ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2020 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 range = n.find_property_range("rest", "coeff");
 116         seq.reserve((range.end-range.begin)/2);
 117
 118         for (auto loc = range.begin; loc < range.end;) {
 119                 ex rest;
 120                 ex coeff;
 121                 n.find_ex_by_loc(loc++, rest, sym_lst);
 122                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 123                 seq.emplace_back(expair(rest, coeff));
 124         }
 125
 126         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 127
 128         canonicalize();
 129         GINAC_ASSERT(is_canonical());
 130 }
 131
 132 void expairseq::archive(archive_node &n) const
 133 {
 134         inherited::archive(n);
 135         for (auto & i : seq) {
 136                 n.add_ex("rest", i.rest);
 137                 n.add_ex("coeff", i.coeff);
 138         }
 139         n.add_ex("overall_coeff", overall_coeff);
 140 }
 141
 142
 143 //////////
 144 // functions overriding virtual functions from base classes
 145 //////////
 146
 147 // public
 148
 149 void expairseq::do_print(const print_context & c, unsigned level) const
 150 {
 151         c.s << "[[";
 152         printseq(c, ',', precedence(), level);
 153         c.s << "]]";
 154 }
 155
 156 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 157 {
 158         c.s << std::string(level, ' ') << class_name() << " @" << this
 159             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 160             << ", nops=" << nops()
 161             << std::endl;
 162         size_t num = seq.size();
 163         for (size_t i=0; i<num; ++i) {
 164                 seq[i].rest.print(c, level + c.delta_indent);
 165                 seq[i].coeff.print(c, level + c.delta_indent);
 166                 if (i != num - 1)
 167                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 168         }
 169         if (!overall_coeff.is_equal(default_overall_coeff())) {
 170                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 171                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 172                 overall_coeff.print(c, level + c.delta_indent);
 173         }
 174         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 175 }
 176
 177 bool expairseq::info(unsigned inf) const
 178 {
 179         switch(inf) {
 180                 case info_flags::expanded:
 181                         return (flags & status_flags::expanded);
 182                 case info_flags::has_indices: {
 183                         if (flags & status_flags::has_indices)
 184                                 return true;
 185                         else if (flags & status_flags::has_no_indices)
 186                                 return false;
 187                         for (auto & i : seq) {
 188                                 if (i.rest.info(info_flags::has_indices)) {
 189                                         this->setflag(status_flags::has_indices);
 190                                         this->clearflag(status_flags::has_no_indices);
 191                                         return true;
 192                                 }
 193                         }
 194                         this->clearflag(status_flags::has_indices);
 195                         this->setflag(status_flags::has_no_indices);
 196                         return false;
 197                 }
 198         }
 199         return inherited::info(inf);
 200 }
 201
 202 size_t expairseq::nops() const
 203 {
 204         if (overall_coeff.is_equal(default_overall_coeff()))
 205                 return seq.size();
 206         else
 207                 return seq.size()+1;
 208 }
 209
 210 ex expairseq::op(size_t i) const
 211 {
 212         if (i < seq.size())
 213                 return recombine_pair_to_ex(seq[i]);
 214         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 215         return overall_coeff;
 216 }
 217
 218 ex expairseq::map(map_function &f) const
 219 {
 220         epvector v;
 221         v.reserve(seq.size()+1);
 222
 223         for (auto & it : seq)
 224                 v.push_back(split_ex_to_pair(f(recombine_pair_to_ex(it))));
 225
 226         if (overall_coeff.is_equal(default_overall_coeff()))
 227                 return thisexpairseq(std::move(v), default_overall_coeff(), true);
 228         else {
 229                 ex newcoeff = f(overall_coeff);
 230                 if(is_a<numeric>(newcoeff))
 231                         return thisexpairseq(std::move(v), newcoeff, true);
 232                 else {
 233                         v.push_back(split_ex_to_pair(newcoeff));
 234                         return thisexpairseq(std::move(v), default_overall_coeff(), true);
 235                 }
 236         }
 237 }
 238
 239 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 240 ex expairseq::eval() const
 241 {
 242         if (flags &status_flags::evaluated)
 243                 return *this;
 244
 245         const epvector evaled = evalchildren();
 246         if (!evaled.empty())
 247                 return dynallocate<expairseq>(std::move(evaled), overall_coeff).setflag(status_flags::evaluated);
 248         else
 249                 return this->hold();
 250 }
 251
 252 epvector* conjugateepvector(const epvector&epv)
 253 {
 254         epvector *newepv = nullptr;
 255         for (auto i=epv.begin(); i!=epv.end(); ++i) {
