ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2000 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 "archive.h"
  30 #include "debugmsg.h"
  31 #include "utils.h"
  32
  33 #ifndef NO_NAMESPACE_GINAC
  34 namespace GiNaC {
  35 #endif // ndef NO_NAMESPACE_GINAC
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 // public
  44
  45 mul::mul()
  46 {
  47     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  48     tinfo_key = TINFO_mul;
  49 }
  50
  51 mul::~mul()
  52 {
  53     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  54     destroy(0);
  55 }
  56
  57 mul::mul(const mul & other)
  58 {
  59     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  60     copy(other);
  61 }
  62
  63 const mul & mul::operator=(const mul & other)
  64 {
  65     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  66     if (this != &other) {
  67         destroy(1);
  68         copy(other);
  69     }
  70     return *this;
  71 }
  72
  73 // protected
  74
  75 void mul::copy(const mul & other)
  76 {
  77     inherited::copy(other);
  78 }
  79
  80 void mul::destroy(bool call_parent)
  81 {
  82     if (call_parent) inherited::destroy(call_parent);
  83 }
  84
  85 //////////
  86 // other constructors
  87 //////////
  88
  89 // public
  90
  91 mul::mul(const ex & lh, const ex & rh)
  92 {
  93     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  94     tinfo_key = TINFO_mul;
  95     overall_coeff=_ex1();
  96     construct_from_2_ex(lh,rh);
  97     GINAC_ASSERT(is_canonical());
  98 }
  99
 100 mul::mul(const exvector & v)
 101 {
 102     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
 103     tinfo_key = TINFO_mul;
 104     overall_coeff=_ex1();
 105     construct_from_exvector(v);
 106     GINAC_ASSERT(is_canonical());
 107 }
 108
 109 /*
 110 mul::mul(const epvector & v, bool do_not_canonicalize)
 111 {
 112     debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
 113     tinfo_key = TINFO_mul;
 114     if (do_not_canonicalize) {
 115         seq=v;
 116 #ifdef EXPAIRSEQ_USE_HASHTAB
 117         combine_same_terms(); // to build hashtab
 118 #endif // def EXPAIRSEQ_USE_HASHTAB
 119     } else {
 120         construct_from_epvector(v);
 121     }
 122     GINAC_ASSERT(is_canonical());
 123 }
 124 */
 125
 126 mul::mul(const epvector & v)
 127 {
 128     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 129     tinfo_key = TINFO_mul;
 130     overall_coeff=_ex1();
 131     construct_from_epvector(v);
 132     GINAC_ASSERT(is_canonical());
 133 }
 134
 135 mul::mul(const epvector & v, const ex & oc)
 136 {
 137     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 138     tinfo_key = TINFO_mul;
 139     overall_coeff=oc;
 140     construct_from_epvector(v);
 141     GINAC_ASSERT(is_canonical());
 142 }
 143
 144 mul::mul(epvector * vp, const ex & oc)
 145 {
 146     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 147     tinfo_key = TINFO_mul;
 148     GINAC_ASSERT(vp!=0);
 149     overall_coeff=oc;
 150     construct_from_epvector(*vp);
 151     delete vp;
 152     GINAC_ASSERT(is_canonical());
 153 }
 154
 155 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 156 {
 157     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 158     tinfo_key = TINFO_mul;
 159     exvector factors;
 160     factors.reserve(3);
 161     factors.push_back(lh);
 162     factors.push_back(mh);
 163     factors.push_back(rh);
 164     overall_coeff=_ex1();
 165     construct_from_exvector(factors);
 166     GINAC_ASSERT(is_canonical());
 167 }
 168
 169 //////////
 170 // archiving
 171 //////////
 172
 173 /** Construct object from archive_node. */
 174 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 175 {
 176     debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 177 }
 178
 179 /** Unarchive the object. */
 180 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
 181 {
 182     return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
 183 }
 184
 185 /** Archive the object. */
 186 void mul::archive(archive_node &n) const
 187 {
 188     inherited::archive(n);
 189 }
 190
 191 //////////
 192 // functions overriding virtual functions from bases classes
 193 //////////
 194
 195 // public
 196
 197 basic * mul::duplicate() const
 198 {
 199     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 200     return new mul(*this);
 201 }
 202
 203 void mul::print(ostream & os, unsigned upper_precedence) const
 204 {
 205     debugmsg("mul print",LOGLEVEL_PRINT);
 206     if (precedence<=upper_precedence) os << "(";
 207     bool first=true;
 208     // first print the overall numeric coefficient:
 209     numeric coeff = ex_to_numeric(overall_coeff);
 210     if (coeff.csgn()==-1) os << '-';
 211     if (!coeff.is_equal(_num1()) &&
