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 void mul::print(std::ostream & os, unsigned upper_precedence) const
 159 {
 160         debugmsg("mul print",LOGLEVEL_PRINT);
 161         if (precedence<=upper_precedence) os << "(";
 162         bool first=true;
 163         // first print the overall numeric coefficient:
 164         numeric coeff = ex_to_numeric(overall_coeff);
 165         if (coeff.csgn()==-1) os << '-';
 166         if (!coeff.is_equal(_num1()) &&
 167                 !coeff.is_equal(_num_1())) {
 168                 if (coeff.is_rational()) {
 169                         if (coeff.is_negative())
 170                                 os << -coeff;
 171                         else
 172                                 os << coeff;
 173                 } else {
 174                         if (coeff.csgn()==-1)
 175                                 (-coeff).print(os, precedence);
 176                         else
 177                                 coeff.print(os, precedence);
 178                 }
 179                 os << '*';
 180         }
 181         // then proceed with the remaining factors:
 182         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 183                 if (!first) {
 184                         os << '*';
 185                 } else {
 186                         first=false;
 187                 }
 188                 recombine_pair_to_ex(*cit).print(os,precedence);
 189         }
 190         if (precedence<=upper_precedence) os << ")";
 191 }
 192
 193 void mul::printraw(std::ostream & os) const
 194 {
 195         debugmsg("mul printraw",LOGLEVEL_PRINT);
 196
 197         os << "*(";
 198         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 199                 os << "(";
 200                 (*it).rest.bp->printraw(os);
 201                 os << ",";
 202                 (*it).coeff.bp->printraw(os);
 203                 os << "),";
 204         }
 205         os << ",hash=" << hashvalue << ",flags=" << flags;
 206         os << ")";
 207 }
 208
 209 void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 210 {
 211         debugmsg("mul print csrc", LOGLEVEL_PRINT);
 212         if (precedence <= upper_precedence)
 213                 os << "(";
 214
 215         if (!overall_coeff.is_equal(_ex1())) {
 216                 overall_coeff.bp->printcsrc(os,type,precedence);
 217                 os << "*";
 218         }
 219
 220         // Print arguments, separated by "*" or "/"
 221         epvector::const_iterator it = seq.begin();
 222         epvector::const_iterator itend = seq.end();
 223         while (it != itend) {
 224
 225                 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 226                 if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 227                         if (type == csrc_types::ctype_cl_N)
 228                                 os << "recip(";
 229                         else
 230                                 os << "1.0/";
 231                 }
 232
 233                 // If the exponent is 1 or -1, it is left out
 234                 if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 235                         it->rest.bp->printcsrc(os, type, precedence);
 236                 else
 237                         // outer parens around ex needed for broken gcc-2.95 parser:
 238                         (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 239
 240                 // Separator is "/" for negative integer powers, "*" otherwise
 241                 ++it;
 242                 if (it != itend) {
 243                         if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 244                                 os << "/";
 245                         else
 246                                 os << "*";
 247                 }
 248         }
 249         if (precedence <= upper_precedence)
 250                 os << ")";
 251 }
 252
 253 bool mul::info(unsigned inf) const
 254 {
 255         switch (inf) {
 256                 case info_flags::polynomial:
 257                 case info_flags::integer_polynomial:
 258                 case info_flags::cinteger_polynomial:
 259                 case info_flags::rational_polynomial:
 260                 case info_flags::crational_polynomial:
 261                 case info_flags::rational_function: {
 262                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 263                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 264                                         return false;
 265                         }
 266                         return overall_coeff.info(inf);
 267                 }
 268                 case info_flags::algebraic: {
 269                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 270                                 if ((recombine_pair_to_ex(*i).info(inf)))
 271                                         return true;
 272                         }
 273                         return false;
 274                 }
 275         }
 276         return inherited::info(inf);
 277 }
 278
 279 typedef std::vector<int> intvector;
 280
 281 int mul::degree(const symbol & s) const
 282 {
 283         int deg_sum = 0;
 284         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 285                 if (ex_to_numeric(cit->coeff).is_integer())
 286                         deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
 287         }
 288         return deg_sum;
 289 }
 290
 291 int mul::ldegree(const symbol & s) const
 292 {
 293         int deg_sum = 0;
 294         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 295                 if (ex_to_numeric(cit->coeff).is_integer())
 296                         deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
 297         }
 298         return deg_sum;
 299 }
 300
 301 ex mul::coeff(const symbol & s, int n) const
 302 {
