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"
38 #if EXPAIRSEQ_USE_HASHTAB
40 #endif // EXPAIRSEQ_USE_HASHTAB
49 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
50 print_func<print_context>(&expairseq::do_print).
51 print_func<print_tree>(&expairseq::do_print_tree))
61 bool operator()(const epp &lh, const epp &rh) const
63 return (*lh).is_less(*rh);
68 // default constructor
73 expairseq::expairseq()
74 #if EXPAIRSEQ_USE_HASHTAB
76 #endif // EXPAIRSEQ_USE_HASHTAB
82 /** For use by copy ctor and assignment operator. */
83 void expairseq::copy(const expairseq &other)
86 overall_coeff = other.overall_coeff;
87 #if EXPAIRSEQ_USE_HASHTAB
89 hashtabsize = other.hashtabsize;
91 hashmask = other.hashmask;
92 hashtab.resize(hashtabsize);
93 epvector::const_iterator osb = other.seq.begin();
94 for (unsigned i=0; i<hashtabsize; ++i) {
96 for (epplist::const_iterator cit=other.hashtab[i].begin();
97 cit!=other.hashtab[i].end(); ++cit) {
98 hashtab[i].push_back(seq.begin()+((*cit)-osb));
104 #endif // EXPAIRSEQ_USE_HASHTAB
109 // other constructors
112 expairseq::expairseq(const ex &lh, const ex &rh)
114 construct_from_2_ex(lh,rh);
115 GINAC_ASSERT(is_canonical());
118 expairseq::expairseq(const exvector &v)
120 construct_from_exvector(v);
121 GINAC_ASSERT(is_canonical());
124 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
127 GINAC_ASSERT(is_a<numeric>(oc));
128 construct_from_epvector(v, do_index_renaming);
129 GINAC_ASSERT(is_canonical());
132 expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
135 GINAC_ASSERT(vp.get()!=0);
136 GINAC_ASSERT(is_a<numeric>(oc));
137 construct_from_epvector(*vp, do_index_renaming);
138 GINAC_ASSERT(is_canonical());
145 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
147 inherited::read_archive(n, sym_lst);
148 archive_node::archive_node_cit first = n.find_first("rest");
149 archive_node::archive_node_cit last = n.find_last("coeff");
151 seq.reserve((last-first)/2);
153 for (archive_node::archive_node_cit loc = first; loc < last;) {
156 n.find_ex_by_loc(loc++, rest, sym_lst);
157 n.find_ex_by_loc(loc++, coeff, sym_lst);
158 seq.push_back(expair(rest, coeff));
161 n.find_ex("overall_coeff", overall_coeff, sym_lst);
164 GINAC_ASSERT(is_canonical());
167 void expairseq::archive(archive_node &n) const
169 inherited::archive(n);
170 epvector::const_iterator i = seq.begin(), iend = seq.end();
172 n.add_ex("rest", i->rest);
173 n.add_ex("coeff", i->coeff);
176 n.add_ex("overall_coeff", overall_coeff);
181 // functions overriding virtual functions from base classes
186 void expairseq::do_print(const print_context & c, unsigned level) const
189 printseq(c, ',', precedence(), level);
193 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
195 c.s << std::string(level, ' ') << class_name() << " @" << this
196 << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
197 << ", nops=" << nops()
199 size_t num = seq.size();
200 for (size_t i=0; i<num; ++i) {
201 seq[i].rest.print(c, level + c.delta_indent);
202 seq[i].coeff.print(c, level + c.delta_indent);
204 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
206 if (!overall_coeff.is_equal(default_overall_coeff())) {
207 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
208 << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
209 overall_coeff.print(c, level + c.delta_indent);
211 c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
212 #if EXPAIRSEQ_USE_HASHTAB
213 c.s << std::string(level + c.delta_indent,' ')
214 << "hashtab size " << hashtabsize << std::endl;
215 if (hashtabsize == 0) return;
217 unsigned count[MAXCOUNT+1];
218 for (int i=0; i<MAXCOUNT+1; ++i)
220 unsigned this_bin_fill;
221 unsigned cum_fill_sq = 0;
222 unsigned cum_fill = 0;
223 for (unsigned i=0; i<hashtabsize; ++i) {
225 if (hashtab[i].size() > 0) {
226 c.s << std::string(level + c.delta_indent, ' ')
227 << "bin " << i << " with entries ";
228 for (epplist::const_iterator it=hashtab[i].begin();
229 it!=hashtab[i].end(); ++it) {
230 c.s << *it-seq.begin() << " ";
234 cum_fill += this_bin_fill;
235 cum_fill_sq += this_bin_fill*this_bin_fill;
237 if (this_bin_fill<MAXCOUNT)
238 ++count[this_bin_fill];
244 double lambda = (1.0*seq.size()) / hashtabsize;
245 for (int k=0; k<MAXCOUNT; ++k) {
248 double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
250 c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
251 << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
252 << int(prob*1000)/10.0 << ")" << std::endl;
254 c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
255 << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
