ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2003 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                 // First print the overall numeric coefficient
 197                 numeric coeff = ex_to<numeric>(overall_coeff);
 198                 if (coeff.csgn() == -1)
 199                         c.s << '-';
 200                 if (!coeff.is_equal(_num1) &&
 201                         !coeff.is_equal(_num_1)) {
 202                         if (coeff.is_rational()) {
 203                                 if (coeff.is_negative())
 204                                         (-coeff).print(c);
 205                                 else
 206                                         coeff.print(c);
 207                         } else {
 208                                 if (coeff.csgn() == -1)
 209                                         (-coeff).print(c, precedence());
 210                                 else
 211                                         coeff.print(c, precedence());
 212                         }
 213                         if (is_a<print_latex>(c))
 214                                 c.s << ' ';
 215                         else
 216                                 c.s << '*';
 217                 }
 218
 219                 // Then proceed with the remaining factors
 220                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 221                 if (is_a<print_latex>(c)) {
 222
 223                         // Separate factors into those with negative numeric exponent
 224                         // and all others
 225                         exvector neg_powers, others;
 226                         while (it != itend) {
 227                                 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
 228                                 if (ex_to<numeric>(it->coeff).is_negative())
 229                                         neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
 230                                 else
 231                                         others.push_back(recombine_pair_to_ex(*it));
 232                                 ++it;
 233                         }
 234
 235                         if (!neg_powers.empty()) {
 236
 237                                 // Factors with negative exponent are printed as a fraction
 238                                 c.s << "\\frac{";
 239                                 mul(others).eval().print(c);
 240                                 c.s << "}{";
 241                                 mul(neg_powers).eval().print(c);
 242                                 c.s << "}";
 243
 244                         } else {
 245
 246                                 // All other factors are printed in the ordinary way
 247                                 exvector::const_iterator vit = others.begin(), vitend = others.end();
 248                                 while (vit != vitend) {
 249                                         c.s << ' ';
 250                                         vit->print(c, precedence());
 251                                         ++vit;
 252                                 }
 253                         }
 254
 255                 } else {
 256
 257                         bool first = true;
 258                         while (it != itend) {
 259                                 if (!first)
 260                                         c.s << '*';
 261                                 else
 262                                         first = false;
 263                                 recombine_pair_to_ex(*it).print(c, precedence());
 264                                 ++it;
 265                         }
 266                 }
 267
 268                 if (precedence() <= level) {
 269                         if (is_a<print_latex>(c))
 270                                 c.s << ")}";
 271                         else
 272                                 c.s << ")";
 273                 }
 274         }
 275 }
 276
 277 bool mul::info(unsigned inf) const
 278 {
 279         switch (inf) {
 280                 case info_flags::polynomial:
 281                 case info_flags::integer_polynomial:
 282                 case info_flags::cinteger_polynomial:
 283                 case info_flags::rational_polynomial:
 284                 case info_flags::crational_polynomial:
 285                 case info_flags::rational_function: {
 286                         epvector::const_iterator i = seq.begin(), end = seq.end();
 287                         while (i != end) {
 288                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 289                                         return false;
 290                                 ++i;
 291                         }
 292                         return overall_coeff.info(inf);
 293                 }
 294                 case info_flags::algebraic: {
 295                         epvector::const_iterator i = seq.begin(), end = seq.end();
 296                         while (i != end) {
 297                                 if ((recombine_pair_to_ex(*i).info(inf)))
 298                                         return true;
 299                                 ++i;
 300                         }
 301                         return false;
 302                 }
 303         }
 304         return inherited::info(inf);
 305 }
 306
 307 int mul::degree(const ex & s) const
 308 {
 309         // Sum up degrees of factors
 310         int deg_sum = 0;
 311         epvector::const_iterator i = seq.begin(), end = seq.end();
 312         while (i != end) {
 313                 if (ex_to<numeric>(i->coeff).is_integer())
 314                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 315                 ++i;
 316         }
 317         return deg_sum;
 318 }
 319
 320 int mul::ldegree(const ex & s) const
 321 {
 322         // Sum up degrees of factors
 323         int deg_sum = 0;
 324         epvector::const_iterator i = seq.begin(), end = seq.end();
 325         while (i != end) {
 326                 if (ex_to<numeric>(i->coeff).is_integer())
 327                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 328                 ++i;
 329         }
 330         return deg_sum;
 331 }
 332
 333 ex mul::coeff(const ex & s, int n) const
 334 {
 335         exvector coeffseq;
 336         coeffseq.reserve(seq.size()+1);
 337
 338         if (n==0) {
 339                 // product of individual coeffs
 340                 // if a non-zero power of s is found, the resulting product will be 0
 341                 epvector::const_iterator i = seq.begin(), end = seq.end();
 342                 while (i != end) {
 343                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 344                         ++i;
 345                 }
 346                 coeffseq.push_back(overall_coeff);
 347                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 348         }
 349
 350         epvector::const_iterator i = seq.begin(), end = seq.end();
 351         bool coeff_found = false;
 352         while (i != end) {
 353                 ex t = recombine_pair_to_ex(*i);
 354                 ex c = t.coeff(s, n);
 355                 if (!c.is_zero()) {
 356                         coeffseq.push_back(c);
 357                         coeff_found = 1;
 358                 } else {
 359                         coeffseq.push_back(t);
 360                 }
 361                 ++i;
 362         }
 363         if (coeff_found) {
 364                 coeffseq.push_back(overall_coeff);
 365                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 366         }
 367
 368         return _ex0;
 369 }
 370
 371 /** Perform automatic term rewriting rules in this class.  In the following
 372  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 373  *  stand for such expressions that contain a plain number.
