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.info(info_flags::negative)) {
 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.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
 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.info(info_flags::negative))
 163                                         c.s << "/";
 164                                 else
 165                                         c.s << "*";
 166                         }
 167                 }
 168
 169                 if (precedence() <= level)
 170                         c.s << ")";
 171
 172         } else if (is_a<print_python_repr>(c)) {
 173                 c.s << class_name() << '(';
 174                 op(0).print(c);
 175                 for (unsigned i=1; i<nops(); ++i) {
 176                         c.s << ',';
 177                         op(i).print(c);
 178                 }
 179                 c.s << ')';
 180         } else {
 181
 182                 if (precedence() <= level) {
 183                         if (is_a<print_latex>(c))
 184                                 c.s << "{(";
 185                         else
 186                                 c.s << "(";
 187                 }
 188
 189                 bool first = true;
 190
 191                 // First print the overall numeric coefficient
 192                 numeric coeff = ex_to<numeric>(overall_coeff);
 193                 if (coeff.csgn() == -1)
 194                         c.s << '-';
 195                 if (!coeff.is_equal(_num1) &&
 196                         !coeff.is_equal(_num_1)) {
 197                         if (coeff.is_rational()) {
 198                                 if (coeff.is_negative())
 199                                         (-coeff).print(c);
 200                                 else
 201                                         coeff.print(c);
 202                         } else {
 203                                 if (coeff.csgn() == -1)
 204                                         (-coeff).print(c, precedence());
 205                                 else
 206                                         coeff.print(c, precedence());
 207                         }
 208                         if (is_a<print_latex>(c))
 209                                 c.s << ' ';
 210                         else
 211                                 c.s << '*';
 212                 }
 213
 214                 // Then proceed with the remaining factors
 215                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 216                 while (it != itend) {
 217                         if (!first) {
 218                                 if (is_a<print_latex>(c))
 219                                         c.s << ' ';
 220                                 else
 221                                         c.s << '*';
 222                         } else {
 223                                 first = false;
 224                         }
 225                         recombine_pair_to_ex(*it).print(c, precedence());
 226                         ++it;
 227                 }
 228
 229                 if (precedence() <= level) {
 230                         if (is_a<print_latex>(c))
 231                                 c.s << ")}";
 232                         else
 233                                 c.s << ")";
 234                 }
 235         }
 236 }
 237
 238 bool mul::info(unsigned inf) const
 239 {
 240         switch (inf) {
 241                 case info_flags::polynomial:
 242                 case info_flags::integer_polynomial:
 243                 case info_flags::cinteger_polynomial:
 244                 case info_flags::rational_polynomial:
 245                 case info_flags::crational_polynomial:
 246                 case info_flags::rational_function: {
 247                         epvector::const_iterator i = seq.begin(), end = seq.end();
 248                         while (i != end) {
 249                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 250                                         return false;
 251                                 ++i;
 252                         }
 253                         return overall_coeff.info(inf);
 254                 }
 255                 case info_flags::algebraic: {
 256                         epvector::const_iterator i = seq.begin(), end = seq.end();
 257                         while (i != end) {
 258                                 if ((recombine_pair_to_ex(*i).info(inf)))
 259                                         return true;
 260                                 ++i;
 261                         }
 262                         return false;
 263                 }
 264         }
 265         return inherited::info(inf);
 266 }
 267
 268 int mul::degree(const ex & s) const
 269 {
 270         // Sum up degrees of factors
 271         int deg_sum = 0;
 272         epvector::const_iterator i = seq.begin(), end = seq.end();
 273         while (i != end) {
 274                 if (ex_to<numeric>(i->coeff).is_integer())
 275                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 276                 ++i;
