ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include "mul.h"
  24 #include "add.h"
  25 #include "power.h"
  26 #include "operators.h"
  27 #include "matrix.h"
  28 #include "indexed.h"
  29 #include "lst.h"
  30 #include "archive.h"
  31 #include "utils.h"
  32 #include "symbol.h"
  33 #include "compiler.h"
  34
  35 #include <iostream>
  36 #include <limits>
  37 #include <stdexcept>
  38 #include <vector>
  39
  40 namespace GiNaC {
  41
  42 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
  43   print_func<print_context>(&mul::do_print).
  44   print_func<print_latex>(&mul::do_print_latex).
  45   print_func<print_csrc>(&mul::do_print_csrc).
  46   print_func<print_tree>(&mul::do_print_tree).
  47   print_func<print_python_repr>(&mul::do_print_python_repr))
  48
  49
  50 //////////
  51 // default constructor
  52 //////////
  53
  54 mul::mul()
  55 {
  56 }
  57
  58 //////////
  59 // other constructors
  60 //////////
  61
  62 // public
  63
  64 mul::mul(const ex & lh, const ex & rh)
  65 {
  66         overall_coeff = _ex1;
  67         construct_from_2_ex(lh,rh);
  68         GINAC_ASSERT(is_canonical());
  69 }
  70
  71 mul::mul(const exvector & v)
  72 {
  73         overall_coeff = _ex1;
  74         construct_from_exvector(v);
  75         GINAC_ASSERT(is_canonical());
  76 }
  77
  78 mul::mul(const epvector & v)
  79 {
  80         overall_coeff = _ex1;
  81         construct_from_epvector(v);
  82         GINAC_ASSERT(is_canonical());
  83 }
  84
  85 mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
  86 {
  87         overall_coeff = oc;
  88         construct_from_epvector(v, do_index_renaming);
  89         GINAC_ASSERT(is_canonical());
  90 }
  91
  92 mul::mul(epvector && vp, const ex & oc, bool do_index_renaming)
  93 {
  94         overall_coeff = oc;
  95         construct_from_epvector(std::move(vp), do_index_renaming);
  96         GINAC_ASSERT(is_canonical());
  97 }
  98
  99 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 100 {
 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 //////////
 116 // functions overriding virtual functions from base classes
 117 //////////
 118
 119 void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
 120 {
 121         const numeric &coeff = ex_to<numeric>(overall_coeff);
 122         if (coeff.csgn() == -1)
 123                 c.s << '-';
 124         if (!coeff.is_equal(*_num1_p) &&
 125                 !coeff.is_equal(*_num_1_p)) {
 126                 if (coeff.is_rational()) {
 127                         if (coeff.is_negative())
 128                                 (-coeff).print(c);
 129                         else
 130                                 coeff.print(c);
 131                 } else {
 132                         if (coeff.csgn() == -1)
 133                                 (-coeff).print(c, precedence());
 134                         else
 135                                 coeff.print(c, precedence());
 136                 }
 137                 c.s << mul_sym;
 138         }
 139 }
 140
 141 void mul::do_print(const print_context & c, unsigned level) const
 142 {
 143         if (precedence() <= level)
 144                 c.s << '(';
 145
 146         print_overall_coeff(c, "*");
 147
 148         epvector::const_iterator it = seq.begin(), itend = seq.end();
 149         bool first = true;
 150         while (it != itend) {
 151                 if (!first)
 152                         c.s << '*';
 153                 else
 154                         first = false;
 155                 recombine_pair_to_ex(*it).print(c, precedence());
 156                 ++it;
 157         }
 158
 159         if (precedence() <= level)
 160                 c.s << ')';
 161 }
 162
 163 void mul::do_print_latex(const print_latex & c, unsigned level) const
 164 {
 165         if (precedence() <= level)
 166                 c.s << "{(";
 167
 168         print_overall_coeff(c, " ");
 169
 170         // Separate factors into those with negative numeric exponent
 171         // and all others
 172         epvector::const_iterator it = seq.begin(), itend = seq.end();
 173         exvector neg_powers, others;
 174         while (it != itend) {
 175                 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
 176                 if (ex_to<numeric>(it->coeff).is_negative())
 177                         neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
 178                 else
 179                         others.push_back(recombine_pair_to_ex(*it));
 180                 ++it;
 181         }
 182
 183         if (!neg_powers.empty()) {
 184
 185                 // Factors with negative exponent are printed as a fraction
 186                 c.s << "\\frac{";
 187                 mul(others).eval().print(c);
 188                 c.s << "}{";
 189                 mul(neg_powers).eval().print(c);
 190                 c.s << "}";
 191
 192         } else {
 193
 194                 // All other factors are printed in the ordinary way
 195                 exvector::const_iterator vit = others.begin(), vitend = others.end();
 196                 while (vit != vitend) {
 197                         c.s << ' ';
 198                         vit->print(c, precedence());
 199                         ++vit;
 200                 }
 201         }
 202
 203         if (precedence() <= level)
 204                 c.s << ")}";
 205 }
 206
 207 void mul::do_print_csrc(const print_csrc & c, unsigned level) const
 208 {
 209         if (precedence() <= level)
 210                 c.s << "(";
 211
 212         if (!overall_coeff.is_equal(_ex1)) {
 213                 if (overall_coeff.is_equal(_ex_1))
 214                         c.s << "-";
 215                 else {
 216                         overall_coeff.print(c, precedence());
 217                         c.s << "*";
 218                 }
 219         }
 220
 221         // Print arguments, separated by "*" or "/"
 222         epvector::const_iterator it = seq.begin(), itend = seq.end();
 223         while (it != itend) {
 224
 225                 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 226                 bool needclosingparenthesis = false;
 227                 if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
 228                         if (is_a<print_csrc_cl_N>(c)) {
 229                                 c.s << "recip(";
 230                                 needclosingparenthesis = true;
 231                         } else
 232                                 c.s << "1.0/";
 233                 }
 234
 235                 // If the exponent is 1 or -1, it is left out
 236                 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
 237                         it->rest.print(c, precedence());
 238                 else if (it->coeff.info(info_flags::negint))
 239                         // Outer parens around ex needed for broken GCC parser:
