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 <iostream>
  24 #include <vector>
  25 #include <stdexcept>
  26
  27 #include "mul.h"
  28 #include "add.h"
  29 #include "power.h"
  30 #include "matrix.h"
  31 #include "archive.h"
  32 #include "utils.h"
  33
  34 namespace GiNaC {
  35
  36 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  37
  38 //////////
  39 // default ctor, dtor, copy ctor, assignment operator and helpers
  40 //////////
  41
  42 mul::mul()
  43 {
  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         tinfo_key = TINFO_mul;
  59         overall_coeff = _ex1;
  60         construct_from_2_ex(lh,rh);
  61         GINAC_ASSERT(is_canonical());
  62 }
  63
  64 mul::mul(const exvector & v)
  65 {
  66         tinfo_key = TINFO_mul;
  67         overall_coeff = _ex1;
  68         construct_from_exvector(v);
  69         GINAC_ASSERT(is_canonical());
  70 }
  71
  72 mul::mul(const epvector & v)
  73 {
  74         tinfo_key = TINFO_mul;
  75         overall_coeff = _ex1;
  76         construct_from_epvector(v);
  77         GINAC_ASSERT(is_canonical());
  78 }
  79
  80 mul::mul(const epvector & v, const ex & oc)
  81 {
  82         tinfo_key = TINFO_mul;
  83         overall_coeff = oc;
  84         construct_from_epvector(v);
  85         GINAC_ASSERT(is_canonical());
  86 }
  87
  88 mul::mul(epvector * vp, const ex & oc)
  89 {
  90         tinfo_key = TINFO_mul;
  91         GINAC_ASSERT(vp!=0);
  92         overall_coeff = oc;
  93         construct_from_epvector(*vp);
  94         delete vp;
  95         GINAC_ASSERT(is_canonical());
  96 }
  97
  98 mul::mul(const ex & lh, const ex & mh, const ex & rh)
  99 {
 100         tinfo_key = TINFO_mul;
 101         exvector factors;
 102         factors.reserve(3);
 103         factors.push_back(lh);
 104         factors.push_back(mh);
 105         factors.push_back(rh);
 106         overall_coeff = _ex1;
 107         construct_from_exvector(factors);
 108         GINAC_ASSERT(is_canonical());
 109 }
 110
 111 //////////
 112 // archiving
 113 //////////
 114
 115 DEFAULT_ARCHIVING(mul)
 116
 117 //////////
 118 // functions overriding virtual functions from base classes
 119 //////////
 120
 121 // public
 122
 123 void mul::print(const print_context & c, unsigned level) const
 124 {
 125         if (is_a<print_tree>(c)) {
 126
 127                 inherited::print(c, level);
 128
 129         } else if (is_a<print_csrc>(c)) {
 130
 131                 if (precedence() <= level)
 132                         c.s << "(";
 133
 134                 if (!overall_coeff.is_equal(_ex1)) {
 135                         overall_coeff.print(c, precedence());
 136                         c.s << "*";
 137                 }
 138
 139                 // Print arguments, separated by "*" or "/"
 140                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 141                 while (it != itend) {
 142
 143                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 144                         if (it == seq.begin() && ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0) {
 145                                 if (is_a<print_csrc_cl_N>(c))
 146                                         c.s << "recip(";
 147                                 else
 148                                         c.s << "1.0/";
 149                         }
 150
 151                         // If the exponent is 1 or -1, it is left out
 152                         if (it->coeff.compare(_ex1) == 0 || it->coeff.compare(_num_1) == 0)
 153                                 it->rest.print(c, precedence());
 154                         else {
 155                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 156                                 (ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
 157                         }
 158
 159                         // Separator is "/" for negative integer powers, "*" otherwise
 160                         ++it;
 161                         if (it != itend) {
 162                                 if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0)
 163                                         c.s << "/";
 164                                 else
 165                                         c.s << "*";
 166                         }
 167                 }
 168
 169                 if (precedence() <= level)
 170                         c.s << ")";
 171
 172         } else {
 173
 174                 if (precedence() <= level) {
 175                         if (is_a<print_latex>(c))
 176                                 c.s << "{(";
 177                         else
 178                                 c.s << "(";
 179                 }
 180
 181                 bool first = true;
 182
 183                 // First print the overall numeric coefficient
 184                 numeric coeff = ex_to<numeric>(overall_coeff);
 185                 if (coeff.csgn() == -1)
 186                         c.s << '-';
 187                 if (!coeff.is_equal(_num1) &&
 188                         !coeff.is_equal(_num_1)) {
 189                         if (coeff.is_rational()) {
 190                                 if (coeff.is_negative())
 191                                         (-coeff).print(c);
 192                                 else
 193                                         coeff.print(c);
 194                         } else {
