ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2011 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(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
  93 {
  94         GINAC_ASSERT(vp.get()!=0);
  95         overall_coeff = oc;
  96         construct_from_epvector(*vp, do_index_renaming);
  97         GINAC_ASSERT(is_canonical());
  98 }
  99
 100 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 101 {
 102         exvector factors;
 103         factors.reserve(3);
 104         factors.push_back(lh);
 105         factors.push_back(mh);
 106         factors.push_back(rh);
 107         overall_coeff = _ex1;
 108         construct_from_exvector(factors);
 109         GINAC_ASSERT(is_canonical());
 110 }
 111
 112 //////////
 113 // archiving
 114 //////////
 115
 116 //////////
 117 // functions overriding virtual functions from base classes
 118 //////////
 119
 120 void mul::print_overall_coeff(const print_context & c, const char *mul_sym) const
 121 {
 122         const numeric &coeff = ex_to<numeric>(overall_coeff);
 123         if (coeff.csgn() == -1)
 124                 c.s << '-';
 125         if (!coeff.is_equal(*_num1_p) &&
 126                 !coeff.is_equal(*_num_1_p)) {
 127                 if (coeff.is_rational()) {
 128                         if (coeff.is_negative())
 129                                 (-coeff).print(c);
 130                         else
 131                                 coeff.print(c);
 132                 } else {
 133                         if (coeff.csgn() == -1)
 134                                 (-coeff).print(c, precedence());
 135                         else
 136                                 coeff.print(c, precedence());
 137                 }
 138                 c.s << mul_sym;
 139         }
 140 }
 141
 142 void mul::do_print(const print_context & c, unsigned level) const
 143 {
 144         if (precedence() <= level)
 145                 c.s << '(';
 146
 147         print_overall_coeff(c, "*");
 148
 149         epvector::const_iterator it = seq.begin(), itend = seq.end();
 150         bool first = true;
 151         while (it != itend) {
 152                 if (!first)
 153                         c.s << '*';
 154                 else
 155                         first = false;
 156                 recombine_pair_to_ex(*it).print(c, precedence());
 157                 ++it;
 158         }
 159
 160         if (precedence() <= level)
 161                 c.s << ')';
 162 }
 163
 164 void mul::do_print_latex(const print_latex & c, unsigned level) const
 165 {
 166         if (precedence() <= level)
 167                 c.s << "{(";
 168
 169         print_overall_coeff(c, " ");
 170
 171         // Separate factors into those with negative numeric exponent
 172         // and all others
 173         epvector::const_iterator it = seq.begin(), itend = seq.end();
 174         exvector neg_powers, others;
 175         while (it != itend) {
 176                 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
 177                 if (ex_to<numeric>(it->coeff).is_negative())
 178                         neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
 179                 else
 180                         others.push_back(recombine_pair_to_ex(*it));
 181                 ++it;
 182         }
 183
 184         if (!neg_powers.empty()) {
 185
 186                 // Factors with negative exponent are printed as a fraction
 187                 c.s << "\\frac{";
 188                 mul(others).eval().print(c);
 189                 c.s << "}{";
 190                 mul(neg_powers).eval().print(c);
 191                 c.s << "}";
 192
 193         } else {
 194
 195                 // All other factors are printed in the ordinary way
 196                 exvector::const_iterator vit = others.begin(), vitend = others.end();
 197                 while (vit != vitend) {
 198                         c.s << ' ';
 199                         vit->print(c, precedence());
 200                         ++vit;
 201                 }
 202         }
 203
 204         if (precedence() <= level)
 205                 c.s << ")}";
 206 }
 207
 208 void mul::do_print_csrc(const print_csrc & c, unsigned level) const
 209 {
 210         if (precedence() <= level)
 211                 c.s << "(";
 212
 213         if (!overall_coeff.is_equal(_ex1)) {
 214                 if (overall_coeff.is_equal(_ex_1))
 215                         c.s << "-";
 216                 else {
 217                         overall_coeff.print(c, precedence());
 218                         c.s << "*";
 219                 }
 220         }
 221
 222         // Print arguments, separated by "*" or "/"
 223         epvector::const_iterator it = seq.begin(), itend = seq.end();
 224         while (it != itend) {
 225
 226                 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 227                 bool needclosingparenthesis = false;
 228                 if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
 229                         if (is_a<print_csrc_cl_N>(c)) {
 230                                 c.s << "recip(";
 231                                 needclosingparenthesis = true;
 232                         } else
 233                                 c.s << "1.0/";
 234                 }
 235
 236                 // If the exponent is 1 or -1, it is left out
 237                 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
 238                         it->rest.print(c, precedence());
 239                 else if (it->coeff.info(info_flags::negint))
 240                         // Outer parens around ex needed for broken GCC parser:
 241                         (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
 242                 else
 243                         // Outer parens around ex needed for broken GCC parser:
 244                         (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
 245
 246                 if (needclosingparenthesis)
 247                         c.s << ")";
 248
 249                 // Separator is "/" for negative integer powers, "*" otherwise
 250                 ++it;
 251                 if (it != itend) {
 252                         if (it->coeff.info(info_flags::negint))
 253                                 c.s << "/";
 254                         else
 255                                 c.s << "*";
