ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999 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
  30 //////////
  31 // default constructor, destructor, copy constructor assignment operator and helpers
  32 //////////
  33
  34 // public
  35
  36 mul::mul()
  37 {
  38     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  39     tinfo_key = TINFO_mul;
  40 }
  41
  42 mul::~mul()
  43 {
  44     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  45     destroy(0);
  46 }
  47
  48 mul::mul(mul const & other)
  49 {
  50     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  51     copy(other);
  52 }
  53
  54 mul const & mul::operator=(mul const & other)
  55 {
  56     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  57     if (this != &other) {
  58         destroy(1);
  59         copy(other);
  60     }
  61     return *this;
  62 }
  63
  64 // protected
  65
  66 void mul::copy(mul const & other)
  67 {
  68     expairseq::copy(other);
  69 }
  70
  71 void mul::destroy(bool call_parent)
  72 {
  73     if (call_parent) expairseq::destroy(call_parent);
  74 }
  75
  76 //////////
  77 // other constructors
  78 //////////
  79
  80 // public
  81
  82 mul::mul(ex const & lh, ex const & rh)
  83 {
  84     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  85     tinfo_key = TINFO_mul;
  86     overall_coeff=exONE();
  87     construct_from_2_ex(lh,rh);
  88     ASSERT(is_canonical());
  89 }
  90
  91 mul::mul(exvector const & v)
  92 {
  93     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
  94     tinfo_key = TINFO_mul;
  95     overall_coeff=exONE();
  96     construct_from_exvector(v);
  97     ASSERT(is_canonical());
  98 }
  99
 100 /*
 101 mul::mul(epvector const & v, bool do_not_canonicalize)
 102 {
 103     debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
 104     tinfo_key = TINFO_mul;
 105     if (do_not_canonicalize) {
 106         seq=v;
 107 #ifdef EXPAIRSEQ_USE_HASHTAB
 108         combine_same_terms(); // to build hashtab
 109 #endif // def EXPAIRSEQ_USE_HASHTAB
 110     } else {
 111         construct_from_epvector(v);
 112     }
 113     ASSERT(is_canonical());
 114 }
 115 */
 116
 117 mul::mul(epvector const & v)
 118 {
 119     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 120     tinfo_key = TINFO_mul;
 121     overall_coeff=exONE();
 122     construct_from_epvector(v);
 123     ASSERT(is_canonical());
 124 }
 125
 126 mul::mul(epvector const & v, ex const & oc)
 127 {
 128     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 129     tinfo_key = TINFO_mul;
 130     overall_coeff=oc;
 131     construct_from_epvector(v);
 132     ASSERT(is_canonical());
 133 }
 134
 135 mul::mul(epvector * vp, ex const & oc)
 136 {
 137     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 138     tinfo_key = TINFO_mul;
 139     ASSERT(vp!=0);
 140     overall_coeff=oc;
 141     construct_from_epvector(*vp);
 142     delete vp;
 143     ASSERT(is_canonical());
 144 }
 145
 146 mul::mul(ex const & lh, ex const & mh, ex const & rh)
 147 {
 148     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 149     tinfo_key = TINFO_mul;
 150     exvector factors;
 151     factors.reserve(3);
 152     factors.push_back(lh);
 153     factors.push_back(mh);
 154     factors.push_back(rh);
 155     overall_coeff=exONE();
 156     construct_from_exvector(factors);
 157     ASSERT(is_canonical());
 158 }
 159
 160 //////////
 161 // functions overriding virtual functions from bases classes
 162 //////////
 163
 164 // public
 165
 166 basic * mul::duplicate() const
 167 {
 168     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 169     return new mul(*this);
 170 }
 171
 172 bool mul::info(unsigned inf) const
 173 {
 174     // TODO: optimize
 175     if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial || inf==info_flags::rational_function) {
 176         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 177             if (!(recombine_pair_to_ex(*it).info(inf)))
 178                 return false;
 179         }
 180         return true;
 181     } else {
 182         return expairseq::info(inf);
 183     }
 184 }
 185
 186 typedef vector<int> intvector;
 187
 188 int mul::degree(symbol const & s) const
 189 {
 190     int deg_sum=0;
 191     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 192         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 193     }
