ginac/expairseq.cpp

   1 /** @file expairseq.cpp
   2  *
   3  *  Implementation of sequences of expression pairs. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include "expairseq.h"
  24 #include "lst.h"
  25 #include "add.h"
  26 #include "mul.h"
  27 #include "power.h"
  28 #include "relational.h"
  29 #include "wildcard.h"
  30 #include "archive.h"
  31 #include "operators.h"
  32 #include "utils.h"
  33 #include "hash_seed.h"
  34 #include "indexed.h"
  35
  36 #include <algorithm>
  37 #include <iostream>
  38 #include <iterator>
  39 #include <stdexcept>
  40 #include <string>
  41
  42 namespace GiNaC {
  43
  44
  45 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
  46   print_func<print_context>(&expairseq::do_print).
  47   print_func<print_tree>(&expairseq::do_print_tree))
  48
  49
  50 //////////
  51 // helper classes
  52 //////////
  53
  54 class epp_is_less
  55 {
  56 public:
  57         bool operator()(const epp &lh, const epp &rh) const
  58         {
  59                 return (*lh).is_less(*rh);
  60         }
  61 };
  62
  63 //////////
  64 // default constructor
  65 //////////
  66
  67 // public
  68
  69 expairseq::expairseq()
  70 {}
  71
  72 // protected
  73
  74 //////////
  75 // other constructors
  76 //////////
  77
  78 expairseq::expairseq(const ex &lh, const ex &rh)
  79 {
  80         construct_from_2_ex(lh,rh);
  81         GINAC_ASSERT(is_canonical());
  82 }
  83
  84 expairseq::expairseq(const exvector &v)
  85 {
  86         construct_from_exvector(v);
  87         GINAC_ASSERT(is_canonical());
  88 }
  89
  90 expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
  91   :  overall_coeff(oc)
  92 {
  93         GINAC_ASSERT(is_a<numeric>(oc));
  94         construct_from_epvector(v, do_index_renaming);
  95         GINAC_ASSERT(is_canonical());
  96 }
  97
  98 expairseq::expairseq(epvector && vp, const ex &oc, bool do_index_renaming)
  99   :  overall_coeff(oc)
 100 {
 101         GINAC_ASSERT(is_a<numeric>(oc));
 102         construct_from_epvector(std::move(vp), do_index_renaming);
 103         GINAC_ASSERT(is_canonical());
 104 }
 105
 106 //////////
 107 // archiving
 108 //////////
 109
 110 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
 111 {
 112         inherited::read_archive(n, sym_lst);
 113         archive_node::archive_node_cit first = n.find_first("rest");
 114         archive_node::archive_node_cit last = n.find_last("coeff");
 115         ++last;
 116         seq.reserve((last-first)/2);
 117
 118         for (archive_node::archive_node_cit loc = first; loc < last;) {
 119                 ex rest;
 120                 ex coeff;
 121                 n.find_ex_by_loc(loc++, rest, sym_lst);
 122                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 123                 seq.push_back(expair(rest, coeff));
 124         }
 125
 126         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 127
 128         canonicalize();
 129         GINAC_ASSERT(is_canonical());
 130 }
 131
 132 void expairseq::archive(archive_node &n) const
 133 {
 134         inherited::archive(n);
 135         epvector::const_iterator i = seq.begin(), iend = seq.end();
 136         while (i != iend) {
 137                 n.add_ex("rest", i->rest);
 138                 n.add_ex("coeff", i->coeff);
 139                 ++i;
 140         }
 141         n.add_ex("overall_coeff", overall_coeff);
 142 }
 143
 144
 145 //////////
 146 // functions overriding virtual functions from base classes
 147 //////////
 148
 149 // public
 150
 151 void expairseq::do_print(const print_context & c, unsigned level) const
 152 {
 153         c.s << "[[";
 154         printseq(c, ',', precedence(), level);
 155         c.s << "]]";
 156 }
 157
 158 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 159 {
 160         c.s << std::string(level, ' ') << class_name() << " @" << this
 161             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 162             << ", nops=" << nops()
 163             << std::endl;
 164         size_t num = seq.size();
 165         for (size_t i=0; i<num; ++i) {
 166                 seq[i].rest.print(c, level + c.delta_indent);
 167                 seq[i].coeff.print(c, level + c.delta_indent);
 168                 if (i != num - 1)
 169                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 170         }
 171         if (!overall_coeff.is_equal(default_overall_coeff())) {
 172                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 173                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 174                 overall_coeff.print(c, level + c.delta_indent);
 175         }
 176         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 177 }
 178
 179 bool expairseq::info(unsigned inf) const
 180 {
 181         switch(inf) {
 182                 case info_flags::expanded:
 183                         return (flags & status_flags::expanded);
 184                 case info_flags::has_indices: {
 185                         if (flags & status_flags::has_indices)
 186                                 return true;
 187                         else if (flags & status_flags::has_no_indices)
 188                                 return false;
 189                         for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