256 << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
258 c.s << std::string(level + c.delta_indent, ' ') << "variance: "
259 << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
261 c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
262 << (1.0*cum_fill)/hashtabsize
263 << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
264 #endif // EXPAIRSEQ_USE_HASHTAB
267 bool expairseq::info(unsigned inf) const
270 case info_flags::expanded:
271 return (flags & status_flags::expanded);
272 case info_flags::has_indices: {
273 if (flags & status_flags::has_indices)
275 else if (flags & status_flags::has_no_indices)
277 for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
278 if (i->rest.info(info_flags::has_indices)) {
279 this->setflag(status_flags::has_indices);
280 this->clearflag(status_flags::has_no_indices);
284 this->clearflag(status_flags::has_indices);
285 this->setflag(status_flags::has_no_indices);
289 return inherited::info(inf);
292 size_t expairseq::nops() const
294 if (overall_coeff.is_equal(default_overall_coeff()))
300 ex expairseq::op(size_t i) const
303 return recombine_pair_to_ex(seq[i]);
304 GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
305 return overall_coeff;
308 ex expairseq::map(map_function &f) const
310 std::auto_ptr<epvector> v(new epvector);
311 v->reserve(seq.size()+1);
313 epvector::const_iterator cit = seq.begin(), last = seq.end();
314 while (cit != last) {
315 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
319 if (overall_coeff.is_equal(default_overall_coeff()))
320 return thisexpairseq(v, default_overall_coeff(), true);
322 ex newcoeff = f(overall_coeff);
323 if(is_a<numeric>(newcoeff))
324 return thisexpairseq(v, newcoeff, true);
326 v->push_back(split_ex_to_pair(newcoeff));
327 return thisexpairseq(v, default_overall_coeff(), true);
332 /** Perform coefficient-wise automatic term rewriting rules in this class. */
333 ex expairseq::eval(int level) const
335 if ((level==1) && (flags &status_flags::evaluated))
338 std::auto_ptr<epvector> vp = evalchildren(level);
342 return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
345 epvector* conjugateepvector(const epvector&epv)
347 epvector *newepv = 0;
348 for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
350 newepv->push_back(i->conjugate());
353 expair x = i->conjugate();
354 if (x.is_equal(*i)) {
357 newepv = new epvector;
358 newepv->reserve(epv.size());
359 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
360 newepv->push_back(*j);
362 newepv->push_back(x);
367 ex expairseq::conjugate() const
369 epvector* newepv = conjugateepvector(seq);
370 ex x = overall_coeff.conjugate();
371 if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
374 ex result = thisexpairseq(newepv ? *newepv : seq, x);
379 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
381 // This differs from basic::match() because we want "a+b+c+d" to
382 // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
384 if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
386 // Check whether global wildcard (one that matches the "rest of the
387 // expression", like "*" above) is present
388 bool has_global_wildcard = false;
390 for (size_t i=0; i<pattern.nops(); i++) {
391 if (is_exactly_a<wildcard>(pattern.op(i))) {
392 has_global_wildcard = true;
393 global_wildcard = pattern.op(i);
398 // Even if the expression does not match the pattern, some of
399 // its subexpressions could match it. For example, x^5*y^(-1)
400 // does not match the pattern $0^5, but its subexpression x^5
401 // does. So, save repl_lst in order to not add bogus entries.
402 exmap tmp_repl = repl_lst;
404 // Unfortunately, this is an O(N^2) operation because we can't
405 // sort the pattern in a useful way...
410 for (size_t i=0; i<nops(); i++)
411 ops.push_back(op(i));
413 // Now, for every term of the pattern, look for a matching term in
414 // the expression and remove the match
415 for (size_t i=0; i<pattern.nops(); i++) {
416 ex p = pattern.op(i);
417 if (has_global_wildcard && p.is_equal(global_wildcard))
419 exvector::iterator it = ops.begin(), itend = ops.end();
420 while (it != itend) {
421 if (it->match(p, tmp_repl)) {
427 return false; // no match found
431 if (has_global_wildcard) {
433 // Assign all the remaining terms to the global wildcard (unless
434 // it has already been matched before, in which case the matches
436 size_t num = ops.size();
437 std::auto_ptr<epvector> vp(new epvector);
439 for (size_t i=0; i<num; i++)
440 vp->push_back(split_ex_to_pair(ops[i]));
441 ex rest = thisexpairseq(vp, default_overall_coeff());
442 for (exmap::const_iterator it = tmp_repl.begin(); it != tmp_repl.end(); ++it) {
