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 #include "compiler.h"
  36
  37 #include <algorithm>
  38 #include <iostream>
  39 #include <iterator>
  40 #include <memory>
  41 #include <stdexcept>
  42 #include <string>
  43
  44 namespace GiNaC {
  45
  46
  47 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  48   print_func<print_context>(&expairseq::do_print).
  49   print_func<print_tree>(&expairseq::do_print_tree))
  50
  51
  52 //////////
  53 // helper classes
  54 //////////
  55
  56 class epp_is_less
  57 {
  58 public:
  59         bool operator()(const epp &lh, const epp &rh) const
  60         {
  61                 return (*lh).is_less(*rh);
  62         }
  63 };
  64
  65 //////////
  66 // default constructor
  67 //////////
  68
  69 // public
  70
  71 expairseq::expairseq()
  72 {}
  73
  74 // protected
  75
  76 //////////
  77 // other constructors
  78 //////////
  79
  80 expairseq::expairseq(const ex &lh, const ex &rh)
  81 {
  82         construct_from_2_ex(lh,rh);
  83         GINAC_ASSERT(is_canonical());
  84 }
  85
  86 expairseq::expairseq(const exvector &v)
  87 {
  88         construct_from_exvector(v);
  89         GINAC_ASSERT(is_canonical());
  90 }
  91
  92 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
  93   :  overall_coeff(oc)
  94 {
  95         GINAC_ASSERT(is_a<numeric>(oc));
  96         construct_from_epvector(v, do_index_renaming);
  97         GINAC_ASSERT(is_canonical());
  98 }
  99
 100 expairseq::expairseq(epvector && vp, const ex &oc, bool do_index_renaming)
 101   :  overall_coeff(oc)
 102 {
 103         GINAC_ASSERT(is_a<numeric>(oc));
 104         construct_from_epvector(std::move(vp), do_index_renaming);
 105         GINAC_ASSERT(is_canonical());
 106 }
 107
 108 //////////
 109 // archiving
 110 //////////
 111
 112 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
 113 {
 114         inherited::read_archive(n, sym_lst);
 115         auto first = n.find_first("rest");
 116         auto last = n.find_last("coeff");
 117         ++last;
 118         seq.reserve((last-first)/2);
 119
 120         for (auto loc = first; loc < last;) {
 121                 ex rest;
 122                 ex coeff;
 123                 n.find_ex_by_loc(loc++, rest, sym_lst);
 124                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 125                 seq.push_back(expair(rest, coeff));
 126         }
 127
 128         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 129
 130         canonicalize();
 131         GINAC_ASSERT(is_canonical());
 132 }
 133
 134 void expairseq::archive(archive_node &n) const
 135 {
 136         inherited::archive(n);
 137         for (auto & i : seq) {
 138                 n.add_ex("rest", i.rest);
 139                 n.add_ex("coeff", i.coeff);
 140         }
 141         n.add_ex("overall_coeff", overall_coeff);
 142 }
 143
 144
 145 //////////
 146 // functions overriding virtual functions from base classes
 147 //////////
 148
 149 // public
 150
 151 void expairseq::do_print(const print_context & c, unsigned level) const
 152 {
 153         c.s << "[[";
 154         printseq(c, ',', precedence(), level);
 155         c.s << "]]";
 156 }
 157
 158 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 159 {
 160         c.s << std::string(level, ' ') << class_name() << " @" << this
 161             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 162             << ", nops=" << nops()
 163             << std::endl;
 164         size_t num = seq.size();
 165         for (size_t i=0; i<num; ++i) {
 166                 seq[i].rest.print(c, level + c.delta_indent);
 167                 seq[i].coeff.print(c, level + c.delta_indent);
 168                 if (i != num - 1)
 169                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 170         }
 171         if (!overall_coeff.is_equal(default_overall_coeff())) {
 172                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 173                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 174                 overall_coeff.print(c, level + c.delta_indent);
 175         }
 176         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 177 }
 178
 179 bool expairseq::info(unsigned inf) const
 180 {
 181         switch(inf) {
 182                 case info_flags::expanded:
 183                         return (flags & status_flags::expanded);
 184                 case info_flags::has_indices: {
 185                         if (flags & status_flags::has_indices)
 186                                 return true;
 187                         else if (flags & status_flags::has_no_indices)
 188                                 return false;
 189                         for (auto & i : seq) {
 190                                 if (i.rest.info(info_flags::has_indices)) {
 191                                         this->setflag(status_flags::has_indices);