 190                                 if (i->rest.info(info_flags::has_indices)) {
 191                                         this->setflag(status_flags::has_indices);
 192                                         this->clearflag(status_flags::has_no_indices);
 193                                         return true;
 194                                 }
 195                         }
 196                         this->clearflag(status_flags::has_indices);
 197                         this->setflag(status_flags::has_no_indices);
 198                         return false;
 199                 }
 200         }
 201         return inherited::info(inf);
 202 }
 203
 204 size_t expairseq::nops() const
 205 {
 206         if (overall_coeff.is_equal(default_overall_coeff()))
 207                 return seq.size();
 208         else
 209                 return seq.size()+1;
 210 }
 211
 212 ex expairseq::op(size_t i) const
 213 {
 214         if (i < seq.size())
 215                 return recombine_pair_to_ex(seq[i]);
 216         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 217         return overall_coeff;
 218 }
 219
 220 ex expairseq::map(map_function &f) const
 221 {
 222         epvector v;
 223         v.reserve(seq.size()+1);
 224
 225         epvector::const_iterator cit = seq.begin(), last = seq.end();
 226         while (cit != last) {
 227                 v.push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 228                 ++cit;
 229         }
 230
 231         if (overall_coeff.is_equal(default_overall_coeff()))
 232                 return thisexpairseq(std::move(v), default_overall_coeff(), true);
 233         else {
 234                 ex newcoeff = f(overall_coeff);
 235                 if(is_a<numeric>(newcoeff))
 236                         return thisexpairseq(std::move(v), newcoeff, true);
 237                 else {
 238                         v.push_back(split_ex_to_pair(newcoeff));
 239                         return thisexpairseq(std::move(v), default_overall_coeff(), true);
 240                 }
 241         }
 242 }
 243
 244 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 245 ex expairseq::eval(int level) const
 246 {
 247         if ((level==1) && (flags &status_flags::evaluated))
 248                 return *this;
 249
 250         epvector evaled = evalchildren(level);
 251         if (!evaled.empty())
 252                 return (new expairseq(std::move(evaled), overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 253         else
 254                 return this->hold();
 255 }
 256
 257 epvector* conjugateepvector(const epvector&epv)
 258 {
 259         epvector *newepv = 0;
 260         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 261                 if(newepv) {
 262                         newepv->push_back(i->conjugate());
 263                         continue;
 264                 }
 265                 expair x = i->conjugate();
 266                 if (x.is_equal(*i)) {
 267                         continue;
 268                 }
 269                 newepv = new epvector;
 270                 newepv->reserve(epv.size());
 271                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 272                         newepv->push_back(*j);
 273                 }
 274                 newepv->push_back(x);
 275         }
 276         return newepv;
 277 }
 278
 279 ex expairseq::conjugate() const
 280 {
 281         epvector* newepv = conjugateepvector(seq);
 282         ex x = overall_coeff.conjugate();
 283         if (newepv) {
 284                 ex result = thisexpairseq(std::move(*newepv), x);
 285                 delete newepv;
 286                 return result;
 287         }
 288         if (are_ex_trivially_equal(x, overall_coeff)) {
 289                 return *this;
 290         }
 291         return thisexpairseq(seq, x);
 292 }
 293
 294 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 295 {
 296         // This differs from basic::match() because we want "a+b+c+d" to
 297         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 298
 299         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 300
 301                 // Check whether global wildcard (one that matches the "rest of the
 302                 // expression", like "*" above) is present
 303                 bool has_global_wildcard = false;
 304                 ex global_wildcard;
 305                 for (size_t i=0; i<pattern.nops(); i++) {
 306                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 307                                 has_global_wildcard = true;
 308                                 global_wildcard = pattern.op(i);
 309                                 break;
 310                         }
 311                 }
 312
 313                 // Even if the expression does not match the pattern, some of
 314                 // its subexpressions could match it. For example, x^5*y^(-1)
 315                 // does not match the pattern $0^5, but its subexpression x^5
 316                 // does. So, save repl_lst in order to not add bogus entries.
 317                 exmap tmp_repl = repl_lst;
 318
 319                 // Unfortunately, this is an O(N^2) operation because we can't
 320                 // sort the pattern in a useful way...