 256                 }
 257         }
 258
 259         if (precedence() <= level)
 260                 c.s << ")";
 261 }
 262
 263 void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
 264 {
 265         c.s << class_name() << '(';
 266         op(0).print(c);
 267         for (size_t i=1; i<nops(); ++i) {
 268                 c.s << ',';
 269                 op(i).print(c);
 270         }
 271         c.s << ')';
 272 }
 273
 274 bool mul::info(unsigned inf) const
 275 {
 276         switch (inf) {
 277                 case info_flags::polynomial:
 278                 case info_flags::integer_polynomial:
 279                 case info_flags::cinteger_polynomial:
 280                 case info_flags::rational_polynomial:
 281                 case info_flags::real:
 282                 case info_flags::rational:
 283                 case info_flags::integer:
 284                 case info_flags::crational:
 285                 case info_flags::cinteger:
 286                 case info_flags::even:
 287                 case info_flags::crational_polynomial:
 288                 case info_flags::rational_function: {
 289                         epvector::const_iterator i = seq.begin(), end = seq.end();
 290                         while (i != end) {
 291                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 292                                         return false;
 293                                 ++i;
 294                         }
 295                         if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even)
 296                                 return true;
 297                         return overall_coeff.info(inf);
 298                 }
 299                 case info_flags::algebraic: {
 300                         epvector::const_iterator i = seq.begin(), end = seq.end();
 301                         while (i != end) {
 302                                 if ((recombine_pair_to_ex(*i).info(inf)))
 303                                         return true;
 304                                 ++i;
 305                         }
 306                         return false;
 307                 }
 308                 case info_flags::positive:
 309                 case info_flags::negative: {
 310                         bool pos = true;
 311                         epvector::const_iterator i = seq.begin(), end = seq.end();
 312                         while (i != end) {
 313                                 const ex& factor = recombine_pair_to_ex(*i++);
 314                                 if (factor.info(info_flags::positive))
 315                                         continue;
 316                                 else if (factor.info(info_flags::negative))
 317                                         pos = !pos;
 318                                 else
 319                                         return false;
 320                         }
 321                         if (overall_coeff.info(info_flags::negative))
 322                                 pos = !pos;
 323                         return (inf ==info_flags::positive? pos : !pos);
 324                 }
 325                 case info_flags::nonnegative: {
 326                         bool pos = true;
 327                         epvector::const_iterator i = seq.begin(), end = seq.end();
 328                         while (i != end) {
 329                                 const ex& factor = recombine_pair_to_ex(*i++);
 330                                 if (factor.info(info_flags::nonnegative) || factor.info(info_flags::positive))
 331                                         continue;
 332                                 else if (factor.info(info_flags::negative))
 333                                         pos = !pos;
 334                                 else
 335                                         return false;
 336                         }
 337                         return (overall_coeff.info(info_flags::negative)? pos : !pos);
 338                 }
 339                 case info_flags::posint:
 340                 case info_flags::negint: {
 341                         bool pos = true;
 342                         epvector::const_iterator i = seq.begin(), end = seq.end();
 343                         while (i != end) {
 344                                 const ex& factor = recombine_pair_to_ex(*i++);
 345                                 if (factor.info(info_flags::posint))
 346                                         continue;
 347                                 else if (factor.info(info_flags::negint))
 348                                         pos = !pos;
 349                                 else
 350                                         return false;
 351                         }
 352                         if (overall_coeff.info(info_flags::negint))
 353                                 pos = !pos;
 354                         else if (!overall_coeff.info(info_flags::posint))
 355                                 return false;
 356                         return (inf ==info_flags::posint? pos : !pos);
 357                 }
 358                 case info_flags::nonnegint: {
 359                         bool pos = true;
 360                         epvector::const_iterator i = seq.begin(), end = seq.end();
 361                         while (i != end) {
 362                                 const ex& factor = recombine_pair_to_ex(*i++);
 363                                 if (factor.info(info_flags::nonnegint) || factor.info(info_flags::posint))
 364                                         continue;
 365                                 else if (factor.info(info_flags::negint))
 366                                         pos = !pos;
 367                                 else
 368                                         return false;
 369                         }
 370                         if (overall_coeff.info(info_flags::negint))
 371                                 pos = !pos;
 372                         else if (!overall_coeff.info(info_flags::posint))
 373                                 return false;
 374                         return pos;
 375                 }
 376         }
 377         return inherited::info(inf);
 378 }
 379
 380 bool mul::is_polynomial(const ex & var) const
 381 {
 382         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 383                 if (!i->rest.is_polynomial(var) ||
