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 namespace GiNaC {
  34
  35 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  36
  37 //////////
  38 // default ctor, dctor, copy ctor assignment operator and helpers
  39 //////////
  40
  41 mul::mul()
  42 {
  43         debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT);
  44         tinfo_key = TINFO_mul;
  45 }
  46
  47 DEFAULT_COPY(mul)
  48 DEFAULT_DESTROY(mul)
  49
  50 //////////
  51 // other ctors
  52 //////////
  53
  54 // public
  55
  56 mul::mul(const ex & lh, const ex & rh)
  57 {
  58         debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT);
  59         tinfo_key = TINFO_mul;
  60         overall_coeff = _ex1();
  61         construct_from_2_ex(lh,rh);
  62         GINAC_ASSERT(is_canonical());
  63 }
  64
  65 mul::mul(const exvector & v)
  66 {
  67         debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT);
  68         tinfo_key = TINFO_mul;
  69         overall_coeff = _ex1();
  70         construct_from_exvector(v);
  71         GINAC_ASSERT(is_canonical());
  72 }
  73
  74 mul::mul(const epvector & v)
  75 {
  76         debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT);
  77         tinfo_key = TINFO_mul;
  78         overall_coeff = _ex1();
  79         construct_from_epvector(v);
  80         GINAC_ASSERT(is_canonical());
  81 }
  82
  83 mul::mul(const epvector & v, const ex & oc)
  84 {
  85         debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
  86         tinfo_key = TINFO_mul;
  87         overall_coeff = oc;
  88         construct_from_epvector(v);
  89         GINAC_ASSERT(is_canonical());
  90 }
  91
  92 mul::mul(epvector * vp, const ex & oc)
  93 {
  94         debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
  95         tinfo_key = TINFO_mul;
  96         GINAC_ASSERT(vp!=0);
  97         overall_coeff = oc;
  98         construct_from_epvector(*vp);
  99         delete vp;
 100         GINAC_ASSERT(is_canonical());
 101 }
 102
 103 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 104 {
 105         debugmsg("mul ctor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 106         tinfo_key = TINFO_mul;
 107         exvector factors;
 108         factors.reserve(3);
 109         factors.push_back(lh);
 110         factors.push_back(mh);
 111         factors.push_back(rh);
 112         overall_coeff = _ex1();
 113         construct_from_exvector(factors);
 114         GINAC_ASSERT(is_canonical());
 115 }
 116
 117 //////////
 118 // archiving
 119 //////////
 120
 121 DEFAULT_ARCHIVING(mul)
 122
 123 //////////
 124 // functions overriding virtual functions from bases classes
 125 //////////
 126
 127 // public
 128
 129 void mul::print(const print_context & c, unsigned level) const
 130 {
 131         debugmsg("mul print", LOGLEVEL_PRINT);
 132
 133         if (is_of_type(c, print_tree)) {
 134
 135                 inherited::print(c, level);
 136
 137         } else if (is_of_type(c, print_csrc)) {
 138
 139                 c.s << "(";
 140
 141                 if (!overall_coeff.is_equal(_ex1())) {
 142                         overall_coeff.bp->print(c, precedence);
 143                         c.s << "*";
 144                 }
 145
 146                 // Print arguments, separated by "*" or "/"
 147                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 148                 while (it != itend) {
 149
 150                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 151                         if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 152                                 if (is_of_type(c, print_csrc_cl_N))
 153                                         c.s << "recip(";
 154                                 else
 155                                         c.s << "1.0/";
 156                         }
 157
 158                         // If the exponent is 1 or -1, it is left out
 159                         if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 160                                 it->rest.print(c, precedence);
 161                         else {
 162                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 163                                 (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).print(c, level);
 164                         }
 165
 166                         // Separator is "/" for negative integer powers, "*" otherwise
 167                         ++it;
 168                         if (it != itend) {
 169                                 if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 170                                         c.s << "/";
 171                                 else
 172                                         c.s << "*";
 173                         }
 174                 }
 175
 176                 if (precedence <= level)
 177                         c.s << ")";
 178
 179         } else {
 180
 181                 if (precedence <= level) {
 182                         if (is_of_type(c, print_latex))