 374  *  - *(...,x;0) -> 0
 375  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 376  *  - *(x;1) -> x
 377  *  - *(;c) -> c
 378  *
 379  *  @param level cut-off in recursive evaluation */
 380 ex mul::eval(int level) const
 381 {
 382         epvector *evaled_seqp = evalchildren(level);
 383         if (evaled_seqp) {
 384                 // do more evaluation later
 385                 return (new mul(evaled_seqp,overall_coeff))->
 386                            setflag(status_flags::dynallocated);
 387         }
 388
 389 #ifdef DO_GINAC_ASSERT
 390         epvector::const_iterator i = seq.begin(), end = seq.end();
 391         while (i != end) {
 392                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 393                              (!(ex_to<numeric>(i->coeff).is_integer())));
 394                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 395                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
 396                     print(print_tree(std::cerr));
 397                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 398                 /* for paranoia */
 399                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 400                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 401                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 402                 /* end paranoia */
 403                 ++i;
 404         }
 405 #endif // def DO_GINAC_ASSERT
 406
 407         if (flags & status_flags::evaluated) {
 408                 GINAC_ASSERT(seq.size()>0);
 409                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 410                 return *this;
 411         }
 412
 413         int seq_size = seq.size();
 414         if (overall_coeff.is_zero()) {
 415                 // *(...,x;0) -> 0
 416                 return _ex0;
 417         } else if (seq_size==0) {
 418                 // *(;c) -> c
 419                 return overall_coeff;
 420         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 421                 // *(x;1) -> x
 422                 return recombine_pair_to_ex(*(seq.begin()));
 423         } else if ((seq_size==1) &&
 424                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 425                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 426                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 427                 const add & addref = ex_to<add>((*seq.begin()).rest);
 428                 epvector *distrseq = new epvector();
 429                 distrseq->reserve(addref.seq.size());
 430                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 431                 while (i != end) {
 432                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 433                         ++i;
 434                 }
 435                 return (new add(distrseq,
 436                                 ex_to<numeric>(addref.overall_coeff).
 437                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 438                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 439         }
 440         return this->hold();
 441 }
 442
 443 ex mul::evalf(int level) const
 444 {
 445         if (level==1)
 446                 return mul(seq,overall_coeff);
 447
 448         if (level==-max_recursion_level)
 449                 throw(std::runtime_error("max recursion level reached"));
 450
 451         epvector *s = new epvector();
 452         s->reserve(seq.size());
 453
 454         --level;
 455         epvector::const_iterator i = seq.begin(), end = seq.end();
 456         while (i != end) {
 457                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 458                                                            i->coeff));
 459                 ++i;
 460         }
 461         return mul(s, overall_coeff.evalf(level));
 462 }
 463
 464 ex mul::evalm(void) const
 465 {
 466         // numeric*matrix
 467         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 468          && is_ex_of_type(seq[0].rest, matrix))
 469                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 470
 471         // Evaluate children first, look whether there are any matrices at all
 472         // (there can be either no matrices or one matrix; if there were more
 473         // than one matrix, it would be a non-commutative product)
 474         epvector *s = new epvector;
 475         s->reserve(seq.size());
 476
 477         bool have_matrix = false;
 478         epvector::iterator the_matrix;
 479
 480         epvector::const_iterator i = seq.begin(), end = seq.end();
 481         while (i != end) {
 482                 const ex &m = recombine_pair_to_ex(*i).evalm();
 483                 s->push_back(split_ex_to_pair(m));
 484                 if (is_ex_of_type(m, matrix)) {
 485                         have_matrix = true;
 486                         the_matrix = s->end() - 1;
 487                 }
 488                 ++i;
 489         }
 490
 491         if (have_matrix) {
 492
 493                 // The product contained a matrix. We will multiply all other factors
 494                 // into that matrix.
