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 "matrix.h"
  30 #include "archive.h"
  31 #include "debugmsg.h"
  32 #include "utils.h"
  33
  34 namespace GiNaC {
  35
  36 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  37
  38 //////////
  39 // default ctor, dctor, copy ctor assignment operator and helpers
  40 //////////
  41
  42 mul::mul()
  43 {
  44         debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT);
  45         tinfo_key = TINFO_mul;
  46 }
  47
  48 DEFAULT_COPY(mul)
  49 DEFAULT_DESTROY(mul)
  50
  51 //////////
  52 // other ctors
  53 //////////
  54
  55 // public
  56
  57 mul::mul(const ex & lh, const ex & rh)
  58 {
  59         debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT);
  60         tinfo_key = TINFO_mul;
  61         overall_coeff = _ex1();
  62         construct_from_2_ex(lh,rh);
  63         GINAC_ASSERT(is_canonical());
  64 }
  65
  66 mul::mul(const exvector & v)
  67 {
  68         debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT);
  69         tinfo_key = TINFO_mul;
  70         overall_coeff = _ex1();
  71         construct_from_exvector(v);
  72         GINAC_ASSERT(is_canonical());
  73 }
  74
  75 mul::mul(const epvector & v)
  76 {
  77         debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT);
  78         tinfo_key = TINFO_mul;
  79         overall_coeff = _ex1();
  80         construct_from_epvector(v);
  81         GINAC_ASSERT(is_canonical());
  82 }
  83
  84 mul::mul(const epvector & v, const ex & oc)
  85 {
  86         debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
  87         tinfo_key = TINFO_mul;
  88         overall_coeff = oc;
  89         construct_from_epvector(v);
  90         GINAC_ASSERT(is_canonical());
  91 }
  92
  93 mul::mul(epvector * vp, const ex & oc)
  94 {
  95         debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
  96         tinfo_key = TINFO_mul;
  97         GINAC_ASSERT(vp!=0);
  98         overall_coeff = oc;
  99         construct_from_epvector(*vp);
 100         delete vp;
 101         GINAC_ASSERT(is_canonical());
 102 }
 103
 104 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 105 {
 106         debugmsg("mul ctor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 107         tinfo_key = TINFO_mul;
 108         exvector factors;
 109         factors.reserve(3);
 110         factors.push_back(lh);
 111         factors.push_back(mh);
 112         factors.push_back(rh);
 113         overall_coeff = _ex1();
 114         construct_from_exvector(factors);
 115         GINAC_ASSERT(is_canonical());
 116 }
 117
 118 //////////
 119 // archiving
 120 //////////
 121
 122 DEFAULT_ARCHIVING(mul)
 123
 124 //////////
 125 // functions overriding virtual functions from bases classes
 126 //////////
 127
 128 // public
 129
 130 void mul::print(const print_context & c, unsigned level) const
 131 {
 132         debugmsg("mul print", LOGLEVEL_PRINT);
 133
 134         if (is_of_type(c, print_tree)) {
 135
 136                 inherited::print(c, level);
 137
 138         } else if (is_of_type(c, print_csrc)) {
 139
 140                 if (precedence() <= level)
 141                         c.s << "(";
 142
 143                 if (!overall_coeff.is_equal(_ex1())) {
 144                         overall_coeff.bp->print(c, precedence());
 145                         c.s << "*";
 146                 }
 147
 148                 // Print arguments, separated by "*" or "/"
 149                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 150                 while (it != itend) {
 151
 152                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 153                         if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 154                                 if (is_of_type(c, print_csrc_cl_N))
 155                                         c.s << "recip(";
 156                                 else
 157                                         c.s << "1.0/";
 158                         }
 159
 160                         // If the exponent is 1 or -1, it is left out
 161                         if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 162                                 it->rest.print(c, precedence());
 163                         else {
 164                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 165                                 (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).print(c, level);
 166                         }
 167
 168                         // Separator is "/" for negative integer powers, "*" otherwise
 169                         ++it;
 170                         if (it != itend) {
 171                                 if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 172                                         c.s << "/";
 173                                 else
 174                                         c.s << "*";
 175                         }
 176                 }
 177
 178                 if (precedence() <= level)
 179                         c.s << ")";
 180
 181         } else {
 182
 183                 if (precedence() <= level) {
 184                         if (is_of_type(c, print_latex))
 185                                 c.s << "{(";
 186                         else
 187                                 c.s << "(";
 188                 }
 189
 190                 bool first = true;
 191
 192                 // First print the overall numeric coefficient
 193                 numeric coeff = ex_to_numeric(overall_coeff);
 194                 if (coeff.csgn() == -1)
 195                         c.s << '-';
