ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 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 // protected
  52
  53 void mul::copy(const mul & other)
  54 {
  55         inherited::copy(other);
  56 }
  57
  58 void mul::destroy(bool call_parent)
  59 {
  60         if (call_parent) inherited::destroy(call_parent);
  61 }
  62
  63 //////////
  64 // other constructors
  65 //////////
  66
  67 // public
  68
  69 mul::mul(const ex & lh, const ex & rh)
  70 {
  71         debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  72         tinfo_key = TINFO_mul;
  73         overall_coeff = _ex1();
  74         construct_from_2_ex(lh,rh);
  75         GINAC_ASSERT(is_canonical());
  76 }
  77
  78 mul::mul(const exvector & v)
  79 {
  80         debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
  81         tinfo_key = TINFO_mul;
  82         overall_coeff = _ex1();
  83         construct_from_exvector(v);
  84         GINAC_ASSERT(is_canonical());
  85 }
  86
  87 mul::mul(const epvector & v)
  88 {
  89         debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
  90         tinfo_key = TINFO_mul;
  91         overall_coeff = _ex1();
  92         construct_from_epvector(v);
  93         GINAC_ASSERT(is_canonical());
  94 }
  95
  96 mul::mul(const epvector & v, const ex & oc)
  97 {
  98         debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
  99         tinfo_key = TINFO_mul;
 100         overall_coeff = oc;
 101         construct_from_epvector(v);
 102         GINAC_ASSERT(is_canonical());
 103 }
 104
 105 mul::mul(epvector * vp, const ex & oc)
 106 {
 107         debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 108         tinfo_key = TINFO_mul;
 109         GINAC_ASSERT(vp!=0);
 110         overall_coeff = oc;
 111         construct_from_epvector(*vp);
 112         delete vp;
 113         GINAC_ASSERT(is_canonical());
 114 }
 115
 116 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 117 {
 118         debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 119         tinfo_key = TINFO_mul;
 120         exvector factors;
 121         factors.reserve(3);
 122         factors.push_back(lh);
 123         factors.push_back(mh);
 124         factors.push_back(rh);
 125         overall_coeff = _ex1();
 126         construct_from_exvector(factors);
 127         GINAC_ASSERT(is_canonical());
 128 }
 129
 130 //////////
 131 // archiving
 132 //////////
 133
 134 /** Construct object from archive_node. */
 135 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 136 {
 137         debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 138 }
 139
 140 /** Unarchive the object. */
 141 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
 142 {
 143         return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
 144 }
 145
 146 /** Archive the object. */
 147 void mul::archive(archive_node &n) const
 148 {
 149         inherited::archive(n);
 150 }
 151
 152 //////////
 153 // functions overriding virtual functions from bases classes
 154 //////////
 155
 156 // public
 157
 158 basic * mul::duplicate() const
 159 {
 160         debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 161         return new mul(*this);
 162 }
 163
 164 void mul::print(std::ostream & os, unsigned upper_precedence) const
 165 {
 166         debugmsg("mul print",LOGLEVEL_PRINT);
 167         if (precedence<=upper_precedence) os << "(";
 168         bool first=true;
 169         // first print the overall numeric coefficient:
 170         numeric coeff = ex_to_numeric(overall_coeff);
 171         if (coeff.csgn()==-1) os << '-';
 172         if (!coeff.is_equal(_num1()) &&
 173                 !coeff.is_equal(_num_1())) {
 174                 if (coeff.is_rational()) {
 175                         if (coeff.is_negative())
 176                                 os << -coeff;
 177                         else
 178                                 os << coeff;
 179                 } else {
 180                         if (coeff.csgn()==-1)
 181                                 (-coeff).print(os, precedence);
 182                         else
 183                                 coeff.print(os, precedence);
 184                 }
 185                 os << '*';
 186         }
 187         // then proceed with the remaining factors:
 188         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 189                 if (!first) {
 190                         os << '*';
 191                 } else {
 192                         first=false;
 193                 }
 194                 recombine_pair_to_ex(*cit).print(os,precedence);
 195         }
 196         if (precedence<=upper_precedence) os << ")";
 197 }
 198
 199 void mul::printraw(std::ostream & os) const
 200 {
 201         debugmsg("mul printraw",LOGLEVEL_PRINT);
 202
 203         os << "*(";
 204         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 205                 os << "(";
 206                 (*it).rest.bp->printraw(os);
 207                 os << ",";
 208                 (*it).coeff.bp->printraw(os);
 209                 os << "),";
 210         }
 211         os << ",hash=" << hashvalue << ",flags=" << flags;
 212         os << ")";
 213 }
 214
 215 void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 216 {
 217         debugmsg("mul print csrc", LOGLEVEL_PRINT);
 218         if (precedence <= upper_precedence)
 219                 os << "(";
 220
 221         if (!overall_coeff.is_equal(_ex1())) {
 222                 overall_coeff.bp->printcsrc(os,type,precedence);
 223                 os << "*";
 224         }
 225
 226         // Print arguments, separated by "*" or "/"
 227         epvector::const_iterator it = seq.begin();
 228         epvector::const_iterator itend = seq.end();
 229         while (it != itend) {
 230
 231                 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 232                 if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 233                         if (type == csrc_types::ctype_cl_N)
 234                                 os << "recip(";
 235                         else
 236                                 os << "1.0/";
 237                 }
 238
 239                 // If the exponent is 1 or -1, it is left out
 240                 if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 241                         it->rest.bp->printcsrc(os, type, precedence);
 242                 else
 243                         // outer parens around ex needed for broken gcc-2.95 parser:
 244                         (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 245
 246                 // Separator is "/" for negative integer powers, "*" otherwise
