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 "utils.h"
  32
  33 namespace GiNaC {
  34
  35 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  36
  37 //////////
  38 // default ctor, dtor, copy ctor, assignment operator and helpers
  39 //////////
  40
  41 mul::mul()
  42 {
  43         tinfo_key = TINFO_mul;
  44 }
  45
  46 DEFAULT_COPY(mul)
  47 DEFAULT_DESTROY(mul)
  48
  49 //////////
  50 // other ctors
  51 //////////
  52
  53 // public
  54
  55 mul::mul(const ex & lh, const ex & rh)
  56 {
  57         tinfo_key = TINFO_mul;
  58         overall_coeff = _ex1;
  59         construct_from_2_ex(lh,rh);
  60         GINAC_ASSERT(is_canonical());
  61 }
  62
  63 mul::mul(const exvector & v)
  64 {
  65         tinfo_key = TINFO_mul;
  66         overall_coeff = _ex1;
  67         construct_from_exvector(v);
  68         GINAC_ASSERT(is_canonical());
  69 }
  70
  71 mul::mul(const epvector & v)
  72 {
  73         tinfo_key = TINFO_mul;
  74         overall_coeff = _ex1;
  75         construct_from_epvector(v);
  76         GINAC_ASSERT(is_canonical());
  77 }
  78
  79 mul::mul(const epvector & v, const ex & oc)
  80 {
  81         tinfo_key = TINFO_mul;
  82         overall_coeff = oc;
  83         construct_from_epvector(v);
  84         GINAC_ASSERT(is_canonical());
  85 }
  86
  87 mul::mul(epvector * vp, const ex & oc)
  88 {
  89         tinfo_key = TINFO_mul;
  90         GINAC_ASSERT(vp!=0);
  91         overall_coeff = oc;
  92         construct_from_epvector(*vp);
  93         delete vp;
  94         GINAC_ASSERT(is_canonical());
  95 }
  96
  97 mul::mul(const ex & lh, const ex & mh, const ex & rh)
  98 {
  99         tinfo_key = TINFO_mul;
 100         exvector factors;
 101         factors.reserve(3);
 102         factors.push_back(lh);
 103         factors.push_back(mh);
 104         factors.push_back(rh);
 105         overall_coeff = _ex1;
 106         construct_from_exvector(factors);
 107         GINAC_ASSERT(is_canonical());
 108 }
 109
 110 //////////
 111 // archiving
 112 //////////
 113
 114 DEFAULT_ARCHIVING(mul)
 115
 116 //////////
 117 // functions overriding virtual functions from base classes
 118 //////////
 119
 120 // public
 121
 122 void mul::print(const print_context & c, unsigned level) const
 123 {
 124         if (is_a<print_tree>(c)) {
 125
 126                 inherited::print(c, level);
 127
 128         } else if (is_a<print_csrc>(c)) {
 129
 130                 if (precedence() <= level)
 131                         c.s << "(";
 132
 133                 if (!overall_coeff.is_equal(_ex1)) {
 134                         overall_coeff.print(c, precedence());
 135                         c.s << "*";
 136                 }
 137
 138                 // Print arguments, separated by "*" or "/"
 139                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 140                 while (it != itend) {
 141
 142                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 143                         if (it == seq.begin() && ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) {
 144                                 if (is_a<print_csrc_cl_N>(c))
 145                                         c.s << "recip(";
 146                                 else
 147                                         c.s << "1.0/";
 148                         }
 149
 150                         // If the exponent is 1 or -1, it is left out
 151                         if (it->coeff.compare(_ex1) == 0 || it->coeff.compare(_num_1) == 0)
 152                                 it->rest.print(c, precedence());
 153                         else {
 154                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 155                                 (ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
 156                         }
 157
 158                         // Separator is "/" for negative integer powers, "*" otherwise
 159                         ++it;
 160                         if (it != itend) {
 161                                 if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0)
 162                                         c.s << "/";
 163                                 else
 164                                         c.s << "*";
 165                         }
 166                 }
 167
 168                 if (precedence() <= level)
 169                         c.s << ")";
 170
 171         } else {
 172
 173                 if (precedence() <= level) {
 174                         if (is_a<print_latex>(c))
 175                                 c.s << "{(";
 176                         else
 177                                 c.s << "(";
 178                 }
 179
 180                 bool first = true;
 181
 182                 // First print the overall numeric coefficient
 183                 numeric coeff = ex_to<numeric>(overall_coeff);
 184                 if (coeff.csgn() == -1)
 185                         c.s << '-';
 186                 if (!coeff.is_equal(_num1) &&