 196                 if (!coeff.is_equal(_num1()) &&
 197                         !coeff.is_equal(_num_1())) {
 198                         if (coeff.is_rational()) {
 199                                 if (coeff.is_negative())
 200                                         (-coeff).print(c);
 201                                 else
 202                                         coeff.print(c);
 203                         } else {
 204                                 if (coeff.csgn() == -1)
 205                                         (-coeff).print(c, precedence());
 206                                 else
 207                                         coeff.print(c, precedence());
 208                         }
 209                         if (is_of_type(c, print_latex))
 210                                 c.s << ' ';
 211                         else
 212                                 c.s << '*';
 213                 }
 214
 215                 // Then proceed with the remaining factors
 216                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 217                 while (it != itend) {
 218                         if (!first) {
 219                                 if (is_of_type(c, print_latex))
 220                                         c.s << ' ';
 221                                 else
 222                                         c.s << '*';
 223                         } else {
 224                                 first = false;
 225                         }
 226                         recombine_pair_to_ex(*it).print(c, precedence());
 227                         it++;
 228                 }
 229
 230                 if (precedence() <= level) {
 231                         if (is_of_type(c, print_latex))
 232                                 c.s << ")}";
 233                         else
 234                                 c.s << ")";
 235                 }
 236         }
 237 }
 238
 239 bool mul::info(unsigned inf) const
 240 {
 241         switch (inf) {
 242                 case info_flags::polynomial:
 243                 case info_flags::integer_polynomial:
 244                 case info_flags::cinteger_polynomial:
 245                 case info_flags::rational_polynomial:
 246                 case info_flags::crational_polynomial:
 247                 case info_flags::rational_function: {
 248                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 249                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 250                                         return false;
 251                         }
 252                         return overall_coeff.info(inf);
 253                 }
 254                 case info_flags::algebraic: {
 255                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 256                                 if ((recombine_pair_to_ex(*i).info(inf)))
 257                                         return true;
 258                         }
 259                         return false;
 260                 }
 261         }
 262         return inherited::info(inf);
 263 }
 264
 265 int mul::degree(const ex & s) const
 266 {
 267         int deg_sum = 0;
 268         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 269                 if (ex_to_numeric(cit->coeff).is_integer())
 270                         deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
 271         }
 272         return deg_sum;
 273 }
 274
 275 int mul::ldegree(const ex & s) const
 276 {
 277         int deg_sum = 0;
 278         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 279                 if (ex_to_numeric(cit->coeff).is_integer())
 280                         deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
 281         }
 282         return deg_sum;
 283 }
 284
 285 ex mul::coeff(const ex & s, int n) const
 286 {
 287         exvector coeffseq;
 288         coeffseq.reserve(seq.size()+1);
 289
 290         if (n==0) {
 291                 // product of individual coeffs
 292                 // if a non-zero power of s is found, the resulting product will be 0
 293                 epvector::const_iterator it = seq.begin();
 294                 while (it!=seq.end()) {
 295                         coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 296                         ++it;
 297                 }
 298                 coeffseq.push_back(overall_coeff);
 299                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 300         }
 301
 302         epvector::const_iterator it=seq.begin();
 303         bool coeff_found = 0;
 304         while (it!=seq.end()) {
 305                 ex t = recombine_pair_to_ex(*it);
 306                 ex c = t.coeff(s,n);
 307                 if (!c.is_zero()) {
 308                         coeffseq.push_back(c);
 309                         coeff_found = 1;
 310                 } else {
 311                         coeffseq.push_back(t);
 312                 }
 313                 ++it;
 314         }
 315         if (coeff_found) {
 316                 coeffseq.push_back(overall_coeff);
 317                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 318         }
 319
 320         return _ex0();
 321 }
 322
 323 ex mul::eval(int level) const
 324 {
 325         // simplifications  *(...,x;0) -> 0
 326         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 327         //                  *(x;1) -> x
 328         //                  *(;c) -> c
 329
 330         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 331
 332         epvector * evaled_seqp = evalchildren(level);
 333         if (evaled_seqp!=0) {
