ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2002 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                         bool needclosingparenthesis = false;
 145                         if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
 146                                 if (is_a<print_csrc_cl_N>(c)) {
 147                                         c.s << "recip(";
 148                                         needclosingparenthesis = true;
 149                                 } else
 150                                         c.s << "1.0/";
 151                         }
 152
 153                         // If the exponent is 1 or -1, it is left out
 154                         if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
 155                                 it->rest.print(c, precedence());
 156                         else if (it->coeff.info(info_flags::negint))
 157                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 158                                 (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
 159                         else
 160                                 // Outer parens around ex needed for broken gcc-2.95 parser:
 161                                 (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
 162
 163                         if (needclosingparenthesis)
 164                                 c.s << ")";
 165
 166                         // Separator is "/" for negative integer powers, "*" otherwise
 167                         ++it;
 168                         if (it != itend) {
 169                                 if (it->coeff.info(info_flags::negint))
 170                                         c.s << "/";
 171                                 else
 172                                         c.s << "*";
 173                         }
 174                 }
 175
 176                 if (precedence() <= level)
 177                         c.s << ")";
 178
 179         } else if (is_a<print_python_repr>(c)) {
 180                 c.s << class_name() << '(';
 181                 op(0).print(c);
 182                 for (unsigned i=1; i<nops(); ++i) {
 183                         c.s << ',';
 184                         op(i).print(c);
 185                 }
 186                 c.s << ')';
 187         } else {
 188
 189                 if (precedence() <= level) {
 190                         if (is_a<print_latex>(c))
 191                                 c.s << "{(";
 192                         else
 193                                 c.s << "(";
 194                 }
 195
 196                 bool first = true;
 197
 198                 // First print the overall numeric coefficient
 199                 numeric coeff = ex_to<numeric>(overall_coeff);
 200                 if (coeff.csgn() == -1)
 201                         c.s << '-';
 202                 if (!coeff.is_equal(_num1) &&
 203                         !coeff.is_equal(_num_1)) {
 204                         if (coeff.is_rational()) {
 205                                 if (coeff.is_negative())
 206                                         (-coeff).print(c);
 207                                 else
 208                                         coeff.print(c);
 209                         } else {
 210                                 if (coeff.csgn() == -1)
 211                                         (-coeff).print(c, precedence());
 212                                 else
 213                                         coeff.print(c, precedence());
 214                         }
 215                         if (is_a<print_latex>(c))
 216                                 c.s << ' ';
 217                         else
 218                                 c.s << '*';
 219                 }
 220
 221                 // Then proceed with the remaining factors
 222                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 223                 while (it != itend) {
 224                         if (!first) {
 225                                 if (is_a<print_latex>(c))
 226                                         c.s << ' ';
 227                                 else
 228                                         c.s << '*';
 229                         } else {
 230                                 first = false;
 231                         }
 232                         recombine_pair_to_ex(*it).print(c, precedence());
 233                         ++it;
 234                 }
 235
 236                 if (precedence() <= level) {
 237                         if (is_a<print_latex>(c))
 238                                 c.s << ")}";
 239                         else
 240                                 c.s << ")";
 241                 }
 242         }
 243 }
 244
 245 bool mul::info(unsigned inf) const
 246 {
 247         switch (inf) {
 248                 case info_flags::polynomial:
 249                 case info_flags::integer_polynomial:
 250                 case info_flags::cinteger_polynomial:
 251                 case info_flags::rational_polynomial:
 252                 case info_flags::crational_polynomial:
 253                 case info_flags::rational_function: {
 254                         epvector::const_iterator i = seq.begin(), end = seq.end();
 255                         while (i != end) {
 256                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 257                                         return false;
 258                                 ++i;
 259                         }
 260                         return overall_coeff.info(inf);
 261                 }
 262                 case info_flags::algebraic: {
 263                         epvector::const_iterator i = seq.begin(), end = seq.end();
 264                         while (i != end) {
 265                                 if ((recombine_pair_to_ex(*i).info(inf)))
 266                                         return true;
 267                                 ++i;
 268                         }
 269                         return false;
 270                 }
 271         }
 272         return inherited::info(inf);
 273 }
 274
 275 int mul::degree(const ex & s) const
 276 {
 277         // Sum up degrees of factors
 278         int deg_sum = 0;
 279         epvector::const_iterator i = seq.begin(), end = seq.end();
 280         while (i != end) {
 281                 if (ex_to<numeric>(i->coeff).is_integer())
 282                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 283                 ++i;
 284         }
 285         return deg_sum;
 286 }
 287
 288 int mul::ldegree(const ex & s) const
 289 {
 290         // Sum up degrees of factors
 291         int deg_sum = 0;
 292         epvector::const_iterator i = seq.begin(), end = seq.end();
 293         while (i != end) {
 294                 if (ex_to<numeric>(i->coeff).is_integer())