 384                     (i->rest.has(var) && !i->coeff.info(info_flags::integer))) {
 385                         return false;
 386                 }
 387         }
 388         return true;
 389 }
 390
 391 int mul::degree(const ex & s) const
 392 {
 393         // Sum up degrees of factors
 394         int deg_sum = 0;
 395         epvector::const_iterator i = seq.begin(), end = seq.end();
 396         while (i != end) {
 397                 if (ex_to<numeric>(i->coeff).is_integer())
 398                         deg_sum += recombine_pair_to_ex(*i).degree(s);
 399                 else {
 400                         if (i->rest.has(s))
 401                                 throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
 402                 }
 403                 ++i;
 404         }
 405         return deg_sum;
 406 }
 407
 408 int mul::ldegree(const ex & s) const
 409 {
 410         // Sum up degrees of factors
 411         int deg_sum = 0;
 412         epvector::const_iterator i = seq.begin(), end = seq.end();
 413         while (i != end) {
 414                 if (ex_to<numeric>(i->coeff).is_integer())
 415                         deg_sum += recombine_pair_to_ex(*i).ldegree(s);
 416                 else {
 417                         if (i->rest.has(s))
 418                                 throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
 419                 }
 420                 ++i;
 421         }
 422         return deg_sum;
 423 }
 424
 425 ex mul::coeff(const ex & s, int n) const
 426 {
 427         exvector coeffseq;
 428         coeffseq.reserve(seq.size()+1);
 429
 430         if (n==0) {
 431                 // product of individual coeffs
 432                 // if a non-zero power of s is found, the resulting product will be 0
 433                 epvector::const_iterator i = seq.begin(), end = seq.end();
 434                 while (i != end) {
 435                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 436                         ++i;
 437                 }
 438                 coeffseq.push_back(overall_coeff);
 439                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 440         }
 441
 442         epvector::const_iterator i = seq.begin(), end = seq.end();
 443         bool coeff_found = false;
 444         while (i != end) {
 445                 ex t = recombine_pair_to_ex(*i);
 446                 ex c = t.coeff(s, n);
 447                 if (!c.is_zero()) {
 448                         coeffseq.push_back(c);
 449                         coeff_found = 1;
 450                 } else {
 451                         coeffseq.push_back(t);
 452                 }
 453                 ++i;
 454         }
 455         if (coeff_found) {
 456                 coeffseq.push_back(overall_coeff);
 457                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 458         }
 459
 460         return _ex0;
 461 }
 462
 463 /** Perform automatic term rewriting rules in this class.  In the following
 464  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 465  *  stand for such expressions that contain a plain number.
 466  *  - *(...,x;0) -> 0
 467  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 468  *  - *(x;1) -> x
 469  *  - *(;c) -> c
 470  *
 471  *  @param level cut-off in recursive evaluation */
 472 ex mul::eval(int level) const
 473 {
 474         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 475         if (evaled_seqp.get()) {
 476                 // do more evaluation later
 477                 return (new mul(evaled_seqp, overall_coeff))->
 478                            setflag(status_flags::dynallocated);
 479         }
 480
 481         if (flags & status_flags::evaluated) {
 482                 GINAC_ASSERT(seq.size()>0);
 483                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 484                 return *this;
 485         }
 486
 487         size_t seq_size = seq.size();
 488         if (overall_coeff.is_zero()) {
 489                 // *(...,x;0) -> 0
 490                 return _ex0;
 491         } else if (seq_size==0) {
 492                 // *(;c) -> c
 493                 return overall_coeff;
 494         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 495                 // *(x;1) -> x
 496                 return recombine_pair_to_ex(*(seq.begin()));
 497         } else if ((seq_size==1) &&
 498                    is_exactly_a<add>((*seq.begin()).rest) &&
 499                    ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
 500                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 501                 const add & addref = ex_to<add>((*seq.begin()).rest);
 502                 std::auto_ptr<epvector> distrseq(new epvector);
 503                 distrseq->reserve(addref.seq.size());
 504                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 505                 while (i != end) {
 506                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 507                         ++i;
 508                 }
 509                 return (new add(distrseq,
 510                                 ex_to<numeric>(addref.overall_coeff).
 511                                 mul_dyn(ex_to<numeric>(overall_coeff)))
 512                        )->setflag(status_flags::dynallocated | status_flags::evaluated);
 513         } else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
 514                 // Strip the content and the unit part from each term. Thus
 515                 // things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)^2
 516
 517                 epvector::const_iterator last = seq.end();
 518                 epvector::const_iterator i = seq.begin();
 519                 epvector::const_iterator j = seq.begin();
 520                 std::auto_ptr<epvector> s(new epvector);
 521                 numeric oc = *_num1_p;
 522                 bool something_changed = false;
 523                 while (i!=last) {
 524                         if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
 525                                 // power::eval has such a rule, no need to handle powers here
 526                                 ++i;
 527                                 continue;
 528                         }
 529
 530                         // XXX: What is the best way to check if the polynomial is a primitive?
