1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2009 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"
37 #if EXPAIRSEQ_USE_HASHTAB
39 #endif // EXPAIRSEQ_USE_HASHTAB
48 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
49 print_func<print_context>(&expairseq::do_print).
50 print_func<print_tree>(&expairseq::do_print_tree))
60 bool operator()(const epp &lh, const epp &rh) const
62 return (*lh).is_less(*rh);
67 // default constructor
72 expairseq::expairseq()
73 #if EXPAIRSEQ_USE_HASHTAB
75 #endif // EXPAIRSEQ_USE_HASHTAB
81 /** For use by copy ctor and assignment operator. */
82 void expairseq::copy(const expairseq &other)
85 overall_coeff = other.overall_coeff;
86 #if EXPAIRSEQ_USE_HASHTAB
88 hashtabsize = other.hashtabsize;
90 hashmask = other.hashmask;
91 hashtab.resize(hashtabsize);
92 epvector::const_iterator osb = other.seq.begin();
93 for (unsigned i=0; i<hashtabsize; ++i) {
95 for (epplist::const_iterator cit=other.hashtab[i].begin();
96 cit!=other.hashtab[i].end(); ++cit) {
97 hashtab[i].push_back(seq.begin()+((*cit)-osb));
103 #endif // EXPAIRSEQ_USE_HASHTAB
108 // other constructors
111 expairseq::expairseq(const ex &lh, const ex &rh)
113 construct_from_2_ex(lh,rh);
114 GINAC_ASSERT(is_canonical());
117 expairseq::expairseq(const exvector &v)
119 construct_from_exvector(v);
120 GINAC_ASSERT(is_canonical());
123 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
126 GINAC_ASSERT(is_a<numeric>(oc));
127 construct_from_epvector(v, do_index_renaming);
128 GINAC_ASSERT(is_canonical());
131 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
134 GINAC_ASSERT(vp.get()!=0);
135 GINAC_ASSERT(is_a<numeric>(oc));
136 construct_from_epvector(*vp, do_index_renaming);
137 GINAC_ASSERT(is_canonical());
144 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
146 inherited::read_archive(n, sym_lst);
147 archive_node::archive_node_cit first = n.find_first("rest");
148 archive_node::archive_node_cit last = n.find_last("coeff");
150 seq.reserve((last-first)/2);
152 for (archive_node::archive_node_cit loc = first; loc < last;) {
155 n.find_ex_by_loc(loc++, rest, sym_lst);
156 n.find_ex_by_loc(loc++, coeff, sym_lst);
157 seq.push_back(expair(rest, coeff));
160 n.find_ex("overall_coeff", overall_coeff, sym_lst);
163 GINAC_ASSERT(is_canonical());
166 void expairseq::archive(archive_node &n) const
168 inherited::archive(n);
169 epvector::const_iterator i = seq.begin(), iend = seq.end();
171 n.add_ex("rest", i->rest);
172 n.add_ex("coeff", i->coeff);
175 n.add_ex("overall_coeff", overall_coeff);
180 // functions overriding virtual functions from base classes
185 void expairseq::do_print(const print_context & c, unsigned level) const
188 printseq(c, ',', precedence(), level);
192 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
194 c.s << std::string(level, ' ') << class_name() << " @" << this
195 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
196 << ", nops=" << nops()
198 size_t num = seq.size();
199 for (size_t i=0; i<num; ++i) {
200 seq[i].rest.print(c, level + c.delta_indent);
201 seq[i].coeff.print(c, level + c.delta_indent);
203 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
205 if (!overall_coeff.is_equal(default_overall_coeff())) {
206 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
207 << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
208 overall_coeff.print(c, level + c.delta_indent);
210 c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
211 #if EXPAIRSEQ_USE_HASHTAB
212 c.s << std::string(level + c.delta_indent,' ')
213 << "hashtab size " << hashtabsize << std::endl;
214 if (hashtabsize == 0) return;
216 unsigned count[MAXCOUNT+1];
217 for (int i=0; i<MAXCOUNT+1; ++i)
219 unsigned this_bin_fill;
220 unsigned cum_fill_sq = 0;
221 unsigned cum_fill = 0;
222 for (unsigned i=0; i<hashtabsize; ++i) {
224 if (hashtab[i].size() > 0) {
225 c.s << std::string(level + c.delta_indent, ' ')
226 << "bin " << i << " with entries ";
227 for (epplist::const_iterator it=hashtab[i].begin();
228 it!=hashtab[i].end(); ++it) {
229 c.s << *it-seq.begin() << " ";
233 cum_fill += this_bin_fill;
234 cum_fill_sq += this_bin_fill*this_bin_fill;
236 if (this_bin_fill<MAXCOUNT)
237 ++count[this_bin_fill];
243 double lambda = (1.0*seq.size()) / hashtabsize;
244 for (int k=0; k<MAXCOUNT; ++k) {
247 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
249 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
250 << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
251 << int(prob*1000)/10.0 << ")" << std::endl;
253 c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
254 << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