 194     return deg_sum;
 195 }
 196
 197 int mul::ldegree(symbol const & s) const
 198 {
 199     int deg_sum=0;
 200     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 201         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 202     }
 203     return deg_sum;
 204 }
 205
 206 ex mul::coeff(symbol const & s, int const n) const
 207 {
 208     exvector coeffseq;
 209     coeffseq.reserve(seq.size()+1);
 210
 211     if (n==0) {
 212         // product of individual coeffs
 213         // if a non-zero power of s is found, the resulting product will be 0
 214         epvector::const_iterator it=seq.begin();
 215         while (it!=seq.end()) {
 216             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 217             ++it;
 218         }
 219         coeffseq.push_back(overall_coeff);
 220         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 221     }
 222
 223     epvector::const_iterator it=seq.begin();
 224     bool coeff_found=0;
 225     while (it!=seq.end()) {
 226         ex t=recombine_pair_to_ex(*it);
 227         ex c=t.coeff(s,n);
 228         if (!c.is_zero()) {
 229             coeffseq.push_back(c);
 230             coeff_found=1;
 231         } else {
 232             coeffseq.push_back(t);
 233         }
 234         ++it;
 235     }
 236     if (coeff_found) {
 237         coeffseq.push_back(overall_coeff);
 238         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 239     }
 240
 241     return exZERO();
 242 }
 243
 244 /*
 245 ex mul::eval(int level) const
 246 {
 247     // simplifications: *(...,x,(c1,1),(c2,1)) -> *(...,x,(c1*c2,1)) (c1, c2 numeric(), move pairs to end first)
 248     //                  *(...,x,1) -> *(...,x)
 249     //                  *(...,x,0) -> 0
 250     //                  *(+(x,y,...),(c,1)) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 251     //                  *(x) -> x
 252     //                  *() -> 1
 253
 254     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 255
 256     if ((level==1)&&(flags & status_flags::evaluated)) {
 257 #ifdef DOASSERT
 258         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 259             ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 260                    (!(ex_to_numeric((*cit).coeff).is_integer())));
 261         }
 262
 263         // test if all numerics were moved to the end and
 264         // all numerics with coeff 1 to the very end
 265         if (seq.size()!=0) {
 266             epvector::const_iterator cit=seq.end();
 267             bool all_coeff_1=true;
 268             bool all_numeric=true;
 269             do {
 270                 cit--;
 271                 if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 272                     ASSERT(all_numeric);
 273                     if ((*cit).coeff.is_equal(exONE())) {
 274                         ASSERT(all_coeff_1);
 275                     } else {
 276                         all_coeff_1=false;
 277                     }
 278                 } else {
 279                     all_numeric=false;
 280                 }
 281             } while (cit!=seq.begin());
 282         }
 283 #endif // def DOASSERT
 284         return *this;
 285     }
 286
 287     epvector newseq;
 288     epvector::iterator it1,it2;
 289     bool seq_copied=false;
 290
 291     epvector * evaled_seqp=evalchildren(level);
 292     if (evaled_seqp!=0) {
 293         // do more evaluation later
 294         return (new mul(evaled_seqp))->setflag(status_flags::dynallocated);
 295     }
 296
 297     // combine pairs with coeff 1 (all numerics should be at end, assert below)
 298     if (seq.size()>1) {
 299         // count number of pairs with coeff 1
 300         unsigned num_coeff_1=0;
 301         bool still_numeric=true;
 302         epvector::const_iterator cit=seq.end();
 303         unsigned first_pos;
 304         unsigned second_pos;
 305         do {
 306             cit--;
 307             if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 308                 if ((*cit).coeff.is_equal(exONE())) {
 309                     num_coeff_1++;
 310                 }
 311             } else {
 312                 still_numeric=false;
 313             }
 314         } while ((cit!=seq.begin())&&still_numeric);
 315         if (num_coeff_1>1) {
 316             newseq=seq;
 317
 318     }
 319
