::archive(n);
172 }
173
174 //////////
175 // functions overriding virtual functions from bases classes
176 //////////
177
178 // public
179
180 basic * mul::duplicate() const
181 {
182     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
183     return new mul(*this);
184 }
185
186 void mul::print(ostream & os, unsigned upper_precedence) const
187 {
188     debugmsg("mul print",LOGLEVEL_PRINT);
189     if (precedence<=upper_precedence) os << "(";
190     bool first=true;
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())
198                 os << -coeff;
199             else
200                 os << coeff;
201         } else {
202             if (coeff.csgn()==-1)
203                 (-coeff).print(os, precedence);
204             else
205                 coeff.print(os, precedence);
206         }
207         os << '*';
208     }
209     // then proceed with the remaining factors:
210     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
211         if (!first) {
212             os << '*';
213         } else {
214             first=false;
215         }
216         recombine_pair_to_ex(*cit).print(os,precedence);
217     }
218     if (precedence<=upper_precedence) os << ")";
219 }
220
221 void mul::printraw(ostream & os) const
222 {
223     debugmsg("mul printraw",LOGLEVEL_PRINT);
224
225     os << "*(";
226     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
227         os << "(";
228         (*it).rest.bp->printraw(os);
229         os << ",";
230         (*it).coeff.bp->printraw(os);
231         os << "),";
232     }
233     os << ",hash=" << hashvalue << ",flags=" << flags;
234     os << ")";
235 }
236
237 void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
238 {
239     debugmsg("mul print csrc", LOGLEVEL_PRINT);
240     if (precedence <= upper_precedence)
241         os << "(";
242
243     if (!overall_coeff.is_equal(_ex1())) {
244         overall_coeff.bp->printcsrc(os,type,precedence);
245         os << "*";
246     }
247     
248     // Print arguments, separated by "*" or "/"
249     epvector::const_iterator it = seq.begin();
250     epvector::const_iterator itend = seq.end();
251     while (it != itend) {
252
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)
256                 os << "recip(";
257             else
258                 os << "1.0/";
259         }
260
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);
264         else
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);
267
268         // Separator is "/" for negative integer powers, "*" otherwise
269         it++;
270         if (it != itend) {
271             if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
272                 os << "/";
273             else
274                 os << "*";
275         }
276     }
277     if (precedence <= upper_precedence)
278         os << ")";
279 }
280
281 bool mul::info(unsigned inf) const
282 {
283     // TODO: optimize
284     if (inf==info_flags::polynomial ||
285         inf==info_flags::integer_polynomial ||
286         inf==info_flags::cinteger_polynomial ||
287         inf==info_flags::rational_polynomial ||
288         inf==info_flags::crational_polynomial ||
289         inf==info_flags::rational_function) {
290         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
291             if (!(recombine_pair_to_ex(*it).info(inf)))
292                 return false;
293         }
294         return overall_coeff.info(inf);
295     } else {
296         return inherited::info(inf);
297     }
298 }
299
300 typedef vector<int> intvector;
301
302 int mul::degree(const symbol & s) const
303 {
304     int deg_sum=0;
305     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
306         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
307     }
308     return deg_sum;
309 }
310
311 int mul::ldegree(const symbol & s) const
312 {
313     int deg_sum=0;
314     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
315         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
316     }
317     return deg_sum;
318 }
319
320 ex mul::coeff(const symbol & s, int n) const
321 {
322     exvector coeffseq;
323     coeffseq.reserve(seq.size()+1);
324     
325     if (n==0) {
326         // product of individual coeffs
327         // if a non-zero power of s is found, the resulting product will be 0
328         epvector::const_iterator it=seq.begin();
329         while (it!=seq.end()) {
330             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
331             ++it;
332         }
333         coeffseq.push_back(overall_coeff);
334         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
335     }
336          
337     epvector::const_iterator it=seq.begin();
338     bool coeff_found=0;
339     while (it!=seq.end()) {
340         ex t=recombine_pair_to_ex(*it);
341         ex c=t.coeff(s,n);
342         if (!c.is_zero()) {
343             coeffseq.push_back(c);
344             coeff_found=1;
345         } else {