255 << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
257 c.s << std::string(level + c.delta_indent, ' ') << "variance: "
258 << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
260 c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
261 << (1.0*cum_fill)/hashtabsize
262 << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
263 #endif // EXPAIRSEQ_USE_HASHTAB
266 bool expairseq::info(unsigned inf) const
269 case info_flags::expanded:
270 return (flags & status_flags::expanded);
271 case info_flags::has_indices: {
272 if (flags & status_flags::has_indices)
274 else if (flags & status_flags::has_no_indices)
276 for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
277 if (i->rest.info(info_flags::has_indices)) {
278 this->setflag(status_flags::has_indices);
279 this->clearflag(status_flags::has_no_indices);
283 this->clearflag(status_flags::has_indices);
284 this->setflag(status_flags::has_no_indices);
288 return inherited::info(inf);
291 size_t expairseq::nops() const
293 if (overall_coeff.is_equal(default_overall_coeff()))
299 ex expairseq::op(size_t i) const
302 return recombine_pair_to_ex(seq[i]);
303 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
304 return overall_coeff;
307 ex expairseq::map(map_function &f) const
309 std::auto_ptr<epvector> v(new epvector);
310 v->reserve(seq.size()+1);
312 epvector::const_iterator cit = seq.begin(), last = seq.end();
313 while (cit != last) {
314 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
318 if (overall_coeff.is_equal(default_overall_coeff()))
319 return thisexpairseq(v, default_overall_coeff(), true);
321 ex newcoeff = f(overall_coeff);
322 if(is_a<numeric>(newcoeff))
323 return thisexpairseq(v, newcoeff, true);
325 v->push_back(split_ex_to_pair(newcoeff));
326 return thisexpairseq(v, default_overall_coeff(), true);
331 /** Perform coefficient-wise automatic term rewriting rules in this class. */
332 ex expairseq::eval(int level) const
334 if ((level==1) && (flags &status_flags::evaluated))
337 std::auto_ptr<epvector> vp = evalchildren(level);
341 return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
344 epvector* conjugateepvector(const epvector&epv)
346 epvector *newepv = 0;
347 for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
349 newepv->push_back(i->conjugate());
352 expair x = i->conjugate();
353 if (x.is_equal(*i)) {
356 newepv = new epvector;
357 newepv->reserve(epv.size());
358 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
359 newepv->push_back(*j);
361 newepv->push_back(x);
366 ex expairseq::conjugate() const
368 epvector* newepv = conjugateepvector(seq);
369 ex x = overall_coeff.conjugate();
370 if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
373 ex result = thisexpairseq(newepv ? *newepv : seq, x);
380 bool expairseq::is_polynomial(const ex & var) const
382 if (!is_exactly_a<add>(*this) && !is_exactly_a<mul>(*this))
383 return basic::is_polynomial(var);
384 for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
385 if (!(i->rest).is_polynomial(var))
391 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
393 // This differs from basic::match() because we want "a+b+c+d" to
394 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
396 if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
398 // Check whether global wildcard (one that matches the "rest of the
399 // expression", like "*" above) is present
400 bool has_global_wildcard = false;
402 for (size_t i=0; i<pattern.nops(); i++) {
403 if (is_exactly_a<wildcard>(pattern.op(i))) {
404 has_global_wildcard = true;
405 global_wildcard = pattern.op(i);
410 // Unfortunately, this is an O(N^2) operation because we can't
411 // sort the pattern in a useful way...
416 for (size_t i=0; i<nops(); i++)
417 ops.push_back(op(i));
419 // Now, for every term of the pattern, look for a matching term in
420 // the expression and remove the match
421 for (size_t i=0; i<pattern.nops(); i++) {
422 ex p = pattern.op(i);
423 if (has_global_wildcard && p.is_equal(global_wildcard))
425 exvector::iterator it = ops.begin(), itend = ops.end();
426 while (it != itend) {
427 if (it->match(p, repl_lst)) {
433 return false; // no match found
437 if (has_global_wildcard) {
439 // Assign all the remaining terms to the global wildcard (unless
440 // it has already been matched before, in which case the matches
442 size_t num = ops.size();
443 std::auto_ptr<epvector> vp(new epvector);
445 for (size_t i=0; i<num; i++)
446 vp->push_back(split_ex_to_pair(ops[i]));
447 ex rest = thisexpairseq(vp, default_overall_coeff());
448 for (exmap::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
449 if (it->first.is_equal(global_wildcard))