443 if (it->first.is_equal(global_wildcard)) {
444 if (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
466 return inherited::match(pattern, repl_lst);
469 ex expairseq::subs(const exmap & m, unsigned options) const
471 std::auto_ptr<epvector> vp = subschildren(m, options);
473 return ex_to<basic>(thisexpairseq(vp, overall_coeff, (options & subs_options::no_index_renaming) == 0));
474 else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
475 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
477 return subs_one_level(m, options);
482 int expairseq::compare_same_type(const basic &other) const
484 GINAC_ASSERT(is_a<expairseq>(other));
485 const expairseq &o = static_cast<const expairseq &>(other);
489 // compare number of elements
490 if (seq.size() != o.seq.size())
491 return (seq.size()<o.seq.size()) ? -1 : 1;
493 // compare overall_coeff
494 cmpval = overall_coeff.compare(o.overall_coeff);
498 #if EXPAIRSEQ_USE_HASHTAB
499 GINAC_ASSERT(hashtabsize==o.hashtabsize);
500 if (hashtabsize==0) {
501 #endif // EXPAIRSEQ_USE_HASHTAB
502 epvector::const_iterator cit1 = seq.begin();
503 epvector::const_iterator cit2 = o.seq.begin();
504 epvector::const_iterator last1 = seq.end();
505 epvector::const_iterator last2 = o.seq.end();
507 for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
508 cmpval = (*cit1).compare(*cit2);
509 if (cmpval!=0) return cmpval;
512 GINAC_ASSERT(cit1==last1);
513 GINAC_ASSERT(cit2==last2);
516 #if EXPAIRSEQ_USE_HASHTAB
519 // compare number of elements in each hashtab entry
520 for (unsigned i=0; i<hashtabsize; ++i) {
521 unsigned cursize=hashtab[i].size();
522 if (cursize != o.hashtab[i].size())
523 return (cursize < o.hashtab[i].size()) ? -1 : 1;
526 // compare individual (sorted) hashtab entries
527 for (unsigned i=0; i<hashtabsize; ++i) {
528 unsigned sz = hashtab[i].size();
530 const epplist &eppl1 = hashtab[i];
531 const epplist &eppl2 = o.hashtab[i];
532 epplist::const_iterator it1 = eppl1.begin();
533 epplist::const_iterator it2 = eppl2.begin();
534 while (it1!=eppl1.end()) {
535 cmpval = (*(*it1)).compare(*(*it2));
545 #endif // EXPAIRSEQ_USE_HASHTAB
548 bool expairseq::is_equal_same_type(const basic &other) const
550 const expairseq &o = static_cast<const expairseq &>(other);
552 // compare number of elements
553 if (seq.size()!=o.seq.size())
556 // compare overall_coeff
557 if (!overall_coeff.is_equal(o.overall_coeff))
560 #if EXPAIRSEQ_USE_HASHTAB
561 // compare number of elements in each hashtab entry
562 if (hashtabsize!=o.hashtabsize) {
563 std::cout << "this:" << std::endl;
564 print(print_tree(std::cout));
565 std::cout << "other:" << std::endl;
566 other.print(print_tree(std::cout));
569 GINAC_ASSERT(hashtabsize==o.hashtabsize);
571 if (hashtabsize==0) {
572 #endif // EXPAIRSEQ_USE_HASHTAB
573 epvector::const_iterator cit1 = seq.begin();
574 epvector::const_iterator cit2 = o.seq.begin();
575 epvector::const_iterator last1 = seq.end();
577 while (cit1!=last1) {
578 if (!(*cit1).is_equal(*cit2)) return false;
584 #if EXPAIRSEQ_USE_HASHTAB
587 for (unsigned i=0; i<hashtabsize; ++i) {
588 if (hashtab[i].size() != o.hashtab[i].size())
592 // compare individual sorted hashtab entries
593 for (unsigned i=0; i<hashtabsize; ++i) {
594 unsigned sz = hashtab[i].size();
596 const epplist &eppl1 = hashtab[i];
597 const epplist &eppl2 = o.hashtab[i];
598 epplist::const_iterator it1 = eppl1.begin();
599 epplist::const_iterator it2 = eppl2.begin();
600 while (it1!=eppl1.end()) {
601 if (!(*(*it1)).is_equal(*(*it2))) return false;
609 #endif // EXPAIRSEQ_USE_HASHTAB
612 unsigned expairseq::return_type() const
614 return return_types::noncommutative_composite;
617 unsigned expairseq::calchash() const
619 unsigned v = make_hash_seed(typeid(*this));
620 epvector::const_iterator i = seq.begin();
621 const epvector::const_iterator end = seq.end();
623 v ^= i->rest.gethash();
624 #if !EXPAIRSEQ_USE_HASHTAB
625 // rotation spoils commutativity!
627 v ^= i->coeff.gethash();
628 #endif // !EXPAIRSEQ_USE_HASHTAB
632 v ^= overall_coeff.gethash();
634 // store calculated hash value only if object is already evaluated
635 if (flags &status_flags::evaluated) {
636 setflag(status_flags::hash_calculated);
643 ex expairseq::expand(unsigned options) const
645 std::auto_ptr<epvector> vp = expandchildren(options);
647 return thisexpairseq(vp, overall_coeff);
649 // The terms have not changed, so it is safe to declare this expanded
650 return (options == 0) ? setflag(status_flags::expanded) : *this;
655 // new virtual functions which can be overridden by derived classes
660 /** Create an object of this type.