 240                         (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
 241                 else
 242                         // Outer parens around ex needed for broken GCC parser:
 243                         (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
 244
 245                 if (needclosingparenthesis)
 246                         c.s << ")";
 247
 248                 // Separator is "/" for negative integer powers, "*" otherwise
 249                 ++it;
 250                 if (it != itend) {
 251                         if (it->coeff.info(info_flags::negint))
 252                                 c.s << "/";
 253                         else
 254                                 c.s << "*";
 255                 }
 256         }
 257
 258         if (precedence() <= level)
 259                 c.s << ")";
 260 }
 261
 262 void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
 263 {
 264         c.s << class_name() << '(';
 265         op(0).print(c);
 266         for (size_t i=1; i<nops(); ++i) {
 267                 c.s << ',';
 268                 op(i).print(c);
 269         }
 270         c.s << ')';
 271 }
 272
 273 bool mul::info(unsigned inf) const
 274 {
 275         switch (inf) {
 276                 case info_flags::polynomial:
 277                 case info_flags::integer_polynomial:
 278                 case info_flags::cinteger_polynomial:
 279                 case info_flags::rational_polynomial:
 280                 case info_flags::real:
 281                 case info_flags::rational:
 282                 case info_flags::integer:
 283                 case info_flags::crational:
 284                 case info_flags::cinteger:
 285                 case info_flags::even:
 286                 case info_flags::crational_polynomial:
 287                 case info_flags::rational_function: {
 288                         epvector::const_iterator i = seq.begin(), end = seq.end();
 289                         while (i != end) {
 290                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 291                                         return false;
 292                                 ++i;
 293                         }
 294                         if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even)
 295                                 return true;
 296                         return overall_coeff.info(inf);
 297                 }
 298                 case info_flags::algebraic: {
 299                         epvector::const_iterator i = seq.begin(), end = seq.end();
 300                         while (i != end) {
 301                                 if ((recombine_pair_to_ex(*i).info(inf)))
 302                                         return true;
 303                                 ++i;
 304                         }
 305                         return false;
 306                 }
 307                 case info_flags::positive:
 308                 case info_flags::negative: {
 309                         if ((inf==info_flags::positive) && (flags & status_flags::is_positive))
 310                                 return true;
 311                         else if ((inf==info_flags::negative) && (flags & status_flags::is_negative))
 312                                 return true;
 313                         if (flags & status_flags::purely_indefinite)
 314                                 return false;
 315
 316                         bool pos = true;
 317                         epvector::const_iterator i = seq.begin(), end = seq.end();
 318                         while (i != end) {
 319                                 const ex& factor = recombine_pair_to_ex(*i++);
 320                                 if (factor.info(info_flags::positive))
 321                                         continue;
 322                                 else if (factor.info(info_flags::negative))
 323                                         pos = !pos;
 324                                 else
 325                                         return false;
 326                         }
 327                         if (overall_coeff.info(info_flags::negative))
 328                                 pos = !pos;
 329                         setflag(pos ? status_flags::is_positive : status_flags::is_negative);
 330                         return (inf == info_flags::positive? pos : !pos);
 331                 }
 332                 case info_flags::nonnegative: {
 333                         if  (flags & status_flags::is_positive)
 334                                 return true;
 335                         bool pos = true;
 336                         epvector::const_iterator i = seq.begin(), end = seq.end();
 337                         while (i != end) {
 338                                 const ex& factor = recombine_pair_to_ex(*i++);
 339                                 if (factor.info(info_flags::nonnegative) || factor.info(info_flags::positive))
 340                                         continue;
 341                                 else if (factor.info(info_flags::negative))
 342                                         pos = !pos;
 343                                 else
 344                                         return false;
 345                         }
 346                         return (overall_coeff.info(info_flags::negative)? !pos : pos);
 347                 }
 348                 case info_flags::posint:
 349                 case info_flags::negint: {
 350                         bool pos = true;
 351                         epvector::const_iterator i = seq.begin(), end = seq.end();
 352                         while (i != end) {
 353                                 const ex& factor = recombine_pair_to_ex(*i++);
 354                                 if (factor.info(info_flags::posint))
 355                                         continue;
 356                                 else if (factor.info(info_flags::negint))
 357                                         pos = !pos;
 358                                 else
 359                                         return false;
 360                         }
 361                         if (overall_coeff.info(info_flags::negint))
 362                                 pos = !pos;
 363                         else if (!overall_coeff.info(info_flags::posint))
 364                                 return false;
 365                         return (inf ==info_flags::posint? pos : !pos);
 366                 }
 367                 case info_flags::nonnegint: {
 368                         bool pos = true;
 369                         epvector::const_iterator i = seq.begin(), end = seq.end();
 370                         while (i != end) {
 371                                 const ex& factor = recombine_pair_to_ex(*i++);
 372                                 if (factor.info(info_flags::nonnegint) || factor.info(info_flags::posint))