450 return rest.is_equal(it->second);
452 repl_lst[global_wildcard] = rest;
457 // No global wildcard, then the match fails if there are any
458 // unmatched terms left
462 return inherited::match(pattern, repl_lst);
465 ex expairseq::subs(const exmap & m, unsigned options) const
467 std::auto_ptr<epvector> vp = subschildren(m, options);
469 return ex_to<basic>(thisexpairseq(vp, overall_coeff, true));
470 else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
471 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
473 return subs_one_level(m, options);
478 int expairseq::compare_same_type(const basic &other) const
480 GINAC_ASSERT(is_a<expairseq>(other));
481 const expairseq &o = static_cast<const expairseq &>(other);
485 // compare number of elements
486 if (seq.size() != o.seq.size())
487 return (seq.size()<o.seq.size()) ? -1 : 1;
489 // compare overall_coeff
490 cmpval = overall_coeff.compare(o.overall_coeff);
494 #if EXPAIRSEQ_USE_HASHTAB
495 GINAC_ASSERT(hashtabsize==o.hashtabsize);
496 if (hashtabsize==0) {
497 #endif // EXPAIRSEQ_USE_HASHTAB
498 epvector::const_iterator cit1 = seq.begin();
499 epvector::const_iterator cit2 = o.seq.begin();
500 epvector::const_iterator last1 = seq.end();
501 epvector::const_iterator last2 = o.seq.end();
503 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
504 cmpval = (*cit1).compare(*cit2);
505 if (cmpval!=0) return cmpval;
508 GINAC_ASSERT(cit1==last1);
509 GINAC_ASSERT(cit2==last2);
512 #if EXPAIRSEQ_USE_HASHTAB
515 // compare number of elements in each hashtab entry
516 for (unsigned i=0; i<hashtabsize; ++i) {
517 unsigned cursize=hashtab[i].size();
518 if (cursize != o.hashtab[i].size())
519 return (cursize < o.hashtab[i].size()) ? -1 : 1;
522 // compare individual (sorted) hashtab entries
523 for (unsigned i=0; i<hashtabsize; ++i) {
524 unsigned sz = hashtab[i].size();
526 const epplist &eppl1 = hashtab[i];
527 const epplist &eppl2 = o.hashtab[i];
528 epplist::const_iterator it1 = eppl1.begin();
529 epplist::const_iterator it2 = eppl2.begin();
530 while (it1!=eppl1.end()) {
531 cmpval = (*(*it1)).compare(*(*it2));
541 #endif // EXPAIRSEQ_USE_HASHTAB
544 bool expairseq::is_equal_same_type(const basic &other) const
546 const expairseq &o = static_cast<const expairseq &>(other);
548 // compare number of elements
549 if (seq.size()!=o.seq.size())
552 // compare overall_coeff
553 if (!overall_coeff.is_equal(o.overall_coeff))
556 #if EXPAIRSEQ_USE_HASHTAB
557 // compare number of elements in each hashtab entry
558 if (hashtabsize!=o.hashtabsize) {
559 std::cout << "this:" << std::endl;
560 print(print_tree(std::cout));
561 std::cout << "other:" << std::endl;
562 other.print(print_tree(std::cout));
565 GINAC_ASSERT(hashtabsize==o.hashtabsize);
567 if (hashtabsize==0) {
568 #endif // EXPAIRSEQ_USE_HASHTAB
569 epvector::const_iterator cit1 = seq.begin();
570 epvector::const_iterator cit2 = o.seq.begin();
571 epvector::const_iterator last1 = seq.end();
573 while (cit1!=last1) {
574 if (!(*cit1).is_equal(*cit2)) return false;
580 #if EXPAIRSEQ_USE_HASHTAB
583 for (unsigned i=0; i<hashtabsize; ++i) {
584 if (hashtab[i].size() != o.hashtab[i].size())
588 // compare individual sorted hashtab entries
589 for (unsigned i=0; i<hashtabsize; ++i) {
590 unsigned sz = hashtab[i].size();
592 const epplist &eppl1 = hashtab[i];
593 const epplist &eppl2 = o.hashtab[i];
594 epplist::const_iterator it1 = eppl1.begin();
595 epplist::const_iterator it2 = eppl2.begin();
596 while (it1!=eppl1.end()) {
597 if (!(*(*it1)).is_equal(*(*it2))) return false;
605 #endif // EXPAIRSEQ_USE_HASHTAB
608 unsigned expairseq::return_type() const
610 return return_types::noncommutative_composite;
613 unsigned expairseq::calchash() const
615 unsigned v = make_hash_seed(typeid(*this));
616 epvector::const_iterator i = seq.begin();
617 const epvector::const_iterator end = seq.end();
619 v ^= i->rest.gethash();
620 #if !EXPAIRSEQ_USE_HASHTAB
621 // rotation spoils commutativity!
623 v ^= i->coeff.gethash();
624 #endif // !EXPAIRSEQ_USE_HASHTAB
628 v ^= overall_coeff.gethash();
630 // store calculated hash value only if object is already evaluated
631 if (flags &status_flags::evaluated) {
632 setflag(status_flags::hash_calculated);
639 ex expairseq::expand(unsigned options) const
641 std::auto_ptr<epvector> vp = expandchildren(options);
643 return thisexpairseq(vp, overall_coeff);
645 // The terms have not changed, so it is safe to declare this expanded
646 return (options == 0) ? setflag(status_flags::expanded) : *this;
651 // new virtual functions which can be overridden by derived classes
656 /** Create an object of this type.