 183                                 c.s << "{(";
 184                         else
 185                                 c.s << "(";
 186                 }
 187
 188                 bool first = true;
 189
 190                 // First print the overall numeric coefficient
 191                 numeric coeff = ex_to_numeric(overall_coeff);
 192                 if (coeff.csgn() == -1)
 193                         c.s << '-';
 194                 if (!coeff.is_equal(_num1()) &&
 195                         !coeff.is_equal(_num_1())) {
 196                         if (coeff.is_rational()) {
 197                                 if (coeff.is_negative())
 198                                         (-coeff).print(c);
 199                                 else
 200                                         coeff.print(c);
 201                         } else {
 202                                 if (coeff.csgn() == -1)
 203                                         (-coeff).print(c, precedence);
 204                                 else
 205                                         coeff.print(c, precedence);
 206                         }
 207                         if (is_of_type(c, print_latex))
 208                                 c.s << ' ';
 209                         else
 210                                 c.s << '*';
 211                 }
 212
 213                 // Then proceed with the remaining factors
 214                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 215                 while (it != itend) {
 216                         if (!first) {
 217                                 if (is_of_type(c, print_latex))
 218                                         c.s << ' ';
 219                                 else
 220                                         c.s << '*';
 221                         } else {
 222                                 first = false;
 223                         }
 224                         recombine_pair_to_ex(*it).print(c, precedence);
 225                         it++;
 226                 }
 227
 228                 if (precedence <= level) {
 229                         if (is_of_type(c, print_latex))
 230                                 c.s << ")}";
 231                         else
 232                                 c.s << ")";
 233                 }
 234         }
 235 }
 236
 237 bool mul::info(unsigned inf) const
 238 {
 239         switch (inf) {
 240                 case info_flags::polynomial:
 241                 case info_flags::integer_polynomial:
 242                 case info_flags::cinteger_polynomial:
 243                 case info_flags::rational_polynomial:
 244                 case info_flags::crational_polynomial:
 245                 case info_flags::rational_function: {
 246                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 247                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 248                                         return false;
 249                         }
 250                         return overall_coeff.info(inf);
 251                 }
 252                 case info_flags::algebraic: {
 253                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 254                                 if ((recombine_pair_to_ex(*i).info(inf)))
 255                                         return true;
 256                         }
 257                         return false;
 258                 }
 259         }
 260         return inherited::info(inf);
 261 }
 262
 263 int mul::degree(const ex & s) const
 264 {
 265         int deg_sum = 0;
 266         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 267                 if (ex_to_numeric(cit->coeff).is_integer())
 268                         deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
 269         }
 270         return deg_sum;
 271 }
 272
 273 int mul::ldegree(const ex & s) const
 274 {
 275         int deg_sum = 0;
 276         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 277                 if (ex_to_numeric(cit->coeff).is_integer())
 278                         deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
 279         }
 280         return deg_sum;
 281 }
 282
 283 ex mul::coeff(const ex & s, int n) const
 284 {
 285         exvector coeffseq;
 286         coeffseq.reserve(seq.size()+1);
 287
 288         if (n==0) {
 289                 // product of individual coeffs
 290                 // if a non-zero power of s is found, the resulting product will be 0
 291                 epvector::const_iterator it = seq.begin();
 292                 while (it!=seq.end()) {
 293                         coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 294                         ++it;
 295                 }
 296                 coeffseq.push_back(overall_coeff);
 297                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 298         }
 299
 300         epvector::const_iterator it=seq.begin();
 301         bool coeff_found = 0;
 302         while (it!=seq.end()) {