 373                                         continue;
 374                                 else if (factor.info(info_flags::negint))
 375                                         pos = !pos;
 376                                 else
 377                                         return false;
 378                         }
 379                         if (overall_coeff.info(info_flags::negint))
 380                                 pos = !pos;
 381                         else if (!overall_coeff.info(info_flags::posint))
 382                                 return false;
 383                         return pos;
 384                 }
 385                 case info_flags::indefinite: {
 386                         if (flags & status_flags::purely_indefinite)
 387                                 return true;
 388                         if (flags & (status_flags::is_positive | status_flags::is_negative))
 389                                 return false;
 390                         epvector::const_iterator i = seq.begin(), end = seq.end();
 391                         while (i != end) {
 392                                 const ex& term = recombine_pair_to_ex(*i);
 393                                 if (term.info(info_flags::positive) || term.info(info_flags::negative))
 394                                         return false;
 395                                 ++i;
 396                         }
 397                         setflag(status_flags::purely_indefinite);
 398                         return true;
 399                 }
 400         }
 401         return inherited::info(inf);
 402 }
 403
 404 bool mul::is_polynomial(const ex & var) const
 405 {
 406         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 407                 if (!i->rest.is_polynomial(var) ||
 408                     (i->rest.has(var) && !i->coeff.info(info_flags::nonnegint))) {
 409                         return false;
 410                 }
 411         }
 412         return true;
 413 }
 414
 415 int mul::degree(const ex & s) const
 416 {
 417         // Sum up degrees of factors
 418         int deg_sum = 0;
 419         epvector::const_iterator i = seq.begin(), end = seq.end();
 420         while (i != end) {
 421                 if (ex_to<numeric>(i->coeff).is_integer())
 422                         deg_sum += recombine_pair_to_ex(*i).degree(s);
 423                 else {
 424                         if (i->rest.has(s))
 425                                 throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
 426                 }
 427                 ++i;
 428         }
 429         return deg_sum;
 430 }
 431
 432 int mul::ldegree(const ex & s) const
 433 {
 434         // Sum up degrees of factors
 435         int deg_sum = 0;
 436         epvector::const_iterator i = seq.begin(), end = seq.end();
 437         while (i != end) {
 438                 if (ex_to<numeric>(i->coeff).is_integer())
 439                         deg_sum += recombine_pair_to_ex(*i).ldegree(s);
 440                 else {
 441                         if (i->rest.has(s))
 442                                 throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
 443                 }
 444                 ++i;
 445         }
 446         return deg_sum;
 447 }
 448
 449 ex mul::coeff(const ex & s, int n) const
 450 {
 451         exvector coeffseq;
 452         coeffseq.reserve(seq.size()+1);
 453
 454         if (n==0) {
 455                 // product of individual coeffs
 456                 // if a non-zero power of s is found, the resulting product will be 0
 457                 epvector::const_iterator i = seq.begin(), end = seq.end();
 458                 while (i != end) {
 459                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 460                         ++i;
 461                 }
 462                 coeffseq.push_back(overall_coeff);
 463                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 464         }
 465
 466         epvector::const_iterator i = seq.begin(), end = seq.end();
 467         bool coeff_found = false;
 468         while (i != end) {
 469                 ex t = recombine_pair_to_ex(*i);
 470                 ex c = t.coeff(s, n);
 471                 if (!c.is_zero()) {
 472                         coeffseq.push_back(c);
 473                         coeff_found = 1;
 474                 } else {
 475                         coeffseq.push_back(t);
 476                 }
 477                 ++i;
 478         }
 479         if (coeff_found) {
 480                 coeffseq.push_back(overall_coeff);
 481                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 482         }
 483
 484         return _ex0;
 485 }
 486
 487 /** Perform automatic term rewriting rules in this class.  In the following
 488  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 489  *  stand for such expressions that contain a plain number.
 490  *  - *(...,x;0) -> 0
 491  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 492  *  - *(x;1) -> x
 493  *  - *(;c) -> c
 494  *
 495  *  @param level cut-off in recursive evaluation */
 496 ex mul::eval(int level) const
 497 {
 498         epvector evaled = evalchildren(level);
 499         if (!evaled.empty()) {
 500                 // do more evaluation later
 501                 return (new mul(std::move(evaled), overall_coeff))->
 502                         setflag(status_flags::dynallocated);
 503         }
 504
 505         if (flags & status_flags::evaluated) {
 506                 GINAC_ASSERT(seq.size()>0);
 507                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 508                 return *this;
 509         }
 510
 511         size_t seq_size = seq.size();
 512         if (overall_coeff.is_zero()) {
 513                 // *(...,x;0) -> 0
 514                 return _ex0;
 515         } else if (seq_size==0) {
 516                 // *(;c) -> c
 517                 return overall_coeff;
 518         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 519                 // *(x;1) -> x
 520                 return recombine_pair_to_ex(*(seq.begin()));
 521         } else if ((seq_size==1) &&
 522                    is_exactly_a<add>((*seq.begin()).rest) &&
 523                    ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
 524                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 525                 const add & addref = ex_to<add>((*seq.begin()).rest);
 526                 epvector distrseq;
 527                 distrseq.reserve(addref.seq.size());
 528                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 529                 while (i != end) {
 530                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 531                         ++i;
 532                 }
 533                 return (new add(std::move(distrseq),
 534                                 ex_to<numeric>(addref.overall_coeff).