 320
 321 #ifdef DOASSERT
 322     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 323         ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 324                (!(ex_to_numeric((*cit).coeff).is_integer())));
 325     }
 326
 327     // test if all numerics were moved to the end and
 328     // all numerics with coeff 1 to the very end
 329     if (seq.size()!=0) {
 330         epvector::const_iterator cit=seq.end();
 331         bool all_coeff_1=true;
 332         bool all_numeric=true;
 333         do {
 334             cit--;
 335             if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 336                 ASSERT(all_numeric);
 337                 if ((*cit).coeff.is_equal(exONE())) {
 338                     ASSERT(all_coeff_1);
 339                 } else {
 340                     all_coeff_1=false;
 341                 }
 342             } else {
 343                 all_numeric=false;
 344             }
 345         } while (cit!=seq.begin());
 346     }
 347 #endif // def DOASSERT
 348
 349     if (flags & status_flags::evaluated) {
 350         return *this;
 351     }
 352
 353     expair const & last_expair=*(seq.end()-1);
 354     expair const & next_to_last_expair=*(seq.end()-2);
 355     int seq_size = seq.size();
 356
 357     // *(...,x,(c1,1),(c2,1)) -> *(...,x,(c1*c2,1)) (c1, c2 numeric())
 358     if ((!seq_copied) && (seq_size>=2) &&
 359         is_ex_exactly_of_type(last_expair.rest,numeric) &&
 360         ex_to_numeric(last_expair.coeff).is_equal(numONE()) &&
 361         is_ex_exactly_of_type(next_to_last_expair.rest,numeric) &&
 362         ex_to_numeric(next_to_last_expair.coeff).is_equal(numONE()) ) {
 363         newseq=seq;
 364         seq_copied=true;
 365         it2=newseq.end()-1;
 366         it1=it2-1;
 367     }
 368     while (seq_copied && (newseq.size()>=2) &&
 369            is_ex_exactly_of_type((*it1).rest,numeric) &&
 370            ex_to_numeric((*it1).coeff).is_equal(numONE()) &&
 371            is_ex_exactly_of_type((*it2).rest,numeric) &&
 372            ex_to_numeric((*it2).coeff).is_equal(numONE()) ) {
 373         *it1=expair(ex_to_numeric((*it1).rest).mul_dyn(ex_to_numeric((*it2).rest)),exONE());
 374         newseq.pop_back();
 375         it2=newseq.end()-1;
 376         it1=it2-1;
 377     }
 378
 379     // *(...,x,1) -> *(...,x)
 380     if ((!seq_copied) && (seq_size>=1) &&
 381         (is_ex_exactly_of_type(last_expair.rest,numeric)) &&
 382         (ex_to_numeric(last_expair.rest).compare(numONE())==0)) {
 383         newseq=seq;
 384         seq_copied=true;
 385         it2=newseq.end()-1;
 386     }
 387     if (seq_copied && (newseq.size()>=1) &&
 388         (is_ex_exactly_of_type((*it2).rest,numeric)) &&
 389         (ex_to_numeric((*it2).rest).compare(numONE())==0)) {
 390         newseq.pop_back();
 391         it2=newseq.end()-1;
 392     }
 393
 394     // *(...,x,0) -> 0
 395     if ((!seq_copied) && (seq_size>=1) &&
 396         (is_ex_exactly_of_type(last_expair.rest,numeric)) &&
 397         (ex_to_numeric(last_expair.rest).is_zero())) {
 398         return exZERO();
 399     }
 400     if (seq_copied && (newseq.size()>=1) &&
 401         (is_ex_exactly_of_type((*it2).rest,numeric)) &&
 402         (ex_to_numeric((*it2).rest).is_zero())) {
 403         return exZERO();
 404     }
 405
 406     // *(+(x,y,...),c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 407     if ((!seq_copied) && (seq_size==2) &&
 408         is_ex_exactly_of_type(next_to_last_expair.rest,add) &&
 409         is_ex_exactly_of_type(last_expair.rest,numeric) &&
 410         ex_to_numeric(last_expair.coeff).is_equal(numONE()) &&
 411         (ex_to_numeric(next_to_last_expair.coeff).compare(numONE())==0)) {
 412         add const & addref=ex_to_add(next_to_last_expair.rest);
 413         epvector distrseq;
 414         distrseq.reserve(addref.seq.size());
 415         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 416             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 417                                    last_expair.rest));
 418         }
 419         // special treatment for the last element if it is numeric (to
 420         // avoid terms like (2/3)*(3/2)) is no longer necessary, this
 421         // is handled in add::combine_pair_with_coeff_to_pair()
 422         return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
