1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2014 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);
378 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
380 // This differs from basic::match() because we want "a+b+c+d" to
381 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
383 if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
385 // Check whether global wildcard (one that matches the "rest of the
386 // expression", like "*" above) is present
387 bool has_global_wildcard = false;
389 for (size_t i=0; i<pattern.nops(); i++) {
390 if (is_exactly_a<wildcard>(pattern.op(i))) {
391 has_global_wildcard = true;
392 global_wildcard = pattern.op(i);
397 // Even if the expression does not match the pattern, some of
398 // its subexpressions could match it. For example, x^5*y^(-1)
399 // does not match the pattern $0^5, but its subexpression x^5
400 // does. So, save repl_lst in order to not add bogus entries.
401 exmap tmp_repl = repl_lst;
403 // Unfortunately, this is an O(N^2) operation because we can't
404 // sort the pattern in a useful way...
409 for (size_t i=0; i<nops(); i++)
410 ops.push_back(op(i));
412 // Now, for every term of the pattern, look for a matching term in
413 // the expression and remove the match
414 for (size_t i=0; i<pattern.nops(); i++) {
415 ex p = pattern.op(i);
416 if (has_global_wildcard && p.is_equal(global_wildcard))
418 exvector::iterator it = ops.begin(), itend = ops.end();
419 while (it != itend) {
420 if (it->match(p, tmp_repl)) {
426 return false; // no match found
430 if (has_global_wildcard) {
432 // Assign all the remaining terms to the global wildcard (unless
433 // it has already been matched before, in which case the matches
435 size_t num = ops.size();
436 std::auto_ptr<epvector> vp(new epvector);
438 for (size_t i=0; i<num; i++)
439 vp->push_back(split_ex_to_pair(ops[i]));
440 ex rest = thisexpairseq(vp, default_overall_coeff());
441 for (exmap::const_iterator it = tmp_repl.begin(); it != tmp_repl.end(); ++it) {
442 if (it->first.is_equal(global_wildcard)) {
443 if (rest.is_equal(it->second)) {
451 repl_lst[global_wildcard] = rest;
456 // No global wildcard, then the match fails if there are any
457 // unmatched terms left
465 return inherited::match(pattern, repl_lst);
468 ex expairseq::subs(const exmap & m, unsigned options) const
470 std::auto_ptr<epvector> vp = subschildren(m, options);
472 return ex_to<basic>(thisexpairseq(vp, overall_coeff, (options & subs_options::no_index_renaming) == 0));
473 else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
474 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
476 return subs_one_level(m, options);
481 int expairseq::compare_same_type(const basic &other) const
483 GINAC_ASSERT(is_a<expairseq>(other));
484 const expairseq &o = static_cast<const expairseq &>(other);
488 // compare number of elements
489 if (seq.size() != o.seq.size())
490 return (seq.size()<o.seq.size()) ? -1 : 1;
492 // compare overall_coeff
493 cmpval = overall_coeff.compare(o.overall_coeff);
497 #if EXPAIRSEQ_USE_HASHTAB
498 GINAC_ASSERT(hashtabsize==o.hashtabsize);
499 if (hashtabsize==0) {
500 #endif // EXPAIRSEQ_USE_HASHTAB
501 epvector::const_iterator cit1 = seq.begin();
502 epvector::const_iterator cit2 = o.seq.begin();
503 epvector::const_iterator last1 = seq.end();
504 epvector::const_iterator last2 = o.seq.end();
506 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
507 cmpval = (*cit1).compare(*cit2);
508 if (cmpval!=0) return cmpval;
511 GINAC_ASSERT(cit1==last1);
512 GINAC_ASSERT(cit2==last2);
515 #if EXPAIRSEQ_USE_HASHTAB
518 // compare number of elements in each hashtab entry
519 for (unsigned i=0; i<hashtabsize; ++i) {
520 unsigned cursize=hashtab[i].size();
521 if (cursize != o.hashtab[i].size())
522 return (cursize < o.hashtab[i].size()) ? -1 : 1;
525 // compare individual (sorted) hashtab entries
526 for (unsigned i=0; i<hashtabsize; ++i) {
527 unsigned sz = hashtab[i].size();
529 const epplist &eppl1 = hashtab[i];
530 const epplist &eppl2 = o.hashtab[i];
