1 /** @file expairseq.cpp
3 * Implementation of sequences of expression pairs. */
6 * GiNaC Copyright (C) 1999-2008 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
29 #include "expairseq.h"
34 #include "relational.h"
37 #include "operators.h"
41 #if EXPAIRSEQ_USE_HASHTAB
43 #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 const void* this_tinfo = (const void*)typeid(*this).name();
616 unsigned v = golden_ratio_hash((p_int)this_tinfo);
617 epvector::const_iterator i = seq.begin();
618 const epvector::const_iterator end = seq.end();
620 v ^= i->rest.gethash();
621 #if !EXPAIRSEQ_USE_HASHTAB
622 // rotation spoils commutativity!
624 v ^= i->coeff.gethash();
625 #endif // !EXPAIRSEQ_USE_HASHTAB
629 v ^= overall_coeff.gethash();
631 // store calculated hash value only if object is already evaluated
632 if (flags &status_flags::evaluated) {
633 setflag(status_flags::hash_calculated);
640 ex expairseq::expand(unsigned options) const
642 std::auto_ptr<epvector> vp = expandchildren(options);
644 return thisexpairseq(vp, overall_coeff);
646 // The terms have not changed, so it is safe to declare this expanded
647 return (options == 0) ? setflag(status_flags::expanded) : *this;
652 // new virtual functions which can be overridden by derived classes
657 /** Create an object of this type.
658 * This method works similar to a constructor. It is useful because expairseq
659 * has (at least) two possible different semantics but we want to inherit
660 * methods thus avoiding code duplication. Sometimes a method in expairseq
661 * has to create a new one of the same semantics, which cannot be done by a
662 * ctor because the name (add, mul,...) is unknown on the expaiseq level. In
663 * order for this trick to work a derived class must of course override this
665 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
667 return expairseq(v, oc, do_index_renaming);
670 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
672 return expairseq(vp, oc, do_index_renaming);
675 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
678 p.rest.print(c, precedence());
680 p.coeff.print(c, precedence());
684 void expairseq::printseq(const print_context & c, char delim,
685 unsigned this_precedence,
686 unsigned upper_precedence) const
688 if (this_precedence <= upper_precedence)
690 epvector::const_iterator it, it_last = seq.end() - 1;
691 for (it=seq.begin(); it!=it_last; ++it) {
692 printpair(c, *it, this_precedence);
695 printpair(c, *it, this_precedence);
696 if (!overall_coeff.is_equal(default_overall_coeff())) {
698 overall_coeff.print(c, this_precedence);
701 if (this_precedence <= upper_precedence)
706 /** Form an expair from an ex, using the corresponding semantics.
707 * @see expairseq::recombine_pair_to_ex() */
708 expair expairseq::split_ex_to_pair(const ex &e) const
710 return expair(e,_ex1);
714 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
717 GINAC_ASSERT(is_exactly_a<numeric>(c));
723 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
726 GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
727 GINAC_ASSERT(is_exactly_a<numeric>(c));
729 return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
733 /** Form an ex out of an expair, using the corresponding semantics.
734 * @see expairseq::split_ex_to_pair() */
735 ex expairseq::recombine_pair_to_ex(const expair &p) const
737 return lst(p.rest,p.coeff);
740 bool expairseq::expair_needs_further_processing(epp it)
742 #if EXPAIRSEQ_USE_HASHTAB
743 //# error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
744 #endif // EXPAIRSEQ_USE_HASHTAB
748 ex expairseq::default_overall_coeff() const
753 void expairseq::combine_overall_coeff(const ex &c)
755 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
756 GINAC_ASSERT(is_exactly_a<numeric>(c));
757 overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
760 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
762 GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
763 GINAC_ASSERT(is_exactly_a<numeric>(c1));
764 GINAC_ASSERT(is_exactly_a<numeric>(c2));
765 overall_coeff = ex_to<numeric>(overall_coeff).