 277         }
 278         return deg_sum;
 279 }
 280
 281 int mul::ldegree(const ex & s) const
 282 {
 283         // Sum up degrees of factors
 284         int deg_sum = 0;
 285         epvector::const_iterator i = seq.begin(), end = seq.end();
 286         while (i != end) {
 287                 if (ex_to<numeric>(i->coeff).is_integer())
 288                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 289                 ++i;
 290         }
 291         return deg_sum;
 292 }
 293
 294 ex mul::coeff(const ex & s, int n) const
 295 {
 296         exvector coeffseq;
 297         coeffseq.reserve(seq.size()+1);
 298
 299         if (n==0) {
 300                 // product of individual coeffs
 301                 // if a non-zero power of s is found, the resulting product will be 0
 302                 epvector::const_iterator i = seq.begin(), end = seq.end();
 303                 while (i != end) {
 304                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 305                         ++i;
 306                 }
 307                 coeffseq.push_back(overall_coeff);
 308                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 309         }
 310
 311         epvector::const_iterator i = seq.begin(), end = seq.end();
 312         bool coeff_found = false;
 313         while (i != end) {
 314                 ex t = recombine_pair_to_ex(*i);
 315                 ex c = t.coeff(s, n);
 316                 if (!c.is_zero()) {
 317                         coeffseq.push_back(c);
 318                         coeff_found = 1;
 319                 } else {
 320                         coeffseq.push_back(t);
 321                 }
 322                 ++i;
 323         }
 324         if (coeff_found) {
 325                 coeffseq.push_back(overall_coeff);
 326                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 327         }
 328
 329         return _ex0;
 330 }
 331
 332 /** Perform automatic term rewriting rules in this class.  In the following
 333  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 334  *  stand for such expressions that contain a plain number.
 335  *  - *(...,x;0) -> 0
 336  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 337  *  - *(x;1) -> x
 338  *  - *(;c) -> c
 339  *
 340  *  @param level cut-off in recursive evaluation */
 341 ex mul::eval(int level) const
 342 {
 343         epvector *evaled_seqp = evalchildren(level);
 344         if (evaled_seqp) {
 345                 // do more evaluation later
 346                 return (new mul(evaled_seqp,overall_coeff))->
 347                            setflag(status_flags::dynallocated);
 348         }
 349
 350 #ifdef DO_GINAC_ASSERT
 351         epvector::const_iterator i = seq.begin(), end = seq.end();
 352         while (i != end) {
 353                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 354                              (!(ex_to<numeric>(i->coeff).is_integer())));
 355                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 356                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 357                     print(print_tree(std::cerr));
 358                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 359                 /* for paranoia */
 360                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 361                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 362                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 363                 /* end paranoia */
 364                 ++i;
 365         }
 366 #endif // def DO_GINAC_ASSERT
 367
 368         if (flags & status_flags::evaluated) {
 369                 GINAC_ASSERT(seq.size()>0);
 370                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 371                 return *this;
 372         }
 373
 374         int seq_size = seq.size();
 375         if (overall_coeff.is_zero()) {
 376                 // *(...,x;0) -> 0
 377                 return _ex0;
 378         } else if (seq_size==0) {
 379                 // *(;c) -> c
 380                 return overall_coeff;
 381         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 382                 // *(x;1) -> x
 383                 return recombine_pair_to_ex(*(seq.begin()));
 384         } else if ((seq_size==1) &&
 385                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 386                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 387                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 388                 const add & addref = ex_to<add>((*seq.begin()).rest);
 389                 epvector *distrseq = new epvector();
 390                 distrseq->reserve(addref.seq.size());
 391                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 392                 while (i != end) {
 393                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 394                         ++i;
 395                 }
 396                 return (new add(distrseq,
 397                                 ex_to<numeric>(addref.overall_coeff).