 321
 322                 // Chop into terms
 323                 exvector ops;
 324                 ops.reserve(nops());
 325                 for (size_t i=0; i<nops(); i++)
 326                         ops.push_back(op(i));
 327
 328                 // Now, for every term of the pattern, look for a matching term in
 329                 // the expression and remove the match
 330                 for (size_t i=0; i<pattern.nops(); i++) {
 331                         ex p = pattern.op(i);
 332                         if (has_global_wildcard && p.is_equal(global_wildcard))
 333                                 continue;
 334                         exvector::iterator it = ops.begin(), itend = ops.end();
 335                         while (it != itend) {
 336                                 if (it->match(p, tmp_repl)) {
 337                                         ops.erase(it);
 338                                         goto found;
 339                                 }
 340                                 ++it;
 341                         }
 342                         return false; // no match found
 343 found:          ;
 344                 }
 345
 346                 if (has_global_wildcard) {
 347
 348                         // Assign all the remaining terms to the global wildcard (unless
 349                         // it has already been matched before, in which case the matches
 350                         // must be equal)
 351                         size_t num = ops.size();
 352                         epvector vp;
 353                         vp.reserve(num);
 354                         for (size_t i=0; i<num; i++)
 355                                 vp.push_back(split_ex_to_pair(ops[i]));
 356                         ex rest = thisexpairseq(std::move(vp), default_overall_coeff());
 357                         for (exmap::const_iterator it = tmp_repl.begin(); it != tmp_repl.end(); ++it) {
 358                                 if (it->first.is_equal(global_wildcard)) {
 359                                         if (rest.is_equal(it->second)) {
 360                                                 repl_lst = tmp_repl;
 361                                                 return true;
 362                                         }
 363                                         return false;
 364                                 }
 365                         }
 366                         repl_lst = tmp_repl;
 367                         repl_lst[global_wildcard] = rest;
 368                         return true;
 369
 370                 } else {
 371
 372                         // No global wildcard, then the match fails if there are any
 373                         // unmatched terms left
 374                         if (ops.empty()) {
 375                                 repl_lst = tmp_repl;
 376                                 return true;
 377                         }
 378                         return false;
 379                 }
 380         }
 381         return inherited::match(pattern, repl_lst);
 382 }
 383
 384 ex expairseq::subs(const exmap & m, unsigned options) const
 385 {
 386         epvector subsed = subschildren(m, options);
 387         if (!subsed.empty())
 388                 return ex_to<basic>(thisexpairseq(std::move(subsed), overall_coeff, (options & subs_options::no_index_renaming) == 0));
 389         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 390                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 391         else
 392                 return subs_one_level(m, options);
 393 }
 394
 395 // protected
 396
 397 int expairseq::compare_same_type(const basic &other) const
 398 {
 399         GINAC_ASSERT(is_a<expairseq>(other));
 400         const expairseq &o = static_cast<const expairseq &>(other);
 401
 402         int cmpval;
 403
 404         // compare number of elements
 405         if (seq.size() != o.seq.size())
 406                 return (seq.size()<o.seq.size()) ? -1 : 1;
 407
 408         // compare overall_coeff
 409         cmpval = overall_coeff.compare(o.overall_coeff);
 410         if (cmpval!=0)
 411                 return cmpval;
 412
 413         epvector::const_iterator cit1 = seq.begin();
 414         epvector::const_iterator cit2 = o.seq.begin();
 415         epvector::const_iterator last1 = seq.end();
 416         epvector::const_iterator last2 = o.seq.end();
 417
 418         for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 419                 cmpval = (*cit1).compare(*cit2);
 420                 if (cmpval!=0) return cmpval;
 421         }
 422
 423         GINAC_ASSERT(cit1==last1);
 424         GINAC_ASSERT(cit2==last2);
 425
 426         return 0;
 427 }
 428
 429 bool expairseq::is_equal_same_type(const basic &other) const
 430 {
 431         const expairseq &o = static_cast<const expairseq &>(other);
 432
 433         // compare number of elements
 434         if (seq.size()!=o.seq.size())
 435                 return false;
 436
 437         // compare overall_coeff
 438         if (!overall_coeff.is_equal(o.overall_coeff))
 439                 return false;
 440
 441         epvector::const_iterator cit1 = seq.begin();
 442         epvector::const_iterator cit2 = o.seq.begin();
 443         epvector::const_iterator last1 = seq.end();
 444
 445         while (cit1!=last1) {
 446                 if (!(*cit1).is_equal(*cit2)) return false;
 447                 ++cit1;
 448                 ++cit2;
 449         }
 450
 451         return true;
 452 }
 453
 454 unsigned expairseq::return_type() const
 455 {
 456         return return_types::noncommutative_composite;
 457 }
 458
 459 unsigned expairseq::calchash() const
 460 {
 461         unsigned v = make_hash_seed(typeid(*this));
 462         epvector::const_iterator i = seq.begin();
 463         const epvector::const_iterator end = seq.end();
 464         while (i != end) {
 465                 v ^= i->rest.gethash();
 466                 v = rotate_left(v);
 467                 v ^= i->coeff.gethash();
 468                 ++i;
 469         }
 470
 471         v ^= overall_coeff.gethash();
 472
 473         // store calculated hash value only if object is already evaluated
 474         if (flags &status_flags::evaluated) {
 475                 setflag(status_flags::hash_calculated);
 476                 hashvalue = v;
 477         }
 478
 479         return v;
 480 }
 481
 482 ex expairseq::expand(unsigned options) const
 483 {
 484         epvector expanded = expandchildren(options);
 485         if (!expanded.empty()) {
 486                 return thisexpairseq(std::move(expanded), overall_coeff);
 487         }
 488         return (options == 0) ? setflag(status_flags::expanded) : *this;
 489 }
 490
 491 //////////
 492 // new virtual functions which can be overridden by derived classes
 493 //////////
 494
 495 // protected
 496
 497 /** Create an object of this type.