 247                 ++it;
 248                 if (it != itend) {
 249                         if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 250                                 os << "/";
 251                         else
 252                                 os << "*";
 253                 }
 254         }
 255         if (precedence <= upper_precedence)
 256                 os << ")";
 257 }
 258
 259 bool mul::info(unsigned inf) const
 260 {
 261         switch (inf) {
 262                 case info_flags::polynomial:
 263                 case info_flags::integer_polynomial:
 264                 case info_flags::cinteger_polynomial:
 265                 case info_flags::rational_polynomial:
 266                 case info_flags::crational_polynomial:
 267                 case info_flags::rational_function: {
 268                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 269                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 270                                         return false;
 271                         }
 272                         return overall_coeff.info(inf);
 273                 }
 274                 case info_flags::algebraic: {
 275                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 276                                 if ((recombine_pair_to_ex(*i).info(inf)))
 277                                         return true;
 278                         }
 279                         return false;
 280                 }
 281         }
 282         return inherited::info(inf);
 283 }
 284
 285 typedef std::vector<int> intvector;
 286
 287 int mul::degree(const symbol & s) const
 288 {
 289         int deg_sum = 0;
 290         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 291                 if (ex_to_numeric(cit->coeff).is_integer())
 292                         deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
 293         }
 294         return deg_sum;
 295 }
 296
 297 int mul::ldegree(const symbol & s) const
 298 {
 299         int deg_sum = 0;
 300         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 301                 if (ex_to_numeric(cit->coeff).is_integer())
 302                         deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
 303         }
 304         return deg_sum;
 305 }
 306
 307 ex mul::coeff(const symbol & s, int n) const
 308 {
 309         exvector coeffseq;
 310         coeffseq.reserve(seq.size()+1);
 311
 312         if (n==0) {
 313                 // product of individual coeffs
 314                 // if a non-zero power of s is found, the resulting product will be 0
 315                 epvector::const_iterator it=seq.begin();
 316                 while (it!=seq.end()) {
 317                         coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 318                         ++it;
 319                 }
 320                 coeffseq.push_back(overall_coeff);
 321                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 322         }
 323
 324         epvector::const_iterator it=seq.begin();
 325         bool coeff_found=0;
 326         while (it!=seq.end()) {
 327                 ex t=recombine_pair_to_ex(*it);
 328                 ex c=t.coeff(s,n);
 329                 if (!c.is_zero()) {
 330                         coeffseq.push_back(c);
 331                         coeff_found=1;
 332                 } else {
 333                         coeffseq.push_back(t);
 334                 }
 335                 ++it;
 336         }
 337         if (coeff_found) {
 338                 coeffseq.push_back(overall_coeff);
 339                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 340         }
 341
 342         return _ex0();
 343 }
 344
 345 ex mul::eval(int level) const
 346 {
 347         // simplifications  *(...,x;0) -> 0
 348         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 349         //                  *(x;1) -> x
 350         //                  *(;c) -> c
 351
 352         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 353
 354         epvector * evaled_seqp=evalchildren(level);
 355         if (evaled_seqp!=0) {
 356                 // do more evaluation later
 357                 return (new mul(evaled_seqp,overall_coeff))->
 358                                    setflag(status_flags::dynallocated);
 359         }
 360
 361 #ifdef DO_GINAC_ASSERT
 362         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 363                 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 364                            (!(ex_to_numeric((*cit).coeff).is_integer())));
 365                 GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 366                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 367                         printtree(cerr,0);
 368                 }
 369                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 370                 /* for paranoia */
 371                 expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 372                 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 373                 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 374                 /* end paranoia */
 375         }
 376 #endif // def DO_GINAC_ASSERT
 377
 378         if (flags & status_flags::evaluated) {
 379                 GINAC_ASSERT(seq.size()>0);
 380                 GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 381                 return *this;
 382         }
 383
 384         int seq_size=seq.size();
 385         if (overall_coeff.is_equal(_ex0())) {
 386                 // *(...,x;0) -> 0
 387                 return _ex0();
 388         } else if (seq_size==0) {
 389                 // *(;c) -> c
 390                 return overall_coeff;
 391         } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 392                 // *(x;1) -> x
 393                 return recombine_pair_to_ex(*(seq.begin()));
 394         } else if ((seq_size==1) &&
 395                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 396                    ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 397                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 398                 const add & addref=ex_to_add((*seq.begin()).rest);
 399                 epvector distrseq;
 400                 distrseq.reserve(addref.seq.size());
 401                 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 402                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
 403                 }
 404                 return (new add(distrseq,
 405                                 ex_to_numeric(addref.overall_coeff).