 398                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 399                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 400         }
 401         return this->hold();
 402 }
 403
 404 ex mul::evalf(int level) const
 405 {
 406         if (level==1)
 407                 return mul(seq,overall_coeff);
 408
 409         if (level==-max_recursion_level)
 410                 throw(std::runtime_error("max recursion level reached"));
 411
 412         epvector *s = new epvector();
 413         s->reserve(seq.size());
 414
 415         --level;
 416         epvector::const_iterator i = seq.begin(), end = seq.end();
 417         while (i != end) {
 418                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 419                                                            i->coeff));
 420                 ++i;
 421         }
 422         return mul(s, overall_coeff.evalf(level));
 423 }
 424
 425 ex mul::evalm(void) const
 426 {
 427         // numeric*matrix
 428         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 429          && is_ex_of_type(seq[0].rest, matrix))
 430                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 431
 432         // Evaluate children first, look whether there are any matrices at all
 433         // (there can be either no matrices or one matrix; if there were more
 434         // than one matrix, it would be a non-commutative product)
 435         epvector *s = new epvector;
 436         s->reserve(seq.size());
 437
 438         bool have_matrix = false;
 439         epvector::iterator the_matrix;
 440
 441         epvector::const_iterator i = seq.begin(), end = seq.end();
 442         while (i != end) {
 443                 const ex &m = recombine_pair_to_ex(*i).evalm();
 444                 s->push_back(split_ex_to_pair(m));
 445                 if (is_ex_of_type(m, matrix)) {
 446                         have_matrix = true;
 447                         the_matrix = s->end() - 1;
 448                 }
 449                 ++i;
 450         }
 451
 452         if (have_matrix) {
 453
 454                 // The product contained a matrix. We will multiply all other factors
 455                 // into that matrix.
 456                 matrix m = ex_to<matrix>(the_matrix->rest);
 457                 s->erase(the_matrix);
 458                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 459                 return m.mul_scalar(scalar);
 460
 461         } else
 462                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 463 }
 464
 465 ex mul::simplify_ncmul(const exvector & v) const
 466 {
 467         if (seq.empty())
 468                 return inherited::simplify_ncmul(v);
 469
 470         // Find first noncommutative element and call its simplify_ncmul()
 471         epvector::const_iterator i = seq.begin(), end = seq.end();
 472         while (i != end) {
 473                 if (i->rest.return_type() == return_types::noncommutative)
 474                         return i->rest.simplify_ncmul(v);
 475                 ++i;
 476         }
 477         return inherited::simplify_ncmul(v);
 478 }
 479
 480 // protected
 481
 482 /** Implementation of ex::diff() for a product.  It applies the product rule.
 483  *  @see ex::diff */
 484 ex mul::derivative(const symbol & s) const
 485 {
 486         unsigned num = seq.size();
 487         exvector addseq;
 488         addseq.reserve(num);
 489
 490         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 491         epvector mulseq = seq;
 492         epvector::const_iterator i = seq.begin(), end = seq.end();
 493         epvector::iterator i2 = mulseq.begin();
 494         while (i != end) {
 495                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 496                                              i->rest.diff(s));
 497                 ep.swap(*i2);
 498                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 499                 ep.swap(*i2);
 500                 ++i; ++i2;
 501         }
 502         return (new add(addseq))->setflag(status_flags::dynallocated);
 503 }
 504
 505 int mul::compare_same_type(const basic & other) const
 506 {
 507         return inherited::compare_same_type(other);
 508 }
 509
 510 bool mul::is_equal_same_type(const basic & other) const
 511 {
 512         return inherited::is_equal_same_type(other);
 513 }
 514
 515 unsigned mul::return_type(void) const
 516 {
 517         if (seq.empty()) {
 518                 // mul without factors: should not happen, but commutes
 519                 return return_types::commutative;
 520         }
 521
 522         bool all_commutative = true;
 523         epvector::const_iterator noncommutative_element; // point to first found nc element
 524
 525         epvector::const_iterator i = seq.begin(), end = seq.end();
 526         while (i != end) {
 527                 unsigned rt = i->rest.return_type();
 528                 if (rt == return_types::noncommutative_composite)
 529                         return rt; // one ncc -> mul also ncc
 530                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 531                         // first nc element found, remember position
 532                         noncommutative_element = i;
 533                         all_commutative = false;
 534                 }
 535                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 536                         // another nc element found, compare type_infos