 498  *  This method works similar to a constructor.  It is useful because expairseq
 499  *  has (at least) two possible different semantics but we want to inherit
 500  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 501  *  has to create a new one of the same semantics, which cannot be done by a
 502  *  ctor because the name (add, mul,...) is unknown on the expairseq level.  In
 503  *  order for this trick to work a derived class must of course override this
 504  *  definition. */
 505 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 506 {
 507         return expairseq(v, oc, do_index_renaming);
 508 }
 509
 510 ex expairseq::thisexpairseq(epvector && vp, const ex &oc, bool do_index_renaming) const
 511 {
 512         return expairseq(std::move(vp), oc, do_index_renaming);
 513 }
 514
 515 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 516 {
 517         c.s << "[[";
 518         p.rest.print(c, precedence());
 519         c.s << ",";
 520         p.coeff.print(c, precedence());
 521         c.s << "]]";
 522 }
 523
 524 void expairseq::printseq(const print_context & c, char delim,
 525                          unsigned this_precedence,
 526                          unsigned upper_precedence) const
 527 {
 528         if (this_precedence <= upper_precedence)
 529                 c.s << "(";
 530         epvector::const_iterator it, it_last = seq.end() - 1;
 531         for (it=seq.begin(); it!=it_last; ++it) {
 532                 printpair(c, *it, this_precedence);
 533                 c.s << delim;
 534         }
 535         printpair(c, *it, this_precedence);
 536         if (!overall_coeff.is_equal(default_overall_coeff())) {
 537                 c.s << delim;
 538                 overall_coeff.print(c, this_precedence);
 539         }
 540
 541         if (this_precedence <= upper_precedence)
 542                 c.s << ")";
 543 }
 544
 545
 546 /** Form an expair from an ex, using the corresponding semantics.
 547  *  @see expairseq::recombine_pair_to_ex() */
 548 expair expairseq::split_ex_to_pair(const ex &e) const
 549 {
 550         return expair(e,_ex1);
 551 }
 552
 553
 554 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 555                                                 const ex &c) const
 556 {
 557         GINAC_ASSERT(is_exactly_a<numeric>(c));
 558
 559         return expair(e,c);
 560 }
 561
 562
 563 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 564                                                   const ex &c) const
 565 {
 566         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 567         GINAC_ASSERT(is_exactly_a<numeric>(c));
 568
 569         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 570 }
 571
 572
 573 /** Form an ex out of an expair, using the corresponding semantics.
 574  *  @see expairseq::split_ex_to_pair() */
 575 ex expairseq::recombine_pair_to_ex(const expair &p) const
 576 {
 577         return lst(p.rest,p.coeff);
 578 }
 579
 580 bool expairseq::expair_needs_further_processing(epp it)
 581 {
 582         return false;
 583 }
 584
 585 ex expairseq::default_overall_coeff() const
 586 {
 587         return _ex0;
 588 }
 589
 590 void expairseq::combine_overall_coeff(const ex &c)
 591 {
 592         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 593         GINAC_ASSERT(is_exactly_a<numeric>(c));
 594         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 595 }
 596
 597 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 598 {
 599         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 600         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 601         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 602         overall_coeff = ex_to<numeric>(overall_coeff).