531 epplist::const_iterator it1 = eppl1.begin();
532 epplist::const_iterator it2 = eppl2.begin();
533 while (it1!=eppl1.end()) {
534 cmpval = (*(*it1)).compare(*(*it2));
544 #endif // EXPAIRSEQ_USE_HASHTAB
547 bool expairseq::is_equal_same_type(const basic &other) const
549 const expairseq &o = static_cast<const expairseq &>(other);
551 // compare number of elements
552 if (seq.size()!=o.seq.size())
555 // compare overall_coeff
556 if (!overall_coeff.is_equal(o.overall_coeff))
559 #if EXPAIRSEQ_USE_HASHTAB
560 // compare number of elements in each hashtab entry
561 if (hashtabsize!=o.hashtabsize) {
562 std::cout << "this:" << std::endl;
563 print(print_tree(std::cout));
564 std::cout << "other:" << std::endl;
565 other.print(print_tree(std::cout));
568 GINAC_ASSERT(hashtabsize==o.hashtabsize);
570 if (hashtabsize==0) {
571 #endif // EXPAIRSEQ_USE_HASHTAB
572 epvector::const_iterator cit1 = seq.begin();
573 epvector::const_iterator cit2 = o.seq.begin();
574 epvector::const_iterator last1 = seq.end();
576 while (cit1!=last1) {
577 if (!(*cit1).is_equal(*cit2)) return false;
583 #if EXPAIRSEQ_USE_HASHTAB
586 for (unsigned i=0; i<hashtabsize; ++i) {
587 if (hashtab[i].size() != o.hashtab[i].size())
591 // compare individual sorted hashtab entries
592 for (unsigned i=0; i<hashtabsize; ++i) {
593 unsigned sz = hashtab[i].size();
595 const epplist &eppl1 = hashtab[i];
596 const epplist &eppl2 = o.hashtab[i];
597 epplist::const_iterator it1 = eppl1.begin();
598 epplist::const_iterator it2 = eppl2.begin();
599 while (it1!=eppl1.end()) {
600 if (!(*(*it1)).is_equal(*(*it2))) return false;
608 #endif // EXPAIRSEQ_USE_HASHTAB
611 unsigned expairseq::return_type() const
613 return return_types::noncommutative_composite;
616 unsigned expairseq::calchash() const
618 unsigned v = make_hash_seed(typeid(*this));
619 epvector::const_iterator i = seq.begin();
620 const epvector::const_iterator end = seq.end();
622 v ^= i->rest.gethash();
623 #if !EXPAIRSEQ_USE_HASHTAB
624 // rotation spoils commutativity!
626 v ^= i->coeff.gethash();
627 #endif // !EXPAIRSEQ_USE_HASHTAB
631 v ^= overall_coeff.gethash();
633 // store calculated hash value only if object is already evaluated
634 if (flags &status_flags::evaluated) {
635 setflag(status_flags::hash_calculated);
642 ex expairseq::expand(unsigned options) const
644 std::auto_ptr<epvector> vp = expandchildren(options);
646 return thisexpairseq(vp, overall_coeff);
648 // The terms have not changed, so it is safe to declare this expanded
649 return (options == 0) ? setflag(status_flags::expanded) : *this;
654 // new virtual functions which can be overridden by derived classes
659 /** Create an object of this type.
660 * This method works similar to a constructor. It is useful because expairseq
661 * has (at least) two possible different semantics but we want to inherit
662 * methods thus avoiding code duplication. Sometimes a method in expairseq
663 * has to create a new one of the same semantics, which cannot be done by a
664 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
665 * order for this trick to work a derived class must of course override this
667 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
669 return expairseq(v, oc, do_index_renaming);
672 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
674 return expairseq(vp, oc, do_index_renaming);
677 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
680 p.rest.print(c, precedence());
682 p.coeff.print(c, precedence());
686 void expairseq::printseq(const print_context & c, char delim,
687 unsigned this_precedence,
688 unsigned upper_precedence) const
690 if (this_precedence <= upper_precedence)
692 epvector::const_iterator it, it_last = seq.end() - 1;
693 for (it=seq.begin(); it!=it_last; ++it) {
694 printpair(c, *it, this_precedence);
697 printpair(c, *it, this_precedence);
698 if (!overall_coeff.is_equal(default_overall_coeff())) {
700 overall_coeff.print(c, this_precedence);
703 if (this_precedence <= upper_precedence)
708 /** Form an expair from an ex, using the corresponding semantics.