766 add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
769 bool expairseq::can_make_flat(const expair &p) const
776 // non-virtual functions in this class
779 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
785 construct_from_exvector(v);
786 #if EXPAIRSEQ_USE_HASHTAB
787 GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
788 GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
789 #endif // EXPAIRSEQ_USE_HASHTAB
792 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
794 if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
795 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
796 #if EXPAIRSEQ_USE_HASHTAB
797 unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
798 ex_to<expairseq>(rh).seq.size();
799 if (calc_hashtabsize(totalsize)!=0) {
800 construct_from_2_ex_via_exvector(lh,rh);
802 #endif // EXPAIRSEQ_USE_HASHTAB
803 if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
804 rh.info(info_flags::has_indices)) {
805 ex newrh=rename_dummy_indices_uniquely(lh, rh);
806 construct_from_2_expairseq(ex_to<expairseq>(lh),
807 ex_to<expairseq>(newrh));
810 construct_from_2_expairseq(ex_to<expairseq>(lh),
811 ex_to<expairseq>(rh));
812 #if EXPAIRSEQ_USE_HASHTAB
814 #endif // EXPAIRSEQ_USE_HASHTAB
817 #if EXPAIRSEQ_USE_HASHTAB
818 unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
819 if (calc_hashtabsize(totalsize)!=0) {
820 construct_from_2_ex_via_exvector(lh, rh);
822 #endif // EXPAIRSEQ_USE_HASHTAB
823 construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
824 #if EXPAIRSEQ_USE_HASHTAB
826 #endif // EXPAIRSEQ_USE_HASHTAB
829 } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
830 #if EXPAIRSEQ_USE_HASHTAB
831 unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
832 if (calc_hashtabsize(totalsize)!=0) {
833 construct_from_2_ex_via_exvector(lh,rh);
835 #endif // EXPAIRSEQ_USE_HASHTAB
836 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
837 #if EXPAIRSEQ_USE_HASHTAB
839 #endif // EXPAIRSEQ_USE_HASHTAB
843 #if EXPAIRSEQ_USE_HASHTAB
844 if (calc_hashtabsize(2)!=0) {
845 construct_from_2_ex_via_exvector(lh,rh);
849 #endif // EXPAIRSEQ_USE_HASHTAB
851 if (is_exactly_a<numeric>(lh)) {
852 if (is_exactly_a<numeric>(rh)) {
853 combine_overall_coeff(lh);
854 combine_overall_coeff(rh);
856 combine_overall_coeff(lh);
857 seq.push_back(split_ex_to_pair(rh));
860 if (is_exactly_a<numeric>(rh)) {
861 combine_overall_coeff(rh);
862 seq.push_back(split_ex_to_pair(lh));
864 expair p1 = split_ex_to_pair(lh);
865 expair p2 = split_ex_to_pair(rh);
867 int cmpval = p1.rest.compare(p2.rest);
869 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
870 if (!ex_to<numeric>(p1.coeff).is_zero()) {
871 // no further processing is necessary, since this
872 // one element will usually be recombined in eval()
889 void expairseq::construct_from_2_expairseq(const expairseq &s1,
892 combine_overall_coeff(s1.overall_coeff);
893 combine_overall_coeff(s2.overall_coeff);
895 epvector::const_iterator first1 = s1.seq.begin();
896 epvector::const_iterator last1 = s1.seq.end();
897 epvector::const_iterator first2 = s2.seq.begin();
898 epvector::const_iterator last2 = s2.seq.end();
900 seq.reserve(s1.seq.size()+s2.seq.size());
902 bool needs_further_processing=false;
904 while (first1!=last1 && first2!=last2) {
905 int cmpval = (*first1).rest.compare((*first2).rest);
909 const numeric &newcoeff = ex_to<numeric>(first1->coeff).
