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