 187                         !coeff.is_equal(_num_1)) {
 188                         if (coeff.is_rational()) {
 189                                 if (coeff.is_negative())
 190                                         (-coeff).print(c);
 191                                 else
 192                                         coeff.print(c);
 193                         } else {
 194                                 if (coeff.csgn() == -1)
 195                                         (-coeff).print(c, precedence());
 196                                 else
 197                                         coeff.print(c, precedence());
 198                         }
 199                         if (is_a<print_latex>(c))
 200                                 c.s << ' ';
 201                         else
 202                                 c.s << '*';
 203                 }
 204
 205                 // Then proceed with the remaining factors
 206                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 207                 while (it != itend) {
 208                         if (!first) {
 209                                 if (is_a<print_latex>(c))
 210                                         c.s << ' ';
 211                                 else
 212                                         c.s << '*';
 213                         } else {
 214                                 first = false;
 215                         }
 216                         recombine_pair_to_ex(*it).print(c, precedence());
 217                         ++it;
 218                 }
 219
 220                 if (precedence() <= level) {
 221                         if (is_a<print_latex>(c))
 222                                 c.s << ")}";
 223                         else
 224                                 c.s << ")";
 225                 }
 226         }
 227 }
 228
 229 bool mul::info(unsigned inf) const
 230 {
 231         switch (inf) {
 232                 case info_flags::polynomial:
 233                 case info_flags::integer_polynomial:
 234                 case info_flags::cinteger_polynomial:
 235                 case info_flags::rational_polynomial:
 236                 case info_flags::crational_polynomial:
 237                 case info_flags::rational_function: {
 238                         epvector::const_iterator i = seq.begin(), end = seq.end();
 239                         while (i != end) {
 240                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 241                                         return false;
 242                                 ++i;
 243                         }
 244                         return overall_coeff.info(inf);
 245                 }
 246                 case info_flags::algebraic: {
 247                         epvector::const_iterator i = seq.begin(), end = seq.end();
 248                         while (i != end) {
 249                                 if ((recombine_pair_to_ex(*i).info(inf)))
 250                                         return true;
 251                                 ++i;
 252                         }
 253                         return false;
 254                 }
 255         }
 256         return inherited::info(inf);
 257 }
 258
 259 int mul::degree(const ex & s) const
 260 {
 261         // Sum up degrees of factors
 262         int deg_sum = 0;
 263         epvector::const_iterator i = seq.begin(), end = seq.end();
 264         while (i != end) {
 265                 if (ex_to<numeric>(i->coeff).is_integer())
 266                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 267                 ++i;
 268         }
 269         return deg_sum;
 270 }
 271
 272 int mul::ldegree(const ex & s) const
 273 {
 274         // Sum up degrees of factors
 275         int deg_sum = 0;
 276         epvector::const_iterator i = seq.begin(), end = seq.end();
 277         while (i != end) {
 278                 if (ex_to<numeric>(i->coeff).is_integer())
 279                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 280                 ++i;
 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 i = seq.begin(), end = seq.end();
 294                 while (i != end) {
 295                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 296                         ++i;
 297                 }
 298                 coeffseq.push_back(overall_coeff);
 299                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 300         }
 301
 302         epvector::const_iterator i = seq.begin(), end = seq.end();
 303         bool coeff_found = false;
 304         while (i != end) {
 305                 ex t = recombine_pair_to_ex(*i);
 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                 ++i;
 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 /** Perform automatic term rewriting rules in this class.  In the following
 324  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 325  *  stand for such expressions that contain a plain number.