 295                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 296                 ++i;
 297         }
 298         return deg_sum;
 299 }
 300
 301 ex mul::coeff(const ex & s, int n) const
 302 {
 303         exvector coeffseq;
 304         coeffseq.reserve(seq.size()+1);
 305
 306         if (n==0) {
 307                 // product of individual coeffs
 308                 // if a non-zero power of s is found, the resulting product will be 0
 309                 epvector::const_iterator i = seq.begin(), end = seq.end();
 310                 while (i != end) {
 311                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 312                         ++i;
 313                 }
 314                 coeffseq.push_back(overall_coeff);
 315                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 316         }
 317
 318         epvector::const_iterator i = seq.begin(), end = seq.end();
 319         bool coeff_found = false;
 320         while (i != end) {
 321                 ex t = recombine_pair_to_ex(*i);
 322                 ex c = t.coeff(s, n);
 323                 if (!c.is_zero()) {
 324                         coeffseq.push_back(c);
 325                         coeff_found = 1;
 326                 } else {
 327                         coeffseq.push_back(t);
 328                 }
 329                 ++i;
 330         }
 331         if (coeff_found) {
 332                 coeffseq.push_back(overall_coeff);
 333                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 334         }
 335
 336         return _ex0;
 337 }
 338
 339 /** Perform automatic term rewriting rules in this class.  In the following
 340  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 341  *  stand for such expressions that contain a plain number.
 342  *  - *(...,x;0) -> 0
 343  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 344  *  - *(x;1) -> x
 345  *  - *(;c) -> c
 346  *
 347  *  @param level cut-off in recursive evaluation */
 348 ex mul::eval(int level) const
 349 {
 350         epvector *evaled_seqp = evalchildren(level);
 351         if (evaled_seqp) {
 352                 // do more evaluation later
 353                 return (new mul(evaled_seqp,overall_coeff))->
 354                            setflag(status_flags::dynallocated);
 355         }
 356
 357 #ifdef DO_GINAC_ASSERT
 358         epvector::const_iterator i = seq.begin(), end = seq.end();
 359         while (i != end) {
 360                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 361                              (!(ex_to<numeric>(i->coeff).is_integer())));
 362                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 363                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 364                     print(print_tree(std::cerr));
 365                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 366                 /* for paranoia */
 367                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 368                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 369                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 370                 /* end paranoia */
 371                 ++i;
 372         }
 373 #endif // def DO_GINAC_ASSERT
 374
 375         if (flags & status_flags::evaluated) {
 376                 GINAC_ASSERT(seq.size()>0);
 377                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 378                 return *this;
 379         }
 380
 381         int seq_size = seq.size();
 382         if (overall_coeff.is_zero()) {
 383                 // *(...,x;0) -> 0
 384                 return _ex0;
 385         } else if (seq_size==0) {
 386                 // *(;c) -> c
 387                 return overall_coeff;
 388         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 389                 // *(x;1) -> x
 390                 return recombine_pair_to_ex(*(seq.begin()));
 391         } else if ((seq_size==1) &&
 392                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 393                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 394                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 395                 const add & addref = ex_to<add>((*seq.begin()).rest);
 396                 epvector *distrseq = new epvector();
 397                 distrseq->reserve(addref.seq.size());
 398                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 399                 while (i != end) {
 400                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 401                         ++i;
 402                 }
 403                 return (new add(distrseq,
 404                                 ex_to<numeric>(addref.overall_coeff).
 405                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 406                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 407         }
 408         return this->hold();
 409 }
 410
 411 ex mul::evalf(int level) const
 412 {
 413         if (level==1)
 414                 return mul(seq,overall_coeff);
 415
 416         if (level==-max_recursion_level)
 417                 throw(std::runtime_error("max recursion level reached"));
 418
 419         epvector *s = new epvector();
 420         s->reserve(seq.size());
 421
 422         --level;
 423         epvector::const_iterator i = seq.begin(), end = seq.end();
 424         while (i != end) {
 425                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 426                                                            i->coeff));
 427                 ++i;
 428         }
 429         return mul(s, overall_coeff.evalf(level));
 430 }
 431
 432 ex mul::evalm(void) const
 433 {
 434         // numeric*matrix
 435         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 436          && is_ex_of_type(seq[0].rest, matrix))
 437                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 438
 439         // Evaluate children first, look whether there are any matrices at all
 440         // (there can be either no matrices or one matrix; if there were more
 441         // than one matrix, it would be a non-commutative product)
 442         epvector *s = new epvector;
 443         s->reserve(seq.size());
 444
 445         bool have_matrix = false;
 446         epvector::iterator the_matrix;
 447
 448         epvector::const_iterator i = seq.begin(), end = seq.end();
 449         while (i != end) {
 450                 const ex &m = recombine_pair_to_ex(*i).evalm();
 451                 s->push_back(split_ex_to_pair(m));
 452                 if (is_ex_of_type(m, matrix)) {
 453                         have_matrix = true;
 454                         the_matrix = s->end() - 1;
 455                 }
 456                 ++i;
 457         }
 458
 459         if (have_matrix) {
 460
 461                 // The product contained a matrix. We will multiply all other factors
 462                 // into that matrix.