910 add(ex_to<numeric>(first2->coeff));
911 if (!newcoeff.is_zero()) {
912 seq.push_back(expair(first1->rest,newcoeff));
913 if (expair_needs_further_processing(seq.end()-1)) {
914 needs_further_processing = true;
919 } else if (cmpval<0) {
920 seq.push_back(*first1);
923 seq.push_back(*first2);
928 while (first1!=last1) {
929 seq.push_back(*first1);
932 while (first2!=last2) {
933 seq.push_back(*first2);
937 if (needs_further_processing) {
940 construct_from_epvector(v);
944 void expairseq::construct_from_expairseq_ex(const expairseq &s,
947 combine_overall_coeff(s.overall_coeff);
948 if (is_exactly_a<numeric>(e)) {
949 combine_overall_coeff(e);
954 epvector::const_iterator first = s.seq.begin();
955 epvector::const_iterator last = s.seq.end();
956 expair p = split_ex_to_pair(e);
958 seq.reserve(s.seq.size()+1);
959 bool p_pushed = false;
961 bool needs_further_processing=false;
963 // merge p into s.seq
964 while (first!=last) {
965 int cmpval = (*first).rest.compare(p.rest);
968 const numeric &newcoeff = ex_to<numeric>(first->coeff).
969 add(ex_to<numeric>(p.coeff));
970 if (!newcoeff.is_zero()) {
971 seq.push_back(expair(first->rest,newcoeff));
972 if (expair_needs_further_processing(seq.end()-1))
973 needs_further_processing = true;
978 } else if (cmpval<0) {
979 seq.push_back(*first);
989 // while loop exited because p was pushed, now push rest of s.seq
990 while (first!=last) {
991 seq.push_back(*first);
995 // while loop exited because s.seq was pushed, now push p
999 if (needs_further_processing) {
1002 construct_from_epvector(v);
1006 void expairseq::construct_from_exvector(const exvector &v)
1008 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1009 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1010 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1011 // (same for (+,*) -> (*,^)
1014 #if EXPAIRSEQ_USE_HASHTAB
1015 combine_same_terms();
1018 combine_same_terms_sorted_seq();
1019 #endif // EXPAIRSEQ_USE_HASHTAB
1022 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
1024 // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
1025 // +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
1026 // +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
1027 // (same for (+,*) -> (*,^)
1029 make_flat(v, do_index_renaming);
1030 #if EXPAIRSEQ_USE_HASHTAB
1031 combine_same_terms();
1034 combine_same_terms_sorted_seq();
1035 #endif // EXPAIRSEQ_USE_HASHTAB
1038 /** Combine this expairseq with argument exvector.
1039 * It cares for associativity as well as for special handling of numerics. */
1040 void expairseq::make_flat(const exvector &v)
1042 exvector::const_iterator cit;
1044 // count number of operands which are of same expairseq derived type
1045 // and their cumulative number of operands
1046 int nexpairseqs = 0;
1048 bool do_idx_rename = false;
1051 while (cit!=v.end()) {
1052 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1054 noperands += ex_to<expairseq>(*cit).seq.size();
1056 if (is_a<mul>(*this) && (!do_idx_rename) &&
1057 cit->info(info_flags::has_indices))
1058 do_idx_rename = true;
1062 // reserve seq and coeffseq which will hold all operands
1063 seq.reserve(v.size()+noperands-nexpairseqs);
1065 // copy elements and split off numerical part
1066 make_flat_inserter mf(v, do_idx_rename);
1068 while (cit!=v.end()) {
1069 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
1070 ex newfactor = mf.handle_factor(*cit, _ex1);
1071 const expairseq &subseqref = ex_to<expairseq>(newfactor);
1072 combine_overall_coeff(subseqref.overall_coeff);
1073 epvector::const_iterator cit_s = subseqref.seq.begin();
1074 while (cit_s!=subseqref.seq.end()) {
1075 seq.push_back(*cit_s);
1079 if (is_exactly_a<numeric>(*cit))
1080 combine_overall_coeff(*cit);
1082 ex newfactor = mf.handle_factor(*cit, _ex1);
1083 seq.push_back(split_ex_to_pair(newfactor));
1090 /** Combine this expairseq with argument epvector.
