ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
   7  *
   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.
  12  *
  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.
  17  *
  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
  21  */
  22
  23 #include "expairseq.h"
  24 #include "lst.h"
  25 #include "add.h"
  26 #include "mul.h"
  27 #include "power.h"
  28 #include "relational.h"
  29 #include "wildcard.h"
  30 #include "archive.h"
  31 #include "operators.h"
  32 #include "utils.h"
  33 #include "hash_seed.h"
  34 #include "indexed.h"
  35
  36 #include <algorithm>
  37 #include <iostream>
  38 #include <iterator>
  39 #include <stdexcept>
  40 #include <string>
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  46   print_func<print_context>(&expairseq::do_print).
  47   print_func<print_tree>(&expairseq::do_print_tree))
  48
  49
  50 //////////
  51 // helper classes
  52 //////////
  53
  54 class epp_is_less
  55 {
  56 public:
  57         bool operator()(const epp &lh, const epp &rh) const
  58         {
  59                 return (*lh).is_less(*rh);
  60         }
  61 };
  62
  63 //////////
  64 // default constructor
  65 //////////
  66
  67 // public
  68
  69 expairseq::expairseq()
  70 {}
  71
  72 // protected
  73
  74 //////////
  75 // other constructors
  76 //////////
  77
  78 expairseq::expairseq(const ex &lh, const ex &rh)
  79 {
  80         construct_from_2_ex(lh,rh);
  81         GINAC_ASSERT(is_canonical());
  82 }
  83
  84 expairseq::expairseq(const exvector &v)
  85 {
  86         construct_from_exvector(v);
  87         GINAC_ASSERT(is_canonical());
  88 }
  89
  90 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
  91   :  overall_coeff(oc)
  92 {
  93         GINAC_ASSERT(is_a<numeric>(oc));
  94         construct_from_epvector(v, do_index_renaming);
  95         GINAC_ASSERT(is_canonical());
  96 }
  97
  98 expairseq::expairseq(epvector && vp, const ex &oc, bool do_index_renaming)
  99   :  overall_coeff(oc)
 100 {
 101         GINAC_ASSERT(is_a<numeric>(oc));
 102         construct_from_epvector(std::move(vp), do_index_renaming);
 103         GINAC_ASSERT(is_canonical());
 104 }
 105
 106 //////////
 107 // archiving
 108 //////////
 109
 110 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
 111 {
 112         inherited::read_archive(n, sym_lst);
 113         auto first = n.find_first("rest");
 114         auto last = n.find_last("coeff");
 115         ++last;
 116         seq.reserve((last-first)/2);
 117
 118         for (auto loc = first; loc < last;) {
 119                 ex rest;
 120                 ex coeff;
 121                 n.find_ex_by_loc(loc++, rest, sym_lst);
 122                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 123                 seq.push_back(expair(rest, coeff));
 124         }
 125
 126         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 127
 128         canonicalize();
 129         GINAC_ASSERT(is_canonical());
 130 }
 131
 132 void expairseq::archive(archive_node &n) const
 133 {
 134         inherited::archive(n);
 135         for (auto & i : seq) {
 136                 n.add_ex("rest", i.rest);
 137                 n.add_ex("coeff", i.coeff);
 138         }
 139         n.add_ex("overall_coeff", overall_coeff);
 140 }
 141
 142
 143 //////////
 144 // functions overriding virtual functions from base classes
 145 //////////
 146
 147 // public
 148
 149 void expairseq::do_print(const print_context & c, unsigned level) const
 150 {
 151         c.s << "[[";
 152         printseq(c, ',', precedence(), level);
 153         c.s << "]]";
 154 }
 155
 156 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 157 {
 158         c.s << std::string(level, ' ') << class_name() << " @" << this
 159             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 160             << ", nops=" << nops()
 161             << std::endl;
 162         size_t num = seq.size();
 163         for (size_t i=0; i<num; ++i) {
 164                 seq[i].rest.print(c, level + c.delta_indent);
 165                 seq[i].coeff.print(c, level + c.delta_indent);
 166                 if (i != num - 1)
 167                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 168         }
 169         if (!overall_coeff.is_equal(default_overall_coeff())) {
 170                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 171                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 172                 overall_coeff.print(c, level + c.delta_indent);
 173         }
 174         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 175 }
 176
 177 bool expairseq::info(unsigned inf) const
 178 {
 179         switch(inf) {
 180                 case info_flags::expanded:
 181                         return (flags & status_flags::expanded);
 182                 case info_flags::has_indices: {
 183                         if (flags & status_flags::has_indices)
 184                                 return true;
 185                         else if (flags & status_flags::has_no_indices)
 186                                 return false;
 187                         for (auto & i : seq) {
