ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 #include <vector>
   6 #include <stdexcept>
   7
   8 #include "ginac.h"
   9
  10 //////////
  11 // default constructor, destructor, copy constructor assignment operator and helpers
  12 //////////
  13
  14 // public
  15
  16 mul::mul()
  17 {
  18     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  19     tinfo_key = TINFO_MUL;
  20 }
  21
  22 mul::~mul()
  23 {
  24     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  25     destroy(0);
  26 }
  27
  28 mul::mul(mul const & other)
  29 {
  30     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  31     copy(other);
  32 }
  33
  34 mul const & mul::operator=(mul const & other)
  35 {
  36     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  37     if (this != &other) {
  38         destroy(1);
  39         copy(other);
  40     }
  41     return *this;
  42 }
  43
  44 // protected
  45
  46 void mul::copy(mul const & other)
  47 {
  48     expairseq::copy(other);
  49 }
  50
  51 void mul::destroy(bool call_parent)
  52 {
  53     if (call_parent) expairseq::destroy(call_parent);
  54 }
  55
  56 //////////
  57 // other constructors
  58 //////////
  59
  60 // public
  61
  62 mul::mul(ex const & lh, ex const & rh)
  63 {
  64     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  65     tinfo_key = TINFO_MUL;
  66     overall_coeff=exONE();
  67     construct_from_2_ex(lh,rh);
  68     ASSERT(is_canonical());
  69 }
  70
  71 mul::mul(exvector const & v)
  72 {
  73     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
  74     tinfo_key = TINFO_MUL;
  75     overall_coeff=exONE();
  76     construct_from_exvector(v);
  77     ASSERT(is_canonical());
  78 }
  79
  80 /*
  81 mul::mul(epvector const & v, bool do_not_canonicalize)
  82 {
  83     debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
  84     tinfo_key = TINFO_MUL;
  85     if (do_not_canonicalize) {
  86         seq=v;
  87 #ifdef EXPAIRSEQ_USE_HASHTAB
  88         combine_same_terms(); // to build hashtab
  89 #endif // def EXPAIRSEQ_USE_HASHTAB
  90     } else {
  91         construct_from_epvector(v);
  92     }
  93     ASSERT(is_canonical());
  94 }
  95 */
  96
  97 mul::mul(epvector const & v)
  98 {
  99     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 100     tinfo_key = TINFO_MUL;
 101     overall_coeff=exONE();
 102     construct_from_epvector(v);
 103     ASSERT(is_canonical());
 104 }
 105
 106 mul::mul(epvector const & v, ex const & oc)
 107 {
 108     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 109     tinfo_key = TINFO_MUL;
 110     overall_coeff=oc;
 111     construct_from_epvector(v);
 112     ASSERT(is_canonical());
 113 }
 114
 115 mul::mul(epvector * vp, ex const & oc)
 116 {
 117     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 118     tinfo_key = TINFO_MUL;
 119     ASSERT(vp!=0);
 120     overall_coeff=oc;
 121     construct_from_epvector(*vp);
 122     delete vp;
 123     ASSERT(is_canonical());
 124 }
 125
 126 mul::mul(ex const & lh, ex const & mh, ex const & rh)
 127 {
 128     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 129     tinfo_key = TINFO_MUL;
 130     exvector factors;
 131     factors.reserve(3);
 132     factors.push_back(lh);
 133     factors.push_back(mh);
 134     factors.push_back(rh);
 135     overall_coeff=exONE();
 136     construct_from_exvector(factors);
 137     ASSERT(is_canonical());
 138 }
 139
 140 //////////
 141 // functions overriding virtual functions from bases classes
 142 //////////
 143
 144 // public
 145
 146 basic * mul::duplicate() const
 147 {
 148     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 149     return new mul(*this);
 150 }
 151
 152 bool mul::info(unsigned inf) const
 153 {
 154     // TODO: optimize
 155     if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial || inf==info_flags::rational_function) {
 156         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 157             if (!(recombine_pair_to_ex(*it).info(inf)))
 158                 return false;
 159         }
 160         return true;
 161     } else {
 162         return expairseq::info(inf);
 163     }
 164 }
 165
 166 typedef vector<int> intvector;
 167
 168 int mul::degree(symbol const & s) const
 169 {
 170     int deg_sum=0;
 171     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 172         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 173     }
 174     return deg_sum;
 175 }
 176
 177 int mul::ldegree(symbol const & s) const
 178 {
 179     int deg_sum=0;
 180     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 181         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 182     }
 183     return deg_sum;
 184 }
 185
 186 ex mul::coeff(symbol const & s, int const n) const
 187 {
 188     exvector coeffseq;
 189     coeffseq.reserve(seq.size()+1);
 190
 191     if (n==0) {
 192         // product of individual coeffs
 193         // if a non-zero power of s is found, the resulting product will be 0
 194         epvector::const_iterator it=seq.begin();
 195         while (it!=seq.end()) {
 196             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 197             ++it;
 198         }