 212         !coeff.is_equal(_num_1())) {
 213         if (coeff.is_rational()) {
 214             if (coeff.is_negative())
 215                 os << -coeff;
 216             else
 217                 os << coeff;
 218         } else {
 219             if (coeff.csgn()==-1)
 220                 (-coeff).print(os, precedence);
 221             else
 222                 coeff.print(os, precedence);
 223         }
 224         os << '*';
 225     }
 226     // then proceed with the remaining factors:
 227     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 228         if (!first) {
 229             os << '*';
 230         } else {
 231             first=false;
 232         }
 233         recombine_pair_to_ex(*cit).print(os,precedence);
 234     }
 235     if (precedence<=upper_precedence) os << ")";
 236 }
 237
 238 void mul::printraw(ostream & os) const
 239 {
 240     debugmsg("mul printraw",LOGLEVEL_PRINT);
 241
 242     os << "*(";
 243     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 244         os << "(";
 245         (*it).rest.bp->printraw(os);
 246         os << ",";
 247         (*it).coeff.bp->printraw(os);
 248         os << "),";
 249     }
 250     os << ",hash=" << hashvalue << ",flags=" << flags;
 251     os << ")";
 252 }
 253
 254 void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
 255 {
 256     debugmsg("mul print csrc", LOGLEVEL_PRINT);
 257     if (precedence <= upper_precedence)
 258         os << "(";
 259
 260     if (!overall_coeff.is_equal(_ex1())) {
 261         overall_coeff.bp->printcsrc(os,type,precedence);
 262         os << "*";
 263     }
 264
 265     // Print arguments, separated by "*" or "/"
 266     epvector::const_iterator it = seq.begin();
 267     epvector::const_iterator itend = seq.end();
 268     while (it != itend) {
 269
 270         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 271         if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 272             if (type == csrc_types::ctype_cl_N)
 273                 os << "recip(";
 274             else
 275                 os << "1.0/";
 276         }
 277
 278         // If the exponent is 1 or -1, it is left out
 279         if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 280             it->rest.bp->printcsrc(os, type, precedence);
 281         else
 282             // outer parens around ex needed for broken gcc-2.95 parser:
 283             (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 284
 285         // Separator is "/" for negative integer powers, "*" otherwise
 286         it++;
 287         if (it != itend) {
 288             if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 289                 os << "/";
 290             else
 291                 os << "*";
 292         }
 293     }
 294     if (precedence <= upper_precedence)
 295         os << ")";
 296 }
 297
 298 bool mul::info(unsigned inf) const
 299 {
 300     // TODO: optimize
 301     if (inf==info_flags::polynomial ||
 302         inf==info_flags::integer_polynomial ||
 303         inf==info_flags::cinteger_polynomial ||
 304         inf==info_flags::rational_polynomial ||
 305         inf==info_flags::crational_polynomial ||
 306         inf==info_flags::rational_function) {
 307         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 308             if (!(recombine_pair_to_ex(*it).info(inf)))
 309                 return false;
 310         }
 311         return overall_coeff.info(inf);
 312     } else {
 313         return inherited::info(inf);
 314     }
 315 }
 316
 317 typedef vector<int> intvector;
 318
 319 int mul::degree(const symbol & s) const
 320 {
 321     int deg_sum=0;
 322     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 323         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 324     }
 325     return deg_sum;
 326 }
 327
 328 int mul::ldegree(const symbol & s) const
 329 {
 330     int deg_sum=0;
 331     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 332         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 333     }
 334     return deg_sum;
 335 }
 336
 337 ex mul::coeff(const symbol & s, int n) const
 338 {
 339     exvector coeffseq;
 340     coeffseq.reserve(seq.size()+1);
 341
 342     if (n==0) {
 343         // product of individual coeffs
 344         // if a non-zero power of s is found, the resulting product will be 0
 345         epvector::const_iterator it=seq.begin();
 346         while (it!=seq.end()) {
 347             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 348             ++it;
 349         }
 350         coeffseq.push_back(overall_coeff);
 351         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 352     }
 353
 354     epvector::const_iterator it=seq.begin();
 355     bool coeff_found=0;