 256                 if (newepv) {
 257                         newepv->push_back(i->conjugate());
 258                         continue;
 259                 }
 260                 expair x = i->conjugate();
 261                 if (x.is_equal(*i)) {
 262                         continue;
 263                 }
 264                 newepv = new epvector;
 265                 newepv->reserve(epv.size());
 266                 for (auto j=epv.begin(); j!=i; ++j) {
 267                         newepv->push_back(*j);
 268                 }
 269                 newepv->push_back(x);
 270         }
 271         return newepv;
 272 }
 273
 274 ex expairseq::conjugate() const
 275 {
 276         std::unique_ptr<epvector> newepv(conjugateepvector(seq));
 277         ex x = overall_coeff.conjugate();
 278         if (newepv) {
 279                 return thisexpairseq(std::move(*newepv), x);
 280         }
 281         if (are_ex_trivially_equal(x, overall_coeff)) {
 282                 return *this;
 283         }
 284         return thisexpairseq(seq, x);
 285 }
 286
 287 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 288 {
 289         // This differs from basic::match() because we want "a+b+c+d" to
 290         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 291
 292         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 293
 294                 // Check whether global wildcard (one that matches the "rest of the
 295                 // expression", like "*" above) is present
 296                 bool has_global_wildcard = false;
 297                 ex global_wildcard;
 298                 for (size_t i=0; i<pattern.nops(); i++) {
 299                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 300                                 has_global_wildcard = true;
 301                                 global_wildcard = pattern.op(i);
 302                                 break;
 303                         }
 304                 }
 305
 306                 // Even if the expression does not match the pattern, some of
 307                 // its subexpressions could match it. For example, x^5*y^(-1)
 308                 // does not match the pattern $0^5, but its subexpression x^5
 309                 // does. So, save repl_lst in order to not add bogus entries.
 310                 exmap tmp_repl = repl_lst;
 311
 312                 // Unfortunately, this is an O(N^2) operation because we can't
 313                 // sort the pattern in a useful way...
 314
 315                 // Chop into terms
 316                 exvector ops;
 317                 ops.reserve(nops());
 318                 for (size_t i=0; i<nops(); i++)
 319                         ops.push_back(op(i));
 320
 321                 // Now, for every term of the pattern, look for a matching term in
 322                 // the expression and remove the match
 323                 for (size_t i=0; i<pattern.nops(); i++) {
 324                         ex p = pattern.op(i);
 325                         if (has_global_wildcard && p.is_equal(global_wildcard))
 326                                 continue;
 327                         auto it = ops.begin(), itend = ops.end();
 328                         while (it != itend) {
 329                                 if (it->match(p, tmp_repl)) {
 330                                         ops.erase(it);
 331                                         goto found;
 332                                 }
 333                                 ++it;
 334                         }
 335                         return false; // no match found
 336 found:          ;
 337                 }
 338
 339                 if (has_global_wildcard) {
 340
 341                         // Assign all the remaining terms to the global wildcard (unless
 342                         // it has already been matched before, in which case the matches
 343                         // must be equal)
 344                         size_t num = ops.size();
 345                         epvector vp;
 346                         vp.reserve(num);
 347                         for (size_t i=0; i<num; i++)
 348                                 vp.push_back(split_ex_to_pair(ops[i]));
 349                         ex rest = thisexpairseq(std::move(vp), default_overall_coeff());
 350                         for (auto & it : tmp_repl) {
 351                                 if (it.first.is_equal(global_wildcard)) {
 352                                         if (rest.is_equal(it.second)) {
 353                                                 repl_lst = tmp_repl;
 354                                                 return true;
 355                                         }
 356                                         return false;
 357                                 }
 358                         }
 359                         repl_lst = tmp_repl;
 360                         repl_lst[global_wildcard] = rest;
 361                         return true;
 362
 363                 } else {
 364
 365                         // No global wildcard, then the match fails if there are any
 366                         // unmatched terms left
 367                         if (ops.empty()) {
 368                                 repl_lst = tmp_repl;
 369                                 return true;
 370                         }
 371                         return false;
 372                 }
 373         }