 463                 matrix m = ex_to<matrix>(the_matrix->rest);
 464                 s->erase(the_matrix);
 465                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 466                 return m.mul_scalar(scalar);
 467
 468         } else
 469                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 470 }
 471
 472 ex mul::simplify_ncmul(const exvector & v) const
 473 {
 474         if (seq.empty())
 475                 return inherited::simplify_ncmul(v);
 476
 477         // Find first noncommutative element and call its simplify_ncmul()
 478         epvector::const_iterator i = seq.begin(), end = seq.end();
 479         while (i != end) {
 480                 if (i->rest.return_type() == return_types::noncommutative)
 481                         return i->rest.simplify_ncmul(v);
 482                 ++i;
 483         }
 484         return inherited::simplify_ncmul(v);
 485 }
 486
 487 // protected
 488
 489 /** Implementation of ex::diff() for a product.  It applies the product rule.
 490  *  @see ex::diff */
 491 ex mul::derivative(const symbol & s) const
 492 {
 493         unsigned num = seq.size();
 494         exvector addseq;
 495         addseq.reserve(num);
 496
 497         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 498         epvector mulseq = seq;
 499         epvector::const_iterator i = seq.begin(), end = seq.end();
 500         epvector::iterator i2 = mulseq.begin();
 501         while (i != end) {
 502                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 503                                              i->rest.diff(s));
 504                 ep.swap(*i2);
 505                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 506                 ep.swap(*i2);
 507                 ++i; ++i2;
 508         }
 509         return (new add(addseq))->setflag(status_flags::dynallocated);
 510 }
 511
 512 int mul::compare_same_type(const basic & other) const
 513 {
 514         return inherited::compare_same_type(other);
 515 }
 516
 517 bool mul::is_equal_same_type(const basic & other) const
 518 {
 519         return inherited::is_equal_same_type(other);
 520 }
 521
 522 unsigned mul::return_type(void) const
 523 {
 524         if (seq.empty()) {
 525                 // mul without factors: should not happen, but commutes
 526                 return return_types::commutative;
 527         }
 528
 529         bool all_commutative = true;
 530         epvector::const_iterator noncommutative_element; // point to first found nc element
 531
 532         epvector::const_iterator i = seq.begin(), end = seq.end();
 533         while (i != end) {
 534                 unsigned rt = i->rest.return_type();
 535                 if (rt == return_types::noncommutative_composite)
 536                         return rt; // one ncc -> mul also ncc
 537                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 538                         // first nc element found, remember position
 539                         noncommutative_element = i;
 540                         all_commutative = false;
 541                 }
 542                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 543                         // another nc element found, compare type_infos
 544                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 545                                 // diffent types -> mul is ncc
 546                                 return return_types::noncommutative_composite;
 547                         }
 548                 }
 549                 ++i;
 550         }
 551         // all factors checked
 552         return all_commutative ? return_types::commutative : return_types::noncommutative;
 553 }
 554
 555 unsigned mul::return_type_tinfo(void) const
 556 {
 557         if (seq.empty())
 558                 return tinfo_key;  // mul without factors: should not happen
 559
 560         // return type_info of first noncommutative element
 561         epvector::const_iterator i = seq.begin(), end = seq.end();
 562         while (i != end) {
 563                 if (i->rest.return_type() == return_types::noncommutative)
 564                         return i->rest.return_type_tinfo();
 565                 ++i;
 566         }
 567         // no noncommutative element found, should not happen
 568         return tinfo_key;
 569 }
 570
 571 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 572 {
 573         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 574 }
 575
 576 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 577 {
 578         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 579 }
 580
 581 expair mul::split_ex_to_pair(const ex & e) const
 582 {
 583         if (is_ex_exactly_of_type(e,power)) {
 584                 const power & powerref = ex_to<power>(e);
 585                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 586                         return expair(powerref.basis,powerref.exponent);
 587         }
 588         return expair(e,_ex1);
 589 }
 590
 591 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 592                                           const ex & c) const
 593 {
 594         // to avoid duplication of power simplification rules,
 595         // we create a temporary power object
 596         // otherwise it would be hard to correctly simplify
 597         // expression like (4^(1/3))^(3/2)
 598         if (are_ex_trivially_equal(c,_ex1))
 599                 return split_ex_to_pair(e);