 303                 ex t = recombine_pair_to_ex(*it);
 304                 ex c = t.coeff(s,n);
 305                 if (!c.is_zero()) {
 306                         coeffseq.push_back(c);
 307                         coeff_found = 1;
 308                 } else {
 309                         coeffseq.push_back(t);
 310                 }
 311                 ++it;
 312         }
 313         if (coeff_found) {
 314                 coeffseq.push_back(overall_coeff);
 315                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 316         }
 317
 318         return _ex0();
 319 }
 320
 321 ex mul::eval(int level) const
 322 {
 323         // simplifications  *(...,x;0) -> 0
 324         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 325         //                  *(x;1) -> x
 326         //                  *(;c) -> c
 327
 328         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 329
 330         epvector * evaled_seqp = evalchildren(level);
 331         if (evaled_seqp!=0) {
 332                 // do more evaluation later
 333                 return (new mul(evaled_seqp,overall_coeff))->
 334                            setflag(status_flags::dynallocated);
 335         }
 336
 337 #ifdef DO_GINAC_ASSERT
 338         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 339                 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul)) ||
 340                              (!(ex_to_numeric((*cit).coeff).is_integer())));
 341                 GINAC_ASSERT(!(cit->is_canonical_numeric()));
 342                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric))
 343                     print(print_tree(std::cerr));
 344                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 345                 /* for paranoia */
 346                 expair p = split_ex_to_pair(recombine_pair_to_ex(*cit));
 347                 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 348                 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 349                 /* end paranoia */
 350         }
 351 #endif // def DO_GINAC_ASSERT
 352
 353         if (flags & status_flags::evaluated) {
 354                 GINAC_ASSERT(seq.size()>0);
 355                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1()));
 356                 return *this;
 357         }
 358
 359         int seq_size = seq.size();
 360         if (overall_coeff.is_equal(_ex0())) {
 361                 // *(...,x;0) -> 0
 362                 return _ex0();
 363         } else if (seq_size==0) {
 364                 // *(;c) -> c
 365                 return overall_coeff;
 366         } else if (seq_size==1 && overall_coeff.is_equal(_ex1())) {
 367                 // *(x;1) -> x
 368                 return recombine_pair_to_ex(*(seq.begin()));
 369         } else if ((seq_size==1) &&
 370                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 371                    ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 372                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 373                 const add & addref = ex_to_add((*seq.begin()).rest);
 374                 epvector distrseq;
 375                 distrseq.reserve(addref.seq.size());
 376                 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 377                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
 378                 }
 379                 return (new add(distrseq,
 380                                 ex_to_numeric(addref.overall_coeff).
 381                                 mul_dyn(ex_to_numeric(overall_coeff))))
 382                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 383         }
 384         return this->hold();
 385 }
 386
 387 ex mul::evalf(int level) const
 388 {
 389         if (level==1)
 390                 return mul(seq,overall_coeff);
 391
 392         if (level==-max_recursion_level)
 393                 throw(std::runtime_error("max recursion level reached"));
 394
 395         epvector s;
 396         s.reserve(seq.size());
 397
 398         --level;
 399         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 400                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
 401                                                           (*it).coeff));
 402         }
 403         return mul(s,overall_coeff.evalf(level));
 404 }
 405
 406 ex mul::simplify_ncmul(const exvector & v) const
 407 {
 408         if (seq.size()==0) {
 409                 return inherited::simplify_ncmul(v);
 410         }
 411
 412         // Find first noncommutative element and call its simplify_ncmul()
 413         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 414                 if (cit->rest.return_type() == return_types::noncommutative)
 415                         return cit->rest.simplify_ncmul(v);
 416         }
 417         return inherited::simplify_ncmul(v);
 418 }
 419
 420 // protected
 421
 422 /** Implementation of ex::diff() for a product.  It applies the product rule.