661 * This method works similar to a constructor. It is useful because expairseq
662 * has (at least) two possible different semantics but we want to inherit
663 * methods thus avoiding code duplication. Sometimes a method in expairseq
664 * has to create a new one of the same semantics, which cannot be done by a
665 * ctor because the name (add, mul,...) is unknown on the expairseq level. In
666 * order for this trick to work a derived class must of course override this
668 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
670 return expairseq(v, oc, do_index_renaming);
673 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
675 return expairseq(vp, oc, do_index_renaming);
678 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
681 p.rest.print(c, precedence());
683 p.coeff.print(c, precedence());
687 void expairseq::printseq(const print_context & c, char delim,
688 unsigned this_precedence,
689 unsigned upper_precedence) const
691 if (this_precedence <= upper_precedence)
693 epvector::const_iterator it, it_last = seq.end() - 1;
694 for (it=seq.begin(); it!=it_last; ++it) {
695 printpair(c, *it, this_precedence);
698 printpair(c, *it, this_precedence);
699 if (!overall_coeff.is_equal(default_overall_coeff())) {
701 overall_coeff.print(c, this_precedence);
704 if (this_precedence <= upper_precedence)
709 /** Form an expair from an ex, using the corresponding semantics.
710 * @see expairseq::recombine_pair_to_ex() */
711 expair expairseq::split_ex_to_pair(const ex &e) const
713 return expair(e,_ex1);
717 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
720 GINAC_ASSERT(is_exactly_a<numeric>(c));
726 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
729 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
730 GINAC_ASSERT(is_exactly_a<numeric>(c));
732 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
736 /** Form an ex out of an expair, using the corresponding semantics.
737 * @see expairseq::split_ex_to_pair() */
738 ex expairseq::recombine_pair_to_ex(const expair &p) const
740 return lst(p.rest,p.coeff);
743 bool expairseq::expair_needs_further_processing(epp it)
745 #if EXPAIRSEQ_USE_HASHTAB
746 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
747 #endif // EXPAIRSEQ_USE_HASHTAB
751 ex expairseq::default_overall_coeff() const
756 void expairseq::combine_overall_coeff(const ex &c)
758 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
759 GINAC_ASSERT(is_exactly_a<numeric>(c));
760 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
763 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
765 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
766 GINAC_ASSERT(is_exactly_a<numeric>(c1));
767 GINAC_ASSERT(is_exactly_a<numeric>(c2));
768 overall_coeff = ex_to<numeric>(overall_coeff).
769 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
772 bool expairseq::can_make_flat(const expair &p) const
779 // non-virtual functions in this class
782 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
788 construct_from_exvector(v);
789 #if EXPAIRSEQ_USE_HASHTAB
790 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
791 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
792 #endif // EXPAIRSEQ_USE_HASHTAB
795 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
797 if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
798 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
799 #if EXPAIRSEQ_USE_HASHTAB
800 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
801 ex_to<expairseq>(rh).seq.size();
802 if (calc_hashtabsize(totalsize)!=0) {
803 construct_from_2_ex_via_exvector(lh,rh);
805 #endif // EXPAIRSEQ_USE_HASHTAB
806 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
807 rh.info(info_flags::has_indices)) {
808 ex newrh=rename_dummy_indices_uniquely(lh, rh);
809 construct_from_2_expairseq(ex_to<expairseq>(lh),
810 ex_to<expairseq>(newrh));
813 construct_from_2_expairseq(ex_to<expairseq>(lh),
814 ex_to<expairseq>(rh));
815 #if EXPAIRSEQ_USE_HASHTAB
817 #endif // EXPAIRSEQ_USE_HASHTAB
820 #if EXPAIRSEQ_USE_HASHTAB
821 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
822 if (calc_hashtabsize(totalsize)!=0) {
823 construct_from_2_ex_via_exvector(lh, rh);
825 #endif // EXPAIRSEQ_USE_HASHTAB
826 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
827 #if EXPAIRSEQ_USE_HASHTAB
829 #endif // EXPAIRSEQ_USE_HASHTAB
832 } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
833 #if EXPAIRSEQ_USE_HASHTAB
834 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
835 if (calc_hashtabsize(totalsize)!=0) {
836 construct_from_2_ex_via_exvector(lh,rh);
838 #endif // EXPAIRSEQ_USE_HASHTAB
839 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
840 #if EXPAIRSEQ_USE_HASHTAB
842 #endif // EXPAIRSEQ_USE_HASHTAB
846 #if EXPAIRSEQ_USE_HASHTAB
847 if (calc_hashtabsize(2)!=0) {
848 construct_from_2_ex_via_exvector(lh,rh);
852 #endif // EXPAIRSEQ_USE_HASHTAB
854 if (is_exactly_a<numeric>(lh)) {
855 if (is_exactly_a<numeric>(rh)) {
856 combine_overall_coeff(lh);
857 combine_overall_coeff(rh);