 195                                 if (coeff.csgn() == -1)
 196                                         (-coeff).print(c, precedence());
 197                                 else
 198                                         coeff.print(c, precedence());
 199                         }
 200                         if (is_a<print_latex>(c))
 201                                 c.s << ' ';
 202                         else
 203                                 c.s << '*';
 204                 }
 205
 206                 // Then proceed with the remaining factors
 207                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 208                 while (it != itend) {
 209                         if (!first) {
 210                                 if (is_a<print_latex>(c))
 211                                         c.s << ' ';
 212                                 else
 213                                         c.s << '*';
 214                         } else {
 215                                 first = false;
 216                         }
 217                         recombine_pair_to_ex(*it).print(c, precedence());
 218                         ++it;
 219                 }
 220
 221                 if (precedence() <= level) {
 222                         if (is_a<print_latex>(c))
 223                                 c.s << ")}";
 224                         else
 225                                 c.s << ")";
 226                 }
 227         }
 228 }
 229
 230 bool mul::info(unsigned inf) const
 231 {
 232         switch (inf) {
 233                 case info_flags::polynomial:
 234                 case info_flags::integer_polynomial:
 235                 case info_flags::cinteger_polynomial:
 236                 case info_flags::rational_polynomial:
 237                 case info_flags::crational_polynomial:
 238                 case info_flags::rational_function: {
 239                         epvector::const_iterator i = seq.begin(), end = seq.end();
 240                         while (i != end) {
 241                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 242                                         return false;
 243                                 ++i;
 244                         }
 245                         return overall_coeff.info(inf);
 246                 }
 247                 case info_flags::algebraic: {
 248                         epvector::const_iterator i = seq.begin(), end = seq.end();
 249                         while (i != end) {
 250                                 if ((recombine_pair_to_ex(*i).info(inf)))
 251                                         return true;
 252                                 ++i;
 253                         }
 254                         return false;
 255                 }
 256         }
 257         return inherited::info(inf);
 258 }
 259
 260 int mul::degree(const ex & s) const
 261 {
 262         // Sum up degrees of factors
 263         int deg_sum = 0;
 264         epvector::const_iterator i = seq.begin(), end = seq.end();
 265         while (i != end) {
 266                 if (ex_to<numeric>(i->coeff).is_integer())
 267                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 268                 ++i;
 269         }
 270         return deg_sum;
 271 }
 272
 273 int mul::ldegree(const ex & s) const
 274 {
 275         // Sum up degrees of factors
 276         int deg_sum = 0;
 277         epvector::const_iterator i = seq.begin(), end = seq.end();
 278         while (i != end) {
 279                 if (ex_to<numeric>(i->coeff).is_integer())
 280                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 281                 ++i;
 282         }
 283         return deg_sum;
 284 }
 285
 286 ex mul::coeff(const ex & s, int n) const
 287 {
 288         exvector coeffseq;
 289         coeffseq.reserve(seq.size()+1);
 290
 291         if (n==0) {
 292                 // product of individual coeffs
 293                 // if a non-zero power of s is found, the resulting product will be 0
 294                 epvector::const_iterator i = seq.begin(), end = seq.end();
 295                 while (i != end) {
 296                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 297                         ++i;
 298                 }
 299                 coeffseq.push_back(overall_coeff);
 300                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 301         }
 302
 303         epvector::const_iterator i = seq.begin(), end = seq.end();
 304         bool coeff_found = false;
 305         while (i != end) {
 306                 ex t = recombine_pair_to_ex(*i);
 307                 ex c = t.coeff(s, n);
 308                 if (!c.is_zero()) {
 309                         coeffseq.push_back(c);
 310                         coeff_found = 1;
 311                 } else {
 312                         coeffseq.push_back(t);
 313                 }
 314                 ++i;
 315         }
 316         if (coeff_found) {
 317                 coeffseq.push_back(overall_coeff);
 318                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 319         }
 320
 321         return _ex0;
 322 }
 323
 324 /** Perform automatic term rewriting rules in this class.  In the following
 325  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 326  *  stand for such expressions that contain a plain number.