 531                         numeric c = i->rest.integer_content();
 532                         const numeric lead_coeff =
 533                                 ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div(c);
 534                         const bool canonicalizable = lead_coeff.is_integer();
 535
 536                         // XXX: The main variable is chosen in a random way, so this code
 537                         // does NOT transform the term into the canonical form (thus, in some
 538                         // very unlucky event it can even loop forever). Hopefully the main
 539                         // variable will be the same for all terms in *this
 540                         const bool unit_normal = lead_coeff.is_pos_integer();
 541                         if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
 542                                 ++i;
 543                                 continue;
 544                         }
 545
 546                         if (! something_changed) {
 547                                 s->reserve(seq_size);
 548                                 something_changed = true;
 549                         }
 550
 551                         while ((j!=i) && (j!=last)) {
 552                                 s->push_back(*j);
 553                                 ++j;
 554                         }
 555
 556                         if (! unit_normal)
 557                                 c = c.mul(*_num_1_p);
 558
 559                         oc = oc.mul(c);
 560
 561                         // divide add by the number in place to save at least 2 .eval() calls
 562                         const add& addref = ex_to<add>(i->rest);
 563                         add* primitive = new add(addref);
 564                         primitive->setflag(status_flags::dynallocated);
 565                         primitive->clearflag(status_flags::hash_calculated);
 566                         primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
 567                         for (epvector::iterator ai = primitive->seq.begin(); ai != primitive->seq.end(); ++ai)
 568                                 ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
 569
 570                         s->push_back(expair(*primitive, _ex1));
 571
 572                         ++i;
 573                         ++j;
 574                 }
 575                 if (something_changed) {
 576                         while (j!=last) {
 577                                 s->push_back(*j);
 578                                 ++j;
 579                         }
 580                         return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
 581                                )->setflag(status_flags::dynallocated);
 582                 }
 583         }
 584
 585         return this->hold();
 586 }
 587
 588 ex mul::evalf(int level) const
 589 {
 590         if (level==1)
 591                 return mul(seq,overall_coeff);
 592
 593         if (level==-max_recursion_level)
 594                 throw(std::runtime_error("max recursion level reached"));
 595
 596         std::auto_ptr<epvector> s(new epvector);
 597         s->reserve(seq.size());
 598
 599         --level;
 600         epvector::const_iterator i = seq.begin(), end = seq.end();
 601         while (i != end) {
 602                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 603                                                            i->coeff));
 604                 ++i;
 605         }
 606         return mul(s, overall_coeff.evalf(level));
 607 }
 608
 609 void mul::find_real_imag(ex & rp, ex & ip) const
 610 {
 611         rp = overall_coeff.real_part();
 612         ip = overall_coeff.imag_part();
 613         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 614                 ex factor = recombine_pair_to_ex(*i);
 615                 ex new_rp = factor.real_part();
 616                 ex new_ip = factor.imag_part();
 617                 if(new_ip.is_zero()) {
 618                         rp *= new_rp;
 619                         ip *= new_rp;
 620                 } else {
 621                         ex temp = rp*new_rp - ip*new_ip;
 622                         ip = ip*new_rp + rp*new_ip;
 623                         rp = temp;
 624                 }
 625         }
 626         rp = rp.expand();
 627         ip = ip.expand();
 628 }
 629
 630 ex mul::real_part() const
 631 {
 632         ex rp, ip;
 633         find_real_imag(rp, ip);
 634         return rp;
 635 }
 636
 637 ex mul::imag_part() const
 638 {
 639         ex rp, ip;
 640         find_real_imag(rp, ip);
 641         return ip;
 642 }
 643
 644 ex mul::evalm() const
 645 {
 646         // numeric*matrix
 647         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 648          && is_a<matrix>(seq[0].rest))
 649                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 650
 651         // Evaluate children first, look whether there are any matrices at all
 652         // (there can be either no matrices or one matrix; if there were more
 653         // than one matrix, it would be a non-commutative product)
 654         std::auto_ptr<epvector> s(new epvector);
 655         s->reserve(seq.size());
 656
 657         bool have_matrix = false;
 658         epvector::iterator the_matrix;
 659
 660         epvector::const_iterator i = seq.begin(), end = seq.end();
 661         while (i != end) {
 662                 const ex &m = recombine_pair_to_ex(*i).evalm();
 663                 s->push_back(split_ex_to_pair(m));
 664                 if (is_a<matrix>(m)) {
 665                         have_matrix = true;
 666                         the_matrix = s->end() - 1;
 667                 }
 668                 ++i;
 669         }
 670
 671         if (have_matrix) {
 672
 673                 // The product contained a matrix. We will multiply all other factors
 674                 // into that matrix.
