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
36 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
39 // default ctor, dtor, copy ctor, assignment operator and helpers
44 tinfo_key = TINFO_mul;
56 mul::mul(const ex & lh, const ex & rh)
58 tinfo_key = TINFO_mul;
60 construct_from_2_ex(lh,rh);
61 GINAC_ASSERT(is_canonical());
64 mul::mul(const exvector & v)
66 tinfo_key = TINFO_mul;
68 construct_from_exvector(v);
69 GINAC_ASSERT(is_canonical());
72 mul::mul(const epvector & v)
74 tinfo_key = TINFO_mul;
76 construct_from_epvector(v);
77 GINAC_ASSERT(is_canonical());
80 mul::mul(const epvector & v, const ex & oc)
82 tinfo_key = TINFO_mul;
84 construct_from_epvector(v);
85 GINAC_ASSERT(is_canonical());
88 mul::mul(epvector * vp, const ex & oc)
90 tinfo_key = TINFO_mul;
93 construct_from_epvector(*vp);
95 GINAC_ASSERT(is_canonical());
98 mul::mul(const ex & lh, const ex & mh, const ex & rh)
100 tinfo_key = TINFO_mul;
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());
115 DEFAULT_ARCHIVING(mul)
118 // functions overriding virtual functions from base classes
123 void mul::print(const print_context & c, unsigned level) const
125 if (is_a<print_tree>(c)) {
127 inherited::print(c, level);
129 } else if (is_a<print_csrc>(c)) {
131 if (precedence() <= level)
134 if (!overall_coeff.is_equal(_ex1)) {
135 overall_coeff.print(c, precedence());
139 // Print arguments, separated by "*" or "/"
140 epvector::const_iterator it = seq.begin(), itend = seq.end();
141 while (it != itend) {
143 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
144 if (it == seq.begin() && ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) {
145 if (is_a<print_csrc_cl_N>(c))
151 // If the exponent is 1 or -1, it is left out
152 if (it->coeff.compare(_ex1) == 0 || it->coeff.compare(_num_1) == 0)
153 it->rest.print(c, precedence());
155 // Outer parens around ex needed for broken gcc-2.95 parser:
156 (ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
159 // Separator is "/" for negative integer powers, "*" otherwise
162 if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0)
169 if (precedence() <= level)
174 if (precedence() <= level) {
175 if (is_a<print_latex>(c))
183 // First print the overall numeric coefficient
184 numeric coeff = ex_to<numeric>(overall_coeff);
185 if (coeff.csgn() == -1)
187 if (!coeff.is_equal(_num1) &&
188 !coeff.is_equal(_num_1)) {
189 if (coeff.is_rational()) {
190 if (coeff.is_negative())
195 if (coeff.csgn() == -1)
196 (-coeff).print(c, precedence());
198 coeff.print(c, precedence());
200 if (is_a<print_latex>(c))
206 // Then proceed with the remaining factors
207 epvector::const_iterator it = seq.begin(), itend = seq.end();
208 while (it != itend) {
210 if (is_a<print_latex>(c))
217 recombine_pair_to_ex(*it).print(c, precedence());
221 if (precedence() <= level) {
222 if (is_a<print_latex>(c))
230 bool mul::info(unsigned inf) const
233 case info_flags::polynomial:
234 case info_flags::integer_polynomial:
235 case info_flags::cinteger_polynomial:
236 case info_flags::rational_polynomial:
237 case info_flags::crational_polynomial:
238 case info_flags::rational_function: {
239 epvector::const_iterator i = seq.begin(), end = seq.end();
241 if (!(recombine_pair_to_ex(*i).info(inf)))
245 return overall_coeff.info(inf);
247 case info_flags::algebraic: {
248 epvector::const_iterator i = seq.begin(), end = seq.end();
250 if ((recombine_pair_to_ex(*i).info(inf)))
257 return inherited::info(inf);
260 int mul::degree(const ex & s) const
262 // Sum up degrees of factors
264 epvector::const_iterator i = seq.begin(), end = seq.end();
266 if (ex_to<numeric>(i->coeff).is_integer())
267 deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
273 int mul::ldegree(const ex & s) const
275 // Sum up degrees of factors
277 epvector::const_iterator i = seq.begin(), end = seq.end();
279 if (ex_to<numeric>(i->coeff).is_integer())
280 deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
286 ex mul::coeff(const ex & s, int n) const
289 coeffseq.reserve(seq.size()+1);
292 // product of individual coeffs
293 // if a non-zero power of s is found, the resulting product will be 0
294 epvector::const_iterator i = seq.begin(), end = seq.end();
296 coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
299 coeffseq.push_back(overall_coeff);
300 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
303 epvector::const_iterator i = seq.begin(), end = seq.end();
304 bool coeff_found = false;
306 ex t = recombine_pair_to_ex(*i);
307 ex c = t.coeff(s, n);
309 coeffseq.push_back(c);
312 coeffseq.push_back(t);
317 coeffseq.push_back(overall_coeff);
318 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
324 /** Perform automatic term rewriting rules in this class. In the following
325 * x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
326 * stand for such expressions that contain a plain number.