709 * @see expairseq::recombine_pair_to_ex() */
710 expair expairseq::split_ex_to_pair(const ex &e) const
712 return expair(e,_ex1);
716 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
719 GINAC_ASSERT(is_exactly_a<numeric>(c));
725 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
728 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
729 GINAC_ASSERT(is_exactly_a<numeric>(c));
731 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
735 /** Form an ex out of an expair, using the corresponding semantics.
736 * @see expairseq::split_ex_to_pair() */
737 ex expairseq::recombine_pair_to_ex(const expair &p) const
739 return lst(p.rest,p.coeff);
742 bool expairseq::expair_needs_further_processing(epp it)
744 #if EXPAIRSEQ_USE_HASHTAB
745 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
746 #endif // EXPAIRSEQ_USE_HASHTAB
750 ex expairseq::default_overall_coeff() const
755 void expairseq::combine_overall_coeff(const ex &c)
757 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
758 GINAC_ASSERT(is_exactly_a<numeric>(c));
759 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
762 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
764 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
765 GINAC_ASSERT(is_exactly_a<numeric>(c1));
766 GINAC_ASSERT(is_exactly_a<numeric>(c2));
767 overall_coeff = ex_to<numeric>(overall_coeff).
768 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
771 bool expairseq::can_make_flat(const expair &p) const
778 // non-virtual functions in this class
781 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
787 construct_from_exvector(v);
788 #if EXPAIRSEQ_USE_HASHTAB
789 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
790 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
791 #endif // EXPAIRSEQ_USE_HASHTAB
794 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
796 if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
797 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
798 #if EXPAIRSEQ_USE_HASHTAB
799 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
800 ex_to<expairseq>(rh).seq.size();
801 if (calc_hashtabsize(totalsize)!=0) {
802 construct_from_2_ex_via_exvector(lh,rh);
804 #endif // EXPAIRSEQ_USE_HASHTAB
805 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
806 rh.info(info_flags::has_indices)) {
807 ex newrh=rename_dummy_indices_uniquely(lh, rh);
808 construct_from_2_expairseq(ex_to<expairseq>(lh),
809 ex_to<expairseq>(newrh));
812 construct_from_2_expairseq(ex_to<expairseq>(lh),
813 ex_to<expairseq>(rh));
814 #if EXPAIRSEQ_USE_HASHTAB
816 #endif // EXPAIRSEQ_USE_HASHTAB
819 #if EXPAIRSEQ_USE_HASHTAB
820 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
821 if (calc_hashtabsize(totalsize)!=0) {
822 construct_from_2_ex_via_exvector(lh, rh);
824 #endif // EXPAIRSEQ_USE_HASHTAB
825 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
826 #if EXPAIRSEQ_USE_HASHTAB
828 #endif // EXPAIRSEQ_USE_HASHTAB
831 } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
832 #if EXPAIRSEQ_USE_HASHTAB
833 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
834 if (calc_hashtabsize(totalsize)!=0) {
835 construct_from_2_ex_via_exvector(lh,rh);
837 #endif // EXPAIRSEQ_USE_HASHTAB
838 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
839 #if EXPAIRSEQ_USE_HASHTAB
841 #endif // EXPAIRSEQ_USE_HASHTAB
845 #if EXPAIRSEQ_USE_HASHTAB
846 if (calc_hashtabsize(2)!=0) {
847 construct_from_2_ex_via_exvector(lh,rh);
851 #endif // EXPAIRSEQ_USE_HASHTAB
853 if (is_exactly_a<numeric>(lh)) {
854 if (is_exactly_a<numeric>(rh)) {
855 combine_overall_coeff(lh);
856 combine_overall_coeff(rh);