 423  *  @see ex::diff */
 424 ex mul::derivative(const symbol & s) const
 425 {
 426         exvector addseq;
 427         addseq.reserve(seq.size());
 428
 429         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 430         for (unsigned i=0; i!=seq.size(); ++i) {
 431                 epvector mulseq = seq;
 432                 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
 433                                              seq[i].rest.diff(s));
 434                 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
 435         }
 436         return (new add(addseq))->setflag(status_flags::dynallocated);
 437 }
 438
 439 int mul::compare_same_type(const basic & other) const
 440 {
 441         return inherited::compare_same_type(other);
 442 }
 443
 444 bool mul::is_equal_same_type(const basic & other) const
 445 {
 446         return inherited::is_equal_same_type(other);
 447 }
 448
 449 unsigned mul::return_type(void) const
 450 {
 451         if (seq.size()==0) {
 452                 // mul without factors: should not happen, but commutes
 453                 return return_types::commutative;
 454         }
 455
 456         bool all_commutative = 1;
 457         unsigned rt;
 458         epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 459
 460         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 461                 rt=(*cit).rest.return_type();
 462                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 463                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 464                         // first nc element found, remember position
 465                         cit_noncommutative_element = cit;
 466                         all_commutative = 0;
 467                 }
 468                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 469                         // another nc element found, compare type_infos
 470                         if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 471                                 // diffent types -> mul is ncc
 472                                 return return_types::noncommutative_composite;
 473                         }
 474                 }
 475         }
 476         // all factors checked
 477         return all_commutative ? return_types::commutative : return_types::noncommutative;
 478 }
 479
 480 unsigned mul::return_type_tinfo(void) const
 481 {
 482         if (seq.size()==0)
 483                 return tinfo_key;  // mul without factors: should not happen
 484
 485         // return type_info of first noncommutative element
 486         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 487                 if ((*cit).rest.return_type()==return_types::noncommutative)
 488                         return (*cit).rest.return_type_tinfo();
 489         }
 490         // no noncommutative element found, should not happen
 491         return tinfo_key;
 492 }
 493
 494 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 495 {
 496         return (new mul(v,oc))->setflag(status_flags::dynallocated);
 497 }
 498
 499 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 500 {
 501         return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 502 }
 503
 504 expair mul::split_ex_to_pair(const ex & e) const
 505 {
 506         if (is_ex_exactly_of_type(e,power)) {
 507                 const power & powerref = ex_to_power(e);
 508                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 509                         return expair(powerref.basis,powerref.exponent);
 510         }
 511         return expair(e,_ex1());
 512 }
 513
 514 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 515                                           const ex & c) const
 516 {
 517         // to avoid duplication of power simplification rules,
 518         // we create a temporary power object
 519         // otherwise it would be hard to correctly simplify
 520         // expression like (4^(1/3))^(3/2)
 521         if (are_ex_trivially_equal(c,_ex1()))
 522                 return split_ex_to_pair(e);
 523
 524         return split_ex_to_pair(power(e,c));
 525 }
 526
 527 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 528                                             const ex & c) const
 529 {
 530         // to avoid duplication of power simplification rules,
 531         // we create a temporary power object
 532         // otherwise it would be hard to correctly simplify
 533         // expression like (4^(1/3))^(3/2)
 534         if (are_ex_trivially_equal(c,_ex1()))
 535                 return p;
 536
 537         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 538 }
 539
 540 ex mul::recombine_pair_to_ex(const expair & p) const
 541 {
 542         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 543                 return p.rest;
 544         else
 545                 return power(p.rest,p.coeff);
 546 }
 547
 548 bool mul::expair_needs_further_processing(epp it)
 549 {
 550         if (is_ex_exactly_of_type((*it).rest,mul) &&
 551                 ex_to_numeric((*it).coeff).is_integer()) {
 552                 // combined pair is product with integer power -> expand it
 553                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 554                 return true;
 555         }
 556         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 557                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 558                 if (!ep.is_equal(*it)) {
 559                         // combined pair is a numeric power which can be simplified
 560                         *it = ep;
 561                         return true;
 562                 }
 563                 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 564                         // combined pair has coeff 1 and must be moved to the end
 565                         return true;
 566                 }
 567         }
 568         return false;
 569 }
 570
 571 ex mul::default_overall_coeff(void) const
 572 {
 573         return _ex1();
 574 }
 575
 576 void mul::combine_overall_coeff(const ex & c)
 577 {
 578         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 579         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 580         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 581 }