657 * This method works similar to a constructor. It is useful because expairseq
658 * has (at least) two possible different semantics but we want to inherit
659 * methods thus avoiding code duplication. Sometimes a method in expairseq
660 * has to create a new one of the same semantics, which cannot be done by a
661 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
662 * order for this trick to work a derived class must of course override this
664 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
666 return expairseq(v, oc, do_index_renaming);
669 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
671 return expairseq(vp, oc, do_index_renaming);
674 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
677 p.rest.print(c, precedence());
679 p.coeff.print(c, precedence());
683 void expairseq::printseq(const print_context & c, char delim,
684 unsigned this_precedence,
685 unsigned upper_precedence) const
687 if (this_precedence <= upper_precedence)
689 epvector::const_iterator it, it_last = seq.end() - 1;
690 for (it=seq.begin(); it!=it_last; ++it) {
691 printpair(c, *it, this_precedence);
694 printpair(c, *it, this_precedence);
695 if (!overall_coeff.is_equal(default_overall_coeff())) {
697 overall_coeff.print(c, this_precedence);
700 if (this_precedence <= upper_precedence)
705 /** Form an expair from an ex, using the corresponding semantics.
706 * @see expairseq::recombine_pair_to_ex() */
707 expair expairseq::split_ex_to_pair(const ex &e) const
709 return expair(e,_ex1);
713 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
716 GINAC_ASSERT(is_exactly_a<numeric>(c));
722 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
725 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
726 GINAC_ASSERT(is_exactly_a<numeric>(c));
728 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
732 /** Form an ex out of an expair, using the corresponding semantics.
733 * @see expairseq::split_ex_to_pair() */
734 ex expairseq::recombine_pair_to_ex(const expair &p) const
736 return lst(p.rest,p.coeff);
739 bool expairseq::expair_needs_further_processing(epp it)
741 #if EXPAIRSEQ_USE_HASHTAB
742 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
743 #endif // EXPAIRSEQ_USE_HASHTAB
747 ex expairseq::default_overall_coeff() const
752 void expairseq::combine_overall_coeff(const ex &c)
754 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
755 GINAC_ASSERT(is_exactly_a<numeric>(c));
756 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
759 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
761 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
762 GINAC_ASSERT(is_exactly_a<numeric>(c1));
763 GINAC_ASSERT(is_exactly_a<numeric>(c2));
764 overall_coeff = ex_to<numeric>(overall_coeff).
765 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
768 bool expairseq::can_make_flat(const expair &p) const
775 // non-virtual functions in this class
778 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
784 construct_from_exvector(v);
785 #if EXPAIRSEQ_USE_HASHTAB
786 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
787 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
788 #endif // EXPAIRSEQ_USE_HASHTAB
791 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
793 if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
794 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
795 #if EXPAIRSEQ_USE_HASHTAB
796 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
797 ex_to<expairseq>(rh).seq.size();
798 if (calc_hashtabsize(totalsize)!=0) {
799 construct_from_2_ex_via_exvector(lh,rh);
801 #endif // EXPAIRSEQ_USE_HASHTAB
802 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
803 rh.info(info_flags::has_indices)) {
804 ex newrh=rename_dummy_indices_uniquely(lh, rh);
805 construct_from_2_expairseq(ex_to<expairseq>(lh),
806 ex_to<expairseq>(newrh));
809 construct_from_2_expairseq(ex_to<expairseq>(lh),
810 ex_to<expairseq>(rh));
811 #if EXPAIRSEQ_USE_HASHTAB
813 #endif // EXPAIRSEQ_USE_HASHTAB
816 #if EXPAIRSEQ_USE_HASHTAB
817 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
818 if (calc_hashtabsize(totalsize)!=0) {
819 construct_from_2_ex_via_exvector(lh, rh);
821 #endif // EXPAIRSEQ_USE_HASHTAB
822 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
823 #if EXPAIRSEQ_USE_HASHTAB
825 #endif // EXPAIRSEQ_USE_HASHTAB
828 } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
829 #if EXPAIRSEQ_USE_HASHTAB
830 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
831 if (calc_hashtabsize(totalsize)!=0) {
832 construct_from_2_ex_via_exvector(lh,rh);
834 #endif // EXPAIRSEQ_USE_HASHTAB
835 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
836 #if EXPAIRSEQ_USE_HASHTAB
838 #endif // EXPAIRSEQ_USE_HASHTAB
842 #if EXPAIRSEQ_USE_HASHTAB
843 if (calc_hashtabsize(2)!=0) {
844 construct_from_2_ex_via_exvector(lh,rh);
848 #endif // EXPAIRSEQ_USE_HASHTAB
850 if (is_exactly_a<numeric>(lh)) {
851 if (is_exactly_a<numeric>(rh)) {
852 combine_overall_coeff(lh);
853 combine_overall_coeff(rh);