 192                                         this->clearflag(status_flags::has_no_indices);
 193                                         return true;
 194                                 }
 195                         }
 196                         this->clearflag(status_flags::has_indices);
 197                         this->setflag(status_flags::has_no_indices);
 198                         return false;
 199                 }
 200         }
 201         return inherited::info(inf);
 202 }
 203
 204 size_t expairseq::nops() const
 205 {
 206         if (overall_coeff.is_equal(default_overall_coeff()))
 207                 return seq.size();
 208         else
 209                 return seq.size()+1;
 210 }
 211
 212 ex expairseq::op(size_t i) const
 213 {
 214         if (i < seq.size())
 215                 return recombine_pair_to_ex(seq[i]);
 216         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 217         return overall_coeff;
 218 }
 219
 220 ex expairseq::map(map_function &f) const
 221 {
 222         epvector v;
 223         v.reserve(seq.size()+1);
 224
 225         for (auto & it : seq)
 226                 v.push_back(split_ex_to_pair(f(recombine_pair_to_ex(it))));
 227
 228         if (overall_coeff.is_equal(default_overall_coeff()))
 229                 return thisexpairseq(std::move(v), default_overall_coeff(), true);
 230         else {
 231                 ex newcoeff = f(overall_coeff);
 232                 if(is_a<numeric>(newcoeff))
 233                         return thisexpairseq(std::move(v), newcoeff, true);
 234                 else {
 235                         v.push_back(split_ex_to_pair(newcoeff));
 236                         return thisexpairseq(std::move(v), default_overall_coeff(), true);
 237                 }
 238         }
 239 }
 240
 241 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 242 ex expairseq::eval(int level) const
 243 {
 244         if ((level==1) && (flags &status_flags::evaluated))
 245                 return *this;
 246
 247         epvector evaled = evalchildren(level);
 248         if (!evaled.empty())
 249                 return dynallocate<expairseq>(std::move(evaled), overall_coeff).setflag(status_flags::evaluated);
 250         else
 251                 return this->hold();
 252 }
 253
 254 epvector* conjugateepvector(const epvector&epv)
 255 {
 256         epvector *newepv = nullptr;
 257         for (auto i=epv.begin(); i!=epv.end(); ++i) {
 258                 if (newepv) {
 259                         newepv->push_back(i->conjugate());
 260                         continue;
 261                 }
 262                 expair x = i->conjugate();
 263                 if (x.is_equal(*i)) {
 264                         continue;
 265                 }
 266                 newepv = new epvector;
 267                 newepv->reserve(epv.size());
 268                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 269                         newepv->push_back(*j);
 270                 }
 271                 newepv->push_back(x);
 272         }
 273         return newepv;
 274 }
 275
 276 ex expairseq::conjugate() const
 277 {
 278         std::unique_ptr<epvector> newepv(conjugateepvector(seq));
 279         ex x = overall_coeff.conjugate();
 280         if (newepv) {
 281                 return thisexpairseq(std::move(*newepv), x);
 282         }
 283         if (are_ex_trivially_equal(x, overall_coeff)) {
 284                 return *this;
 285         }
 286         return thisexpairseq(seq, x);
 287 }
 288
 289 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 290 {
 291         // This differs from basic::match() because we want "a+b+c+d" to
 292         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 293
 294         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 295
 296                 // Check whether global wildcard (one that matches the "rest of the
 297                 // expression", like "*" above) is present
 298                 bool has_global_wildcard = false;
 299                 ex global_wildcard;
 300                 for (size_t i=0; i<pattern.nops(); i++) {
 301                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 302                                 has_global_wildcard = true;
 303                                 global_wildcard = pattern.op(i);
 304                                 break;
 305                         }
 306                 }
 307
 308                 // Even if the expression does not match the pattern, some of
 309                 // its subexpressions could match it. For example, x^5*y^(-1)
 310                 // does not match the pattern $0^5, but its subexpression x^5
 311                 // does. So, save repl_lst in order to not add bogus entries.
 312                 exmap tmp_repl = repl_lst;
 313
 314                 // Unfortunately, this is an O(N^2) operation because we can't
 315                 // sort the pattern in a useful way...