 603                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 604 }
 605
 606 bool expairseq::can_make_flat(const expair &p) const
 607 {
 608         return true;
 609 }
 610
 611
 612 //////////
 613 // non-virtual functions in this class
 614 //////////
 615
 616 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 617 {
 618         exvector v;
 619         v.reserve(2);
 620         v.push_back(lh);
 621         v.push_back(rh);
 622         construct_from_exvector(v);
 623 }
 624
 625 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 626 {
 627         if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
 628                 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 629                         if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 630                                 rh.info(info_flags::has_indices)) {
 631                                 ex newrh=rename_dummy_indices_uniquely(lh, rh);
 632                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 633                                                            ex_to<expairseq>(newrh));
 634                         }
 635                         else
 636                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 637                                                            ex_to<expairseq>(rh));
 638                         return;
 639                 } else {
 640                         construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 641                         return;
 642                 }
 643         } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 644                 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 645                 return;
 646         }
 647
 648         if (is_exactly_a<numeric>(lh)) {
 649                 if (is_exactly_a<numeric>(rh)) {
 650                         combine_overall_coeff(lh);
 651                         combine_overall_coeff(rh);
 652                 } else {
 653                         combine_overall_coeff(lh);
 654                         seq.push_back(split_ex_to_pair(rh));
 655                 }
 656         } else {
 657                 if (is_exactly_a<numeric>(rh)) {
 658                         combine_overall_coeff(rh);
 659                         seq.push_back(split_ex_to_pair(lh));
 660                 } else {
 661                         expair p1 = split_ex_to_pair(lh);
 662                         expair p2 = split_ex_to_pair(rh);
 663
 664                         int cmpval = p1.rest.compare(p2.rest);
 665                         if (cmpval==0) {
 666                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 667                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 668                                         // no further processing is necessary, since this
 669                                         // one element will usually be recombined in eval()
 670                                         seq.push_back(p1);
 671                                 }
 672                         } else {
 673                                 seq.reserve(2);
 674                                 if (cmpval<0) {
 675                                         seq.push_back(p1);
 676                                         seq.push_back(p2);
 677                                 } else {
 678                                         seq.push_back(p2);
 679                                         seq.push_back(p1);
 680                                 }
 681                         }
 682                 }
 683         }
 684 }
 685
 686 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 687                                            const expairseq &s2)
 688 {
 689         combine_overall_coeff(s1.overall_coeff);
 690         combine_overall_coeff(s2.overall_coeff);
 691
 692         epvector::const_iterator first1 = s1.seq.begin();
 693         epvector::const_iterator last1 = s1.seq.end();
 694         epvector::const_iterator first2 = s2.seq.begin();
 695         epvector::const_iterator last2 = s2.seq.end();
 696
 697         seq.reserve(s1.seq.size()+s2.seq.size());
 698
 699         bool needs_further_processing=false;
 700
 701         while (first1!=last1 && first2!=last2) {
 702                 int cmpval = (*first1).rest.compare((*first2).rest);
 703
 704                 if (cmpval==0) {
 705                         // combine terms
 706                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 707                                                    add(ex_to<numeric>(first2->coeff));
 708                         if (!newcoeff.is_zero()) {
 709                                 seq.push_back(expair(first1->rest,newcoeff));
 710                                 if (expair_needs_further_processing(seq.end()-1)) {
 711                                         needs_further_processing = true;
 712                                 }
 713                         }
 714                         ++first1;
 715                         ++first2;
 716                 } else if (cmpval<0) {
 717                         seq.push_back(*first1);
 718                         ++first1;
 719                 } else {
 720                         seq.push_back(*first2);
 721                         ++first2;
 722                 }
 723         }
 724
 725         while (first1!=last1) {
 726                 seq.push_back(*first1);
 727                 ++first1;
 728         }
 729         while (first2!=last2) {
 730                 seq.push_back(*first2);
 731                 ++first2;
 732         }
 733
 734         if (needs_further_processing) {
 735                 epvector v = seq;
 736                 seq.clear();
 737                 construct_from_epvector(std::move(v));
 738         }
 739 }
 740
 741 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 742                                             const ex &e)
 743 {
 744         combine_overall_coeff(s.overall_coeff);
 745         if (is_exactly_a<numeric>(e)) {