 495                 matrix m = ex_to<matrix>(the_matrix->rest);
 496                 s->erase(the_matrix);
 497                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 498                 return m.mul_scalar(scalar);
 499
 500         } else
 501                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 502 }
 503
 504 ex mul::simplify_ncmul(const exvector & v) const
 505 {
 506         if (seq.empty())
 507                 return inherited::simplify_ncmul(v);
 508
 509         // Find first noncommutative element and call its simplify_ncmul()
 510         epvector::const_iterator i = seq.begin(), end = seq.end();
 511         while (i != end) {
 512                 if (i->rest.return_type() == return_types::noncommutative)
 513                         return i->rest.simplify_ncmul(v);
 514                 ++i;
 515         }
 516         return inherited::simplify_ncmul(v);
 517 }
 518
 519 // protected
 520
 521 /** Implementation of ex::diff() for a product.  It applies the product rule.
 522  *  @see ex::diff */
 523 ex mul::derivative(const symbol & s) const
 524 {
 525         unsigned num = seq.size();
 526         exvector addseq;
 527         addseq.reserve(num);
 528
 529         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 530         epvector mulseq = seq;
 531         epvector::const_iterator i = seq.begin(), end = seq.end();
 532         epvector::iterator i2 = mulseq.begin();
 533         while (i != end) {
 534                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 535                                              i->rest.diff(s));
 536                 ep.swap(*i2);
 537                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 538                 ep.swap(*i2);
 539                 ++i; ++i2;
 540         }
 541         return (new add(addseq))->setflag(status_flags::dynallocated);
 542 }
 543
 544 int mul::compare_same_type(const basic & other) const
 545 {
 546         return inherited::compare_same_type(other);
 547 }
 548
 549 bool mul::is_equal_same_type(const basic & other) const
 550 {
 551         return inherited::is_equal_same_type(other);
 552 }
 553
 554 unsigned mul::return_type(void) const
 555 {
 556         if (seq.empty()) {
 557                 // mul without factors: should not happen, but commutes
 558                 return return_types::commutative;
 559         }
 560
 561         bool all_commutative = true;
 562         epvector::const_iterator noncommutative_element; // point to first found nc element
 563
 564         epvector::const_iterator i = seq.begin(), end = seq.end();
 565         while (i != end) {
 566                 unsigned rt = i->rest.return_type();
 567                 if (rt == return_types::noncommutative_composite)
 568                         return rt; // one ncc -> mul also ncc
 569                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 570                         // first nc element found, remember position
 571                         noncommutative_element = i;
 572                         all_commutative = false;
 573                 }
 574                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 575                         // another nc element found, compare type_infos
 576                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 577                                 // diffent types -> mul is ncc
 578                                 return return_types::noncommutative_composite;
 579                         }
 580                 }
 581                 ++i;
 582         }
 583         // all factors checked
 584         return all_commutative ? return_types::commutative : return_types::noncommutative;
 585 }
 586
 587 unsigned mul::return_type_tinfo(void) const
 588 {
 589         if (seq.empty())
 590                 return tinfo_key;  // mul without factors: should not happen
 591
 592         // return type_info of first noncommutative element
 593         epvector::const_iterator i = seq.begin(), end = seq.end();
 594         while (i != end) {
 595                 if (i->rest.return_type() == return_types::noncommutative)
 596                         return i->rest.return_type_tinfo();
 597                 ++i;
 598         }
 599         // no noncommutative element found, should not happen
 600         return tinfo_key;
 601 }
 602
 603 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 604 {
 605         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 606 }
 607
 608 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 609 {
 610         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 611 }
 612
 613 expair mul::split_ex_to_pair(const ex & e) const
 614 {
 615         if (is_ex_exactly_of_type(e,power)) {
 616                 const power & powerref = ex_to<power>(e);
 617                 if (is_ex_exactly_of_type(powerref.exponent,numeric))
 618                         return expair(powerref.basis,powerref.exponent);
 619         }
 620         return expair(e,_ex1);
 621 }
 622
 623 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 624                                           const ex & c) const
 625 {
 626         // to avoid duplication of power simplification rules,
 627         // we create a temporary power object
 628         // otherwise it would be hard to correctly simplify
 629         // expression like (4^(1/3))^(3/2)
 630         if (are_ex_trivially_equal(c,_ex1))
 631                 return split_ex_to_pair(e);