 423                                               status_flags::evaluated );
 424     }
 425     if (seq_copied && (newseq.size()==2) &&
 426         is_ex_exactly_of_type(newseq[0].rest,add) &&
 427         is_ex_exactly_of_type(newseq[1].rest,numeric) &&
 428         ex_to_numeric(newseq[1].coeff).is_equal(numONE()) &&
 429         (ex_to_numeric(newseq[0].coeff).compare(numONE())==0)) {
 430         add const & addref=ex_to_add(newseq[0].rest);
 431         epvector distrseq;
 432         distrseq.reserve(addref.seq.size());
 433         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 434             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 435                                    newseq[1].rest));
 436         }
 437         // special treatment for the last element if it is numeric (to
 438         // avoid terms like (2/3)*(3/2)) is no longer necessary, this
 439         // is handled in add::combine_pair_with_coeff_to_pair()
 440         return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
 441                                               status_flags::evaluated );
 442     }
 443
 444     // *() -> 1
 445     if ((!seq_copied) && (seq_size==0)) {
 446         return exONE();
 447     } else if (seq_copied && (newseq.size()==0)) {
 448         return exONE();
 449     }
 450
 451     // *(x) -> x
 452     if ((!seq_copied) && (seq_size==1)) {
 453         return recombine_pair_to_ex(*(seq.begin()));
 454     } else if (seq_copied && (newseq.size()==1)) {
 455         return recombine_pair_to_ex(*(newseq.begin()));
 456     }
 457
 458     if (!seq_copied) return this->hold();
 459
 460     return (new mul(newseq,1))->setflag(status_flags::dynallocated  |
 461                                         status_flags::evaluated );
 462 }
 463 */
 464
 465 ex mul::eval(int level) const
 466 {
 467     // simplifications  *(...,x;0) -> 0
 468     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 469     //                  *(x;1) -> x
 470     //                  *(;c) -> c
 471
 472     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 473
 474     epvector * evaled_seqp=evalchildren(level);
 475     if (evaled_seqp!=0) {
 476         // do more evaluation later
 477         return (new mul(evaled_seqp,overall_coeff))->
 478                    setflag(status_flags::dynallocated);
 479     }
 480
 481 #ifdef DOASSERT
 482     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 483         ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 484                (!(ex_to_numeric((*cit).coeff).is_integer())));
 485         ASSERT(!((*cit).is_numeric_with_coeff_1()));
 486         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 487             printtree(cerr,0);
 488         }
 489         ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 490         /* for paranoia */
 491         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 492         ASSERT(p.rest.is_equal((*cit).rest));
 493         ASSERT(p.coeff.is_equal((*cit).coeff));
 494         /* end paranoia */
 495     }
 496 #endif // def DOASSERT
 497
 498     if (flags & status_flags::evaluated) {
 499         ASSERT(seq.size()>0);
 500         ASSERT((seq.size()>1)||!overall_coeff.is_equal(exONE()));
 501         return *this;
 502     }
 503
 504     int seq_size=seq.size();
 505     if (overall_coeff.is_equal(exZERO())) {
 506         // *(...,x;0) -> 0
 507         return exZERO();
 508     } else if (seq_size==0) {
 509         // *(;c) -> c
 510         return overall_coeff;
 511     } else if ((seq_size==1)&&overall_coeff.is_equal(exONE())) {
 512         // *(x;1) -> x
 513         return recombine_pair_to_ex(*(seq.begin()));
 514     } else if ((seq_size==1) &&
 515                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 516                ex_to_numeric((*seq.begin()).coeff).is_equal(numONE())) {
 517         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 518         add const & addref=ex_to_add((*seq.begin()).rest);
 519         epvector distrseq;
 520         distrseq.reserve(addref.seq.size());
 521         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 522             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 523                                    overall_coeff));
 524         }
 525         return (new add(distrseq,
 526                         ex_to_numeric(addref.overall_coeff).
