- introduced info_flag::algebraic.
[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     switch (inf) {
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)))
292                     return false;
293             }
294             return overall_coeff.info(inf);
295         }
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)))
299                     return true;
300             }
301             return false;
302         }
303     }
304     return inherited::info(inf);
305 }
306
307 typedef vector<int> intvector;
308
309 int mul::degree(const symbol & s) const
310 {
311     int deg_sum = 0;
312     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
313         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
314     }
315     return deg_sum;
316 }
317
318 int mul::ldegree(const symbol & s) const
319 {
320     int deg_sum = 0;
321     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
322         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
323     }
324     return deg_sum;
325 }
326
327 ex mul::coeff(const symbol & s, int n) const
328 {
329     exvector coeffseq;
330     coeffseq.reserve(seq.size()+1);
331     
332     if (n==0) {
333         // product of individual coeffs
334         // if a non-zero power of s is found, the resulting product will be 0
335         epvector::const_iterator it=seq.begin();
336         while (it!=seq.end()) {
337             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
338             ++it;
339         }
340         coeffseq.push_back(overall_coeff);
341         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
342     }
343          
344     epvector::const_iterator it=seq.begin();
345     bool coeff_found=0;
346     while (it!=seq.end()) {
347         ex t=recombine_pair_to_ex(*it);
348         ex c=t.coeff(s,n);
349         if (!c.is_zero()) {
350             coeffseq.push_back(c);
351             coeff_found=1;
352         } else {
353             coeffseq.push_back(t);
354         }
355         ++it;
356     }
357     if (coeff_found) {
358         coeffseq.push_back(overall_coeff);
359         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
360     }
361     
362     return _ex0();
363 }
364
365 ex mul::eval(int level) const
366 {
367     // simplifications  *(...,x;0) -> 0
368     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
369     //                  *(x;1) -> x
370     //                  *(;c) -> c
371
372     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
373
374     epvector * evaled_seqp=evalchildren(level);
375     if (evaled_seqp!=0) {
376         // do more evaluation later
377         return (new mul(evaled_seqp,overall_coeff))->
378                    setflag(status_flags::dynallocated);
379     }
380
381 #ifdef DO_GINAC_ASSERT
382     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
383         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
384                (!(ex_to_numeric((*cit).coeff).is_integer())));
385         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
386         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
387             printtree(cerr,0);
388         }
389         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
390         /* for paranoia */
391         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
392         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
393         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
394         /* end paranoia */
395     }
396 #endif // def DO_GINAC_ASSERT
397
398     if (flags & status_flags::evaluated) {
399         GINAC_ASSERT(seq.size()>0);
400         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
401         return *this;
402     }
403
404     int seq_size=seq.size();
405     if (overall_coeff.is_equal(_ex0())) {
406         // *(...,x;0) -> 0
407         return _ex0();
408     } else if (seq_size==0) {
409         // *(;c) -> c
410         return overall_coeff;
411     } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
412         // *(x;1) -> x
413         return recombine_pair_to_ex(*(seq.begin()));
414     } else if ((seq_size==1) &&
415                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
416                ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
417         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
418         const add & addref=ex_to_add((*seq.begin()).rest);
419         epvector distrseq;
420         distrseq.reserve(addref.seq.size());
421         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
422             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
423                                    overall_coeff));
424         }
425         return (new add(distrseq,
426                         ex_to_numeric(addref.overall_coeff).
427                         mul_dyn(ex_to_numeric(overall_coeff))))
428             ->setflag(status_flags::dynallocated |
429                       status_flags::evaluated);
430     }
431     return this->hold();
432 }
433
434 ex mul::evalf(int level) const
435 {
436     if (level==1)
437         return mul(seq,overall_coeff);
438     
439     if (level==-max_recursion_level)
440         throw(std::runtime_error("max recursion level reached"));
441     
442     epvector s;
443     s.reserve(seq.size());
444     
445     --level;
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),
448                                                   (*it).coeff));
449     }
450     return mul(s,overall_coeff.evalf(level));
451 }
452
453 exvector mul::get_indices(void) const
454 {
455     // return union of indices of factors
456     exvector iv;
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) {
461             iv.push_back(*cit2);
462         }
463     }
464     return iv;
465 }
466
467 ex mul::simplify_ncmul(const exvector & v) const
468 {
469     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
470 }
471
472 // protected
473
474 /** Implementation of ex::diff() for a product. It applies the product rule.