 535                                 mul_dyn(ex_to<numeric>(overall_coeff)))
 536                        )->setflag(status_flags::dynallocated | status_flags::evaluated);
 537         } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
 538                 // Strip the content and the unit part from each term. Thus
 539                 // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)^2
 540
 541                 epvector::const_iterator last = seq.end();
 542                 epvector::const_iterator i = seq.begin();
 543                 epvector::const_iterator j = seq.begin();
 544                 epvector s;
 545                 numeric oc = *_num1_p;
 546                 bool something_changed = false;
 547                 while (i!=last) {
 548                         if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
 549                                 // power::eval has such a rule, no need to handle powers here
 550                                 ++i;
 551                                 continue;
 552                         }
 553
 554                         // XXX: What is the best way to check if the polynomial is a primitive?
 555                         numeric c = i->rest.integer_content();
 556                         const numeric lead_coeff =
 557                                 ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div(c);
 558                         const bool canonicalizable = lead_coeff.is_integer();
 559
 560                         // XXX: The main variable is chosen in a random way, so this code
 561                         // does NOT transform the term into the canonical form (thus, in some
 562                         // very unlucky event it can even loop forever). Hopefully the main
 563                         // variable will be the same for all terms in *this
 564                         const bool unit_normal = lead_coeff.is_pos_integer();
 565                         if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
 566                                 ++i;
 567                                 continue;
 568                         }
 569
 570                         if (! something_changed) {
 571                                 s.reserve(seq_size);
 572                                 something_changed = true;
 573                         }
 574
 575                         while ((j!=i) && (j!=last)) {
 576                                 s.push_back(*j);
 577                                 ++j;
 578                         }
 579
 580                         if (! unit_normal)
 581                                 c = c.mul(*_num_1_p);
 582
 583                         oc = oc.mul(c);
 584
 585                         // divide add by the number in place to save at least 2 .eval() calls
 586                         const add& addref = ex_to<add>(i->rest);
 587                         add* primitive = new add(addref);
 588                         primitive->setflag(status_flags::dynallocated);
 589                         primitive->clearflag(status_flags::hash_calculated);
 590                         primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
 591                         for (epvector::iterator ai = primitive->seq.begin(); ai != primitive->seq.end(); ++ai)
 592                                 ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
 593
 594                         s.push_back(expair(*primitive, _ex1));
 595
 596                         ++i;
 597                         ++j;
 598                 }
 599                 if (something_changed) {
 600                         while (j!=last) {
 601                                 s.push_back(*j);
 602                                 ++j;
 603                         }
 604                         return (new mul(std::move(s), ex_to<numeric>(overall_coeff).mul_dyn(oc))
 605                                )->setflag(status_flags::dynallocated);
 606                 }
 607         }
 608
 609         return this->hold();
 610 }
 611
 612 ex mul::evalf(int level) const
 613 {
 614         if (level==1)
 615                 return mul(seq,overall_coeff);
 616
 617         if (level==-max_recursion_level)
 618                 throw(std::runtime_error("max recursion level reached"));
 619
 620         epvector s;
 621         s.reserve(seq.size());
 622
 623         --level;
 624         epvector::const_iterator i = seq.begin(), end = seq.end();
 625         while (i != end) {
 626                 s.push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 627                                                           i->coeff));
 628                 ++i;
 629         }
 630         return mul(std::move(s), overall_coeff.evalf(level));
 631 }
 632
 633 void mul::find_real_imag(ex & rp, ex & ip) const
 634 {
 635         rp = overall_coeff.real_part();
 636         ip = overall_coeff.imag_part();
 637         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 638                 ex factor = recombine_pair_to_ex(*i);
 639                 ex new_rp = factor.real_part();
 640                 ex new_ip = factor.imag_part();
 641                 if(new_ip.is_zero()) {
 642                         rp *= new_rp;
 643                         ip *= new_rp;
 644                 } else {
 645                         ex temp = rp*new_rp - ip*new_ip;
 646                         ip = ip*new_rp + rp*new_ip;
 647                         rp = temp;
 648                 }
 649         }
 650         rp = rp.expand();
 651         ip = ip.expand();
 652 }
 653
 654 ex mul::real_part() const
 655 {
 656         ex rp, ip;
 657         find_real_imag(rp, ip);
 658         return rp;
 659 }
 660
 661 ex mul::imag_part() const
 662 {
 663         ex rp, ip;
 664         find_real_imag(rp, ip);
 665         return ip;
 666 }
 667
 668 ex mul::evalm() const
 669 {
 670         // numeric*matrix
 671         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 672          && is_a<matrix>(seq[0].rest))
 673                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 674
 675         // Evaluate children first, look whether there are any matrices at all
 676         // (there can be either no matrices or one matrix; if there were more
 677         // than one matrix, it would be a non-commutative product)
 678         epvector s;
 679         s.reserve(seq.size());
 680
 681         bool have_matrix = false;
 682         epvector::iterator the_matrix;
 683
 684         epvector::const_iterator i = seq.begin(), end = seq.end();
 685         while (i != end) {
 686                 const ex &m = recombine_pair_to_ex(*i).evalm();
 687                 s.push_back(split_ex_to_pair(m));
 688                 if (is_a<matrix>(m)) {
 689                         have_matrix = true;
 690                         the_matrix = s.end() - 1;
 691                 }
 692                 ++i;
 693         }
 694
 695         if (have_matrix) {
 696
 697                 // The product contained a matrix. We will multiply all other factors
 698                 // into that matrix.