 188                                 if (i.rest.info(info_flags::has_indices)) {
 189                                         this->setflag(status_flags::has_indices);
 190                                         this->clearflag(status_flags::has_no_indices);
 191                                         return true;
 192                                 }
 193                         }
 194                         this->clearflag(status_flags::has_indices);
 195                         this->setflag(status_flags::has_no_indices);
 196                         return false;
 197                 }
 198         }
 199         return inherited::info(inf);
 200 }
 201
 202 size_t expairseq::nops() const
 203 {
 204         if (overall_coeff.is_equal(default_overall_coeff()))
 205                 return seq.size();
 206         else
 207                 return seq.size()+1;
 208 }
 209
 210 ex expairseq::op(size_t i) const
 211 {
 212         if (i < seq.size())
 213                 return recombine_pair_to_ex(seq[i]);
 214         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 215         return overall_coeff;
 216 }
 217
 218 ex expairseq::map(map_function &f) const
 219 {
 220         epvector v;
 221         v.reserve(seq.size()+1);
 222
 223         for (auto & it : seq)
 224                 v.push_back(split_ex_to_pair(f(recombine_pair_to_ex(it))));
 225
 226         if (overall_coeff.is_equal(default_overall_coeff()))
 227                 return thisexpairseq(std::move(v), default_overall_coeff(), true);
 228         else {
 229                 ex newcoeff = f(overall_coeff);
 230                 if(is_a<numeric>(newcoeff))
 231                         return thisexpairseq(std::move(v), newcoeff, true);
 232                 else {
 233                         v.push_back(split_ex_to_pair(newcoeff));
 234                         return thisexpairseq(std::move(v), default_overall_coeff(), true);
 235                 }
 236         }
 237 }
 238
 239 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 240 ex expairseq::eval(int level) const
 241 {
 242         if ((level==1) && (flags &status_flags::evaluated))
 243                 return *this;
 244
 245         epvector evaled = evalchildren(level);
 246         if (!evaled.empty())
 247                 return (new expairseq(std::move(evaled), overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 248         else
 249                 return this->hold();
 250 }
 251
 252 epvector* conjugateepvector(const epvector&epv)
 253 {
 254         epvector *newepv = nullptr;
 255         for (auto i=epv.begin(); i!=epv.end(); ++i) {
 256                 if (newepv) {
 257                         newepv->push_back(i->conjugate());
 258                         continue;
 259                 }
 260                 expair x = i->conjugate();
 261                 if (x.is_equal(*i)) {
 262                         continue;
 263                 }
 264                 newepv = new epvector;
 265                 newepv->reserve(epv.size());
 266                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 267                         newepv->push_back(*j);
 268                 }
 269                 newepv->push_back(x);
 270         }
 271         return newepv;
 272 }
 273
 274 ex expairseq::conjugate() const
 275 {
 276         std::unique_ptr<epvector> newepv(conjugateepvector(seq));
 277         ex x = overall_coeff.conjugate();
 278         if (newepv) {
 279                 return thisexpairseq(std::move(*newepv), x);
 280         }
 281         if (are_ex_trivially_equal(x, overall_coeff)) {
 282                 return *this;
 283         }
 284         return thisexpairseq(seq, x);
 285 }
 286
 287 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 288 {
 289         // This differs from basic::match() because we want "a+b+c+d" to
 290         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 291
 292         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 293
 294                 // Check whether global wildcard (one that matches the "rest of the
 295                 // expression", like "*" above) is present
 296                 bool has_global_wildcard = false;
 297                 ex global_wildcard;
 298                 for (size_t i=0; i<pattern.nops(); i++) {
 299                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 300                                 has_global_wildcard = true;
 301                                 global_wildcard = pattern.op(i);
 302                                 break;
 303                         }
 304                 }
 305
 306                 // Even if the expression does not match the pattern, some of
 307                 // its subexpressions could match it. For example, x^5*y^(-1)
 308                 // does not match the pattern $0^5, but its subexpression x^5
 309                 // does. So, save repl_lst in order to not add bogus entries.
 310                 exmap tmp_repl = repl_lst;
 311
 312                 // Unfortunately, this is an O(N^2) operation because we can't
 313                 // sort the pattern in a useful way...