 527                         mul_dyn(ex_to_numeric(overall_coeff))))
 528             ->setflag(status_flags::dynallocated  |
 529                       status_flags::evaluated );
 530     }
 531     return this->hold();
 532 }
 533
 534 /*
 535 ex mul::eval(int level) const
 536 {
 537     // simplifications: *(...,x,c1,c2) -> *(...,x,c1*c2) (c1, c2 numeric())
 538     //                  *(...,(c1,c2)) -> (...,(c1^c2,1)) (normalize)
 539     //                  *(...,x,1) -> +(...,x)
 540     //                  *(...,x,0) -> 0
 541     //                  *(+(x,y,...),c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 542     //                  *(x) -> x
 543     //                  *() -> 1
 544
 545     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 546
 547     epvector newseq=seq;
 548     epvector::iterator it1,it2;
 549
 550     // *(...,x,c1,c2) -> *(...,x,c1*c2) (c1, c2 numeric())
 551     it2=newseq.end()-1;
 552     it1=it2-1;
 553     while ((newseq.size()>=2)&&is_exactly_of_type(*(*it1).rest.bp,numeric)&&
 554                                is_exactly_of_type(*(*it2).rest.bp,numeric)) {
 555         *it1=expair(ex_to_numeric((*it1).rest).power(ex_to_numeric((*it1).coeff))
 556                     .mul(ex_to_numeric((*it2).rest).power(ex_to_numeric((*it2).coeff))),exONE());
 557         newseq.pop_back();
 558         it2=newseq.end()-1;
 559         it1=it2-1;
 560     }
 561
 562     if ((newseq.size()>=1)&&is_exactly_of_type(*(*it2).rest.bp,numeric)) {
 563         // *(...,(c1,c2)) -> (...,(c1^c2,1)) (normalize)
 564         *it2=expair(ex_to_numeric((*it2).rest).power(ex_to_numeric((*it2).coeff)),exONE());
 565         // *(...,x,1) -> *(...,x)
 566         if (static_cast<numeric &>(*(*it2).rest.bp).compare(numONE())==0) {
 567             newseq.pop_back();
 568             it2=newseq.end()-1;
 569         }
 570     }
 571
 572     // *(...,x,0) -> 0
 573     if ((newseq.size()>=1)&&is_exactly_of_type(*(*it2).rest.bp,numeric)) {
 574         if (static_cast<numeric &>(*(*it2).rest.bp).is_zero()==0) {
 575             return exZERO();
 576         }
 577     }
 578
 579     // *(+(x,y,...),c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 580     if ((newseq.size()==2)&&is_ex_exactly_of_type(newseq[0].rest,add)&&
 581         is_ex_exactly_of_type(newseq[1].rest,numeric)&&
 582         (ex_to_numeric(newseq[0].coeff).compare(numONE())==0)) {
 583         add const & addref=ex_to_add(newseq[0].rest);
 584         numeric const & numref=ex_to_numeric(newseq[1].rest);
 585         epvector distrseq;
 586         distrseq.reserve(addref.seq.size());
 587         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 588             distrseq.push_back(expair((*cit).rest,ex_to_numeric((*cit).coeff).mul(numref)));
 589         }
 590         return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
 591                                               status_flags::evaluated );
 592     }
 593
 594     if (newseq.size()==0) {
 595         // *() -> 1
 596         return exONE();
 597     } else if (newseq.size()==1) {
 598         // *(x) -> x
 599         return recombine_pair_to_ex(*newseq.begin());
 600     }
 601
 602     return (new mul(newseq,1))->setflag(status_flags::dynallocated  |
 603                                         status_flags::evaluated );
 604 }
 605 */
 606
 607 exvector mul::get_indices(void) const
 608 {
 609     // return union of indices of factors
 610     exvector iv;
 611     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 612         exvector subiv=(*cit).rest.get_indices();
 613         iv.reserve(iv.size()+subiv.size());
 614         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 615             iv.push_back(*cit2);
 616         }
 617     }
 618     return iv;
 619 }
 620
 621 ex mul::simplify_ncmul(exvector const & v) const
 622 {
 623     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 624 }
 625
 626 // protected
 627
 628 int mul::compare_same_type(basic const & other) const
 629 {
 630     return expairseq::compare_same_type(other);
 631 }
 632
 633 bool mul::is_equal_same_type(basic const & other) const
 634 {
 635     return expairseq::is_equal_same_type(other);
 636 }
 637
 638 unsigned mul::return_type(void) const
 639 {
 640     if (seq.size()==0) {
 641         // mul without factors: should not happen, but commutes
 642         return return_types::commutative;
 643     }
 644
 645     bool all_commutative=1;
 646     unsigned rt;
 647     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 648
 649     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 650         rt=(*cit).rest.return_type();
 651         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 652         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 653             // first nc element found, remember position
