1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2015 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #include "expairseq.h"
28 #include "relational.h"
31 #include "operators.h"
33 #include "hash_seed.h"
45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
46 print_func<print_context>(&expairseq::do_print).
47 print_func<print_tree>(&expairseq::do_print_tree))
57 bool operator()(const epp &lh, const epp &rh) const
59 return (*lh).is_less(*rh);
64 // default constructor
69 expairseq::expairseq()
78 expairseq::expairseq(const ex &lh, const ex &rh)
80 construct_from_2_ex(lh,rh);
81 GINAC_ASSERT(is_canonical());
84 expairseq::expairseq(const exvector &v)
86 construct_from_exvector(v);
87 GINAC_ASSERT(is_canonical());
90 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
93 GINAC_ASSERT(is_a<numeric>(oc));
94 construct_from_epvector(v, do_index_renaming);
95 GINAC_ASSERT(is_canonical());
98 expairseq::expairseq(epvector && vp, const ex &oc, bool do_index_renaming)
101 GINAC_ASSERT(is_a<numeric>(oc));
102 construct_from_epvector(std::move(vp), do_index_renaming);
103 GINAC_ASSERT(is_canonical());
110 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
112 inherited::read_archive(n, sym_lst);
113 archive_node::archive_node_cit first = n.find_first("rest");
114 archive_node::archive_node_cit last = n.find_last("coeff");
116 seq.reserve((last-first)/2);
118 for (archive_node::archive_node_cit loc = first; loc < last;) {
121 n.find_ex_by_loc(loc++, rest, sym_lst);
122 n.find_ex_by_loc(loc++, coeff, sym_lst);
123 seq.push_back(expair(rest, coeff));
126 n.find_ex("overall_coeff", overall_coeff, sym_lst);
129 GINAC_ASSERT(is_canonical());
132 void expairseq::archive(archive_node &n) const
134 inherited::archive(n);
135 epvector::const_iterator i = seq.begin(), iend = seq.end();
137 n.add_ex("rest", i->rest);
138 n.add_ex("coeff", i->coeff);
141 n.add_ex("overall_coeff", overall_coeff);
146 // functions overriding virtual functions from base classes
151 void expairseq::do_print(const print_context & c, unsigned level) const
154 printseq(c, ',', precedence(), level);
158 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
160 c.s << std::string(level, ' ') << class_name() << " @" << this
161 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
162 << ", nops=" << nops()
164 size_t num = seq.size();
165 for (size_t i=0; i<num; ++i) {
166 seq[i].rest.print(c, level + c.delta_indent);
167 seq[i].coeff.print(c, level + c.delta_indent);
169 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
171 if (!overall_coeff.is_equal(default_overall_coeff())) {
172 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
173 << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
174 overall_coeff.print(c, level + c.delta_indent);
176 c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
179 bool expairseq::info(unsigned inf) const
182 case info_flags::expanded:
183 return (flags & status_flags::expanded);
184 case info_flags::has_indices: {
185 if (flags & status_flags::has_indices)
187 else if (flags & status_flags::has_no_indices)
189 for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
190 if (i->rest.info(info_flags::has_indices)) {
191 this->setflag(status_flags::has_indices);
192 this->clearflag(status_flags::has_no_indices);
196 this->clearflag(status_flags::has_indices);
197 this->setflag(status_flags::has_no_indices);
201 return inherited::info(inf);
204 size_t expairseq::nops() const
206 if (overall_coeff.is_equal(default_overall_coeff()))
212 ex expairseq::op(size_t i) const
215 return recombine_pair_to_ex(seq[i]);
216 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
217 return overall_coeff;
220 ex expairseq::map(map_function &f) const
223 v.reserve(seq.size()+1);
225 epvector::const_iterator cit = seq.begin(), last = seq.end();
226 while (cit != last) {
227 v.push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
231 if (overall_coeff.is_equal(default_overall_coeff()))
232 return thisexpairseq(std::move(v), default_overall_coeff(), true);
234 ex newcoeff = f(overall_coeff);
235 if(is_a<numeric>(newcoeff))
236 return thisexpairseq(std::move(v), newcoeff, true);
238 v.push_back(split_ex_to_pair(newcoeff));
