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 #include "utils.h"
  31
  32 #ifndef NO_GINAC_NAMESPACE
  33 namespace GiNaC {
  34 #endif // ndef NO_GINAC_NAMESPACE
  35
  36 //////////
  37 // default constructor, destructor, copy constructor assignment operator and helpers
  38 //////////
  39
  40 // public
  41
  42 mul::mul()
  43 {
  44     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  45     tinfo_key = TINFO_mul;
  46 }
  47
  48 mul::~mul()
  49 {
  50     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  51     destroy(0);
  52 }
  53
  54 mul::mul(mul const & other)
  55 {
  56     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  57     copy(other);
  58 }
  59
  60 mul const & mul::operator=(mul const & other)
  61 {
  62     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  63     if (this != &other) {
  64         destroy(1);
  65         copy(other);
  66     }
  67     return *this;
  68 }
  69
  70 // protected
  71
  72 void mul::copy(mul const & other)
  73 {
  74     expairseq::copy(other);
  75 }
  76
  77 void mul::destroy(bool call_parent)
  78 {
  79     if (call_parent) expairseq::destroy(call_parent);
  80 }
  81
  82 //////////
  83 // other constructors
  84 //////////
  85
  86 // public
  87
  88 mul::mul(ex const & lh, ex const & rh)
  89 {
  90     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  91     tinfo_key = TINFO_mul;
  92     overall_coeff=_ex1();
  93     construct_from_2_ex(lh,rh);
  94     GINAC_ASSERT(is_canonical());
  95 }
  96
  97 mul::mul(exvector const & v)
  98 {
  99     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
 100     tinfo_key = TINFO_mul;
 101     overall_coeff=_ex1();
 102     construct_from_exvector(v);
 103     GINAC_ASSERT(is_canonical());
 104 }
 105
 106 /*
 107 mul::mul(epvector const & v, bool do_not_canonicalize)
 108 {
 109     debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
 110     tinfo_key = TINFO_mul;
 111     if (do_not_canonicalize) {
 112         seq=v;
 113 #ifdef EXPAIRSEQ_USE_HASHTAB
 114         combine_same_terms(); // to build hashtab
 115 #endif // def EXPAIRSEQ_USE_HASHTAB
 116     } else {
 117         construct_from_epvector(v);
 118     }
 119     GINAC_ASSERT(is_canonical());
 120 }
 121 */
 122
 123 mul::mul(epvector const & v)
 124 {
 125     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 126     tinfo_key = TINFO_mul;
 127     overall_coeff=_ex1();
 128     construct_from_epvector(v);
 129     GINAC_ASSERT(is_canonical());
 130 }
 131
 132 mul::mul(epvector const & v, ex const & oc)
 133 {
 134     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 135     tinfo_key = TINFO_mul;
 136     overall_coeff=oc;
 137     construct_from_epvector(v);
 138     GINAC_ASSERT(is_canonical());
 139 }
 140
 141 mul::mul(epvector * vp, ex const & oc)
 142 {
 143     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 144     tinfo_key = TINFO_mul;
 145     GINAC_ASSERT(vp!=0);
 146     overall_coeff=oc;
 147     construct_from_epvector(*vp);
 148     delete vp;
 149     GINAC_ASSERT(is_canonical());
 150 }
 151
 152 mul::mul(ex const & lh, ex const & mh, ex const & rh)
 153 {
 154     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 155     tinfo_key = TINFO_mul;
 156     exvector factors;
 157     factors.reserve(3);
 158     factors.push_back(lh);
 159     factors.push_back(mh);
 160     factors.push_back(rh);
 161     overall_coeff=_ex1();
 162     construct_from_exvector(factors);
 163     GINAC_ASSERT(is_canonical());
 164 }
 165
 166 //////////
 167 // functions overriding virtual functions from bases classes
 168 //////////
 169
 170 // public
 171
 172 basic * mul::duplicate() const
 173 {
 174     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 175     return new mul(*this);
 176 }
 177
 178 void mul::print(ostream & os, unsigned upper_precedence) const
 179 {
 180     debugmsg("mul print",LOGLEVEL_PRINT);
 181     if (precedence<=upper_precedence) os << "(";
 182     bool first=true;
 183     // first print the overall numeric coefficient:
 184     if (ex_to_numeric(overall_coeff).csgn()==-1) os << '-';
 185     if (!overall_coeff.is_equal(_ex1()) &&
 186         !overall_coeff.is_equal(_ex_1())) {
 187         if (ex_to_numeric(overall_coeff).csgn()==-1)
 188             (_num_1()*overall_coeff).print(os, precedence);
 189         else
 190             overall_coeff.print(os, precedence);
 191         os << '*';
 192     }
 193     // then proceed with the remaining factors:
 194     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 195         if (!first) {