855 combine_overall_coeff(lh);
856 seq.push_back(split_ex_to_pair(rh));
859 if (is_exactly_a<numeric>(rh)) {
860 combine_overall_coeff(rh);
861 seq.push_back(split_ex_to_pair(lh));
863 expair p1 = split_ex_to_pair(lh);
864 expair p2 = split_ex_to_pair(rh);
866 int cmpval = p1.rest.compare(p2.rest);
868 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
869 if (!ex_to<numeric>(p1.coeff).is_zero()) {
870 // no further processing is necessary, since this
871 // one element will usually be recombined in eval()
888 void expairseq::construct_from_2_expairseq(const expairseq &s1,
891 combine_overall_coeff(s1.overall_coeff);
892 combine_overall_coeff(s2.overall_coeff);
894 epvector::const_iterator first1 = s1.seq.begin();
895 epvector::const_iterator last1 = s1.seq.end();
896 epvector::const_iterator first2 = s2.seq.begin();
897 epvector::const_iterator last2 = s2.seq.end();
899 seq.reserve(s1.seq.size()+s2.seq.size());
901 bool needs_further_processing=false;
903 while (first1!=last1 && first2!=last2) {
904 int cmpval = (*first1).rest.compare((*first2).rest);
908 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
909 add(ex_to<numeric>(first2->coeff));
910 if (!newcoeff.is_zero()) {
911 seq.push_back(expair(first1->rest,newcoeff));
912 if (expair_needs_further_processing(seq.end()-1)) {
913 needs_further_processing = true;
918 } else if (cmpval<0) {
919 seq.push_back(*first1);
922 seq.push_back(*first2);
927 while (first1!=last1) {
928 seq.push_back(*first1);
931 while (first2!=last2) {
932 seq.push_back(*first2);
936 if (needs_further_processing) {
939 construct_from_epvector(v);
943 void expairseq::construct_from_expairseq_ex(const expairseq &s,
946 combine_overall_coeff(s.overall_coeff);
947 if (is_exactly_a<numeric>(e)) {
948 combine_overall_coeff(e);
953 epvector::const_iterator first = s.seq.begin();
954 epvector::const_iterator last = s.seq.end();
955 expair p = split_ex_to_pair(e);
957 seq.reserve(s.seq.size()+1);
958 bool p_pushed = false;
960 bool needs_further_processing=false;
962 // merge p into s.seq
963 while (first!=last) {
964 int cmpval = (*first).rest.compare(p.rest);
967 const numeric &newcoeff = ex_to<numeric>(first->coeff).
968 add(ex_to<numeric>(p.coeff));
969 if (!newcoeff.is_zero()) {
970 seq.push_back(expair(first->rest,newcoeff));
971 if (expair_needs_further_processing(seq.end()-1))
972 needs_further_processing = true;
977 } else if (cmpval<0) {
978 seq.push_back(*first);
988 // while loop exited because p was pushed, now push rest of s.seq
989 while (first!=last) {
990 seq.push_back(*first);
994 // while loop exited because s.seq was pushed, now push p
998 if (needs_further_processing) {
1001 construct_from_epvector(v);
1005 void expairseq::construct_from_exvector(const exvector &v)
1007 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1008 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1009 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1010 // (same for (+,*) -> (*,^)
1013 #if EXPAIRSEQ_USE_HASHTAB
1014 combine_same_terms();
1017 combine_same_terms_sorted_seq();
1018 #endif // EXPAIRSEQ_USE_HASHTAB
1021 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1023 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1024 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1025 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1026 // (same for (+,*) -> (*,^)
1028 make_flat(v, do_index_renaming);
1029 #if EXPAIRSEQ_USE_HASHTAB
1030 combine_same_terms();
1033 combine_same_terms_sorted_seq();
1034 #endif // EXPAIRSEQ_USE_HASHTAB
1037 /** Combine this expairseq with argument exvector.
1038 * It cares for associativity as well as for special handling of numerics. */
1039 void expairseq::make_flat(const exvector &v)
1041 exvector::const_iterator cit;
1043 // count number of operands which are of same expairseq derived type
1044 // and their cumulative number of operands
1045 int nexpairseqs = 0;
1047 bool do_idx_rename = false;
1050 while (cit!=v.end()) {
1051 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1053 noperands += ex_to<expairseq>(*cit).seq.size();
1055 if (is_a<mul>(*this) && (!do_idx_rename) &&
1056 cit->info(info_flags::has_indices))
1057 do_idx_rename = true;
1061 // reserve seq and coeffseq which will hold all operands
1062 seq.reserve(v.size()+noperands-nexpairseqs);
1064 // copy elements and split off numerical part
1065 make_flat_inserter mf(v, do_idx_rename);
1067 while (cit!=v.end()) {
1068 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1069 ex newfactor = mf.handle_factor(*cit, _ex1);
1070 const expairseq &subseqref = ex_to<expairseq>(newfactor);
1071 combine_overall_coeff(subseqref.overall_coeff);
1072 epvector::const_iterator cit_s = subseqref.seq.begin();
1073 while (cit_s!=subseqref.seq.end()) {
1074 seq.push_back(*cit_s);
1078 if (is_exactly_a<numeric>(*cit))
1079 combine_overall_coeff(*cit);
1081 ex newfactor = mf.handle_factor(*cit, _ex1);
1082 seq.push_back(split_ex_to_pair(newfactor));
1089 /** Combine this expairseq with argument epvector.
