ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <vector>
  24 #include <stdexcept>
  25
  26 #include "mul.h"
  27 #include "add.h"
  28 #include "power.h"
  29 #include "debugmsg.h"
  30
  31 #ifndef NO_GINAC_NAMESPACE
  32 namespace GiNaC {
  33 #endif // ndef NO_GINAC_NAMESPACE
  34
  35 //////////
  36 // default constructor, destructor, copy constructor assignment operator and helpers
  37 //////////
  38
  39 // public
  40
  41 mul::mul()
  42 {
  43     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  44     tinfo_key = TINFO_mul;
  45 }
  46
  47 mul::~mul()
  48 {
  49     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  50     destroy(0);
  51 }
  52
  53 mul::mul(mul const & other)
  54 {
  55     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  56     copy(other);
  57 }
  58
  59 mul const & mul::operator=(mul const & other)
  60 {
  61     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  62     if (this != &other) {
  63         destroy(1);
  64         copy(other);
  65     }
  66     return *this;
  67 }
  68
  69 // protected
  70
  71 void mul::copy(mul const & other)
  72 {
  73     expairseq::copy(other);
  74 }
  75
  76 void mul::destroy(bool call_parent)
  77 {
  78     if (call_parent) expairseq::destroy(call_parent);
  79 }
  80
  81 //////////
  82 // other constructors
  83 //////////
  84
  85 // public
  86
  87 mul::mul(ex const & lh, ex const & rh)
  88 {
  89     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  90     tinfo_key = TINFO_mul;
  91     overall_coeff=exONE();
  92     construct_from_2_ex(lh,rh);
  93     GINAC_ASSERT(is_canonical());
  94 }
  95
  96 mul::mul(exvector const & v)
  97 {
  98     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
  99     tinfo_key = TINFO_mul;
 100     overall_coeff=exONE();
 101     construct_from_exvector(v);
 102     GINAC_ASSERT(is_canonical());
 103 }
 104
 105 /*
 106 mul::mul(epvector const & v, bool do_not_canonicalize)
 107 {
 108     debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
 109     tinfo_key = TINFO_mul;
 110     if (do_not_canonicalize) {
 111         seq=v;
 112 #ifdef EXPAIRSEQ_USE_HASHTAB
 113         combine_same_terms(); // to build hashtab
 114 #endif // def EXPAIRSEQ_USE_HASHTAB
 115     } else {
 116         construct_from_epvector(v);
 117     }
 118     GINAC_ASSERT(is_canonical());
 119 }
 120 */
 121
 122 mul::mul(epvector const & v)
 123 {
 124     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 125     tinfo_key = TINFO_mul;
 126     overall_coeff=exONE();
 127     construct_from_epvector(v);
 128     GINAC_ASSERT(is_canonical());
 129 }
 130
 131 mul::mul(epvector const & v, ex const & oc)
 132 {
 133     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 134     tinfo_key = TINFO_mul;
 135     overall_coeff=oc;
 136     construct_from_epvector(v);
 137     GINAC_ASSERT(is_canonical());
 138 }
 139
 140 mul::mul(epvector * vp, ex const & oc)
 141 {
 142     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 143     tinfo_key = TINFO_mul;
 144     GINAC_ASSERT(vp!=0);
 145     overall_coeff=oc;
 146     construct_from_epvector(*vp);
 147     delete vp;
 148     GINAC_ASSERT(is_canonical());
 149 }
 150
 151 mul::mul(ex const & lh, ex const & mh, ex const & rh)
 152 {
 153     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 154     tinfo_key = TINFO_mul;
 155     exvector factors;
 156     factors.reserve(3);
 157     factors.push_back(lh);
 158     factors.push_back(mh);
 159     factors.push_back(rh);
 160     overall_coeff=exONE();
 161     construct_from_exvector(factors);
 162     GINAC_ASSERT(is_canonical());
 163 }
 164
 165 //////////
 166 // functions overriding virtual functions from bases classes
 167 //////////
 168
 169 // public
 170
 171 basic * mul::duplicate() const
 172 {
 173     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 174     return new mul(*this);
 175 }
 176
 177 void mul::print(ostream & os, unsigned upper_precedence) const
 178 {
 179     debugmsg("mul print",LOGLEVEL_PRINT);
 180     if (precedence<=upper_precedence) os << "(";
 181     bool first=true;
 182     // first print the overall numeric coefficient:
 183     if (ex_to_numeric(overall_coeff).csgn()==-1) os << '-';
 184     if (!overall_coeff.is_equal(exONE()) &&
 185         !overall_coeff.is_equal(exMINUSONE())) {
 186         if (ex_to_numeric(overall_coeff).csgn()==-1)
 187             (numMINUSONE()*overall_coeff).print(os, precedence);
 188         else
 189             overall_coeff.print(os, precedence);
 190         os << '*';
 191     }
 192     // then proceed with the remaining factors:
 193     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 194         if (!first) {
 195             os << '*';
 196         } else {
 197             first=false;
 198         }
 199         recombine_pair_to_ex(*cit).print(os,precedence);
 200     }
 201     if (precedence<=upper_precedence) os << ")";
 202 }
 203
 204 void mul::printraw(ostream & os) const
 205 {
 206     debugmsg("mul printraw",LOGLEVEL_PRINT);
 207
 208     os << "*(";
 209     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 210         os << "(";
 211         (*it).rest.bp->printraw(os);
 212         os << ",";
 213         (*it).coeff.bp->printraw(os);
 214         os << "),";
 215     }
 216     os << ",hash=" << hashvalue << ",flags=" << flags;
 217     os << ")";
 218 }
 219
 220 void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
 221 {
 222     debugmsg("mul print csrc", LOGLEVEL_PRINT);
 223     if (precedence <= upper_precedence)
 224         os << "(";
 225
 226     if (!overall_coeff.is_equal(exONE())) {
 227         overall_coeff.bp->printcsrc(os,type,precedence);
 228         os << "*";
 229     }
 230
 231     // Print arguments, separated by "*" or "/"
 232     epvector::const_iterator it = seq.begin();
 233     epvector::const_iterator itend = seq.end();
 234     while (it != itend) {
 235
 236         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 237         if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(numZERO()) < 0) {
 238             if (type == csrc_types::ctype_cl_N)
 239                 os << "recip(";
 240             else
 241                 os << "1.0/";
 242         }
 243
 244         // If the exponent is 1 or -1, it is left out
 245         if (it->coeff.compare(exONE()) == 0 || it->coeff.compare(numMINUSONE()) == 0)
 246             it->rest.bp->printcsrc(os, type, precedence);
 247         else
 248             // outer parens around ex needed for broken gcc-2.95 parser:
 249             (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 250
 251         // Separator is "/" for negative integer powers, "*" otherwise
 252         it++;
 253         if (it != itend) {
 254             if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(numZERO()) < 0)
 255                 os << "/";
 256             else
 257                 os << "*";
 258         }
 259     }
 260     if (precedence <= upper_precedence)
 261         os << ")";
 262 }
 263
 264 bool mul::info(unsigned inf) const
 265 {
 266     // TODO: optimize
 267     if (inf==info_flags::polynomial ||
 268         inf==info_flags::integer_polynomial ||
 269         inf==info_flags::cinteger_polynomial ||
 270         inf==info_flags::rational_polynomial ||
 271         inf==info_flags::crational_polynomial ||
 272         inf==info_flags::rational_function) {
 273         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 274             if (!(recombine_pair_to_ex(*it).info(inf)))
 275                 return false;
 276         }
 277         return overall_coeff.info(inf);
 278     } else {
 279         return expairseq::info(inf);
 280     }
 281 }
 282
 283 typedef vector<int> intvector;
 284
 285 int mul::degree(symbol const & s) const
 286 {
 287     int deg_sum=0;
 288     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 289         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 290     }
 291     return deg_sum;
 292 }
 293
 294 int mul::ldegree(symbol const & s) const
 295 {
 296     int deg_sum=0;
 297     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 298         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 299     }
 300     return deg_sum;
 301 }
 302
 303 ex mul::coeff(symbol const & s, int const n) const
 304 {
 305     exvector coeffseq;
 306     coeffseq.reserve(seq.size()+1);
 307
 308     if (n==0) {
 309         // product of individual coeffs
 310         // if a non-zero power of s is found, the resulting product will be 0
 311         epvector::const_iterator it=seq.begin();
 312         while (it!=seq.end()) {
 313             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 314             ++it;
 315         }
 316         coeffseq.push_back(overall_coeff);
 317         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 318     }
 319
 320     epvector::const_iterator it=seq.begin();
 321     bool coeff_found=0;
 322     while (it!=seq.end()) {
 323         ex t=recombine_pair_to_ex(*it);
 324         ex c=t.coeff(s,n);
 325         if (!c.is_zero()) {
 326             coeffseq.push_back(c);
 327             coeff_found=1;
 328         } else {
 329             coeffseq.push_back(t);
 330         }
 331         ++it;
 332     }