 654             cit_noncommutative_element=cit;
 655             all_commutative=0;
 656         }
 657         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 658                 // another nc element found, compare type_infos
 659             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 660                 // diffent types -> mul is ncc
 661                 return return_types::noncommutative_composite;
 662             }
 663         }
 664     }
 665     // all factors checked
 666     return all_commutative ? return_types::commutative : return_types::noncommutative;
 667 }
 668
 669 unsigned mul::return_type_tinfo(void) const
 670 {
 671     if (seq.size()==0) {
 672         // mul without factors: should not happen
 673         return tinfo_key;
 674     }
 675     // return type_info of first noncommutative element
 676     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 677         if ((*cit).rest.return_type()==return_types::noncommutative) {
 678             return (*cit).rest.return_type_tinfo();
 679         }
 680     }
 681     // no noncommutative element found, should not happen
 682     return tinfo_key;
 683 }
 684
 685 ex mul::thisexpairseq(epvector const & v, ex const & oc) const
 686 {
 687     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 688 }
 689
 690 ex mul::thisexpairseq(epvector * vp, ex const & oc) const
 691 {
 692     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 693 }
 694
 695 expair mul::split_ex_to_pair(ex const & e) const
 696 {
 697     if (is_ex_exactly_of_type(e,power)) {
 698         power const & powerref=ex_to_power(e);
 699         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 700             return expair(powerref.basis,powerref.exponent);
 701         }
 702     }
 703     return expair(e,exONE());
 704 }
 705
 706 expair mul::combine_ex_with_coeff_to_pair(ex const & e,
 707                                           ex const & c) const
 708 {
 709     // to avoid duplication of power simplification rules,
 710     // we create a temporary power object
 711     // otherwise it would be hard to correctly simplify
 712     // expression like (4^(1/3))^(3/2)
 713     if (are_ex_trivially_equal(c,exONE())) {
 714         return split_ex_to_pair(e);
 715     }
 716     return split_ex_to_pair(power(e,c));
 717 }
 718
 719 expair mul::combine_pair_with_coeff_to_pair(expair const & p,
 720                                             ex const & c) const
 721 {
 722     // to avoid duplication of power simplification rules,
 723     // we create a temporary power object
 724     // otherwise it would be hard to correctly simplify
 725     // expression like (4^(1/3))^(3/2)
 726     if (are_ex_trivially_equal(c,exONE())) {
 727         return p;
 728     }
 729     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 730 }
 731
 732 ex mul::recombine_pair_to_ex(expair const & p) const
 733 {
 734     // if (p.coeff.compare(exONE())==0) {
 735     // if (are_ex_trivially_equal(p.coeff,exONE())) {
 736     if (ex_to_numeric(p.coeff).is_equal(numONE())) {
 737         return p.rest;
 738     } else {
 739         return power(p.rest,p.coeff);
 740     }
 741 }
 742
 743 bool mul::expair_needs_further_processing(epp it)
 744 {
 745     if (is_ex_exactly_of_type((*it).rest,mul) &&
 746         ex_to_numeric((*it).coeff).is_integer()) {
 747         // combined pair is product with integer power -> expand it
 748         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 749         return true;
 750     }
 751     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 752         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 753         if (!ep.is_equal(*it)) {
 754             // combined pair is a numeric power which can be simplified
 755             *it=ep;
 756             return true;
 757         }
 758         if (ex_to_numeric((*it).coeff).is_equal(numONE())) {
 759             // combined pair has coeff 1 and must be moved to the end
 760             return true;
 761         }
 762     }
 763     return false;
 764 }
 765
 766 ex mul::default_overall_coeff(void) const
 767 {
 768     return exONE();
 769 }
 770
 771 void mul::combine_overall_coeff(ex const & c)
 772 {
 773     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 774     ASSERT(is_ex_exactly_of_type(c,numeric));
 775     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 776 }
 777
 778 void mul::combine_overall_coeff(ex const & c1, ex const & c2)
 779 {
 780     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 781     ASSERT(is_ex_exactly_of_type(c1,numeric));
 782     ASSERT(is_ex_exactly_of_type(c2,numeric));
 783     overall_coeff = ex_to_numeric(overall_coeff).