859 combine_overall_coeff(lh);
860 seq.push_back(split_ex_to_pair(rh));
863 if (is_exactly_a<numeric>(rh)) {
864 combine_overall_coeff(rh);
865 seq.push_back(split_ex_to_pair(lh));
867 expair p1 = split_ex_to_pair(lh);
868 expair p2 = split_ex_to_pair(rh);
870 int cmpval = p1.rest.compare(p2.rest);
872 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
873 if (!ex_to<numeric>(p1.coeff).is_zero()) {
874 // no further processing is necessary, since this
875 // one element will usually be recombined in eval()
892 void expairseq::construct_from_2_expairseq(const expairseq &s1,
895 combine_overall_coeff(s1.overall_coeff);
896 combine_overall_coeff(s2.overall_coeff);
898 epvector::const_iterator first1 = s1.seq.begin();
899 epvector::const_iterator last1 = s1.seq.end();
900 epvector::const_iterator first2 = s2.seq.begin();
901 epvector::const_iterator last2 = s2.seq.end();
903 seq.reserve(s1.seq.size()+s2.seq.size());
905 bool needs_further_processing=false;
907 while (first1!=last1 && first2!=last2) {
908 int cmpval = (*first1).rest.compare((*first2).rest);
912 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
913 add(ex_to<numeric>(first2->coeff));
914 if (!newcoeff.is_zero()) {
915 seq.push_back(expair(first1->rest,newcoeff));
916 if (expair_needs_further_processing(seq.end()-1)) {
917 needs_further_processing = true;
922 } else if (cmpval<0) {
923 seq.push_back(*first1);
926 seq.push_back(*first2);
931 while (first1!=last1) {
932 seq.push_back(*first1);
935 while (first2!=last2) {
936 seq.push_back(*first2);
940 if (needs_further_processing) {
943 construct_from_epvector(v);
947 void expairseq::construct_from_expairseq_ex(const expairseq &s,
950 combine_overall_coeff(s.overall_coeff);
951 if (is_exactly_a<numeric>(e)) {
952 combine_overall_coeff(e);
957 epvector::const_iterator first = s.seq.begin();
958 epvector::const_iterator last = s.seq.end();
959 expair p = split_ex_to_pair(e);
961 seq.reserve(s.seq.size()+1);
962 bool p_pushed = false;
964 bool needs_further_processing=false;
966 // merge p into s.seq
967 while (first!=last) {
968 int cmpval = (*first).rest.compare(p.rest);
971 const numeric &newcoeff = ex_to<numeric>(first->coeff).
972 add(ex_to<numeric>(p.coeff));
973 if (!newcoeff.is_zero()) {
974 seq.push_back(expair(first->rest,newcoeff));
975 if (expair_needs_further_processing(seq.end()-1))
976 needs_further_processing = true;
981 } else if (cmpval<0) {
982 seq.push_back(*first);
992 // while loop exited because p was pushed, now push rest of s.seq
993 while (first!=last) {
994 seq.push_back(*first);
998 // while loop exited because s.seq was pushed, now push p
1002 if (needs_further_processing) {
1005 construct_from_epvector(v);
1009 void expairseq::construct_from_exvector(const exvector &v)
1011 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1012 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1013 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
1014 // (same for (+,*) -> (*,^)
1017 #if EXPAIRSEQ_USE_HASHTAB
1018 combine_same_terms();
1021 combine_same_terms_sorted_seq();
1022 #endif // EXPAIRSEQ_USE_HASHTAB
1025 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1027 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1028 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1029 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
1030 // same for (+,*) -> (*,^)
1032 make_flat(v, do_index_renaming);
1033 #if EXPAIRSEQ_USE_HASHTAB
1034 combine_same_terms();
1037 combine_same_terms_sorted_seq();
1038 #endif // EXPAIRSEQ_USE_HASHTAB
1041 /** Combine this expairseq with argument exvector.
1042 * It cares for associativity as well as for special handling of numerics. */
1043 void expairseq::make_flat(const exvector &v)
1045 exvector::const_iterator cit;
1047 // count number of operands which are of same expairseq derived type
1048 // and their cumulative number of operands
1049 int nexpairseqs = 0;
1051 bool do_idx_rename = false;
1054 while (cit!=v.end()) {
1055 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1057 noperands += ex_to<expairseq>(*cit).seq.size();
1059 if (is_a<mul>(*this) && (!do_idx_rename) &&
1060 cit->info(info_flags::has_indices))
1061 do_idx_rename = true;
1065 // reserve seq and coeffseq which will hold all operands
1066 seq.reserve(v.size()+noperands-nexpairseqs);
1068 // copy elements and split off numerical part
1069 make_flat_inserter mf(v, do_idx_rename);
1071 while (cit!=v.end()) {
1072 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1073 ex newfactor = mf.handle_factor(*cit, _ex1);
1074 const expairseq &subseqref = ex_to<expairseq>(newfactor);
1075 combine_overall_coeff(subseqref.overall_coeff);
1076 epvector::const_iterator cit_s = subseqref.seq.begin();
1077 while (cit_s!=subseqref.seq.end()) {
1078 seq.push_back(*cit_s);
1082 if (is_exactly_a<numeric>(*cit))
1083 combine_overall_coeff(*cit);
1085 ex newfactor = mf.handle_factor(*cit, _ex1);
1086 seq.push_back(split_ex_to_pair(newfactor));
1093 /** Combine this expairseq with argument epvector.