346             coeffseq.push_back(t);
347         }
348         ++it;
349     }
350     if (coeff_found) {
351         coeffseq.push_back(overall_coeff);
352         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
353     }
354     
355     return _ex0();
356 }
357
358 ex mul::eval(int level) const
359 {
360     // simplifications  *(...,x;0) -> 0
361     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
362     //                  *(x;1) -> x
363     //                  *(;c) -> c
364
365     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
366
367     epvector * evaled_seqp=evalchildren(level);
368     if (evaled_seqp!=0) {
369         // do more evaluation later
370         return (new mul(evaled_seqp,overall_coeff))->
371                    setflag(status_flags::dynallocated);
372     }
373
374 #ifdef DO_GINAC_ASSERT
375     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
376         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
377                (!(ex_to_numeric((*cit).coeff).is_integer())));
378         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
379         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
380             printtree(cerr,0);
381         }
382         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
383         /* for paranoia */
384         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
385         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
386         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
387         /* end paranoia */
388     }
389 #endif // def DO_GINAC_ASSERT
390
391     if (flags & status_flags::evaluated) {
392         GINAC_ASSERT(seq.size()>0);
393         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
394         return *this;
395     }
396
397     int seq_size=seq.size();
398     if (overall_coeff.is_equal(_ex0())) {
399         // *(...,x;0) -> 0
400         return _ex0();
401     } else if (seq_size==0) {
402         // *(;c) -> c
403         return overall_coeff;
404     } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
405         // *(x;1) -> x
406         return recombine_pair_to_ex(*(seq.begin()));
407     } else if ((seq_size==1) &&
408                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
409                ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
410         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
411         const add & addref=ex_to_add((*seq.begin()).rest);
412         epvector distrseq;
413         distrseq.reserve(addref.seq.size());
414         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
415             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
416                                    overall_coeff));
417         }
418         return (new add(distrseq,
419                         ex_to_numeric(addref.overall_coeff).
420                         mul_dyn(ex_to_numeric(overall_coeff))))
421             ->setflag(status_flags::dynallocated  |
422                       status_flags::evaluated );
423     }
424     return this->hold();
425 }
426
427 exvector mul::get_indices(void) const
428 {
429     // return union of indices of factors
430     exvector iv;
431     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
432         exvector subiv=(*cit).rest.get_indices();
433         iv.reserve(iv.size()+subiv.size());
434         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
435             iv.push_back(*cit2);
436         }
437     }
438     return iv;
439 }
440
441 ex mul::simplify_ncmul(const exvector & v) const
442 {
443     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
444 }
445
446 // protected
447
448 /** Implementation of ex::diff() for a product. It applies the product rule.
449  *  @see ex::diff */
450 ex mul::derivative(const symbol & s) const
451 {
452     exvector new_seq;
453     new_seq.reserve(seq.size());
454
455     // D(a*b*c)=D(a)*b*c+a*D(b)*c+a*b*D(c)
456     for (unsigned i=0; i!=seq.size(); i++) {
457         epvector sub_seq=seq;
458         sub_seq[i] = split_ex_to_pair(sub_seq[i].coeff*
459                                       power(sub_seq[i].rest,sub_seq[i].coeff-1)*
460                                       sub_seq[i].rest.diff(s));
461         new_seq.push_back((new mul(sub_seq,overall_coeff))->setflag(status_flags::dynallocated));
462     }
463     return (new add(new_seq))->setflag(status_flags::dynallocated);
464 }
465
466 int mul::compare_same_type(const basic & other) const
467 {
468     return inherited::compare_same_type(other);
469 }
470
471 bool mul::is_equal_same_type(const basic & other) const
472 {
473     return inherited::is_equal_same_type(other);
474 }
475
476 unsigned mul::return_type(void) const
477 {
478     if (seq.size()==0) {
479         // mul without factors: should not happen, but commutes
480         return return_types::commutative;
481     }
482
483     bool all_commutative=1;
484     unsigned rt;
