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