239 return thisexpairseq(std::move(v), default_overall_coeff(), true);
244 /** Perform coefficient-wise automatic term rewriting rules in this class. */
245 ex expairseq::eval(int level) const
247 if ((level==1) && (flags &status_flags::evaluated))
250 epvector evaled = evalchildren(level);
252 return (new expairseq(std::move(evaled), overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
257 epvector* conjugateepvector(const epvector&epv)
259 epvector *newepv = 0;
260 for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
262 newepv->push_back(i->conjugate());
265 expair x = i->conjugate();
266 if (x.is_equal(*i)) {
269 newepv = new epvector;
270 newepv->reserve(epv.size());
271 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
272 newepv->push_back(*j);
274 newepv->push_back(x);
279 ex expairseq::conjugate() const
281 epvector* newepv = conjugateepvector(seq);
282 ex x = overall_coeff.conjugate();
284 ex result = thisexpairseq(std::move(*newepv), x);
288 if (are_ex_trivially_equal(x, overall_coeff)) {
291 return thisexpairseq(seq, x);
294 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
296 // This differs from basic::match() because we want "a+b+c+d" to
297 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
299 if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
301 // Check whether global wildcard (one that matches the "rest of the
302 // expression", like "*" above) is present
303 bool has_global_wildcard = false;
305 for (size_t i=0; i<pattern.nops(); i++) {
306 if (is_exactly_a<wildcard>(pattern.op(i))) {
307 has_global_wildcard = true;
308 global_wildcard = pattern.op(i);
313 // Even if the expression does not match the pattern, some of
314 // its subexpressions could match it. For example, x^5*y^(-1)
315 // does not match the pattern $0^5, but its subexpression x^5
316 // does. So, save repl_lst in order to not add bogus entries.
317 exmap tmp_repl = repl_lst;
319 // Unfortunately, this is an O(N^2) operation because we can't
320 // sort the pattern in a useful way...
325 for (size_t i=0; i<nops(); i++)
326 ops.push_back(op(i));
328 // Now, for every term of the pattern, look for a matching term in
329 // the expression and remove the match
330 for (size_t i=0; i<pattern.nops(); i++) {
331 ex p = pattern.op(i);
332 if (has_global_wildcard && p.is_equal(global_wildcard))
334 exvector::iterator it = ops.begin(), itend = ops.end();
335 while (it != itend) {
336 if (it->match(p, tmp_repl)) {
342 return false; // no match found
346 if (has_global_wildcard) {
348 // Assign all the remaining terms to the global wildcard (unless
349 // it has already been matched before, in which case the matches
351 size_t num = ops.size();
354 for (size_t i=0; i<num; i++)
355 vp.push_back(split_ex_to_pair(ops[i]));
356 ex rest = thisexpairseq(std::move(vp), default_overall_coeff());
357 for (exmap::const_iterator it = tmp_repl.begin(); it != tmp_repl.end(); ++it) {
358 if (it->first.is_equal(global_wildcard)) {
359 if (rest.is_equal(it->second)) {
367 repl_lst[global_wildcard] = rest;
372 // No global wildcard, then the match fails if there are any
373 // unmatched terms left
381 return inherited::match(pattern, repl_lst);
384 ex expairseq::subs(const exmap & m, unsigned options) const
386 epvector subsed = subschildren(m, options);
388 return ex_to<basic>(thisexpairseq(std::move(subsed), overall_coeff, (options & subs_options::no_index_renaming) == 0));
389 else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
390 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
392 return subs_one_level(m, options);
397 int expairseq::compare_same_type(const basic &other) const
399 GINAC_ASSERT(is_a<expairseq>(other));
400 const expairseq &o = static_cast<const expairseq &>(other);
404 // compare number of elements
405 if (seq.size() != o.seq.size())
406 return (seq.size()<o.seq.size()) ? -1 : 1;
408 // compare overall_coeff
409 cmpval = overall_coeff.compare(o.overall_coeff);
413 epvector::const_iterator cit1 = seq.begin();
414 epvector::const_iterator cit2 = o.seq.begin();
415 epvector::const_iterator last1 = seq.end();
416 epvector::const_iterator last2 = o.seq.end();
418 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