 784                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 785 }
 786
 787 bool mul::can_make_flat(expair const & p) const
 788 {
 789     ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 790     // this assertion will probably fail somewhere
 791     // it would require a more careful make_flat, obeying the power laws
 792     // probably should return true only if p.coeff is integer
 793     return ex_to_numeric(p.coeff).is_equal(numONE());
 794 }
 795
 796 ex mul::expand(unsigned options) const
 797 {
 798     exvector sub_expanded_seq;
 799     intvector positions_of_adds;
 800     intvector number_of_add_operands;
 801
 802     epvector * expanded_seqp=expandchildren(options);
 803
 804     epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 805
 806     positions_of_adds.resize(expanded_seq.size());
 807     number_of_add_operands.resize(expanded_seq.size());
 808
 809     int number_of_adds=0;
 810     int number_of_expanded_terms=1;
 811
 812     unsigned current_position=0;
 813     epvector::const_iterator last=expanded_seq.end();
 814     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 815         if (is_ex_exactly_of_type((*cit).rest,add)&&
 816             (ex_to_numeric((*cit).coeff).is_equal(numONE()))) {
 817             positions_of_adds[number_of_adds]=current_position;
 818             add const & expanded_addref=ex_to_add((*cit).rest);
 819             int addref_nops=expanded_addref.nops();
 820             number_of_add_operands[number_of_adds]=addref_nops;
 821             number_of_expanded_terms *= addref_nops;
 822             number_of_adds++;
 823         }
 824         current_position++;
 825     }
 826
 827     if (number_of_adds==0) {
 828         if (expanded_seqp==0) {
 829             return this->setflag(status_flags::expanded);
 830         }
 831         return (new mul(expanded_seqp,overall_coeff))->
 832                      setflag(status_flags::dynallocated ||
 833                              status_flags::expanded);
 834     }
 835
 836     exvector distrseq;
 837     distrseq.reserve(number_of_expanded_terms);
 838
 839     intvector k;
 840     k.resize(number_of_adds);
 841
 842     int l;
 843     for (l=0; l<number_of_adds; l++) {
 844         k[l]=0;
 845     }
 846
 847     while (1) {
 848         epvector term;
 849         term=expanded_seq;
 850         for (l=0; l<number_of_adds; l++) {
 851             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 852             ASSERT(term[positions_of_adds[l]].coeff.compare(exONE())==0);
 853             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 854         }
 855         /*
 856         cout << "mul::expand() term begin" << endl;
 857         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
 858             cout << "rest" << endl;
 859             (*cit).rest.printtree(cout);
 860             cout << "coeff" << endl;
 861             (*cit).coeff.printtree(cout);
 862         }
 863         cout << "mul::expand() term end" << endl;
 864         */
 865         distrseq.push_back((new mul(term,overall_coeff))->
 866                                 setflag(status_flags::dynallocated |
 867                                         status_flags::expanded));
 868
 869         // increment k[]
 870         l=number_of_adds-1;
 871         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 872             k[l]=0;
 873             l--;
 874         }
 875         if (l<0) break;
 876     }
 877
 878     if (expanded_seqp!=0) {
 879         delete expanded_seqp;
 880     }
 881     /*
 882     cout << "mul::expand() distrseq begin" << endl;
 883     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
 884         (*cit).printtree(cout);
 885     }
 886     cout << "mul::expand() distrseq end" << endl;
 887     */
 888
 889     return (new add(distrseq))->setflag(status_flags::dynallocated |
 890                                         status_flags::expanded);