 196             os << '*';
 197         } else {
 198             first=false;
 199         }
 200         recombine_pair_to_ex(*cit).print(os,precedence);
 201     }
 202     if (precedence<=upper_precedence) os << ")";
 203 }
 204
 205 void mul::printraw(ostream & os) const
 206 {
 207     debugmsg("mul printraw",LOGLEVEL_PRINT);
 208
 209     os << "*(";
 210     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 211         os << "(";
 212         (*it).rest.bp->printraw(os);
 213         os << ",";
 214         (*it).coeff.bp->printraw(os);
 215         os << "),";
 216     }
 217     os << ",hash=" << hashvalue << ",flags=" << flags;
 218     os << ")";
 219 }
 220
 221 void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
 222 {
 223     debugmsg("mul print csrc", LOGLEVEL_PRINT);
 224     if (precedence <= upper_precedence)
 225         os << "(";
 226
 227     if (!overall_coeff.is_equal(_ex1())) {
 228         overall_coeff.bp->printcsrc(os,type,precedence);
 229         os << "*";
 230     }
 231
 232     // Print arguments, separated by "*" or "/"
 233     epvector::const_iterator it = seq.begin();
 234     epvector::const_iterator itend = seq.end();
 235     while (it != itend) {
 236
 237         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 238         if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 239             if (type == csrc_types::ctype_cl_N)
 240                 os << "recip(";
 241             else
 242                 os << "1.0/";
 243         }
 244
 245         // If the exponent is 1 or -1, it is left out
 246         if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 247             it->rest.bp->printcsrc(os, type, precedence);
 248         else
 249             // outer parens around ex needed for broken gcc-2.95 parser:
 250             (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 251
 252         // Separator is "/" for negative integer powers, "*" otherwise
 253         it++;
 254         if (it != itend) {
 255             if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 256                 os << "/";
 257             else
 258                 os << "*";
 259         }
 260     }
 261     if (precedence <= upper_precedence)
 262         os << ")";
 263 }
 264
 265 bool mul::info(unsigned inf) const
 266 {
 267     // TODO: optimize
 268     if (inf==info_flags::polynomial ||
 269         inf==info_flags::integer_polynomial ||
 270         inf==info_flags::cinteger_polynomial ||
 271         inf==info_flags::rational_polynomial ||
 272         inf==info_flags::crational_polynomial ||
 273         inf==info_flags::rational_function) {
 274         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 275             if (!(recombine_pair_to_ex(*it).info(inf)))
 276                 return false;
 277         }
 278         return overall_coeff.info(inf);
 279     } else {
 280         return expairseq::info(inf);
 281     }
 282 }
 283
 284 typedef vector<int> intvector;
 285
 286 int mul::degree(symbol const & s) const
 287 {
 288     int deg_sum=0;
 289     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 290         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 291     }
 292     return deg_sum;
 293 }
 294
 295 int mul::ldegree(symbol const & s) const
 296 {
 297     int deg_sum=0;
 298     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 299         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 300     }
 301     return deg_sum;
 302 }
 303
 304 ex mul::coeff(symbol const & s, int const n) const
 305 {
 306     exvector coeffseq;
 307     coeffseq.reserve(seq.size()+1);
 308
 309     if (n==0) {
 310         // product of individual coeffs
 311         // if a non-zero power of s is found, the resulting product will be 0
 312         epvector::const_iterator it=seq.begin();
 313         while (it!=seq.end()) {
 314             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 315             ++it;
 316         }
 317         coeffseq.push_back(overall_coeff);
 318         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 319     }
 320
 321     epvector::const_iterator it=seq.begin();
 322     bool coeff_found=0;
 323     while (it!=seq.end()) {
 324         ex t=recombine_pair_to_ex(*it);
 325         ex c=t.coeff(s,n);
 326         if (!c.is_zero()) {
 327             coeffseq.push_back(c);
 328             coeff_found=1;
 329         } else {
 330             coeffseq.push_back(t);
 331         }
 332         ++it;
 333     }
 334     if (coeff_found) {
 335         coeffseq.push_back(overall_coeff);