 316
 317                 // Chop into terms
 318                 exvector ops;
 319                 ops.reserve(nops());
 320                 for (size_t i=0; i<nops(); i++)
 321                         ops.push_back(op(i));
 322
 323                 // Now, for every term of the pattern, look for a matching term in
 324                 // the expression and remove the match
 325                 for (size_t i=0; i<pattern.nops(); i++) {
 326                         ex p = pattern.op(i);
 327                         if (has_global_wildcard && p.is_equal(global_wildcard))
 328                                 continue;
 329                         auto it = ops.begin(), itend = ops.end();
 330                         while (it != itend) {
 331                                 if (it->match(p, tmp_repl)) {
 332                                         ops.erase(it);
 333                                         goto found;
 334                                 }
 335                                 ++it;
 336                         }
 337                         return false; // no match found
 338 found:          ;
 339                 }
 340
 341                 if (has_global_wildcard) {
 342
 343                         // Assign all the remaining terms to the global wildcard (unless
 344                         // it has already been matched before, in which case the matches
 345                         // must be equal)
 346                         size_t num = ops.size();
 347                         epvector vp;
 348                         vp.reserve(num);
 349                         for (size_t i=0; i<num; i++)
 350                                 vp.push_back(split_ex_to_pair(ops[i]));
 351                         ex rest = thisexpairseq(std::move(vp), default_overall_coeff());
 352                         for (auto & it : tmp_repl) {
 353                                 if (it.first.is_equal(global_wildcard)) {
 354                                         if (rest.is_equal(it.second)) {
 355                                                 repl_lst = tmp_repl;
 356                                                 return true;
 357                                         }
 358                                         return false;
 359                                 }
 360                         }
 361                         repl_lst = tmp_repl;
 362                         repl_lst[global_wildcard] = rest;
 363                         return true;
 364
 365                 } else {
 366
 367                         // No global wildcard, then the match fails if there are any
 368                         // unmatched terms left
 369                         if (ops.empty()) {
 370                                 repl_lst = tmp_repl;
 371                                 return true;
 372                         }
 373                         return false;
 374                 }
 375         }
 376         return inherited::match(pattern, repl_lst);
 377 }
 378
 379 ex expairseq::subs(const exmap & m, unsigned options) const
 380 {
 381         epvector subsed = subschildren(m, options);
 382         if (!subsed.empty())
 383                 return ex_to<basic>(thisexpairseq(std::move(subsed), overall_coeff, (options & subs_options::no_index_renaming) == 0));
 384         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 385                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 386         else
 387                 return subs_one_level(m, options);
 388 }
 389
 390 // protected
 391
 392 int expairseq::compare_same_type(const basic &other) const
 393 {
 394         GINAC_ASSERT(is_a<expairseq>(other));
 395         const expairseq &o = static_cast<const expairseq &>(other);
 396
 397         int cmpval;
 398
 399         // compare number of elements
 400         if (seq.size() != o.seq.size())
 401                 return (seq.size()<o.seq.size()) ? -1 : 1;
 402
 403         // compare overall_coeff
 404         cmpval = overall_coeff.compare(o.overall_coeff);
 405         if (cmpval!=0)
 406                 return cmpval;
 407
 408         auto cit1 = seq.begin(), last1 = seq.end();
 409         auto cit2 = o.seq.begin(), last2 = o.seq.end();
 410         for (; (cit1!=last1) && (cit2!=last2); ++cit1, ++cit2) {
 411                 cmpval = (*cit1).compare(*cit2);
 412                 if (cmpval!=0) return cmpval;
 413         }
 414
 415         GINAC_ASSERT(cit1==last1);
 416         GINAC_ASSERT(cit2==last2);
 417
 418         return 0;
 419 }
 420
 421 bool expairseq::is_equal_same_type(const basic &other) const
 422 {
 423         const expairseq &o = static_cast<const expairseq &>(other);
 424
 425         // compare number of elements
 426         if (seq.size()!=o.seq.size())
 427                 return false;
 428
 429         // compare overall_coeff
 430         if (!overall_coeff.is_equal(o.overall_coeff))
 431                 return false;
 432
 433         auto cit2 = o.seq.begin();
 434         for (auto & cit1 : seq) {
 435                 if (!cit1.is_equal(*cit2))
 436                         return false;
 437                 ++cit2;
 438         }
 439
 440         return true;
 441 }
 442
 443 unsigned expairseq::return_type() const
 444 {
 445         return return_types::noncommutative_composite;
 446 }
 447
 448 unsigned expairseq::calchash() const
 449 {
 450         unsigned v = make_hash_seed(typeid(*this));
 451         for (auto & i : seq) {
 452                 v ^= i.rest.gethash();
 453                 v = rotate_left(v);
 454                 v ^= i.coeff.gethash();
 455         }
 456
 457         v ^= overall_coeff.gethash();
 458
 459         // store calculated hash value only if object is already evaluated
 460         if (flags &status_flags::evaluated) {
 461                 setflag(status_flags::hash_calculated);
 462                 hashvalue = v;
 463         }
 464
 465         return v;
 466 }
 467
 468 ex expairseq::expand(unsigned options) const
 469 {
 470         epvector expanded = expandchildren(options);
 471         if (!expanded.empty()) {
 472                 return thisexpairseq(std::move(expanded), overall_coeff);
 473         }
 474         return (options == 0) ? setflag(status_flags::expanded) : *this;
 475 }
 476
 477 //////////
 478 // new virtual functions which can be overridden by derived classes
 479 //////////
 480
 481 // protected
 482
 483 /** Create an object of this type.