 314
 315                 // Chop into terms
 316                 exvector ops;
 317                 ops.reserve(nops());
 318                 for (size_t i=0; i<nops(); i++)
 319                         ops.push_back(op(i));
 320
 321                 // Now, for every term of the pattern, look for a matching term in
 322                 // the expression and remove the match
 323                 for (size_t i=0; i<pattern.nops(); i++) {
 324                         ex p = pattern.op(i);
 325                         if (has_global_wildcard && p.is_equal(global_wildcard))
 326                                 continue;
 327                         auto it = ops.begin(), itend = ops.end();
 328                         while (it != itend) {
 329                                 if (it->match(p, tmp_repl)) {
 330                                         ops.erase(it);
 331                                         goto found;
 332                                 }
 333                                 ++it;
 334                         }
 335                         return false; // no match found
 336 found:          ;
 337                 }
 338
 339                 if (has_global_wildcard) {
 340
 341                         // Assign all the remaining terms to the global wildcard (unless
 342                         // it has already been matched before, in which case the matches
 343                         // must be equal)
 344                         size_t num = ops.size();
 345                         epvector vp;
 346                         vp.reserve(num);
 347                         for (size_t i=0; i<num; i++)
 348                                 vp.push_back(split_ex_to_pair(ops[i]));
 349                         ex rest = thisexpairseq(std::move(vp), default_overall_coeff());
 350                         for (auto & it : tmp_repl) {
 351                                 if (it.first.is_equal(global_wildcard)) {
 352                                         if (rest.is_equal(it.second)) {
 353                                                 repl_lst = tmp_repl;
 354                                                 return true;
 355                                         }
 356                                         return false;
 357                                 }
 358                         }
 359                         repl_lst = tmp_repl;
 360                         repl_lst[global_wildcard] = rest;
 361                         return true;
 362
 363                 } else {
 364
 365                         // No global wildcard, then the match fails if there are any
 366                         // unmatched terms left
 367                         if (ops.empty()) {
 368                                 repl_lst = tmp_repl;
 369                                 return true;
 370                         }
 371                         return false;
 372                 }
 373         }
 374         return inherited::match(pattern, repl_lst);
 375 }
 376
 377 ex expairseq::subs(const exmap & m, unsigned options) const
 378 {
 379         epvector subsed = subschildren(m, options);
 380         if (!subsed.empty())
 381                 return ex_to<basic>(thisexpairseq(std::move(subsed), overall_coeff, (options & subs_options::no_index_renaming) == 0));
 382         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 383                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 384         else
 385                 return subs_one_level(m, options);
 386 }
 387
 388 // protected
 389
 390 int expairseq::compare_same_type(const basic &other) const
 391 {
 392         GINAC_ASSERT(is_a<expairseq>(other));
 393         const expairseq &o = static_cast<const expairseq &>(other);
 394
 395         int cmpval;
 396
 397         // compare number of elements
 398         if (seq.size() != o.seq.size())
 399                 return (seq.size()<o.seq.size()) ? -1 : 1;
 400
 401         // compare overall_coeff
 402         cmpval = overall_coeff.compare(o.overall_coeff);
 403         if (cmpval!=0)
 404                 return cmpval;
 405
 406         auto cit1 = seq.begin(), last1 = seq.end();
 407         auto cit2 = o.seq.begin(), last2 = o.seq.end();
 408         for (; (cit1!=last1) && (cit2!=last2); ++cit1, ++cit2) {
 409                 cmpval = (*cit1).compare(*cit2);
 410                 if (cmpval!=0) return cmpval;
 411         }
 412
 413         GINAC_ASSERT(cit1==last1);
 414         GINAC_ASSERT(cit2==last2);
 415
 416         return 0;
 417 }
 418
 419 bool expairseq::is_equal_same_type(const basic &other) const
 420 {
 421         const expairseq &o = static_cast<const expairseq &>(other);
 422
 423         // compare number of elements
 424         if (seq.size()!=o.seq.size())
 425                 return false;
 426
 427         // compare overall_coeff
 428         if (!overall_coeff.is_equal(o.overall_coeff))
 429                 return false;
 430
 431         auto cit2 = o.seq.begin();
 432         for (auto & cit1 : seq) {
 433                 if (!cit1.is_equal(*cit2))
 434                         return false;
 435                 ++cit2;
 436         }
 437
 438         return true;
 439 }
 440
 441 unsigned expairseq::return_type() const
 442 {
 443         return return_types::noncommutative_composite;
 444 }
 445
 446 unsigned expairseq::calchash() const
 447 {
 448         unsigned v = make_hash_seed(typeid(*this));
 449         for (auto & i : seq) {
 450                 v ^= i.rest.gethash();
 451                 v = rotate_left(v);
 452                 v ^= i.coeff.gethash();
 453         }
 454
 455         v ^= overall_coeff.gethash();
 456
 457         // store calculated hash value only if object is already evaluated
 458         if (flags &status_flags::evaluated) {
 459                 setflag(status_flags::hash_calculated);
 460                 hashvalue = v;
 461         }
 462
 463         return v;
 464 }
 465
 466 ex expairseq::expand(unsigned options) const
 467 {
 468         epvector expanded = expandchildren(options);
 469         if (!expanded.empty()) {
 470                 return thisexpairseq(std::move(expanded), overall_coeff);
 471         }
 472         return (options == 0) ? setflag(status_flags::expanded) : *this;
 473 }
 474
 475 //////////
 476 // new virtual functions which can be overridden by derived classes
 477 //////////
 478
 479 // protected
 480
 481 /** Create an object of this type.