328 * - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
332 * @param level cut-off in recursive evaluation */
333 ex mul::eval(int level) const
335 epvector *evaled_seqp = evalchildren(level);
337 // do more evaluation later
338 return (new mul(evaled_seqp,overall_coeff))->
339 setflag(status_flags::dynallocated);
342 #ifdef DO_GINAC_ASSERT
343 epvector::const_iterator i = seq.begin(), end = seq.end();
345 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
346 (!(ex_to<numeric>(i->coeff).is_integer())));
347 GINAC_ASSERT(!(i->is_canonical_numeric()));
348 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
349 print(print_tree(std::cerr));
350 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
352 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
353 GINAC_ASSERT(p.rest.is_equal(i->rest));
354 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
358 #endif // def DO_GINAC_ASSERT
360 if (flags & status_flags::evaluated) {
361 GINAC_ASSERT(seq.size()>0);
362 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
366 int seq_size = seq.size();
367 if (overall_coeff.is_zero()) {
370 } else if (seq_size==0) {
372 return overall_coeff;
373 } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
375 return recombine_pair_to_ex(*(seq.begin()));
376 } else if ((seq_size==1) &&
377 is_ex_exactly_of_type((*seq.begin()).rest,add) &&
378 ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
379 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
380 const add & addref = ex_to<add>((*seq.begin()).rest);
381 epvector *distrseq = new epvector();
382 distrseq->reserve(addref.seq.size());
383 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
385 distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
388 return (new add(distrseq,
389 ex_to<numeric>(addref.overall_coeff).
390 mul_dyn(ex_to<numeric>(overall_coeff))))
391 ->setflag(status_flags::dynallocated | status_flags::evaluated);
396 ex mul::evalf(int level) const
399 return mul(seq,overall_coeff);
401 if (level==-max_recursion_level)
402 throw(std::runtime_error("max recursion level reached"));
404 epvector *s = new epvector();
405 s->reserve(seq.size());
408 epvector::const_iterator i = seq.begin(), end = seq.end();
410 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
414 return mul(s, overall_coeff.evalf(level));
417 ex mul::evalm(void) const
420 if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
421 && is_ex_of_type(seq[0].rest, matrix))
422 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
424 // Evaluate children first, look whether there are any matrices at all
425 // (there can be either no matrices or one matrix; if there were more
426 // than one matrix, it would be a non-commutative product)
427 epvector *s = new epvector;
428 s->reserve(seq.size());
430 bool have_matrix = false;
431 epvector::iterator the_matrix;
433 epvector::const_iterator i = seq.begin(), end = seq.end();
435 const ex &m = recombine_pair_to_ex(*i).evalm();
436 s->push_back(split_ex_to_pair(m));
437 if (is_ex_of_type(m, matrix)) {
439 the_matrix = s->end() - 1;
446 // The product contained a matrix. We will multiply all other factors
448 matrix m = ex_to<matrix>(the_matrix->rest);
449 s->erase(the_matrix);
450 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
451 return m.mul_scalar(scalar);
454 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
457 ex mul::simplify_ncmul(const exvector & v) const
460 return inherited::simplify_ncmul(v);
462 // Find first noncommutative element and call its simplify_ncmul()
463 epvector::const_iterator i = seq.begin(), end = seq.end();
465 if (i->rest.return_type() == return_types::noncommutative)
466 return i->rest.simplify_ncmul(v);
469 return inherited::simplify_ncmul(v);
474 /** Implementation of ex::diff() for a product. It applies the product rule.