 699                 matrix m = ex_to<matrix>(the_matrix->rest);
 700                 s.erase(the_matrix);
 701                 ex scalar = (new mul(std::move(s), overall_coeff))->setflag(status_flags::dynallocated);
 702                 return m.mul_scalar(scalar);
 703
 704         } else
 705                 return (new mul(std::move(s), overall_coeff))->setflag(status_flags::dynallocated);
 706 }
 707
 708 ex mul::eval_ncmul(const exvector & v) const
 709 {
 710         if (seq.empty())
 711                 return inherited::eval_ncmul(v);
 712
 713         // Find first noncommutative element and call its eval_ncmul()
 714         epvector::const_iterator i = seq.begin(), end = seq.end();
 715         while (i != end) {
 716                 if (i->rest.return_type() == return_types::noncommutative)
 717                         return i->rest.eval_ncmul(v);
 718                 ++i;
 719         }
 720         return inherited::eval_ncmul(v);
 721 }
 722
 723 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls)
 724 {
 725         ex origbase;
 726         int origexponent;
 727         int origexpsign;
 728
 729         if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
 730                 origbase = origfactor.op(0);
 731                 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
 732                 origexponent = expon > 0 ? expon : -expon;
 733                 origexpsign = expon > 0 ? 1 : -1;
 734         } else {
 735                 origbase = origfactor;
 736                 origexponent = 1;
 737                 origexpsign = 1;
 738         }
 739
 740         ex patternbase;
 741         int patternexponent;
 742         int patternexpsign;
 743
 744         if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
 745                 patternbase = patternfactor.op(0);
 746                 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
 747                 patternexponent = expon > 0 ? expon : -expon;
 748                 patternexpsign = expon > 0 ? 1 : -1;
 749         } else {
 750                 patternbase = patternfactor;
 751                 patternexponent = 1;
 752                 patternexpsign = 1;
 753         }
 754
 755         exmap saverepls = repls;
 756         if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
 757                 return false;
 758         repls = saverepls;
 759
 760         int newnummatches = origexponent / patternexponent;
 761         if (newnummatches < nummatches)
 762                 nummatches = newnummatches;
 763         return true;
 764 }
 765
 766 /** Checks whether e matches to the pattern pat and the (possibly to be updated)
 767   * list of replacements repls. This matching is in the sense of algebraic
 768   * substitutions. Matching starts with pat.op(factor) of the pattern because
 769   * the factors before this one have already been matched. The (possibly
 770   * updated) number of matches is in nummatches. subsed[i] is true for factors
 771   * that already have been replaced by previous substitutions and matched[i]
 772   * is true for factors that have been matched by the current match.
 773   */
 774 bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls,
 775                                   int factor, int &nummatches, const std::vector<bool> &subsed,
 776                                   std::vector<bool> &matched)
 777 {
 778         GINAC_ASSERT(subsed.size() == e.nops());
 779         GINAC_ASSERT(matched.size() == e.nops());
 780
 781         if (factor == (int)pat.nops())
 782                 return true;
 783
 784         for (size_t i=0; i<e.nops(); ++i) {
 785                 if(subsed[i] || matched[i])
 786                         continue;
 787                 exmap newrepls = repls;
 788                 int newnummatches = nummatches;
 789                 if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
 790                         matched[i] = true;
 791                         if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
 792                                         newnummatches, subsed, matched)) {
 793                                 repls = newrepls;
 794                                 nummatches = newnummatches;
 795                                 return true;
 796                         }
 797                         else
 798                                 matched[i] = false;
 799                 }
 800         }
 801
 802         return false;
 803 }
 804
 805 bool mul::has(const ex & pattern, unsigned options) const
 806 {
 807         if(!(options & has_options::algebraic))
 808                 return basic::has(pattern,options);
 809         if(is_a<mul>(pattern)) {
 810                 exmap repls;
 811                 int nummatches = std::numeric_limits<int>::max();
 812                 std::vector<bool> subsed(nops(), false);
 813                 std::vector<bool> matched(nops(), false);
 814                 if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
 815                                 subsed, matched))
 816                         return true;
 817         }
 818         return basic::has(pattern, options);
 819 }
 820
 821 ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
 822 {
 823         std::vector<bool> subsed(nops(), false);
 824         ex divide_by = 1;
 825         ex multiply_by = 1;
 826
 827         for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
 828
 829                 if (is_exactly_a<mul>(it->first)) {
 830 retry1:
 831                         int nummatches = std::numeric_limits<int>::max();
 832                         std::vector<bool> currsubsed(nops(), false);
 833                         exmap repls;
 834
 835                         if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
 836                                 continue;
 837
 838                         for (size_t j=0; j<subsed.size(); j++)
 839                                 if (currsubsed[j])
 840                                         subsed[j] = true;
 841                         ex subsed_pattern
 842                                 = it->first.subs(repls, subs_options::no_pattern);
 843                         divide_by *= power(subsed_pattern, nummatches);
 844                         ex subsed_result
 845                                 = it->second.subs(repls, subs_options::no_pattern);
 846                         multiply_by *= power(subsed_result, nummatches);
 847                         goto retry1;
 848
 849                 } else {
 850
 851                         for (size_t j=0; j<this->nops(); j++) {
 852                                 int nummatches = std::numeric_limits<int>::max();
 853                                 exmap repls;
 854                                 if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
 855                                         subsed[j] = true;
 856                                         ex subsed_pattern
 857                                                 = it->first.subs(repls, subs_options::no_pattern);
 858                                         divide_by *= power(subsed_pattern, nummatches);
 859                                         ex subsed_result
 860                                                 = it->second.subs(repls, subs_options::no_pattern);
 861                                         multiply_by *= power(subsed_result, nummatches);
 862                                 }
 863                         }
 864                 }
 865         }
 866
 867         bool subsfound = false;
 868         for (size_t i=0; i<subsed.size(); i++) {
 869                 if (subsed[i]) {
 870                         subsfound = true;
 871                         break;
 872                 }
 873         }
 874         if (!subsfound)
 875                 return subs_one_level(m, options | subs_options::algebraic);
 876
 877         return ((*this)/divide_by)*multiply_by;
 878 }
 879
 880 ex mul::conjugate() const
 881 {
 882         // The base class' method is wrong here because we have to be careful at
 883         // branch cuts. power::conjugate takes care of that already, so use it.
