211855a6613d2cc9dfabe370ae6272e7b4460143
[ginac.git] / ginac / mul.cpp
1 /** @file mul.cpp
2  *
3  *  Implementation of GiNaC's products of expressions. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2002 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 <iostream>
24 #include <vector>
25 #include <stdexcept>
26
27 #include "mul.h"
28 #include "add.h"
29 #include "power.h"
30 #include "matrix.h"
31 #include "archive.h"
32 #include "utils.h"
33
34 namespace GiNaC {
35
36 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
37
38 //////////
39 // default ctor, dtor, copy ctor, assignment operator and helpers
40 //////////
41
42 mul::mul()
43 {
44         tinfo_key = TINFO_mul;
45 }
46
47 DEFAULT_COPY(mul)
48 DEFAULT_DESTROY(mul)
49
50 //////////
51 // other ctors
52 //////////
53
54 // public
55
56 mul::mul(const ex & lh, const ex & rh)
57 {
58         tinfo_key = TINFO_mul;
59         overall_coeff = _ex1;
60         construct_from_2_ex(lh,rh);
61         GINAC_ASSERT(is_canonical());
62 }
63
64 mul::mul(const exvector & v)
65 {
66         tinfo_key = TINFO_mul;
67         overall_coeff = _ex1;
68         construct_from_exvector(v);
69         GINAC_ASSERT(is_canonical());
70 }
71
72 mul::mul(const epvector & v)
73 {
74         tinfo_key = TINFO_mul;
75         overall_coeff = _ex1;
76         construct_from_epvector(v);
77         GINAC_ASSERT(is_canonical());
78 }
79
80 mul::mul(const epvector & v, const ex & oc)
81 {
82         tinfo_key = TINFO_mul;
83         overall_coeff = oc;
84         construct_from_epvector(v);
85         GINAC_ASSERT(is_canonical());
86 }
87
88 mul::mul(epvector * vp, const ex & oc)
89 {
90         tinfo_key = TINFO_mul;
91         GINAC_ASSERT(vp!=0);
92         overall_coeff = oc;
93         construct_from_epvector(*vp);
94         delete vp;
95         GINAC_ASSERT(is_canonical());
96 }
97
98 mul::mul(const ex & lh, const ex & mh, const ex & rh)
99 {
100         tinfo_key = TINFO_mul;
101         exvector factors;
102         factors.reserve(3);
103         factors.push_back(lh);
104         factors.push_back(mh);
105         factors.push_back(rh);
106         overall_coeff = _ex1;
107         construct_from_exvector(factors);
108         GINAC_ASSERT(is_canonical());
109 }
110
111 //////////
112 // archiving
113 //////////
114
115 DEFAULT_ARCHIVING(mul)
116
117 //////////
118 // functions overriding virtual functions from base classes
119 //////////
120
121 // public
122
123 void mul::print(const print_context & c, unsigned level) const
124 {
125         if (is_a<print_tree>(c)) {
126
127                 inherited::print(c, level);
128
129         } else if (is_a<print_csrc>(c)) {
130
131                 if (precedence() <= level)
132                         c.s << "(";
133
134                 if (!overall_coeff.is_equal(_ex1)) {
135                         overall_coeff.print(c, precedence());
136                         c.s << "*";
137                 }
138
139                 // Print arguments, separated by "*" or "/"
140                 epvector::const_iterator it = seq.begin(), itend = seq.end();
141                 while (it != itend) {
142
143                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
144                         bool needclosingparenthesis = false;
145                         if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
146                                 if (is_a<print_csrc_cl_N>(c)) {
147                                         c.s << "recip(";
148                                         needclosingparenthesis = true;
149                                 } else
150                                         c.s << "1.0/";
151                         }
152
153                         // If the exponent is 1 or -1, it is left out
154                         if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
155                                 it->rest.print(c, precedence());
156                         else if (it->coeff.info(info_flags::negint))
157                                 // Outer parens around ex needed for broken gcc-2.95 parser:
158                                 (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
159                         else
160                                 // Outer parens around ex needed for broken gcc-2.95 parser:
161                                 (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
162
163                         if (needclosingparenthesis)
164                                 c.s << ")";
165
166                         // Separator is "/" for negative integer powers, "*" otherwise
167                         ++it;
168                         if (it != itend) {
169                                 if (it->coeff.info(info_flags::negint))
170                                         c.s << "/";
171                                 else
172                                         c.s << "*";
173                         }
174                 }
175
176                 if (precedence() <= level)
177                         c.s << ")";
178
179         } else if (is_a<print_python_repr>(c)) {
180                 c.s << class_name() << '(';
181                 op(0).print(c);
182                 for (unsigned i=1; i<nops(); ++i) {
183                         c.s << ',';
184                         op(i).print(c);
185                 }
186                 c.s << ')';
187         } else {
188
189                 if (precedence() <= level) {
190                         if (is_a<print_latex>(c))
191                                 c.s << "{(";
192                         else
193                                 c.s << "(";
194                 }
195
196                 bool first = true;
197
198                 // First print the overall numeric coefficient