 326  *  - *(...,x;0) -> 0
 327  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 328  *  - *(x;1) -> x
 329  *  - *(;c) -> c
 330  *
 331  *  @param level cut-off in recursive evaluation */
 332 ex mul::eval(int level) const
 333 {
 334         epvector *evaled_seqp = evalchildren(level);
 335         if (evaled_seqp) {
 336                 // do more evaluation later
 337                 return (new mul(evaled_seqp,overall_coeff))->
 338                            setflag(status_flags::dynallocated);
 339         }
 340
 341 #ifdef DO_GINAC_ASSERT
 342         epvector::const_iterator i = seq.begin(), end = seq.end();
 343         while (i != end) {
 344                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 345                              (!(ex_to<numeric>(i->coeff).is_integer())));
 346                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 347                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 348                     print(print_tree(std::cerr));
 349                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 350                 /* for paranoia */
 351                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 352                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 353                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 354                 /* end paranoia */
 355                 ++i;
 356         }
 357 #endif // def DO_GINAC_ASSERT
 358
 359         if (flags & status_flags::evaluated) {
 360                 GINAC_ASSERT(seq.size()>0);
 361                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 362                 return *this;
 363         }
 364
 365         int seq_size = seq.size();
 366         if (overall_coeff.is_zero()) {
 367                 // *(...,x;0) -> 0
 368                 return _ex0;
 369         } else if (seq_size==0) {
 370                 // *(;c) -> c
 371                 return overall_coeff;
 372         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 373                 // *(x;1) -> x
 374                 return recombine_pair_to_ex(*(seq.begin()));
 375         } else if ((seq_size==1) &&
 376                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 377                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 378                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 379                 const add & addref = ex_to<add>((*seq.begin()).rest);
 380                 epvector *distrseq = new epvector();
 381                 distrseq->reserve(addref.seq.size());
 382                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 383                 while (i != end) {
 384                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 385                         ++i;
 386                 }
 387                 return (new add(distrseq,
 388                                 ex_to<numeric>(addref.overall_coeff).
 389                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 390                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 391         }
 392         return this->hold();
 393 }
 394
 395 ex mul::evalf(int level) const
 396 {
 397         if (level==1)
 398                 return mul(seq,overall_coeff);
 399
 400         if (level==-max_recursion_level)
 401                 throw(std::runtime_error("max recursion level reached"));
 402
 403         epvector *s = new epvector();
 404         s->reserve(seq.size());
 405
 406         --level;
 407         epvector::const_iterator i = seq.begin(), end = seq.end();
 408         while (i != end) {
 409                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 410                                                            i->coeff));
 411                 ++i;
 412         }
 413         return mul(s, overall_coeff.evalf(level));
 414 }
 415
 416 ex mul::evalm(void) const
 417 {
 418         // numeric*matrix
 419         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 420          && is_ex_of_type(seq[0].rest, matrix))
 421                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 422
 423         // Evaluate children first, look whether there are any matrices at all
 424         // (there can be either no matrices or one matrix; if there were more
 425         // than one matrix, it would be a non-commutative product)
 426         epvector *s = new epvector;
 427         s->reserve(seq.size());
 428
 429         bool have_matrix = false;
 430         epvector::iterator the_matrix;
 431
 432         epvector::const_iterator i = seq.begin(), end = seq.end();
 433         while (i != end) {
 434                 const ex &m = recombine_pair_to_ex(*i).evalm();
 435                 s->push_back(split_ex_to_pair(m));
 436                 if (is_ex_of_type(m, matrix)) {
 437                         have_matrix = true;
 438                         the_matrix = s->end() - 1;
 439                 }
 440                 ++i;
 441         }
 442
 443         if (have_matrix) {
 444
 445                 // The product contained a matrix. We will multiply all other factors
 446                 // into that matrix.
 447                 matrix m = ex_to<matrix>(the_matrix->rest);
 448                 s->erase(the_matrix);
 449                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 450                 return m.mul_scalar(scalar);
 451
 452         } else
 453                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 454 }
 455
 456 ex mul::simplify_ncmul(const exvector & v) const
 457 {
 458         if (seq.empty())
 459                 return inherited::simplify_ncmul(v);
 460
 461         // Find first noncommutative element and call its simplify_ncmul()
 462         epvector::const_iterator i = seq.begin(), end = seq.end();
 463         while (i != end) {
 464                 if (i->rest.return_type() == return_types::noncommutative)
 465                         return i->rest.simplify_ncmul(v);
 466                 ++i;
 467         }
 468         return inherited::simplify_ncmul(v);
 469 }
 470
 471 // protected
 472
 473 /** Implementation of ex::diff() for a product.  It applies the product rule.