 356     while (it!=seq.end()) {
 357         ex t=recombine_pair_to_ex(*it);
 358         ex c=t.coeff(s,n);
 359         if (!c.is_zero()) {
 360             coeffseq.push_back(c);
 361             coeff_found=1;
 362         } else {
 363             coeffseq.push_back(t);
 364         }
 365         ++it;
 366     }
 367     if (coeff_found) {
 368         coeffseq.push_back(overall_coeff);
 369         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 370     }
 371
 372     return _ex0();
 373 }
 374
 375 ex mul::eval(int level) const
 376 {
 377     // simplifications  *(...,x;0) -> 0
 378     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 379     //                  *(x;1) -> x
 380     //                  *(;c) -> c
 381
 382     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 383
 384     epvector * evaled_seqp=evalchildren(level);
 385     if (evaled_seqp!=0) {
 386         // do more evaluation later
 387         return (new mul(evaled_seqp,overall_coeff))->
 388                    setflag(status_flags::dynallocated);
 389     }
 390
 391 #ifdef DO_GINAC_ASSERT
 392     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 393         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 394                (!(ex_to_numeric((*cit).coeff).is_integer())));
 395         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 396         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 397             printtree(cerr,0);
 398         }
 399         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 400         /* for paranoia */
 401         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 402         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 403         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 404         /* end paranoia */
 405     }
 406 #endif // def DO_GINAC_ASSERT
 407
 408     if (flags & status_flags::evaluated) {
 409         GINAC_ASSERT(seq.size()>0);
 410         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 411         return *this;
 412     }
 413
 414     int seq_size=seq.size();
 415     if (overall_coeff.is_equal(_ex0())) {
 416         // *(...,x;0) -> 0
 417         return _ex0();
 418     } else if (seq_size==0) {
 419         // *(;c) -> c
 420         return overall_coeff;
 421     } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 422         // *(x;1) -> x
 423         return recombine_pair_to_ex(*(seq.begin()));
 424     } else if ((seq_size==1) &&
 425                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 426                ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 427         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 428         const add & addref=ex_to_add((*seq.begin()).rest);
 429         epvector distrseq;
 430         distrseq.reserve(addref.seq.size());
 431         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 432             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 433                                    overall_coeff));
 434         }
 435         return (new add(distrseq,
 436                         ex_to_numeric(addref.overall_coeff).
 437                         mul_dyn(ex_to_numeric(overall_coeff))))
 438             ->setflag(status_flags::dynallocated  |
 439                       status_flags::evaluated );
 440     }
 441     return this->hold();
 442 }
 443
 444 exvector mul::get_indices(void) const
 445 {
 446     // return union of indices of factors
 447     exvector iv;
 448     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 449         exvector subiv=(*cit).rest.get_indices();
 450         iv.reserve(iv.size()+subiv.size());
 451         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 452             iv.push_back(*cit2);
 453         }
 454     }
 455     return iv;
 456 }
 457
 458 ex mul::simplify_ncmul(const exvector & v) const
 459 {
 460     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 461 }
 462
 463 // protected
 464
 465 int mul::compare_same_type(const basic & other) const
 466 {
 467     return inherited::compare_same_type(other);
 468 }
 469
 470 bool mul::is_equal_same_type(const basic & other) const
 471 {
 472     return inherited::is_equal_same_type(other);
 473 }
 474
 475 unsigned mul::return_type(void) const
 476 {
 477     if (seq.size()==0) {
 478         // mul without factors: should not happen, but commutes
 479         return return_types::commutative;
 480     }
 481
 482     bool all_commutative=1;
 483     unsigned rt;
 484     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 485
 486     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 487         rt=(*cit).rest.return_type();
 488         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 489         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 490             // first nc element found, remember position
