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(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming)
  99   :  overall_coeff(oc)
 100 {
 101         GINAC_ASSERT(vp.get()!=0);
 102         GINAC_ASSERT(is_a<numeric>(oc));
 103         construct_from_epvector(*vp, do_index_renaming);
 104         GINAC_ASSERT(is_canonical());
 105 }
 106
 107 //////////
 108 // archiving
 109 //////////
 110
 111 void expairseq::read_archive(const archive_node &n, lst &sym_lst)
 112 {
 113         inherited::read_archive(n, sym_lst);
 114         archive_node::archive_node_cit first = n.find_first("rest");
 115         archive_node::archive_node_cit last = n.find_last("coeff");
 116         ++last;
 117         seq.reserve((last-first)/2);
 118
 119         for (archive_node::archive_node_cit loc = first; loc < last;) {
 120                 ex rest;
 121                 ex coeff;
 122                 n.find_ex_by_loc(loc++, rest, sym_lst);
 123                 n.find_ex_by_loc(loc++, coeff, sym_lst);
 124                 seq.push_back(expair(rest, coeff));
 125         }
 126
 127         n.find_ex("overall_coeff", overall_coeff, sym_lst);
 128
 129         canonicalize();
 130         GINAC_ASSERT(is_canonical());
 131 }
 132
 133 void expairseq::archive(archive_node &n) const
 134 {
 135         inherited::archive(n);
 136         epvector::const_iterator i = seq.begin(), iend = seq.end();
 137         while (i != iend) {
 138                 n.add_ex("rest", i->rest);
 139                 n.add_ex("coeff", i->coeff);
 140                 ++i;
 141         }
 142         n.add_ex("overall_coeff", overall_coeff);
 143 }
 144
 145
 146 //////////
 147 // functions overriding virtual functions from base classes
 148 //////////
 149
 150 // public
 151
 152 void expairseq::do_print(const print_context & c, unsigned level) const
 153 {
 154         c.s << "[[";
 155         printseq(c, ',', precedence(), level);
 156         c.s << "]]";
 157 }
 158
 159 void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 160 {
 161         c.s << std::string(level, ' ') << class_name() << " @" << this
 162             << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
 163             << ", nops=" << nops()
 164             << std::endl;
 165         size_t num = seq.size();
 166         for (size_t i=0; i<num; ++i) {
 167                 seq[i].rest.print(c, level + c.delta_indent);
 168                 seq[i].coeff.print(c, level + c.delta_indent);
 169                 if (i != num - 1)
 170                         c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
 171         }
 172         if (!overall_coeff.is_equal(default_overall_coeff())) {
 173                 c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
 174                     << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
 175                 overall_coeff.print(c, level + c.delta_indent);
 176         }
 177         c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 178 }
 179
 180 bool expairseq::info(unsigned inf) const
 181 {
 182         switch(inf) {
 183                 case info_flags::expanded:
 184                         return (flags & status_flags::expanded);
 185                 case info_flags::has_indices: {
 186                         if (flags & status_flags::has_indices)
 187                                 return true;
 188                         else if (flags & status_flags::has_no_indices)
 189                                 return false;
 190                         for (epvector::const_iterator i = seq.begin(); i != seq.end(); ++i) {
 191                                 if (i->rest.info(info_flags::has_indices)) {
 192                                         this->setflag(status_flags::has_indices);
 193                                         this->clearflag(status_flags::has_no_indices);
 194                                         return true;
 195                                 }
 196                         }
 197                         this->clearflag(status_flags::has_indices);
 198                         this->setflag(status_flags::has_no_indices);
 199                         return false;
 200                 }
 201         }
 202         return inherited::info(inf);
 203 }
 204
 205 size_t expairseq::nops() const
 206 {
 207         if (overall_coeff.is_equal(default_overall_coeff()))
 208                 return seq.size();
 209         else
 210                 return seq.size()+1;
 211 }
 212
 213 ex expairseq::op(size_t i) const
 214 {
 215         if (i < seq.size())
 216                 return recombine_pair_to_ex(seq[i]);
 217         GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 218         return overall_coeff;
 219 }
 220
 221 ex expairseq::map(map_function &f) const
 222 {
 223         std::auto_ptr<epvector> v(new epvector);
 224         v->reserve(seq.size()+1);
 225
 226         epvector::const_iterator cit = seq.begin(), last = seq.end();
 227         while (cit != last) {
 228                 v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
 229                 ++cit;
 230         }
 231
 232         if (overall_coeff.is_equal(default_overall_coeff()))
 233                 return thisexpairseq(v, default_overall_coeff(), true);
 234         else {