 884         epvector *newepv = 0;
 885         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 886                 if (newepv) {
 887                         newepv->push_back(split_ex_to_pair(recombine_pair_to_ex(*i).conjugate()));
 888                         continue;
 889                 }
 890                 ex x = recombine_pair_to_ex(*i);
 891                 ex c = x.conjugate();
 892                 if (c.is_equal(x)) {
 893                         continue;
 894                 }
 895                 newepv = new epvector;
 896                 newepv->reserve(seq.size());
 897                 for (epvector::const_iterator j=seq.begin(); j!=i; ++j) {
 898                         newepv->push_back(*j);
 899                 }
 900                 newepv->push_back(split_ex_to_pair(c));
 901         }
 902         ex x = overall_coeff.conjugate();
 903         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 904                 return *this;
 905         }
 906         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 907         delete newepv;
 908         return result;
 909 }
 910
 911
 912 // protected
 913
 914 /** Implementation of ex::diff() for a product.  It applies the product rule.
 915  *  @see ex::diff */
 916 ex mul::derivative(const symbol & s) const
 917 {
 918         size_t num = seq.size();
 919         exvector addseq;
 920         addseq.reserve(num);
 921
 922         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 923         epvector mulseq = seq;
 924         epvector::const_iterator i = seq.begin(), end = seq.end();
 925         epvector::iterator i2 = mulseq.begin();
 926         while (i != end) {
 927                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 928                                              i->rest.diff(s));
 929                 ep.swap(*i2);
 930                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 931                 ep.swap(*i2);
 932                 ++i; ++i2;
 933         }
 934         return (new add(addseq))->setflag(status_flags::dynallocated);
 935 }
 936
 937 int mul::compare_same_type(const basic & other) const
 938 {
 939         return inherited::compare_same_type(other);
 940 }
 941
 942 unsigned mul::return_type() const
 943 {
 944         if (seq.empty()) {
 945                 // mul without factors: should not happen, but commutates
 946                 return return_types::commutative;
 947         }
 948
 949         bool all_commutative = true;
 950         epvector::const_iterator noncommutative_element; // point to first found nc element
 951
 952         epvector::const_iterator i = seq.begin(), end = seq.end();
 953         while (i != end) {
 954                 unsigned rt = i->rest.return_type();
 955                 if (rt == return_types::noncommutative_composite)
 956                         return rt; // one ncc -> mul also ncc
 957                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 958                         // first nc element found, remember position
 959                         noncommutative_element = i;
 960                         all_commutative = false;
 961                 }
 962                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 963                         // another nc element found, compare type_infos
 964                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 965                                         // different types -> mul is ncc
 966                                         return return_types::noncommutative_composite;
 967                         }
 968                 }
 969                 ++i;
 970         }
 971         // all factors checked
 972         return all_commutative ? return_types::commutative : return_types::noncommutative;
 973 }
 974
 975 return_type_t mul::return_type_tinfo() const
 976 {
 977         if (seq.empty())
 978                 return make_return_type_t<mul>(); // mul without factors: should not happen
 979
 980         // return type_info of first noncommutative element
 981         epvector::const_iterator i = seq.begin(), end = seq.end();
 982         while (i != end) {
 983                 if (i->rest.return_type() == return_types::noncommutative)
 984                         return i->rest.return_type_tinfo();
 985                 ++i;
 986         }
 987         // no noncommutative element found, should not happen
 988         return make_return_type_t<mul>();
 989 }
 990
 991 ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 992 {
 993         return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
 994 }
 995
 996 ex mul::thisexpairseq(epvector && vp, const ex & oc, bool do_index_renaming) const
 997 {
 998         return (new mul(std::move(vp), oc, do_index_renaming))->setflag(status_flags::dynallocated);
 999 }
1000
1001 expair mul::split_ex_to_pair(const ex & e) const
1002 {
1003         if (is_exactly_a<power>(e)) {
1004                 const power & powerref = ex_to<power>(e);
1005                 if (is_exactly_a<numeric>(powerref.exponent))
1006                         return expair(powerref.basis,powerref.exponent);
1007         }
1008         return expair(e,_ex1);
1009 }
1010
1011 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
1012                                           const ex & c) const
1013 {
1014         // to avoid duplication of power simplification rules,
1015         // we create a temporary power object
1016         // otherwise it would be hard to correctly evaluate
1017         // expression like (4^(1/3))^(3/2)
1018         if (c.is_equal(_ex1))
1019                 return split_ex_to_pair(e);
1020
1021         return split_ex_to_pair(power(e,c));
1022 }
1023
1024 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
1025                                             const ex & c) const
1026 {
1027         // to avoid duplication of power simplification rules,
1028         // we create a temporary power object
1029         // otherwise it would be hard to correctly evaluate
1030         // expression like (4^(1/3))^(3/2)
1031         if (c.is_equal(_ex1))
1032                 return p;
1033
1034         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
1035 }
1036
1037 ex mul::recombine_pair_to_ex(const expair & p) const
1038 {
1039         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
1040                 return p.rest;
1041         else
1042                 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
1043 }
1044
1045 bool mul::expair_needs_further_processing(epp it)
1046 {
1047         if (is_exactly_a<mul>(it->rest) &&
1048             ex_to<numeric>(it->coeff).is_integer()) {
1049                 // combined pair is product with integer power -> expand it
1050                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
1051                 return true;
1052         }
1053         if (is_exactly_a<numeric>(it->rest)) {
1054                 if (it->coeff.is_equal(_ex1)) {
1055                         // pair has coeff 1 and must be moved to the end
1056                         return true;
1057                 }
1058                 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
1059                 if (!ep.is_equal(*it)) {
1060                         // combined pair is a numeric power which can be simplified
1061                         *it = ep;
1062                         return true;
1063                 }
1064         }
1065         return false;
1066 }
1067
1068 ex mul::default_overall_coeff() const
1069 {
1070         return _ex1;
1071 }
1072
1073 void mul::combine_overall_coeff(const ex & c)