858 combine_overall_coeff(lh);
859 seq.push_back(split_ex_to_pair(rh));
862 if (is_exactly_a<numeric>(rh)) {
863 combine_overall_coeff(rh);
864 seq.push_back(split_ex_to_pair(lh));
866 expair p1 = split_ex_to_pair(lh);
867 expair p2 = split_ex_to_pair(rh);
869 int cmpval = p1.rest.compare(p2.rest);
871 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
872 if (!ex_to<numeric>(p1.coeff).is_zero()) {
873 // no further processing is necessary, since this
874 // one element will usually be recombined in eval()
891 void expairseq::construct_from_2_expairseq(const expairseq &s1,
894 combine_overall_coeff(s1.overall_coeff);
895 combine_overall_coeff(s2.overall_coeff);
897 epvector::const_iterator first1 = s1.seq.begin();
898 epvector::const_iterator last1 = s1.seq.end();
899 epvector::const_iterator first2 = s2.seq.begin();
900 epvector::const_iterator last2 = s2.seq.end();
902 seq.reserve(s1.seq.size()+s2.seq.size());
904 bool needs_further_processing=false;
906 while (first1!=last1 && first2!=last2) {
907 int cmpval = (*first1).rest.compare((*first2).rest);
911 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
912 add(ex_to<numeric>(first2->coeff));
913 if (!newcoeff.is_zero()) {
914 seq.push_back(expair(first1->rest,newcoeff));
915 if (expair_needs_further_processing(seq.end()-1)) {
916 needs_further_processing = true;
921 } else if (cmpval<0) {
922 seq.push_back(*first1);
925 seq.push_back(*first2);
930 while (first1!=last1) {
931 seq.push_back(*first1);
934 while (first2!=last2) {
935 seq.push_back(*first2);
939 if (needs_further_processing) {
942 construct_from_epvector(v);
946 void expairseq::construct_from_expairseq_ex(const expairseq &s,
949 combine_overall_coeff(s.overall_coeff);
950 if (is_exactly_a<numeric>(e)) {
951 combine_overall_coeff(e);
956 epvector::const_iterator first = s.seq.begin();
957 epvector::const_iterator last = s.seq.end();
958 expair p = split_ex_to_pair(e);
960 seq.reserve(s.seq.size()+1);
961 bool p_pushed = false;
963 bool needs_further_processing=false;
965 // merge p into s.seq
966 while (first!=last) {
967 int cmpval = (*first).rest.compare(p.rest);
970 const numeric &newcoeff = ex_to<numeric>(first->coeff).
971 add(ex_to<numeric>(p.coeff));
972 if (!newcoeff.is_zero()) {
973 seq.push_back(expair(first->rest,newcoeff));
974 if (expair_needs_further_processing(seq.end()-1))
975 needs_further_processing = true;
980 } else if (cmpval<0) {
981 seq.push_back(*first);
991 // while loop exited because p was pushed, now push rest of s.seq
992 while (first!=last) {
993 seq.push_back(*first);
997 // while loop exited because s.seq was pushed, now push p
1001 if (needs_further_processing) {
1004 construct_from_epvector(v);
1008 void expairseq::construct_from_exvector(const exvector &v)
1010 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1011 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1012 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
1013 // (same for (+,*) -> (*,^)
1016 #if EXPAIRSEQ_USE_HASHTAB
1017 combine_same_terms();
1020 combine_same_terms_sorted_seq();
1021 #endif // EXPAIRSEQ_USE_HASHTAB
1024 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1026 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1027 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1028 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
1029 // same for (+,*) -> (*,^)
1031 make_flat(v, do_index_renaming);
1032 #if EXPAIRSEQ_USE_HASHTAB
1033 combine_same_terms();
1036 combine_same_terms_sorted_seq();
1037 #endif // EXPAIRSEQ_USE_HASHTAB
1040 /** Combine this expairseq with argument exvector.