 235                 ex newcoeff = f(overall_coeff);
 236                 if(is_a<numeric>(newcoeff))
 237                         return thisexpairseq(v, newcoeff, true);
 238                 else {
 239                         v->push_back(split_ex_to_pair(newcoeff));
 240                         return thisexpairseq(v, default_overall_coeff(), true);
 241                 }
 242         }
 243 }
 244
 245 /** Perform coefficient-wise automatic term rewriting rules in this class. */
 246 ex expairseq::eval(int level) const
 247 {
 248         if ((level==1) && (flags &status_flags::evaluated))
 249                 return *this;
 250
 251         std::auto_ptr<epvector> vp = evalchildren(level);
 252         if (vp.get() == 0)
 253                 return this->hold();
 254
 255         return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 256 }
 257
 258 epvector* conjugateepvector(const epvector&epv)
 259 {
 260         epvector *newepv = 0;
 261         for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
 262                 if(newepv) {
 263                         newepv->push_back(i->conjugate());
 264                         continue;
 265                 }
 266                 expair x = i->conjugate();
 267                 if (x.is_equal(*i)) {
 268                         continue;
 269                 }
 270                 newepv = new epvector;
 271                 newepv->reserve(epv.size());
 272                 for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
 273                         newepv->push_back(*j);
 274                 }
 275                 newepv->push_back(x);
 276         }
 277         return newepv;
 278 }
 279
 280 ex expairseq::conjugate() const
 281 {
 282         epvector* newepv = conjugateepvector(seq);
 283         ex x = overall_coeff.conjugate();
 284         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 285                 return *this;
 286         }
 287         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 288         delete newepv;
 289         return result;
 290 }
 291
 292 bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 293 {
 294         // This differs from basic::match() because we want "a+b+c+d" to
 295         // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 296
 297         if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
 298
 299                 // Check whether global wildcard (one that matches the "rest of the
 300                 // expression", like "*" above) is present
 301                 bool has_global_wildcard = false;
 302                 ex global_wildcard;
 303                 for (size_t i=0; i<pattern.nops(); i++) {
 304                         if (is_exactly_a<wildcard>(pattern.op(i))) {
 305                                 has_global_wildcard = true;
 306                                 global_wildcard = pattern.op(i);
 307                                 break;
 308                         }
 309                 }
 310
 311                 // Even if the expression does not match the pattern, some of
 312                 // its subexpressions could match it. For example, x^5*y^(-1)
 313                 // does not match the pattern $0^5, but its subexpression x^5
 314                 // does. So, save repl_lst in order to not add bogus entries.
 315                 exmap tmp_repl = repl_lst;
 316
 317                 // Unfortunately, this is an O(N^2) operation because we can't
 318                 // sort the pattern in a useful way...
 319
 320                 // Chop into terms
 321                 exvector ops;
 322                 ops.reserve(nops());
 323                 for (size_t i=0; i<nops(); i++)
 324                         ops.push_back(op(i));
 325
 326                 // Now, for every term of the pattern, look for a matching term in
 327                 // the expression and remove the match
 328                 for (size_t i=0; i<pattern.nops(); i++) {
 329                         ex p = pattern.op(i);
 330                         if (has_global_wildcard && p.is_equal(global_wildcard))
 331                                 continue;
 332                         exvector::iterator it = ops.begin(), itend = ops.end();
 333                         while (it != itend) {
 334                                 if (it->match(p, tmp_repl)) {
 335                                         ops.erase(it);
 336                                         goto found;
 337                                 }
 338                                 ++it;
 339                         }
 340                         return false; // no match found
 341 found:          ;
 342                 }
 343
 344                 if (has_global_wildcard) {
 345
 346                         // Assign all the remaining terms to the global wildcard (unless
 347                         // it has already been matched before, in which case the matches
 348                         // must be equal)
 349                         size_t num = ops.size();
 350                         std::auto_ptr<epvector> vp(new epvector);
 351                         vp->reserve(num);
 352                         for (size_t i=0; i<num; i++)
 353                                 vp->push_back(split_ex_to_pair(ops[i]));