476 ex mul::derivative(const symbol & s) const
478 unsigned num = seq.size();
482 // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
483 epvector mulseq = seq;
484 epvector::const_iterator i = seq.begin(), end = seq.end();
485 epvector::iterator i2 = mulseq.begin();
487 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
490 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
494 return (new add(addseq))->setflag(status_flags::dynallocated);
497 int mul::compare_same_type(const basic & other) const
499 return inherited::compare_same_type(other);
502 bool mul::is_equal_same_type(const basic & other) const
504 return inherited::is_equal_same_type(other);
507 unsigned mul::return_type(void) const
510 // mul without factors: should not happen, but commutes
511 return return_types::commutative;
514 bool all_commutative = true;
515 epvector::const_iterator noncommutative_element; // point to first found nc element
517 epvector::const_iterator i = seq.begin(), end = seq.end();
519 unsigned rt = i->rest.return_type();
520 if (rt == return_types::noncommutative_composite)
521 return rt; // one ncc -> mul also ncc
522 if ((rt == return_types::noncommutative) && (all_commutative)) {
523 // first nc element found, remember position
524 noncommutative_element = i;
525 all_commutative = false;
527 if ((rt == return_types::noncommutative) && (!all_commutative)) {
528 // another nc element found, compare type_infos
529 if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
530 // diffent types -> mul is ncc
531 return return_types::noncommutative_composite;
536 // all factors checked
537 return all_commutative ? return_types::commutative : return_types::noncommutative;
540 unsigned mul::return_type_tinfo(void) const
543 return tinfo_key; // mul without factors: should not happen
545 // return type_info of first noncommutative element
546 epvector::const_iterator i = seq.begin(), end = seq.end();
548 if (i->rest.return_type() == return_types::noncommutative)
549 return i->rest.return_type_tinfo();
552 // no noncommutative element found, should not happen
556 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
558 return (new mul(v, oc))->setflag(status_flags::dynallocated);
561 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
563 return (new mul(vp, oc))->setflag(status_flags::dynallocated);
566 expair mul::split_ex_to_pair(const ex & e) const
568 if (is_ex_exactly_of_type(e,power)) {
569 const power & powerref = ex_to<power>(e);
570 if (is_ex_exactly_of_type(powerref.exponent,numeric))
571 return expair(powerref.basis,powerref.exponent);
573 return expair(e,_ex1);
576 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
579 // to avoid duplication of power simplification rules,
580 // we create a temporary power object
581 // otherwise it would be hard to correctly simplify
582 // expression like (4^(1/3))^(3/2)
583 if (are_ex_trivially_equal(c,_ex1))
584 return split_ex_to_pair(e);
586 return split_ex_to_pair(power(e,c));
589 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
592 // to avoid duplication of power simplification rules,
593 // we create a temporary power object
594 // otherwise it would be hard to correctly simplify
595 // expression like (4^(1/3))^(3/2)
596 if (are_ex_trivially_equal(c,_ex1))
599 return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
602 ex mul::recombine_pair_to_ex(const expair & p) const
604 if (ex_to<numeric>(p.coeff).is_equal(_num1))
607 return power(p.rest,p.coeff);
610 bool mul::expair_needs_further_processing(epp it)
612 if (is_ex_exactly_of_type((*it).rest,mul) &&
613 ex_to<numeric>((*it).coeff).is_integer()) {
614 // combined pair is product with integer power -> expand it
615 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
618 if (is_ex_exactly_of_type((*it).rest,numeric)) {
619 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
620 if (!ep.is_equal(*it)) {
621 // combined pair is a numeric power which can be simplified
625 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
626 // combined pair has coeff 1 and must be moved to the end