199                 numeric coeff = ex_to<numeric>(overall_coeff);
200                 if (coeff.csgn() == -1)
201                         c.s << '-';
202                 if (!coeff.is_equal(_num1) &&
203                         !coeff.is_equal(_num_1)) {
204                         if (coeff.is_rational()) {
205                                 if (coeff.is_negative())
206                                         (-coeff).print(c);
207                                 else
208                                         coeff.print(c);
209                         } else {
210                                 if (coeff.csgn() == -1)
211                                         (-coeff).print(c, precedence());
212                                 else
213                                         coeff.print(c, precedence());
214                         }
215                         if (is_a<print_latex>(c))
216                                 c.s << ' ';
217                         else
218                                 c.s << '*';
219                 }
220
221                 // Then proceed with the remaining factors
222                 epvector::const_iterator it = seq.begin(), itend = seq.end();
223                 while (it != itend) {
224                         if (!first) {
225                                 if (is_a<print_latex>(c))
226                                         c.s << ' ';
227                                 else
228                                         c.s << '*';
229                         } else {
230                                 first = false;
231                         }
232                         recombine_pair_to_ex(*it).print(c, precedence());
233                         ++it;
234                 }
235
236                 if (precedence() <= level) {
237                         if (is_a<print_latex>(c))
238                                 c.s << ")}";
239                         else
240                                 c.s << ")";
241                 }
242         }
243 }
244
245 bool mul::info(unsigned inf) const
246 {
247         switch (inf) {
248                 case info_flags::polynomial:
249                 case info_flags::integer_polynomial:
250                 case info_flags::cinteger_polynomial:
251                 case info_flags::rational_polynomial:
252                 case info_flags::crational_polynomial:
253                 case info_flags::rational_function: {
254                         epvector::const_iterator i = seq.begin(), end = seq.end();
255                         while (i != end) {
256                                 if (!(recombine_pair_to_ex(*i).info(inf)))
257                                         return false;
258                                 ++i;
259                         }
260                         return overall_coeff.info(inf);
261                 }
262                 case info_flags::algebraic: {
263                         epvector::const_iterator i = seq.begin(), end = seq.end();
264                         while (i != end) {
265                                 if ((recombine_pair_to_ex(*i).info(inf)))
266                                         return true;
267                                 ++i;
268                         }
269                         return false;
270                 }
271         }
272         return inherited::info(inf);
273 }
274
275 int mul::degree(const ex & s) const
276 {
277         // Sum up degrees of factors
278         int deg_sum = 0;
279         epvector::const_iterator i = seq.begin(), end = seq.end();
280         while (i != end) {
281                 if (ex_to<numeric>(i->coeff).is_integer())
282                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
283                 ++i;
284         }
285         return deg_sum;
286 }
287
288 int mul::ldegree(const ex & s) const
289 {
290         // Sum up degrees of factors
291         int deg_sum = 0;
292         epvector::const_iterator i = seq.begin(), end = seq.end();
293         while (i != end) {
294                 if (ex_to<numeric>(i->coeff).is_integer())
295                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
296                 ++i;
297         }
298         return deg_sum;
299 }
300
301 ex mul::coeff(const ex & s, int n) const
302 {
303         exvector coeffseq;
304         coeffseq.reserve(seq.size()+1);
305         
306         if (n==0) {
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 i = seq.begin(), end = seq.end();
310                 while (i != end) {
311                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
312                         ++i;
313                 }
314                 coeffseq.push_back(overall_coeff);
315                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
316         }
317         
318         epvector::const_iterator i = seq.begin(), end = seq.end();
319         bool coeff_found = false;
320         while (i != end) {
321                 ex t = recombine_pair_to_ex(*i);
322                 ex c = t.coeff(s, n);
323                 if (!c.is_zero()) {
324                         coeffseq.push_back(c);
325                         coeff_found = 1;
326                 } else {
327                         coeffseq.push_back(t);
328                 }
329                 ++i;
330         }
331         if (coeff_found) {
332                 coeffseq.push_back(overall_coeff);
333                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
334         }
335         
336         return _ex0;
337 }
338
339 /** Perform automatic term rewriting rules in this class.  In the following
340  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
341  *  stand for such expressions that contain a plain number.