 537                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 538                                 // diffent types -> mul is ncc
 539                                 return return_types::noncommutative_composite;
 540                         }
 541                 }
 542                 ++i;
 543         }
 544         // all factors checked
 545         return all_commutative ? return_types::commutative : return_types::noncommutative;
 546 }
 547
 548 unsigned mul::return_type_tinfo(void) const
 549 {
 550         if (seq.empty())
 551                 return tinfo_key;  // mul without factors: should not happen
 552
 553         // return type_info of first noncommutative element
 554         epvector::const_iterator i = seq.begin(), end = seq.end();
 555         while (i != end) {
 556                 if (i->rest.return_type() == return_types::noncommutative)
 557                         return i->rest.return_type_tinfo();
 558                 ++i;
 559         }
 560         // no noncommutative element found, should not happen
 561         return tinfo_key;
 562 }
 563
 564 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 565 {
 566         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 567 }
 568
 569 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 570 {
 571         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 572 }
 573
 574 expair mul::split_ex_to_pair(const ex & e) const
 575 {
 576         if (is_ex_exactly_of_type(e,power)) {
 577                 const power & powerref = ex_to<power>(e);
 578                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 579                         return expair(powerref.basis,powerref.exponent);
 580         }
 581         return expair(e,_ex1);
 582 }
 583
 584 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 585                                           const ex & c) const
 586 {
 587         // to avoid duplication of power simplification rules,
 588         // we create a temporary power object
 589         // otherwise it would be hard to correctly simplify
 590         // expression like (4^(1/3))^(3/2)
 591         if (are_ex_trivially_equal(c,_ex1))
 592                 return split_ex_to_pair(e);
 593
 594         return split_ex_to_pair(power(e,c));
 595 }
 596
 597 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 598                                             const ex & c) const
 599 {
 600         // to avoid duplication of power simplification rules,
 601         // we create a temporary power object
 602         // otherwise it would be hard to correctly simplify
 603         // expression like (4^(1/3))^(3/2)
 604         if (are_ex_trivially_equal(c,_ex1))
 605                 return p;
 606
 607         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 608 }
 609
 610 ex mul::recombine_pair_to_ex(const expair & p) const
 611 {
 612         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 613                 return p.rest;
 614         else
 615                 return power(p.rest,p.coeff);
 616 }
 617
 618 bool mul::expair_needs_further_processing(epp it)
 619 {
 620         if (is_ex_exactly_of_type((*it).rest,mul) &&
 621                 ex_to<numeric>((*it).coeff).is_integer()) {
 622                 // combined pair is product with integer power -> expand it
 623                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 624                 return true;
 625         }
 626         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 627                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 628                 if (!ep.is_equal(*it)) {
 629                         // combined pair is a numeric power which can be simplified
 630                         *it = ep;
 631                         return true;
 632                 }
 633                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 634                         // combined pair has coeff 1 and must be moved to the end
 635                         return true;
 636                 }
 637         }
 638         return false;
 639 }
 640
 641 ex mul::default_overall_coeff(void) const
 642 {
 643         return _ex1;
 644 }
 645
 646 void mul::combine_overall_coeff(const ex & c)
 647 {
 648         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 649         GINAC_ASSERT(is_exactly_a<numeric>(c));
 650         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 651 }
 652
 653 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 654 {
 655         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 656         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 657         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 658         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 659 }
 660
 661 bool mul::can_make_flat(const expair & p) const
 662 {
 663         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 664         // this assertion will probably fail somewhere
 665         // it would require a more careful make_flat, obeying the power laws
 666         // probably should return true only if p.coeff is integer
 667         return ex_to<numeric>(p.coeff).is_equal(_num1);
 668 }
 669
 670 ex mul::expand(unsigned options) const
 671 {
 672         // First, expand the children
 673         epvector * expanded_seqp = expandchildren(options);
