ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
   7  *
   8  *  This program is free software; you can redistribute it and/or modify
   9  *  it under the terms of the GNU General Public License as published by
  10  *  the Free Software Foundation; either version 2 of the License, or
  11  *  (at your option) any later version.
  12  *
  13  *  This program is distributed in the hope that it will be useful,
  14  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  15  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  16  *  GNU General Public License for more details.
  17  *
  18  *  You should have received a copy of the GNU General Public License
  19  *  along with this program; if not, write to the Free Software
  20  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  21  */
  22
  23 #include <vector>
  24 #include <stdexcept>
  25
  26 #include "mul.h"
  27 #include "add.h"
  28 #include "power.h"
  29 #include "archive.h"
  30 #include "debugmsg.h"
  31 #include "utils.h"
  32
  33 #ifndef NO_NAMESPACE_GINAC
  34 namespace GiNaC {
  35 #endif // ndef NO_NAMESPACE_GINAC
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 // public
  44
  45 mul::mul()
  46 {
  47         debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  48         tinfo_key = TINFO_mul;
  49 }
  50
  51 mul::~mul()
  52 {
  53         debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  54         destroy(false);
  55 }
  56
  57 mul::mul(const mul & other)
  58 {
  59         debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  60         copy(other);
  61 }
  62
  63 const mul & mul::operator=(const mul & other)
  64 {
  65         debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  66         if (this != &other) {
  67                 destroy(true);
  68                 copy(other);
  69         }
  70         return *this;
  71 }
  72
  73 // protected
  74
  75 void mul::copy(const mul & other)
  76 {
  77         inherited::copy(other);
  78 }
  79
  80 void mul::destroy(bool call_parent)
  81 {
  82         if (call_parent) inherited::destroy(call_parent);
  83 }
  84
  85 //////////
  86 // other constructors
  87 //////////
  88
  89 // public
  90
  91 mul::mul(const ex & lh, const ex & rh)
  92 {
  93         debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  94         tinfo_key = TINFO_mul;
  95         overall_coeff = _ex1();
  96         construct_from_2_ex(lh,rh);
  97         GINAC_ASSERT(is_canonical());
  98 }
  99
 100 mul::mul(const exvector & v)
 101 {
 102         debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
 103         tinfo_key = TINFO_mul;
 104         overall_coeff = _ex1();
 105         construct_from_exvector(v);
 106         GINAC_ASSERT(is_canonical());
 107 }
 108
 109 mul::mul(const epvector & v)
 110 {
 111         debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 112         tinfo_key = TINFO_mul;
 113         overall_coeff = _ex1();
 114         construct_from_epvector(v);
 115         GINAC_ASSERT(is_canonical());
 116 }
 117
 118 mul::mul(const epvector & v, const ex & oc)
 119 {
 120         debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 121         tinfo_key = TINFO_mul;
 122         overall_coeff = oc;
 123         construct_from_epvector(v);
 124         GINAC_ASSERT(is_canonical());
 125 }
 126
 127 mul::mul(epvector * vp, const ex & oc)
 128 {
 129         debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 130         tinfo_key = TINFO_mul;
 131         GINAC_ASSERT(vp!=0);
 132         overall_coeff = oc;
 133         construct_from_epvector(*vp);
 134         delete vp;
 135         GINAC_ASSERT(is_canonical());
 136 }
 137
 138 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 139 {
 140         debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 141         tinfo_key = TINFO_mul;
 142         exvector factors;
 143         factors.reserve(3);
 144         factors.push_back(lh);
 145         factors.push_back(mh);
 146         factors.push_back(rh);
 147         overall_coeff = _ex1();
 148         construct_from_exvector(factors);
 149         GINAC_ASSERT(is_canonical());
 150 }
 151
 152 //////////
 153 // archiving
 154 //////////
 155
 156 /** Construct object from archive_node. */
 157 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 158 {
 159         debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 160 }
 161
 162 /** Unarchive the object. */
 163 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
 164 {
 165         return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
 166 }
 167
 168 /** Archive the object. */
 169 void mul::archive(archive_node &n) const
 170 {
 171         inherited::archive(n);
 172 }
 173
 174 //////////
 175 // functions overriding virtual functions from bases classes
 176 //////////
 177
 178 // public
 179
 180 basic * mul::duplicate() const
 181 {
 182         debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 183         return new mul(*this);
 184 }
 185
 186 void mul::print(std::ostream & os, unsigned upper_precedence) const
 187 {
 188         debugmsg("mul print",LOGLEVEL_PRINT);
 189         if (precedence<=upper_precedence) os << "(";
 190         bool first=true;
 191         // first print the overall numeric coefficient:
 192         numeric coeff = ex_to_numeric(overall_coeff);
 193         if (coeff.csgn()==-1) os << '-';
 194         if (!coeff.is_equal(_num1()) &&
 195                 !coeff.is_equal(_num_1())) {
 196                 if (coeff.is_rational()) {