 354                         ex rest = thisexpairseq(vp, default_overall_coeff());
 355                         for (exmap::const_iterator it = tmp_repl.begin(); it != tmp_repl.end(); ++it) {
 356                                 if (it->first.is_equal(global_wildcard)) {
 357                                         if (rest.is_equal(it->second)) {
 358                                                 repl_lst = tmp_repl;
 359                                                 return true;
 360                                         }
 361                                         return false;
 362                                 }
 363                         }
 364                         repl_lst = tmp_repl;
 365                         repl_lst[global_wildcard] = rest;
 366                         return true;
 367
 368                 } else {
 369
 370                         // No global wildcard, then the match fails if there are any
 371                         // unmatched terms left
 372                         if (ops.empty()) {
 373                                 repl_lst = tmp_repl;
 374                                 return true;
 375                         }
 376                         return false;
 377                 }
 378         }
 379         return inherited::match(pattern, repl_lst);
 380 }
 381
 382 ex expairseq::subs(const exmap & m, unsigned options) const
 383 {
 384         std::auto_ptr<epvector> vp = subschildren(m, options);
 385         if (vp.get())
 386                 return ex_to<basic>(thisexpairseq(vp, overall_coeff, (options & subs_options::no_index_renaming) == 0));
 387         else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
 388                 return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
 389         else
 390                 return subs_one_level(m, options);
 391 }
 392
 393 // protected
 394
 395 int expairseq::compare_same_type(const basic &other) const
 396 {
 397         GINAC_ASSERT(is_a<expairseq>(other));
 398         const expairseq &o = static_cast<const expairseq &>(other);
 399
 400         int cmpval;
 401
 402         // compare number of elements
 403         if (seq.size() != o.seq.size())
 404                 return (seq.size()<o.seq.size()) ? -1 : 1;
 405
 406         // compare overall_coeff
 407         cmpval = overall_coeff.compare(o.overall_coeff);
 408         if (cmpval!=0)
 409                 return cmpval;
 410
 411         epvector::const_iterator cit1 = seq.begin();
 412         epvector::const_iterator cit2 = o.seq.begin();
 413         epvector::const_iterator last1 = seq.end();
 414         epvector::const_iterator last2 = o.seq.end();
 415
 416         for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
 417                 cmpval = (*cit1).compare(*cit2);
 418                 if (cmpval!=0) return cmpval;
 419         }
 420
 421         GINAC_ASSERT(cit1==last1);
 422         GINAC_ASSERT(cit2==last2);
 423
 424         return 0;
 425 }
 426
 427 bool expairseq::is_equal_same_type(const basic &other) const
 428 {
 429         const expairseq &o = static_cast<const expairseq &>(other);
 430
 431         // compare number of elements
 432         if (seq.size()!=o.seq.size())
 433                 return false;
 434
 435         // compare overall_coeff
 436         if (!overall_coeff.is_equal(o.overall_coeff))
 437                 return false;
 438
 439         epvector::const_iterator cit1 = seq.begin();
 440         epvector::const_iterator cit2 = o.seq.begin();
 441         epvector::const_iterator last1 = seq.end();
 442
 443         while (cit1!=last1) {
 444                 if (!(*cit1).is_equal(*cit2)) return false;
 445                 ++cit1;
 446                 ++cit2;
 447         }
 448
 449         return true;
 450 }
 451
 452 unsigned expairseq::return_type() const
 453 {
 454         return return_types::noncommutative_composite;
 455 }
 456
 457 unsigned expairseq::calchash() const
 458 {
 459         unsigned v = make_hash_seed(typeid(*this));
 460         epvector::const_iterator i = seq.begin();
 461         const epvector::const_iterator end = seq.end();
 462         while (i != end) {
 463                 v ^= i->rest.gethash();
 464                 // rotation spoils commutativity!
 465                 v = rotate_left(v);
 466                 v ^= i->coeff.gethash();
 467                 ++i;
 468         }
 469
 470         v ^= overall_coeff.gethash();
 471
 472         // store calculated hash value only if object is already evaluated
 473         if (flags &status_flags::evaluated) {
 474                 setflag(status_flags::hash_calculated);
 475                 hashvalue = v;
 476         }
 477
 478         return v;
 479 }
 480
 481 ex expairseq::expand(unsigned options) const
 482 {
 483         std::auto_ptr<epvector> vp = expandchildren(options);
 484         if (vp.get())
 485                 return thisexpairseq(vp, overall_coeff);
 486         else {
 487                 // The terms have not changed, so it is safe to declare this expanded
 488                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 489         }
 490 }
 491
 492 //////////
 493 // new virtual functions which can be overridden by derived classes
 494 //////////
 495
 496 // protected
 497
 498 /** Create an object of this type.