 674         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 675
 676         // Now, look for all the factors that are sums and multiply each one out
 677         // with the next one that is found while collecting the factors which are
 678         // not sums
 679         int number_of_adds = 0;
 680         ex last_expanded = _ex1;
 681         epvector non_adds;
 682         non_adds.reserve(expanded_seq.size());
 683         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 684         while (cit != last) {
 685                 if (is_ex_exactly_of_type(cit->rest, add) &&
 686                         (cit->coeff.is_equal(_ex1))) {
 687                         ++number_of_adds;
 688                         if (is_ex_exactly_of_type(last_expanded, add)) {
 689                                 const add & add1 = ex_to<add>(last_expanded);
 690                                 const add & add2 = ex_to<add>(cit->rest);
 691                                 int n1 = add1.nops();
 692                                 int n2 = add2.nops();
 693                                 exvector distrseq;
 694                                 distrseq.reserve(n1*n2);
 695                                 for (int i1=0; i1<n1; ++i1) {
 696                                         for (int i2=0; i2<n2; ++i2) {
 697                                                 distrseq.push_back(add1.op(i1) * add2.op(i2));
 698                                         }
 699                                 }
 700                                 last_expanded = (new add(distrseq))->
 701                                                  setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 702                         } else {
 703                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 704                                 last_expanded = cit->rest;
 705                         }
 706                 } else {
 707                         non_adds.push_back(*cit);
 708                 }
 709                 ++cit;
 710         }
 711         if (expanded_seqp)
 712                 delete expanded_seqp;
 713
 714         // Now the only remaining thing to do is to multiply the factors which
 715         // were not sums into the "last_expanded" sum
 716         if (is_ex_exactly_of_type(last_expanded, add)) {
 717                 const add & finaladd = ex_to<add>(last_expanded);
 718                 exvector distrseq;
 719                 int n = finaladd.nops();
 720                 distrseq.reserve(n);
 721                 for (int i=0; i<n; ++i) {
 722                         epvector factors = non_adds;
 723                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 724                         distrseq.push_back((new mul(factors, overall_coeff))->
 725                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 726                 }
 727                 return ((new add(distrseq))->
 728                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 729         }
 730         non_adds.push_back(split_ex_to_pair(last_expanded));
 731         return (new mul(non_adds, overall_coeff))->
 732                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 733 }
 734
 735
 736 //////////
 737 // new virtual functions which can be overridden by derived classes
 738 //////////
 739
 740 // none
 741
 742 //////////
 743 // non-virtual functions in this class
 744 //////////
 745
 746
 747 /** Member-wise expand the expairs representing this sequence.  This must be
 748  *  overridden from expairseq::expandchildren() and done iteratively in order
 749  *  to allow for early cancallations and thus safe memory.
 750  *
 751  *  @see mul::expand()
 752  *  @return pointer to epvector containing expanded representation or zero
 753  *  pointer, if sequence is unchanged. */
 754 epvector * mul::expandchildren(unsigned options) const
 755 {
 756         const epvector::const_iterator last = seq.end();
 757         epvector::const_iterator cit = seq.begin();
 758         while (cit!=last) {
 759                 const ex & factor = recombine_pair_to_ex(*cit);
 760                 const ex & expanded_factor = factor.expand(options);
 761                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 762
 763                         // something changed, copy seq, eval and return it
 764                         epvector *s = new epvector;
 765                         s->reserve(seq.size());
 766
 767                         // copy parts of seq which are known not to have changed
 768                         epvector::const_iterator cit2 = seq.begin();
 769                         while (cit2!=cit) {
 770                                 s->push_back(*cit2);
 771                                 ++cit2;
 772                         }
 773                         // copy first changed element
 774                         s->push_back(split_ex_to_pair(expanded_factor));
 775                         ++cit2;
 776                         // copy rest
 777                         while (cit2!=last) {
 778                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 779                                 ++cit2;
 780                         }
 781                         return s;
 782                 }
 783                 ++cit;
 784         }
 785
 786         return 0; // nothing has changed
 787 }
 788
 789 } // namespace GiNaC