 197                         if (coeff.is_negative())
 198                                 os << -coeff;
 199                         else
 200                                 os << coeff;
 201                 } else {
 202                         if (coeff.csgn()==-1)
 203                                 (-coeff).print(os, precedence);
 204                         else
 205                                 coeff.print(os, precedence);
 206                 }
 207                 os << '*';
 208         }
 209         // then proceed with the remaining factors:
 210         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 211                 if (!first) {
 212                         os << '*';
 213                 } else {
 214                         first=false;
 215                 }
 216                 recombine_pair_to_ex(*cit).print(os,precedence);
 217         }
 218         if (precedence<=upper_precedence) os << ")";
 219 }
 220
 221 void mul::printraw(std::ostream & os) const
 222 {
 223         debugmsg("mul printraw",LOGLEVEL_PRINT);
 224
 225         os << "*(";
 226         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 227                 os << "(";
 228                 (*it).rest.bp->printraw(os);
 229                 os << ",";
 230                 (*it).coeff.bp->printraw(os);
 231                 os << "),";
 232         }
 233         os << ",hash=" << hashvalue << ",flags=" << flags;
 234         os << ")";
 235 }
 236
 237 void mul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 238 {
 239         debugmsg("mul print csrc", LOGLEVEL_PRINT);
 240         if (precedence <= upper_precedence)
 241                 os << "(";
 242
 243         if (!overall_coeff.is_equal(_ex1())) {
 244                 overall_coeff.bp->printcsrc(os,type,precedence);
 245                 os << "*";
 246         }
 247
 248         // Print arguments, separated by "*" or "/"
 249         epvector::const_iterator it = seq.begin();
 250         epvector::const_iterator itend = seq.end();
 251         while (it != itend) {
 252
 253                 // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 254                 if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 255                         if (type == csrc_types::ctype_cl_N)
 256                                 os << "recip(";
 257                         else
 258                                 os << "1.0/";
 259                 }
 260
 261                 // If the exponent is 1 or -1, it is left out
 262                 if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 263                         it->rest.bp->printcsrc(os, type, precedence);
 264                 else
 265                         // outer parens around ex needed for broken gcc-2.95 parser:
 266                         (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 267
 268                 // Separator is "/" for negative integer powers, "*" otherwise
 269                 ++it;
 270                 if (it != itend) {
 271                         if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 272                                 os << "/";
 273                         else
 274                                 os << "*";
 275                 }
 276         }
 277         if (precedence <= upper_precedence)
 278                 os << ")";
 279 }
 280
 281 bool mul::info(unsigned inf) const
 282 {
 283         switch (inf) {
 284                 case info_flags::polynomial:
 285                 case info_flags::integer_polynomial:
 286                 case info_flags::cinteger_polynomial:
 287                 case info_flags::rational_polynomial:
 288                 case info_flags::crational_polynomial:
 289                 case info_flags::rational_function: {
 290                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 291                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 292                                         return false;
 293                         }
 294                         return overall_coeff.info(inf);
 295                 }
 296                 case info_flags::algebraic: {
 297                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 298                                 if ((recombine_pair_to_ex(*i).info(inf)))
 299                                         return true;
 300                         }
 301                         return false;
 302                 }
 303         }
 304         return inherited::info(inf);
 305 }
 306
 307 typedef std::vector<int> intvector;
 308
 309 int mul::degree(const symbol & s) const
 310 {
 311         int deg_sum = 0;
 312         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 313                 deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 314         }
 315         return deg_sum;
 316 }
 317
 318 int mul::ldegree(const symbol & s) const
 319 {
 320         int deg_sum = 0;
 321         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 322                 deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 323         }
 324         return deg_sum;
 325 }
 326
 327 ex mul::coeff(const symbol & s, int n) const
 328 {
 329         exvector coeffseq;
 330         coeffseq.reserve(seq.size()+1);
 331
 332         if (n==0) {
 333                 // product of individual coeffs
 334                 // if a non-zero power of s is found, the resulting product will be 0
 335                 epvector::const_iterator it=seq.begin();
 336                 while (it!=seq.end()) {