 374         return inherited::match(pattern, repl_lst);
 375 }
 376
 377 ex expairseq::subs(const exmap & m, unsigned options) const
 378 {
 379         epvector subsed = subschildren(m, options);
 380         if (!subsed.empty())
 381                 return ex_to<basic>(thisexpairseq(std::move(subsed), overall_coeff, (options & subs_options::no_index_renaming) == 0));
 382         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 383                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 384         else
 385                 return subs_one_level(m, options);
 386 }
 387
 388 // protected
 389
 390 int expairseq::compare_same_type(const basic &other) const
 391 {
 392         GINAC_ASSERT(is_a<expairseq>(other));
 393         const expairseq &o = static_cast<const expairseq &>(other);
 394
 395         int cmpval;
 396
 397         // compare number of elements
 398         if (seq.size() != o.seq.size())
 399                 return (seq.size()<o.seq.size()) ? -1 : 1;
 400
 401         // compare overall_coeff
 402         cmpval = overall_coeff.compare(o.overall_coeff);
 403         if (cmpval!=0)
 404                 return cmpval;
 405
 406         auto cit1 = seq.begin(), last1 = seq.end();
 407         auto cit2 = o.seq.begin(), last2 = o.seq.end();
 408         for (; (cit1!=last1) && (cit2!=last2); ++cit1, ++cit2) {
 409                 cmpval = (*cit1).compare(*cit2);
 410                 if (cmpval!=0) return cmpval;
 411         }
 412
 413         GINAC_ASSERT(cit1==last1);
 414         GINAC_ASSERT(cit2==last2);
 415
 416         return 0;
 417 }
 418
 419 bool expairseq::is_equal_same_type(const basic &other) const
 420 {
 421         const expairseq &o = static_cast<const expairseq &>(other);
 422
 423         // compare number of elements
 424         if (seq.size()!=o.seq.size())
 425                 return false;
 426
 427         // compare overall_coeff
 428         if (!overall_coeff.is_equal(o.overall_coeff))
 429                 return false;
 430
 431         auto cit2 = o.seq.begin();
 432         for (auto & cit1 : seq) {
 433                 if (!cit1.is_equal(*cit2))
 434                         return false;
 435                 ++cit2;
 436         }
 437
 438         return true;
 439 }
 440
 441 unsigned expairseq::return_type() const
 442 {
 443         return return_types::noncommutative_composite;
 444 }
 445
 446 unsigned expairseq::calchash() const
 447 {
 448         unsigned v = make_hash_seed(typeid(*this));
 449         for (auto & i : seq) {
 450                 v ^= i.rest.gethash();
 451                 v = rotate_left(v);
 452                 v ^= i.coeff.gethash();
 453         }
 454
 455         v ^= overall_coeff.gethash();
 456
 457         // store calculated hash value only if object is already evaluated
 458         if (flags &status_flags::evaluated) {
 459                 setflag(status_flags::hash_calculated);
 460                 hashvalue = v;
 461         }
 462
 463         return v;
 464 }
 465
 466 ex expairseq::expand(unsigned options) const
 467 {
 468         epvector expanded = expandchildren(options);
 469         if (!expanded.empty()) {
 470                 return thisexpairseq(std::move(expanded), overall_coeff);
 471         }
 472         return (options == 0) ? setflag(status_flags::expanded) : *this;
 473 }
 474
 475 //////////
 476 // new virtual functions which can be overridden by derived classes
 477 //////////
 478
 479 // protected
 480
 481 /** Create an object of this type.
 482  *  This method works similar to a constructor.  It is useful because expairseq
 483  *  has (at least) two possible different semantics but we want to inherit
 484  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 485  *  has to create a new one of the same semantics, which cannot be done by a
 486  *  ctor because the name (add, mul,...) is unknown on the expairseq level.  In
 487  *  order for this trick to work a derived class must of course override this
 488  *  definition. */
 489 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 490 {
 491         return expairseq(v, oc, do_index_renaming);
 492 }
 493
 494 ex expairseq::thisexpairseq(epvector && vp, const ex &oc, bool do_index_renaming) const
 495 {
 496         return expairseq(std::move(vp), oc, do_index_renaming);
 497 }
 498
 499 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 500 {
 501         c.s << "[[";
 502         p.rest.print(c, precedence());
 503         c.s << ",";
 504         p.coeff.print(c, precedence());
 505         c.s << "]]";
 506 }
 507
 508 void expairseq::printseq(const print_context & c, char delim,
 509                          unsigned this_precedence,
 510                          unsigned upper_precedence) const
 511 {
 512         if (this_precedence <= upper_precedence)
 513                 c.s << "(";
 514         auto it = seq.begin(), it_last = seq.end() - 1;
 515         for (; it!=it_last; ++it) {
 516                 printpair(c, *it, this_precedence);
 517                 c.s << delim;
 518         }
 519         printpair(c, *it, this_precedence);
 520         if (!overall_coeff.is_equal(default_overall_coeff())) {
 521                 c.s << delim;
 522                 overall_coeff.print(c, this_precedence);
 523         }
 524
 525         if (this_precedence <= upper_precedence)
 526                 c.s << ")";
 527 }
 528
 529
 530 /** Form an expair from an ex, using the corresponding semantics.
