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