 337                         coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 338                         ++it;
 339                 }
 340                 coeffseq.push_back(overall_coeff);
 341                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 342         }
 343
 344         epvector::const_iterator it=seq.begin();
 345         bool coeff_found=0;
 346         while (it!=seq.end()) {
 347                 ex t=recombine_pair_to_ex(*it);
 348                 ex c=t.coeff(s,n);
 349                 if (!c.is_zero()) {
 350                         coeffseq.push_back(c);
 351                         coeff_found=1;
 352                 } else {
 353                         coeffseq.push_back(t);
 354                 }
 355                 ++it;
 356         }
 357         if (coeff_found) {
 358                 coeffseq.push_back(overall_coeff);
 359                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 360         }
 361
 362         return _ex0();
 363 }
 364
 365 ex mul::eval(int level) const
 366 {
 367         // simplifications  *(...,x;0) -> 0
 368         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 369         //                  *(x;1) -> x
 370         //                  *(;c) -> c
 371
 372         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 373
 374         epvector * evaled_seqp=evalchildren(level);
 375         if (evaled_seqp!=0) {
 376                 // do more evaluation later
 377                 return (new mul(evaled_seqp,overall_coeff))->
 378                                    setflag(status_flags::dynallocated);
 379         }
 380
 381 #ifdef DO_GINAC_ASSERT
 382         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 383                 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 384                            (!(ex_to_numeric((*cit).coeff).is_integer())));
 385                 GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 386                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 387                         printtree(cerr,0);
 388                 }
 389                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 390                 /* for paranoia */
 391                 expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 392                 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 393                 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 394                 /* end paranoia */
 395         }
 396 #endif // def DO_GINAC_ASSERT
 397
 398         if (flags & status_flags::evaluated) {
 399                 GINAC_ASSERT(seq.size()>0);
 400                 GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 401                 return *this;
 402         }
 403
 404         int seq_size=seq.size();
 405         if (overall_coeff.is_equal(_ex0())) {
 406                 // *(...,x;0) -> 0
 407                 return _ex0();
 408         } else if (seq_size==0) {
 409                 // *(;c) -> c
 410                 return overall_coeff;
 411         } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 412                 // *(x;1) -> x
 413                 return recombine_pair_to_ex(*(seq.begin()));
 414         } else if ((seq_size==1) &&
 415                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 416                    ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 417                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 418                 const add & addref=ex_to_add((*seq.begin()).rest);
 419                 epvector distrseq;
 420                 distrseq.reserve(addref.seq.size());
 421                 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 422                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
 423                 }
 424                 return (new add(distrseq,
 425                                 ex_to_numeric(addref.overall_coeff).
 426                                 mul_dyn(ex_to_numeric(overall_coeff))))
 427                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 428         }
 429         return this->hold();
 430 }
 431
 432 ex mul::evalf(int level) const
 433 {
 434         if (level==1)
 435                 return mul(seq,overall_coeff);
 436
 437         if (level==-max_recursion_level)
 438                 throw(std::runtime_error("max recursion level reached"));
 439
 440         epvector s;
 441         s.reserve(seq.size());
 442
 443         --level;
 444         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 445                 s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
 446                                                           (*it).coeff));
 447         }
 448         return mul(s,overall_coeff.evalf(level));
 449 }
 450
 451 exvector mul::get_indices(void) const
 452 {
 453         // return union of indices of factors
 454         exvector iv;
 455         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 456                 exvector subiv=(*cit).rest.get_indices();
 457                 iv.reserve(iv.size()+subiv.size());
 458                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 459                         iv.push_back(*cit2);
 460                 }
 461         }
 462         return iv;
 463 }
 464
 465 ex mul::simplify_ncmul(const exvector & v) const
 466 {
 467         throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 468 }
 469
 470 // protected
 471
 472 /** Implementation of ex::diff() for a product.  It applies the product rule.