 336         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 337     }
 338
 339     return _ex0();
 340 }
 341
 342 ex mul::eval(int level) const
 343 {
 344     // simplifications  *(...,x;0) -> 0
 345     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 346     //                  *(x;1) -> x
 347     //                  *(;c) -> c
 348
 349     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 350
 351     epvector * evaled_seqp=evalchildren(level);
 352     if (evaled_seqp!=0) {
 353         // do more evaluation later
 354         return (new mul(evaled_seqp,overall_coeff))->
 355                    setflag(status_flags::dynallocated);
 356     }
 357
 358 #ifdef DO_GINAC_ASSERT
 359     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 360         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 361                (!(ex_to_numeric((*cit).coeff).is_integer())));
 362         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 363         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 364             printtree(cerr,0);
 365         }
 366         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 367         /* for paranoia */
 368         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 369         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 370         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 371         /* end paranoia */
 372     }
 373 #endif // def DO_GINAC_ASSERT
 374
 375     if (flags & status_flags::evaluated) {
 376         GINAC_ASSERT(seq.size()>0);
 377         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 378         return *this;
 379     }
 380
 381     int seq_size=seq.size();
 382     if (overall_coeff.is_equal(_ex0())) {
 383         // *(...,x;0) -> 0
 384         return _ex0();
 385     } else if (seq_size==0) {
 386         // *(;c) -> c
 387         return overall_coeff;
 388     } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 389         // *(x;1) -> x
 390         return recombine_pair_to_ex(*(seq.begin()));
 391     } else if ((seq_size==1) &&
 392                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 393                ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 394         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 395         add const & addref=ex_to_add((*seq.begin()).rest);
 396         epvector distrseq;
 397         distrseq.reserve(addref.seq.size());
 398         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 399             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 400                                    overall_coeff));
 401         }
 402         return (new add(distrseq,
 403                         ex_to_numeric(addref.overall_coeff).
 404                         mul_dyn(ex_to_numeric(overall_coeff))))
 405             ->setflag(status_flags::dynallocated  |
 406                       status_flags::evaluated );
 407     }
 408     return this->hold();
 409 }
 410
 411 exvector mul::get_indices(void) const
 412 {
 413     // return union of indices of factors
 414     exvector iv;
 415     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 416         exvector subiv=(*cit).rest.get_indices();
 417         iv.reserve(iv.size()+subiv.size());
 418         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 419             iv.push_back(*cit2);
 420         }
 421     }
 422     return iv;
 423 }
 424
 425 ex mul::simplify_ncmul(exvector const & v) const
 426 {
 427     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 428 }
 429
 430 // protected
 431
 432 int mul::compare_same_type(basic const & other) const
 433 {
 434     return expairseq::compare_same_type(other);
 435 }
 436
 437 bool mul::is_equal_same_type(basic const & other) const
 438 {
 439     return expairseq::is_equal_same_type(other);
 440 }
 441
 442 unsigned mul::return_type(void) const
 443 {
 444     if (seq.size()==0) {
 445         // mul without factors: should not happen, but commutes
 446         return return_types::commutative;
 447     }
 448
 449     bool all_commutative=1;
 450     unsigned rt;
 451     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 452
 453     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 454         rt=(*cit).rest.return_type();
 455         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 456         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 457             // first nc element found, remember position
 458             cit_noncommutative_element=cit;
 459             all_commutative=0;
 460         }