1041 * It cares for associativity as well as for special handling of numerics. */
1042 void expairseq::make_flat(const exvector &v)
1044 exvector::const_iterator cit;
1046 // count number of operands which are of same expairseq derived type
1047 // and their cumulative number of operands
1048 int nexpairseqs = 0;
1050 bool do_idx_rename = false;
1053 while (cit!=v.end()) {
1054 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1056 noperands += ex_to<expairseq>(*cit).seq.size();
1058 if (is_a<mul>(*this) && (!do_idx_rename) &&
1059 cit->info(info_flags::has_indices))
1060 do_idx_rename = true;
1064 // reserve seq and coeffseq which will hold all operands
1065 seq.reserve(v.size()+noperands-nexpairseqs);
1067 // copy elements and split off numerical part
1068 make_flat_inserter mf(v, do_idx_rename);
1070 while (cit!=v.end()) {
1071 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1072 ex newfactor = mf.handle_factor(*cit, _ex1);
1073 const expairseq &subseqref = ex_to<expairseq>(newfactor);
1074 combine_overall_coeff(subseqref.overall_coeff);
1075 epvector::const_iterator cit_s = subseqref.seq.begin();
1076 while (cit_s!=subseqref.seq.end()) {
1077 seq.push_back(*cit_s);
1081 if (is_exactly_a<numeric>(*cit))
1082 combine_overall_coeff(*cit);
1084 ex newfactor = mf.handle_factor(*cit, _ex1);
1085 seq.push_back(split_ex_to_pair(newfactor));
1092 /** Combine this expairseq with argument epvector.
1093 * It cares for associativity as well as for special handling of numerics. */
1094 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1096 epvector::const_iterator cit;
1098 // count number of operands which are of same expairseq derived type
1099 // and their cumulative number of operands
1100 int nexpairseqs = 0;
1102 bool really_need_rename_inds = false;
1105 while (cit!=v.end()) {
1106 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
1108 noperands += ex_to<expairseq>(cit->rest).seq.size();
1110 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1111 cit->rest.info(info_flags::has_indices))
1112 really_need_rename_inds = true;
1115 do_index_renaming = do_index_renaming && really_need_rename_inds;
1117 // reserve seq and coeffseq which will hold all operands
1118 seq.reserve(v.size()+noperands-nexpairseqs);
1119 make_flat_inserter mf(v, do_index_renaming);
1121 // copy elements and split off numerical part
1123 while (cit!=v.end()) {
1124 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
1125 this->can_make_flat(*cit)) {
1126 ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1127 const expairseq &subseqref = ex_to<expairseq>(newrest);
1128 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1129 ex_to<numeric>(cit->coeff));
1130 epvector::const_iterator cit_s = subseqref.seq.begin();
1131 while (cit_s!=subseqref.seq.end()) {
1132 seq.push_back(expair(cit_s->rest,
1133 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1134 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1139 if (cit->is_canonical_numeric())
1140 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1142 ex rest = cit->rest;
1143 ex newrest = mf.handle_factor(rest, cit->coeff);
1144 if (are_ex_trivially_equal(newrest, rest))
1145 seq.push_back(*cit);
1147 seq.push_back(expair(newrest, cit->coeff));
1154 /** Brings this expairseq into a sorted (canonical) form. */
1155 void expairseq::canonicalize()
1157 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1161 /** Compact a presorted expairseq by combining all matching expairs to one
1162 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1164 void expairseq::combine_same_terms_sorted_seq()
1169 bool needs_further_processing = false;
1171 epvector::iterator itin1 = seq.begin();
1172 epvector::iterator itin2 = itin1+1;
1173 epvector::iterator itout = itin1;
1174 epvector::iterator last = seq.end();
1175 // must_copy will be set to true the first time some combination is
1176 // possible from then on the sequence has changed and must be compacted
1177 bool must_copy = false;
1178 while (itin2!=last) {
1179 if (itin1->rest.compare(itin2->rest)==0) {
1180 itin1->coeff = ex_to<numeric>(itin1->coeff).