 891 }
 892
 893 /*
 894 ex mul::expand(unsigned options) const
 895 {
 896     exvector sub_expanded_seq;
 897     intvector positions_of_adds;
 898     intvector number_of_add_operands;
 899
 900     sub_expanded_seq.resize(seq.size());
 901     positions_of_adds.resize(seq.size());
 902     number_of_add_operands.reserve(seq.size());
 903
 904     int number_of_adds=0;
 905     int number_of_expanded_terms=1;
 906     for (unsigned current_position=0; current_position<seq.size(); current_position++) {
 907         ex const & expanded_ex=recombine_pair_to_ex(seq[current_position]).expand(options);
 908         if (is_ex_exactly_of_type(expanded_ex,add)) {
 909             positions_of_adds[number_of_adds]=current_position;
 910             add const & expanded_addref=ex_to_add(expanded_ex);
 911             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 912             number_of_expanded_terms *= expanded_addref.seq.size();
 913             number_of_adds++;
 914         }
 915         sub_expanded_seq.push_back(expanded_ex);
 916     }
 917
 918     exvector distrseq;
 919     distrseq.reserve(number_of_expanded_terms);
 920
 921     intvector k;
 922     k.resize(number_of_adds);
 923
 924     int l;
 925     for (l=0; l<number_of_adds; l++) {
 926         k[l]=0;
 927     }
 928
 929     while (1) {
 930         exvector term;
 931         term=sub_expanded_seq;
 932         for (l=0; l<number_of_adds; l++) {
 933             add const & addref=ex_to_add(sub_expanded_seq[positions_of_adds[l]]);
 934             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 935         }
 936         distrseq.push_back((new mul(term))->setflag(status_flags::dynallocated |
 937                                                     status_flags::expanded));
 938
 939         // increment k[]
 940         l=number_of_adds-1;
 941         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 942             k[l]=0;
 943             l--;
 944         }
 945         if (l<0) break;
 946     }
 947
 948     return (new add(distrseq))->setflag(status_flags::dynallocated |
 949                                         status_flags::expanded);
 950 }
 951 */
 952
 953 //////////
 954 // new virtual functions which can be overridden by derived classes
 955 //////////
 956
 957 // none
 958
 959 //////////
 960 // non-virtual functions in this class
 961 //////////
 962
 963 epvector * mul::expandchildren(unsigned options) const
 964 {
 965     epvector::const_iterator last=seq.end();
 966     epvector::const_iterator cit=seq.begin();
 967     while (cit!=last) {
 968         ex const & factor=recombine_pair_to_ex(*cit);
 969         ex const & expanded_factor=factor.expand(options);
 970         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 971
 972             // something changed, copy seq, eval and return it
 973             epvector *s=new epvector;
 974             s->reserve(seq.size());
 975
 976             // copy parts of seq which are known not to have changed
 977             epvector::const_iterator cit2=seq.begin();
 978             while (cit2!=cit) {
 979                 s->push_back(*cit2);
 980                 ++cit2;
 981             }
 982             // copy first changed element
 983             s->push_back(split_ex_to_pair(expanded_factor));
 984             ++cit2;
 985             // copy rest
 986             while (cit2!=last) {
 987                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 988                 ++cit2;
 989             }
 990             return s;
 991         }
 992         ++cit;
 993     }
 994
 995     return 0; // nothing has changed
 996 }
 997
 998 //////////
 999 // static member variables
1000 //////////
1001
1002 // protected
1003
1004 unsigned mul::precedence=50;
1005
1006
1007 //////////
1008 // global constants
1009 //////////
1010
1011 const mul some_mul;
1012 type_info const & typeid_mul=typeid(some_mul);
1013
1014