 499  *  This method works similar to a constructor.  It is useful because expairseq
 500  *  has (at least) two possible different semantics but we want to inherit
 501  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
 502  *  has to create a new one of the same semantics, which cannot be done by a
 503  *  ctor because the name (add, mul,...) is unknown on the expairseq level.  In
 504  *  order for this trick to work a derived class must of course override this
 505  *  definition. */
 506 ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 507 {
 508         return expairseq(v, oc, do_index_renaming);
 509 }
 510
 511 ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc, bool do_index_renaming) const
 512 {
 513         return expairseq(vp, oc, do_index_renaming);
 514 }
 515
 516 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 517 {
 518         c.s << "[[";
 519         p.rest.print(c, precedence());
 520         c.s << ",";
 521         p.coeff.print(c, precedence());
 522         c.s << "]]";
 523 }
 524
 525 void expairseq::printseq(const print_context & c, char delim,
 526                          unsigned this_precedence,
 527                          unsigned upper_precedence) const
 528 {
 529         if (this_precedence <= upper_precedence)
 530                 c.s << "(";
 531         epvector::const_iterator it, it_last = seq.end() - 1;
 532         for (it=seq.begin(); it!=it_last; ++it) {
 533                 printpair(c, *it, this_precedence);
 534                 c.s << delim;
 535         }
 536         printpair(c, *it, this_precedence);
 537         if (!overall_coeff.is_equal(default_overall_coeff())) {
 538                 c.s << delim;
 539                 overall_coeff.print(c, this_precedence);
 540         }
 541
 542         if (this_precedence <= upper_precedence)
 543                 c.s << ")";
 544 }
 545
 546
 547 /** Form an expair from an ex, using the corresponding semantics.
 548  *  @see expairseq::recombine_pair_to_ex() */
 549 expair expairseq::split_ex_to_pair(const ex &e) const
 550 {
 551         return expair(e,_ex1);
 552 }
 553
 554
 555 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 556                                                 const ex &c) const
 557 {
 558         GINAC_ASSERT(is_exactly_a<numeric>(c));
 559
 560         return expair(e,c);
 561 }
 562
 563
 564 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
 565                                                   const ex &c) const
 566 {
 567         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 568         GINAC_ASSERT(is_exactly_a<numeric>(c));
 569
 570         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 571 }
 572
 573
 574 /** Form an ex out of an expair, using the corresponding semantics.
 575  *  @see expairseq::split_ex_to_pair() */
 576 ex expairseq::recombine_pair_to_ex(const expair &p) const
 577 {
 578         return lst(p.rest,p.coeff);
 579 }
 580
 581 bool expairseq::expair_needs_further_processing(epp it)
 582 {
 583         return false;
 584 }
 585
 586 ex expairseq::default_overall_coeff() const
 587 {
 588         return _ex0;
 589 }
 590
 591 void expairseq::combine_overall_coeff(const ex &c)
 592 {
 593         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 594         GINAC_ASSERT(is_exactly_a<numeric>(c));
 595         overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 596 }
 597
 598 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 599 {
 600         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 601         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 602         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 603         overall_coeff = ex_to<numeric>(overall_coeff).
 604                         add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 605 }
 606
 607 bool expairseq::can_make_flat(const expair &p) const
 608 {
 609         return true;
 610 }
 611
 612
 613 //////////
 614 // non-virtual functions in this class
 615 //////////
 616
 617 void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 618 {
 619         exvector v;
 620         v.reserve(2);
 621         v.push_back(lh);
 622         v.push_back(rh);
 623         construct_from_exvector(v);
 624 }
 625
 626 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 627 {
 628         if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
 629                 if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 630                         if (is_a<mul>(lh) && lh.info(info_flags::has_indices) &&
 631                                 rh.info(info_flags::has_indices)) {
 632                                 ex newrh=rename_dummy_indices_uniquely(lh, rh);
 633                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 634                                                            ex_to<expairseq>(newrh));
 635                         }
 636                         else
 637                                 construct_from_2_expairseq(ex_to<expairseq>(lh),
 638                                                            ex_to<expairseq>(rh));
 639                         return;
 640                 } else {
 641                         construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 642                         return;
 643                 }
 644         } else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
 645                 construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 646                 return;
 647         }
 648
 649         if (is_exactly_a<numeric>(lh)) {
 650                 if (is_exactly_a<numeric>(rh)) {
 651                         combine_overall_coeff(lh);
 652                         combine_overall_coeff(rh);
 653                 } else {
 654                         combine_overall_coeff(lh);
 655                         seq.push_back(split_ex_to_pair(rh));
 656                 }
 657         } else {
 658                 if (is_exactly_a<numeric>(rh)) {
 659                         combine_overall_coeff(rh);
 660                         seq.push_back(split_ex_to_pair(lh));
 661                 } else {
 662                         expair p1 = split_ex_to_pair(lh);
 663                         expair p2 = split_ex_to_pair(rh);
 664
 665                         int cmpval = p1.rest.compare(p2.rest);
 666                         if (cmpval==0) {
 667                                 p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
 668                                 if (!ex_to<numeric>(p1.coeff).is_zero()) {
 669                                         // no further processing is necessary, since this
 670                                         // one element will usually be recombined in eval()
 671                                         seq.push_back(p1);
 672                                 }
 673                         } else {
 674                                 seq.reserve(2);
 675                                 if (cmpval<0) {
 676                                         seq.push_back(p1);
 677                                         seq.push_back(p2);
 678                                 } else {
 679                                         seq.push_back(p2);
 680                                         seq.push_back(p1);
 681                                 }
 682                         }
 683                 }
 684         }
 685 }
 686
 687 void expairseq::construct_from_2_expairseq(const expairseq &s1,
 688                                            const expairseq &s2)
 689 {
 690         combine_overall_coeff(s1.overall_coeff);
 691         combine_overall_coeff(s2.overall_coeff);
 692
 693         epvector::const_iterator first1 = s1.seq.begin();
 694         epvector::const_iterator last1 = s1.seq.end();
 695         epvector::const_iterator first2 = s2.seq.begin();
 696         epvector::const_iterator last2 = s2.seq.end();
 697
 698         seq.reserve(s1.seq.size()+s2.seq.size());
 699
 700         bool needs_further_processing=false;
 701
 702         while (first1!=last1 && first2!=last2) {
 703                 int cmpval = (*first1).rest.compare((*first2).rest);
 704
 705                 if (cmpval==0) {
 706                         // combine terms
 707                         const numeric &newcoeff = ex_to<numeric>(first1->coeff).