1074 {
1075         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
1076         GINAC_ASSERT(is_exactly_a<numeric>(c));
1077         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
1078 }
1079
1080 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
1081 {
1082         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
1083         GINAC_ASSERT(is_exactly_a<numeric>(c1));
1084         GINAC_ASSERT(is_exactly_a<numeric>(c2));
1085         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
1086 }
1087
1088 bool mul::can_make_flat(const expair & p) const
1089 {
1090         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
1091         // this assertion will probably fail somewhere
1092         // it would require a more careful make_flat, obeying the power laws
1093         // probably should return true only if p.coeff is integer
1094         return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
1095 }
1096
1097 bool mul::can_be_further_expanded(const ex & e)
1098 {
1099         if (is_exactly_a<mul>(e)) {
1100                 for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
1101                         if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
1102                                 return true;
1103                 }
1104         } else if (is_exactly_a<power>(e)) {
1105                 if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
1106                         return true;
1107         }
1108         return false;
1109 }
1110
1111 ex mul::expand(unsigned options) const
1112 {
1113         {
1114         // trivial case: expanding the monomial (~ 30% of all calls)
1115                 epvector::const_iterator i = seq.begin(), seq_end = seq.end();
1116                 while ((i != seq.end()) &&  is_a<symbol>(i->rest) && i->coeff.info(info_flags::integer))
1117                         ++i;
1118                 if (i == seq_end) {
1119                         setflag(status_flags::expanded);
1120                         return *this;
1121                 }
1122         }
1123
1124         // do not rename indices if the object has no indices at all
1125         if ((!(options & expand_options::expand_rename_idx)) &&
1126                         this->info(info_flags::has_indices))
1127                 options |= expand_options::expand_rename_idx;
1128
1129         const bool skip_idx_rename = !(options & expand_options::expand_rename_idx);
1130
1131         // First, expand the children
1132         epvector expanded = expandchildren(options);
1133         const epvector & expanded_seq = (expanded.empty() ? seq : expanded);
1134
1135         // Now, look for all the factors that are sums and multiply each one out
1136         // with the next one that is found while collecting the factors which are
1137         // not sums
1138         ex last_expanded = _ex1;
1139
1140         epvector non_adds;
1141         non_adds.reserve(expanded_seq.size());
1142
1143         for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
1144                 if (is_exactly_a<add>(cit->rest) &&
1145                         (cit->coeff.is_equal(_ex1))) {
1146                         if (is_exactly_a<add>(last_expanded)) {
1147
1148                                 // Expand a product of two sums, aggressive version.
1149                                 // Caring for the overall coefficients in separate loops can
1150                                 // sometimes give a performance gain of up to 15%!
1151
1152                                 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
1153                                 // add2 is for the inner loop and should be the bigger of the two sums
1154                                 // in the presence of asymptotically good sorting:
1155                                 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
1156                                 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
1157                                 const epvector::const_iterator add1begin = add1.seq.begin();
1158                                 const epvector::const_iterator add1end   = add1.seq.end();
1159                                 const epvector::const_iterator add2begin = add2.seq.begin();
1160                                 const epvector::const_iterator add2end   = add2.seq.end();
1161                                 epvector distrseq;
1162                                 distrseq.reserve(add1.seq.size()+add2.seq.size());
1163
1164                                 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
1165                                 if (!add1.overall_coeff.is_zero()) {
1166                                         if (add1.overall_coeff.is_equal(_ex1))
1167                                                 distrseq.insert(distrseq.end(),add2begin,add2end);
1168                                         else
1169                                                 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
1170                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
1171                                 }
1172
1173                                 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
1174                                 if (!add2.overall_coeff.is_zero()) {
1175                                         if (add2.overall_coeff.is_equal(_ex1))
1176                                                 distrseq.insert(distrseq.end(),add1begin,add1end);
1177                                         else
1178                                                 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
1179                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
1180                                 }
1181
1182                                 // Compute the new overall coefficient and put it together:
1183                                 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
1184
1185                                 exvector add1_dummy_indices, add2_dummy_indices, add_indices;
1186                                 lst dummy_subs;
1187
1188                                 if (!skip_idx_rename) {
1189                                         for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
1190                                                 add_indices = get_all_dummy_indices_safely(i->rest);
1191                                                 add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
1192                                         }
1193                                         for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
1194                                                 add_indices = get_all_dummy_indices_safely(i->rest);
1195                                                 add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
1196                                         }
1197
1198                                         sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
1199                                         sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
1200                                         dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
1201                                 }
1202
1203                                 // Multiply explicitly all non-numeric terms of add1 and add2:
1204                                 for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
1205                                         // We really have to combine terms here in order to compactify
1206                                         // the result.  Otherwise it would become waayy tooo bigg.