1091 * It cares for associativity as well as for special handling of numerics. */
1092 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
1094 epvector::const_iterator cit;
1096 // count number of operands which are of same expairseq derived type
1097 // and their cumulative number of operands
1098 int nexpairseqs = 0;
1100 bool really_need_rename_inds = false;
1103 while (cit!=v.end()) {
1104 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
1106 noperands += ex_to<expairseq>(cit->rest).seq.size();
1108 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
1109 cit->rest.info(info_flags::has_indices))
1110 really_need_rename_inds = true;
1113 do_index_renaming = do_index_renaming && really_need_rename_inds;
1115 // reserve seq and coeffseq which will hold all operands
1116 seq.reserve(v.size()+noperands-nexpairseqs);
1117 make_flat_inserter mf(v, do_index_renaming);
1119 // copy elements and split off numerical part
1121 while (cit!=v.end()) {
1122 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
1123 this->can_make_flat(*cit)) {
1124 ex newrest = mf.handle_factor(cit->rest, cit->coeff);
1125 const expairseq &subseqref = ex_to<expairseq>(newrest);
1126 combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
1127 ex_to<numeric>(cit->coeff));
1128 epvector::const_iterator cit_s = subseqref.seq.begin();
1129 while (cit_s!=subseqref.seq.end()) {
1130 seq.push_back(expair(cit_s->rest,
1131 ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
1132 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
1137 if (cit->is_canonical_numeric())
1138 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
1140 ex rest = cit->rest;
1141 ex newrest = mf.handle_factor(rest, cit->coeff);
1142 if (are_ex_trivially_equal(newrest, rest))
1143 seq.push_back(*cit);
1145 seq.push_back(expair(newrest, cit->coeff));
1152 /** Brings this expairseq into a sorted (canonical) form. */
1153 void expairseq::canonicalize()
1155 std::sort(seq.begin(), seq.end(), expair_rest_is_less());
1159 /** Compact a presorted expairseq by combining all matching expairs to one
1160 * each. On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
1162 void expairseq::combine_same_terms_sorted_seq()
1167 bool needs_further_processing = false;
1169 epvector::iterator itin1 = seq.begin();
1170 epvector::iterator itin2 = itin1+1;
1171 epvector::iterator itout = itin1;
1172 epvector::iterator last = seq.end();
1173 // must_copy will be set to true the first time some combination is
1174 // possible from then on the sequence has changed and must be compacted
1175 bool must_copy = false;
1176 while (itin2!=last) {
1177 if (itin1->rest.compare(itin2->rest)==0) {
1178 itin1->coeff = ex_to<numeric>(itin1->coeff).
1179 add_dyn(ex_to<numeric>(itin2->coeff));
1180 if (expair_needs_further_processing(itin1))
1181 needs_further_processing = true;
1184 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1193 if (!ex_to<numeric>(itin1->coeff).is_zero()) {
1199 seq.erase(itout,last);
1201 if (needs_further_processing) {
1204 construct_from_epvector(v);
1208 #if EXPAIRSEQ_USE_HASHTAB
1210 unsigned expairseq::calc_hashtabsize(unsigned sz) const
1213 unsigned nearest_power_of_2 = 1 << log2(sz);
1214 // if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
1215 // size = nearest_power_of_2*hashtabfactor;
1216 size = nearest_power_of_2/hashtabfactor;
1217 if (size<minhashtabsize)
1220 // hashtabsize must be a power of 2
1221 GINAC_ASSERT((1U << log2(size))==size);
1225 unsigned expairseq::calc_hashindex(const ex &e) const
1227 // calculate hashindex
1229 if (is_a<numeric>(e)) {
1230 hashindex = hashmask;
1232 hashindex = e.gethash() & hashmask;
1233 // last hashtab entry is reserved for numerics
1234 if (hashindex==hashmask) hashindex = 0;
1236 GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
1240 void expairseq::shrink_hashtab()
1242 unsigned new_hashtabsize;
1243 while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
1244 GINAC_ASSERT(new_hashtabsize<hashtabsize);
1245 if (new_hashtabsize==0) {
1252 // shrink by a factor of 2
1253 unsigned half_hashtabsize = hashtabsize/2;
1254 for (unsigned i=0; i<half_hashtabsize-1; ++i)
1255 hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
1256 // special treatment for numeric hashes