 708                                                    add(ex_to<numeric>(first2->coeff));
 709                         if (!newcoeff.is_zero()) {
 710                                 seq.push_back(expair(first1->rest,newcoeff));
 711                                 if (expair_needs_further_processing(seq.end()-1)) {
 712                                         needs_further_processing = true;
 713                                 }
 714                         }
 715                         ++first1;
 716                         ++first2;
 717                 } else if (cmpval<0) {
 718                         seq.push_back(*first1);
 719                         ++first1;
 720                 } else {
 721                         seq.push_back(*first2);
 722                         ++first2;
 723                 }
 724         }
 725
 726         while (first1!=last1) {
 727                 seq.push_back(*first1);
 728                 ++first1;
 729         }
 730         while (first2!=last2) {
 731                 seq.push_back(*first2);
 732                 ++first2;
 733         }
 734
 735         if (needs_further_processing) {
 736                 epvector v = seq;
 737                 seq.clear();
 738                 construct_from_epvector(v);
 739         }
 740 }
 741
 742 void expairseq::construct_from_expairseq_ex(const expairseq &s,
 743                                             const ex &e)
 744 {
 745         combine_overall_coeff(s.overall_coeff);
 746         if (is_exactly_a<numeric>(e)) {
 747                 combine_overall_coeff(e);
 748                 seq = s.seq;
 749                 return;
 750         }
 751
 752         epvector::const_iterator first = s.seq.begin();
 753         epvector::const_iterator last = s.seq.end();
 754         expair p = split_ex_to_pair(e);
 755
 756         seq.reserve(s.seq.size()+1);
 757         bool p_pushed = false;
 758
 759         bool needs_further_processing=false;
 760
 761         // merge p into s.seq
 762         while (first!=last) {
 763                 int cmpval = (*first).rest.compare(p.rest);
 764                 if (cmpval==0) {
 765                         // combine terms
 766                         const numeric &newcoeff = ex_to<numeric>(first->coeff).
 767                                                    add(ex_to<numeric>(p.coeff));
 768                         if (!newcoeff.is_zero()) {
 769                                 seq.push_back(expair(first->rest,newcoeff));
 770                                 if (expair_needs_further_processing(seq.end()-1))
 771                                         needs_further_processing = true;
 772                         }
 773                         ++first;
 774                         p_pushed = true;
 775                         break;
 776                 } else if (cmpval<0) {
 777                         seq.push_back(*first);
 778                         ++first;
 779                 } else {
 780                         seq.push_back(p);
 781                         p_pushed = true;
 782                         break;
 783                 }
 784         }
 785
 786         if (p_pushed) {
 787                 // while loop exited because p was pushed, now push rest of s.seq
 788                 while (first!=last) {
 789                         seq.push_back(*first);
 790                         ++first;
 791                 }
 792         } else {
 793                 // while loop exited because s.seq was pushed, now push p
 794                 seq.push_back(p);
 795         }
 796
 797         if (needs_further_processing) {
 798                 epvector v = seq;
 799                 seq.clear();
 800                 construct_from_epvector(v);
 801         }
 802 }
 803
 804 void expairseq::construct_from_exvector(const exvector &v)
 805 {
 806         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 807         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 808         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 809         //                  (same for (+,*) -> (*,^)
 810
 811         make_flat(v);
 812         canonicalize();
 813         combine_same_terms_sorted_seq();
 814 }
 815
 816 void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
 817 {
 818         // simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 819         //                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
 820         //                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 821         //                  same for (+,*) -> (*,^)
 822
 823         make_flat(v, do_index_renaming);
 824         canonicalize();
 825         combine_same_terms_sorted_seq();
 826 }
 827
 828 /** Combine this expairseq with argument exvector.