1094 * It cares for associativity as well as for special handling of numerics. */
1095 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1097 epvector::const_iterator cit;
1099 // count number of operands which are of same expairseq derived type
1100 // and their cumulative number of operands
1101 int nexpairseqs = 0;
1103 bool really_need_rename_inds = false;
1106 while (cit!=v.end()) {
1107 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
1109 noperands += ex_to<expairseq>(cit->rest).seq.size();
1111 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1112 cit->rest.info(info_flags::has_indices))
1113 really_need_rename_inds = true;
1116 do_index_renaming = do_index_renaming && really_need_rename_inds;
1118 // reserve seq and coeffseq which will hold all operands
1119 seq.reserve(v.size()+noperands-nexpairseqs);
1120 make_flat_inserter mf(v, do_index_renaming);
1122 // copy elements and split off numerical part
1124 while (cit!=v.end()) {
1125 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
1126 this->can_make_flat(*cit)) {
1127 ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1128 const expairseq &subseqref = ex_to<expairseq>(newrest);
1129 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1130 ex_to<numeric>(cit->coeff));
1131 epvector::const_iterator cit_s = subseqref.seq.begin();
1132 while (cit_s!=subseqref.seq.end()) {
1133 seq.push_back(expair(cit_s->rest,
1134 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1135 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1140 if (cit->is_canonical_numeric())
1141 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1143 ex rest = cit->rest;
1144 ex newrest = mf.handle_factor(rest, cit->coeff);
1145 if (are_ex_trivially_equal(newrest, rest))
1146 seq.push_back(*cit);
1148 seq.push_back(expair(newrest, cit->coeff));
1155 /** Brings this expairseq into a sorted (canonical) form. */
1156 void expairseq::canonicalize()
1158 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1162 /** Compact a presorted expairseq by combining all matching expairs to one
1163 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1165 void expairseq::combine_same_terms_sorted_seq()
1170 bool needs_further_processing = false;
1172 epvector::iterator itin1 = seq.begin();
1173 epvector::iterator itin2 = itin1+1;
1174 epvector::iterator itout = itin1;
1175 epvector::iterator last = seq.end();
1176 // must_copy will be set to true the first time some combination is
1177 // possible from then on the sequence has changed and must be compacted
1178 bool must_copy = false;
1179 while (itin2!=last) {
1180 if (itin1->rest.compare(itin2->rest)==0) {
1181 itin1->coeff = ex_to<numeric>(itin1->coeff).
1182 add_dyn(ex_to<numeric>(itin2->coeff));
1183 if (expair_needs_further_processing(itin1))
1184 needs_further_processing = true;
1187 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1196 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1202 seq.erase(itout,last);
1204 if (needs_further_processing) {
1207 construct_from_epvector(v);
1211 #if EXPAIRSEQ_USE_HASHTAB
1213 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1216 unsigned nearest_power_of_2 = 1 << log2(sz);
1217 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1218 // size = nearest_power_of_2*hashtabfactor;
1219 size = nearest_power_of_2/hashtabfactor;
1220 if (size<minhashtabsize)
1223 // hashtabsize must be a power of 2
1224 GINAC_ASSERT((1U << log2(size))==size);
1228 unsigned expairseq::calc_hashindex(const ex &e) const
1230 // calculate hashindex
1232 if (is_a<numeric>(e)) {
1233 hashindex = hashmask;
1235 hashindex = e.gethash() & hashmask;
1236 // last hashtab entry is reserved for numerics
1237 if (hashindex==hashmask) hashindex = 0;
1239 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1243 void expairseq::shrink_hashtab()
1245 unsigned new_hashtabsize;
1246 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1247 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1248 if (new_hashtabsize==0) {
1255 // shrink by a factor of 2
1256 unsigned half_hashtabsize = hashtabsize/2;
1257 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1258 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1259 // special treatment for numeric hashes
1260 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1261 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1262 hashtab.resize(half_hashtabsize);
1263 hashtabsize = half_hashtabsize;
1264 hashmask = hashtabsize-1;
1268 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1271 return; // nothing to do
1273 // calculate hashindex of element to be deleted
1274 unsigned hashindex = calc_hashindex((*element).rest);
1276 // find it in hashtab and remove it
1277 epplist &eppl = hashtab[hashindex];
1278 epplist::iterator epplit = eppl.begin();
1279 bool erased = false;
1280 while (epplit!=eppl.end()) {
1281 if (*epplit == element) {
1289 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1290 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1292 unsigned hashindex = calc_hashindex(element->rest);
1293 epplist &eppl = hashtab[hashindex];
1294 epplist::iterator epplit = eppl.begin();
1295 bool erased = false;
1296 while (epplit!=eppl.end()) {
1297 if (*epplit == element) {
1304 GINAC_ASSERT(erased);
1306 GINAC_ASSERT(erased);
1309 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1310 epvector::iterator newpos)
1312 GINAC_ASSERT(hashtabsize!=0);
1314 // calculate hashindex of element which was moved