485     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
486
487     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
488         rt=(*cit).rest.return_type();
489         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
490         if ((rt==return_types::noncommutative)&&(all_commutative)) {
491             // first nc element found, remember position
492             cit_noncommutative_element=cit;
493             all_commutative=0;
494         }
495         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
496             // another nc element found, compare type_infos
497             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
498                 // diffent types -> mul is ncc
499                 return return_types::noncommutative_composite;
500             }
501         }
502     }
503     // all factors checked
504     return all_commutative ? return_types::commutative : return_types::noncommutative;
505 }
506    
507 unsigned mul::return_type_tinfo(void) const
508 {
509     if (seq.size()==0) {
510         // mul without factors: should not happen
511         return tinfo_key;
512     }
513     // return type_info of first noncommutative element
514     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
515         if ((*cit).rest.return_type()==return_types::noncommutative) {
516             return (*cit).rest.return_type_tinfo();
517         }
518     }
519     // no noncommutative element found, should not happen
520     return tinfo_key;
521 }
522
523 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
524 {
525     return (new mul(v,oc))->setflag(status_flags::dynallocated);
526 }
527
528 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
529 {
530     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
531 }
532
533 expair mul::split_ex_to_pair(const ex & e) const
534 {
535     if (is_ex_exactly_of_type(e,power)) {
536         const power & powerref=ex_to_power(e);
537         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
538             return expair(powerref.basis,powerref.exponent);
539         }
540     }
541     return expair(e,_ex1());
542 }
543     
544 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
545                                           const ex & c) const
546 {
547     // to avoid duplication of power simplification rules,
548     // we create a temporary power object
549     // otherwise it would be hard to correctly simplify
550     // expression like (4^(1/3))^(3/2)
551     if (are_ex_trivially_equal(c,_ex1())) {
552         return split_ex_to_pair(e);
553     }
554     return split_ex_to_pair(power(e,c));
555 }
556     
557 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
558                                             const ex & c) const
559 {
560     // to avoid duplication of power simplification rules,
561     // we create a temporary power object
562     // otherwise it would be hard to correctly simplify
563     // expression like (4^(1/3))^(3/2)
564     if (are_ex_trivially_equal(c,_ex1())) {
565         return p;
566     }
567     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
568 }
569     
570 ex mul::recombine_pair_to_ex(const expair & p) const
571 {
572     // if (p.coeff.compare(_ex1())==0) {
573     // if (are_ex_trivially_equal(p.coeff,_ex1())) {
574     if (ex_to_numeric(p.coeff).is_equal(_num1())) {
575         return p.rest;
576     } else {
577         return power(p.rest,p.coeff);
578     }
579 }
580
581 bool mul::expair_needs_further_processing(epp it)
582 {
583     if (is_ex_exactly_of_type((*it).rest,mul) &&
584         ex_to_numeric((*it).coeff).is_integer()) {
585         // combined pair is product with integer power -> expand it
586         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
587         return true;
588     }
589     if (is_ex_exactly_of_type((*it).rest,numeric)) {
590         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
591         if (!ep.is_equal(*it)) {
592             // combined pair is a numeric power which can be simplified
593             *it=ep;
594             return true;
595         }
596         if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
597             // combined pair has coeff 1 and must be moved to the end
598             return true;
599         }
600     }
601     return false;
602 }       
603
604 ex mul::default_overall_coeff(void) const
605 {
606     return _ex1();
607 }
608
609 void mul::combine_overall_coeff(const ex & c)
610 {
611     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
612     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
613     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
614 }
615
616 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
617 {
618     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
619     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
620     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
621     overall_coeff = ex_to_numeric(overall_coeff).