 675                 matrix m = ex_to<matrix>(the_matrix->rest);
 676                 s->erase(the_matrix);
 677                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 678                 return m.mul_scalar(scalar);
 679
 680         } else
 681                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 682 }
 683
 684 ex mul::eval_ncmul(const exvector & v) const
 685 {
 686         if (seq.empty())
 687                 return inherited::eval_ncmul(v);
 688
 689         // Find first noncommutative element and call its eval_ncmul()
 690         epvector::const_iterator i = seq.begin(), end = seq.end();
 691         while (i != end) {
 692                 if (i->rest.return_type() == return_types::noncommutative)
 693                         return i->rest.eval_ncmul(v);
 694                 ++i;
 695         }
 696         return inherited::eval_ncmul(v);
 697 }
 698
 699 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& repls)
 700 {
 701         ex origbase;
 702         int origexponent;
 703         int origexpsign;
 704
 705         if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
 706                 origbase = origfactor.op(0);
 707                 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
 708                 origexponent = expon > 0 ? expon : -expon;
 709                 origexpsign = expon > 0 ? 1 : -1;
 710         } else {
 711                 origbase = origfactor;
 712                 origexponent = 1;
 713                 origexpsign = 1;
 714         }
 715
 716         ex patternbase;
 717         int patternexponent;
 718         int patternexpsign;
 719
 720         if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
 721                 patternbase = patternfactor.op(0);
 722                 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
 723                 patternexponent = expon > 0 ? expon : -expon;
 724                 patternexpsign = expon > 0 ? 1 : -1;
 725         } else {
 726                 patternbase = patternfactor;
 727                 patternexponent = 1;
 728                 patternexpsign = 1;
 729         }
 730
 731         exmap saverepls = repls;
 732         if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
 733                 return false;
 734         repls = saverepls;
 735
 736         int newnummatches = origexponent / patternexponent;
 737         if (newnummatches < nummatches)
 738                 nummatches = newnummatches;
 739         return true;
 740 }
 741
 742 /** Checks wheter e matches to the pattern pat and the (possibly to be updated)
 743   * list of replacements repls. This matching is in the sense of algebraic
 744   * substitutions. Matching starts with pat.op(factor) of the pattern because
 745   * the factors before this one have already been matched. The (possibly
 746   * updated) number of matches is in nummatches. subsed[i] is true for factors
 747   * that already have been replaced by previous substitutions and matched[i]
 748   * is true for factors that have been matched by the current match.
 749   */
 750 bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls,
 751                                   int factor, int &nummatches, const std::vector<bool> &subsed,
 752                                   std::vector<bool> &matched)
 753 {
 754         GINAC_ASSERT(subsed.size() == e.nops());
 755         GINAC_ASSERT(matched.size() == e.nops());
 756
 757         if (factor == (int)pat.nops())
 758                 return true;
 759
 760         for (size_t i=0; i<e.nops(); ++i) {
 761                 if(subsed[i] || matched[i])
 762                         continue;
 763                 exmap newrepls = repls;
 764                 int newnummatches = nummatches;
 765                 if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
 766                         matched[i] = true;
 767                         if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
 768                                         newnummatches, subsed, matched)) {
 769                                 repls = newrepls;
 770                                 nummatches = newnummatches;
 771                                 return true;
 772                         }
 773                         else
 774                                 matched[i] = false;
 775                 }
 776         }
 777
 778         return false;
 779 }
 780
 781 bool mul::has(const ex & pattern, unsigned options) const
 782 {
 783         if(!(options&has_options::algebraic))
 784                 return basic::has(pattern,options);
 785         if(is_a<mul>(pattern)) {
 786                 exmap repls;
 787                 int nummatches = std::numeric_limits<int>::max();
 788                 std::vector<bool> subsed(nops(), false);
 789                 std::vector<bool> matched(nops(), false);
 790                 if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
 791                                 subsed, matched))
 792                         return true;
 793         }
 794         return basic::has(pattern, options);
 795 }
 796
 797 ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
 798 {
 799         std::vector<bool> subsed(nops(), false);
 800         ex divide_by = 1;
 801         ex multiply_by = 1;
 802
 803         for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
 804
 805                 if (is_exactly_a<mul>(it->first)) {
 806 retry1:
 807                         int nummatches = std::numeric_limits<int>::max();
 808                         std::vector<bool> currsubsed(nops(), false);
 809                         exmap repls;
 810
 811                         if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
 812                                 continue;
 813
 814                         for (size_t j=0; j<subsed.size(); j++)
 815                                 if (currsubsed[j])
 816                                         subsed[j] = true;
 817                         ex subsed_pattern
 818                                 = it->first.subs(repls, subs_options::no_pattern);
 819                         divide_by *= power(subsed_pattern, nummatches);
 820                         ex subsed_result
 821                                 = it->second.subs(repls, subs_options::no_pattern);
 822                         multiply_by *= power(subsed_result, nummatches);
 823                         goto retry1;
 824
 825                 } else {
 826
 827                         for (size_t j=0; j<this->nops(); j++) {
 828                                 int nummatches = std::numeric_limits<int>::max();
 829                                 exmap repls;
 830                                 if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
 831                                         subsed[j] = true;
 832                                         ex subsed_pattern
 833                                                 = it->first.subs(repls, subs_options::no_pattern);
 834                                         divide_by *= power(subsed_pattern, nummatches);
 835                                         ex subsed_result
 836                                                 = it->second.subs(repls, subs_options::no_pattern);
 837                                         multiply_by *= power(subsed_result, nummatches);
 838                                 }
 839                         }
 840                 }
 841         }
 842
 843         bool subsfound = false;
 844         for (size_t i=0; i<subsed.size(); i++) {
 845                 if (subsed[i]) {
 846                         subsfound = true;
 847                         break;
 848                 }
 849         }
 850         if (!subsfound)
 851                 return subs_one_level(m, options | subs_options::algebraic);
 852
 853         return ((*this)/divide_by)*multiply_by;
 854 }
 855
 856 ex mul::conjugate() const
 857 {
 858         // The base class' method is wrong here because we have to be careful at
 859         // branch cuts. power::conjugate takes care of that already, so use it.