 406                                 mul_dyn(ex_to_numeric(overall_coeff))))
 407                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 408         }
 409         return this->hold();
 410 }
 411
 412 ex mul::evalf(int level) const
 413 {
 414         if (level==1)
 415                 return mul(seq,overall_coeff);
 416
 417         if (level==-max_recursion_level)
 418                 throw(std::runtime_error("max recursion level reached"));
 419
 420         epvector s;
 421         s.reserve(seq.size());
 422
 423         --level;
 424         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 425                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
 426                                                           (*it).coeff));
 427         }
 428         return mul(s,overall_coeff.evalf(level));
 429 }
 430
 431 exvector mul::get_indices(void) const
 432 {
 433         // return union of indices of factors
 434         exvector iv;
 435         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 436                 exvector subiv=(*cit).rest.get_indices();
 437                 iv.reserve(iv.size()+subiv.size());
 438                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 439                         iv.push_back(*cit2);
 440                 }
 441         }
 442         return iv;
 443 }
 444
 445 ex mul::simplify_ncmul(const exvector & v) const
 446 {
 447         throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 448 }
 449
 450 // protected
 451
 452 /** Implementation of ex::diff() for a product.  It applies the product rule.
 453  *  @see ex::diff */
 454 ex mul::derivative(const symbol & s) const
 455 {
 456         exvector addseq;
 457         addseq.reserve(seq.size());
 458
 459         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 460         for (unsigned i=0; i!=seq.size(); ++i) {
 461                 epvector mulseq = seq;
 462                 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
 463                                              seq[i].rest.diff(s));
 464                 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
 465         }
 466         return (new add(addseq))->setflag(status_flags::dynallocated);
 467 }
 468
 469 int mul::compare_same_type(const basic & other) const
 470 {
 471         return inherited::compare_same_type(other);
 472 }
 473
 474 bool mul::is_equal_same_type(const basic & other) const
 475 {
 476         return inherited::is_equal_same_type(other);
 477 }
 478
 479 unsigned mul::return_type(void) const
 480 {
 481         if (seq.size()==0) {
 482                 // mul without factors: should not happen, but commutes
 483                 return return_types::commutative;
 484         }
 485
 486         bool all_commutative = 1;
 487         unsigned rt;
 488         epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 489
 490         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 491                 rt=(*cit).rest.return_type();
 492                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 493                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 494                         // first nc element found, remember position
 495                         cit_noncommutative_element = cit;
 496                         all_commutative = 0;
 497                 }
 498                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 499                         // another nc element found, compare type_infos
 500                         if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 501                                 // diffent types -> mul is ncc
 502                                 return return_types::noncommutative_composite;
 503                         }
 504                 }
 505         }
 506         // all factors checked
 507         return all_commutative ? return_types::commutative : return_types::noncommutative;
 508 }
 509
 510 unsigned mul::return_type_tinfo(void) const
 511 {
 512         if (seq.size()==0) {
 513                 // mul without factors: should not happen
 514                 return tinfo_key;
 515         }
 516         // return type_info of first noncommutative element
 517         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 518                 if ((*cit).rest.return_type()==return_types::noncommutative) {
 519                         return (*cit).rest.return_type_tinfo();
 520                 }
 521         }
 522         // no noncommutative element found, should not happen
 523         return tinfo_key;
 524 }
 525
 526 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 527 {
 528         return (new mul(v,oc))->setflag(status_flags::dynallocated);
 529 }
 530
 531 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 532 {
 533         return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 534 }
 535
 536 expair mul::split_ex_to_pair(const ex & e) const
 537 {
 538         if (is_ex_exactly_of_type(e,power)) {
 539                 const power & powerref=ex_to_power(e);
 540                 if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 541                         return expair(powerref.basis,powerref.exponent);
 542                 }
 543         }
 544         return expair(e,_ex1());
 545 }
 546
 547 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 548                                           const ex & c) const
 549 {
 550         // to avoid duplication of power simplification rules,
 551         // we create a temporary power object
 552         // otherwise it would be hard to correctly simplify
 553         // expression like (4^(1/3))^(3/2)
 554         if (are_ex_trivially_equal(c,_ex1()))
 555                 return split_ex_to_pair(e);
 556
 557         return split_ex_to_pair(power(e,c));
 558 }
 559