 600
 601         return split_ex_to_pair(power(e,c));
 602 }
 603
 604 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 605                                             const ex & c) const
 606 {
 607         // to avoid duplication of power simplification rules,
 608         // we create a temporary power object
 609         // otherwise it would be hard to correctly simplify
 610         // expression like (4^(1/3))^(3/2)
 611         if (are_ex_trivially_equal(c,_ex1))
 612                 return p;
 613
 614         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 615 }
 616
 617 ex mul::recombine_pair_to_ex(const expair & p) const
 618 {
 619         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 620                 return p.rest;
 621         else
 622                 return power(p.rest,p.coeff);
 623 }
 624
 625 bool mul::expair_needs_further_processing(epp it)
 626 {
 627         if (is_ex_exactly_of_type((*it).rest,mul) &&
 628                 ex_to<numeric>((*it).coeff).is_integer()) {
 629                 // combined pair is product with integer power -> expand it
 630                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 631                 return true;
 632         }
 633         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 634                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 635                 if (!ep.is_equal(*it)) {
 636                         // combined pair is a numeric power which can be simplified
 637                         *it = ep;
 638                         return true;
 639                 }
 640                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 641                         // combined pair has coeff 1 and must be moved to the end
 642                         return true;
 643                 }
 644         }
 645         return false;
 646 }
 647
 648 ex mul::default_overall_coeff(void) const
 649 {
 650         return _ex1;
 651 }
 652
 653 void mul::combine_overall_coeff(const ex & c)
 654 {
 655         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 656         GINAC_ASSERT(is_exactly_a<numeric>(c));
 657         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 658 }
 659
 660 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 661 {
 662         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 663         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 664         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 665         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 666 }
 667
 668 bool mul::can_make_flat(const expair & p) const
 669 {
 670         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 671         // this assertion will probably fail somewhere
 672         // it would require a more careful make_flat, obeying the power laws
 673         // probably should return true only if p.coeff is integer
 674         return ex_to<numeric>(p.coeff).is_equal(_num1);
 675 }
 676
 677 ex mul::expand(unsigned options) const
 678 {
 679         // First, expand the children
 680         epvector * expanded_seqp = expandchildren(options);
 681         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 682
 683         // Now, look for all the factors that are sums and multiply each one out
 684         // with the next one that is found while collecting the factors which are
 685         // not sums
 686         int number_of_adds = 0;
 687         ex last_expanded = _ex1;
 688         epvector non_adds;
 689         non_adds.reserve(expanded_seq.size());
 690         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 691         while (cit != last) {
 692                 if (is_ex_exactly_of_type(cit->rest, add) &&
 693                         (cit->coeff.is_equal(_ex1))) {
 694                         ++number_of_adds;
 695                         if (is_ex_exactly_of_type(last_expanded, add)) {
 696 #if 0
 697                                 // Expand a product of two sums, simple and robust version.
 698                                 const add & add1 = ex_to<add>(last_expanded);
 699                                 const add & add2 = ex_to<add>(cit->rest);
 700                                 const int n1 = add1.nops();
 701                                 const int n2 = add2.nops();
 702                                 ex tmp_accu;
 703                                 exvector distrseq;
 704                                 distrseq.reserve(n2);
 705                                 for (int i1=0; i1<n1; ++i1) {
 706                                         distrseq.clear();
 707                                         // cache the first operand (for efficiency):
 708                                         const ex op1 = add1.op(i1);
 709                                         for (int i2=0; i2<n2; ++i2)
 710                                                 distrseq.push_back(op1 * add2.op(i2));
 711                                         tmp_accu += (new add(distrseq))->
 712                                                      setflag(status_flags::dynallocated);
 713                                 }
 714                                 last_expanded = tmp_accu;
 715 #else
 716                                 // Expand a product of two sums, aggressive version.
 717                                 // Caring for the overall coefficients in separate loops can
 718                                 // sometimes give a performance gain of up to 15%!