 860         epvector *newepv = 0;
 861         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 862                 if (newepv) {
 863                         newepv->push_back(split_ex_to_pair(recombine_pair_to_ex(*i).conjugate()));
 864                         continue;
 865                 }
 866                 ex x = recombine_pair_to_ex(*i);
 867                 ex c = x.conjugate();
 868                 if (c.is_equal(x)) {
 869                         continue;
 870                 }
 871                 newepv = new epvector;
 872                 newepv->reserve(seq.size());
 873                 for (epvector::const_iterator j=seq.begin(); j!=i; ++j) {
 874                         newepv->push_back(*j);
 875                 }
 876                 newepv->push_back(split_ex_to_pair(c));
 877         }
 878         ex x = overall_coeff.conjugate();
 879         if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
 880                 return *this;
 881         }
 882         ex result = thisexpairseq(newepv ? *newepv : seq, x);
 883         delete newepv;
 884         return result;
 885 }
 886
 887
 888 // protected
 889
 890 /** Implementation of ex::diff() for a product.  It applies the product rule.
 891  *  @see ex::diff */
 892 ex mul::derivative(const symbol & s) const
 893 {
 894         size_t num = seq.size();
 895         exvector addseq;
 896         addseq.reserve(num);
 897
 898         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 899         epvector mulseq = seq;
 900         epvector::const_iterator i = seq.begin(), end = seq.end();
 901         epvector::iterator i2 = mulseq.begin();
 902         while (i != end) {
 903                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 904                                              i->rest.diff(s));
 905                 ep.swap(*i2);
 906                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 907                 ep.swap(*i2);
 908                 ++i; ++i2;
 909         }
 910         return (new add(addseq))->setflag(status_flags::dynallocated);
 911 }
 912
 913 int mul::compare_same_type(const basic & other) const
 914 {
 915         return inherited::compare_same_type(other);
 916 }
 917
 918 unsigned mul::return_type() const
 919 {
 920         if (seq.empty()) {
 921                 // mul without factors: should not happen, but commutates
 922                 return return_types::commutative;
 923         }
 924
 925         bool all_commutative = true;
 926         epvector::const_iterator noncommutative_element; // point to first found nc element
 927
 928         epvector::const_iterator i = seq.begin(), end = seq.end();
 929         while (i != end) {
 930                 unsigned rt = i->rest.return_type();
 931                 if (rt == return_types::noncommutative_composite)
 932                         return rt; // one ncc -> mul also ncc
 933                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 934                         // first nc element found, remember position
 935                         noncommutative_element = i;
 936                         all_commutative = false;
 937                 }
 938                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 939                         // another nc element found, compare type_infos
 940                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 941                                         // different types -> mul is ncc
 942                                         return return_types::noncommutative_composite;
 943                         }
 944                 }
 945                 ++i;
 946         }
 947         // all factors checked
 948         return all_commutative ? return_types::commutative : return_types::noncommutative;
 949 }
 950
 951 return_type_t mul::return_type_tinfo() const
 952 {
 953         if (seq.empty())
 954                 return make_return_type_t<mul>(); // mul without factors: should not happen
 955
 956         // return type_info of first noncommutative element
 957         epvector::const_iterator i = seq.begin(), end = seq.end();
 958         while (i != end) {
 959                 if (i->rest.return_type() == return_types::noncommutative)
 960                         return i->rest.return_type_tinfo();
 961                 ++i;
 962         }
 963         // no noncommutative element found, should not happen
 964         return make_return_type_t<mul>();
 965 }
 966
 967 ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 968 {
 969         return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
 970 }
 971
 972 ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 973 {
 974         return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated);
 975 }
 976
 977 expair mul::split_ex_to_pair(const ex & e) const
 978 {
 979         if (is_exactly_a<power>(e)) {
 980                 const power & powerref = ex_to<power>(e);
 981                 if (is_exactly_a<numeric>(powerref.exponent))
 982                         return expair(powerref.basis,powerref.exponent);
 983         }
 984         return expair(e,_ex1);
 985 }
 986
 987 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 988                                           const ex & c) const
 989 {
 990         // to avoid duplication of power simplification rules,
 991         // we create a temporary power object
 992         // otherwise it would be hard to correctly evaluate
 993         // expression like (4^(1/3))^(3/2)
 994         if (c.is_equal(_ex1))
 995                 return split_ex_to_pair(e);
 996
 997         return split_ex_to_pair(power(e,c));
 998 }
 999
1000 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
1001                                             const ex & c) const
1002 {
1003         // to avoid duplication of power simplification rules,
1004         // we create a temporary power object
1005         // otherwise it would be hard to correctly evaluate
1006         // expression like (4^(1/3))^(3/2)
1007         if (c.is_equal(_ex1))
1008                 return p;
1009
1010         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
1011 }
1012
1013 ex mul::recombine_pair_to_ex(const expair & p) const
1014 {
1015         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
1016                 return p.rest;
1017         else
1018                 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
1019 }
1020
1021 bool mul::expair_needs_further_processing(epp it)
1022 {
1023         if (is_exactly_a<mul>(it->rest) &&
1024             ex_to<numeric>(it->coeff).is_integer()) {
1025                 // combined pair is product with integer power -> expand it
1026                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
1027                 return true;
1028         }
1029         if (is_exactly_a<numeric>(it->rest)) {
1030                 if (it->coeff.is_equal(_ex1)) {
1031                         // pair has coeff 1 and must be moved to the end
1032                         return true;
1033                 }
1034                 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
1035                 if (!ep.is_equal(*it)) {
1036                         // combined pair is a numeric power which can be simplified
1037                         *it = ep;
1038                         return true;
1039                 }
1040         }
1041         return false;
1042 }
1043
1044 ex mul::default_overall_coeff() const
1045 {
1046         return _ex1;
1047 }
1048
1049 void mul::combine_overall_coeff(const ex & c)
1050 {