 473  *  @see ex::diff */
 474 ex mul::derivative(const symbol & s) const
 475 {
 476         exvector addseq;
 477         addseq.reserve(seq.size());
 478
 479         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 480         for (unsigned i=0; i!=seq.size(); ++i) {
 481                 epvector mulseq = seq;
 482                 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
 483                                              seq[i].rest.diff(s));
 484                 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
 485         }
 486         return (new add(addseq))->setflag(status_flags::dynallocated);
 487 }
 488
 489 int mul::compare_same_type(const basic & other) const
 490 {
 491         return inherited::compare_same_type(other);
 492 }
 493
 494 bool mul::is_equal_same_type(const basic & other) const
 495 {
 496         return inherited::is_equal_same_type(other);
 497 }
 498
 499 unsigned mul::return_type(void) const
 500 {
 501         if (seq.size()==0) {
 502                 // mul without factors: should not happen, but commutes
 503                 return return_types::commutative;
 504         }
 505
 506         bool all_commutative = 1;
 507         unsigned rt;
 508         epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 509
 510         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 511                 rt=(*cit).rest.return_type();
 512                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 513                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 514                         // first nc element found, remember position
 515                         cit_noncommutative_element = cit;
 516                         all_commutative = 0;
 517                 }
 518                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 519                         // another nc element found, compare type_infos
 520                         if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 521                                 // diffent types -> mul is ncc
 522                                 return return_types::noncommutative_composite;
 523                         }
 524                 }
 525         }
 526         // all factors checked
 527         return all_commutative ? return_types::commutative : return_types::noncommutative;
 528 }
 529
 530 unsigned mul::return_type_tinfo(void) const
 531 {
 532         if (seq.size()==0) {
 533                 // mul without factors: should not happen
 534                 return tinfo_key;
 535         }
 536         // return type_info of first noncommutative element
 537         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 538                 if ((*cit).rest.return_type()==return_types::noncommutative) {
 539                         return (*cit).rest.return_type_tinfo();
 540                 }
 541         }
 542         // no noncommutative element found, should not happen
 543         return tinfo_key;
 544 }
 545
 546 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 547 {
 548         return (new mul(v,oc))->setflag(status_flags::dynallocated);
 549 }
 550
 551 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 552 {
 553         return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 554 }
 555
 556 expair mul::split_ex_to_pair(const ex & e) const
 557 {
 558         if (is_ex_exactly_of_type(e,power)) {
 559                 const power & powerref=ex_to_power(e);
 560                 if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 561                         return expair(powerref.basis,powerref.exponent);
 562                 }
 563         }
 564         return expair(e,_ex1());
 565 }
 566
 567 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 568                                           const ex & c) const
 569 {
 570         // to avoid duplication of power simplification rules,
 571         // we create a temporary power object
 572         // otherwise it would be hard to correctly simplify
 573         // expression like (4^(1/3))^(3/2)
 574         if (are_ex_trivially_equal(c,_ex1()))
 575                 return split_ex_to_pair(e);
 576
 577         return split_ex_to_pair(power(e,c));
 578 }
 579
 580 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 581                                             const ex & c) const
 582 {
 583         // to avoid duplication of power simplification rules,
 584         // we create a temporary power object
 585         // otherwise it would be hard to correctly simplify
 586         // expression like (4^(1/3))^(3/2)
 587         if (are_ex_trivially_equal(c,_ex1()))
 588                 return p;
 589
 590         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 591 }
 592
 593 ex mul::recombine_pair_to_ex(const expair & p) const
 594 {
 595         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 596                 return p.rest;
 597         else
 598                 return power(p.rest,p.coeff);
 599 }
 600
 601 bool mul::expair_needs_further_processing(epp it)
 602 {
 603         if (is_ex_exactly_of_type((*it).rest,mul) &&
 604                 ex_to_numeric((*it).coeff).is_integer()) {
 605                 // combined pair is product with integer power -> expand it
 606                 *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 607                 return true;
 608         }
 609         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 610                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 611                 if (!ep.is_equal(*it)) {
 612                         // combined pair is a numeric power which can be simplified
 613                         *it=ep;
 614                         return true;
 615                 }
 616                 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 617                         // combined pair has coeff 1 and must be moved to the end
 618                         return true;
 619                 }
 620         }
 621         return false;
 622 }
 623
 624 ex mul::default_overall_coeff(void) const
 625 {
 626         return _ex1();
 627 }
 628
 629 void mul::combine_overall_coeff(const ex & c)
 630 {