 461         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 462             // another nc element found, compare type_infos
 463             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 464                 // diffent types -> mul is ncc
 465                 return return_types::noncommutative_composite;
 466             }
 467         }
 468     }
 469     // all factors checked
 470     return all_commutative ? return_types::commutative : return_types::noncommutative;
 471 }
 472
 473 unsigned mul::return_type_tinfo(void) const
 474 {
 475     if (seq.size()==0) {
 476         // mul without factors: should not happen
 477         return tinfo_key;
 478     }
 479     // return type_info of first noncommutative element
 480     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 481         if ((*cit).rest.return_type()==return_types::noncommutative) {
 482             return (*cit).rest.return_type_tinfo();
 483         }
 484     }
 485     // no noncommutative element found, should not happen
 486     return tinfo_key;
 487 }
 488
 489 ex mul::thisexpairseq(epvector const & v, ex const & oc) const
 490 {
 491     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 492 }
 493
 494 ex mul::thisexpairseq(epvector * vp, ex const & oc) const
 495 {
 496     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 497 }
 498
 499 expair mul::split_ex_to_pair(ex const & e) const
 500 {
 501     if (is_ex_exactly_of_type(e,power)) {
 502         power const & powerref=ex_to_power(e);
 503         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 504             return expair(powerref.basis,powerref.exponent);
 505         }
 506     }
 507     return expair(e,_ex1());
 508 }
 509
 510 expair mul::combine_ex_with_coeff_to_pair(ex const & e,
 511                                           ex const & c) const
 512 {
 513     // to avoid duplication of power simplification rules,
 514     // we create a temporary power object
 515     // otherwise it would be hard to correctly simplify
 516     // expression like (4^(1/3))^(3/2)
 517     if (are_ex_trivially_equal(c,_ex1())) {
 518         return split_ex_to_pair(e);
 519     }
 520     return split_ex_to_pair(power(e,c));
 521 }
 522
 523 expair mul::combine_pair_with_coeff_to_pair(expair const & p,
 524                                             ex const & c) const
 525 {
 526     // to avoid duplication of power simplification rules,
 527     // we create a temporary power object
 528     // otherwise it would be hard to correctly simplify
 529     // expression like (4^(1/3))^(3/2)
 530     if (are_ex_trivially_equal(c,_ex1())) {
 531         return p;
 532     }
 533     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 534 }
 535
 536 ex mul::recombine_pair_to_ex(expair const & p) const
 537 {
 538     // if (p.coeff.compare(_ex1())==0) {
 539     // if (are_ex_trivially_equal(p.coeff,_ex1())) {
 540     if (ex_to_numeric(p.coeff).is_equal(_num1())) {
 541         return p.rest;
 542     } else {
 543         return power(p.rest,p.coeff);
 544     }
 545 }
 546
 547 bool mul::expair_needs_further_processing(epp it)
 548 {
 549     if (is_ex_exactly_of_type((*it).rest,mul) &&
 550         ex_to_numeric((*it).coeff).is_integer()) {
 551         // combined pair is product with integer power -> expand it
 552         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 553         return true;
 554     }
 555     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 556         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 557         if (!ep.is_equal(*it)) {
 558             // combined pair is a numeric power which can be simplified
 559             *it=ep;
 560             return true;
 561         }
 562         if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 563             // combined pair has coeff 1 and must be moved to the end
 564             return true;
 565         }
 566     }
 567     return false;
 568 }
 569
 570 ex mul::default_overall_coeff(void) const
 571 {
 572     return _ex1();
 573 }
 574
 575 void mul::combine_overall_coeff(ex const & c)
 576 {
 577     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 578     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 579     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 580 }
 581
 582 void mul::combine_overall_coeff(ex const & c1, ex const & c2)
 583 {
 584     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 585     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 586     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 587     overall_coeff = ex_to_numeric(overall_coeff).