1181 add_dyn(ex_to<numeric>(itin2->coeff));
1182 if (expair_needs_further_processing(itin1))
1183 needs_further_processing = true;
1186 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1195 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1201 seq.erase(itout,last);
1203 if (needs_further_processing) {
1206 construct_from_epvector(v);
1210 #if EXPAIRSEQ_USE_HASHTAB
1212 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1215 unsigned nearest_power_of_2 = 1 << log2(sz);
1216 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1217 // size = nearest_power_of_2*hashtabfactor;
1218 size = nearest_power_of_2/hashtabfactor;
1219 if (size<minhashtabsize)
1222 // hashtabsize must be a power of 2
1223 GINAC_ASSERT((1U << log2(size))==size);
1227 unsigned expairseq::calc_hashindex(const ex &e) const
1229 // calculate hashindex
1231 if (is_a<numeric>(e)) {
1232 hashindex = hashmask;
1234 hashindex = e.gethash() & hashmask;
1235 // last hashtab entry is reserved for numerics
1236 if (hashindex==hashmask) hashindex = 0;
1238 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1242 void expairseq::shrink_hashtab()
1244 unsigned new_hashtabsize;
1245 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1246 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1247 if (new_hashtabsize==0) {
1254 // shrink by a factor of 2
1255 unsigned half_hashtabsize = hashtabsize/2;
1256 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1257 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1258 // special treatment for numeric hashes
1259 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1260 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1261 hashtab.resize(half_hashtabsize);
1262 hashtabsize = half_hashtabsize;
1263 hashmask = hashtabsize-1;
1267 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1270 return; // nothing to do
1272 // calculate hashindex of element to be deleted
1273 unsigned hashindex = calc_hashindex((*element).rest);
1275 // find it in hashtab and remove it
1276 epplist &eppl = hashtab[hashindex];
1277 epplist::iterator epplit = eppl.begin();
1278 bool erased = false;
1279 while (epplit!=eppl.end()) {
1280 if (*epplit == element) {
1288 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1289 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1291 unsigned hashindex = calc_hashindex(element->rest);
1292 epplist &eppl = hashtab[hashindex];
1293 epplist::iterator epplit = eppl.begin();
1294 bool erased = false;
1295 while (epplit!=eppl.end()) {
1296 if (*epplit == element) {
1303 GINAC_ASSERT(erased);
1305 GINAC_ASSERT(erased);
1308 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1309 epvector::iterator newpos)
1311 GINAC_ASSERT(hashtabsize!=0);
1313 // calculate hashindex of element which was moved
1314 unsigned hashindex=calc_hashindex((*newpos).rest);
1316 // find it in hashtab and modify it
1317 epplist &eppl = hashtab[hashindex];
1318 epplist::iterator epplit = eppl.begin();
1319 while (epplit!=eppl.end()) {
1320 if (*epplit == oldpos) {
1326 GINAC_ASSERT(epplit!=eppl.end());
1329 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1331 epplist::const_iterator current = eppl.begin();
1332 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1335 eppl.insert(current,elem);
1338 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1339 epvector::iterator &last_non_zero,
1340 std::vector<bool> &touched,
1341 unsigned &number_of_zeroes)
1343 epp current = seq.begin();
1345 while (current!=first_numeric) {
1346 if (is_exactly_a<numeric>(current->rest)) {
1348 iter_swap(current,first_numeric);
1350 // calculate hashindex
1351 unsigned currenthashindex = calc_hashindex(current->rest);
1353 // test if there is already a matching expair in the hashtab-list
1354 epplist &eppl=hashtab[currenthashindex];
1355 epplist::iterator epplit = eppl.begin();
1356 while (epplit!=eppl.end()) {
1357 if (current->rest.is_equal((*epplit)->rest))
1361 if (epplit==eppl.end()) {
1362 // no matching expair found, append this to end of list
1363 sorted_insert(eppl,current);
1366 // epplit points to a matching expair, combine it with current
1367 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1368 add_dyn(ex_to<numeric>(current->coeff));
1370 // move obsolete current expair to end by swapping with last_non_zero element
1371 // if this was a numeric, it is swapped with the expair before first_numeric
1372 iter_swap(current,last_non_zero);
1374 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1377 // test if combined term has coeff 0 and can be removed is done later
1378 touched[(*epplit)-seq.begin()] = true;
1384 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1385 epvector::iterator &last_non_zero,
1386 std::vector<bool> &touched,
1387 unsigned &number_of_zeroes)
1389 // move terms with coeff 0 to end and remove them from hashtab
1390 // check only those elements which have been touched
1391 epp current = seq.begin();
1393 while (current!=first_numeric) {
1397 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1401 remove_hashtab_entry(current);
1403 // move element to the end, unless it is already at the end
1404 if (current!=last_non_zero) {
1405 iter_swap(current,last_non_zero);
1407 bool numeric_swapped = first_numeric!=last_non_zero;
1408 if (numeric_swapped)
1409 iter_swap(first_numeric,current);
1410 epvector::iterator changed_entry;
1412 if (numeric_swapped)
1413 changed_entry = first_numeric;
1415 changed_entry = last_non_zero;
1420 if (first_numeric!=current) {
1422 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1423 move_hashtab_entry(changed_entry,current);
1424 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1433 GINAC_ASSERT(i==current-seq.begin());
1436 /** True if one of the coeffs vanishes, otherwise false.