 829  *  It cares for associativity as well as for special handling of numerics. */
 830 void expairseq::make_flat(const exvector &v)
 831 {
 832         exvector::const_iterator cit;
 833
 834         // count number of operands which are of same expairseq derived type
 835         // and their cumulative number of operands
 836         int nexpairseqs = 0;
 837         int noperands = 0;
 838         bool do_idx_rename = false;
 839
 840         cit = v.begin();
 841         while (cit!=v.end()) {
 842                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
 843                         ++nexpairseqs;
 844                         noperands += ex_to<expairseq>(*cit).seq.size();
 845                 }
 846                 if (is_a<mul>(*this) && (!do_idx_rename) &&
 847                                 cit->info(info_flags::has_indices))
 848                         do_idx_rename = true;
 849                 ++cit;
 850         }
 851
 852         // reserve seq and coeffseq which will hold all operands
 853         seq.reserve(v.size()+noperands-nexpairseqs);
 854
 855         // copy elements and split off numerical part
 856         make_flat_inserter mf(v, do_idx_rename);
 857         cit = v.begin();
 858         while (cit!=v.end()) {
 859                 if (typeid(ex_to<basic>(*cit)) == typeid(*this)) {
 860                         ex newfactor = mf.handle_factor(*cit, _ex1);
 861                         const expairseq &subseqref = ex_to<expairseq>(newfactor);
 862                         combine_overall_coeff(subseqref.overall_coeff);
 863                         epvector::const_iterator cit_s = subseqref.seq.begin();
 864                         while (cit_s!=subseqref.seq.end()) {
 865                                 seq.push_back(*cit_s);
 866                                 ++cit_s;
 867                         }
 868                 } else {
 869                         if (is_exactly_a<numeric>(*cit))
 870                                 combine_overall_coeff(*cit);
 871                         else {
 872                                 ex newfactor = mf.handle_factor(*cit, _ex1);
 873                                 seq.push_back(split_ex_to_pair(newfactor));
 874                         }
 875                 }
 876                 ++cit;
 877         }
 878 }
 879
 880 /** Combine this expairseq with argument epvector.
 881  *  It cares for associativity as well as for special handling of numerics. */
 882 void expairseq::make_flat(const epvector &v, bool do_index_renaming)
 883 {
 884         epvector::const_iterator cit;
 885
 886         // count number of operands which are of same expairseq derived type
 887         // and their cumulative number of operands
 888         int nexpairseqs = 0;
 889         int noperands = 0;
 890         bool really_need_rename_inds = false;
 891
 892         cit = v.begin();
 893         while (cit!=v.end()) {
 894                 if (typeid(ex_to<basic>(cit->rest)) == typeid(*this)) {
 895                         ++nexpairseqs;
 896                         noperands += ex_to<expairseq>(cit->rest).seq.size();
 897                 }
 898                 if ((!really_need_rename_inds) && is_a<mul>(*this) &&
 899                                 cit->rest.info(info_flags::has_indices))
 900                         really_need_rename_inds = true;
 901                 ++cit;
 902         }
 903         do_index_renaming = do_index_renaming && really_need_rename_inds;
 904
 905         // reserve seq and coeffseq which will hold all operands
 906         seq.reserve(v.size()+noperands-nexpairseqs);
 907         make_flat_inserter mf(v, do_index_renaming);
 908
 909         // copy elements and split off numerical part
 910         cit = v.begin();
 911         while (cit!=v.end()) {
 912                 if ((typeid(ex_to<basic>(cit->rest)) == typeid(*this)) &&
 913                     this->can_make_flat(*cit)) {
 914                         ex newrest = mf.handle_factor(cit->rest, cit->coeff);
 915                         const expairseq &subseqref = ex_to<expairseq>(newrest);
 916                         combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
 917                                                             ex_to<numeric>(cit->coeff));
 918                         epvector::const_iterator cit_s = subseqref.seq.begin();
 919                         while (cit_s!=subseqref.seq.end()) {
 920                                 seq.push_back(expair(cit_s->rest,
 921                                                      ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
 922                                 //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
 923                                 //                                              (*cit).coeff));
 924                                 ++cit_s;
 925                         }
 926                 } else {
 927                         if (cit->is_canonical_numeric())
 928                                 combine_overall_coeff(mf.handle_factor(cit->rest, _ex1));
 929                         else {
 930                                 ex rest = cit->rest;
 931                                 ex newrest = mf.handle_factor(rest, cit->coeff);
 932                                 if (are_ex_trivially_equal(newrest, rest))
 933                                         seq.push_back(*cit);
 934                                 else
 935                                         seq.push_back(expair(newrest, cit->coeff));
 936                         }
 937                 }
 938                 ++cit;
 939         }
 940 }
 941
 942 /** Brings this expairseq into a sorted (canonical) form. */
 943 void expairseq::canonicalize()
 944 {
 945         std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 946 }
 947
 948
 949 /** Compact a presorted expairseq by combining all matching expairs to one
 950  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
 951  *  instance. */
 952 void expairseq::combine_same_terms_sorted_seq()
 953 {
 954         if (seq.size()<2)
 955                 return;
 956
 957         bool needs_further_processing = false;
 958
 959         epvector::iterator itin1 = seq.begin();
 960         epvector::iterator itin2 = itin1+1;
 961         epvector::iterator itout = itin1;
 962         epvector::iterator last = seq.end();
 963         // must_copy will be set to true the first time some combination is
 964         // possible from then on the sequence has changed and must be compacted
 965         bool must_copy = false;
 966         while (itin2!=last) {
 967                 if (itin1->rest.compare(itin2->rest)==0) {
 968                         itin1->coeff = ex_to<numeric>(itin1->coeff).