342  *  - *(...,x;0) -> 0
343  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
344  *  - *(x;1) -> x
345  *  - *(;c) -> c
346  *
347  *  @param level cut-off in recursive evaluation */
348 ex mul::eval(int level) const
349 {
350         epvector *evaled_seqp = evalchildren(level);
351         if (evaled_seqp) {
352                 // do more evaluation later
353                 return (new mul(evaled_seqp,overall_coeff))->
354                            setflag(status_flags::dynallocated);
355         }
356         
357 #ifdef DO_GINAC_ASSERT
358         epvector::const_iterator i = seq.begin(), end = seq.end();
359         while (i != end) {
360                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
361                              (!(ex_to<numeric>(i->coeff).is_integer())));
362                 GINAC_ASSERT(!(i->is_canonical_numeric()));
363                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
364                     print(print_tree(std::cerr));
365                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
366                 /* for paranoia */
367                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
368                 GINAC_ASSERT(p.rest.is_equal(i->rest));
369                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
370                 /* end paranoia */
371                 ++i;
372         }
373 #endif // def DO_GINAC_ASSERT
374         
375         if (flags & status_flags::evaluated) {
376                 GINAC_ASSERT(seq.size()>0);
377                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
378                 return *this;
379         }
380         
381         int seq_size = seq.size();
382         if (overall_coeff.is_zero()) {
383                 // *(...,x;0) -> 0
384                 return _ex0;
385         } else if (seq_size==0) {
386                 // *(;c) -> c
387                 return overall_coeff;
388         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
389                 // *(x;1) -> x
390                 return recombine_pair_to_ex(*(seq.begin()));
391         } else if ((seq_size==1) &&
392                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
393                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
394                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
395                 const add & addref = ex_to<add>((*seq.begin()).rest);
396                 epvector *distrseq = new epvector();
397                 distrseq->reserve(addref.seq.size());
398                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
399                 while (i != end) {
400                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
401                         ++i;
402                 }
403                 return (new add(distrseq,
404                                 ex_to<numeric>(addref.overall_coeff).
405                                 mul_dyn(ex_to<numeric>(overall_coeff))))
406                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
407         }
408         return this->hold();
409 }
410
411 ex mul::evalf(int level) const
412 {
413         if (level==1)
414                 return mul(seq,overall_coeff);
415         
416         if (level==-max_recursion_level)
417                 throw(std::runtime_error("max recursion level reached"));
418         
419         epvector *s = new epvector();
420         s->reserve(seq.size());
421
422         --level;
423         epvector::const_iterator i = seq.begin(), end = seq.end();
424         while (i != end) {
425                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
426                                                            i->coeff));
427                 ++i;
428         }
429         return mul(s, overall_coeff.evalf(level));
430 }
431
432 ex mul::evalm(void) const
433 {
434         // numeric*matrix
435         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
436          && is_ex_of_type(seq[0].rest, matrix))
437                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
438
439         // Evaluate children first, look whether there are any matrices at all
440         // (there can be either no matrices or one matrix; if there were more
441         // than one matrix, it would be a non-commutative product)
442         epvector *s = new epvector;
443         s->reserve(seq.size());
444
445         bool have_matrix = false;
446         epvector::iterator the_matrix;
447
448         epvector::const_iterator i = seq.begin(), end = seq.end();
449         while (i != end) {
450                 const ex &m = recombine_pair_to_ex(*i).evalm();
451                 s->push_back(split_ex_to_pair(m));
452                 if (is_ex_of_type(m, matrix)) {
453                         have_matrix = true;
454                         the_matrix = s->end() - 1;
455                 }
456                 ++i;
457         }
458
459         if (have_matrix) {
460
461                 // The product contained a matrix. We will multiply all other factors
462                 // into that matrix.