 631         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 632         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 633         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 634 }
 635
 636 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 637 {
 638         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 639         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 640         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 641         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 642 }
 643
 644 bool mul::can_make_flat(const expair & p) const
 645 {
 646         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 647         // this assertion will probably fail somewhere
 648         // it would require a more careful make_flat, obeying the power laws
 649         // probably should return true only if p.coeff is integer
 650         return ex_to_numeric(p.coeff).is_equal(_num1());
 651 }
 652
 653 ex mul::expand(unsigned options) const
 654 {
 655         if (flags & status_flags::expanded)
 656                 return *this;
 657
 658         exvector sub_expanded_seq;
 659         intvector positions_of_adds;
 660         intvector number_of_add_operands;
 661
 662         epvector * expanded_seqp = expandchildren(options);
 663
 664         const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 665
 666         positions_of_adds.resize(expanded_seq.size());
 667         number_of_add_operands.resize(expanded_seq.size());
 668
 669         int number_of_adds = 0;
 670         int number_of_expanded_terms = 1;
 671
 672         unsigned current_position = 0;
 673         epvector::const_iterator last = expanded_seq.end();
 674         for (epvector::const_iterator cit = expanded_seq.begin(); cit!=last; ++cit) {
 675                 if (is_ex_exactly_of_type((*cit).rest,add) &&
 676                         ((*cit).coeff.is_equal(_ex1()))) {
 677                         positions_of_adds[number_of_adds] = current_position;
 678                         const add & expanded_addref = ex_to_add((*cit).rest);
 679                         unsigned addref_nops = expanded_addref.nops();
 680                         number_of_add_operands[number_of_adds] = addref_nops;
 681                         number_of_expanded_terms *= addref_nops;
 682                         ++number_of_adds;
 683                 }
 684                 ++current_position;
 685         }
 686
 687         if (number_of_adds==0) {
 688                 if (expanded_seqp==0)
 689                         return this->setflag(status_flags::expanded);
 690                 else
 691                         return ((new mul(expanded_seqp,overall_coeff))->
 692                                setflag(status_flags::dynallocated | status_flags::expanded));
 693         }
 694
 695         exvector distrseq;
 696         distrseq.reserve(number_of_expanded_terms);
 697
 698         intvector k;
 699         k.resize(number_of_adds, 0);
 700
 701         for (;;) {
 702                 epvector term;
 703                 term = expanded_seq;
 704                 for (int l=0; l<number_of_adds; ++l) {
 705                         const add & addref = ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 706                         GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
 707                         term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 708                 }
 709                 distrseq.push_back((new mul(term,overall_coeff))->
 710                                     setflag(status_flags::dynallocated | status_flags::expanded));
 711
 712                 // increment k[]
 713                 int l = number_of_adds-1;
 714                 while ((l>=0) && ((++k[l])>=number_of_add_operands[l])) {
 715                         k[l] = 0;
 716                         --l;
 717                 }
 718                 if (l < 0) break;
 719         }
 720
 721         if (expanded_seqp!=0)
 722                 delete expanded_seqp;
 723
 724         return (new add(distrseq))->setflag(status_flags::dynallocated |
 725                                                                                 status_flags::expanded);
 726 }
 727
 728 //////////
 729 // new virtual functions which can be overridden by derived classes
 730 //////////
 731
 732 // none
 733
 734 //////////
 735 // non-virtual functions in this class
 736 //////////
 737
 738 epvector * mul::expandchildren(unsigned options) const
 739 {
 740         epvector::const_iterator last = seq.end();
 741         epvector::const_iterator cit = seq.begin();
 742         while (cit!=last) {
 743                 const ex & factor = recombine_pair_to_ex(*cit);
 744                 const ex & expanded_factor = factor.expand(options);
 745                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 746
 747                         // something changed, copy seq, eval and return it
 748                         epvector *s=new epvector;
 749                         s->reserve(seq.size());
 750
 751                         // copy parts of seq which are known not to have changed
 752                         epvector::const_iterator cit2 = seq.begin();
 753                         while (cit2!=cit) {
 754                                 s->push_back(*cit2);
 755                                 ++cit2;
 756                         }
 757                         // copy first changed element
 758                         s->push_back(split_ex_to_pair(expanded_factor));
 759                         ++cit2;
 760                         // copy rest
 761                         while (cit2!=last) {
 762                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 763                                 ++cit2;
 764                         }
 765                         return s;
 766                 }
 767                 ++cit;
 768         }
 769
 770         return 0; // nothing has changed
 771 }
 772
 773 //////////
 774 // static member variables
 775 //////////
 776
 777 // protected
 778
 779 unsigned mul::precedence = 50;
 780
 781
 782 //////////
 783 // global constants
 784 //////////
 785
 786 const mul some_mul;
 787 const std::type_info & typeid_mul = typeid(some_mul);
 788
 789 #ifndef NO_NAMESPACE_GINAC
 790 } // namespace GiNaC
 791 #endif // ndef NO_NAMESPACE_GINAC