 582
 583 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 584 {
 585         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 586         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 587         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 588         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 589 }
 590
 591 bool mul::can_make_flat(const expair & p) const
 592 {
 593         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 594         // this assertion will probably fail somewhere
 595         // it would require a more careful make_flat, obeying the power laws
 596         // probably should return true only if p.coeff is integer
 597         return ex_to_numeric(p.coeff).is_equal(_num1());
 598 }
 599
 600 ex mul::expand(unsigned options) const
 601 {
 602         if (flags & status_flags::expanded)
 603                 return *this;
 604
 605         exvector sub_expanded_seq;
 606
 607         epvector * expanded_seqp = expandchildren(options);
 608
 609         const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 610
 611         int number_of_adds = 0;
 612         epvector non_adds;
 613         non_adds.reserve(expanded_seq.size());
 614         epvector::const_iterator cit = expanded_seq.begin();
 615         epvector::const_iterator last = expanded_seq.end();
 616         ex last_expanded = _ex1();
 617         while (cit!=last) {
 618                 if (is_ex_exactly_of_type((*cit).rest,add) &&
 619                         ((*cit).coeff.is_equal(_ex1()))) {
 620                         ++number_of_adds;
 621                         if (is_ex_exactly_of_type(last_expanded,add)) {
 622                                 // expand adds
 623                                 const add & add1 = ex_to_add(last_expanded);
 624                                 const add & add2 = ex_to_add((*cit).rest);
 625                                 int n1 = add1.nops();
 626                                 int n2 = add2.nops();
 627                                 exvector distrseq;
 628                                 distrseq.reserve(n1*n2);
 629                                 for (int i1=0; i1<n1; ++i1) {
 630                                         for (int i2=0; i2<n2; ++i2) {
 631                                                 distrseq.push_back(add1.op(i1)*add2.op(i2));
 632                                         }
 633                                 }
 634                                 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
 635                         } else {
 636                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 637                                 last_expanded = (*cit).rest;
 638                         }
 639                 } else {
 640                         non_adds.push_back(*cit);
 641                 }
 642                 ++cit;
 643         }
 644         if (expanded_seqp)
 645                 delete expanded_seqp;
 646
 647         if (is_ex_exactly_of_type(last_expanded,add)) {
 648                 add const & finaladd = ex_to_add(last_expanded);
 649                 exvector distrseq;
 650                 int n = finaladd.nops();
 651                 distrseq.reserve(n);
 652                 for (int i=0; i<n; ++i) {
 653                         epvector factors = non_adds;
 654                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 655                         distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
 656                 }
 657                 return ((new add(distrseq))->
 658                         setflag(status_flags::dynallocated | status_flags::expanded));
 659         }
 660         non_adds.push_back(split_ex_to_pair(last_expanded));
 661         return (new mul(non_adds,overall_coeff))->
 662                 setflag(status_flags::dynallocated | status_flags::expanded);
 663 }
 664
 665
 666 //////////
 667 // new virtual functions which can be overridden by derived classes
 668 //////////
 669
 670 // none
 671
 672 //////////
 673 // non-virtual functions in this class
 674 //////////
 675
 676
 677 /** Member-wise expand the expairs representing this sequence.  This must be
 678  *  overridden from expairseq::expandchildren() and done iteratively in order
 679  *  to allow for early cancallations and thus safe memory.
 680  *
 681  *  @see mul::expand()
 682  *  @return pointer to epvector containing expanded representation or zero
 683  *  pointer, if sequence is unchanged. */
 684 epvector * mul::expandchildren(unsigned options) const
 685 {
 686         epvector::const_iterator last = seq.end();
 687         epvector::const_iterator cit = seq.begin();
 688         while (cit!=last) {
 689                 const ex & factor = recombine_pair_to_ex(*cit);
 690                 const ex & expanded_factor = factor.expand(options);
 691                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 692
 693                         // something changed, copy seq, eval and return it
 694                         epvector *s = new epvector;
 695                         s->reserve(seq.size());
 696
 697                         // copy parts of seq which are known not to have changed
 698                         epvector::const_iterator cit2 = seq.begin();
 699                         while (cit2!=cit) {
 700                                 s->push_back(*cit2);
 701                                 ++cit2;
 702                         }
 703                         // copy first changed element
 704                         s->push_back(split_ex_to_pair(expanded_factor));
 705                         ++cit2;
 706                         // copy rest
 707                         while (cit2!=last) {
 708                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 709                                 ++cit2;
 710                         }
 711                         return s;
 712                 }
 713                 ++cit;
 714         }
 715
 716         return 0; // nothing has changed
 717 }
 718
 719 //////////
 720 // static member variables
 721 //////////
 722
 723 // protected
 724
 725 unsigned mul::precedence = 50;
 726
 727 } // namespace GiNaC