1437 * This would be an invariant violation, so this should only be used for
1438 * debugging purposes. */
1439 bool expairseq::has_coeff_0() const
1441 epvector::const_iterator i = seq.begin(), end = seq.end();
1443 if (i->coeff.is_zero())
1450 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1451 epvector::const_iterator last_non_zero)
1453 if (first_numeric == seq.end()) return; // no numerics
1455 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1456 while (current != last) {
1457 sorted_insert(hashtab[hashmask], current);
1462 void expairseq::combine_same_terms()
1464 // combine same terms, drop term with coeff 0, move numerics to end
1466 // calculate size of hashtab
1467 hashtabsize = calc_hashtabsize(seq.size());
1469 // hashtabsize is a power of 2
1470 hashmask = hashtabsize-1;
1474 hashtab.resize(hashtabsize);
1476 if (hashtabsize==0) {
1478 combine_same_terms_sorted_seq();
1479 GINAC_ASSERT(!has_coeff_0());
1483 // iterate through seq, move numerics to end,
1484 // fill hashtab and combine same terms
1485 epvector::iterator first_numeric = seq.end();
1486 epvector::iterator last_non_zero = seq.end()-1;
1488 size_t num = seq.size();
1489 std::vector<bool> touched(num);
1491 unsigned number_of_zeroes = 0;
1493 GINAC_ASSERT(!has_coeff_0());
1494 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1496 // there should not be any terms with coeff 0 from the beginning,
1497 // so it should be safe to skip this step
1498 if (number_of_zeroes!=0) {
1499 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1502 add_numerics_to_hashtab(first_numeric,last_non_zero);
1504 // pop zero elements
1505 for (unsigned i=0; i<number_of_zeroes; ++i) {
1509 // shrink hashtabsize to calculated value
1510 GINAC_ASSERT(!has_coeff_0());
1514 GINAC_ASSERT(!has_coeff_0());
1517 #endif // EXPAIRSEQ_USE_HASHTAB
1519 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1520 * debugging or in assertions since being sorted is an invariance. */
1521 bool expairseq::is_canonical() const
1523 if (seq.size() <= 1)
1526 #if EXPAIRSEQ_USE_HASHTAB
1527 if (hashtabsize > 0) return 1; // not canoncalized
1528 #endif // EXPAIRSEQ_USE_HASHTAB
1530 epvector::const_iterator it = seq.begin(), itend = seq.end();
1531 epvector::const_iterator it_last = it;
1532 for (++it; it!=itend; it_last=it, ++it) {
1533 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1534 if (!is_exactly_a<numeric>(it_last->rest) ||
1535 !is_exactly_a<numeric>(it->rest)) {
1536 // double test makes it easier to set a breakpoint...
1537 if (!is_exactly_a<numeric>(it_last->rest) ||
1538 !is_exactly_a<numeric>(it->rest)) {
1539 printpair(std::clog, *it_last, 0);
1541 printpair(std::clog, *it, 0);
1543 std::clog << "pair1:" << std::endl;
1544 it_last->rest.print(print_tree(std::clog));
1545 it_last->coeff.print(print_tree(std::clog));
1546 std::clog << "pair2:" << std::endl;
1547 it->rest.print(print_tree(std::clog));
1548 it->coeff.print(print_tree(std::clog));
1558 /** Member-wise expand the expairs in this sequence.