622                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
623 }
624
625 bool mul::can_make_flat(const expair & p) const
626 {
627     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
628     // this assertion will probably fail somewhere
629     // it would require a more careful make_flat, obeying the power laws
630     // probably should return true only if p.coeff is integer
631     return ex_to_numeric(p.coeff).is_equal(_num1());
632 }
633
634 ex mul::expand(unsigned options) const
635 {
636     exvector sub_expanded_seq;
637     intvector positions_of_adds;
638     intvector number_of_add_operands;
639
640     epvector * expanded_seqp=expandchildren(options);
641
642     const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
643
644     positions_of_adds.resize(expanded_seq.size());
645     number_of_add_operands.resize(expanded_seq.size());
646
647     int number_of_adds=0;
648     int number_of_expanded_terms=1;
649
650     unsigned current_position=0;
651     epvector::const_iterator last=expanded_seq.end();
652     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
653         if (is_ex_exactly_of_type((*cit).rest,add)&&
654             (ex_to_numeric((*cit).coeff).is_equal(_num1()))) {
655             positions_of_adds[number_of_adds]=current_position;
656             const add & expanded_addref=ex_to_add((*cit).rest);
657             unsigned addref_nops=expanded_addref.nops();
658             number_of_add_operands[number_of_adds]=addref_nops;
659             number_of_expanded_terms *= addref_nops;
660             number_of_adds++;
661         }
662         current_position++;
663     }
664
665     if (number_of_adds==0) {
666         if (expanded_seqp==0) {
667             return this->setflag(status_flags::expanded);
668         }
669         return (new mul(expanded_seqp,overall_coeff))->
670                      setflag(status_flags::dynallocated ||
671                              status_flags::expanded);
672     }
673
674     exvector distrseq;
675     distrseq.reserve(number_of_expanded_terms);
676
677     intvector k;
678     k.resize(number_of_adds);
679     
680     int l;
681     for (l=0; l<number_of_adds; l++) {
682         k[l]=0;
683     }
684
685     while (1) {
686         epvector term;
687         term=expanded_seq;
688         for (l=0; l<number_of_adds; l++) {
689             const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
690             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
691             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
692         }
693         /*
694         cout << "mul::expand() term begin" << endl;
695         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
696             cout << "rest" << endl;
697             (*cit).rest.printtree(cout);
698             cout << "coeff" << endl;
699             (*cit).coeff.printtree(cout);
700         }
701         cout << "mul::expand() term end" << endl;
702         */
703         distrseq.push_back((new mul(term,overall_coeff))->
704                                 setflag(status_flags::dynallocated |
705                                         status_flags::expanded));
706
707         // increment k[]
708         l=number_of_adds-1;
709         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
710             k[l]=0;    
711             l--;
712         }
713         if (l<0) break;
714     }
715
716     if (expanded_seqp!=0) {
717         delete expanded_seqp;
718     }
719     /*
720     cout << "mul::expand() distrseq begin" << endl;
721     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
722         (*cit).printtree(cout);
723     }
724     cout << "mul::expand() distrseq end" << endl;
725     */
726
727     return (new add(distrseq))->setflag(status_flags::dynallocated |
728                                         status_flags::expanded);
729 }
730
731 //////////
732 // new virtual functions which can be overridden by derived classes
733 //////////
734
735 // none
736
737 //////////
738 // non-virtual functions in this class
739 //////////
740
741 epvector * mul::expandchildren(unsigned options) const
742 {
743     epvector::const_iterator last=seq.end();
744     epvector::const_iterator cit=seq.begin();
745     while (cit!=last) {
746         const ex & factor=recombine_pair_to_ex(*cit);
747         const ex & expanded_factor=factor.expand(options);
748         if (!are_ex_trivially_equal(factor,expanded_factor)) {
749
750             // something changed, copy seq, eval and return it
751             epvector *s=new epvector;
752             s->reserve(seq.size());
753
754             // copy parts of seq which are known not to have changed
755             epvector::const_iterator cit2=seq.begin();
756             while (cit2!=cit) {
757                 s->push_back(*cit2);
758                 ++cit2;
759             }
760             // copy first changed element
761             s->push_back(split_ex_to_pair(expanded_factor));
762             ++cit2;
763             // copy rest
764             while (cit2!=last) {
765                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
766                 ++cit2;
767             }
768             return s;
769         }
770         ++cit;
771     }
772     
773     return 0; // nothing has changed
774 }
775    
776 //////////
777 // static member variables
778 //////////
779
780 // protected
781
782 unsigned mul::precedence=50;
783
784
785 //////////
786 // global constants
787 //////////
788
789 const mul some_mul;
790 const type_info & typeid_mul=typeid(some_mul);
791
792 #ifndef NO_NAMESPACE_GINAC
793 } // namespace GiNaC
794 #endif // ndef NO_NAMESPACE_GINAC