 588                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 589 }
 590
 591 bool mul::can_make_flat(expair const & p) const
 592 {
 593     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 594     // this assertion will probably fail somewhere
 595     // it would require a more careful make_flat, obeying the power laws
 596     // probably should return true only if p.coeff is integer
 597     return ex_to_numeric(p.coeff).is_equal(_num1());
 598 }
 599
 600 ex mul::expand(unsigned options) const
 601 {
 602     exvector sub_expanded_seq;
 603     intvector positions_of_adds;
 604     intvector number_of_add_operands;
 605
 606     epvector * expanded_seqp=expandchildren(options);
 607
 608     epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 609
 610     positions_of_adds.resize(expanded_seq.size());
 611     number_of_add_operands.resize(expanded_seq.size());
 612
 613     int number_of_adds=0;
 614     int number_of_expanded_terms=1;
 615
 616     unsigned current_position=0;
 617     epvector::const_iterator last=expanded_seq.end();
 618     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 619         if (is_ex_exactly_of_type((*cit).rest,add)&&
 620             (ex_to_numeric((*cit).coeff).is_equal(_num1()))) {
 621             positions_of_adds[number_of_adds]=current_position;
 622             add const & expanded_addref=ex_to_add((*cit).rest);
 623             int addref_nops=expanded_addref.nops();
 624             number_of_add_operands[number_of_adds]=addref_nops;
 625             number_of_expanded_terms *= addref_nops;
 626             number_of_adds++;
 627         }
 628         current_position++;
 629     }
 630
 631     if (number_of_adds==0) {
 632         if (expanded_seqp==0) {
 633             return this->setflag(status_flags::expanded);
 634         }
 635         return (new mul(expanded_seqp,overall_coeff))->
 636                      setflag(status_flags::dynallocated ||
 637                              status_flags::expanded);
 638     }
 639
 640     exvector distrseq;
 641     distrseq.reserve(number_of_expanded_terms);
 642
 643     intvector k;
 644     k.resize(number_of_adds);
 645
 646     int l;
 647     for (l=0; l<number_of_adds; l++) {
 648         k[l]=0;
 649     }
 650
 651     while (1) {
 652         epvector term;
 653         term=expanded_seq;
 654         for (l=0; l<number_of_adds; l++) {
 655             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 656             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
 657             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 658         }
 659         /*
 660         cout << "mul::expand() term begin" << endl;
 661         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
 662             cout << "rest" << endl;
 663             (*cit).rest.printtree(cout);
 664             cout << "coeff" << endl;
 665             (*cit).coeff.printtree(cout);
 666         }
 667         cout << "mul::expand() term end" << endl;
 668         */
 669         distrseq.push_back((new mul(term,overall_coeff))->
 670                                 setflag(status_flags::dynallocated |
 671                                         status_flags::expanded));
 672
 673         // increment k[]
 674         l=number_of_adds-1;
 675         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 676             k[l]=0;
 677             l--;
 678         }
 679         if (l<0) break;
 680     }
 681
 682     if (expanded_seqp!=0) {
 683         delete expanded_seqp;
 684     }
 685     /*
 686     cout << "mul::expand() distrseq begin" << endl;
 687     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
 688         (*cit).printtree(cout);
 689     }
 690     cout << "mul::expand() distrseq end" << endl;
 691     */
 692
 693     return (new add(distrseq))->setflag(status_flags::dynallocated |
 694                                         status_flags::expanded);
 695 }
 696
 697 //////////
 698 // new virtual functions which can be overridden by derived classes
 699 //////////
 700
 701 // none
 702
 703 //////////
 704 // non-virtual functions in this class
 705 //////////
 706
 707 epvector * mul::expandchildren(unsigned options) const
 708 {
 709     epvector::const_iterator last=seq.end();
 710     epvector::const_iterator cit=seq.begin();
 711     while (cit!=last) {
 712         ex const & factor=recombine_pair_to_ex(*cit);
 713         ex const & expanded_factor=factor.expand(options);
 714         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 715
 716             // something changed, copy seq, eval and return it
 717             epvector *s=new epvector;
 718             s->reserve(seq.size());
 719
 720             // copy parts of seq which are known not to have changed
 721             epvector::const_iterator cit2=seq.begin();
 722             while (cit2!=cit) {
 723                 s->push_back(*cit2);
 724                 ++cit2;
 725             }
 726             // copy first changed element
 727             s->push_back(split_ex_to_pair(expanded_factor));
 728             ++cit2;
 729             // copy rest
 730             while (cit2!=last) {
 731                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 732                 ++cit2;
 733             }
 734             return s;
 735         }
 736         ++cit;
 737     }
 738
 739     return 0; // nothing has changed
 740 }
 741
 742 //////////
 743 // static member variables
 744 //////////
 745
 746 // protected
 747
 748 unsigned mul::precedence=50;
 749
 750
 751 //////////
 752 // global constants
 753 //////////
 754
 755 const mul some_mul;
 756 type_info const & typeid_mul=typeid(some_mul);
 757
 758 #ifndef NO_GINAC_NAMESPACE
 759 } // namespace GiNaC
 760 #endif // ndef NO_GINAC_NAMESPACE