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