 560 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 561                                             const ex & c) const
 562 {
 563         // to avoid duplication of power simplification rules,
 564         // we create a temporary power object
 565         // otherwise it would be hard to correctly simplify
 566         // expression like (4^(1/3))^(3/2)
 567         if (are_ex_trivially_equal(c,_ex1()))
 568                 return p;
 569
 570         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 571 }
 572
 573 ex mul::recombine_pair_to_ex(const expair & p) const
 574 {
 575         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 576                 return p.rest;
 577         else
 578                 return power(p.rest,p.coeff);
 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).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         if (flags & status_flags::expanded)
 636                 return *this;
 637
 638         exvector sub_expanded_seq;
 639         intvector positions_of_adds;
 640
 641         epvector * expanded_seqp = expandchildren(options);
 642
 643         const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 644
 645         int number_of_adds = 0;
 646         epvector non_adds;
 647         non_adds.reserve(expanded_seq.size());
 648         epvector::const_iterator cit = expanded_seq.begin();
 649         epvector::const_iterator last = expanded_seq.end();
 650         ex last_expanded=_ex1();
 651         while (cit!=last) {
 652                 if (is_ex_exactly_of_type((*cit).rest,add) &&
 653                         ((*cit).coeff.is_equal(_ex1()))) {
 654                         ++number_of_adds;
 655                         if (is_ex_exactly_of_type(last_expanded,add)) {
 656                                 // expand adds
 657                                 const add & add1 = ex_to_add(last_expanded);
 658                                 const add & add2 = ex_to_add((*cit).rest);
 659                                 int n1 = add1.nops();
 660                                 int n2 = add2.nops();
 661                                 exvector distrseq;
 662                                 distrseq.reserve(n1*n2);
 663                                 for (int i1=0; i1<n1; ++i1) {
 664                                         for (int i2=0; i2<n2; ++i2) {
 665                                                 distrseq.push_back(add1.op(i1)*add2.op(i2));
 666                                         }
 667                                 }
 668                                 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
 669                         } else {
 670                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 671                                 last_expanded = (*cit).rest;
 672                         }
 673                 } else {
 674                         non_adds.push_back(*cit);
 675                 }
 676                 ++cit;
 677         }
 678
 679         if (is_ex_exactly_of_type(last_expanded,add)) {
 680                 add const & finaladd = ex_to_add(last_expanded);
 681                 exvector distrseq;
 682                 int n = finaladd.nops();
 683                 distrseq.reserve(n);
 684                 for (int i=0; i<n; ++i) {
 685                         epvector factors = non_adds;
 686                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 687                         distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
 688                 }
 689                 return ((new add(distrseq))->
 690                         setflag(status_flags::dynallocated | status_flags::expanded));
 691         }
 692         non_adds.push_back(split_ex_to_pair(last_expanded));
 693         return (new mul(non_adds,overall_coeff))->
 694                 setflag(status_flags::dynallocated | status_flags::expanded);
 695 }
 696
 697
 698 //////////
 699 // new virtual functions which can be overridden by derived classes
 700 //////////
 701
 702 // none
 703
 704 //////////
 705 // non-virtual functions in this class
 706 //////////
 707
 708 epvector * mul::expandchildren(unsigned options) const
 709 {
 710         epvector::const_iterator last = seq.end();
 711         epvector::const_iterator cit = seq.begin();
 712         while (cit!=last) {
 713                 const ex & factor = recombine_pair_to_ex(*cit);
 714                 const ex & expanded_factor = factor.expand(options);
 715                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 716
 717                         // something changed, copy seq, eval and return it
 718                         epvector *s=new epvector;
 719                         s->reserve(seq.size());
 720
 721                         // copy parts of seq which are known not to have changed
 722                         epvector::const_iterator cit2 = seq.begin();
 723                         while (cit2!=cit) {
 724                                 s->push_back(*cit2);
 725                                 ++cit2;
 726                         }
 727                         // copy first changed element
 728                         s->push_back(split_ex_to_pair(expanded_factor));
 729                         ++cit2;
 730                         // copy rest
 731                         while (cit2!=last) {
 732                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 733                                 ++cit2;
 734                         }
 735                         return s;
 736                 }
 737                 ++cit;
 738         }
 739
 740         return 0; // nothing has changed
 741 }
 742
 743 //////////
 744 // static member variables
 745 //////////
 746
 747 // protected
 748
 749 unsigned mul::precedence = 50;
 750
 751 #ifndef NO_NAMESPACE_GINAC
 752 } // namespace GiNaC
 753 #endif // ndef NO_NAMESPACE_GINAC