1051         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
1052         GINAC_ASSERT(is_exactly_a<numeric>(c));
1053         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
1054 }
1055
1056 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
1057 {
1058         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
1059         GINAC_ASSERT(is_exactly_a<numeric>(c1));
1060         GINAC_ASSERT(is_exactly_a<numeric>(c2));
1061         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
1062 }
1063
1064 bool mul::can_make_flat(const expair & p) const
1065 {
1066         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
1067         // this assertion will probably fail somewhere
1068         // it would require a more careful make_flat, obeying the power laws
1069         // probably should return true only if p.coeff is integer
1070         return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
1071 }
1072
1073 bool mul::can_be_further_expanded(const ex & e)
1074 {
1075         if (is_exactly_a<mul>(e)) {
1076                 for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
1077                         if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
1078                                 return true;
1079                 }
1080         } else if (is_exactly_a<power>(e)) {
1081                 if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
1082                         return true;
1083         }
1084         return false;
1085 }
1086
1087 ex mul::expand(unsigned options) const
1088 {
1089         {
1090         // trivial case: expanding the monomial (~ 30% of all calls)
1091                 epvector::const_iterator i = seq.begin(), seq_end = seq.end();
1092                 while ((i != seq.end()) &&  is_a<symbol>(i->rest) && i->coeff.info(info_flags::integer))
1093                         ++i;
1094                 if (i == seq_end) {
1095                         setflag(status_flags::expanded);
1096                         return *this;
1097                 }
1098         }
1099
1100         // do not rename indices if the object has no indices at all
1101         if ((!(options & expand_options::expand_rename_idx)) &&
1102                         this->info(info_flags::has_indices))
1103                 options |= expand_options::expand_rename_idx;
1104
1105         const bool skip_idx_rename = !(options & expand_options::expand_rename_idx);
1106
1107         // First, expand the children
1108         std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
1109         const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
1110
1111         // Now, look for all the factors that are sums and multiply each one out
1112         // with the next one that is found while collecting the factors which are
1113         // not sums
1114         ex last_expanded = _ex1;
1115
1116         epvector non_adds;
1117         non_adds.reserve(expanded_seq.size());
1118
1119         for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
1120                 if (is_exactly_a<add>(cit->rest) &&
1121                         (cit->coeff.is_equal(_ex1))) {
1122                         if (is_exactly_a<add>(last_expanded)) {
1123
1124                                 // Expand a product of two sums, aggressive version.
1125                                 // Caring for the overall coefficients in separate loops can
1126                                 // sometimes give a performance gain of up to 15%!
1127
1128                                 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
1129                                 // add2 is for the inner loop and should be the bigger of the two sums
1130                                 // in the presence of asymptotically good sorting:
1131                                 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
1132                                 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
1133                                 const epvector::const_iterator add1begin = add1.seq.begin();
1134                                 const epvector::const_iterator add1end   = add1.seq.end();
1135                                 const epvector::const_iterator add2begin = add2.seq.begin();
1136                                 const epvector::const_iterator add2end   = add2.seq.end();
1137                                 epvector distrseq;
1138                                 distrseq.reserve(add1.seq.size()+add2.seq.size());
1139
1140                                 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
1141                                 if (!add1.overall_coeff.is_zero()) {
1142                                         if (add1.overall_coeff.is_equal(_ex1))
1143                                                 distrseq.insert(distrseq.end(),add2begin,add2end);
1144                                         else
1145                                                 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
1146                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
1147                                 }
1148
1149                                 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
1150                                 if (!add2.overall_coeff.is_zero()) {
1151                                         if (add2.overall_coeff.is_equal(_ex1))
1152                                                 distrseq.insert(distrseq.end(),add1begin,add1end);
1153                                         else
1154                                                 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
1155                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
1156                                 }
1157
1158                                 // Compute the new overall coefficient and put it together:
1159                                 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
1160
1161                                 exvector add1_dummy_indices, add2_dummy_indices, add_indices;
1162                                 lst dummy_subs;
1163
1164                                 if (!skip_idx_rename) {
1165                                         for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
1166                                                 add_indices = get_all_dummy_indices_safely(i->rest);
1167                                                 add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
1168                                         }
1169                                         for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
1170                                                 add_indices = get_all_dummy_indices_safely(i->rest);
1171                                                 add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
1172                                         }
1173
1174                                         sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
1175                                         sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
1176                                         dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
1177                                 }
1178
1179                                 // Multiply explicitly all non-numeric terms of add1 and add2:
1180                                 for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
1181                                         // We really have to combine terms here in order to compactify
1182                                         // the result.  Otherwise it would become waayy tooo bigg.