 484  *  This method works similar to a constructor.  It is useful because expairseq
 485  *  has (at least) two possible different semantics but we want to inherit
 486  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 487  *  has to create a new one of the same semantics, which cannot be done by a
 488  *  ctor because the name (add, mul,...) is unknown on the expairseq level.  In
 489  *  order for this trick to work a derived class must of course override this
 490  *  definition. */
 491 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 492 {
 493         return expairseq(v, oc, do_index_renaming);
 494 }
 495
 496 ex expairseq::thisexpairseq(epvector && vp, const ex &oc, bool do_index_renaming) const
 497 {
 498         return expairseq(std::move(vp), oc, do_index_renaming);
 499 }
 500
 501 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 502 {
 503         c.s << "[[";
 504         p.rest.print(c, precedence());
 505         c.s << ",";
 506         p.coeff.print(c, precedence());
 507         c.s << "]]";
 508 }
 509
 510 void expairseq::printseq(const print_context & c, char delim,
 511                          unsigned this_precedence,
 512                          unsigned upper_precedence) const
 513 {
 514         if (this_precedence <= upper_precedence)
 515                 c.s << "(";
 516         auto it = seq.begin(), it_last = seq.end() - 1;
 517         for (; it!=it_last; ++it) {
 518                 printpair(c, *it, this_precedence);
 519                 c.s << delim;
 520         }
 521         printpair(c, *it, this_precedence);
 522         if (!overall_coeff.is_equal(default_overall_coeff())) {
 523                 c.s << delim;
 524                 overall_coeff.print(c, this_precedence);
 525         }
 526
 527         if (this_precedence <= upper_precedence)
 528                 c.s << ")";
 529 }
 530
 531
 532 /** Form an expair from an ex, using the corresponding semantics.
 533  *  @see expairseq::recombine_pair_to_ex() */
 534 expair expairseq::split_ex_to_pair(const ex &e) const
 535 {
 536         return expair(e,_ex1);
 537 }
 538
 539
 540 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 541                                                 const ex &c) const
 542 {
 543         GINAC_ASSERT(is_exactly_a<numeric>(c));
 544
 545         return expair(e,c);
 546 }
 547
 548
 549 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 550                                                   const ex &c) const
 551 {
 552         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 553         GINAC_ASSERT(is_exactly_a<numeric>(c));
 554
 555         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 556 }
 557
 558
 559 /** Form an ex out of an expair, using the corresponding semantics.
 560  *  @see expairseq::split_ex_to_pair() */
 561 ex expairseq::recombine_pair_to_ex(const expair &p) const
 562 {
 563         return lst{p.rest, p.coeff};
 564 }
 565
 566 bool expairseq::expair_needs_further_processing(epp it)
 567 {
 568         return false;
 569 }
 570
 571 ex expairseq::default_overall_coeff() const
 572 {
 573         return _ex0;
 574 }
 575
 576 void expairseq::combine_overall_coeff(const ex &c)
 577 {
 578         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 579         GINAC_ASSERT(is_exactly_a<numeric>(c));
 580         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 581 }
 582
 583 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 584 {
 585         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 586         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 587         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 588         overall_coeff = ex_to<numeric>(overall_coeff).