 969                                        add_dyn(ex_to<numeric>(itin2->coeff));
 970                         if (expair_needs_further_processing(itin1))
 971                                 needs_further_processing = true;
 972                         must_copy = true;
 973                 } else {
 974                         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 975                                 if (must_copy)
 976                                         *itout = *itin1;
 977                                 ++itout;
 978                         }
 979                         itin1 = itin2;
 980                 }
 981                 ++itin2;
 982         }
 983         if (!ex_to<numeric>(itin1->coeff).is_zero()) {
 984                 if (must_copy)
 985                         *itout = *itin1;
 986                 ++itout;
 987         }
 988         if (itout!=last)
 989                 seq.erase(itout,last);
 990
 991         if (needs_further_processing) {
 992                 epvector v = seq;
 993                 seq.clear();
 994                 construct_from_epvector(v);
 995         }
 996 }
 997
 998 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
 999  *  debugging or in assertions since being sorted is an invariance. */
1000 bool expairseq::is_canonical() const
1001 {
1002         if (seq.size() <= 1)
1003                 return 1;
1004
1005         epvector::const_iterator it = seq.begin(), itend = seq.end();
1006         epvector::const_iterator it_last = it;
1007         for (++it; it!=itend; it_last=it, ++it) {
1008                 if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
1009                         if (!is_exactly_a<numeric>(it_last->rest) ||
1010                                 !is_exactly_a<numeric>(it->rest)) {
1011                                 // double test makes it easier to set a breakpoint...
1012                                 if (!is_exactly_a<numeric>(it_last->rest) ||
1013                                         !is_exactly_a<numeric>(it->rest)) {
1014                                         printpair(std::clog, *it_last, 0);
1015                                         std::clog << ">";
1016                                         printpair(std::clog, *it, 0);
1017                                         std::clog << "\n";
1018                                         std::clog << "pair1:" << std::endl;
1019                                         it_last->rest.print(print_tree(std::clog));
1020                                         it_last->coeff.print(print_tree(std::clog));
1021                                         std::clog << "pair2:" << std::endl;
1022                                         it->rest.print(print_tree(std::clog));
1023                                         it->coeff.print(print_tree(std::clog));
1024                                         return 0;
1025                                 }
1026                         }
1027                 }
1028         }
1029         return 1;
1030 }
1031
1032
1033 /** Member-wise expand the expairs in this sequence.
1034  *
1035  *  @see expairseq::expand()
1036  *  @return pointer to epvector containing expanded pairs or zero pointer,
1037  *  if no members were changed. */
1038 std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
1039 {
1040         const epvector::const_iterator last = seq.end();
1041         epvector::const_iterator cit = seq.begin();
1042         while (cit!=last) {
1043                 const ex &expanded_ex = cit->rest.expand(options);
1044                 if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
1045
1046                         // something changed, copy seq, eval and return it
1047                         std::auto_ptr<epvector> s(new epvector);
1048                         s->reserve(seq.size());
1049
1050                         // copy parts of seq which are known not to have changed
1051                         epvector::const_iterator cit2 = seq.begin();
1052                         while (cit2!=cit) {
1053                                 s->push_back(*cit2);
1054                                 ++cit2;
1055                         }
1056
1057                         // copy first changed element
1058                         s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
1059                                                                    cit2->coeff));
1060                         ++cit2;
1061
1062                         // copy rest
1063                         while (cit2!=last) {
1064                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
1065                                                                            cit2->coeff));
1066                                 ++cit2;
1067                         }
1068                         return s;
1069                 }
1070                 ++cit;
1071         }
1072
1073         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1074 }
1075
1076
1077 /** Member-wise evaluate the expairs in this sequence.