 327  *  - *(...,x;0) -> 0
 328  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 329  *  - *(x;1) -> x
 330  *  - *(;c) -> c
 331  *
 332  *  @param level cut-off in recursive evaluation */
 333 ex mul::eval(int level) const
 334 {
 335         epvector *evaled_seqp = evalchildren(level);
 336         if (evaled_seqp) {
 337                 // do more evaluation later
 338                 return (new mul(evaled_seqp,overall_coeff))->
 339                            setflag(status_flags::dynallocated);
 340         }
 341
 342 #ifdef DO_GINAC_ASSERT
 343         epvector::const_iterator i = seq.begin(), end = seq.end();
 344         while (i != end) {
 345                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 346                              (!(ex_to<numeric>(i->coeff).is_integer())));
 347                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 348                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 349                     print(print_tree(std::cerr));
 350                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 351                 /* for paranoia */
 352                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 353                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 354                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 355                 /* end paranoia */
 356                 ++i;
 357         }
 358 #endif // def DO_GINAC_ASSERT
 359
 360         if (flags & status_flags::evaluated) {
 361                 GINAC_ASSERT(seq.size()>0);
 362                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 363                 return *this;
 364         }
 365
 366         int seq_size = seq.size();
 367         if (overall_coeff.is_zero()) {
 368                 // *(...,x;0) -> 0
 369                 return _ex0;
 370         } else if (seq_size==0) {
 371                 // *(;c) -> c
 372                 return overall_coeff;
 373         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 374                 // *(x;1) -> x
 375                 return recombine_pair_to_ex(*(seq.begin()));
 376         } else if ((seq_size==1) &&
 377                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 378                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 379                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 380                 const add & addref = ex_to<add>((*seq.begin()).rest);
 381                 epvector *distrseq = new epvector();
 382                 distrseq->reserve(addref.seq.size());
 383                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 384                 while (i != end) {
 385                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 386                         ++i;
 387                 }
 388                 return (new add(distrseq,
 389                                 ex_to<numeric>(addref.overall_coeff).
 390                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 391                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 392         }
 393         return this->hold();
 394 }
 395
 396 ex mul::evalf(int level) const
 397 {
 398         if (level==1)
 399                 return mul(seq,overall_coeff);
 400
 401         if (level==-max_recursion_level)
 402                 throw(std::runtime_error("max recursion level reached"));
 403
 404         epvector *s = new epvector();
 405         s->reserve(seq.size());
 406
 407         --level;
 408         epvector::const_iterator i = seq.begin(), end = seq.end();
 409         while (i != end) {
 410                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 411                                                            i->coeff));
 412                 ++i;
 413         }
 414         return mul(s, overall_coeff.evalf(level));
 415 }
 416
 417 ex mul::evalm(void) const
 418 {
 419         // numeric*matrix
 420         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 421          && is_ex_of_type(seq[0].rest, matrix))
 422                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 423
 424         // Evaluate children first, look whether there are any matrices at all
 425         // (there can be either no matrices or one matrix; if there were more
 426         // than one matrix, it would be a non-commutative product)
 427         epvector *s = new epvector;
 428         s->reserve(seq.size());
 429
 430         bool have_matrix = false;
 431         epvector::iterator the_matrix;
 432
 433         epvector::const_iterator i = seq.begin(), end = seq.end();
 434         while (i != end) {
 435                 const ex &m = recombine_pair_to_ex(*i).evalm();
 436                 s->push_back(split_ex_to_pair(m));
 437                 if (is_ex_of_type(m, matrix)) {
 438                         have_matrix = true;
 439                         the_matrix = s->end() - 1;
 440                 }
 441                 ++i;
 442         }
 443
 444         if (have_matrix) {
 445
 446                 // The product contained a matrix. We will multiply all other factors
 447                 // into that matrix.
 448                 matrix m = ex_to<matrix>(the_matrix->rest);
 449                 s->erase(the_matrix);
 450                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 451                 return m.mul_scalar(scalar);
 452
 453         } else
 454                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 455 }
 456
 457 ex mul::simplify_ncmul(const exvector & v) const
 458 {
 459         if (seq.empty())
 460                 return inherited::simplify_ncmul(v);
 461
 462         // Find first noncommutative element and call its simplify_ncmul()
 463         epvector::const_iterator i = seq.begin(), end = seq.end();
 464         while (i != end) {
 465                 if (i->rest.return_type() == return_types::noncommutative)
 466                         return i->rest.simplify_ncmul(v);
 467                 ++i;
 468         }
 469         return inherited::simplify_ncmul(v);
 470 }
 471
 472 // protected
 473
 474 /** Implementation of ex::diff() for a product.  It applies the product rule.