475  *  @see ex::diff */
476 ex mul::derivative(const symbol & s) const
477 {
478     exvector new_seq;
479     new_seq.reserve(seq.size());
480
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 sub_seq = seq;
484         sub_seq[i] = split_ex_to_pair(sub_seq[i].coeff*
485                                       power(sub_seq[i].rest,sub_seq[i].coeff-1)*
486                                       sub_seq[i].rest.diff(s));
487         new_seq.push_back((new mul(sub_seq,overall_coeff))->setflag(status_flags::dynallocated));
488     }
489     return (new add(new_seq))->setflag(status_flags::dynallocated);
490 }
491
492 int mul::compare_same_type(const basic & other) const
493 {
494     return inherited::compare_same_type(other);
495 }
496
497 bool mul::is_equal_same_type(const basic & other) const
498 {
499     return inherited::is_equal_same_type(other);
500 }
501
502 unsigned mul::return_type(void) const
503 {
504     if (seq.size()==0) {
505         // mul without factors: should not happen, but commutes
506         return return_types::commutative;
507     }
508
509     bool all_commutative = 1;
510     unsigned rt;
511     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
512
513     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
514         rt=(*cit).rest.return_type();
515         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
516         if ((rt==return_types::noncommutative)&&(all_commutative)) {
517             // first nc element found, remember position
518             cit_noncommutative_element = cit;
519             all_commutative = 0;
520         }
521         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
522             // another nc element found, compare type_infos
523             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
524                 // diffent types -> mul is ncc
525                 return return_types::noncommutative_composite;
526             }
527         }
528     }
529     // all factors checked
530     return all_commutative ? return_types::commutative : return_types::noncommutative;
531 }
532    
533 unsigned mul::return_type_tinfo(void) const
534 {
535     if (seq.size()==0) {
536         // mul without factors: should not happen
537         return tinfo_key;
538     }
539     // return type_info of first noncommutative element
540     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
541         if ((*cit).rest.return_type()==return_types::noncommutative) {
542             return (*cit).rest.return_type_tinfo();
543         }
544     }
545     // no noncommutative element found, should not happen
546     return tinfo_key;
547 }
548
549 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
550 {
551     return (new mul(v,oc))->setflag(status_flags::dynallocated);
552 }
553
554 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
555 {
556     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
557 }
558
559 expair mul::split_ex_to_pair(const ex & e) const
560 {
561     if (is_ex_exactly_of_type(e,power)) {
562         const power & powerref=ex_to_power(e);
563         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
564             return expair(powerref.basis,powerref.exponent);
565         }
566     }
567     return expair(e,_ex1());
568 }
569     
570 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
571                                           const ex & c) const
572 {
573     // to avoid duplication of power simplification rules,
574     // we create a temporary power object
575     // otherwise it would be hard to correctly simplify
576     // expression like (4^(1/3))^(3/2)
577     if (are_ex_trivially_equal(c,_ex1())) {
578         return split_ex_to_pair(e);
579     }
580     return split_ex_to_pair(power(e,c));
581 }
582     
583 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
584                                             const ex & c) const
585 {
586     // to avoid duplication of power simplification rules,
587     // we create a temporary power object
588     // otherwise it would be hard to correctly simplify
589     // expression like (4^(1/3))^(3/2)
590     if (are_ex_trivially_equal(c,_ex1())) {
591         return p;
592     }
593     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
594 }
595     
596 ex mul::recombine_pair_to_ex(const expair & p) const
597 {
598     // if (p.coeff.compare(_ex1())==0) {
599     // if (are_ex_trivially_equal(p.coeff,_ex1())) {
600     if (ex_to_numeric(p.coeff).is_equal(_num1())) {
601         return p.rest;
602     } else {
603         return power(p.rest,p.coeff);
604     }
605 }
606
607 bool mul::expair_needs_further_processing(epp it)
608 {
609     if (is_ex_exactly_of_type((*it).rest,mul) &&
610         ex_to_numeric((*it).coeff).is_integer()) {
611         // combined pair is product with integer power -> expand it
612         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
613         return true;
614     }
615     if (is_ex_exactly_of_type((*it).rest,numeric)) {
616         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
617         if (!ep.is_equal(*it)) {
618             // combined pair is a numeric power which can be simplified
619             *it=ep;
620             return true;
621         }
622         if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
623             // combined pair has coeff 1 and must be moved to the end
624             return true;
625         }
626     }
627     return false;
628 }       
629
630 ex mul::default_overall_coeff(void) const
631 {
632     return _ex1();
633 }
634
635 void mul::combine_overall_coeff(const ex & c)
636 {
637     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
638     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
639     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
640 }
641
642 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
643 {
644     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
645     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
646     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
647     overall_coeff = ex_to_numeric(overall_coeff).