1090 * It cares for associativity as well as for special handling of numerics. */
1091 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1093 epvector::const_iterator cit;
1095 // count number of operands which are of same expairseq derived type
1096 // and their cumulative number of operands
1097 int nexpairseqs = 0;
1099 bool really_need_rename_inds = false;
1102 while (cit!=v.end()) {
1103 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
1105 noperands += ex_to<expairseq>(cit->rest).seq.size();
1107 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1108 cit->rest.info(info_flags::has_indices))
1109 really_need_rename_inds = true;
1112 do_index_renaming = do_index_renaming && really_need_rename_inds;
1114 // reserve seq and coeffseq which will hold all operands
1115 seq.reserve(v.size()+noperands-nexpairseqs);
1116 make_flat_inserter mf(v, do_index_renaming);
1118 // copy elements and split off numerical part
1120 while (cit!=v.end()) {
1121 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
1122 this->can_make_flat(*cit)) {
1123 ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1124 const expairseq &subseqref = ex_to<expairseq>(newrest);
1125 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1126 ex_to<numeric>(cit->coeff));
1127 epvector::const_iterator cit_s = subseqref.seq.begin();
1128 while (cit_s!=subseqref.seq.end()) {
1129 seq.push_back(expair(cit_s->rest,
1130 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1131 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1136 if (cit->is_canonical_numeric())
1137 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1139 ex rest = cit->rest;
1140 ex newrest = mf.handle_factor(rest, cit->coeff);
1141 if (are_ex_trivially_equal(newrest, rest))
1142 seq.push_back(*cit);
1144 seq.push_back(expair(newrest, cit->coeff));
1151 /** Brings this expairseq into a sorted (canonical) form. */
1152 void expairseq::canonicalize()
1154 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1158 /** Compact a presorted expairseq by combining all matching expairs to one
1159 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1161 void expairseq::combine_same_terms_sorted_seq()
1166 bool needs_further_processing = false;
1168 epvector::iterator itin1 = seq.begin();
1169 epvector::iterator itin2 = itin1+1;
1170 epvector::iterator itout = itin1;
1171 epvector::iterator last = seq.end();
1172 // must_copy will be set to true the first time some combination is
1173 // possible from then on the sequence has changed and must be compacted
1174 bool must_copy = false;
1175 while (itin2!=last) {
1176 if (itin1->rest.compare(itin2->rest)==0) {
1177 itin1->coeff = ex_to<numeric>(itin1->coeff).
1178 add_dyn(ex_to<numeric>(itin2->coeff));
1179 if (expair_needs_further_processing(itin1))
1180 needs_further_processing = true;
1183 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1192 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1198 seq.erase(itout,last);
1200 if (needs_further_processing) {
1203 construct_from_epvector(v);
1207 #if EXPAIRSEQ_USE_HASHTAB
1209 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1212 unsigned nearest_power_of_2 = 1 << log2(sz);
1213 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1214 // size = nearest_power_of_2*hashtabfactor;
1215 size = nearest_power_of_2/hashtabfactor;
1216 if (size<minhashtabsize)
1219 // hashtabsize must be a power of 2
1220 GINAC_ASSERT((1U << log2(size))==size);
1224 unsigned expairseq::calc_hashindex(const ex &e) const
1226 // calculate hashindex
1228 if (is_a<numeric>(e)) {
1229 hashindex = hashmask;
1231 hashindex = e.gethash() & hashmask;
1232 // last hashtab entry is reserved for numerics
1233 if (hashindex==hashmask) hashindex = 0;
1235 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1239 void expairseq::shrink_hashtab()
1241 unsigned new_hashtabsize;
1242 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1243 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1244 if (new_hashtabsize==0) {
1251 // shrink by a factor of 2
1252 unsigned half_hashtabsize = hashtabsize/2;
1253 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1254 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1255 // special treatment for numeric hashes
1256 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1257 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1258 hashtab.resize(half_hashtabsize);
1259 hashtabsize = half_hashtabsize;
1260 hashmask = hashtabsize-1;
1264 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1267 return; // nothing to do
1269 // calculate hashindex of element to be deleted
1270 unsigned hashindex = calc_hashindex((*element).rest);
1272 // find it in hashtab and remove it
1273 epplist &eppl = hashtab[hashindex];
1274 epplist::iterator epplit = eppl.begin();
1275 bool erased = false;
1276 while (epplit!=eppl.end()) {
1277 if (*epplit == element) {
1285 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1286 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1288 unsigned hashindex = calc_hashindex(element->rest);
1289 epplist &eppl = hashtab[hashindex];
1290 epplist::iterator epplit = eppl.begin();
1291 bool erased = false;
1292 while (epplit!=eppl.end()) {
1293 if (*epplit == element) {
1300 GINAC_ASSERT(erased);
1302 GINAC_ASSERT(erased);
1305 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1306 epvector::iterator newpos)
1308 GINAC_ASSERT(hashtabsize!=0);
1310 // calculate hashindex of element which was moved