 474  *  @see ex::diff */
 475 ex mul::derivative(const symbol & s) const
 476 {
 477         unsigned num = seq.size();
 478         exvector addseq;
 479         addseq.reserve(num);
 480
 481         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 482         epvector mulseq = seq;
 483         epvector::const_iterator i = seq.begin(), end = seq.end();
 484         epvector::iterator i2 = mulseq.begin();
 485         while (i != end) {
 486                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 487                                              i->rest.diff(s));
 488                 ep.swap(*i2);
 489                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 490                 ep.swap(*i2);
 491                 ++i; ++i2;
 492         }
 493         return (new add(addseq))->setflag(status_flags::dynallocated);
 494 }
 495
 496 int mul::compare_same_type(const basic & other) const
 497 {
 498         return inherited::compare_same_type(other);
 499 }
 500
 501 bool mul::is_equal_same_type(const basic & other) const
 502 {
 503         return inherited::is_equal_same_type(other);
 504 }
 505
 506 unsigned mul::return_type(void) const
 507 {
 508         if (seq.empty()) {
 509                 // mul without factors: should not happen, but commutes
 510                 return return_types::commutative;
 511         }
 512
 513         bool all_commutative = true;
 514         epvector::const_iterator noncommutative_element; // point to first found nc element
 515
 516         epvector::const_iterator i = seq.begin(), end = seq.end();
 517         while (i != end) {
 518                 unsigned rt = i->rest.return_type();
 519                 if (rt == return_types::noncommutative_composite)
 520                         return rt; // one ncc -> mul also ncc
 521                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 522                         // first nc element found, remember position
 523                         noncommutative_element = i;
 524                         all_commutative = false;
 525                 }
 526                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 527                         // another nc element found, compare type_infos
 528                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 529                                 // diffent types -> mul is ncc
 530                                 return return_types::noncommutative_composite;
 531                         }
 532                 }
 533                 ++i;
 534         }
 535         // all factors checked
 536         return all_commutative ? return_types::commutative : return_types::noncommutative;
 537 }
 538
 539 unsigned mul::return_type_tinfo(void) const
 540 {
 541         if (seq.empty())
 542                 return tinfo_key;  // mul without factors: should not happen
 543
 544         // return type_info of first noncommutative element
 545         epvector::const_iterator i = seq.begin(), end = seq.end();
 546         while (i != end) {
 547                 if (i->rest.return_type() == return_types::noncommutative)
 548                         return i->rest.return_type_tinfo();
 549                 ++i;
 550         }
 551         // no noncommutative element found, should not happen
 552         return tinfo_key;
 553 }
 554
 555 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 556 {
 557         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 558 }
 559
 560 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 561 {
 562         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 563 }
 564
 565 expair mul::split_ex_to_pair(const ex & e) const
 566 {
 567         if (is_ex_exactly_of_type(e,power)) {
 568                 const power & powerref = ex_to<power>(e);
 569                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 570                         return expair(powerref.basis,powerref.exponent);
 571         }
 572         return expair(e,_ex1);
 573 }
 574
 575 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 576                                           const ex & c) const
 577 {
 578         // to avoid duplication of power simplification rules,
 579         // we create a temporary power object
 580         // otherwise it would be hard to correctly simplify
 581         // expression like (4^(1/3))^(3/2)
 582         if (are_ex_trivially_equal(c,_ex1))
 583                 return split_ex_to_pair(e);
 584
 585         return split_ex_to_pair(power(e,c));
 586 }
 587
 588 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 589                                             const ex & c) const
 590 {
 591         // to avoid duplication of power simplification rules,
 592         // we create a temporary power object
 593         // otherwise it would be hard to correctly simplify
 594         // expression like (4^(1/3))^(3/2)
 595         if (are_ex_trivially_equal(c,_ex1))
 596                 return p;
 597
 598         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 599 }
 600
 601 ex mul::recombine_pair_to_ex(const expair & p) const
 602 {
 603         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 604                 return p.rest;
 605         else
 606                 return power(p.rest,p.coeff);
 607 }
 608
 609 bool mul::expair_needs_further_processing(epp it)
 610 {
 611         if (is_ex_exactly_of_type((*it).rest,mul) &&
 612                 ex_to<numeric>((*it).coeff).is_integer()) {
 613                 // combined pair is product with integer power -> expand it
 614                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 615                 return true;
 616         }
 617         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 618                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 619                 if (!ep.is_equal(*it)) {
 620                         // combined pair is a numeric power which can be simplified
 621                         *it = ep;
 622                         return true;
 623                 }
 624                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 625                         // combined pair has coeff 1 and must be moved to the end
 626                         return true;
 627                 }
 628         }
 629         return false;
 630 }
 631
 632 ex mul::default_overall_coeff(void) const
 633 {
 634         return _ex1;
 635 }
 636
 637 void mul::combine_overall_coeff(const ex & c)
 638 {