1183                                         numeric oc(*_num0_p);
1184                                         epvector distrseq2;
1185                                         distrseq2.reserve(add1.seq.size());
1186                                         const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ?
1187                                                         i2->rest :
1188                                                         i2->rest.subs(ex_to<lst>(dummy_subs.op(0)),
1189                                                                 ex_to<lst>(dummy_subs.op(1)), subs_options::no_pattern));
1190                                         for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
1191                                                 // Don't push_back expairs which might have a rest that evaluates to a numeric,
1192                                                 // since that would violate an invariant of expairseq:
1193                                                 const ex rest = (new mul(i1->rest, i2_new))->setflag(status_flags::dynallocated);
1194                                                 if (is_exactly_a<numeric>(rest)) {
1195                                                         oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
1196                                                 } else {
1197                                                         distrseq2.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
1198                                                 }
1199                                         }
1200                                         tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated);
1201                                 }
1202                                 last_expanded = tmp_accu;
1203                         } else {
1204                                 if (!last_expanded.is_equal(_ex1))
1205                                         non_adds.push_back(split_ex_to_pair(last_expanded));
1206                                 last_expanded = cit->rest;
1207                         }
1208
1209                 } else {
1210                         non_adds.push_back(*cit);
1211                 }
1212         }
1213
1214         // Now the only remaining thing to do is to multiply the factors which
1215         // were not sums into the "last_expanded" sum
1216         if (is_exactly_a<add>(last_expanded)) {
1217                 size_t n = last_expanded.nops();
1218                 exvector distrseq;
1219                 distrseq.reserve(n);
1220                 exvector va;
1221                 if (! skip_idx_rename) {
1222                         va = get_all_dummy_indices_safely(mul(non_adds));
1223                         sort(va.begin(), va.end(), ex_is_less());
1224                 }
1225
1226                 for (size_t i=0; i<n; ++i) {
1227                         epvector factors = non_adds;
1228                         if (skip_idx_rename)
1229                                 factors.push_back(split_ex_to_pair(last_expanded.op(i)));
1230                         else
1231                                 factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
1232                         ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
1233                         if (can_be_further_expanded(term)) {
1234                                 distrseq.push_back(term.expand());
1235                         } else {
1236                                 if (options == 0)
1237                                         ex_to<basic>(term).setflag(status_flags::expanded);
1238                                 distrseq.push_back(term);
1239                         }
1240                 }
1241
1242                 return ((new add(distrseq))->
1243                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
1244         }
1245
1246         non_adds.push_back(split_ex_to_pair(last_expanded));
1247         ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
1248         if (can_be_further_expanded(result)) {
1249                 return result.expand();
1250         } else {
1251                 if (options == 0)
1252                         ex_to<basic>(result).setflag(status_flags::expanded);
1253                 return result;
1254         }
1255 }
1256
1257
1258 //////////
1259 // new virtual functions which can be overridden by derived classes
1260 //////////
1261
1262 // none
1263
1264 //////////
1265 // non-virtual functions in this class
1266 //////////
1267
1268
1269 /** Member-wise expand the expairs representing this sequence.  This must be
1270  *  overridden from expairseq::expandchildren() and done iteratively in order
1271  *  to allow for early cancallations and thus safe memory.
1272  *
1273  *  @see mul::expand()
1274  *  @return pointer to epvector containing expanded representation or zero
1275  *  pointer, if sequence is unchanged. */
1276 std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
1277 {
1278         const epvector::const_iterator last = seq.end();
1279         epvector::const_iterator cit = seq.begin();
1280         while (cit!=last) {
1281                 const ex & factor = recombine_pair_to_ex(*cit);
1282                 const ex & expanded_factor = factor.expand(options);
1283                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
1284
1285                         // something changed, copy seq, eval and return it
1286                         std::auto_ptr<epvector> s(new epvector);
1287                         s->reserve(seq.size());
1288
1289                         // copy parts of seq which are known not to have changed
1290                         epvector::const_iterator cit2 = seq.begin();
1291                         while (cit2!=cit) {
1292                                 s->push_back(*cit2);
1293                                 ++cit2;
1294                         }
1295
1296                         // copy first changed element
1297                         s->push_back(split_ex_to_pair(expanded_factor));
1298                         ++cit2;
1299
1300                         // copy rest
1301                         while (cit2!=last) {
1302                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
1303                                 ++cit2;
1304                         }
1305                         return s;
1306                 }
1307                 ++cit;
1308         }
1309
1310         return std::auto_ptr<epvector>(0); // nothing has changed
1311 }
1312
1313 GINAC_BIND_UNARCHIVER(mul);
1314
1315 } // namespace GiNaC