 632
 633         return split_ex_to_pair(power(e,c));
 634 }
 635
 636 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 637                                             const ex & c) const
 638 {
 639         // to avoid duplication of power simplification rules,
 640         // we create a temporary power object
 641         // otherwise it would be hard to correctly simplify
 642         // expression like (4^(1/3))^(3/2)
 643         if (are_ex_trivially_equal(c,_ex1))
 644                 return p;
 645
 646         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 647 }
 648
 649 ex mul::recombine_pair_to_ex(const expair & p) const
 650 {
 651         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 652                 return p.rest;
 653         else
 654                 return power(p.rest,p.coeff);
 655 }
 656
 657 bool mul::expair_needs_further_processing(epp it)
 658 {
 659         if (is_ex_exactly_of_type((*it).rest,mul) &&
 660                 ex_to<numeric>((*it).coeff).is_integer()) {
 661                 // combined pair is product with integer power -> expand it
 662                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 663                 return true;
 664         }
 665         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 666                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 667                 if (!ep.is_equal(*it)) {
 668                         // combined pair is a numeric power which can be simplified
 669                         *it = ep;
 670                         return true;
 671                 }
 672                 if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 673                         // combined pair has coeff 1 and must be moved to the end
 674                         return true;
 675                 }
 676         }
 677         return false;
 678 }
 679
 680 ex mul::default_overall_coeff(void) const
 681 {
 682         return _ex1;
 683 }
 684
 685 void mul::combine_overall_coeff(const ex & c)
 686 {
 687         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 688         GINAC_ASSERT(is_exactly_a<numeric>(c));
 689         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 690 }
 691
 692 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 693 {
 694         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 695         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 696         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 697         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 698 }
 699
 700 bool mul::can_make_flat(const expair & p) const
 701 {
 702         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 703         // this assertion will probably fail somewhere
 704         // it would require a more careful make_flat, obeying the power laws
 705         // probably should return true only if p.coeff is integer
 706         return ex_to<numeric>(p.coeff).is_equal(_num1);
 707 }
 708
 709 ex mul::expand(unsigned options) const
 710 {
 711         // First, expand the children
 712         epvector * expanded_seqp = expandchildren(options);
 713         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 714
 715         // Now, look for all the factors that are sums and multiply each one out
 716         // with the next one that is found while collecting the factors which are
 717         // not sums
 718         int number_of_adds = 0;
 719         ex last_expanded = _ex1;
 720         epvector non_adds;
 721         non_adds.reserve(expanded_seq.size());
 722         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 723         while (cit != last) {
 724                 if (is_ex_exactly_of_type(cit->rest, add) &&
 725                         (cit->coeff.is_equal(_ex1))) {
 726                         ++number_of_adds;
 727                         if (is_ex_exactly_of_type(last_expanded, add)) {
 728 #if 0
 729                                 // Expand a product of two sums, simple and robust version.
 730                                 const add & add1 = ex_to<add>(last_expanded);
 731                                 const add & add2 = ex_to<add>(cit->rest);
 732                                 const int n1 = add1.nops();
 733                                 const int n2 = add2.nops();
 734                                 ex tmp_accu;
 735                                 exvector distrseq;
 736                                 distrseq.reserve(n2);
 737                                 for (int i1=0; i1<n1; ++i1) {
 738                                         distrseq.clear();
 739                                         // cache the first operand (for efficiency):
 740                                         const ex op1 = add1.op(i1);
 741                                         for (int i2=0; i2<n2; ++i2)
 742                                                 distrseq.push_back(op1 * add2.op(i2));
 743                                         tmp_accu += (new add(distrseq))->
 744                                                      setflag(status_flags::dynallocated);
 745                                 }
 746                                 last_expanded = tmp_accu;
 747 #else
 748                                 // Expand a product of two sums, aggressive version.
 749                                 // Caring for the overall coefficients in separate loops can
 750                                 // sometimes give a performance gain of up to 15%!