 475  *  @see ex::diff */
 476 ex mul::derivative(const symbol & s) const
 477 {
 478         unsigned num = seq.size();
 479         exvector addseq;
 480         addseq.reserve(num);
 481
 482         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 483         epvector mulseq = seq;
 484         epvector::const_iterator i = seq.begin(), end = seq.end();
 485         epvector::iterator i2 = mulseq.begin();
 486         while (i != end) {
 487                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 488                                              i->rest.diff(s));
 489                 ep.swap(*i2);
 490                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 491                 ep.swap(*i2);
 492                 ++i; ++i2;
 493         }
 494         return (new add(addseq))->setflag(status_flags::dynallocated);
 495 }
 496
 497 int mul::compare_same_type(const basic & other) const
 498 {
 499         return inherited::compare_same_type(other);
 500 }
 501
 502 bool mul::is_equal_same_type(const basic & other) const
 503 {
 504         return inherited::is_equal_same_type(other);
 505 }
 506
 507 unsigned mul::return_type(void) const
 508 {
 509         if (seq.empty()) {
 510                 // mul without factors: should not happen, but commutes
 511                 return return_types::commutative;
 512         }
 513
 514         bool all_commutative = true;
 515         epvector::const_iterator noncommutative_element; // point to first found nc element
 516
 517         epvector::const_iterator i = seq.begin(), end = seq.end();
 518         while (i != end) {
 519                 unsigned rt = i->rest.return_type();
 520                 if (rt == return_types::noncommutative_composite)
 521                         return rt; // one ncc -> mul also ncc
 522                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 523                         // first nc element found, remember position
 524                         noncommutative_element = i;
 525                         all_commutative = false;
 526                 }
 527                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 528                         // another nc element found, compare type_infos
 529                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 530                                 // diffent types -> mul is ncc
 531                                 return return_types::noncommutative_composite;
 532                         }
 533                 }
 534                 ++i;
 535         }
 536         // all factors checked
 537         return all_commutative ? return_types::commutative : return_types::noncommutative;
 538 }
 539
 540 unsigned mul::return_type_tinfo(void) const
 541 {
 542         if (seq.empty())
 543                 return tinfo_key;  // mul without factors: should not happen
 544
 545         // return type_info of first noncommutative element
 546         epvector::const_iterator i = seq.begin(), end = seq.end();
 547         while (i != end) {
 548                 if (i->rest.return_type() == return_types::noncommutative)
 549                         return i->rest.return_type_tinfo();
 550                 ++i;
 551         }
 552         // no noncommutative element found, should not happen
 553         return tinfo_key;
 554 }
 555
 556 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 557 {
 558         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 559 }
 560
 561 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 562 {
 563         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 564 }
 565
 566 expair mul::split_ex_to_pair(const ex & e) const
 567 {
 568         if (is_ex_exactly_of_type(e,power)) {
 569                 const power & powerref = ex_to<power>(e);
 570                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 571                         return expair(powerref.basis,powerref.exponent);
 572         }
 573         return expair(e,_ex1);
 574 }
 575
 576 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 577                                           const ex & c) const
 578 {
 579         // to avoid duplication of power simplification rules,
 580         // we create a temporary power object
 581         // otherwise it would be hard to correctly simplify
 582         // expression like (4^(1/3))^(3/2)
 583         if (are_ex_trivially_equal(c,_ex1))
 584                 return split_ex_to_pair(e);
 585
 586         return split_ex_to_pair(power(e,c));
 587 }
 588
 589 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 590                                             const ex & c) const
 591 {
 592         // to avoid duplication of power simplification rules,
 593         // we create a temporary power object
 594         // otherwise it would be hard to correctly simplify
 595         // expression like (4^(1/3))^(3/2)
 596         if (are_ex_trivially_equal(c,_ex1))
 597                 return p;
 598
 599         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 600 }
 601
 602 ex mul::recombine_pair_to_ex(const expair & p) const
 603 {
 604         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 605                 return p.rest;
 606         else
 607                 return power(p.rest,p.coeff);
 608 }
 609
 610 bool mul::expair_needs_further_processing(epp it)
 611 {
 612         if (is_ex_exactly_of_type((*it).rest,mul) &&
 613                 ex_to<numeric>((*it).coeff).is_integer()) {
 614                 // combined pair is product with integer power -> expand it
 615                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 616                 return true;
 617         }
 618         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 619                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 620                 if (!ep.is_equal(*it)) {
 621                         // combined pair is a numeric power which can be simplified
 622                         *it = ep;
 623                         return true;
 624                 }
 625                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 626                         // combined pair has coeff 1 and must be moved to the end
 627                         return true;
 628                 }
 629         }
 630         return false;
 631 }
 632
 633 ex mul::default_overall_coeff(void) const
 634 {
 635         return _ex1;
 636 }
 637
 638 void mul::combine_overall_coeff(const ex & c)
 639 {