463                 matrix m = ex_to<matrix>(the_matrix->rest);
464                 s->erase(the_matrix);
465                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
466                 return m.mul_scalar(scalar);
467
468         } else
469                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
470 }
471
472 ex mul::simplify_ncmul(const exvector & v) const
473 {
474         if (seq.empty())
475                 return inherited::simplify_ncmul(v);
476
477         // Find first noncommutative element and call its simplify_ncmul()
478         epvector::const_iterator i = seq.begin(), end = seq.end();
479         while (i != end) {
480                 if (i->rest.return_type() == return_types::noncommutative)
481                         return i->rest.simplify_ncmul(v);
482                 ++i;
483         }
484         return inherited::simplify_ncmul(v);
485 }
486
487 // protected
488
489 /** Implementation of ex::diff() for a product.  It applies the product rule.
490  *  @see ex::diff */
491 ex mul::derivative(const symbol & s) const
492 {
493         unsigned num = seq.size();
494         exvector addseq;
495         addseq.reserve(num);
496         
497         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
498         epvector mulseq = seq;
499         epvector::const_iterator i = seq.begin(), end = seq.end();
500         epvector::iterator i2 = mulseq.begin();
501         while (i != end) {
502                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
503                                              i->rest.diff(s));
504                 ep.swap(*i2);
505                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
506                 ep.swap(*i2);
507                 ++i; ++i2;
508         }
509         return (new add(addseq))->setflag(status_flags::dynallocated);
510 }
511
512 int mul::compare_same_type(const basic & other) const
513 {
514         return inherited::compare_same_type(other);
515 }
516
517 bool mul::is_equal_same_type(const basic & other) const
518 {
519         return inherited::is_equal_same_type(other);
520 }
521
522 unsigned mul::return_type(void) const
523 {
524         if (seq.empty()) {
525                 // mul without factors: should not happen, but commutes
526                 return return_types::commutative;
527         }
528         
529         bool all_commutative = true;
530         epvector::const_iterator noncommutative_element; // point to first found nc element
531         
532         epvector::const_iterator i = seq.begin(), end = seq.end();
533         while (i != end) {
534                 unsigned rt = i->rest.return_type();
535                 if (rt == return_types::noncommutative_composite)
536                         return rt; // one ncc -> mul also ncc
537                 if ((rt == return_types::noncommutative) && (all_commutative)) {
538                         // first nc element found, remember position
539                         noncommutative_element = i;
540                         all_commutative = false;
541                 }
542                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
543                         // another nc element found, compare type_infos
544                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
545                                 // diffent types -> mul is ncc
546                                 return return_types::noncommutative_composite;
547                         }
548                 }
549                 ++i;
550         }
551         // all factors checked
552         return all_commutative ? return_types::commutative : return_types::noncommutative;
553 }
554    
555 unsigned mul::return_type_tinfo(void) const
556 {
557         if (seq.empty())
558                 return tinfo_key;  // mul without factors: should not happen
559         
560         // return type_info of first noncommutative element
561         epvector::const_iterator i = seq.begin(), end = seq.end();
562         while (i != end) {
563                 if (i->rest.return_type() == return_types::noncommutative)
564                         return i->rest.return_type_tinfo();
565                 ++i;
566         }
567         // no noncommutative element found, should not happen
568         return tinfo_key;
569 }
570
571 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
572 {
573         return (new mul(v, oc))->setflag(status_flags::dynallocated);
574 }
575
576 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
577 {
578         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
579 }
580
581 expair mul::split_ex_to_pair(const ex & e) const
582 {
583         if (is_ex_exactly_of_type(e,power)) {
584                 const power & powerref = ex_to<power>(e);
585                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
586                         return expair(powerref.basis,powerref.exponent);
587         }
588         return expair(e,_ex1);
589 }
590         
591 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
592                                           const ex & c) const
593 {
594         // to avoid duplication of power simplification rules,
595         // we create a temporary power object
596         // otherwise it would be hard to correctly simplify
597         // expression like (4^(1/3))^(3/2)
598         if (are_ex_trivially_equal(c,_ex1))