419 cmpval = (*cit1).compare(*cit2);
420 if (cmpval!=0) return cmpval;
423 GINAC_ASSERT(cit1==last1);
424 GINAC_ASSERT(cit2==last2);
429 bool expairseq::is_equal_same_type(const basic &other) const
431 const expairseq &o = static_cast<const expairseq &>(other);
433 // compare number of elements
434 if (seq.size()!=o.seq.size())
437 // compare overall_coeff
438 if (!overall_coeff.is_equal(o.overall_coeff))
441 epvector::const_iterator cit1 = seq.begin();
442 epvector::const_iterator cit2 = o.seq.begin();
443 epvector::const_iterator last1 = seq.end();
445 while (cit1!=last1) {
446 if (!(*cit1).is_equal(*cit2)) return false;
454 unsigned expairseq::return_type() const
456 return return_types::noncommutative_composite;
459 unsigned expairseq::calchash() const
461 unsigned v = make_hash_seed(typeid(*this));
462 epvector::const_iterator i = seq.begin();
463 const epvector::const_iterator end = seq.end();
465 v ^= i->rest.gethash();
467 v ^= i->coeff.gethash();
471 v ^= overall_coeff.gethash();
473 // store calculated hash value only if object is already evaluated
474 if (flags &status_flags::evaluated) {
475 setflag(status_flags::hash_calculated);
482 ex expairseq::expand(unsigned options) const
484 epvector expanded = expandchildren(options);
485 if (!expanded.empty()) {
486 return thisexpairseq(std::move(expanded), overall_coeff);
488 return (options == 0) ? setflag(status_flags::expanded) : *this;
492 // new virtual functions which can be overridden by derived classes
497 /** Create an object of this type.
498 * This method works similar to a constructor. It is useful because expairseq
499 * has (at least) two possible different semantics but we want to inherit
500 * methods thus avoiding code duplication. Sometimes a method in expairseq
501 * has to create a new one of the same semantics, which cannot be done by a
502 * ctor because the name (add, mul,...) is unknown on the expairseq level. In
503 * order for this trick to work a derived class must of course override this
505 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
507 return expairseq(v, oc, do_index_renaming);
510 ex expairseq::thisexpairseq(epvector && vp, const ex &oc, bool do_index_renaming) const
512 return expairseq(std::move(vp), oc, do_index_renaming);
515 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
518 p.rest.print(c, precedence());
520 p.coeff.print(c, precedence());
524 void expairseq::printseq(const print_context & c, char delim,
525 unsigned this_precedence,
526 unsigned upper_precedence) const
528 if (this_precedence <= upper_precedence)
530 epvector::const_iterator it, it_last = seq.end() - 1;
531 for (it=seq.begin(); it!=it_last; ++it) {
532 printpair(c, *it, this_precedence);
535 printpair(c, *it, this_precedence);
536 if (!overall_coeff.is_equal(default_overall_coeff())) {
538 overall_coeff.print(c, this_precedence);
541 if (this_precedence <= upper_precedence)
546 /** Form an expair from an ex, using the corresponding semantics.
547 * @see expairseq::recombine_pair_to_ex() */
548 expair expairseq::split_ex_to_pair(const ex &e) const
550 return expair(e,_ex1);
554 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
557 GINAC_ASSERT(is_exactly_a<numeric>(c));
563 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
566 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
567 GINAC_ASSERT(is_exactly_a<numeric>(c));
569 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
573 /** Form an ex out of an expair, using the corresponding semantics.
574 * @see expairseq::split_ex_to_pair() */
575 ex expairseq::recombine_pair_to_ex(const expair &p) const
577 return lst(p.rest,p.coeff);
580 bool expairseq::expair_needs_further_processing(epp it)
585 ex expairseq::default_overall_coeff() const
590 void expairseq::combine_overall_coeff(const ex &c)
592 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
593 GINAC_ASSERT(is_exactly_a<numeric>(c));
594 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
597 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
599 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
600 GINAC_ASSERT(is_exactly_a<numeric>(c1));
601 GINAC_ASSERT(is_exactly_a<numeric>(c2));
602 overall_coeff = ex_to<numeric>(overall_coeff).