 199         coeffseq.push_back(overall_coeff);
 200         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 201     }
 202
 203     epvector::const_iterator it=seq.begin();
 204     bool coeff_found=0;
 205     while (it!=seq.end()) {
 206         ex t=recombine_pair_to_ex(*it);
 207         ex c=t.coeff(s,n);
 208         if (!c.is_zero()) {
 209             coeffseq.push_back(c);
 210             coeff_found=1;
 211         } else {
 212             coeffseq.push_back(t);
 213         }
 214         ++it;
 215     }
 216     if (coeff_found) {
 217         coeffseq.push_back(overall_coeff);
 218         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 219     }
 220
 221     return exZERO();
 222 }
 223
 224 /*
 225 ex mul::eval(int level) const
 226 {
 227     // simplifications: *(...,x,(c1,1),(c2,1)) -> *(...,x,(c1*c2,1)) (c1, c2 numeric(), move pairs to end first)
 228     //                  *(...,x,1) -> *(...,x)
 229     //                  *(...,x,0) -> 0
 230     //                  *(+(x,y,...),(c,1)) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 231     //                  *(x) -> x
 232     //                  *() -> 1
 233
 234     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 235
 236     if ((level==1)&&(flags & status_flags::evaluated)) {
 237 #ifdef DOASSERT
 238         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 239             ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 240                    (!(ex_to_numeric((*cit).coeff).is_integer())));
 241         }
 242
 243         // test if all numerics were moved to the end and
 244         // all numerics with coeff 1 to the very end
 245         if (seq.size()!=0) {
 246             epvector::const_iterator cit=seq.end();
 247             bool all_coeff_1=true;
 248             bool all_numeric=true;
 249             do {
 250                 cit--;
 251                 if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 252                     ASSERT(all_numeric);
 253                     if ((*cit).coeff.is_equal(exONE())) {
 254                         ASSERT(all_coeff_1);
 255                     } else {
 256                         all_coeff_1=false;
 257                     }
 258                 } else {
 259                     all_numeric=false;
 260                 }
 261             } while (cit!=seq.begin());
 262         }
 263 #endif // def DOASSERT
 264         return *this;
 265     }
 266
 267     epvector newseq;
 268     epvector::iterator it1,it2;
 269     bool seq_copied=false;
 270
 271     epvector * evaled_seqp=evalchildren(level);
 272     if (evaled_seqp!=0) {
 273         // do more evaluation later
 274         return (new mul(evaled_seqp))->setflag(status_flags::dynallocated);
 275     }
 276
 277     // combine pairs with coeff 1 (all numerics should be at end, assert below)
 278     if (seq.size()>1) {
 279         // count number of pairs with coeff 1
 280         unsigned num_coeff_1=0;
 281         bool still_numeric=true;
 282         epvector::const_iterator cit=seq.end();
 283         unsigned first_pos;
 284         unsigned second_pos;
 285         do {
 286             cit--;
 287             if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 288                 if ((*cit).coeff.is_equal(exONE())) {
 289                     num_coeff_1++;
 290                 }
 291             } else {
 292                 still_numeric=false;
 293             }
 294         } while ((cit!=seq.begin())&&still_numeric);
 295         if (num_coeff_1>1) {
 296             newseq=seq;
 297
 298     }
 299
 300
 301 #ifdef DOASSERT
 302     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 303         ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 304                (!(ex_to_numeric((*cit).coeff).is_integer())));
 305     }
 306
 307     // test if all numerics were moved to the end and
 308     // all numerics with coeff 1 to the very end
 309     if (seq.size()!=0) {
 310         epvector::const_iterator cit=seq.end();
 311         bool all_coeff_1=true;
 312         bool all_numeric=true;
 313         do {
 314             cit--;
 315             if (is_ex_exactly_of_type((*cit).rest,numeric)) {
 316                 ASSERT(all_numeric);
 317                 if ((*cit).coeff.is_equal(exONE())) {
 318                     ASSERT(all_coeff_1);
 319                 } else {
 320                     all_coeff_1=false;
 321                 }
 322             } else {
 323                 all_numeric=false;
 324             }
 325         } while (cit!=seq.begin());
 326     }
 327 #endif // def DOASSERT
 328
 329     if (flags & status_flags::evaluated) {
 330         return *this;
 331     }
 332
 333     expair const & last_expair=*(seq.end()-1);
 334     expair const & next_to_last_expair=*(seq.end()-2);
 335     int seq_size = seq.size();
 336
 337     // *(...,x,(c1,1),(c2,1)) -> *(...,x,(c1*c2,1)) (c1, c2 numeric())
 338     if ((!seq_copied) && (seq_size>=2) &&
 339         is_ex_exactly_of_type(last_expair.rest,numeric) &&
 340         ex_to_numeric(last_expair.coeff).is_equal(numONE()) &&
 341         is_ex_exactly_of_type(next_to_last_expair.rest,numeric) &&