 751
 752                                 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
 753                                 // add2 is for the inner loop and should be the bigger of the two sums
 754                                 // in the presence of asymptotically good sorting:
 755                                 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
 756                                 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
 757                                 const epvector::const_iterator add1begin = add1.seq.begin();
 758                                 const epvector::const_iterator add1end   = add1.seq.end();
 759                                 const epvector::const_iterator add2begin = add2.seq.begin();
 760                                 const epvector::const_iterator add2end   = add2.seq.end();
 761                                 epvector distrseq;
 762                                 distrseq.reserve(add1.seq.size()+add2.seq.size());
 763                                 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
 764                                 if (!add1.overall_coeff.is_zero()) {
 765                                         if (add1.overall_coeff.is_equal(_ex1))
 766                                                 distrseq.insert(distrseq.end(),add2begin,add2end);
 767                                         else
 768                                                 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
 769                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
 770                                 }
 771                                 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
 772                                 if (!add2.overall_coeff.is_zero()) {
 773                                         if (add2.overall_coeff.is_equal(_ex1))
 774                                                 distrseq.insert(distrseq.end(),add1begin,add1end);
 775                                         else
 776                                                 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
 777                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
 778                                 }
 779                                 // Compute the new overall coefficient and put it together:
 780                                 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
 781                                 // Multiply explicitly all non-numeric terms of add1 and add2:
 782                                 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
 783                                         // We really have to combine terms here in order to compactify
 784                                         // the result.  Otherwise it would become waayy tooo bigg.
 785                                         numeric oc;
 786                                         distrseq.clear();
 787                                         for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
 788                                                 // Don't push_back expairs which might have a rest that evaluates to a numeric,
 789                                                 // since that would violate an invariant of expairseq:
 790                                                 const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
 791                                                 if (is_ex_exactly_of_type(rest, numeric))
 792                                                         oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
 793                                                 else
 794                                                         distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
 795                                         }
 796                                         tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
 797                                 }
 798                                 last_expanded = tmp_accu;
 799 #endif
 800                         } else {
 801                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 802                                 last_expanded = cit->rest;
 803                         }
 804                 } else {
 805                         non_adds.push_back(*cit);
 806                 }
 807                 ++cit;
 808         }
 809         if (expanded_seqp)
 810                 delete expanded_seqp;
 811
 812         // Now the only remaining thing to do is to multiply the factors which
 813         // were not sums into the "last_expanded" sum
 814         if (is_ex_exactly_of_type(last_expanded, add)) {
 815                 const add & finaladd = ex_to<add>(last_expanded);
 816                 exvector distrseq;
 817                 int n = finaladd.nops();
 818                 distrseq.reserve(n);
 819                 for (int i=0; i<n; ++i) {
 820                         epvector factors = non_adds;
 821                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 822                         distrseq.push_back((new mul(factors, overall_coeff))->
 823                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 824                 }
 825                 return ((new add(distrseq))->
 826                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 827         }
 828         non_adds.push_back(split_ex_to_pair(last_expanded));
 829         return (new mul(non_adds, overall_coeff))->
 830                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 831 }
 832
 833
 834 //////////
 835 // new virtual functions which can be overridden by derived classes
 836 //////////
 837
 838 // none
 839
 840 //////////
 841 // non-virtual functions in this class
 842 //////////
 843
 844
 845 /** Member-wise expand the expairs representing this sequence.  This must be
 846  *  overridden from expairseq::expandchildren() and done iteratively in order
 847  *  to allow for early cancallations and thus safe memory.
 848  *
 849  *  @see mul::expand()
 850  *  @return pointer to epvector containing expanded representation or zero
 851  *  pointer, if sequence is unchanged. */
 852 epvector * mul::expandchildren(unsigned options) const
 853 {
 854         const epvector::const_iterator last = seq.end();
 855         epvector::const_iterator cit = seq.begin();
 856         while (cit!=last) {
 857                 const ex & factor = recombine_pair_to_ex(*cit);
 858                 const ex & expanded_factor = factor.expand(options);
 859                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 860
 861                         // something changed, copy seq, eval and return it
 862                         epvector *s = new epvector;
 863                         s->reserve(seq.size());
 864
 865                         // copy parts of seq which are known not to have changed
 866                         epvector::const_iterator cit2 = seq.begin();
 867                         while (cit2!=cit) {
 868                                 s->push_back(*cit2);
 869                                 ++cit2;
 870                         }
 871                         // copy first changed element
 872                         s->push_back(split_ex_to_pair(expanded_factor));
 873                         ++cit2;
 874                         // copy rest
 875                         while (cit2!=last) {
 876                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 877                                 ++cit2;
 878                         }
 879                         return s;
 880                 }
 881                 ++cit;
 882         }
 883
 884         return 0; // nothing has changed
 885 }
 886
 887 } // namespace GiNaC