603 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
606 bool expairseq::can_make_flat(const expair &p) const
613 // non-virtual functions in this class
616 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
622 construct_from_exvector(v);
625 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
627 if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
628 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
629 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
630 rh.info(info_flags::has_indices)) {
631 ex newrh=rename_dummy_indices_uniquely(lh, rh);
632 construct_from_2_expairseq(ex_to<expairseq>(lh),
633 ex_to<expairseq>(newrh));
636 construct_from_2_expairseq(ex_to<expairseq>(lh),
637 ex_to<expairseq>(rh));
640 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
643 } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
644 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
648 if (is_exactly_a<numeric>(lh)) {
649 if (is_exactly_a<numeric>(rh)) {
650 combine_overall_coeff(lh);
651 combine_overall_coeff(rh);
653 combine_overall_coeff(lh);
654 seq.push_back(split_ex_to_pair(rh));
657 if (is_exactly_a<numeric>(rh)) {
658 combine_overall_coeff(rh);
659 seq.push_back(split_ex_to_pair(lh));
661 expair p1 = split_ex_to_pair(lh);
662 expair p2 = split_ex_to_pair(rh);
664 int cmpval = p1.rest.compare(p2.rest);
666 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
667 if (!ex_to<numeric>(p1.coeff).is_zero()) {
668 // no further processing is necessary, since this
669 // one element will usually be recombined in eval()
686 void expairseq::construct_from_2_expairseq(const expairseq &s1,
689 combine_overall_coeff(s1.overall_coeff);
690 combine_overall_coeff(s2.overall_coeff);
692 epvector::const_iterator first1 = s1.seq.begin();
693 epvector::const_iterator last1 = s1.seq.end();
694 epvector::const_iterator first2 = s2.seq.begin();
695 epvector::const_iterator last2 = s2.seq.end();
697 seq.reserve(s1.seq.size()+s2.seq.size());
699 bool needs_further_processing=false;
701 while (first1!=last1 && first2!=last2) {
702 int cmpval = (*first1).rest.compare((*first2).rest);
706 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
707 add(ex_to<numeric>(first2->coeff));
708 if (!newcoeff.is_zero()) {
709 seq.push_back(expair(first1->rest,newcoeff));
710 if (expair_needs_further_processing(seq.end()-1)) {
711 needs_further_processing = true;
716 } else if (cmpval<0) {
717 seq.push_back(*first1);
720 seq.push_back(*first2);
725 while (first1!=last1) {
726 seq.push_back(*first1);
729 while (first2!=last2) {
730 seq.push_back(*first2);
734 if (needs_further_processing) {
737 construct_from_epvector(std::move(v));
741 void expairseq::construct_from_expairseq_ex(const expairseq &s,
744 combine_overall_coeff(s.overall_coeff);
745 if (is_exactly_a<numeric>(e)) {
746 combine_overall_coeff(e);
751 epvector::const_iterator first = s.seq.begin();
752 epvector::const_iterator last = s.seq.end();
753 expair p = split_ex_to_pair(e);
755 seq.reserve(s.seq.size()+1);
756 bool p_pushed = false;
758 bool needs_further_processing=false;
760 // merge p into s.seq
761 while (first!=last) {
762 int cmpval = (*first).rest.compare(p.rest);
765 const numeric &newcoeff = ex_to<numeric>(first->coeff).
766 add(ex_to<numeric>(p.coeff));
767 if (!newcoeff.is_zero()) {
768 seq.push_back(expair(first->rest,newcoeff));
769 if (expair_needs_further_processing(seq.end()-1))
770 needs_further_processing = true;
775 } else if (cmpval<0) {
776 seq.push_back(*first);
786 // while loop exited because p was pushed, now push rest of s.seq
787 while (first!=last) {
788 seq.push_back(*first);
792 // while loop exited because s.seq was pushed, now push p
796 if (needs_further_processing) {
799 construct_from_epvector(std::move(v));
803 void expairseq::construct_from_exvector(const exvector &v)
805 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
806 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
807 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
808 // (same for (+,*) -> (*,^)
812 combine_same_terms_sorted_seq();
815 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
817 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
818 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
819 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
820 // same for (+,*) -> (*,^)
822 make_flat(v, do_index_renaming);
824 combine_same_terms_sorted_seq();
827 void expairseq::construct_from_epvector(epvector &&v, bool do_index_renaming)
829 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
830 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
831 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
832 // same for (+,*) -> (*,^)
834 make_flat(std::move(v), do_index_renaming);
836 combine_same_terms_sorted_seq();
839 /** Combine this expairseq with argument exvector.