599                 return split_ex_to_pair(e);
600         
601         return split_ex_to_pair(power(e,c));
602 }
603         
604 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
605                                             const ex & c) const
606 {
607         // to avoid duplication of power simplification rules,
608         // we create a temporary power object
609         // otherwise it would be hard to correctly simplify
610         // expression like (4^(1/3))^(3/2)
611         if (are_ex_trivially_equal(c,_ex1))
612                 return p;
613         
614         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
615 }
616         
617 ex mul::recombine_pair_to_ex(const expair & p) const
618 {
619         if (ex_to<numeric>(p.coeff).is_equal(_num1)) 
620                 return p.rest;
621         else
622                 return power(p.rest,p.coeff);
623 }
624
625 bool mul::expair_needs_further_processing(epp it)
626 {
627         if (is_ex_exactly_of_type((*it).rest,mul) &&
628                 ex_to<numeric>((*it).coeff).is_integer()) {
629                 // combined pair is product with integer power -> expand it
630                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
631                 return true;
632         }
633         if (is_ex_exactly_of_type((*it).rest,numeric)) {
634                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
635                 if (!ep.is_equal(*it)) {
636                         // combined pair is a numeric power which can be simplified
637                         *it = ep;
638                         return true;
639                 }
640                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
641                         // combined pair has coeff 1 and must be moved to the end
642                         return true;
643                 }
644         }
645         return false;
646 }       
647
648 ex mul::default_overall_coeff(void) const
649 {
650         return _ex1;
651 }
652
653 void mul::combine_overall_coeff(const ex & c)
654 {
655         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
656         GINAC_ASSERT(is_exactly_a<numeric>(c));
657         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
658 }
659
660 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
661 {
662         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
663         GINAC_ASSERT(is_exactly_a<numeric>(c1));
664         GINAC_ASSERT(is_exactly_a<numeric>(c2));
665         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
666 }
667
668 bool mul::can_make_flat(const expair & p) const
669 {
670         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
671         // this assertion will probably fail somewhere
672         // it would require a more careful make_flat, obeying the power laws
673         // probably should return true only if p.coeff is integer
674         return ex_to<numeric>(p.coeff).is_equal(_num1);
675 }
676
677 ex mul::expand(unsigned options) const
678 {
679         // First, expand the children
680         epvector * expanded_seqp = expandchildren(options);
681         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
682
683         // Now, look for all the factors that are sums and multiply each one out
684         // with the next one that is found while collecting the factors which are
685         // not sums
686         int number_of_adds = 0;
687         ex last_expanded = _ex1;
688         epvector non_adds;
689         non_adds.reserve(expanded_seq.size());
690         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
691         while (cit != last) {
692                 if (is_ex_exactly_of_type(cit->rest, add) &&
693                         (cit->coeff.is_equal(_ex1))) {
694                         ++number_of_adds;
695                         if (is_ex_exactly_of_type(last_expanded, add)) {
696 #if 0
697                                 // Expand a product of two sums, simple and robust version.
698                                 const add & add1 = ex_to<add>(last_expanded);
699                                 const add & add2 = ex_to<add>(cit->rest);
700                                 const int n1 = add1.nops();
701                                 const int n2 = add2.nops();
702                                 ex tmp_accu;
703                                 exvector distrseq;
704                                 distrseq.reserve(n2);
705                                 for (int i1=0; i1<n1; ++i1) {
706                                         distrseq.clear();
707                                         // cache the first operand (for efficiency):
708                                         const ex op1 = add1.op(i1);
709                                         for (int i2=0; i2<n2; ++i2)
710                                                 distrseq.push_back(op1 * add2.op(i2));
711                                         tmp_accu += (new add(distrseq))->
712                                                      setflag(status_flags::dynallocated);
713                                 }
714                                 last_expanded = tmp_accu;
715 #else
716                                 // Expand a product of two sums, aggressive version.
717                                 // Caring for the overall coefficients in separate loops can
718                                 // sometimes give a performance gain of up to 15%!