 482  *  This method works similar to a constructor.  It is useful because expairseq
 483  *  has (at least) two possible different semantics but we want to inherit
 484  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 485  *  has to create a new one of the same semantics, which cannot be done by a
 486  *  ctor because the name (add, mul,...) is unknown on the expairseq level.  In
 487  *  order for this trick to work a derived class must of course override this
 488  *  definition. */
 489 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 490 {
 491         return expairseq(v, oc, do_index_renaming);
 492 }
 493
 494 ex expairseq::thisexpairseq(epvector && vp, const ex &oc, bool do_index_renaming) const
 495 {
 496         return expairseq(std::move(vp), oc, do_index_renaming);
 497 }
 498
 499 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 500 {
 501         c.s << "[[";
 502         p.rest.print(c, precedence());
 503         c.s << ",";
 504         p.coeff.print(c, precedence());
 505         c.s << "]]";
 506 }
 507
 508 void expairseq::printseq(const print_context & c, char delim,
 509                          unsigned this_precedence,
 510                          unsigned upper_precedence) const
 511 {
 512         if (this_precedence <= upper_precedence)
 513                 c.s << "(";
 514         auto it = seq.begin(), it_last = seq.end() - 1;
 515         for (; it!=it_last; ++it) {
 516                 printpair(c, *it, this_precedence);
 517                 c.s << delim;
 518         }
 519         printpair(c, *it, this_precedence);
 520         if (!overall_coeff.is_equal(default_overall_coeff())) {
 521                 c.s << delim;
 522                 overall_coeff.print(c, this_precedence);
 523         }
 524
 525         if (this_precedence <= upper_precedence)
 526                 c.s << ")";
 527 }
 528
 529
 530 /** Form an expair from an ex, using the corresponding semantics.
 531  *  @see expairseq::recombine_pair_to_ex() */
 532 expair expairseq::split_ex_to_pair(const ex &e) const
 533 {
 534         return expair(e,_ex1);
 535 }
 536
 537
 538 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 539                                                 const ex &c) const
 540 {
 541         GINAC_ASSERT(is_exactly_a<numeric>(c));
 542
 543         return expair(e,c);
 544 }
 545
 546
 547 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 548                                                   const ex &c) const
 549 {
 550         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 551         GINAC_ASSERT(is_exactly_a<numeric>(c));
 552
 553         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 554 }
 555
 556
 557 /** Form an ex out of an expair, using the corresponding semantics.
 558  *  @see expairseq::split_ex_to_pair() */
 559 ex expairseq::recombine_pair_to_ex(const expair &p) const
 560 {
 561         return lst(p.rest,p.coeff);
 562 }
 563
 564 bool expairseq::expair_needs_further_processing(epp it)
 565 {
 566         return false;
 567 }
 568
 569 ex expairseq::default_overall_coeff() const
 570 {
 571         return _ex0;
 572 }
 573
 574 void expairseq::combine_overall_coeff(const ex &c)
 575 {
 576         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 577         GINAC_ASSERT(is_exactly_a<numeric>(c));
 578         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 579 }
 580
 581 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 582 {
 583         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 584         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 585         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 586         overall_coeff = ex_to<numeric>(overall_coeff).