633 ex mul::default_overall_coeff(void) const
638 void mul::combine_overall_coeff(const ex & c)
640 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
641 GINAC_ASSERT(is_exactly_a<numeric>(c));
642 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
645 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
647 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
648 GINAC_ASSERT(is_exactly_a<numeric>(c1));
649 GINAC_ASSERT(is_exactly_a<numeric>(c2));
650 overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
653 bool mul::can_make_flat(const expair & p) const
655 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
656 // this assertion will probably fail somewhere
657 // it would require a more careful make_flat, obeying the power laws
658 // probably should return true only if p.coeff is integer
659 return ex_to<numeric>(p.coeff).is_equal(_num1);
662 ex mul::expand(unsigned options) const
664 // First, expand the children
665 epvector * expanded_seqp = expandchildren(options);
666 const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
668 // Now, look for all the factors that are sums and multiply each one out
669 // with the next one that is found while collecting the factors which are
671 int number_of_adds = 0;
672 ex last_expanded = _ex1;
674 non_adds.reserve(expanded_seq.size());
675 epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
676 while (cit != last) {
677 if (is_ex_exactly_of_type(cit->rest, add) &&
678 (cit->coeff.is_equal(_ex1))) {
680 if (is_ex_exactly_of_type(last_expanded, add)) {
681 const add & add1 = ex_to<add>(last_expanded);
682 const add & add2 = ex_to<add>(cit->rest);
683 int n1 = add1.nops();
684 int n2 = add2.nops();
686 distrseq.reserve(n1*n2);
687 for (int i1=0; i1<n1; ++i1) {
688 for (int i2=0; i2<n2; ++i2) {
689 distrseq.push_back(add1.op(i1) * add2.op(i2));
692 last_expanded = (new add(distrseq))->
693 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
695 non_adds.push_back(split_ex_to_pair(last_expanded));
696 last_expanded = cit->rest;
699 non_adds.push_back(*cit);
704 delete expanded_seqp;
706 // Now the only remaining thing to do is to multiply the factors which
707 // were not sums into the "last_expanded" sum
708 if (is_ex_exactly_of_type(last_expanded, add)) {
709 const add & finaladd = ex_to<add>(last_expanded);
711 int n = finaladd.nops();
713 for (int i=0; i<n; ++i) {
714 epvector factors = non_adds;
715 factors.push_back(split_ex_to_pair(finaladd.op(i)));
716 distrseq.push_back((new mul(factors, overall_coeff))->
717 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
719 return ((new add(distrseq))->
720 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
722 non_adds.push_back(split_ex_to_pair(last_expanded));
723 return (new mul(non_adds, overall_coeff))->
724 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
729 // new virtual functions which can be overridden by derived classes
735 // non-virtual functions in this class
739 /** Member-wise expand the expairs representing this sequence. This must be
740 * overridden from expairseq::expandchildren() and done iteratively in order
741 * to allow for early cancallations and thus safe memory.
744 * @return pointer to epvector containing expanded representation or zero
745 * pointer, if sequence is unchanged. */
746 epvector * mul::expandchildren(unsigned options) const
748 const epvector::const_iterator last = seq.end();
749 epvector::const_iterator cit = seq.begin();
751 const ex & factor = recombine_pair_to_ex(*cit);
752 const ex & expanded_factor = factor.expand(options);
753 if (!are_ex_trivially_equal(factor,expanded_factor)) {
755 // something changed, copy seq, eval and return it
756 epvector *s = new epvector;
757 s->reserve(seq.size());
759 // copy parts of seq which are known not to have changed
760 epvector::const_iterator cit2 = seq.begin();
765 // copy first changed element
766 s->push_back(split_ex_to_pair(expanded_factor));
770 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
778 return 0; // nothing has changed