 303         exvector coeffseq;
 304         coeffseq.reserve(seq.size()+1);
 305
 306         if (n==0) {
 307                 // product of individual coeffs
 308                 // if a non-zero power of s is found, the resulting product will be 0
 309                 epvector::const_iterator it=seq.begin();
 310                 while (it!=seq.end()) {
 311                         coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 312                         ++it;
 313                 }
 314                 coeffseq.push_back(overall_coeff);
 315                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 316         }
 317
 318         epvector::const_iterator it=seq.begin();
 319         bool coeff_found=0;
 320         while (it!=seq.end()) {
 321                 ex t=recombine_pair_to_ex(*it);
 322                 ex c=t.coeff(s,n);
 323                 if (!c.is_zero()) {
 324                         coeffseq.push_back(c);
 325                         coeff_found=1;
 326                 } else {
 327                         coeffseq.push_back(t);
 328                 }
 329                 ++it;
 330         }
 331         if (coeff_found) {
 332                 coeffseq.push_back(overall_coeff);
 333                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 334         }
 335
 336         return _ex0();
 337 }
 338
 339 ex mul::eval(int level) const
 340 {
 341         // simplifications  *(...,x;0) -> 0
 342         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 343         //                  *(x;1) -> x
 344         //                  *(;c) -> c
 345
 346         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 347
 348         epvector * evaled_seqp=evalchildren(level);
 349         if (evaled_seqp!=0) {
 350                 // do more evaluation later
 351                 return (new mul(evaled_seqp,overall_coeff))->
 352                                    setflag(status_flags::dynallocated);
 353         }
 354
 355 #ifdef DO_GINAC_ASSERT
 356         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 357                 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 358                            (!(ex_to_numeric((*cit).coeff).is_integer())));
 359                 GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 360                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 361                         printtree(cerr,0);
 362                 }
 363                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 364                 /* for paranoia */
 365                 expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 366                 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 367                 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 368                 /* end paranoia */
 369         }
 370 #endif // def DO_GINAC_ASSERT
 371
 372         if (flags & status_flags::evaluated) {
 373                 GINAC_ASSERT(seq.size()>0);
 374                 GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 375                 return *this;
 376         }
 377
 378         int seq_size=seq.size();
 379         if (overall_coeff.is_equal(_ex0())) {
 380                 // *(...,x;0) -> 0
 381                 return _ex0();
 382         } else if (seq_size==0) {
 383                 // *(;c) -> c
 384                 return overall_coeff;
 385         } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 386                 // *(x;1) -> x
 387                 return recombine_pair_to_ex(*(seq.begin()));
 388         } else if ((seq_size==1) &&
 389                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 390                    ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 391                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 392                 const add & addref=ex_to_add((*seq.begin()).rest);
 393                 epvector distrseq;
 394                 distrseq.reserve(addref.seq.size());
 395                 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 396                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
 397                 }
 398                 return (new add(distrseq,
 399                                 ex_to_numeric(addref.overall_coeff).
 400                                 mul_dyn(ex_to_numeric(overall_coeff))))
 401                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 402         }
 403         return this->hold();
 404 }
 405
 406 ex mul::evalf(int level) const
 407 {
 408         if (level==1)
 409                 return mul(seq,overall_coeff);
 410
 411         if (level==-max_recursion_level)
 412                 throw(std::runtime_error("max recursion level reached"));
 413
 414         epvector s;
 415         s.reserve(seq.size());
 416
 417         --level;
 418         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 419                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
 420                                                           (*it).coeff));
 421         }
 422         return mul(s,overall_coeff.evalf(level));
 423 }
 424
 425 exvector mul::get_indices(void) const
 426 {
 427         // return union of indices of factors
 428         exvector iv;
 429         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 430                 exvector subiv=(*cit).rest.get_indices();
 431                 iv.reserve(iv.size()+subiv.size());
 432                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 433                         iv.push_back(*cit2);
 434                 }
 435         }
 436         return iv;
 437 }
 438
 439 ex mul::simplify_ncmul(const exvector & v) const
 440 {
 441         throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 442 }
 443
 444 // protected
 445
 446 /** Implementation of ex::diff() for a product.  It applies the product rule.