 531  *  @see expairseq::recombine_pair_to_ex() */
 532 expair expairseq::split_ex_to_pair(const ex &e) const
 533 {
 534         return expair(e,_ex1);
 535 }
 536
 537
 538 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 539                                                 const ex &c) const
 540 {
 541         GINAC_ASSERT(is_exactly_a<numeric>(c));
 542
 543         return expair(e,c);
 544 }
 545
 546
 547 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 548                                                   const ex &c) const
 549 {
 550         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 551         GINAC_ASSERT(is_exactly_a<numeric>(c));
 552
 553         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 554 }
 555
 556
 557 /** Form an ex out of an expair, using the corresponding semantics.
 558  *  @see expairseq::split_ex_to_pair() */
 559 ex expairseq::recombine_pair_to_ex(const expair &p) const
 560 {
 561         return lst{p.rest, p.coeff};
 562 }
 563
 564 bool expairseq::expair_needs_further_processing(epp it)
 565 {
 566         if (is_exactly_a<numeric>(it->rest) &&
 567             it->coeff.is_equal(_ex1)) {
 568                 // the pair {<n>, 1} has yet to be absorbed into overall_coeff
 569                 return true;
 570         }
 571         return false;
 572 }
 573
 574 ex expairseq::default_overall_coeff() const
 575 {
 576         return _ex0;
 577 }
 578
 579 void expairseq::combine_overall_coeff(const ex &c)
 580 {
 581         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 582         GINAC_ASSERT(is_exactly_a<numeric>(c));
 583         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 584 }
 585
 586 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 587 {
 588         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 589         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 590         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 591         overall_coeff = ex_to<numeric>(overall_coeff).
 592                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 593 }
 594
 595 bool expairseq::can_make_flat(const expair &p) const
 596 {
 597         return true;
 598 }
 599
 600
 601 //////////
 602 // non-virtual functions in this class
 603 //////////
 604
 605 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 606 {
 607         const std::type_info& typeid_this = typeid(*this);
 608         if (typeid(ex_to<basic>(lh)) == typeid_this) {
 609                 if (typeid(ex_to<basic>(rh)) == typeid_this) {
 610                         if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 611                                 rh.info(info_flags::has_indices)) {
 612                                 ex newrh=rename_dummy_indices_uniquely(lh, rh);
 613                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 614                                                            ex_to<expairseq>(newrh));
 615                         }
 616                         else
 617                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 618                                                            ex_to<expairseq>(rh));
 619                         return;
 620                 } else {
 621                         construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 622                         return;
 623                 }
 624         } else if (typeid(ex_to<basic>(rh)) == typeid_this) {
 625                 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 626                 return;
 627         }
 628
 629         if (is_exactly_a<numeric>(lh)) {
 630                 if (is_exactly_a<numeric>(rh)) {
 631                         combine_overall_coeff(lh);
 632                         combine_overall_coeff(rh);
 633                 } else {
 634                         combine_overall_coeff(lh);
 635                         seq.push_back(split_ex_to_pair(rh));
 636                 }
 637         } else {
 638                 if (is_exactly_a<numeric>(rh)) {
 639                         combine_overall_coeff(rh);
 640                         seq.push_back(split_ex_to_pair(lh));
 641                 } else {
 642                         expair p1 = split_ex_to_pair(lh);
 643                         expair p2 = split_ex_to_pair(rh);
 644
 645                         int cmpval = p1.rest.compare(p2.rest);
 646                         if (cmpval==0) {
 647                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 648                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 649                                         // no further processing is necessary, since this
 650                                         // one element will usually be recombined in eval()
 651                                         seq.push_back(p1);
 652                                 }
 653                         } else {
 654                                 seq.reserve(2);
 655                                 if (cmpval<0) {
 656                                         seq.push_back(p1);
 657                                         seq.push_back(p2);
 658                                 } else {
 659                                         seq.push_back(p2);
 660                                         seq.push_back(p1);
 661                                 }
 662                         }
 663                 }
 664         }
 665 }
 666
 667 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 668                                            const expairseq &s2)
 669 {
 670         combine_overall_coeff(s1.overall_coeff);
 671         combine_overall_coeff(s2.overall_coeff);
 672
 673         auto first1 = s1.seq.begin(), last1 = s1.seq.end();