 333     if (coeff_found) {
 334         coeffseq.push_back(overall_coeff);
 335         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 336     }
 337
 338     return exZERO();
 339 }
 340
 341 ex mul::eval(int level) const
 342 {
 343     // simplifications  *(...,x;0) -> 0
 344     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 345     //                  *(x;1) -> x
 346     //                  *(;c) -> c
 347
 348     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 349
 350     epvector * evaled_seqp=evalchildren(level);
 351     if (evaled_seqp!=0) {
 352         // do more evaluation later
 353         return (new mul(evaled_seqp,overall_coeff))->
 354                    setflag(status_flags::dynallocated);
 355     }
 356
 357 #ifdef DO_GINAC_ASSERT
 358     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 359         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 360                (!(ex_to_numeric((*cit).coeff).is_integer())));
 361         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 362         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 363             printtree(cerr,0);
 364         }
 365         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 366         /* for paranoia */
 367         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 368         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 369         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 370         /* end paranoia */
 371     }
 372 #endif // def DO_GINAC_ASSERT
 373
 374     if (flags & status_flags::evaluated) {
 375         GINAC_ASSERT(seq.size()>0);
 376         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(exONE()));
 377         return *this;
 378     }
 379
 380     int seq_size=seq.size();
 381     if (overall_coeff.is_equal(exZERO())) {
 382         // *(...,x;0) -> 0
 383         return exZERO();
 384     } else if (seq_size==0) {
 385         // *(;c) -> c
 386         return overall_coeff;
 387     } else if ((seq_size==1)&&overall_coeff.is_equal(exONE())) {
 388         // *(x;1) -> x
 389         return recombine_pair_to_ex(*(seq.begin()));
 390     } else if ((seq_size==1) &&
 391                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 392                ex_to_numeric((*seq.begin()).coeff).is_equal(numONE())) {
 393         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 394         add const & addref=ex_to_add((*seq.begin()).rest);
 395         epvector distrseq;
 396         distrseq.reserve(addref.seq.size());
 397         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 398             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 399                                    overall_coeff));
 400         }
 401         return (new add(distrseq,
 402                         ex_to_numeric(addref.overall_coeff).
 403                         mul_dyn(ex_to_numeric(overall_coeff))))
 404             ->setflag(status_flags::dynallocated  |
 405                       status_flags::evaluated );
 406     }
 407     return this->hold();
 408 }
 409
 410 exvector mul::get_indices(void) const
 411 {
 412     // return union of indices of factors
 413     exvector iv;
 414     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 415         exvector subiv=(*cit).rest.get_indices();
 416         iv.reserve(iv.size()+subiv.size());
 417         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 418             iv.push_back(*cit2);
 419         }
 420     }
 421     return iv;
 422 }
 423
 424 ex mul::simplify_ncmul(exvector const & v) const
 425 {
 426     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 427 }
 428
 429 // protected
 430
 431 int mul::compare_same_type(basic const & other) const
 432 {
 433     return expairseq::compare_same_type(other);
 434 }
 435
 436 bool mul::is_equal_same_type(basic const & other) const
 437 {
 438     return expairseq::is_equal_same_type(other);
 439 }
 440
 441 unsigned mul::return_type(void) const
 442 {
 443     if (seq.size()==0) {
 444         // mul without factors: should not happen, but commutes
 445         return return_types::commutative;
 446     }
 447
 448     bool all_commutative=1;
 449     unsigned rt;
 450     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 451
 452     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 453         rt=(*cit).rest.return_type();
 454         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 455         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 456             // first nc element found, remember position
 457             cit_noncommutative_element=cit;
 458             all_commutative=0;