 447  *  @see ex::diff */
 448 ex mul::derivative(const symbol & s) const
 449 {
 450         exvector addseq;
 451         addseq.reserve(seq.size());
 452
 453         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 454         for (unsigned i=0; i!=seq.size(); ++i) {
 455                 epvector mulseq = seq;
 456                 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
 457                                              seq[i].rest.diff(s));
 458                 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
 459         }
 460         return (new add(addseq))->setflag(status_flags::dynallocated);
 461 }
 462
 463 int mul::compare_same_type(const basic & other) const
 464 {
 465         return inherited::compare_same_type(other);
 466 }
 467
 468 bool mul::is_equal_same_type(const basic & other) const
 469 {
 470         return inherited::is_equal_same_type(other);
 471 }
 472
 473 unsigned mul::return_type(void) const
 474 {
 475         if (seq.size()==0) {
 476                 // mul without factors: should not happen, but commutes
 477                 return return_types::commutative;
 478         }
 479
 480         bool all_commutative = 1;
 481         unsigned rt;
 482         epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 483
 484         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 485                 rt=(*cit).rest.return_type();
 486                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 487                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 488                         // first nc element found, remember position
 489                         cit_noncommutative_element = cit;
 490                         all_commutative = 0;
 491                 }
 492                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 493                         // another nc element found, compare type_infos
 494                         if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 495                                 // diffent types -> mul is ncc
 496                                 return return_types::noncommutative_composite;
 497                         }
 498                 }
 499         }
 500         // all factors checked
 501         return all_commutative ? return_types::commutative : return_types::noncommutative;
 502 }
 503
 504 unsigned mul::return_type_tinfo(void) const
 505 {
 506         if (seq.size()==0) {
 507                 // mul without factors: should not happen
 508                 return tinfo_key;
 509         }
 510         // return type_info of first noncommutative element
 511         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 512                 if ((*cit).rest.return_type()==return_types::noncommutative) {
 513                         return (*cit).rest.return_type_tinfo();
 514                 }
 515         }
 516         // no noncommutative element found, should not happen
 517         return tinfo_key;
 518 }
 519
 520 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 521 {
 522         return (new mul(v,oc))->setflag(status_flags::dynallocated);
 523 }
 524
 525 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 526 {
 527         return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 528 }
 529
 530 expair mul::split_ex_to_pair(const ex & e) const
 531 {
 532         if (is_ex_exactly_of_type(e,power)) {
 533                 const power & powerref=ex_to_power(e);
 534                 if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 535                         return expair(powerref.basis,powerref.exponent);
 536                 }
 537         }
 538         return expair(e,_ex1());
 539 }
 540
 541 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 542                                           const ex & c) const
 543 {
 544         // to avoid duplication of power simplification rules,
 545         // we create a temporary power object
 546         // otherwise it would be hard to correctly simplify
 547         // expression like (4^(1/3))^(3/2)
 548         if (are_ex_trivially_equal(c,_ex1()))
 549                 return split_ex_to_pair(e);
 550
 551         return split_ex_to_pair(power(e,c));
 552 }
 553
 554 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 555                                             const ex & c) const
 556 {
 557         // to avoid duplication of power simplification rules,
 558         // we create a temporary power object
 559         // otherwise it would be hard to correctly simplify
 560         // expression like (4^(1/3))^(3/2)
 561         if (are_ex_trivially_equal(c,_ex1()))
 562                 return p;
 563
 564         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 565 }
 566
 567 ex mul::recombine_pair_to_ex(const expair & p) const
 568 {
 569         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 570                 return p.rest;
 571         else
 572                 return power(p.rest,p.coeff);
 573 }
 574
 575 bool mul::expair_needs_further_processing(epp it)
 576 {
 577         if (is_ex_exactly_of_type((*it).rest,mul) &&
 578                 ex_to_numeric((*it).coeff).is_integer()) {
 579                 // combined pair is product with integer power -> expand it
 580                 *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 581                 return true;
 582         }
 583         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 584                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 585                 if (!ep.is_equal(*it)) {
 586                         // combined pair is a numeric power which can be simplified
 587                         *it=ep;
 588                         return true;
 589                 }
 590                 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 591                         // combined pair has coeff 1 and must be moved to the end
 592                         return true;
 593                 }
 594         }
 595         return false;
 596 }
 597
 598 ex mul::default_overall_coeff(void) const
 599 {
 600         return _ex1();