 589                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 590 }
 591
 592 bool expairseq::can_make_flat(const expair &p) const
 593 {
 594         return true;
 595 }
 596
 597
 598 //////////
 599 // non-virtual functions in this class
 600 //////////
 601
 602 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 603 {
 604         exvector v;
 605         v.reserve(2);
 606         v.push_back(lh);
 607         v.push_back(rh);
 608         construct_from_exvector(v);
 609 }
 610
 611 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 612 {
 613         if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
 614                 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 615                         if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 616                                 rh.info(info_flags::has_indices)) {
 617                                 ex newrh=rename_dummy_indices_uniquely(lh, rh);
 618                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 619                                                            ex_to<expairseq>(newrh));
 620                         }
 621                         else
 622                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 623                                                            ex_to<expairseq>(rh));
 624                         return;
 625                 } else {
 626                         construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 627                         return;
 628                 }
 629         } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 630                 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 631                 return;
 632         }
 633
 634         if (is_exactly_a<numeric>(lh)) {
 635                 if (is_exactly_a<numeric>(rh)) {
 636                         combine_overall_coeff(lh);
 637                         combine_overall_coeff(rh);
 638                 } else {
 639                         combine_overall_coeff(lh);
 640                         seq.push_back(split_ex_to_pair(rh));
 641                 }
 642         } else {
 643                 if (is_exactly_a<numeric>(rh)) {
 644                         combine_overall_coeff(rh);
 645                         seq.push_back(split_ex_to_pair(lh));
 646                 } else {
 647                         expair p1 = split_ex_to_pair(lh);
 648                         expair p2 = split_ex_to_pair(rh);
 649
 650                         int cmpval = p1.rest.compare(p2.rest);
 651                         if (cmpval==0) {
 652                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 653                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 654                                         // no further processing is necessary, since this
 655                                         // one element will usually be recombined in eval()
 656                                         seq.push_back(p1);
 657                                 }
 658                         } else {
 659                                 seq.reserve(2);
 660                                 if (cmpval<0) {
 661                                         seq.push_back(p1);
 662                                         seq.push_back(p2);
 663                                 } else {
 664                                         seq.push_back(p2);
 665                                         seq.push_back(p1);
 666                                 }
 667                         }
 668                 }
 669         }
 670 }
 671
 672 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 673                                            const expairseq &s2)
 674 {
 675         combine_overall_coeff(s1.overall_coeff);
 676         combine_overall_coeff(s2.overall_coeff);
 677
 678         auto first1 = s1.seq.begin(), last1 = s1.seq.end();
 679         auto first2 = s2.seq.begin(), last2 = s2.seq.end();
 680
 681         seq.reserve(s1.seq.size()+s2.seq.size());
 682
 683         bool needs_further_processing=false;
 684
 685         while (first1!=last1 && first2!=last2) {
 686                 int cmpval = (*first1).rest.compare((*first2).rest);
 687
 688                 if (cmpval==0) {
 689                         // combine terms
 690                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 691                                                    add(ex_to<numeric>(first2->coeff));
 692                         if (!newcoeff.is_zero()) {
 693                                 seq.push_back(expair(first1->rest,newcoeff));
 694                                 if (expair_needs_further_processing(seq.end()-1)) {
 695                                         needs_further_processing = true;
 696                                 }
 697                         }
 698                         ++first1;
 699                         ++first2;
 700                 } else if (cmpval<0) {
 701                         seq.push_back(*first1);
 702                         ++first1;
 703                 } else {
 704                         seq.push_back(*first2);
 705                         ++first2;
 706                 }
 707         }
 708
 709         while (first1!=last1) {
 710                 seq.push_back(*first1);
 711                 ++first1;
 712         }
 713         while (first2!=last2) {
 714                 seq.push_back(*first2);
 715                 ++first2;
 716         }
 717
 718         if (needs_further_processing) {
 719                 // Clear seq and start over.
 720                 epvector v = std::move(seq);
 721                 construct_from_epvector(std::move(v));
 722         }
 723 }
 724
 725 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 726                                             const ex &e)
 727 {
 728         combine_overall_coeff(s.overall_coeff);
 729         if (is_exactly_a<numeric>(e)) {
 730                 combine_overall_coeff(e);
 731                 seq = s.seq;
 732                 return;
 733         }
 734
 735         auto first = s.seq.begin(), last = s.seq.end();
 736         expair p = split_ex_to_pair(e);
 737
 738         seq.reserve(s.seq.size()+1);
 739         bool p_pushed = false;
 740
 741         bool needs_further_processing=false;
 742
 743         // merge p into s.seq
 744         while (first!=last) {
 745                 int cmpval = (*first).rest.compare(p.rest);
 746                 if (cmpval==0) {
 747                         // combine terms
 748                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 749                                                    add(ex_to<numeric>(p.coeff));
 750                         if (!newcoeff.is_zero()) {
 751                                 seq.push_back(expair(first->rest,newcoeff));
 752                                 if (expair_needs_further_processing(seq.end()-1))
 753                                         needs_further_processing = true;
 754                         }
 755                         ++first;
 756                         p_pushed = true;
 757                         break;
 758                 } else if (cmpval<0) {
 759                         seq.push_back(*first);
 760                         ++first;
 761                 } else {
 762                         seq.push_back(p);
 763                         p_pushed = true;
 764                         break;
 765                 }
 766         }
 767
 768         if (p_pushed) {
 769                 // while loop exited because p was pushed, now push rest of s.seq
 770                 while (first!=last) {
 771                         seq.push_back(*first);
 772                         ++first;
 773                 }
 774         } else {
 775                 // while loop exited because s.seq was pushed, now push p
 776                 seq.push_back(p);
 777         }
 778
 779         if (needs_further_processing) {
 780                 // Clear seq and start over.