 587                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 588 }
 589
 590 bool expairseq::can_make_flat(const expair &p) const
 591 {
 592         return true;
 593 }
 594
 595
 596 //////////
 597 // non-virtual functions in this class
 598 //////////
 599
 600 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 601 {
 602         exvector v;
 603         v.reserve(2);
 604         v.push_back(lh);
 605         v.push_back(rh);
 606         construct_from_exvector(v);
 607 }
 608
 609 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 610 {
 611         if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
 612                 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 613                         if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 614                                 rh.info(info_flags::has_indices)) {
 615                                 ex newrh=rename_dummy_indices_uniquely(lh, rh);
 616                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 617                                                            ex_to<expairseq>(newrh));
 618                         }
 619                         else
 620                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 621                                                            ex_to<expairseq>(rh));
 622                         return;
 623                 } else {
 624                         construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 625                         return;
 626                 }
 627         } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 628                 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 629                 return;
 630         }
 631
 632         if (is_exactly_a<numeric>(lh)) {
 633                 if (is_exactly_a<numeric>(rh)) {
 634                         combine_overall_coeff(lh);
 635                         combine_overall_coeff(rh);
 636                 } else {
 637                         combine_overall_coeff(lh);
 638                         seq.push_back(split_ex_to_pair(rh));
 639                 }
 640         } else {
 641                 if (is_exactly_a<numeric>(rh)) {
 642                         combine_overall_coeff(rh);
 643                         seq.push_back(split_ex_to_pair(lh));
 644                 } else {
 645                         expair p1 = split_ex_to_pair(lh);
 646                         expair p2 = split_ex_to_pair(rh);
 647
 648                         int cmpval = p1.rest.compare(p2.rest);
 649                         if (cmpval==0) {
 650                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 651                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 652                                         // no further processing is necessary, since this
 653                                         // one element will usually be recombined in eval()
 654                                         seq.push_back(p1);
 655                                 }
 656                         } else {
 657                                 seq.reserve(2);
 658                                 if (cmpval<0) {
 659                                         seq.push_back(p1);
 660                                         seq.push_back(p2);
 661                                 } else {
 662                                         seq.push_back(p2);
 663                                         seq.push_back(p1);
 664                                 }
 665                         }
 666                 }
 667         }
 668 }
 669
 670 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 671                                            const expairseq &s2)
 672 {
 673         combine_overall_coeff(s1.overall_coeff);
 674         combine_overall_coeff(s2.overall_coeff);
 675
 676         auto first1 = s1.seq.begin(), last1 = s1.seq.end();
 677         auto first2 = s2.seq.begin(), last2 = s2.seq.end();
 678
 679         seq.reserve(s1.seq.size()+s2.seq.size());
 680
 681         bool needs_further_processing=false;
 682
 683         while (first1!=last1 && first2!=last2) {
 684                 int cmpval = (*first1).rest.compare((*first2).rest);
 685
 686                 if (cmpval==0) {
 687                         // combine terms
 688                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 689                                                    add(ex_to<numeric>(first2->coeff));
 690                         if (!newcoeff.is_zero()) {
 691                                 seq.push_back(expair(first1->rest,newcoeff));
 692                                 if (expair_needs_further_processing(seq.end()-1)) {
 693                                         needs_further_processing = true;
 694                                 }
 695                         }
 696                         ++first1;
 697                         ++first2;
 698                 } else if (cmpval<0) {
 699                         seq.push_back(*first1);
 700                         ++first1;
 701                 } else {
 702                         seq.push_back(*first2);
 703                         ++first2;
 704                 }
 705         }
 706
 707         while (first1!=last1) {
 708                 seq.push_back(*first1);
 709                 ++first1;
 710         }
 711         while (first2!=last2) {
 712                 seq.push_back(*first2);
 713                 ++first2;
 714         }
 715
 716         if (needs_further_processing) {
 717                 epvector v = seq;
 718                 seq.clear();
 719                 construct_from_epvector(std::move(v));
 720         }
 721 }
 722
 723 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 724                                             const ex &e)
 725 {
 726         combine_overall_coeff(s.overall_coeff);
 727         if (is_exactly_a<numeric>(e)) {
 728                 combine_overall_coeff(e);
 729                 seq = s.seq;
 730                 return;
 731         }
 732
 733         auto first = s.seq.begin(), last = s.seq.end();
 734         expair p = split_ex_to_pair(e);
 735
 736         seq.reserve(s.seq.size()+1);
 737         bool p_pushed = false;
 738
 739         bool needs_further_processing=false;
 740
 741         // merge p into s.seq
 742         while (first!=last) {
 743                 int cmpval = (*first).rest.compare(p.rest);
 744                 if (cmpval==0) {
 745                         // combine terms
 746                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 747                                                    add(ex_to<numeric>(p.coeff));
 748                         if (!newcoeff.is_zero()) {
 749                                 seq.push_back(expair(first->rest,newcoeff));
 750                                 if (expair_needs_further_processing(seq.end()-1))
 751                                         needs_further_processing = true;
 752                         }
 753                         ++first;
 754                         p_pushed = true;
 755                         break;
 756                 } else if (cmpval<0) {
 757                         seq.push_back(*first);
 758                         ++first;
 759                 } else {
 760                         seq.push_back(p);
 761                         p_pushed = true;
 762                         break;
 763                 }
 764         }
 765
 766         if (p_pushed) {
 767                 // while loop exited because p was pushed, now push rest of s.seq
 768                 while (first!=last) {
 769                         seq.push_back(*first);
 770                         ++first;
 771                 }
 772         } else {
 773                 // while loop exited because s.seq was pushed, now push p
 774                 seq.push_back(p);
 775         }
 776
 777         if (needs_further_processing) {
 778                 epvector v = seq;
 779                 seq.clear();
 780                 construct_from_epvector(std::move(v));
 781         }
 782 }
 783
 784 void expairseq::construct_from_exvector(const exvector &v)
 785 {
 786         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 787         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 788         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 789         //                  (same for (+,*) -> (*,^)
 790
 791         make_flat(v);
 792         canonicalize();
 793         combine_same_terms_sorted_seq();
 794 }
 795
 796 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
 797 {
 798         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 799         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 800         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 801         //                  same for (+,*) -> (*,^)
 802
 803         make_flat(v, do_index_renaming);
 804         canonicalize();
 805         combine_same_terms_sorted_seq();
 806 }
 807
 808 void expairseq::construct_from_epvector(epvector &&v, bool do_index_renaming)
 809 {
 810         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 811         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 812         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 813         //                  same for (+,*) -> (*,^)
 814
 815         make_flat(std::move(v), do_index_renaming);
 816         canonicalize();
 817         combine_same_terms_sorted_seq();
 818 }
 819
 820 /** Combine this expairseq with argument exvector.