 334                 // do more evaluation later
 335                 return (new mul(evaled_seqp,overall_coeff))->
 336                            setflag(status_flags::dynallocated);
 337         }
 338
 339 #ifdef DO_GINAC_ASSERT
 340         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 341                 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul)) ||
 342                              (!(ex_to_numeric((*cit).coeff).is_integer())));
 343                 GINAC_ASSERT(!(cit->is_canonical_numeric()));
 344                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric))
 345                     print(print_tree(std::cerr));
 346                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 347                 /* for paranoia */
 348                 expair p = split_ex_to_pair(recombine_pair_to_ex(*cit));
 349                 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 350                 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 351                 /* end paranoia */
 352         }
 353 #endif // def DO_GINAC_ASSERT
 354
 355         if (flags & status_flags::evaluated) {
 356                 GINAC_ASSERT(seq.size()>0);
 357                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1()));
 358                 return *this;
 359         }
 360
 361         int seq_size = seq.size();
 362         if (overall_coeff.is_equal(_ex0())) {
 363                 // *(...,x;0) -> 0
 364                 return _ex0();
 365         } else if (seq_size==0) {
 366                 // *(;c) -> c
 367                 return overall_coeff;
 368         } else if (seq_size==1 && overall_coeff.is_equal(_ex1())) {
 369                 // *(x;1) -> x
 370                 return recombine_pair_to_ex(*(seq.begin()));
 371         } else if ((seq_size==1) &&
 372                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 373                    ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 374                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 375                 const add & addref = ex_to_add((*seq.begin()).rest);
 376                 epvector distrseq;
 377                 distrseq.reserve(addref.seq.size());
 378                 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 379                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
 380                 }
 381                 return (new add(distrseq,
 382                                 ex_to_numeric(addref.overall_coeff).
 383                                 mul_dyn(ex_to_numeric(overall_coeff))))
 384                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 385         }
 386         return this->hold();
 387 }
 388
 389 ex mul::evalf(int level) const
 390 {
 391         if (level==1)
 392                 return mul(seq,overall_coeff);
 393
 394         if (level==-max_recursion_level)
 395                 throw(std::runtime_error("max recursion level reached"));
 396
 397         epvector s;
 398         s.reserve(seq.size());
 399
 400         --level;
 401         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 402                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
 403                                                           (*it).coeff));
 404         }
 405         return mul(s,overall_coeff.evalf(level));
 406 }
 407
 408 ex mul::evalm(void) const
 409 {
 410         // numeric*matrix
 411         if (seq.size() == 1 && is_ex_of_type(seq[0].rest, matrix))
 412                 return ex_to_matrix(seq[0].rest).mul(ex_to_numeric(overall_coeff));
 413
 414         // Evaluate children first, look whether there are any matrices at all
 415         // (there can be either no matrices or one matrix; if there were more
 416         // than one matrix, it would be a non-commutative product)
 417         epvector *s = new epvector;
 418         s->reserve(seq.size());
 419
 420         bool have_matrix = false;
 421         epvector::iterator the_matrix;
 422
 423         epvector::const_iterator it = seq.begin(), itend = seq.end();
 424         while (it != itend) {
 425                 const ex &m = recombine_pair_to_ex(*it).evalm();
 426                 s->push_back(split_ex_to_pair(m));
 427                 if (is_ex_of_type(m, matrix)) {
 428                         have_matrix = true;
 429                         the_matrix = s->end() - 1;
 430                 }
 431                 it++;
 432         }
 433
 434         if (have_matrix) {
 435
 436                 // The product contained a matrix. We will multiply all other factors
 437                 // into that matrix.
 438                 matrix m = ex_to_matrix(the_matrix->rest);
 439                 s->erase(the_matrix);
 440                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 441                 return m.mul_scalar(scalar);
 442
 443         } else
 444                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 445 }
 446
 447 ex mul::simplify_ncmul(const exvector & v) const
 448 {
 449         if (seq.size()==0) {
 450                 return inherited::simplify_ncmul(v);
 451         }
 452
 453         // Find first noncommutative element and call its simplify_ncmul()
 454         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 455                 if (cit->rest.return_type() == return_types::noncommutative)
 456                         return cit->rest.simplify_ncmul(v);
 457         }
 458         return inherited::simplify_ncmul(v);
 459 }
 460
 461 // protected
 462
 463 /** Implementation of ex::diff() for a product.  It applies the product rule.