 491             cit_noncommutative_element=cit;
 492             all_commutative=0;
 493         }
 494         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 495             // another nc element found, compare type_infos
 496             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 497                 // diffent types -> mul is ncc
 498                 return return_types::noncommutative_composite;
 499             }
 500         }
 501     }
 502     // all factors checked
 503     return all_commutative ? return_types::commutative : return_types::noncommutative;
 504 }
 505
 506 unsigned mul::return_type_tinfo(void) const
 507 {
 508     if (seq.size()==0) {
 509         // mul without factors: should not happen
 510         return tinfo_key;
 511     }
 512     // return type_info of first noncommutative element
 513     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 514         if ((*cit).rest.return_type()==return_types::noncommutative) {
 515             return (*cit).rest.return_type_tinfo();
 516         }
 517     }
 518     // no noncommutative element found, should not happen
 519     return tinfo_key;
 520 }
 521
 522 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 523 {
 524     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 525 }
 526
 527 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 528 {
 529     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 530 }
 531
 532 expair mul::split_ex_to_pair(const ex & e) const
 533 {
 534     if (is_ex_exactly_of_type(e,power)) {
 535         const power & powerref=ex_to_power(e);
 536         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 537             return expair(powerref.basis,powerref.exponent);
 538         }
 539     }
 540     return expair(e,_ex1());
 541 }
 542
 543 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 544                                           const ex & c) const
 545 {
 546     // to avoid duplication of power simplification rules,
 547     // we create a temporary power object
 548     // otherwise it would be hard to correctly simplify
 549     // expression like (4^(1/3))^(3/2)
 550     if (are_ex_trivially_equal(c,_ex1())) {
 551         return split_ex_to_pair(e);
 552     }
 553     return split_ex_to_pair(power(e,c));
 554 }
 555
 556 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 557                                             const ex & c) const
 558 {
 559     // to avoid duplication of power simplification rules,
 560     // we create a temporary power object
 561     // otherwise it would be hard to correctly simplify
 562     // expression like (4^(1/3))^(3/2)
 563     if (are_ex_trivially_equal(c,_ex1())) {
 564         return p;
 565     }
 566     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 567 }
 568
 569 ex mul::recombine_pair_to_ex(const expair & p) const
 570 {
 571     // if (p.coeff.compare(_ex1())==0) {
 572     // if (are_ex_trivially_equal(p.coeff,_ex1())) {
 573     if (ex_to_numeric(p.coeff).is_equal(_num1())) {
 574         return p.rest;
 575     } else {
 576         return power(p.rest,p.coeff);
 577     }
 578 }
 579
 580 bool mul::expair_needs_further_processing(epp it)
 581 {
 582     if (is_ex_exactly_of_type((*it).rest,mul) &&
 583         ex_to_numeric((*it).coeff).is_integer()) {
 584         // combined pair is product with integer power -> expand it
 585         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 586         return true;
 587     }
 588     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 589         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 590         if (!ep.is_equal(*it)) {
 591             // combined pair is a numeric power which can be simplified
 592             *it=ep;
 593             return true;
 594         }
 595         if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 596             // combined pair has coeff 1 and must be moved to the end
 597             return true;
 598         }
 599     }
 600     return false;
 601 }
 602
 603 ex mul::default_overall_coeff(void) const
 604 {
 605     return _ex1();
 606 }
 607
 608 void mul::combine_overall_coeff(const ex & c)
 609 {
 610     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 611     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 612     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 613 }
 614
 615 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 616 {
 617     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 618     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 619     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 620     overall_coeff = ex_to_numeric(overall_coeff).