 719
 720                                 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
 721                                 // add2 is for the inner loop and should be the bigger of the two sums
 722                                 // in the presence of asymptotically good sorting:
 723                                 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
 724                                 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
 725                                 const epvector::const_iterator add1begin = add1.seq.begin();
 726                                 const epvector::const_iterator add1end   = add1.seq.end();
 727                                 const epvector::const_iterator add2begin = add2.seq.begin();
 728                                 const epvector::const_iterator add2end   = add2.seq.end();
 729                                 epvector distrseq;
 730                                 distrseq.reserve(add1.seq.size()+add2.seq.size());
 731                                 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
 732                                 if (!add1.overall_coeff.is_zero()) {
 733                                         if (add1.overall_coeff.is_equal(_ex1))
 734                                                 distrseq.insert(distrseq.end(),add2begin,add2end);
 735                                         else
 736                                                 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
 737                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
 738                                 }
 739                                 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
 740                                 if (!add2.overall_coeff.is_zero()) {
 741                                         if (add2.overall_coeff.is_equal(_ex1))
 742                                                 distrseq.insert(distrseq.end(),add1begin,add1end);
 743                                         else
 744                                                 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
 745                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
 746                                 }
 747                                 // Compute the new overall coefficient and put it together:
 748                                 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
 749                                 // Multiply explicitly all non-numeric terms of add1 and add2:
 750                                 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
 751                                         // We really have to combine terms here in order to compactify
 752                                         // the result.  Otherwise it would become waayy tooo bigg.
 753                                         numeric oc;
 754                                         distrseq.clear();
 755                                         for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
 756                                                 // Don't push_back expairs which might have a rest that evaluates to a numeric,
 757                                                 // since that would violate an invariant of expairseq:
 758                                                 const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
 759                                                 if (is_ex_exactly_of_type(rest, numeric))
 760                                                         oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
 761                                                 else
 762                                                         distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
 763                                         }
 764                                         tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
 765                                 }
 766                                 last_expanded = tmp_accu;
 767 #endif
 768                         } else {
 769                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 770                                 last_expanded = cit->rest;
 771                         }
 772                 } else {
 773                         non_adds.push_back(*cit);
 774                 }
 775                 ++cit;
 776         }
 777         if (expanded_seqp)
 778                 delete expanded_seqp;
 779
 780         // Now the only remaining thing to do is to multiply the factors which
 781         // were not sums into the "last_expanded" sum
 782         if (is_ex_exactly_of_type(last_expanded, add)) {
 783                 const add & finaladd = ex_to<add>(last_expanded);
 784                 exvector distrseq;
 785                 int n = finaladd.nops();
 786                 distrseq.reserve(n);
 787                 for (int i=0; i<n; ++i) {
 788                         epvector factors = non_adds;
 789                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 790                         distrseq.push_back((new mul(factors, overall_coeff))->
 791                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 792                 }
 793                 return ((new add(distrseq))->
 794                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 795         }
 796         non_adds.push_back(split_ex_to_pair(last_expanded));
 797         return (new mul(non_adds, overall_coeff))->
 798                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 799 }
 800
 801
 802 //////////
 803 // new virtual functions which can be overridden by derived classes
 804 //////////
 805
 806 // none
 807
 808 //////////
 809 // non-virtual functions in this class
 810 //////////
 811
 812
 813 /** Member-wise expand the expairs representing this sequence.  This must be
 814  *  overridden from expairseq::expandchildren() and done iteratively in order
 815  *  to allow for early cancallations and thus safe memory.
 816  *
 817  *  @see mul::expand()
 818  *  @return pointer to epvector containing expanded representation or zero
 819  *  pointer, if sequence is unchanged. */
 820 epvector * mul::expandchildren(unsigned options) const
 821 {
 822         const epvector::const_iterator last = seq.end();
 823         epvector::const_iterator cit = seq.begin();
 824         while (cit!=last) {
 825                 const ex & factor = recombine_pair_to_ex(*cit);
 826                 const ex & expanded_factor = factor.expand(options);
 827                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 828
 829                         // something changed, copy seq, eval and return it
 830                         epvector *s = new epvector;
 831                         s->reserve(seq.size());
 832
 833                         // copy parts of seq which are known not to have changed
 834                         epvector::const_iterator cit2 = seq.begin();
 835                         while (cit2!=cit) {
 836                                 s->push_back(*cit2);
 837                                 ++cit2;
 838                         }
 839                         // copy first changed element
 840                         s->push_back(split_ex_to_pair(expanded_factor));
 841                         ++cit2;
 842                         // copy rest
 843                         while (cit2!=last) {
 844                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 845                                 ++cit2;
 846                         }
 847                         return s;
 848                 }
 849                 ++cit;
 850         }
 851
 852         return 0; // nothing has changed
 853 }
 854
 855 } // namespace GiNaC