 781                 epvector v = std::move(seq);
 782                 construct_from_epvector(std::move(v));
 783         }
 784 }
 785
 786 void expairseq::construct_from_exvector(const exvector &v)
 787 {
 788         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 789         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 790         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 791         //                  (same for (+,*) -> (*,^)
 792
 793         make_flat(v);
 794         canonicalize();
 795         combine_same_terms_sorted_seq();
 796 }
 797
 798 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
 799 {
 800         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 801         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 802         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 803         //                  same for (+,*) -> (*,^)
 804
 805         make_flat(v, do_index_renaming);
 806         canonicalize();
 807         combine_same_terms_sorted_seq();
 808 }
 809
 810 void expairseq::construct_from_epvector(epvector &&v, bool do_index_renaming)
 811 {
 812         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 813         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 814         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 815         //                  same for (+,*) -> (*,^)
 816
 817         make_flat(std::move(v), do_index_renaming);
 818         canonicalize();
 819         combine_same_terms_sorted_seq();
 820 }
 821
 822 /** Combine this expairseq with argument exvector.
 823  *  It cares for associativity as well as for special handling of numerics. */
 824 void expairseq::make_flat(const exvector &v)
 825 {
 826         // count number of operands which are of same expairseq derived type
 827         // and their cumulative number of operands
 828         int nexpairseqs = 0;
 829         int noperands = 0;
 830         bool do_idx_rename = false;
 831
 832         for (auto & cit : v) {
 833                 if (typeid(ex_to<basic>(cit)) == typeid(*this)) {
 834                         ++nexpairseqs;
 835                         noperands += ex_to<expairseq>(cit).seq.size();
 836                 }
 837                 if (is_a<mul>(*this) && (!do_idx_rename) &&
 838                     cit.info(info_flags::has_indices))
 839                         do_idx_rename = true;
 840         }
 841
 842         // reserve seq and coeffseq which will hold all operands
 843         seq.reserve(v.size()+noperands-nexpairseqs);
 844
 845         // copy elements and split off numerical part
 846         make_flat_inserter mf(v, do_idx_rename);
 847         for (auto & cit : v) {
 848                 if (typeid(ex_to<basic>(cit)) == typeid(*this)) {
 849                         ex newfactor = mf.handle_factor(cit, _ex1);
 850                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
 851                         combine_overall_coeff(subseqref.overall_coeff);
 852                         for (auto & cit_s : subseqref.seq) {
 853                                 seq.push_back(cit_s);
 854                         }
 855                 } else {
 856                         if (is_exactly_a<numeric>(cit))
 857                                 combine_overall_coeff(cit);
 858                         else {
 859                                 ex newfactor = mf.handle_factor(cit, _ex1);
 860                                 seq.push_back(split_ex_to_pair(newfactor));
 861                         }
 862                 }
 863         }
 864 }
 865
 866 /** Combine this expairseq with argument epvector.
 867  *  It cares for associativity as well as for special handling of numerics. */
 868 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
 869 {
 870         // count number of operands which are of same expairseq derived type
 871         // and their cumulative number of operands
 872         int nexpairseqs = 0;
 873         int noperands = 0;
 874         bool really_need_rename_inds = false;
 875
 876         for (auto & cit : v) {
 877                 if (typeid(ex_to<basic>(cit.rest)) == typeid(*this)) {
 878                         ++nexpairseqs;
 879                         noperands += ex_to<expairseq>(cit.rest).seq.size();
 880                 }
 881                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
 882                     cit.rest.info(info_flags::has_indices))
 883                         really_need_rename_inds = true;
 884         }
 885         do_index_renaming = do_index_renaming && really_need_rename_inds;
 886
 887         // reserve seq and coeffseq which will hold all operands
 888         seq.reserve(v.size()+noperands-nexpairseqs);
 889         make_flat_inserter mf(v, do_index_renaming);
 890
 891         // copy elements and split off numerical part
 892         for (auto & cit : v) {
 893                 if (typeid(ex_to<basic>(cit.rest)) == typeid(*this) &&
 894                     this->can_make_flat(cit)) {
 895                         ex newrest = mf.handle_factor(cit.rest, cit.coeff);
 896                         const expairseq &subseqref = ex_to<expairseq>(newrest);
 897                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
 898                                               ex_to<numeric>(cit.coeff));
 899                         for (auto & cit_s : subseqref.seq) {
 900                                 seq.push_back(expair(cit_s.rest,
 901                                                      ex_to<numeric>(cit_s.coeff).mul_dyn(ex_to<numeric>(cit.coeff))));
 902                         }
 903                 } else {
 904                         if (cit.is_canonical_numeric())
 905                                 combine_overall_coeff(mf.handle_factor(cit.rest, _ex1));
 906                         else {
 907                                 ex rest = cit.rest;
 908                                 ex newrest = mf.handle_factor(rest, cit.coeff);
 909                                 if (are_ex_trivially_equal(newrest, rest))
 910                                         seq.push_back(cit);
 911                                 else