648                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
649 }
650
651 bool mul::can_make_flat(const expair & p) const
652 {
653     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
654     // this assertion will probably fail somewhere
655     // it would require a more careful make_flat, obeying the power laws
656     // probably should return true only if p.coeff is integer
657     return ex_to_numeric(p.coeff).is_equal(_num1());
658 }
659
660 ex mul::expand(unsigned options) const
661 {
662     if (flags & status_flags::expanded)
663         return *this;
664     
665     exvector sub_expanded_seq;
666     intvector positions_of_adds;
667     intvector number_of_add_operands;
668     
669     epvector * expanded_seqp = expandchildren(options);
670     
671     const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
672     
673     positions_of_adds.resize(expanded_seq.size());
674     number_of_add_operands.resize(expanded_seq.size());
675     
676     int number_of_adds = 0;
677     int number_of_expanded_terms = 1;
678     
679     unsigned current_position = 0;
680     epvector::const_iterator last = expanded_seq.end();
681     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
682         if (is_ex_exactly_of_type((*cit).rest,add)&&
683             (ex_to_numeric((*cit).coeff).is_equal(_num1()))) {
684             positions_of_adds[number_of_adds] = current_position;
685             const add & expanded_addref = ex_to_add((*cit).rest);
686             unsigned addref_nops = expanded_addref.nops();
687             number_of_add_operands[number_of_adds] = addref_nops;
688             number_of_expanded_terms *= addref_nops;
689             number_of_adds++;
690         }
691         current_position++;
692     }
693     
694     if (number_of_adds==0) {
695         if (expanded_seqp==0) {
696             return this->setflag(status_flags::expanded);
697         }
698         return (new mul(expanded_seqp,overall_coeff))->
699             setflag(status_flags::dynallocated |
700                     status_flags::expanded);
701     }
702     
703     exvector distrseq;
704     distrseq.reserve(number_of_expanded_terms);
705     
706     intvector k;
707     k.resize(number_of_adds);
708     
709     int l;
710     for (l=0; l<number_of_adds; l++) {
711         k[l]=0;
712     }
713     
714     while (1) {
715         epvector term;
716         term = expanded_seq;
717         for (l=0; l<number_of_adds; l++) {
718             const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
719             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
720             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
721         }
722         distrseq.push_back((new mul(term,overall_coeff))->
723                            setflag(status_flags::dynallocated |
724                                    status_flags::expanded));
725         
726         // increment k[]
727         l=number_of_adds-1;
728         while ((l>=0) && ((++k[l])>=number_of_add_operands[l])) {
729             k[l]=0;    
730             l--;
731         }
732         if (l<0) break;
733     }
734     
735     if (expanded_seqp!=0)
736         delete expanded_seqp;
737     
738     return (new add(distrseq))->setflag(status_flags::dynallocated |
739                                         status_flags::expanded);
740 }
741
742 //////////
743 // new virtual functions which can be overridden by derived classes
744 //////////
745
746 // none
747
748 //////////
749 // non-virtual functions in this class
750 //////////
751
752 epvector * mul::expandchildren(unsigned options) const
753 {
754     epvector::const_iterator last = seq.end();
755     epvector::const_iterator cit = seq.begin();
756     while (cit!=last) {
757         const ex & factor = recombine_pair_to_ex(*cit);
758         const ex & expanded_factor = factor.expand(options);
759         if (!are_ex_trivially_equal(factor,expanded_factor)) {
760             
761             // something changed, copy seq, eval and return it
762             epvector *s=new epvector;
763             s->reserve(seq.size());
764             
765             // copy parts of seq which are known not to have changed
766             epvector::const_iterator cit2 = seq.begin();
767             while (cit2!=cit) {
768                 s->push_back(*cit2);
769                 ++cit2;
770             }
771             // copy first changed element
772             s->push_back(split_ex_to_pair(expanded_factor));
773             ++cit2;
774             // copy rest
775             while (cit2!=last) {
776                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
777                 ++cit2;
778             }
779             return s;
780         }
781         ++cit;
782     }
783     
784     return 0; // nothing has changed
785 }
786    
787 //////////
788 // static member variables
789 //////////
790
791 // protected
792
793 unsigned mul::precedence = 50;
794
795
796 //////////
797 // global constants
798 //////////
799
800 const mul some_mul;
801 const type_info & typeid_mul = typeid(some_mul);
802
803 #ifndef NO_NAMESPACE_GINAC
804 } // namespace GiNaC
805 #endif // ndef NO_NAMESPACE_GINAC