1257 hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
1258 hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
1259 hashtab.resize(half_hashtabsize);
1260 hashtabsize = half_hashtabsize;
1261 hashmask = hashtabsize-1;
1265 void expairseq::remove_hashtab_entry(epvector::const_iterator element)
1268 return; // nothing to do
1270 // calculate hashindex of element to be deleted
1271 unsigned hashindex = calc_hashindex((*element).rest);
1273 // find it in hashtab and remove it
1274 epplist &eppl = hashtab[hashindex];
1275 epplist::iterator epplit = eppl.begin();
1276 bool erased = false;
1277 while (epplit!=eppl.end()) {
1278 if (*epplit == element) {
1286 std::cout << "tried to erase " << element-seq.begin() << std::endl;
1287 std::cout << "size " << seq.end()-seq.begin() << std::endl;
1289 unsigned hashindex = calc_hashindex(element->rest);
1290 epplist &eppl = hashtab[hashindex];
1291 epplist::iterator epplit = eppl.begin();
1292 bool erased = false;
1293 while (epplit!=eppl.end()) {
1294 if (*epplit == element) {
1301 GINAC_ASSERT(erased);
1303 GINAC_ASSERT(erased);
1306 void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
1307 epvector::iterator newpos)
1309 GINAC_ASSERT(hashtabsize!=0);
1311 // calculate hashindex of element which was moved
1312 unsigned hashindex=calc_hashindex((*newpos).rest);
1314 // find it in hashtab and modify it
1315 epplist &eppl = hashtab[hashindex];
1316 epplist::iterator epplit = eppl.begin();
1317 while (epplit!=eppl.end()) {
1318 if (*epplit == oldpos) {
1324 GINAC_ASSERT(epplit!=eppl.end());
1327 void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
1329 epplist::const_iterator current = eppl.begin();
1330 while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
1333 eppl.insert(current,elem);
1336 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
1337 epvector::iterator &last_non_zero,
1338 std::vector<bool> &touched,
1339 unsigned &number_of_zeroes)
1341 epp current = seq.begin();
1343 while (current!=first_numeric) {
1344 if (is_exactly_a<numeric>(current->rest)) {
1346 iter_swap(current,first_numeric);
1348 // calculate hashindex
1349 unsigned currenthashindex = calc_hashindex(current->rest);
1351 // test if there is already a matching expair in the hashtab-list
1352 epplist &eppl=hashtab[currenthashindex];
1353 epplist::iterator epplit = eppl.begin();
1354 while (epplit!=eppl.end()) {
1355 if (current->rest.is_equal((*epplit)->rest))
1359 if (epplit==eppl.end()) {
1360 // no matching expair found, append this to end of list
1361 sorted_insert(eppl,current);
1364 // epplit points to a matching expair, combine it with current
1365 (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
1366 add_dyn(ex_to<numeric>(current->coeff));
1368 // move obsolete current expair to end by swapping with last_non_zero element
1369 // if this was a numeric, it is swapped with the expair before first_numeric
1370 iter_swap(current,last_non_zero);
1372 if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
1375 // test if combined term has coeff 0 and can be removed is done later
1376 touched[(*epplit)-seq.begin()] = true;
1382 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
1383 epvector::iterator &last_non_zero,
1384 std::vector<bool> &touched,
1385 unsigned &number_of_zeroes)
1387 // move terms with coeff 0 to end and remove them from hashtab
1388 // check only those elements which have been touched
1389 epp current = seq.begin();
1391 while (current!=first_numeric) {
1395 } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
1399 remove_hashtab_entry(current);
1401 // move element to the end, unless it is already at the end
1402 if (current!=last_non_zero) {
1403 iter_swap(current,last_non_zero);
1405 bool numeric_swapped = first_numeric!=last_non_zero;
1406 if (numeric_swapped)
1407 iter_swap(first_numeric,current);
1408 epvector::iterator changed_entry;
1410 if (numeric_swapped)
1411 changed_entry = first_numeric;
1413 changed_entry = last_non_zero;
1418 if (first_numeric!=current) {
1420 // change entry in hashtab which referred to first_numeric or last_non_zero to current
1421 move_hashtab_entry(changed_entry,current);
1422 touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
1431 GINAC_ASSERT(i==current-seq.begin());
1434 /** True if one of the coeffs vanishes, otherwise false.