 459         }
 460         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 461             // another nc element found, compare type_infos
 462             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 463                 // diffent types -> mul is ncc
 464                 return return_types::noncommutative_composite;
 465             }
 466         }
 467     }
 468     // all factors checked
 469     return all_commutative ? return_types::commutative : return_types::noncommutative;
 470 }
 471
 472 unsigned mul::return_type_tinfo(void) const
 473 {
 474     if (seq.size()==0) {
 475         // mul without factors: should not happen
 476         return tinfo_key;
 477     }
 478     // return type_info of first noncommutative element
 479     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 480         if ((*cit).rest.return_type()==return_types::noncommutative) {
 481             return (*cit).rest.return_type_tinfo();
 482         }
 483     }
 484     // no noncommutative element found, should not happen
 485     return tinfo_key;
 486 }
 487
 488 ex mul::thisexpairseq(epvector const & v, ex const & oc) const
 489 {
 490     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 491 }
 492
 493 ex mul::thisexpairseq(epvector * vp, ex const & oc) const
 494 {
 495     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 496 }
 497
 498 expair mul::split_ex_to_pair(ex const & e) const
 499 {
 500     if (is_ex_exactly_of_type(e,power)) {
 501         power const & powerref=ex_to_power(e);
 502         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 503             return expair(powerref.basis,powerref.exponent);
 504         }
 505     }
 506     return expair(e,exONE());
 507 }
 508
 509 expair mul::combine_ex_with_coeff_to_pair(ex const & e,
 510                                           ex const & c) const
 511 {
 512     // to avoid duplication of power simplification rules,
 513     // we create a temporary power object
 514     // otherwise it would be hard to correctly simplify
 515     // expression like (4^(1/3))^(3/2)
 516     if (are_ex_trivially_equal(c,exONE())) {
 517         return split_ex_to_pair(e);
 518     }
 519     return split_ex_to_pair(power(e,c));
 520 }
 521
 522 expair mul::combine_pair_with_coeff_to_pair(expair const & p,
 523                                             ex const & c) const
 524 {
 525     // to avoid duplication of power simplification rules,
 526     // we create a temporary power object
 527     // otherwise it would be hard to correctly simplify
 528     // expression like (4^(1/3))^(3/2)
 529     if (are_ex_trivially_equal(c,exONE())) {
 530         return p;
 531     }
 532     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 533 }
 534
 535 ex mul::recombine_pair_to_ex(expair const & p) const
 536 {
 537     // if (p.coeff.compare(exONE())==0) {
 538     // if (are_ex_trivially_equal(p.coeff,exONE())) {
 539     if (ex_to_numeric(p.coeff).is_equal(numONE())) {
 540         return p.rest;
 541     } else {
 542         return power(p.rest,p.coeff);
 543     }
 544 }
 545
 546 bool mul::expair_needs_further_processing(epp it)
 547 {
 548     if (is_ex_exactly_of_type((*it).rest,mul) &&
 549         ex_to_numeric((*it).coeff).is_integer()) {
 550         // combined pair is product with integer power -> expand it
 551         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 552         return true;
 553     }
 554     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 555         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 556         if (!ep.is_equal(*it)) {
 557             // combined pair is a numeric power which can be simplified
 558             *it=ep;
 559             return true;
 560         }
 561         if (ex_to_numeric((*it).coeff).is_equal(numONE())) {
 562             // combined pair has coeff 1 and must be moved to the end
 563             return true;
 564         }
 565     }
 566     return false;
 567 }
 568
 569 ex mul::default_overall_coeff(void) const
 570 {
 571     return exONE();
 572 }
 573
 574 void mul::combine_overall_coeff(ex const & c)
 575 {
 576     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 577     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 578     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 579 }
 580
 581 void mul::combine_overall_coeff(ex const & c1, ex const & c2)
 582 {
 583     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 584     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 585     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 586     overall_coeff = ex_to_numeric(overall_coeff).