1315 unsigned hashindex=calc_hashindex((*newpos).rest);
1317 // find it in hashtab and modify it
1318 epplist &eppl = hashtab[hashindex];
1319 epplist::iterator epplit = eppl.begin();
1320 while (epplit!=eppl.end()) {
1321 if (*epplit == oldpos) {
1327 GINAC_ASSERT(epplit!=eppl.end());
1330 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1332 epplist::const_iterator current = eppl.begin();
1333 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1336 eppl.insert(current,elem);
1339 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1340 epvector::iterator &last_non_zero,
1341 std::vector<bool> &touched,
1342 unsigned &number_of_zeroes)
1344 epp current = seq.begin();
1346 while (current!=first_numeric) {
1347 if (is_exactly_a<numeric>(current->rest)) {
1349 iter_swap(current,first_numeric);
1351 // calculate hashindex
1352 unsigned currenthashindex = calc_hashindex(current->rest);
1354 // test if there is already a matching expair in the hashtab-list
1355 epplist &eppl=hashtab[currenthashindex];
1356 epplist::iterator epplit = eppl.begin();
1357 while (epplit!=eppl.end()) {
1358 if (current->rest.is_equal((*epplit)->rest))
1362 if (epplit==eppl.end()) {
1363 // no matching expair found, append this to end of list
1364 sorted_insert(eppl,current);
1367 // epplit points to a matching expair, combine it with current
1368 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1369 add_dyn(ex_to<numeric>(current->coeff));
1371 // move obsolete current expair to end by swapping with last_non_zero element
1372 // if this was a numeric, it is swapped with the expair before first_numeric
1373 iter_swap(current,last_non_zero);
1375 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1378 // test if combined term has coeff 0 and can be removed is done later
1379 touched[(*epplit)-seq.begin()] = true;
1385 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1386 epvector::iterator &last_non_zero,
1387 std::vector<bool> &touched,
1388 unsigned &number_of_zeroes)
1390 // move terms with coeff 0 to end and remove them from hashtab
1391 // check only those elements which have been touched
1392 epp current = seq.begin();
1394 while (current!=first_numeric) {
1398 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1402 remove_hashtab_entry(current);
1404 // move element to the end, unless it is already at the end
1405 if (current!=last_non_zero) {
1406 iter_swap(current,last_non_zero);
1408 bool numeric_swapped = first_numeric!=last_non_zero;
1409 if (numeric_swapped)
1410 iter_swap(first_numeric,current);
1411 epvector::iterator changed_entry;
1413 if (numeric_swapped)
1414 changed_entry = first_numeric;
1416 changed_entry = last_non_zero;
1421 if (first_numeric!=current) {
1423 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1424 move_hashtab_entry(changed_entry,current);
1425 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1434 GINAC_ASSERT(i==current-seq.begin());
1437 /** True if one of the coeffs vanishes, otherwise false.
1438 * This would be an invariant violation, so this should only be used for
1439 * debugging purposes. */
1440 bool expairseq::has_coeff_0() const
1442 epvector::const_iterator i = seq.begin(), end = seq.end();
1444 if (i->coeff.is_zero())
1451 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1452 epvector::const_iterator last_non_zero)
1454 if (first_numeric == seq.end()) return; // no numerics
1456 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1457 while (current != last) {
1458 sorted_insert(hashtab[hashmask], current);
1463 void expairseq::combine_same_terms()
1465 // combine same terms, drop term with coeff 0, move numerics to end
1467 // calculate size of hashtab
1468 hashtabsize = calc_hashtabsize(seq.size());
1470 // hashtabsize is a power of 2
1471 hashmask = hashtabsize-1;
1475 hashtab.resize(hashtabsize);
1477 if (hashtabsize==0) {
1479 combine_same_terms_sorted_seq();
1480 GINAC_ASSERT(!has_coeff_0());
1484 // iterate through seq, move numerics to end,
1485 // fill hashtab and combine same terms
1486 epvector::iterator first_numeric = seq.end();
1487 epvector::iterator last_non_zero = seq.end()-1;
1489 size_t num = seq.size();
1490 std::vector<bool> touched(num);
1492 unsigned number_of_zeroes = 0;
1494 GINAC_ASSERT(!has_coeff_0());
1495 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1497 // there should not be any terms with coeff 0 from the beginning,
1498 // so it should be safe to skip this step
1499 if (number_of_zeroes!=0) {
1500 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1503 add_numerics_to_hashtab(first_numeric,last_non_zero);
1505 // pop zero elements
1506 for (unsigned i=0; i<number_of_zeroes; ++i) {
1510 // shrink hashtabsize to calculated value
1511 GINAC_ASSERT(!has_coeff_0());
1515 GINAC_ASSERT(!has_coeff_0());
1518 #endif // EXPAIRSEQ_USE_HASHTAB
1520 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1521 * debugging or in assertions since being sorted is an invariance. */
1522 bool expairseq::is_canonical() const
1524 if (seq.size() <= 1)
1527 #if EXPAIRSEQ_USE_HASHTAB
1528 if (hashtabsize > 0) return 1; // not canonicalized
1529 #endif // EXPAIRSEQ_USE_HASHTAB
1531 epvector::const_iterator it = seq.begin(), itend = seq.end();
1532 epvector::const_iterator it_last = it;
1533 for (++it; it!=itend; it_last=it, ++it) {
1534 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1535 if (!is_exactly_a<numeric>(it_last->rest) ||
1536 !is_exactly_a<numeric>(it->rest)) {
1537 // double test makes it easier to set a breakpoint...