1435 * This would be an invariant violation, so this should only be used for
1436 * debugging purposes. */
1437 bool expairseq::has_coeff_0() const
1439 epvector::const_iterator i = seq.begin(), end = seq.end();
1441 if (i->coeff.is_zero())
1448 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
1449 epvector::const_iterator last_non_zero)
1451 if (first_numeric == seq.end()) return; // no numerics
1453 epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
1454 while (current != last) {
1455 sorted_insert(hashtab[hashmask], current);
1460 void expairseq::combine_same_terms()
1462 // combine same terms, drop term with coeff 0, move numerics to end
1464 // calculate size of hashtab
1465 hashtabsize = calc_hashtabsize(seq.size());
1467 // hashtabsize is a power of 2
1468 hashmask = hashtabsize-1;
1472 hashtab.resize(hashtabsize);
1474 if (hashtabsize==0) {
1476 combine_same_terms_sorted_seq();
1477 GINAC_ASSERT(!has_coeff_0());
1481 // iterate through seq, move numerics to end,
1482 // fill hashtab and combine same terms
1483 epvector::iterator first_numeric = seq.end();
1484 epvector::iterator last_non_zero = seq.end()-1;
1486 size_t num = seq.size();
1487 std::vector<bool> touched(num);
1489 unsigned number_of_zeroes = 0;
1491 GINAC_ASSERT(!has_coeff_0());
1492 build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
1494 // there should not be any terms with coeff 0 from the beginning,
1495 // so it should be safe to skip this step
1496 if (number_of_zeroes!=0) {
1497 drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
1500 add_numerics_to_hashtab(first_numeric,last_non_zero);
1502 // pop zero elements
1503 for (unsigned i=0; i<number_of_zeroes; ++i) {
1507 // shrink hashtabsize to calculated value
1508 GINAC_ASSERT(!has_coeff_0());
1512 GINAC_ASSERT(!has_coeff_0());
1515 #endif // EXPAIRSEQ_USE_HASHTAB
1517 /** Check if this expairseq is in sorted (canonical) form. Useful mainly for
1518 * debugging or in assertions since being sorted is an invariance. */
1519 bool expairseq::is_canonical() const
1521 if (seq.size() <= 1)
1524 #if EXPAIRSEQ_USE_HASHTAB
1525 if (hashtabsize > 0) return 1; // not canoncalized
1526 #endif // EXPAIRSEQ_USE_HASHTAB
1528 epvector::const_iterator it = seq.begin(), itend = seq.end();
1529 epvector::const_iterator it_last = it;
1530 for (++it; it!=itend; it_last=it, ++it) {
1531 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1532 if (!is_exactly_a<numeric>(it_last->rest) ||
1533 !is_exactly_a<numeric>(it->rest)) {
1534 // double test makes it easier to set a breakpoint...
1535 if (!is_exactly_a<numeric>(it_last->rest) ||
1536 !is_exactly_a<numeric>(it->rest)) {
1537 printpair(std::clog, *it_last, 0);
1539 printpair(std::clog, *it, 0);
1541 std::clog << "pair1:" << std::endl;
1542 it_last->rest.print(print_tree(std::clog));
1543 it_last->coeff.print(print_tree(std::clog));
1544 std::clog << "pair2:" << std::endl;
1545 it->rest.print(print_tree(std::clog));
1546 it->coeff.print(print_tree(std::clog));
1556 /** Member-wise expand the expairs in this sequence.