 640         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 641         GINAC_ASSERT(is_exactly_a<numeric>(c));
 642         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 643 }
 644
 645 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 646 {
 647         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 648         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 649         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 650         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 651 }
 652
 653 bool mul::can_make_flat(const expair & p) const
 654 {
 655         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 656         // this assertion will probably fail somewhere
 657         // it would require a more careful make_flat, obeying the power laws
 658         // probably should return true only if p.coeff is integer
 659         return ex_to<numeric>(p.coeff).is_equal(_num1);
 660 }
 661
 662 ex mul::expand(unsigned options) const
 663 {
 664         // First, expand the children
 665         epvector * expanded_seqp = expandchildren(options);
 666         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 667
 668         // Now, look for all the factors that are sums and multiply each one out
 669         // with the next one that is found while collecting the factors which are
 670         // not sums
 671         int number_of_adds = 0;
 672         ex last_expanded = _ex1;
 673         epvector non_adds;
 674         non_adds.reserve(expanded_seq.size());
 675         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 676         while (cit != last) {
 677                 if (is_ex_exactly_of_type(cit->rest, add) &&
 678                         (cit->coeff.is_equal(_ex1))) {
 679                         ++number_of_adds;
 680                         if (is_ex_exactly_of_type(last_expanded, add)) {
 681                                 const add & add1 = ex_to<add>(last_expanded);
 682                                 const add & add2 = ex_to<add>(cit->rest);
 683                                 int n1 = add1.nops();
 684                                 int n2 = add2.nops();
 685                                 exvector distrseq;
 686                                 distrseq.reserve(n1*n2);
 687                                 for (int i1=0; i1<n1; ++i1) {
 688                                         for (int i2=0; i2<n2; ++i2) {
 689                                                 distrseq.push_back(add1.op(i1) * add2.op(i2));
 690                                         }
 691                                 }
 692                                 last_expanded = (new add(distrseq))->
 693                                                  setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 694                         } else {
 695                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 696                                 last_expanded = cit->rest;
 697                         }
 698                 } else {
 699                         non_adds.push_back(*cit);
 700                 }
 701                 ++cit;
 702         }
 703         if (expanded_seqp)
 704                 delete expanded_seqp;
 705
 706         // Now the only remaining thing to do is to multiply the factors which
 707         // were not sums into the "last_expanded" sum
 708         if (is_ex_exactly_of_type(last_expanded, add)) {
 709                 const add & finaladd = ex_to<add>(last_expanded);
 710                 exvector distrseq;
 711                 int n = finaladd.nops();
 712                 distrseq.reserve(n);
 713                 for (int i=0; i<n; ++i) {
 714                         epvector factors = non_adds;
 715                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 716                         distrseq.push_back((new mul(factors, overall_coeff))->
 717                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 718                 }
 719                 return ((new add(distrseq))->
 720                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 721         }
 722         non_adds.push_back(split_ex_to_pair(last_expanded));
 723         return (new mul(non_adds, overall_coeff))->
 724                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 725 }
 726
 727
 728 //////////
 729 // new virtual functions which can be overridden by derived classes
 730 //////////
 731
 732 // none
 733
 734 //////////
 735 // non-virtual functions in this class
 736 //////////
 737
 738
 739 /** Member-wise expand the expairs representing this sequence.  This must be
 740  *  overridden from expairseq::expandchildren() and done iteratively in order
 741  *  to allow for early cancallations and thus safe memory.
 742  *
 743  *  @see mul::expand()
 744  *  @return pointer to epvector containing expanded representation or zero
 745  *  pointer, if sequence is unchanged. */
 746 epvector * mul::expandchildren(unsigned options) const
 747 {
 748         epvector::const_iterator last = seq.end();
 749         epvector::const_iterator cit = seq.begin();
 750         while (cit!=last) {
 751                 const ex & factor = recombine_pair_to_ex(*cit);
 752                 const ex & expanded_factor = factor.expand(options);
 753                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 754
 755                         // something changed, copy seq, eval and return it
 756                         epvector *s = new epvector;
 757                         s->reserve(seq.size());
 758
 759                         // copy parts of seq which are known not to have changed
 760                         epvector::const_iterator cit2 = seq.begin();
 761                         while (cit2!=cit) {
 762                                 s->push_back(*cit2);
 763                                 ++cit2;
 764                         }
 765                         // copy first changed element
 766                         s->push_back(split_ex_to_pair(expanded_factor));
 767                         ++cit2;
 768                         // copy rest
 769                         while (cit2!=last) {
 770                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 771                                 ++cit2;
 772                         }
 773                         return s;
 774                 }
 775                 ++cit;
 776         }
 777
 778         return 0; // nothing has changed
 779 }
 780
 781 } // namespace GiNaC