1538 if (!is_exactly_a<numeric>(it_last->rest) ||
1539 !is_exactly_a<numeric>(it->rest)) {
1540 printpair(std::clog, *it_last, 0);
1542 printpair(std::clog, *it, 0);
1544 std::clog << "pair1:" << std::endl;
1545 it_last->rest.print(print_tree(std::clog));
1546 it_last->coeff.print(print_tree(std::clog));
1547 std::clog << "pair2:" << std::endl;
1548 it->rest.print(print_tree(std::clog));
1549 it->coeff.print(print_tree(std::clog));
1559 /** Member-wise expand the expairs in this sequence.
1561 * @see expairseq::expand()
1562 * @return pointer to epvector containing expanded pairs or zero pointer,
1563 * if no members were changed. */
1564 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1566 const epvector::const_iterator last = seq.end();
1567 epvector::const_iterator cit = seq.begin();
1569 const ex &expanded_ex = cit->rest.expand(options);
1570 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1572 // something changed, copy seq, eval and return it
1573 std::auto_ptr<epvector> s(new epvector);
1574 s->reserve(seq.size());
1576 // copy parts of seq which are known not to have changed
1577 epvector::const_iterator cit2 = seq.begin();
1579 s->push_back(*cit2);
1583 // copy first changed element
1584 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1589 while (cit2!=last) {
1590 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1599 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1603 /** Member-wise evaluate the expairs in this sequence.
1605 * @see expairseq::eval()
1606 * @return pointer to epvector containing evaluated pairs or zero pointer,
1607 * if no members were changed. */
1608 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1610 // returns a NULL pointer if nothing had to be evaluated
1611 // returns a pointer to a newly created epvector otherwise
1612 // (which has to be deleted somewhere else)
1614 if (likely(level==1))
1615 return std::auto_ptr<epvector>(0);
1617 if (level == -max_recursion_level)
1618 throw(std::runtime_error("max recursion level reached"));
1621 epvector::const_iterator last = seq.end();
1622 epvector::const_iterator cit = seq.begin();
1624 const ex &evaled_ex = cit->rest.eval(level);
1625 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1627 // something changed, copy seq, eval and return it
1628 std::auto_ptr<epvector> s(new epvector);
1629 s->reserve(seq.size());
1631 // copy parts of seq which are known not to have changed
1632 epvector::const_iterator cit2=seq.begin();
1634 s->push_back(*cit2);
1638 // copy first changed element
1639 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1644 while (cit2!=last) {
1645 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1654 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1657 /** Member-wise substitute in this sequence.
1659 * @see expairseq::subs()
1660 * @return pointer to epvector containing pairs after application of subs,
1661 * or NULL pointer if no members were changed. */
1662 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1664 // When any of the objects to be substituted is a product or power
1665 // we have to recombine the pairs because the numeric coefficients may
1666 // be part of the search pattern.
1667 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1669 // Search the list of substitutions and cache our findings
1670 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1671 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1672 options |= subs_options::pattern_is_product;
1676 if (!(options & subs_options::pattern_is_product))
1677 options |= subs_options::pattern_is_not_product;
1680 if (options & subs_options::pattern_is_product) {
1682 // Substitute in the recombined pairs
1683 epvector::const_iterator cit = seq.begin(), last = seq.end();
1684 while (cit != last) {
1686 const ex &orig_ex = recombine_pair_to_ex(*cit);
1687 const ex &subsed_ex = orig_ex.subs(m, options);
1688 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1690 // Something changed, copy seq, subs and return it
1691 std::auto_ptr<epvector> s(new epvector);
1692 s->reserve(seq.size());
1694 // Copy parts of seq which are known not to have changed
1695 s->insert(s->begin(), seq.begin(), cit);
1697 // Copy first changed element
1698 s->push_back(split_ex_to_pair(subsed_ex));
1702 while (cit != last) {
1703 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1714 // Substitute only in the "rest" part of the pairs
1715 epvector::const_iterator cit = seq.begin(), last = seq.end();
1716 while (cit != last) {
1718 const ex &subsed_ex = cit->rest.subs(m, options);
1719 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1721 // Something changed, copy seq, subs and return it
1722 std::auto_ptr<epvector> s(new epvector);
1723 s->reserve(seq.size());
1725 // Copy parts of seq which are known not to have changed
1726 s->insert(s->begin(), seq.begin(), cit);
1728 // Copy first changed element
1729 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1733 while (cit != last) {
1734 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1744 // Nothing has changed
1745 return std::auto_ptr<epvector>(0);
1749 // static member variables
1752 #if EXPAIRSEQ_USE_HASHTAB
1753 unsigned expairseq::maxhashtabsize = 0x4000000U;
1754 unsigned expairseq::minhashtabsize = 0x1000U;
1755 unsigned expairseq::hashtabfactor = 1;
1756 #endif // EXPAIRSEQ_USE_HASHTAB
1758 } // namespace GiNaC