 587                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 588 }
 589
 590 bool mul::can_make_flat(expair const & p) const
 591 {
 592     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 593     // this assertion will probably fail somewhere
 594     // it would require a more careful make_flat, obeying the power laws
 595     // probably should return true only if p.coeff is integer
 596     return ex_to_numeric(p.coeff).is_equal(numONE());
 597 }
 598
 599 ex mul::expand(unsigned options) const
 600 {
 601     exvector sub_expanded_seq;
 602     intvector positions_of_adds;
 603     intvector number_of_add_operands;
 604
 605     epvector * expanded_seqp=expandchildren(options);
 606
 607     epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 608
 609     positions_of_adds.resize(expanded_seq.size());
 610     number_of_add_operands.resize(expanded_seq.size());
 611
 612     int number_of_adds=0;
 613     int number_of_expanded_terms=1;
 614
 615     unsigned current_position=0;
 616     epvector::const_iterator last=expanded_seq.end();
 617     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 618         if (is_ex_exactly_of_type((*cit).rest,add)&&
 619             (ex_to_numeric((*cit).coeff).is_equal(numONE()))) {
 620             positions_of_adds[number_of_adds]=current_position;
 621             add const & expanded_addref=ex_to_add((*cit).rest);
 622             int addref_nops=expanded_addref.nops();
 623             number_of_add_operands[number_of_adds]=addref_nops;
 624             number_of_expanded_terms *= addref_nops;
 625             number_of_adds++;
 626         }
 627         current_position++;
 628     }
 629
 630     if (number_of_adds==0) {
 631         if (expanded_seqp==0) {
 632             return this->setflag(status_flags::expanded);
 633         }
 634         return (new mul(expanded_seqp,overall_coeff))->
 635                      setflag(status_flags::dynallocated ||
 636                              status_flags::expanded);
 637     }
 638
 639     exvector distrseq;
 640     distrseq.reserve(number_of_expanded_terms);
 641
 642     intvector k;
 643     k.resize(number_of_adds);
 644
 645     int l;
 646     for (l=0; l<number_of_adds; l++) {
 647         k[l]=0;
 648     }
 649
 650     while (1) {
 651         epvector term;
 652         term=expanded_seq;
 653         for (l=0; l<number_of_adds; l++) {
 654             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 655             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(exONE())==0);
 656             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 657         }
 658         /*
 659         cout << "mul::expand() term begin" << endl;
 660         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
 661             cout << "rest" << endl;
 662             (*cit).rest.printtree(cout);
 663             cout << "coeff" << endl;
 664             (*cit).coeff.printtree(cout);
 665         }
 666         cout << "mul::expand() term end" << endl;
 667         */
 668         distrseq.push_back((new mul(term,overall_coeff))->
 669                                 setflag(status_flags::dynallocated |
 670                                         status_flags::expanded));
 671
 672         // increment k[]
 673         l=number_of_adds-1;
 674         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 675             k[l]=0;
 676             l--;
 677         }
 678         if (l<0) break;
 679     }
 680
 681     if (expanded_seqp!=0) {
 682         delete expanded_seqp;
 683     }
 684     /*
 685     cout << "mul::expand() distrseq begin" << endl;
 686     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
 687         (*cit).printtree(cout);
 688     }
 689     cout << "mul::expand() distrseq end" << endl;
 690     */
 691
 692     return (new add(distrseq))->setflag(status_flags::dynallocated |
 693                                         status_flags::expanded);
 694 }
 695
 696 //////////
 697 // new virtual functions which can be overridden by derived classes
 698 //////////
 699
 700 // none
 701
 702 //////////
 703 // non-virtual functions in this class
 704 //////////
 705
 706 epvector * mul::expandchildren(unsigned options) const
 707 {
 708     epvector::const_iterator last=seq.end();
 709     epvector::const_iterator cit=seq.begin();
 710     while (cit!=last) {
 711         ex const & factor=recombine_pair_to_ex(*cit);
 712         ex const & expanded_factor=factor.expand(options);
 713         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 714
 715             // something changed, copy seq, eval and return it
 716             epvector *s=new epvector;
 717             s->reserve(seq.size());
 718
 719             // copy parts of seq which are known not to have changed
 720             epvector::const_iterator cit2=seq.begin();
 721             while (cit2!=cit) {
 722                 s->push_back(*cit2);
 723                 ++cit2;
 724             }
 725             // copy first changed element
 726             s->push_back(split_ex_to_pair(expanded_factor));
 727             ++cit2;
 728             // copy rest
 729             while (cit2!=last) {
 730                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 731                 ++cit2;
 732             }
 733             return s;
 734         }
 735         ++cit;
 736     }
 737
 738     return 0; // nothing has changed
 739 }
 740
 741 //////////
 742 // static member variables
 743 //////////
 744
 745 // protected
 746
 747 unsigned mul::precedence=50;
 748
 749
 750 //////////
 751 // global constants
 752 //////////
 753
 754 const mul some_mul;
 755 type_info const & typeid_mul=typeid(some_mul);
 756
 757 #ifndef NO_GINAC_NAMESPACE
 758 } // namespace GiNaC
 759 #endif // ndef NO_GINAC_NAMESPACE