 674         auto first2 = s2.seq.begin(), last2 = s2.seq.end();
 675
 676         seq.reserve(s1.seq.size()+s2.seq.size());
 677
 678         bool needs_further_processing=false;
 679
 680         while (first1!=last1 && first2!=last2) {
 681                 int cmpval = (*first1).rest.compare((*first2).rest);
 682
 683                 if (cmpval==0) {
 684                         // combine terms
 685                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 686                                                    add(ex_to<numeric>(first2->coeff));
 687                         if (!newcoeff.is_zero()) {
 688                                 seq.push_back(expair(first1->rest,newcoeff));
 689                                 if (expair_needs_further_processing(seq.end()-1)) {
 690                                         needs_further_processing = true;
 691                                 }
 692                         }
 693                         ++first1;
 694                         ++first2;
 695                 } else if (cmpval<0) {
 696                         seq.push_back(*first1);
 697                         ++first1;
 698                 } else {
 699                         seq.push_back(*first2);
 700                         ++first2;
 701                 }
 702         }
 703
 704         while (first1!=last1) {
 705                 seq.push_back(*first1);
 706                 ++first1;
 707         }
 708         while (first2!=last2) {
 709                 seq.push_back(*first2);
 710                 ++first2;
 711         }
 712
 713         if (needs_further_processing) {
 714                 // Clear seq and start over.
 715                 epvector v = std::move(seq);
 716                 construct_from_epvector(std::move(v));
 717         }
 718 }
 719
 720 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 721                                             const ex &e)
 722 {
 723         combine_overall_coeff(s.overall_coeff);
 724         if (is_exactly_a<numeric>(e)) {
 725                 combine_overall_coeff(e);
 726                 seq = s.seq;
 727                 return;
 728         }
 729
 730         auto first = s.seq.begin(), last = s.seq.end();
 731         expair p = split_ex_to_pair(e);
 732
 733         seq.reserve(s.seq.size()+1);
 734         bool p_pushed = false;
 735
 736         bool needs_further_processing=false;
 737
 738         // merge p into s.seq
 739         while (first!=last) {
 740                 int cmpval = (*first).rest.compare(p.rest);
 741                 if (cmpval==0) {
 742                         // combine terms
 743                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 744                                                    add(ex_to<numeric>(p.coeff));
 745                         if (!newcoeff.is_zero()) {
 746                                 seq.push_back(expair(first->rest,newcoeff));
 747                                 if (expair_needs_further_processing(seq.end()-1))
 748                                         needs_further_processing = true;
 749                         }
 750                         ++first;
 751                         p_pushed = true;
 752                         break;
 753                 } else if (cmpval<0) {
 754                         seq.push_back(*first);
 755                         ++first;
 756                 } else {
 757                         seq.push_back(p);
 758                         p_pushed = true;
 759                         break;
 760                 }
 761         }
 762
 763         if (p_pushed) {
 764                 // while loop exited because p was pushed, now push rest of s.seq
 765                 while (first!=last) {
 766                         seq.push_back(*first);
 767                         ++first;
 768                 }
 769         } else {
 770                 // while loop exited because s.seq was pushed, now push p
 771                 seq.push_back(p);
 772         }
 773
 774         if (needs_further_processing) {
 775                 // Clear seq and start over.
 776                 epvector v = std::move(seq);
 777                 construct_from_epvector(std::move(v));
 778         }
 779 }
 780
 781 void expairseq::construct_from_exvector(const exvector &v)
 782 {
 783         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 784         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 785         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 786         //                  (same for (+,*) -> (*,^)
 787
 788         make_flat(v);
 789         canonicalize();
 790         combine_same_terms_sorted_seq();
 791 }
 792
 793 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
 794 {
 795         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 796         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 797         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 798         //                  same for (+,*) -> (*,^)
 799
 800         make_flat(v, do_index_renaming);
 801         canonicalize();
 802         combine_same_terms_sorted_seq();
 803 }
 804
 805 void expairseq::construct_from_epvector(epvector &&v, bool do_index_renaming)
 806 {
 807         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 808         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 809         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 810         //                  same for (+,*) -> (*,^)
 811
 812         make_flat(std::move(v), do_index_renaming);
 813         canonicalize();
 814         combine_same_terms_sorted_seq();
 815 }
 816
 817 /** Combine this expairseq with argument exvector.