 821  *  It cares for associativity as well as for special handling of numerics. */
 822 void expairseq::make_flat(const exvector &v)
 823 {
 824         // count number of operands which are of same expairseq derived type
 825         // and their cumulative number of operands
 826         int nexpairseqs = 0;
 827         int noperands = 0;
 828         bool do_idx_rename = false;
 829
 830         for (auto & cit : v) {
 831                 if (typeid(ex_to<basic>(cit)) == typeid(*this)) {
 832                         ++nexpairseqs;
 833                         noperands += ex_to<expairseq>(cit).seq.size();
 834                 }
 835                 if (is_a<mul>(*this) && (!do_idx_rename) &&
 836                     cit.info(info_flags::has_indices))
 837                         do_idx_rename = true;
 838         }
 839
 840         // reserve seq and coeffseq which will hold all operands
 841         seq.reserve(v.size()+noperands-nexpairseqs);
 842
 843         // copy elements and split off numerical part
 844         make_flat_inserter mf(v, do_idx_rename);
 845         for (auto & cit : v) {
 846                 if (typeid(ex_to<basic>(cit)) == typeid(*this)) {
 847                         ex newfactor = mf.handle_factor(cit, _ex1);
 848                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
 849                         combine_overall_coeff(subseqref.overall_coeff);
 850                         for (auto & cit_s : subseqref.seq) {
 851                                 seq.push_back(cit_s);
 852                         }
 853                 } else {
 854                         if (is_exactly_a<numeric>(cit))
 855                                 combine_overall_coeff(cit);
 856                         else {
 857                                 ex newfactor = mf.handle_factor(cit, _ex1);
 858                                 seq.push_back(split_ex_to_pair(newfactor));
 859                         }
 860                 }
 861         }
 862 }
 863
 864 /** Combine this expairseq with argument epvector.
 865  *  It cares for associativity as well as for special handling of numerics. */
 866 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
 867 {
 868         // count number of operands which are of same expairseq derived type
 869         // and their cumulative number of operands
 870         int nexpairseqs = 0;
 871         int noperands = 0;
 872         bool really_need_rename_inds = false;
 873
 874         for (auto & cit : v) {
 875                 if (typeid(ex_to<basic>(cit.rest)) == typeid(*this)) {
 876                         ++nexpairseqs;
 877                         noperands += ex_to<expairseq>(cit.rest).seq.size();
 878                 }
 879                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
 880                     cit.rest.info(info_flags::has_indices))
 881                         really_need_rename_inds = true;
 882         }
 883         do_index_renaming = do_index_renaming && really_need_rename_inds;
 884
 885         // reserve seq and coeffseq which will hold all operands
 886         seq.reserve(v.size()+noperands-nexpairseqs);
 887         make_flat_inserter mf(v, do_index_renaming);
 888
 889         // copy elements and split off numerical part
 890         for (auto & cit : v) {
 891                 if (typeid(ex_to<basic>(cit.rest)) == typeid(*this) &&
 892                     this->can_make_flat(cit)) {
 893                         ex newrest = mf.handle_factor(cit.rest, cit.coeff);
 894                         const expairseq &subseqref = ex_to<expairseq>(newrest);
 895                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
 896                                               ex_to<numeric>(cit.coeff));
 897                         for (auto & cit_s : subseqref.seq) {
 898                                 seq.push_back(expair(cit_s.rest,
 899                                                      ex_to<numeric>(cit_s.coeff).mul_dyn(ex_to<numeric>(cit.coeff))));
 900                         }
 901                 } else {
 902                         if (cit.is_canonical_numeric())
 903                                 combine_overall_coeff(mf.handle_factor(cit.rest, _ex1));
 904                         else {
 905                                 ex rest = cit.rest;
 906                                 ex newrest = mf.handle_factor(rest, cit.coeff);
 907                                 if (are_ex_trivially_equal(newrest, rest))
 908                                         seq.push_back(cit);
 909                                 else
 910                                         seq.push_back(expair(newrest, cit.coeff));
 911                         }
 912                 }
 913         }
 914 }
 915
 916 /** Brings this expairseq into a sorted (canonical) form. */
 917 void expairseq::canonicalize()
 918 {
 919         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 920 }
 921
 922
 923 /** Compact a presorted expairseq by combining all matching expairs to one
 924  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
 925  *  instance. */
 926 void expairseq::combine_same_terms_sorted_seq()
 927 {
 928         if (seq.size()<2)
 929                 return;
 930
 931         bool needs_further_processing = false;
 932
 933         auto itin1 = seq.begin();
 934         auto itin2 = itin1 + 1;