1311 unsigned hashindex=calc_hashindex((*newpos).rest);
1313 // find it in hashtab and modify it
1314 epplist &eppl = hashtab[hashindex];
1315 epplist::iterator epplit = eppl.begin();
1316 while (epplit!=eppl.end()) {
1317 if (*epplit == oldpos) {
1323 GINAC_ASSERT(epplit!=eppl.end());
1326 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1328 epplist::const_iterator current = eppl.begin();
1329 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1332 eppl.insert(current,elem);
1335 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1336 epvector::iterator &last_non_zero,
1337 std::vector<bool> &touched,
1338 unsigned &number_of_zeroes)
1340 epp current = seq.begin();
1342 while (current!=first_numeric) {
1343 if (is_exactly_a<numeric>(current->rest)) {
1345 iter_swap(current,first_numeric);
1347 // calculate hashindex
1348 unsigned currenthashindex = calc_hashindex(current->rest);
1350 // test if there is already a matching expair in the hashtab-list
1351 epplist &eppl=hashtab[currenthashindex];
1352 epplist::iterator epplit = eppl.begin();
1353 while (epplit!=eppl.end()) {
1354 if (current->rest.is_equal((*epplit)->rest))
1358 if (epplit==eppl.end()) {
1359 // no matching expair found, append this to end of list
1360 sorted_insert(eppl,current);
1363 // epplit points to a matching expair, combine it with current
1364 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1365 add_dyn(ex_to<numeric>(current->coeff));
1367 // move obsolete current expair to end by swapping with last_non_zero element
1368 // if this was a numeric, it is swapped with the expair before first_numeric
1369 iter_swap(current,last_non_zero);
1371 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1374 // test if combined term has coeff 0 and can be removed is done later
1375 touched[(*epplit)-seq.begin()] = true;
1381 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1382 epvector::iterator &last_non_zero,
1383 std::vector<bool> &touched,
1384 unsigned &number_of_zeroes)
1386 // move terms with coeff 0 to end and remove them from hashtab
1387 // check only those elements which have been touched
1388 epp current = seq.begin();
1390 while (current!=first_numeric) {
1394 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1398 remove_hashtab_entry(current);
1400 // move element to the end, unless it is already at the end
1401 if (current!=last_non_zero) {
1402 iter_swap(current,last_non_zero);
1404 bool numeric_swapped = first_numeric!=last_non_zero;
1405 if (numeric_swapped)
1406 iter_swap(first_numeric,current);
1407 epvector::iterator changed_entry;
1409 if (numeric_swapped)
1410 changed_entry = first_numeric;
1412 changed_entry = last_non_zero;
1417 if (first_numeric!=current) {
1419 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1420 move_hashtab_entry(changed_entry,current);
1421 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1430 GINAC_ASSERT(i==current-seq.begin());
1433 /** True if one of the coeffs vanishes, otherwise false.
1434 * This would be an invariant violation, so this should only be used for
1435 * debugging purposes. */
1436 bool expairseq::has_coeff_0() const
1438 epvector::const_iterator i = seq.begin(), end = seq.end();
1440 if (i->coeff.is_zero())
1447 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1448 epvector::const_iterator last_non_zero)
1450 if (first_numeric == seq.end()) return; // no numerics
1452 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1453 while (current != last) {
1454 sorted_insert(hashtab[hashmask], current);
1459 void expairseq::combine_same_terms()
1461 // combine same terms, drop term with coeff 0, move numerics to end
1463 // calculate size of hashtab
1464 hashtabsize = calc_hashtabsize(seq.size());
1466 // hashtabsize is a power of 2
1467 hashmask = hashtabsize-1;
1471 hashtab.resize(hashtabsize);
1473 if (hashtabsize==0) {
1475 combine_same_terms_sorted_seq();
1476 GINAC_ASSERT(!has_coeff_0());
1480 // iterate through seq, move numerics to end,
1481 // fill hashtab and combine same terms
1482 epvector::iterator first_numeric = seq.end();
1483 epvector::iterator last_non_zero = seq.end()-1;
1485 size_t num = seq.size();
1486 std::vector<bool> touched(num);
1488 unsigned number_of_zeroes = 0;
1490 GINAC_ASSERT(!has_coeff_0());
1491 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1493 // there should not be any terms with coeff 0 from the beginning,
1494 // so it should be safe to skip this step
1495 if (number_of_zeroes!=0) {
1496 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1499 add_numerics_to_hashtab(first_numeric,last_non_zero);
1501 // pop zero elements
1502 for (unsigned i=0; i<number_of_zeroes; ++i) {
1506 // shrink hashtabsize to calculated value
1507 GINAC_ASSERT(!has_coeff_0());
1511 GINAC_ASSERT(!has_coeff_0());
1514 #endif // EXPAIRSEQ_USE_HASHTAB
1516 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1517 * debugging or in assertions since being sorted is an invariance. */
1518 bool expairseq::is_canonical() const
1520 if (seq.size() <= 1)
1523 #if EXPAIRSEQ_USE_HASHTAB
1524 if (hashtabsize > 0) return 1; // not canoncalized
1525 #endif // EXPAIRSEQ_USE_HASHTAB
1527 epvector::const_iterator it = seq.begin(), itend = seq.end();
1528 epvector::const_iterator it_last = it;
1529 for (++it; it!=itend; it_last=it, ++it) {
1530 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1531 if (!is_exactly_a<numeric>(it_last->rest) ||
1532 !is_exactly_a<numeric>(it->rest)) {
1533 // double test makes it easier to set a breakpoint...