 818  *  It cares for associativity as well as for special handling of numerics. */
 819 void expairseq::make_flat(const exvector &v)
 820 {
 821         // count number of operands which are of same expairseq derived type
 822         // and their cumulative number of operands
 823         int nexpairseqs = 0;
 824         int noperands = 0;
 825         bool do_idx_rename = false;
 826
 827         const std::type_info& typeid_this = typeid(*this);
 828         for (auto & cit : v) {
 829                 if (typeid(ex_to<basic>(cit)) == typeid_this) {
 830                         ++nexpairseqs;
 831                         noperands += ex_to<expairseq>(cit).seq.size();
 832                 }
 833                 if (is_a<mul>(*this) && (!do_idx_rename) &&
 834                     cit.info(info_flags::has_indices))
 835                         do_idx_rename = true;
 836         }
 837
 838         // reserve seq and coeffseq which will hold all operands
 839         seq.reserve(v.size()+noperands-nexpairseqs);
 840
 841         // copy elements and split off numerical part
 842         make_flat_inserter mf(v, do_idx_rename);
 843         for (auto & cit : v) {
 844                 if (typeid(ex_to<basic>(cit)) == typeid_this) {
 845                         ex newfactor = mf.handle_factor(cit, _ex1);
 846                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
 847                         combine_overall_coeff(subseqref.overall_coeff);
 848                         for (auto & cit_s : subseqref.seq) {
 849                                 seq.push_back(cit_s);
 850                         }
 851                 } else {
 852                         if (is_exactly_a<numeric>(cit))
 853                                 combine_overall_coeff(cit);
 854                         else {
 855                                 ex newfactor = mf.handle_factor(cit, _ex1);
 856                                 seq.push_back(split_ex_to_pair(newfactor));
 857                         }
 858                 }
 859         }
 860 }
 861
 862 /** Combine this expairseq with argument epvector.
 863  *  It cares for associativity as well as for special handling of numerics. */
 864 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
 865 {
 866         // count number of operands which are of same expairseq derived type
 867         // and their cumulative number of operands
 868         int nexpairseqs = 0;
 869         int noperands = 0;
 870         bool really_need_rename_inds = false;
 871
 872         const std::type_info& typeid_this = typeid(*this);
 873         for (auto & cit : v) {
 874                 if (typeid(ex_to<basic>(cit.rest)) == typeid_this) {
 875                         ++nexpairseqs;
 876                         noperands += ex_to<expairseq>(cit.rest).seq.size();
 877                 }
 878                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
 879                     cit.rest.info(info_flags::has_indices))
 880                         really_need_rename_inds = true;
 881         }
 882         do_index_renaming = do_index_renaming && really_need_rename_inds;
 883
 884         // reserve seq and coeffseq which will hold all operands
 885         seq.reserve(v.size()+noperands-nexpairseqs);
 886         make_flat_inserter mf(v, do_index_renaming);
 887
 888         // copy elements and split off numerical part
 889         for (auto & cit : v) {
 890                 if (typeid(ex_to<basic>(cit.rest)) == typeid_this &&
 891                     this->can_make_flat(cit)) {
 892                         ex newrest = mf.handle_factor(cit.rest, cit.coeff);
 893                         const expairseq &subseqref = ex_to<expairseq>(newrest);
 894                         combine_overall_coeff(subseqref.overall_coeff, cit.coeff);
 895                         for (auto & cit_s : subseqref.seq) {
 896                                 seq.push_back(expair(cit_s.rest,
 897                                                      ex_to<numeric>(cit_s.coeff).mul_dyn(ex_to<numeric>(cit.coeff))));
 898                         }
 899                 } else {
 900                         if (cit.is_canonical_numeric())
 901                                 combine_overall_coeff(mf.handle_factor(cit.rest, _ex1));
 902                         else {
 903                                 ex rest = cit.rest;
 904                                 ex newrest = mf.handle_factor(rest, cit.coeff);
 905                                 if (are_ex_trivially_equal(newrest, rest))
 906                                         seq.push_back(cit);
 907                                 else
 908                                         seq.push_back(expair(newrest, cit.coeff));
 909                         }
 910                 }
 911         }
 912 }
 913
 914 /** Brings this expairseq into a sorted (canonical) form. */
 915 void expairseq::canonicalize()
 916 {
 917         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 918 }
 919
 920
 921 /** Compact a presorted expairseq by combining all matching expairs to one
 922  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
 923  *  instance. */
 924 void expairseq::combine_same_terms_sorted_seq()
 925 {
 926         if (seq.size()<2)
 927                 return;
 928
 929         bool needs_further_processing = false;
 930
 931         auto itin1 = seq.begin();
 932         auto itin2 = itin1 + 1;
 933         auto itout = itin1;
 934         auto last = seq.end();
 935         // must_copy will be set to true the first time some combination is
 936         // possible from then on the sequence has changed and must be compacted
 937         bool must_copy = false;
 938         while (itin2!=last) {
 939                 if (itin1->rest.compare(itin2->rest)==0) {
 940                         itin1->coeff = ex_to<numeric>(itin1->coeff).