719
720                                 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
721                                 // add2 is for the inner loop and should be the bigger of the two sums
722                                 // in the presence of asymptotically good sorting:
723                                 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
724                                 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
725                                 const epvector::const_iterator add1begin = add1.seq.begin();
726                                 const epvector::const_iterator add1end   = add1.seq.end();
727                                 const epvector::const_iterator add2begin = add2.seq.begin();
728                                 const epvector::const_iterator add2end   = add2.seq.end();
729                                 epvector distrseq;
730                                 distrseq.reserve(add1.seq.size()+add2.seq.size());
731                                 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
732                                 if (!add1.overall_coeff.is_zero()) {
733                                         if (add1.overall_coeff.is_equal(_ex1))
734                                                 distrseq.insert(distrseq.end(),add2begin,add2end);
735                                         else
736                                                 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
737                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
738                                 }
739                                 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
740                                 if (!add2.overall_coeff.is_zero()) {
741                                         if (add2.overall_coeff.is_equal(_ex1))
742                                                 distrseq.insert(distrseq.end(),add1begin,add1end);
743                                         else
744                                                 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
745                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
746                                 }
747                                 // Compute the new overall coefficient and put it together:
748                                 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
749                                 // Multiply explicitly all non-numeric terms of add1 and add2:
750                                 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
751                                         // We really have to combine terms here in order to compactify
752                                         // the result.  Otherwise it would become waayy tooo bigg.
753                                         numeric oc;
754                                         distrseq.clear();
755                                         for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
756                                                 // Don't push_back expairs which might have a rest that evaluates to a numeric,
757                                                 // since that would violate an invariant of expairseq:
758                                                 const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
759                                                 if (is_ex_exactly_of_type(rest, numeric))
760                                                         oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
761                                                 else
762                                                         distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
763                                         }
764                                         tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
765                                 }
766                                 last_expanded = tmp_accu;
767 #endif
768                         } else {
769                                 non_adds.push_back(split_ex_to_pair(last_expanded));
770                                 last_expanded = cit->rest;
771                         }
772                 } else {
773                         non_adds.push_back(*cit);
774                 }
775                 ++cit;
776         }
777         if (expanded_seqp)
778                 delete expanded_seqp;
779         
780         // Now the only remaining thing to do is to multiply the factors which
781         // were not sums into the "last_expanded" sum
782         if (is_ex_exactly_of_type(last_expanded, add)) {
783                 const add & finaladd = ex_to<add>(last_expanded);
784                 exvector distrseq;
785                 int n = finaladd.nops();
786                 distrseq.reserve(n);
787                 for (int i=0; i<n; ++i) {
788                         epvector factors = non_adds;
789                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
790                         distrseq.push_back((new mul(factors, overall_coeff))->
791                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
792                 }
793                 return ((new add(distrseq))->
794                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
795         }
796         non_adds.push_back(split_ex_to_pair(last_expanded));
797         return (new mul(non_adds, overall_coeff))->
798                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
799 }
800
801   
802 //////////
803 // new virtual functions which can be overridden by derived classes
804 //////////
805
806 // none
807
808 //////////
809 // non-virtual functions in this class
810 //////////
811
812
813 /** Member-wise expand the expairs representing this sequence.  This must be
814  *  overridden from expairseq::expandchildren() and done iteratively in order
815  *  to allow for early cancallations and thus safe memory.
816  *
817  *  @see mul::expand()
818  *  @return pointer to epvector containing expanded representation or zero
819  *  pointer, if sequence is unchanged. */
820 epvector * mul::expandchildren(unsigned options) const
821 {
822         const epvector::const_iterator last = seq.end();
823         epvector::const_iterator cit = seq.begin();
824         while (cit!=last) {
825                 const ex & factor = recombine_pair_to_ex(*cit);
826                 const ex & expanded_factor = factor.expand(options);
827                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
828                         
829                         // something changed, copy seq, eval and return it
830                         epvector *s = new epvector;
831                         s->reserve(seq.size());
832                         
833                         // copy parts of seq which are known not to have changed
834                         epvector::const_iterator cit2 = seq.begin();
835                         while (cit2!=cit) {
836                                 s->push_back(*cit2);
837                                 ++cit2;
838                         }
839                         // copy first changed element
840                         s->push_back(split_ex_to_pair(expanded_factor));
841                         ++cit2;
842                         // copy rest
843                         while (cit2!=last) {
844                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
845                                 ++cit2;
846                         }
847                         return s;
848                 }
849                 ++cit;
850         }
851         
852         return 0; // nothing has changed
853 }
854
855 } // namespace GiNaC