 639         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 640         GINAC_ASSERT(is_exactly_a<numeric>(c));
 641         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 642 }
 643
 644 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 645 {
 646         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 647         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 648         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 649         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 650 }
 651
 652 bool mul::can_make_flat(const expair & p) const
 653 {
 654         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 655         // this assertion will probably fail somewhere
 656         // it would require a more careful make_flat, obeying the power laws
 657         // probably should return true only if p.coeff is integer
 658         return ex_to<numeric>(p.coeff).is_equal(_num1);
 659 }
 660
 661 ex mul::expand(unsigned options) const
 662 {
 663         // First, expand the children
 664         epvector * expanded_seqp = expandchildren(options);
 665         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 666
 667         // Now, look for all the factors that are sums and multiply each one out
 668         // with the next one that is found while collecting the factors which are
 669         // not sums
 670         int number_of_adds = 0;
 671         ex last_expanded = _ex1;
 672         epvector non_adds;
 673         non_adds.reserve(expanded_seq.size());
 674         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 675         while (cit != last) {
 676                 if (is_ex_exactly_of_type(cit->rest, add) &&
 677                         (cit->coeff.is_equal(_ex1))) {
 678                         ++number_of_adds;
 679                         if (is_ex_exactly_of_type(last_expanded, add)) {
 680                                 const add & add1 = ex_to<add>(last_expanded);
 681                                 const add & add2 = ex_to<add>(cit->rest);
 682                                 int n1 = add1.nops();
 683                                 int n2 = add2.nops();
 684                                 exvector distrseq;
 685                                 distrseq.reserve(n1*n2);
 686                                 for (int i1=0; i1<n1; ++i1) {
 687                                         for (int i2=0; i2<n2; ++i2) {
 688                                                 distrseq.push_back(add1.op(i1) * add2.op(i2));
 689                                         }
 690                                 }
 691                                 last_expanded = (new add(distrseq))->
 692                                                  setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 693                         } else {
 694                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 695                                 last_expanded = cit->rest;
 696                         }
 697                 } else {
 698                         non_adds.push_back(*cit);
 699                 }
 700                 ++cit;
 701         }
 702         if (expanded_seqp)
 703                 delete expanded_seqp;
 704
 705         // Now the only remaining thing to do is to multiply the factors which
 706         // were not sums into the "last_expanded" sum
 707         if (is_ex_exactly_of_type(last_expanded, add)) {
 708                 const add & finaladd = ex_to<add>(last_expanded);
 709                 exvector distrseq;
 710                 int n = finaladd.nops();
 711                 distrseq.reserve(n);
 712                 for (int i=0; i<n; ++i) {
 713                         epvector factors = non_adds;
 714                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 715                         distrseq.push_back((new mul(factors, overall_coeff))->
 716                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 717                 }
 718                 return ((new add(distrseq))->
 719                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 720         }
 721         non_adds.push_back(split_ex_to_pair(last_expanded));
 722         return (new mul(non_adds, overall_coeff))->
 723                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 724 }
 725
 726
 727 //////////
 728 // new virtual functions which can be overridden by derived classes
 729 //////////
 730
 731 // none
 732
 733 //////////
 734 // non-virtual functions in this class
 735 //////////
 736
 737
 738 /** Member-wise expand the expairs representing this sequence.  This must be
 739  *  overridden from expairseq::expandchildren() and done iteratively in order
 740  *  to allow for early cancallations and thus safe memory.
 741  *
 742  *  @see mul::expand()
 743  *  @return pointer to epvector containing expanded representation or zero
 744  *  pointer, if sequence is unchanged. */
 745 epvector * mul::expandchildren(unsigned options) const
 746 {
 747         epvector::const_iterator last = seq.end();
 748         epvector::const_iterator cit = seq.begin();
 749         while (cit!=last) {
 750                 const ex & factor = recombine_pair_to_ex(*cit);
 751                 const ex & expanded_factor = factor.expand(options);
 752                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 753
 754                         // something changed, copy seq, eval and return it
 755                         epvector *s = new epvector;
 756                         s->reserve(seq.size());
 757
 758                         // copy parts of seq which are known not to have changed
 759                         epvector::const_iterator cit2 = seq.begin();
 760                         while (cit2!=cit) {
 761                                 s->push_back(*cit2);
 762                                 ++cit2;
 763                         }
 764                         // copy first changed element
 765                         s->push_back(split_ex_to_pair(expanded_factor));
 766                         ++cit2;
 767                         // copy rest
 768                         while (cit2!=last) {
 769                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 770                                 ++cit2;
 771                         }
 772                         return s;
 773                 }
 774                 ++cit;
 775         }
 776
 777         return 0; // nothing has changed
 778 }
 779
 780 } // namespace GiNaC