 941                                        add_dyn(ex_to<numeric>(itin2->coeff));
 942                         if (expair_needs_further_processing(itin1))
 943                                 needs_further_processing = true;
 944                         must_copy = true;
 945                 } else {
 946                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 947                                 if (must_copy)
 948                                         *itout = *itin1;
 949                                 ++itout;
 950                         }
 951                         itin1 = itin2;
 952                 }
 953                 ++itin2;
 954         }
 955         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 956                 if (must_copy)
 957                         *itout = *itin1;
 958                 ++itout;
 959         }
 960         if (itout!=last)
 961                 seq.erase(itout,last);
 962
 963         if (needs_further_processing) {
 964                 // Clear seq and start over.
 965                 epvector v = std::move(seq);
 966                 construct_from_epvector(std::move(v));
 967         }
 968 }
 969
 970 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
 971  *  debugging or in assertions since being sorted is an invariance. */
 972 bool expairseq::is_canonical() const
 973 {
 974         if (seq.size() <= 1)
 975                 return 1;
 976
 977         auto it = seq.begin(), itend = seq.end();
 978         auto it_last = it;
 979         for (++it; it!=itend; it_last=it, ++it) {
 980                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
 981                         if (!is_exactly_a<numeric>(it_last->rest) ||
 982                                 !is_exactly_a<numeric>(it->rest)) {
 983                                 // double test makes it easier to set a breakpoint...
 984                                 if (!is_exactly_a<numeric>(it_last->rest) ||
 985                                         !is_exactly_a<numeric>(it->rest)) {
 986                                         printpair(std::clog, *it_last, 0);
 987                                         std::clog << ">";
 988                                         printpair(std::clog, *it, 0);
 989                                         std::clog << "\n";
 990                                         std::clog << "pair1:" << std::endl;
 991                                         it_last->rest.print(print_tree(std::clog));
 992                                         it_last->coeff.print(print_tree(std::clog));
 993                                         std::clog << "pair2:" << std::endl;
 994                                         it->rest.print(print_tree(std::clog));
 995                                         it->coeff.print(print_tree(std::clog));
 996                                         return 0;
 997                                 }
 998                         }
 999                 }
1000         }
1001         return 1;
1002 }
1003
1004 /** Member-wise expand the expairs in this sequence.
1005  *
1006  *  @see expairseq::expand()
1007  *  @return epvector containing expanded pairs, empty if no members
1008  *    had to be changed. */
1009 epvector expairseq::expandchildren(unsigned options) const
1010 {
1011         auto cit = seq.begin(), last = seq.end();
1012         while (cit!=last) {
1013                 const ex expanded_ex = cit->rest.expand(options);
1014                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1015
1016                         // something changed, copy seq, eval and return it
1017                         epvector s;
1018                         s.reserve(seq.size());
1019
1020                         // copy parts of seq which are known not to have changed
1021                         s.insert(s.begin(), seq.begin(), cit);
1022
1023                         // copy first changed element
1024                         s.push_back(expair(expanded_ex, cit->coeff));
1025                         ++cit;
1026
1027                         // copy rest
1028                         while (cit != last) {
1029                                 s.push_back(expair(cit->rest.expand(options), cit->coeff));
1030                                 ++cit;
1031                         }
1032                         return s;
1033                 }
1034
1035                 ++cit;
1036         }
1037
1038         return epvector(); // empty signalling nothing has changed
1039 }
1040
1041
1042 /** Member-wise evaluate the expairs in this sequence.
