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