 746                 combine_overall_coeff(e);
 747                 seq = s.seq;
 748                 return;
 749         }
 750
 751         epvector::const_iterator first = s.seq.begin();
 752         epvector::const_iterator last = s.seq.end();
 753         expair p = split_ex_to_pair(e);
 754
 755         seq.reserve(s.seq.size()+1);
 756         bool p_pushed = false;
 757
 758         bool needs_further_processing=false;
 759
 760         // merge p into s.seq
 761         while (first!=last) {
 762                 int cmpval = (*first).rest.compare(p.rest);
 763                 if (cmpval==0) {
 764                         // combine terms
 765                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 766                                                    add(ex_to<numeric>(p.coeff));
 767                         if (!newcoeff.is_zero()) {
 768                                 seq.push_back(expair(first->rest,newcoeff));
 769                                 if (expair_needs_further_processing(seq.end()-1))
 770                                         needs_further_processing = true;
 771                         }
 772                         ++first;
 773                         p_pushed = true;
 774                         break;
 775                 } else if (cmpval<0) {
 776                         seq.push_back(*first);
 777                         ++first;
 778                 } else {
 779                         seq.push_back(p);
 780                         p_pushed = true;
 781                         break;
 782                 }
 783         }
 784
 785         if (p_pushed) {
 786                 // while loop exited because p was pushed, now push rest of s.seq
 787                 while (first!=last) {
 788                         seq.push_back(*first);
 789                         ++first;
 790                 }
 791         } else {
 792                 // while loop exited because s.seq was pushed, now push p
 793                 seq.push_back(p);
 794         }
 795
 796         if (needs_further_processing) {
 797                 epvector v = seq;
 798                 seq.clear();
 799                 construct_from_epvector(std::move(v));
 800         }
 801 }
 802
 803 void expairseq::construct_from_exvector(const exvector &v)
 804 {
 805         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 806         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 807         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 808         //                  (same for (+,*) -> (*,^)
 809
 810         make_flat(v);
 811         canonicalize();
 812         combine_same_terms_sorted_seq();
 813 }
 814
 815 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
 816 {
 817         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 818         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 819         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 820         //                  same for (+,*) -> (*,^)
 821
 822         make_flat(v, do_index_renaming);
 823         canonicalize();
 824         combine_same_terms_sorted_seq();
 825 }
 826
 827 void expairseq::construct_from_epvector(epvector &&v, bool do_index_renaming)
 828 {
 829         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 830         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 831         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 832         //                  same for (+,*) -> (*,^)
 833
 834         make_flat(std::move(v), do_index_renaming);
 835         canonicalize();
 836         combine_same_terms_sorted_seq();
 837 }
 838
 839 /** Combine this expairseq with argument exvector.
 840  *  It cares for associativity as well as for special handling of numerics. */
 841 void expairseq::make_flat(const exvector &v)
 842 {
 843         exvector::const_iterator cit;
 844
 845         // count number of operands which are of same expairseq derived type
 846         // and their cumulative number of operands
 847         int nexpairseqs = 0;
 848         int noperands = 0;
 849         bool do_idx_rename = false;
 850
 851         cit = v.begin();
 852         while (cit!=v.end()) {
 853                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
 854                         ++nexpairseqs;
 855                         noperands += ex_to<expairseq>(*cit).seq.size();
 856                 }
 857                 if (is_a<mul>(*this) && (!do_idx_rename) &&
 858                                 cit->info(info_flags::has_indices))
 859                         do_idx_rename = true;
 860                 ++cit;
 861         }
 862
 863         // reserve seq and coeffseq which will hold all operands
 864         seq.reserve(v.size()+noperands-nexpairseqs);
 865
 866         // copy elements and split off numerical part
 867         make_flat_inserter mf(v, do_idx_rename);
 868         cit = v.begin();
 869         while (cit!=v.end()) {
 870                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
 871                         ex newfactor = mf.handle_factor(*cit, _ex1);
 872                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
 873                         combine_overall_coeff(subseqref.overall_coeff);
 874                         epvector::const_iterator cit_s = subseqref.seq.begin();
 875                         while (cit_s!=subseqref.seq.end()) {
 876                                 seq.push_back(*cit_s);
 877                                 ++cit_s;
 878                         }
 879                 } else {
 880                         if (is_exactly_a<numeric>(*cit))
 881                                 combine_overall_coeff(*cit);
 882                         else {
 883                                 ex newfactor = mf.handle_factor(*cit, _ex1);
 884                                 seq.push_back(split_ex_to_pair(newfactor));
 885                         }
 886                 }
 887                 ++cit;
 888         }
 889 }
 890
 891 /** Combine this expairseq with argument epvector.