1558 * @see expairseq::expand()
1559 * @return pointer to epvector containing expanded pairs or zero pointer,
1560 * if no members were changed. */
1561 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1563 const epvector::const_iterator last = seq.end();
1564 epvector::const_iterator cit = seq.begin();
1566 const ex &expanded_ex = cit->rest.expand(options);
1567 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1569 // something changed, copy seq, eval and return it
1570 std::auto_ptr<epvector> s(new epvector);
1571 s->reserve(seq.size());
1573 // copy parts of seq which are known not to have changed
1574 epvector::const_iterator cit2 = seq.begin();
1576 s->push_back(*cit2);
1580 // copy first changed element
1581 s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1586 while (cit2!=last) {
1587 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1596 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1600 /** Member-wise evaluate the expairs in this sequence.
1602 * @see expairseq::eval()
1603 * @return pointer to epvector containing evaluated pairs or zero pointer,
1604 * if no members were changed. */
1605 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1607 // returns a NULL pointer if nothing had to be evaluated
1608 // returns a pointer to a newly created epvector otherwise
1609 // (which has to be deleted somewhere else)
1612 return std::auto_ptr<epvector>(0);
1614 if (level == -max_recursion_level)
1615 throw(std::runtime_error("max recursion level reached"));
1618 epvector::const_iterator last = seq.end();
1619 epvector::const_iterator cit = seq.begin();
1621 const ex &evaled_ex = cit->rest.eval(level);
1622 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1624 // something changed, copy seq, eval and return it
1625 std::auto_ptr<epvector> s(new epvector);
1626 s->reserve(seq.size());
1628 // copy parts of seq which are known not to have changed
1629 epvector::const_iterator cit2=seq.begin();
1631 s->push_back(*cit2);
1635 // copy first changed element
1636 s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1641 while (cit2!=last) {
1642 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1651 return std::auto_ptr<epvector>(0); // signalling nothing has changed
1654 /** Member-wise substitute in this sequence.
1656 * @see expairseq::subs()
1657 * @return pointer to epvector containing pairs after application of subs,
1658 * or NULL pointer if no members were changed. */
1659 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1661 // When any of the objects to be substituted is a product or power
1662 // we have to recombine the pairs because the numeric coefficients may
1663 // be part of the search pattern.
1664 if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1666 // Search the list of substitutions and cache our findings
1667 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1668 if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1669 options |= subs_options::pattern_is_product;
1673 if (!(options & subs_options::pattern_is_product))
1674 options |= subs_options::pattern_is_not_product;
1677 if (options & subs_options::pattern_is_product) {
1679 // Substitute in the recombined pairs
1680 epvector::const_iterator cit = seq.begin(), last = seq.end();
1681 while (cit != last) {
1683 const ex &orig_ex = recombine_pair_to_ex(*cit);
1684 const ex &subsed_ex = orig_ex.subs(m, options);
1685 if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1687 // Something changed, copy seq, subs and return it
1688 std::auto_ptr<epvector> s(new epvector);
1689 s->reserve(seq.size());
1691 // Copy parts of seq which are known not to have changed
1692 s->insert(s->begin(), seq.begin(), cit);
1694 // Copy first changed element
1695 s->push_back(split_ex_to_pair(subsed_ex));
1699 while (cit != last) {
1700 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1711 // Substitute only in the "rest" part of the pairs
1712 epvector::const_iterator cit = seq.begin(), last = seq.end();
1713 while (cit != last) {
1715 const ex &subsed_ex = cit->rest.subs(m, options);
1716 if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1718 // Something changed, copy seq, subs and return it
1719 std::auto_ptr<epvector> s(new epvector);
1720 s->reserve(seq.size());
1722 // Copy parts of seq which are known not to have changed
1723 s->insert(s->begin(), seq.begin(), cit);
1725 // Copy first changed element
1726 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1730 while (cit != last) {
1731 s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1741 // Nothing has changed
1742 return std::auto_ptr<epvector>(0);
1746 // static member variables
1749 #if EXPAIRSEQ_USE_HASHTAB
1750 unsigned expairseq::maxhashtabsize = 0x4000000U;
1751 unsigned expairseq::minhashtabsize = 0x1000U;
1752 unsigned expairseq::hashtabfactor = 1;
1753 #endif // EXPAIRSEQ_USE_HASHTAB
1755 } // namespace GiNaC