 601 }
 602
 603 void mul::combine_overall_coeff(const ex & c)
 604 {
 605         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 606         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 607         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 608 }
 609
 610 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 611 {
 612         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 613         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 614         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 615         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 616 }
 617
 618 bool mul::can_make_flat(const expair & p) const
 619 {
 620         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 621         // this assertion will probably fail somewhere
 622         // it would require a more careful make_flat, obeying the power laws
 623         // probably should return true only if p.coeff is integer
 624         return ex_to_numeric(p.coeff).is_equal(_num1());
 625 }
 626
 627 ex mul::expand(unsigned options) const
 628 {
 629         if (flags & status_flags::expanded)
 630                 return *this;
 631
 632         exvector sub_expanded_seq;
 633         intvector positions_of_adds;
 634
 635         epvector * expanded_seqp = expandchildren(options);
 636
 637         const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 638
 639         int number_of_adds = 0;
 640         epvector non_adds;
 641         non_adds.reserve(expanded_seq.size());
 642         epvector::const_iterator cit = expanded_seq.begin();
 643         epvector::const_iterator last = expanded_seq.end();
 644         ex last_expanded=_ex1();
 645         while (cit!=last) {
 646                 if (is_ex_exactly_of_type((*cit).rest,add) &&
 647                         ((*cit).coeff.is_equal(_ex1()))) {
 648                         ++number_of_adds;
 649                         if (is_ex_exactly_of_type(last_expanded,add)) {
 650                                 // expand adds
 651                                 const add & add1 = ex_to_add(last_expanded);
 652                                 const add & add2 = ex_to_add((*cit).rest);
 653                                 int n1 = add1.nops();
 654                                 int n2 = add2.nops();
 655                                 exvector distrseq;
 656                                 distrseq.reserve(n1*n2);
 657                                 for (int i1=0; i1<n1; ++i1) {
 658                                         for (int i2=0; i2<n2; ++i2) {
 659                                                 distrseq.push_back(add1.op(i1)*add2.op(i2));
 660                                         }
 661                                 }
 662                                 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
 663                         } else {
 664                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 665                                 last_expanded = (*cit).rest;
 666                         }
 667                 } else {
 668                         non_adds.push_back(*cit);
 669                 }
 670                 ++cit;
 671         }
 672
 673         if (is_ex_exactly_of_type(last_expanded,add)) {
 674                 add const & finaladd = ex_to_add(last_expanded);
 675                 exvector distrseq;
 676                 int n = finaladd.nops();
 677                 distrseq.reserve(n);
 678                 for (int i=0; i<n; ++i) {
 679                         epvector factors = non_adds;
 680                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 681                         distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
 682                 }
 683                 return ((new add(distrseq))->
 684                         setflag(status_flags::dynallocated | status_flags::expanded));
 685         }
 686         non_adds.push_back(split_ex_to_pair(last_expanded));
 687         return (new mul(non_adds,overall_coeff))->
 688                 setflag(status_flags::dynallocated | status_flags::expanded);
 689 }
 690
 691
 692 //////////
 693 // new virtual functions which can be overridden by derived classes
 694 //////////
 695
 696 // none
 697
 698 //////////
 699 // non-virtual functions in this class
 700 //////////
 701
 702 epvector * mul::expandchildren(unsigned options) const
 703 {
 704         epvector::const_iterator last = seq.end();
 705         epvector::const_iterator cit = seq.begin();
 706         while (cit!=last) {
 707                 const ex & factor = recombine_pair_to_ex(*cit);
 708                 const ex & expanded_factor = factor.expand(options);
 709                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 710
 711                         // something changed, copy seq, eval and return it
 712                         epvector *s=new epvector;
 713                         s->reserve(seq.size());
 714
 715                         // copy parts of seq which are known not to have changed
 716                         epvector::const_iterator cit2 = seq.begin();
 717                         while (cit2!=cit) {
 718                                 s->push_back(*cit2);
 719                                 ++cit2;
 720                         }
 721                         // copy first changed element
 722                         s->push_back(split_ex_to_pair(expanded_factor));
 723                         ++cit2;
 724                         // copy rest
 725                         while (cit2!=last) {
 726                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 727                                 ++cit2;
 728                         }
 729                         return s;
 730                 }
 731                 ++cit;
 732         }
 733
 734         return 0; // nothing has changed
 735 }
 736
 737 //////////
 738 // static member variables
 739 //////////
 740
 741 // protected
 742
 743 unsigned mul::precedence = 50;
 744
 745 #ifndef NO_NAMESPACE_GINAC
 746 } // namespace GiNaC
 747 #endif // ndef NO_NAMESPACE_GINAC