 892  *  It cares for associativity as well as for special handling of numerics. */
 893 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
 894 {
 895         epvector::const_iterator cit;
 896
 897         // count number of operands which are of same expairseq derived type
 898         // and their cumulative number of operands
 899         int nexpairseqs = 0;
 900         int noperands = 0;
 901         bool really_need_rename_inds = false;
 902
 903         cit = v.begin();
 904         while (cit!=v.end()) {
 905                 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
 906                         ++nexpairseqs;
 907                         noperands += ex_to<expairseq>(cit->rest).seq.size();
 908                 }
 909                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
 910                                 cit->rest.info(info_flags::has_indices))
 911                         really_need_rename_inds = true;
 912                 ++cit;
 913         }
 914         do_index_renaming = do_index_renaming && really_need_rename_inds;
 915
 916         // reserve seq and coeffseq which will hold all operands
 917         seq.reserve(v.size()+noperands-nexpairseqs);
 918         make_flat_inserter mf(v, do_index_renaming);
 919
 920         // copy elements and split off numerical part
 921         cit = v.begin();
 922         while (cit!=v.end()) {
 923                 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
 924                     this->can_make_flat(*cit)) {
 925                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
 926                         const expairseq &subseqref = ex_to<expairseq>(newrest);
 927                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
 928                                               ex_to<numeric>(cit->coeff));
 929                         epvector::const_iterator cit_s = subseqref.seq.begin();
 930                         while (cit_s!=subseqref.seq.end()) {
 931                                 seq.push_back(expair(cit_s->rest,
 932                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
 933                                 ++cit_s;
 934                         }
 935                 } else {
 936                         if (cit->is_canonical_numeric())
 937                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
 938                         else {
 939                                 ex rest = cit->rest;
 940                                 ex newrest = mf.handle_factor(rest, cit->coeff);
 941                                 if (are_ex_trivially_equal(newrest, rest))
 942                                         seq.push_back(*cit);
 943                                 else
 944                                         seq.push_back(expair(newrest, cit->coeff));
 945                         }
 946                 }
 947                 ++cit;
 948         }
 949 }
 950
 951 /** Brings this expairseq into a sorted (canonical) form. */
 952 void expairseq::canonicalize()
 953 {
 954         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 955 }
 956
 957
 958 /** Compact a presorted expairseq by combining all matching expairs to one
 959  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
 960  *  instance. */
 961 void expairseq::combine_same_terms_sorted_seq()
 962 {
 963         if (seq.size()<2)
 964                 return;
 965
 966         bool needs_further_processing = false;
 967
 968         epvector::iterator itin1 = seq.begin();
 969         epvector::iterator itin2 = itin1+1;
 970         epvector::iterator itout = itin1;
 971         epvector::iterator last = seq.end();
 972         // must_copy will be set to true the first time some combination is
 973         // possible from then on the sequence has changed and must be compacted
 974         bool must_copy = false;
 975         while (itin2!=last) {
 976                 if (itin1->rest.compare(itin2->rest)==0) {
 977                         itin1->coeff = ex_to<numeric>(itin1->coeff).
 978                                        add_dyn(ex_to<numeric>(itin2->coeff));
 979                         if (expair_needs_further_processing(itin1))
 980                                 needs_further_processing = true;
 981                         must_copy = true;
 982                 } else {
 983                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 984                                 if (must_copy)
 985                                         *itout = *itin1;
 986                                 ++itout;
 987                         }
 988                         itin1 = itin2;
 989                 }
 990                 ++itin2;
 991         }
 992         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 993                 if (must_copy)
 994                         *itout = *itin1;
 995                 ++itout;
 996         }
 997         if (itout!=last)
 998                 seq.erase(itout,last);
 999
1000         if (needs_further_processing) {
1001                 epvector v = seq;
1002                 seq.clear();
1003                 construct_from_epvector(std::move(v));
1004         }
1005 }
1006
1007 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
1008  *  debugging or in assertions since being sorted is an invariance. */
1009 bool expairseq::is_canonical() const
1010 {
1011         if (seq.size() <= 1)
1012                 return 1;
1013
1014         epvector::const_iterator it = seq.begin(), itend = seq.end();
1015         epvector::const_iterator it_last = it;
1016         for (++it; it!=itend; it_last=it, ++it) {
1017                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1018                         if (!is_exactly_a<numeric>(it_last->rest) ||
1019                                 !is_exactly_a<numeric>(it->rest)) {
1020                                 // double test makes it easier to set a breakpoint...
1021                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1022                                         !is_exactly_a<numeric>(it->rest)) {
1023                                         printpair(std::clog, *it_last, 0);
1024                                         std::clog << ">";
1025                                         printpair(std::clog, *it, 0);
1026                                         std::clog << "\n";
1027                                         std::clog << "pair1:" << std::endl;
1028                                         it_last->rest.print(print_tree(std::clog));
1029                                         it_last->coeff.print(print_tree(std::clog));
1030                                         std::clog << "pair2:" << std::endl;
1031                                         it->rest.print(print_tree(std::clog));
1032                                         it->coeff.print(print_tree(std::clog));
1033                                         return 0;
1034                                 }
1035                         }
1036                 }
1037         }
1038         return 1;
1039 }
1040
1041 /** Member-wise expand the expairs in this sequence.