 912                                         seq.push_back(expair(newrest, cit.coeff));
 913                         }
 914                 }
 915         }
 916 }
 917
 918 /** Brings this expairseq into a sorted (canonical) form. */
 919 void expairseq::canonicalize()
 920 {
 921         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 922 }
 923
 924
 925 /** Compact a presorted expairseq by combining all matching expairs to one
 926  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
 927  *  instance. */
 928 void expairseq::combine_same_terms_sorted_seq()
 929 {
 930         if (seq.size()<2)
 931                 return;
 932
 933         bool needs_further_processing = false;
 934
 935         auto itin1 = seq.begin();
 936         auto itin2 = itin1 + 1;
 937         auto itout = itin1;
 938         auto last = seq.end();
 939         // must_copy will be set to true the first time some combination is
 940         // possible from then on the sequence has changed and must be compacted
 941         bool must_copy = false;
 942         while (itin2!=last) {
 943                 if (itin1->rest.compare(itin2->rest)==0) {
 944                         itin1->coeff = ex_to<numeric>(itin1->coeff).
 945                                        add_dyn(ex_to<numeric>(itin2->coeff));
 946                         if (expair_needs_further_processing(itin1))
 947                                 needs_further_processing = true;
 948                         must_copy = true;
 949                 } else {
 950                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 951                                 if (must_copy)
 952                                         *itout = *itin1;
 953                                 ++itout;
 954                         }
 955                         itin1 = itin2;
 956                 }
 957                 ++itin2;
 958         }
 959         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 960                 if (must_copy)
 961                         *itout = *itin1;
 962                 ++itout;
 963         }
 964         if (itout!=last)
 965                 seq.erase(itout,last);
 966
 967         if (needs_further_processing) {
 968                 // Clear seq and start over.
 969                 epvector v = std::move(seq);
 970                 construct_from_epvector(std::move(v));
 971         }
 972 }
 973
 974 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
 975  *  debugging or in assertions since being sorted is an invariance. */
 976 bool expairseq::is_canonical() const
 977 {
 978         if (seq.size() <= 1)
 979                 return 1;
 980
 981         auto it = seq.begin(), itend = seq.end();
 982         auto it_last = it;
 983         for (++it; it!=itend; it_last=it, ++it) {
 984                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
 985                         if (!is_exactly_a<numeric>(it_last->rest) ||
 986                                 !is_exactly_a<numeric>(it->rest)) {
 987                                 // double test makes it easier to set a breakpoint...
 988                                 if (!is_exactly_a<numeric>(it_last->rest) ||
 989                                         !is_exactly_a<numeric>(it->rest)) {
 990                                         printpair(std::clog, *it_last, 0);
 991                                         std::clog << ">";
 992                                         printpair(std::clog, *it, 0);
 993                                         std::clog << "\n";
 994                                         std::clog << "pair1:" << std::endl;
 995                                         it_last->rest.print(print_tree(std::clog));
 996                                         it_last->coeff.print(print_tree(std::clog));
 997                                         std::clog << "pair2:" << std::endl;
 998                                         it->rest.print(print_tree(std::clog));
 999                                         it->coeff.print(print_tree(std::clog));
1000                                         return 0;
1001                                 }
1002                         }
1003                 }
1004         }
1005         return 1;
1006 }
1007
1008 /** Member-wise expand the expairs in this sequence.
1009  *
1010  *  @see expairseq::expand()
1011  *  @return epvector containing expanded pairs, empty if no members
1012  *    had to be changed. */
1013 epvector expairseq::expandchildren(unsigned options) const
1014 {
1015         auto cit = seq.begin(), last = seq.end();
1016         while (cit!=last) {
1017                 const ex &expanded_ex = cit->rest.expand(options);
1018                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1019
1020                         // something changed, copy seq, eval and return it
1021                         epvector s;
1022                         s.reserve(seq.size());
1023
1024                         // copy parts of seq which are known not to have changed
1025                         auto cit2 = seq.begin();
1026                         while (cit2!=cit) {
1027                                 s.push_back(*cit2);
1028                                 ++cit2;
1029                         }
1030
1031                         // copy first changed element
1032                         s.push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1033                                                                   cit2->coeff));
1034                         ++cit2;
1035
1036                         // copy rest
1037                         while (cit2!=last) {
1038                                 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1039                                                                           cit2->coeff));
1040                                 ++cit2;
1041                         }
1042                         return s;
1043                 }
1044                 ++cit;
1045         }
1046
1047         return epvector(); // empty signalling nothing has changed
1048 }
1049
1050
1051 /** Member-wise evaluate the expairs in this sequence.