 464  *  @see ex::diff */
 465 ex mul::derivative(const symbol & s) const
 466 {
 467         exvector addseq;
 468         addseq.reserve(seq.size());
 469
 470         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 471         for (unsigned i=0; i!=seq.size(); ++i) {
 472                 epvector mulseq = seq;
 473                 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
 474                                              seq[i].rest.diff(s));
 475                 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
 476         }
 477         return (new add(addseq))->setflag(status_flags::dynallocated);
 478 }
 479
 480 int mul::compare_same_type(const basic & other) const
 481 {
 482         return inherited::compare_same_type(other);
 483 }
 484
 485 bool mul::is_equal_same_type(const basic & other) const
 486 {
 487         return inherited::is_equal_same_type(other);
 488 }
 489
 490 unsigned mul::return_type(void) const
 491 {
 492         if (seq.size()==0) {
 493                 // mul without factors: should not happen, but commutes
 494                 return return_types::commutative;
 495         }
 496
 497         bool all_commutative = 1;
 498         unsigned rt;
 499         epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 500
 501         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 502                 rt=(*cit).rest.return_type();
 503                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 504                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 505                         // first nc element found, remember position
 506                         cit_noncommutative_element = cit;
 507                         all_commutative = 0;
 508                 }
 509                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 510                         // another nc element found, compare type_infos
 511                         if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 512                                 // diffent types -> mul is ncc
 513                                 return return_types::noncommutative_composite;
 514                         }
 515                 }
 516         }
 517         // all factors checked
 518         return all_commutative ? return_types::commutative : return_types::noncommutative;
 519 }
 520
 521 unsigned mul::return_type_tinfo(void) const
 522 {
 523         if (seq.size()==0)
 524                 return tinfo_key;  // mul without factors: should not happen
 525
 526         // return type_info of first noncommutative element
 527         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 528                 if ((*cit).rest.return_type()==return_types::noncommutative)
 529                         return (*cit).rest.return_type_tinfo();
 530         }
 531         // no noncommutative element found, should not happen
 532         return tinfo_key;
 533 }
 534
 535 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 536 {
 537         return (new mul(v,oc))->setflag(status_flags::dynallocated);
 538 }
 539
 540 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 541 {
 542         return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 543 }
 544
 545 expair mul::split_ex_to_pair(const ex & e) const
 546 {
 547         if (is_ex_exactly_of_type(e,power)) {
 548                 const power & powerref = ex_to_power(e);
 549                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 550                         return expair(powerref.basis,powerref.exponent);
 551         }
 552         return expair(e,_ex1());
 553 }
 554
 555 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 556                                           const ex & c) const
 557 {
 558         // to avoid duplication of power simplification rules,
 559         // we create a temporary power object
 560         // otherwise it would be hard to correctly simplify
 561         // expression like (4^(1/3))^(3/2)
 562         if (are_ex_trivially_equal(c,_ex1()))
 563                 return split_ex_to_pair(e);
 564
 565         return split_ex_to_pair(power(e,c));
 566 }
 567
 568 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 569                                             const ex & c) const
 570 {
 571         // to avoid duplication of power simplification rules,
 572         // we create a temporary power object
 573         // otherwise it would be hard to correctly simplify
 574         // expression like (4^(1/3))^(3/2)
 575         if (are_ex_trivially_equal(c,_ex1()))
 576                 return p;
 577
 578         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 579 }
 580
 581 ex mul::recombine_pair_to_ex(const expair & p) const
 582 {
 583         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 584                 return p.rest;
 585         else
 586                 return power(p.rest,p.coeff);
 587 }
 588
 589 bool mul::expair_needs_further_processing(epp it)
 590 {
 591         if (is_ex_exactly_of_type((*it).rest,mul) &&
 592                 ex_to_numeric((*it).coeff).is_integer()) {
 593                 // combined pair is product with integer power -> expand it
 594                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 595                 return true;
 596         }
 597         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 598                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 599                 if (!ep.is_equal(*it)) {
 600                         // combined pair is a numeric power which can be simplified
 601                         *it = ep;
 602                         return true;
 603                 }
 604                 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 605                         // combined pair has coeff 1 and must be moved to the end
 606                         return true;
 607                 }
 608         }
 609         return false;
 610 }
 611
 612 ex mul::default_overall_coeff(void) const
 613 {
 614         return _ex1();
 615 }
 616
 617 void mul::combine_overall_coeff(const ex & c)
 618 {