1043  *
1044  *  @see expairseq::eval()
1045  *  @return epvector containing evaluated pairs, empty if no members
1046  *    had to be changed. */
1047 epvector expairseq::evalchildren() const
1048 {
1049         auto cit = seq.begin(), last = seq.end();
1050         while (cit!=last) {
1051                 const expair evaled_pair = combine_ex_with_coeff_to_pair(cit->rest, cit->coeff);
1052                 if (unlikely(!evaled_pair.is_equal(*cit))) {
1053
1054                         // something changed: copy seq, eval and return it
1055                         epvector s;
1056                         s.reserve(seq.size());
1057
1058                         // copy parts of seq which are known not to have changed
1059                         s.insert(s.begin(), seq.begin(), cit);
1060
1061                         // copy first changed element
1062                         s.push_back(evaled_pair);
1063                         ++cit;
1064
1065                         // copy rest
1066                         while (cit != last) {
1067                                 s.push_back(combine_ex_with_coeff_to_pair(cit->rest, cit->coeff));
1068                                 ++cit;
1069                         }
1070                         return s;
1071                 }
1072
1073                 ++cit;
1074         }
1075
1076         return epvector(); // signalling nothing has changed
1077 }
1078
1079 /** Member-wise substitute in this sequence.
1080  *
1081  *  @see expairseq::subs()
1082  *  @return epvector containing expanded pairs, empty if no members
1083  *    had to be changed. */
1084 epvector expairseq::subschildren(const exmap & m, unsigned options) const
1085 {
1086         // When any of the objects to be substituted is a product or power
1087         // we have to recombine the pairs because the numeric coefficients may
1088         // be part of the search pattern.
1089         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1090
1091                 // Search the list of substitutions and cache our findings
1092                 for (auto & it : m) {
1093                         if (is_exactly_a<mul>(it.first) || is_exactly_a<power>(it.first)) {
1094                                 options |= subs_options::pattern_is_product;
1095                                 break;
1096                         }
1097                 }
1098                 if (!(options & subs_options::pattern_is_product))
1099                         options |= subs_options::pattern_is_not_product;
1100         }
1101
1102         if (options & subs_options::pattern_is_product) {
1103
1104                 // Substitute in the recombined pairs
1105                 auto cit = seq.begin(), last = seq.end();
1106                 while (cit != last) {
1107
1108                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1109                         const ex &subsed_ex = orig_ex.subs(m, options);
1110                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1111
1112                                 // Something changed: copy seq, subs and return it
1113                                 epvector s;
1114                                 s.reserve(seq.size());
1115
1116                                 // Copy parts of seq which are known not to have changed
1117                                 s.insert(s.begin(), seq.begin(), cit);
1118
1119                                 // Copy first changed element
1120                                 s.push_back(split_ex_to_pair(subsed_ex));
1121                                 ++cit;
1122
1123                                 // Copy rest
1124                                 while (cit != last) {
1125                                         s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1126                                         ++cit;
1127                                 }
1128                                 return s;
1129                         }
1130
1131                         ++cit;
1132                 }
1133
1134         } else {
1135
1136                 // Substitute only in the "rest" part of the pairs
1137                 auto cit = seq.begin(), last = seq.end();
1138                 while (cit != last) {
1139
1140                         const ex subsed_rest = cit->rest.subs(m, options);
1141                         const expair subsed_pair = combine_ex_with_coeff_to_pair(subsed_rest, cit->coeff);
1142                         if (!subsed_pair.is_equal(*cit)) {
1143
1144                                 // Something changed: copy seq, subs and return it
1145                                 epvector s;
1146                                 s.reserve(seq.size());
1147
1148                                 // Copy parts of seq which are known not to have changed
1149                                 s.insert(s.begin(), seq.begin(), cit);
1150
1151                                 // Copy first changed element
1152                                 s.push_back(subsed_pair);
1153                                 ++cit;
1154
1155                                 // Copy rest
1156                                 while (cit != last) {
1157                                         s.push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1158                                         ++cit;
1159                                 }
1160                                 return s;
1161                         }
1162
1163                         ++cit;
1164                 }
1165         }
1166
1167         // Nothing has changed
1168         return epvector();
1169 }
1170
1171 //////////
1172 // static member variables
1173 //////////
1174
1175 } // namespace GiNaC