1560 * @see expairseq::expand()
1561 * @return pointer to epvector containing expanded pairs or zero pointer,
1562 * if no members were changed. */
1563 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1565 const epvector::const_iterator last = seq.end();
1566 epvector::const_iterator cit = seq.begin();
1568 const ex &expanded_ex = cit->rest.expand(options);
1569 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1571 // something changed, copy seq, eval and return it
1572 std::auto_ptr<epvector> s(new epvector);
1573 s->reserve(seq.size());
1575 // copy parts of seq which are known not to have changed
1576 epvector::const_iterator cit2 = seq.begin();
1578 s->push_back(*cit2);
1582 // copy first changed element
1583 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1588 while (cit2!=last) {
1589 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1598 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1602 /** Member-wise evaluate the expairs in this sequence.
1604 * @see expairseq::eval()
1605 * @return pointer to epvector containing evaluated pairs or zero pointer,
1606 * if no members were changed. */
1607 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1609 // returns a NULL pointer if nothing had to be evaluated
1610 // returns a pointer to a newly created epvector otherwise
1611 // (which has to be deleted somewhere else)
1614 return std::auto_ptr<epvector>(0);
1616 if (level == -max_recursion_level)
1617 throw(std::runtime_error("max recursion level reached"));
1620 epvector::const_iterator last = seq.end();
1621 epvector::const_iterator cit = seq.begin();
1623 const ex &evaled_ex = cit->rest.eval(level);
1624 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1626 // something changed, copy seq, eval and return it
1627 std::auto_ptr<epvector> s(new epvector);
1628 s->reserve(seq.size());
1630 // copy parts of seq which are known not to have changed
1631 epvector::const_iterator cit2=seq.begin();
1633 s->push_back(*cit2);
1637 // copy first changed element
1638 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1643 while (cit2!=last) {
1644 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1653 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1656 /** Member-wise substitute in this sequence.
1658 * @see expairseq::subs()
1659 * @return pointer to epvector containing pairs after application of subs,
1660 * or NULL pointer if no members were changed. */
1661 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1663 // When any of the objects to be substituted is a product or power
1664 // we have to recombine the pairs because the numeric coefficients may
1665 // be part of the search pattern.
1666 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1668 // Search the list of substitutions and cache our findings
1669 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1670 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1671 options |= subs_options::pattern_is_product;
1675 if (!(options & subs_options::pattern_is_product))
1676 options |= subs_options::pattern_is_not_product;
1679 if (options & subs_options::pattern_is_product) {
1681 // Substitute in the recombined pairs
1682 epvector::const_iterator cit = seq.begin(), last = seq.end();
1683 while (cit != last) {
1685 const ex &orig_ex = recombine_pair_to_ex(*cit);
1686 const ex &subsed_ex = orig_ex.subs(m, options);
1687 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1689 // Something changed, copy seq, subs and return it
1690 std::auto_ptr<epvector> s(new epvector);
1691 s->reserve(seq.size());
1693 // Copy parts of seq which are known not to have changed
1694 s->insert(s->begin(), seq.begin(), cit);
1696 // Copy first changed element
1697 s->push_back(split_ex_to_pair(subsed_ex));
1701 while (cit != last) {
1702 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1713 // Substitute only in the "rest" part of the pairs
1714 epvector::const_iterator cit = seq.begin(), last = seq.end();
1715 while (cit != last) {
1717 const ex &subsed_ex = cit->rest.subs(m, options);
1718 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1720 // Something changed, copy seq, subs and return it
1721 std::auto_ptr<epvector> s(new epvector);
1722 s->reserve(seq.size());
1724 // Copy parts of seq which are known not to have changed
1725 s->insert(s->begin(), seq.begin(), cit);
1727 // Copy first changed element
1728 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1732 while (cit != last) {
1733 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1743 // Nothing has changed
1744 return std::auto_ptr<epvector>(0);
1748 // static member variables
1751 #if EXPAIRSEQ_USE_HASHTAB
1752 unsigned expairseq::maxhashtabsize = 0x4000000U;
1753 unsigned expairseq::minhashtabsize = 0x1000U;
1754 unsigned expairseq::hashtabfactor = 1;
1755 #endif // EXPAIRSEQ_USE_HASHTAB
1757 } // namespace GiNaC