 619         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 620         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 621         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 622 }
 623
 624 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 625 {
 626         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 627         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 628         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 629         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 630 }
 631
 632 bool mul::can_make_flat(const expair & p) const
 633 {
 634         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 635         // this assertion will probably fail somewhere
 636         // it would require a more careful make_flat, obeying the power laws
 637         // probably should return true only if p.coeff is integer
 638         return ex_to_numeric(p.coeff).is_equal(_num1());
 639 }
 640
 641 ex mul::expand(unsigned options) const
 642 {
 643         if (flags & status_flags::expanded)
 644                 return *this;
 645
 646         exvector sub_expanded_seq;
 647
 648         epvector * expanded_seqp = expandchildren(options);
 649
 650         const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 651
 652         int number_of_adds = 0;
 653         epvector non_adds;
 654         non_adds.reserve(expanded_seq.size());
 655         epvector::const_iterator cit = expanded_seq.begin();
 656         epvector::const_iterator last = expanded_seq.end();
 657         ex last_expanded = _ex1();
 658         while (cit!=last) {
 659                 if (is_ex_exactly_of_type((*cit).rest,add) &&
 660                         ((*cit).coeff.is_equal(_ex1()))) {
 661                         ++number_of_adds;
 662                         if (is_ex_exactly_of_type(last_expanded,add)) {
 663                                 // expand adds
 664                                 const add & add1 = ex_to_add(last_expanded);
 665                                 const add & add2 = ex_to_add((*cit).rest);
 666                                 int n1 = add1.nops();
 667                                 int n2 = add2.nops();
 668                                 exvector distrseq;
 669                                 distrseq.reserve(n1*n2);
 670                                 for (int i1=0; i1<n1; ++i1) {
 671                                         for (int i2=0; i2<n2; ++i2) {
 672                                                 distrseq.push_back(add1.op(i1)*add2.op(i2));
 673                                         }
 674                                 }
 675                                 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
 676                         } else {
 677                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 678                                 last_expanded = (*cit).rest;
 679                         }
 680                 } else {
 681                         non_adds.push_back(*cit);
 682                 }
 683                 ++cit;
 684         }
 685         if (expanded_seqp)
 686                 delete expanded_seqp;
 687
 688         if (is_ex_exactly_of_type(last_expanded,add)) {
 689                 add const & finaladd = ex_to_add(last_expanded);
 690                 exvector distrseq;
 691                 int n = finaladd.nops();
 692                 distrseq.reserve(n);
 693                 for (int i=0; i<n; ++i) {
 694                         epvector factors = non_adds;
 695                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 696                         distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
 697                 }
 698                 return ((new add(distrseq))->
 699                         setflag(status_flags::dynallocated | status_flags::expanded));
 700         }
 701         non_adds.push_back(split_ex_to_pair(last_expanded));
 702         return (new mul(non_adds,overall_coeff))->
 703                 setflag(status_flags::dynallocated | status_flags::expanded);
 704 }
 705
 706
 707 //////////
 708 // new virtual functions which can be overridden by derived classes
 709 //////////
 710
 711 // none
 712
 713 //////////
 714 // non-virtual functions in this class
 715 //////////
 716
 717
 718 /** Member-wise expand the expairs representing this sequence.  This must be
 719  *  overridden from expairseq::expandchildren() and done iteratively in order
 720  *  to allow for early cancallations and thus safe memory.
 721  *
 722  *  @see mul::expand()
 723  *  @return pointer to epvector containing expanded representation or zero
 724  *  pointer, if sequence is unchanged. */
 725 epvector * mul::expandchildren(unsigned options) const
 726 {
 727         epvector::const_iterator last = seq.end();
 728         epvector::const_iterator cit = seq.begin();
 729         while (cit!=last) {
 730                 const ex & factor = recombine_pair_to_ex(*cit);
 731                 const ex & expanded_factor = factor.expand(options);
 732                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 733
 734                         // something changed, copy seq, eval and return it
 735                         epvector *s = new epvector;
 736                         s->reserve(seq.size());
 737
 738                         // copy parts of seq which are known not to have changed
 739                         epvector::const_iterator cit2 = seq.begin();
 740                         while (cit2!=cit) {
 741                                 s->push_back(*cit2);
 742                                 ++cit2;
 743                         }
 744                         // copy first changed element
 745                         s->push_back(split_ex_to_pair(expanded_factor));
 746                         ++cit2;
 747                         // copy rest
 748                         while (cit2!=last) {
 749                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 750                                 ++cit2;
 751                         }
 752                         return s;
 753                 }
 754                 ++cit;
 755         }
 756
 757         return 0; // nothing has changed
 758 }
 759
 760 } // namespace GiNaC