 621                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 622 }
 623
 624 bool mul::can_make_flat(const expair & p) const
 625 {
 626     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 627     // this assertion will probably fail somewhere
 628     // it would require a more careful make_flat, obeying the power laws
 629     // probably should return true only if p.coeff is integer
 630     return ex_to_numeric(p.coeff).is_equal(_num1());
 631 }
 632
 633 ex mul::expand(unsigned options) const
 634 {
 635     exvector sub_expanded_seq;
 636     intvector positions_of_adds;
 637     intvector number_of_add_operands;
 638
 639     epvector * expanded_seqp=expandchildren(options);
 640
 641     const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 642
 643     positions_of_adds.resize(expanded_seq.size());
 644     number_of_add_operands.resize(expanded_seq.size());
 645
 646     int number_of_adds=0;
 647     int number_of_expanded_terms=1;
 648
 649     unsigned current_position=0;
 650     epvector::const_iterator last=expanded_seq.end();
 651     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 652         if (is_ex_exactly_of_type((*cit).rest,add)&&
 653             (ex_to_numeric((*cit).coeff).is_equal(_num1()))) {
 654             positions_of_adds[number_of_adds]=current_position;
 655             const add & expanded_addref=ex_to_add((*cit).rest);
 656             unsigned addref_nops=expanded_addref.nops();
 657             number_of_add_operands[number_of_adds]=addref_nops;
 658             number_of_expanded_terms *= addref_nops;
 659             number_of_adds++;
 660         }
 661         current_position++;
 662     }
 663
 664     if (number_of_adds==0) {
 665         if (expanded_seqp==0) {
 666             return this->setflag(status_flags::expanded);
 667         }
 668         return (new mul(expanded_seqp,overall_coeff))->
 669                      setflag(status_flags::dynallocated ||
 670                              status_flags::expanded);
 671     }
 672
 673     exvector distrseq;
 674     distrseq.reserve(number_of_expanded_terms);
 675
 676     intvector k;
 677     k.resize(number_of_adds);
 678
 679     int l;
 680     for (l=0; l<number_of_adds; l++) {
 681         k[l]=0;
 682     }
 683
 684     while (1) {
 685         epvector term;
 686         term=expanded_seq;
 687         for (l=0; l<number_of_adds; l++) {
 688             const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 689             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
 690             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 691         }
 692         /*
 693         cout << "mul::expand() term begin" << endl;
 694         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
 695             cout << "rest" << endl;
 696             (*cit).rest.printtree(cout);
 697             cout << "coeff" << endl;
 698             (*cit).coeff.printtree(cout);
 699         }
 700         cout << "mul::expand() term end" << endl;
 701         */
 702         distrseq.push_back((new mul(term,overall_coeff))->
 703                                 setflag(status_flags::dynallocated |
 704                                         status_flags::expanded));
 705
 706         // increment k[]
 707         l=number_of_adds-1;
 708         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 709             k[l]=0;
 710             l--;
 711         }
 712         if (l<0) break;
 713     }
 714
 715     if (expanded_seqp!=0) {
 716         delete expanded_seqp;
 717     }
 718     /*
 719     cout << "mul::expand() distrseq begin" << endl;
 720     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
 721         (*cit).printtree(cout);
 722     }
 723     cout << "mul::expand() distrseq end" << endl;
 724     */
 725
 726     return (new add(distrseq))->setflag(status_flags::dynallocated |
 727                                         status_flags::expanded);
 728 }
 729
 730 //////////
 731 // new virtual functions which can be overridden by derived classes
 732 //////////
 733
 734 // none
 735
 736 //////////
 737 // non-virtual functions in this class
 738 //////////
 739
 740 epvector * mul::expandchildren(unsigned options) const
 741 {
 742     epvector::const_iterator last=seq.end();
 743     epvector::const_iterator cit=seq.begin();
 744     while (cit!=last) {
 745         const ex & factor=recombine_pair_to_ex(*cit);
 746         const ex & expanded_factor=factor.expand(options);
 747         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 748
 749             // something changed, copy seq, eval and return it
 750             epvector *s=new epvector;
 751             s->reserve(seq.size());
 752
 753             // copy parts of seq which are known not to have changed
 754             epvector::const_iterator cit2=seq.begin();
 755             while (cit2!=cit) {
 756                 s->push_back(*cit2);
 757                 ++cit2;
 758             }
 759             // copy first changed element
 760             s->push_back(split_ex_to_pair(expanded_factor));
 761             ++cit2;
 762             // copy rest
 763             while (cit2!=last) {
 764                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 765                 ++cit2;
 766             }
 767             return s;
 768         }
 769         ++cit;
 770     }
 771
 772     return 0; // nothing has changed
 773 }
 774
 775 //////////
 776 // static member variables
 777 //////////
 778
 779 // protected
 780
 781 unsigned mul::precedence=50;
 782
 783
 784 //////////
 785 // global constants
 786 //////////
 787
 788 const mul some_mul;
 789 const type_info & typeid_mul=typeid(some_mul);
 790
 791 #ifndef NO_NAMESPACE_GINAC
 792 } // namespace GiNaC
 793 #endif // ndef NO_NAMESPACE_GINAC