1042  *
1043  *  @see expairseq::expand()
1044  *  @return epvector containing expanded pairs, empty if no members
1045  *    had to be changed. */
1046 epvector expairseq::expandchildren(unsigned options) const
1047 {
1048         const epvector::const_iterator last = seq.end();
1049         epvector::const_iterator cit = seq.begin();
1050         while (cit!=last) {
1051                 const ex &expanded_ex = cit->rest.expand(options);
1052                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
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                         epvector::const_iterator cit2 = seq.begin();
1060                         while (cit2!=cit) {
1061                                 s.push_back(*cit2);
1062                                 ++cit2;
1063                         }
1064
1065                         // copy first changed element
1066                         s.push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1067                                                                   cit2->coeff));
1068                         ++cit2;
1069
1070                         // copy rest
1071                         while (cit2!=last) {
1072                                 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1073                                                                           cit2->coeff));
1074                                 ++cit2;
1075                         }
1076                         return s;
1077                 }
1078                 ++cit;
1079         }
1080
1081         return epvector(); // empty signalling nothing has changed
1082 }
1083
1084
1085 /** Member-wise evaluate the expairs in this sequence.
1086  *
1087  *  @see expairseq::eval()
1088  *  @return epvector containing evaluated pairs, empty if no members
1089  *    had to be changed. */
1090 epvector expairseq::evalchildren(int level) const
1091 {
1092         if (level==1)
1093                 return epvector();  // nothing had to be evaluated
1094
1095         if (level == -max_recursion_level)
1096                 throw(std::runtime_error("max recursion level reached"));
1097
1098         --level;
1099         epvector::const_iterator last = seq.end();
1100         epvector::const_iterator cit = seq.begin();
1101         while (cit!=last) {
1102                 const ex evaled_ex = cit->rest.eval(level);
1103                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1104
1105                         // something changed, copy seq, eval and return it
1106                         epvector s;
1107                         s.reserve(seq.size());
1108
1109                         // copy parts of seq which are known not to have changed
1110                         epvector::const_iterator cit2=seq.begin();
1111                         while (cit2!=cit) {
1112                                 s.push_back(*cit2);
1113                                 ++cit2;
1114                         }
1115
1116                         // copy first changed element
1117                         s.push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1118                                                                   cit2->coeff));
1119                         ++cit2;
1120
1121                         // copy rest
1122                         while (cit2!=last) {
1123                                 s.push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1124                                                                           cit2->coeff));
1125                                 ++cit2;
1126                         }
1127                         return std::move(s);
1128                 }
1129                 ++cit;
1130         }
1131
1132         return epvector(); // signalling nothing has changed
1133 }
1134
1135 /** Member-wise substitute in this sequence.
1136  *
1137  *  @see expairseq::subs()
1138  *  @return epvector containing expanded pairs, empty if no members
1139  *    had to be changed. */
1140 epvector expairseq::subschildren(const exmap & m, unsigned options) const
1141 {
1142         // When any of the objects to be substituted is a product or power
1143         // we have to recombine the pairs because the numeric coefficients may
1144         // be part of the search pattern.
1145         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1146
1147                 // Search the list of substitutions and cache our findings
1148                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1149                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1150                                 options |= subs_options::pattern_is_product;
1151                                 break;
1152                         }
1153                 }
1154                 if (!(options & subs_options::pattern_is_product))
1155                         options |= subs_options::pattern_is_not_product;
1156         }
1157
1158         if (options & subs_options::pattern_is_product) {
1159
1160                 // Substitute in the recombined pairs
1161                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1162                 while (cit != last) {
1163
1164                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1165                         const ex &subsed_ex = orig_ex.subs(m, options);
1166                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1167
1168                                 // Something changed, copy seq, subs and return it
1169                                 epvector s;
1170                                 s.reserve(seq.size());
1171
1172                                 // Copy parts of seq which are known not to have changed
1173                                 s.insert(s.begin(), seq.begin(), cit);
1174
1175                                 // Copy first changed element
1176                                 s.push_back(split_ex_to_pair(subsed_ex));
1177                                 ++cit;
1178
1179                                 // Copy rest
1180                                 while (cit != last) {
1181                                         s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1182                                         ++cit;
1183                                 }
1184                                 return s;
1185                         }
1186
1187                         ++cit;
1188                 }
1189
1190         } else {
1191
1192                 // Substitute only in the "rest" part of the pairs
1193                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1194                 while (cit != last) {
1195
1196                         const ex &subsed_ex = cit->rest.subs(m, options);
1197                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1198
1199                                 // Something changed, copy seq, subs and return it
1200                                 epvector s;
1201                                 s.reserve(seq.size());
1202
1203                                 // Copy parts of seq which are known not to have changed
1204                                 s.insert(s.begin(), seq.begin(), cit);
1205
1206                                 // Copy first changed element
1207                                 s.push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1208                                 ++cit;
1209
1210                                 // Copy rest
1211                                 while (cit != last) {
1212                                         s.push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1213                                         ++cit;
1214                                 }
1215                                 return s;
1216                         }
1217
1218                         ++cit;
1219                 }
1220         }
1221
1222         // Nothing has changed
1223         return epvector();
1224 }
1225
1226 //////////
1227 // static member variables
1228 //////////
1229
1230 } // namespace GiNaC