1052  *
1053  *  @see expairseq::eval()
1054  *  @return epvector containing evaluated pairs, empty if no members
1055  *    had to be changed. */
1056 epvector expairseq::evalchildren(int level) const
1057 {
1058         if (likely(level==1))
1059                 return epvector();  // nothing had to be evaluated
1060
1061         if (level == -max_recursion_level)
1062                 throw(std::runtime_error("max recursion level reached"));
1063
1064         --level;
1065         auto cit = seq.begin(), last = seq.end();
1066         while (cit!=last) {
1067                 const ex evaled_ex = cit->rest.eval(level);
1068                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1069
1070                         // something changed, copy seq, eval and return it
1071                         epvector s;
1072                         s.reserve(seq.size());
1073
1074                         // copy parts of seq which are known not to have changed
1075                         auto cit2 = seq.begin();
1076                         while (cit2!=cit) {
1077                                 s.push_back(*cit2);
1078                                 ++cit2;
1079                         }
1080
1081                         // copy first changed element
1082                         s.push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1083                                                                   cit2->coeff));
1084                         ++cit2;
1085
1086                         // copy rest
1087                         while (cit2!=last) {
1088                                 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1089                                                                           cit2->coeff));
1090                                 ++cit2;
1091                         }
1092                         return std::move(s);
1093                 }
1094                 ++cit;
1095         }
1096
1097         return epvector(); // signalling nothing has changed
1098 }
1099
1100 /** Member-wise substitute in this sequence.
1101  *
1102  *  @see expairseq::subs()
1103  *  @return epvector containing expanded pairs, empty if no members
1104  *    had to be changed. */
1105 epvector expairseq::subschildren(const exmap & m, unsigned options) const
1106 {
1107         // When any of the objects to be substituted is a product or power
1108         // we have to recombine the pairs because the numeric coefficients may
1109         // be part of the search pattern.
1110         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1111
1112                 // Search the list of substitutions and cache our findings
1113                 for (auto & it : m) {
1114                         if (is_exactly_a<mul>(it.first) || is_exactly_a<power>(it.first)) {
1115                                 options |= subs_options::pattern_is_product;
1116                                 break;
1117                         }
1118                 }
1119                 if (!(options & subs_options::pattern_is_product))
1120                         options |= subs_options::pattern_is_not_product;
1121         }
1122
1123         if (options & subs_options::pattern_is_product) {
1124
1125                 // Substitute in the recombined pairs
1126                 auto cit = seq.begin(), last = seq.end();
1127                 while (cit != last) {
1128
1129                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1130                         const ex &subsed_ex = orig_ex.subs(m, options);
1131                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1132
1133                                 // Something changed, copy seq, subs and return it
1134                                 epvector s;
1135                                 s.reserve(seq.size());
1136
1137                                 // Copy parts of seq which are known not to have changed
1138                                 s.insert(s.begin(), seq.begin(), cit);
1139
1140                                 // Copy first changed element
1141                                 s.push_back(split_ex_to_pair(subsed_ex));
1142                                 ++cit;
1143
1144                                 // Copy rest
1145                                 while (cit != last) {
1146                                         s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1147                                         ++cit;
1148                                 }
1149                                 return s;
1150                         }
1151
1152                         ++cit;
1153                 }
1154
1155         } else {
1156
1157                 // Substitute only in the "rest" part of the pairs
1158                 auto cit = seq.begin(), last = seq.end();
1159                 while (cit != last) {
1160
1161                         const ex &subsed_ex = cit->rest.subs(m, options);
1162                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1163
1164                                 // Something changed, copy seq, subs and return it
1165                                 epvector s;
1166                                 s.reserve(seq.size());
1167
1168                                 // Copy parts of seq which are known not to have changed
1169                                 s.insert(s.begin(), seq.begin(), cit);
1170
1171                                 // Copy first changed element
1172                                 s.push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1173                                 ++cit;
1174
1175                                 // Copy rest
1176                                 while (cit != last) {
1177                                         s.push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1178                                         ++cit;
1179                                 }
1180                                 return s;
1181                         }
1182
1183                         ++cit;
1184                 }
1185         }
1186
1187         // Nothing has changed
1188         return epvector();
1189 }
1190
1191 //////////
1192 // static member variables
1193 //////////
1194
1195 } // namespace GiNaC