 935         auto itout = itin1;
 936         auto last = seq.end();
 937         // must_copy will be set to true the first time some combination is
 938         // possible from then on the sequence has changed and must be compacted
 939         bool must_copy = false;
 940         while (itin2!=last) {
 941                 if (itin1->rest.compare(itin2->rest)==0) {
 942                         itin1->coeff = ex_to<numeric>(itin1->coeff).
 943                                        add_dyn(ex_to<numeric>(itin2->coeff));
 944                         if (expair_needs_further_processing(itin1))
 945                                 needs_further_processing = true;
 946                         must_copy = true;
 947                 } else {
 948                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 949                                 if (must_copy)
 950                                         *itout = *itin1;
 951                                 ++itout;
 952                         }
 953                         itin1 = itin2;
 954                 }
 955                 ++itin2;
 956         }
 957         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 958                 if (must_copy)
 959                         *itout = *itin1;
 960                 ++itout;
 961         }
 962         if (itout!=last)
 963                 seq.erase(itout,last);
 964
 965         if (needs_further_processing) {
 966                 epvector v = seq;
 967                 seq.clear();
 968                 construct_from_epvector(std::move(v));
 969         }
 970 }
 971
 972 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
 973  *  debugging or in assertions since being sorted is an invariance. */
 974 bool expairseq::is_canonical() const
 975 {
 976         if (seq.size() <= 1)
 977                 return 1;
 978
 979         auto it = seq.begin(), itend = seq.end();
 980         auto it_last = it;
 981         for (++it; it!=itend; it_last=it, ++it) {
 982                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
 983                         if (!is_exactly_a<numeric>(it_last->rest) ||
 984                                 !is_exactly_a<numeric>(it->rest)) {
 985                                 // double test makes it easier to set a breakpoint...
 986                                 if (!is_exactly_a<numeric>(it_last->rest) ||
 987                                         !is_exactly_a<numeric>(it->rest)) {
 988                                         printpair(std::clog, *it_last, 0);
 989                                         std::clog << ">";
 990                                         printpair(std::clog, *it, 0);
 991                                         std::clog << "\n";
 992                                         std::clog << "pair1:" << std::endl;
 993                                         it_last->rest.print(print_tree(std::clog));
 994                                         it_last->coeff.print(print_tree(std::clog));
 995                                         std::clog << "pair2:" << std::endl;
 996                                         it->rest.print(print_tree(std::clog));
 997                                         it->coeff.print(print_tree(std::clog));
 998                                         return 0;
 999                                 }
1000                         }
1001                 }
1002         }
1003         return 1;
1004 }
1005
1006 /** Member-wise expand the expairs in this sequence.
1007  *
1008  *  @see expairseq::expand()
1009  *  @return epvector containing expanded pairs, empty if no members
1010  *    had to be changed. */
1011 epvector expairseq::expandchildren(unsigned options) const
1012 {
1013         auto cit = seq.begin(), last = seq.end();
1014         while (cit!=last) {
1015                 const ex &expanded_ex = cit->rest.expand(options);
1016                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1017
1018                         // something changed, copy seq, eval and return it
1019                         epvector s;
1020                         s.reserve(seq.size());
1021
1022                         // copy parts of seq which are known not to have changed
1023                         auto cit2 = seq.begin();
1024                         while (cit2!=cit) {
1025                                 s.push_back(*cit2);
1026                                 ++cit2;
1027                         }
1028
1029                         // copy first changed element
1030                         s.push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1031                                                                   cit2->coeff));
1032                         ++cit2;
1033
1034                         // copy rest
1035                         while (cit2!=last) {
1036                                 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1037                                                                           cit2->coeff));
1038                                 ++cit2;
1039                         }
1040                         return s;
1041                 }
1042                 ++cit;
1043         }
1044
1045         return epvector(); // empty signalling nothing has changed
1046 }
1047
1048
1049 /** Member-wise evaluate the expairs in this sequence.