840 * It cares for associativity as well as for special handling of numerics. */
841 void expairseq::make_flat(const exvector &v)
843 exvector::const_iterator cit;
845 // count number of operands which are of same expairseq derived type
846 // and their cumulative number of operands
849 bool do_idx_rename = false;
852 while (cit!=v.end()) {
853 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
855 noperands += ex_to<expairseq>(*cit).seq.size();
857 if (is_a<mul>(*this) && (!do_idx_rename) &&
858 cit->info(info_flags::has_indices))
859 do_idx_rename = true;
863 // reserve seq and coeffseq which will hold all operands
864 seq.reserve(v.size()+noperands-nexpairseqs);
866 // copy elements and split off numerical part
867 make_flat_inserter mf(v, do_idx_rename);
869 while (cit!=v.end()) {
870 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
871 ex newfactor = mf.handle_factor(*cit, _ex1);
872 const expairseq &subseqref = ex_to<expairseq>(newfactor);
873 combine_overall_coeff(subseqref.overall_coeff);
874 epvector::const_iterator cit_s = subseqref.seq.begin();
875 while (cit_s!=subseqref.seq.end()) {
876 seq.push_back(*cit_s);
880 if (is_exactly_a<numeric>(*cit))
881 combine_overall_coeff(*cit);
883 ex newfactor = mf.handle_factor(*cit, _ex1);
884 seq.push_back(split_ex_to_pair(newfactor));
891 /** Combine this expairseq with argument epvector.
892 * It cares for associativity as well as for special handling of numerics. */
893 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
895 epvector::const_iterator cit;
897 // count number of operands which are of same expairseq derived type
898 // and their cumulative number of operands
901 bool really_need_rename_inds = false;
904 while (cit!=v.end()) {
905 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
907 noperands += ex_to<expairseq>(cit->rest).seq.size();
909 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
910 cit->rest.info(info_flags::has_indices))
911 really_need_rename_inds = true;
914 do_index_renaming = do_index_renaming && really_need_rename_inds;
916 // reserve seq and coeffseq which will hold all operands
917 seq.reserve(v.size()+noperands-nexpairseqs);
918 make_flat_inserter mf(v, do_index_renaming);
920 // copy elements and split off numerical part
922 while (cit!=v.end()) {
923 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
924 this->can_make_flat(*cit)) {
925 ex newrest = mf.handle_factor(cit->rest, cit->coeff);
926 const expairseq &subseqref = ex_to<expairseq>(newrest);
927 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
928 ex_to<numeric>(cit->coeff));
929 epvector::const_iterator cit_s = subseqref.seq.begin();
930 while (cit_s!=subseqref.seq.end()) {
931 seq.push_back(expair(cit_s->rest,
932 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
936 if (cit->is_canonical_numeric())
937 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
940 ex newrest = mf.handle_factor(rest, cit->coeff);
941 if (are_ex_trivially_equal(newrest, rest))
944 seq.push_back(expair(newrest, cit->coeff));
951 /** Brings this expairseq into a sorted (canonical) form. */
952 void expairseq::canonicalize()
954 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
958 /** Compact a presorted expairseq by combining all matching expairs to one
959 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
961 void expairseq::combine_same_terms_sorted_seq()
966 bool needs_further_processing = false;
968 epvector::iterator itin1 = seq.begin();
969 epvector::iterator itin2 = itin1+1;
970 epvector::iterator itout = itin1;
971 epvector::iterator last = seq.end();
972 // must_copy will be set to true the first time some combination is
973 // possible from then on the sequence has changed and must be compacted
974 bool must_copy = false;
975 while (itin2!=last) {
976 if (itin1->rest.compare(itin2->rest)==0) {
977 itin1->coeff = ex_to<numeric>(itin1->coeff).
978 add_dyn(ex_to<numeric>(itin2->coeff));
979 if (expair_needs_further_processing(itin1))
980 needs_further_processing = true;
983 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
992 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
998 seq.erase(itout,last);
1000 if (needs_further_processing) {
1003 construct_from_epvector(std::move(v));
1007 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1008 * debugging or in assertions since being sorted is an invariance. */
1009 bool expairseq::is_canonical() const
1011 if (seq.size() <= 1)
1014 epvector::const_iterator it = seq.begin(), itend = seq.end();
1015 epvector::const_iterator it_last = it;
1016 for (++it; it!=itend; it_last=it, ++it) {
1017 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1018 if (!is_exactly_a<numeric>(it_last->rest) ||
1019 !is_exactly_a<numeric>(it->rest)) {
1020 // double test makes it easier to set a breakpoint...