1534 if (!is_exactly_a<numeric>(it_last->rest) ||
1535 !is_exactly_a<numeric>(it->rest)) {
1536 printpair(std::clog, *it_last, 0);
1538 printpair(std::clog, *it, 0);
1540 std::clog << "pair1:" << std::endl;
1541 it_last->rest.print(print_tree(std::clog));
1542 it_last->coeff.print(print_tree(std::clog));
1543 std::clog << "pair2:" << std::endl;
1544 it->rest.print(print_tree(std::clog));
1545 it->coeff.print(print_tree(std::clog));
1555 /** Member-wise expand the expairs in this sequence.
1557 * @see expairseq::expand()
1558 * @return pointer to epvector containing expanded pairs or zero pointer,
1559 * if no members were changed. */
1560 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1562 const epvector::const_iterator last = seq.end();
1563 epvector::const_iterator cit = seq.begin();
1565 const ex &expanded_ex = cit->rest.expand(options);
1566 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1568 // something changed, copy seq, eval and return it
1569 std::auto_ptr<epvector> s(new epvector);
1570 s->reserve(seq.size());
1572 // copy parts of seq which are known not to have changed
1573 epvector::const_iterator cit2 = seq.begin();
1575 s->push_back(*cit2);
1579 // copy first changed element
1580 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1585 while (cit2!=last) {
1586 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1595 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1599 /** Member-wise evaluate the expairs in this sequence.
1601 * @see expairseq::eval()
1602 * @return pointer to epvector containing evaluated pairs or zero pointer,
1603 * if no members were changed. */
1604 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1606 // returns a NULL pointer if nothing had to be evaluated
1607 // returns a pointer to a newly created epvector otherwise
1608 // (which has to be deleted somewhere else)
1611 return std::auto_ptr<epvector>(0);
1613 if (level == -max_recursion_level)
1614 throw(std::runtime_error("max recursion level reached"));
1617 epvector::const_iterator last = seq.end();
1618 epvector::const_iterator cit = seq.begin();
1620 const ex &evaled_ex = cit->rest.eval(level);
1621 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1623 // something changed, copy seq, eval and return it
1624 std::auto_ptr<epvector> s(new epvector);
1625 s->reserve(seq.size());
1627 // copy parts of seq which are known not to have changed
1628 epvector::const_iterator cit2=seq.begin();
1630 s->push_back(*cit2);
1634 // copy first changed element
1635 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1640 while (cit2!=last) {
1641 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1650 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1653 /** Member-wise substitute in this sequence.
1655 * @see expairseq::subs()
1656 * @return pointer to epvector containing pairs after application of subs,
1657 * or NULL pointer if no members were changed. */
1658 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1660 // When any of the objects to be substituted is a product or power
1661 // we have to recombine the pairs because the numeric coefficients may
1662 // be part of the search pattern.
1663 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1665 // Search the list of substitutions and cache our findings
1666 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1667 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1668 options |= subs_options::pattern_is_product;
1672 if (!(options & subs_options::pattern_is_product))
1673 options |= subs_options::pattern_is_not_product;
1676 if (options & subs_options::pattern_is_product) {
1678 // Substitute in the recombined pairs
1679 epvector::const_iterator cit = seq.begin(), last = seq.end();
1680 while (cit != last) {
1682 const ex &orig_ex = recombine_pair_to_ex(*cit);
1683 const ex &subsed_ex = orig_ex.subs(m, options);
1684 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1686 // Something changed, copy seq, subs and return it
1687 std::auto_ptr<epvector> s(new epvector);
1688 s->reserve(seq.size());
1690 // Copy parts of seq which are known not to have changed
1691 s->insert(s->begin(), seq.begin(), cit);
1693 // Copy first changed element
1694 s->push_back(split_ex_to_pair(subsed_ex));
1698 while (cit != last) {
1699 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1710 // Substitute only in the "rest" part of the pairs
1711 epvector::const_iterator cit = seq.begin(), last = seq.end();
1712 while (cit != last) {
1714 const ex &subsed_ex = cit->rest.subs(m, options);
1715 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1717 // Something changed, copy seq, subs and return it
1718 std::auto_ptr<epvector> s(new epvector);
1719 s->reserve(seq.size());
1721 // Copy parts of seq which are known not to have changed
1722 s->insert(s->begin(), seq.begin(), cit);
1724 // Copy first changed element
1725 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1729 while (cit != last) {
1730 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1740 // Nothing has changed
1741 return std::auto_ptr<epvector>(0);
1745 // static member variables
1748 #if EXPAIRSEQ_USE_HASHTAB
1749 unsigned expairseq::maxhashtabsize = 0x4000000U;
1750 unsigned expairseq::minhashtabsize = 0x1000U;
1751 unsigned expairseq::hashtabfactor = 1;
1752 #endif // EXPAIRSEQ_USE_HASHTAB
1754 } // namespace GiNaC