1050  *
1051  *  @see expairseq::eval()
1052  *  @return epvector containing evaluated pairs, empty if no members
1053  *    had to be changed. */
1054 epvector expairseq::evalchildren(int level) const
1055 {
1056         if (level==1)
1057                 return epvector();  // nothing had to be evaluated
1058
1059         if (level == -max_recursion_level)
1060                 throw(std::runtime_error("max recursion level reached"));
1061
1062         --level;
1063         auto cit = seq.begin(), last = seq.end();
1064         while (cit!=last) {
1065                 const ex evaled_ex = cit->rest.eval(level);
1066                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1067
1068                         // something changed, copy seq, eval and return it
1069                         epvector s;
1070                         s.reserve(seq.size());
1071
1072                         // copy parts of seq which are known not to have changed
1073                         auto cit2 = seq.begin();
1074                         while (cit2!=cit) {
1075                                 s.push_back(*cit2);
1076                                 ++cit2;
1077                         }
1078
1079                         // copy first changed element
1080                         s.push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1081                                                                   cit2->coeff));
1082                         ++cit2;
1083
1084                         // copy rest
1085                         while (cit2!=last) {
1086                                 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1087                                                                           cit2->coeff));
1088                                 ++cit2;
1089                         }
1090                         return std::move(s);
1091                 }
1092                 ++cit;
1093         }
1094
1095         return epvector(); // signalling nothing has changed
1096 }
1097
1098 /** Member-wise substitute in this sequence.
1099  *
1100  *  @see expairseq::subs()
1101  *  @return epvector containing expanded pairs, empty if no members
1102  *    had to be changed. */
1103 epvector expairseq::subschildren(const exmap & m, unsigned options) const
1104 {
1105         // When any of the objects to be substituted is a product or power
1106         // we have to recombine the pairs because the numeric coefficients may
1107         // be part of the search pattern.
1108         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1109
1110                 // Search the list of substitutions and cache our findings
1111                 for (auto & it : m) {
1112                         if (is_exactly_a<mul>(it.first) || is_exactly_a<power>(it.first)) {
1113                                 options |= subs_options::pattern_is_product;
1114                                 break;
1115                         }
1116                 }
1117                 if (!(options & subs_options::pattern_is_product))
1118                         options |= subs_options::pattern_is_not_product;
1119         }
1120
1121         if (options & subs_options::pattern_is_product) {
1122
1123                 // Substitute in the recombined pairs
1124                 auto cit = seq.begin(), last = seq.end();
1125                 while (cit != last) {
1126
1127                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1128                         const ex &subsed_ex = orig_ex.subs(m, options);
1129                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1130
1131                                 // Something changed, copy seq, subs and return it
1132                                 epvector s;
1133                                 s.reserve(seq.size());
1134
1135                                 // Copy parts of seq which are known not to have changed
1136                                 s.insert(s.begin(), seq.begin(), cit);
1137
1138                                 // Copy first changed element
1139                                 s.push_back(split_ex_to_pair(subsed_ex));
1140                                 ++cit;
1141
1142                                 // Copy rest
1143                                 while (cit != last) {
1144                                         s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1145                                         ++cit;
1146                                 }
1147                                 return s;
1148                         }
1149
1150                         ++cit;
1151                 }
1152
1153         } else {
1154
1155                 // Substitute only in the "rest" part of the pairs
1156                 auto cit = seq.begin(), last = seq.end();
1157                 while (cit != last) {
1158
1159                         const ex &subsed_ex = cit->rest.subs(m, options);
1160                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1161
1162                                 // Something changed, copy seq, subs and return it
1163                                 epvector s;
1164                                 s.reserve(seq.size());
1165
1166                                 // Copy parts of seq which are known not to have changed
1167                                 s.insert(s.begin(), seq.begin(), cit);
1168
1169                                 // Copy first changed element
1170                                 s.push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1171                                 ++cit;
1172
1173                                 // Copy rest
1174                                 while (cit != last) {
1175                                         s.push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1176                                         ++cit;
1177                                 }
1178                                 return s;
1179                         }
1180
1181                         ++cit;
1182                 }
1183         }
1184
1185         // Nothing has changed
1186         return epvector();
1187 }
1188
1189 //////////
1190 // static member variables
1191 //////////
1192
1193 } // namespace GiNaC