1021 if (!is_exactly_a<numeric>(it_last->rest) ||
1022 !is_exactly_a<numeric>(it->rest)) {
1023 printpair(std::clog, *it_last, 0);
1025 printpair(std::clog, *it, 0);
1027 std::clog << "pair1:" << std::endl;
1028 it_last->rest.print(print_tree(std::clog));
1029 it_last->coeff.print(print_tree(std::clog));
1030 std::clog << "pair2:" << std::endl;
1031 it->rest.print(print_tree(std::clog));
1032 it->coeff.print(print_tree(std::clog));
1041 /** Member-wise expand the expairs in this sequence.
1043 * @see expairseq::expand()
1044 * @return epvector containing expanded pairs, empty if no members
1045 * had to be changed. */
1046 epvector expairseq::expandchildren(unsigned options) const
1048 const epvector::const_iterator last = seq.end();
1049 epvector::const_iterator cit = seq.begin();
1051 const ex &expanded_ex = cit->rest.expand(options);
1052 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1054 // something changed, copy seq, eval and return it
1056 s.reserve(seq.size());
1058 // copy parts of seq which are known not to have changed
1059 epvector::const_iterator cit2 = seq.begin();
1065 // copy first changed element
1066 s.push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1071 while (cit2!=last) {
1072 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1081 return epvector(); // empty signalling nothing has changed
1085 /** Member-wise evaluate the expairs in this sequence.
1087 * @see expairseq::eval()
1088 * @return epvector containing evaluated pairs, empty if no members
1089 * had to be changed. */
1090 epvector expairseq::evalchildren(int level) const
1093 return epvector(); // nothing had to be evaluated
1095 if (level == -max_recursion_level)
1096 throw(std::runtime_error("max recursion level reached"));
1099 epvector::const_iterator last = seq.end();
1100 epvector::const_iterator cit = seq.begin();
1102 const ex evaled_ex = cit->rest.eval(level);
1103 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1105 // something changed, copy seq, eval and return it
1107 s.reserve(seq.size());
1109 // copy parts of seq which are known not to have changed
1110 epvector::const_iterator cit2=seq.begin();
1116 // copy first changed element
1117 s.push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1122 while (cit2!=last) {
1123 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1127 return std::move(s);
1132 return epvector(); // signalling nothing has changed
1135 /** Member-wise substitute in this sequence.
1137 * @see expairseq::subs()
1138 * @return epvector containing expanded pairs, empty if no members
1139 * had to be changed. */
1140 epvector expairseq::subschildren(const exmap & m, unsigned options) const
1142 // When any of the objects to be substituted is a product or power
1143 // we have to recombine the pairs because the numeric coefficients may
1144 // be part of the search pattern.
1145 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1147 // Search the list of substitutions and cache our findings
1148 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1149 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1150 options |= subs_options::pattern_is_product;
1154 if (!(options & subs_options::pattern_is_product))
1155 options |= subs_options::pattern_is_not_product;
1158 if (options & subs_options::pattern_is_product) {
1160 // Substitute in the recombined pairs
1161 epvector::const_iterator cit = seq.begin(), last = seq.end();
1162 while (cit != last) {
1164 const ex &orig_ex = recombine_pair_to_ex(*cit);
1165 const ex &subsed_ex = orig_ex.subs(m, options);
1166 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1168 // Something changed, copy seq, subs and return it
1170 s.reserve(seq.size());
1172 // Copy parts of seq which are known not to have changed
1173 s.insert(s.begin(), seq.begin(), cit);
1175 // Copy first changed element
1176 s.push_back(split_ex_to_pair(subsed_ex));
1180 while (cit != last) {
1181 s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1192 // Substitute only in the "rest" part of the pairs
1193 epvector::const_iterator cit = seq.begin(), last = seq.end();
1194 while (cit != last) {
1196 const ex &subsed_ex = cit->rest.subs(m, options);
1197 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1199 // Something changed, copy seq, subs and return it
1201 s.reserve(seq.size());
1203 // Copy parts of seq which are known not to have changed
1204 s.insert(s.begin(), seq.begin(), cit);
1206 // Copy first changed element
1207 s.push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1211 while (cit != last) {
1212 s.push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1222 // Nothing has changed
1227 // static member variables
1230 } // namespace GiNaC