1207                                         numeric oc(*_num0_p);
1208                                         epvector distrseq2;
1209                                         distrseq2.reserve(add1.seq.size());
1210                                         const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ?
1211                                                         i2->rest :
1212                                                         i2->rest.subs(ex_to<lst>(dummy_subs.op(0)),
1213                                                                 ex_to<lst>(dummy_subs.op(1)), subs_options::no_pattern));
1214                                         for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
1215                                                 // Don't push_back expairs which might have a rest that evaluates to a numeric,
1216                                                 // since that would violate an invariant of expairseq:
1217                                                 const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated);
1218                                                 if (is_exactly_a<numeric>(rest)) {
1219                                                         oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
1220                                                 } else {
1221                                                         distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
1222                                                 }
1223                                         }
1224                                         tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated);
1225                                 }
1226                                 last_expanded = tmp_accu;
1227                         } else {
1228                                 if (!last_expanded.is_equal(_ex1))
1229                                         non_adds.push_back(split_ex_to_pair(last_expanded));
1230                                 last_expanded = cit->rest;
1231                         }
1232
1233                 } else {
1234                         non_adds.push_back(*cit);
1235                 }
1236         }
1237
1238         // Now the only remaining thing to do is to multiply the factors which
1239         // were not sums into the "last_expanded" sum
1240         if (is_exactly_a<add>(last_expanded)) {
1241                 size_t n = last_expanded.nops();
1242                 exvector distrseq;
1243                 distrseq.reserve(n);
1244                 exvector va;
1245                 if (! skip_idx_rename) {
1246                         va = get_all_dummy_indices_safely(mul(non_adds));
1247                         sort(va.begin(), va.end(), ex_is_less());
1248                 }
1249
1250                 for (size_t i=0; i<n; ++i) {
1251                         epvector factors = non_adds;
1252                         if (skip_idx_rename)
1253                                 factors.push_back(split_ex_to_pair(last_expanded.op(i)));
1254                         else
1255                                 factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
1256                         ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
1257                         if (can_be_further_expanded(term)) {
1258                                 distrseq.push_back(term.expand());
1259                         } else {
1260                                 if (options == 0)
1261                                         ex_to<basic>(term).setflag(status_flags::expanded);
1262                                 distrseq.push_back(term);
1263                         }
1264                 }
1265
1266                 return ((new add(distrseq))->
1267                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
1268         }
1269
1270         non_adds.push_back(split_ex_to_pair(last_expanded));
1271         ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
1272         if (can_be_further_expanded(result)) {
1273                 return result.expand();
1274         } else {
1275                 if (options == 0)
1276                         ex_to<basic>(result).setflag(status_flags::expanded);
1277                 return result;
1278         }
1279 }
1280
1281
1282 //////////
1283 // new virtual functions which can be overridden by derived classes
1284 //////////
1285
1286 // none
1287
1288 //////////
1289 // non-virtual functions in this class
1290 //////////
1291
1292
1293 /** Member-wise expand the expairs representing this sequence.  This must be
1294  *  overridden from expairseq::expandchildren() and done iteratively in order
1295  *  to allow for early cancellations and thus safe memory.
1296  *
1297  *  @see mul::expand()
1298  *  @return epvector containing expanded pairs, empty if no members
1299  *    had to be changed. */
1300 epvector mul::expandchildren(unsigned options) const
1301 {
1302         const epvector::const_iterator last = seq.end();
1303         epvector::const_iterator cit = seq.begin();
1304         while (cit!=last) {
1305                 const ex & factor = recombine_pair_to_ex(*cit);
1306                 const ex & expanded_factor = factor.expand(options);
1307                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
1308
1309                         // something changed, copy seq, eval and return it
1310                         epvector s;
1311                         s.reserve(seq.size());
1312
1313                         // copy parts of seq which are known not to have changed
1314                         epvector::const_iterator cit2 = seq.begin();
1315                         while (cit2!=cit) {
1316                                 s.push_back(*cit2);
1317                                 ++cit2;
1318                         }
1319
1320                         // copy first changed element
1321                         s.push_back(split_ex_to_pair(expanded_factor));
1322                         ++cit2;
1323
1324                         // copy rest
1325                         while (cit2!=last) {
1326                                 s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
1327                                 ++cit2;
1328                         }
1329                         return s;
1330                 }
1331                 ++cit;
1332         }
1333
1334         return epvector(); // nothing has changed
1335 }
1336
1337 GINAC_BIND_UNARCHIVER(mul);
1338
1339 } // namespace GiNaC