1078  *
1079  *  @see expairseq::eval()
1080  *  @return pointer to epvector containing evaluated pairs or zero pointer,
1081  *  if no members were changed. */
1082 std::auto_ptr<epvector> expairseq::evalchildren(int level) const
1083 {
1084         // returns a NULL pointer if nothing had to be evaluated
1085         // returns a pointer to a newly created epvector otherwise
1086         // (which has to be deleted somewhere else)
1087
1088         if (level==1)
1089                 return std::auto_ptr<epvector>(0);
1090
1091         if (level == -max_recursion_level)
1092                 throw(std::runtime_error("max recursion level reached"));
1093
1094         --level;
1095         epvector::const_iterator last = seq.end();
1096         epvector::const_iterator cit = seq.begin();
1097         while (cit!=last) {
1098                 const ex &evaled_ex = cit->rest.eval(level);
1099                 if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
1100
1101                         // something changed, copy seq, eval and return it
1102                         std::auto_ptr<epvector> s(new epvector);
1103                         s->reserve(seq.size());
1104
1105                         // copy parts of seq which are known not to have changed
1106                         epvector::const_iterator cit2=seq.begin();
1107                         while (cit2!=cit) {
1108                                 s->push_back(*cit2);
1109                                 ++cit2;
1110                         }
1111
1112                         // copy first changed element
1113                         s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
1114                                                                    cit2->coeff));
1115                         ++cit2;
1116
1117                         // copy rest
1118                         while (cit2!=last) {
1119                                 s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
1120                                                                            cit2->coeff));
1121                                 ++cit2;
1122                         }
1123                         return s;
1124                 }
1125                 ++cit;
1126         }
1127
1128         return std::auto_ptr<epvector>(0); // signalling nothing has changed
1129 }
1130
1131 /** Member-wise substitute in this sequence.
1132  *
1133  *  @see expairseq::subs()
1134  *  @return pointer to epvector containing pairs after application of subs,
1135  *    or NULL pointer if no members were changed. */
1136 std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
1137 {
1138         // When any of the objects to be substituted is a product or power
1139         // we have to recombine the pairs because the numeric coefficients may
1140         // be part of the search pattern.
1141         if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
1142
1143                 // Search the list of substitutions and cache our findings
1144                 for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
1145                         if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
1146                                 options |= subs_options::pattern_is_product;
1147                                 break;
1148                         }
1149                 }
1150                 if (!(options & subs_options::pattern_is_product))
1151                         options |= subs_options::pattern_is_not_product;
1152         }
1153
1154         if (options & subs_options::pattern_is_product) {
1155
1156                 // Substitute in the recombined pairs
1157                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1158                 while (cit != last) {
1159
1160                         const ex &orig_ex = recombine_pair_to_ex(*cit);
1161                         const ex &subsed_ex = orig_ex.subs(m, options);
1162                         if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
1163
1164                                 // Something changed, copy seq, subs and return it
1165                                 std::auto_ptr<epvector> s(new epvector);
1166                                 s->reserve(seq.size());
1167
1168                                 // Copy parts of seq which are known not to have changed
1169                                 s->insert(s->begin(), seq.begin(), cit);
1170
1171                                 // Copy first changed element
1172                                 s->push_back(split_ex_to_pair(subsed_ex));
1173                                 ++cit;
1174
1175                                 // Copy rest
1176                                 while (cit != last) {
1177                                         s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
1178                                         ++cit;
1179                                 }
1180                                 return s;
1181                         }
1182
1183                         ++cit;
1184                 }
1185
1186         } else {
1187
1188                 // Substitute only in the "rest" part of the pairs
1189                 epvector::const_iterator cit = seq.begin(), last = seq.end();
1190                 while (cit != last) {
1191
1192                         const ex &subsed_ex = cit->rest.subs(m, options);
1193                         if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
1194
1195                                 // Something changed, copy seq, subs and return it
1196                                 std::auto_ptr<epvector> s(new epvector);
1197                                 s->reserve(seq.size());
1198
1199                                 // Copy parts of seq which are known not to have changed
1200                                 s->insert(s->begin(), seq.begin(), cit);
1201
1202                                 // Copy first changed element
1203                                 s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
1204                                 ++cit;
1205
1206                                 // Copy rest
1207                                 while (cit != last) {
1208                                         s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
1209                                         ++cit;
1210                                 }
1211                                 return s;
1212                         }
1213
1214                         ++cit;
1215                 }
1216         }
1217
1218         // Nothing has changed
1219         return std::auto_ptr<epvector>(0);
1220 }
1221
1222 //////////
1223 // static member variables
1224 //////////
1225
1226 } // namespace GiNaC