 342         ex_to_numeric(next_to_last_expair.coeff).is_equal(numONE()) ) {
 343         newseq=seq;
 344         seq_copied=true;
 345         it2=newseq.end()-1;
 346         it1=it2-1;
 347     }
 348     while (seq_copied && (newseq.size()>=2) &&
 349            is_ex_exactly_of_type((*it1).rest,numeric) &&
 350            ex_to_numeric((*it1).coeff).is_equal(numONE()) &&
 351            is_ex_exactly_of_type((*it2).rest,numeric) &&
 352            ex_to_numeric((*it2).coeff).is_equal(numONE()) ) {
 353         *it1=expair(ex_to_numeric((*it1).rest).mul_dyn(ex_to_numeric((*it2).rest)),exONE());
 354         newseq.pop_back();
 355         it2=newseq.end()-1;
 356         it1=it2-1;
 357     }
 358
 359     // *(...,x,1) -> *(...,x)
 360     if ((!seq_copied) && (seq_size>=1) &&
 361         (is_ex_exactly_of_type(last_expair.rest,numeric)) &&
 362         (ex_to_numeric(last_expair.rest).compare(numONE())==0)) {
 363         newseq=seq;
 364         seq_copied=true;
 365         it2=newseq.end()-1;
 366     }
 367     if (seq_copied && (newseq.size()>=1) &&
 368         (is_ex_exactly_of_type((*it2).rest,numeric)) &&
 369         (ex_to_numeric((*it2).rest).compare(numONE())==0)) {
 370         newseq.pop_back();
 371         it2=newseq.end()-1;
 372     }
 373
 374     // *(...,x,0) -> 0
 375     if ((!seq_copied) && (seq_size>=1) &&
 376         (is_ex_exactly_of_type(last_expair.rest,numeric)) &&
 377         (ex_to_numeric(last_expair.rest).is_zero())) {
 378         return exZERO();
 379     }
 380     if (seq_copied && (newseq.size()>=1) &&
 381         (is_ex_exactly_of_type((*it2).rest,numeric)) &&
 382         (ex_to_numeric((*it2).rest).is_zero())) {
 383         return exZERO();
 384     }
 385
 386     // *(+(x,y,...),c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 387     if ((!seq_copied) && (seq_size==2) &&
 388         is_ex_exactly_of_type(next_to_last_expair.rest,add) &&
 389         is_ex_exactly_of_type(last_expair.rest,numeric) &&
 390         ex_to_numeric(last_expair.coeff).is_equal(numONE()) &&
 391         (ex_to_numeric(next_to_last_expair.coeff).compare(numONE())==0)) {
 392         add const & addref=ex_to_add(next_to_last_expair.rest);
 393         epvector distrseq;
 394         distrseq.reserve(addref.seq.size());
 395         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 396             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 397                                    last_expair.rest));
 398         }
 399         // special treatment for the last element if it is numeric (to
 400         // avoid terms like (2/3)*(3/2)) is no longer necessary, this
 401         // is handled in add::combine_pair_with_coeff_to_pair()
 402         return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
 403                                               status_flags::evaluated );
 404     }
 405     if (seq_copied && (newseq.size()==2) &&
 406         is_ex_exactly_of_type(newseq[0].rest,add) &&
 407         is_ex_exactly_of_type(newseq[1].rest,numeric) &&
 408         ex_to_numeric(newseq[1].coeff).is_equal(numONE()) &&
 409         (ex_to_numeric(newseq[0].coeff).compare(numONE())==0)) {
 410         add const & addref=ex_to_add(newseq[0].rest);
 411         epvector distrseq;
 412         distrseq.reserve(addref.seq.size());
 413         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 414             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 415                                    newseq[1].rest));
 416         }
 417         // special treatment for the last element if it is numeric (to
 418         // avoid terms like (2/3)*(3/2)) is no longer necessary, this
 419         // is handled in add::combine_pair_with_coeff_to_pair()
 420         return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
 421                                               status_flags::evaluated );
 422     }
 423
 424     // *() -> 1
 425     if ((!seq_copied) && (seq_size==0)) {
 426         return exONE();
 427     } else if (seq_copied && (newseq.size()==0)) {
 428         return exONE();
 429     }
 430
 431     // *(x) -> x
 432     if ((!seq_copied) && (seq_size==1)) {
 433         return recombine_pair_to_ex(*(seq.begin()));
 434     } else if (seq_copied && (newseq.size()==1)) {
 435         return recombine_pair_to_ex(*(newseq.begin()));
 436     }
 437
 438     if (!seq_copied) return this->hold();
 439
 440     return (new mul(newseq,1))->setflag(status_flags::dynallocated  |
 441                                         status_flags::evaluated );
 442 }
 443 */
 444
 445 ex mul::eval(int level) const
 446 {
 447     // simplifications  *(...,x;0) -> 0
 448     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 449     //                  *(x;1) -> x
 450     //                  *(;c) -> c
 451
 452     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 453
 454     epvector * evaled_seqp=evalchildren(level);
 455     if (evaled_seqp!=0) {
 456         // do more evaluation later
 457         return (new mul(evaled_seqp,overall_coeff))->
 458                    setflag(status_flags::dynallocated);
 459     }
 460
 461 #ifdef DOASSERT
 462     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 463         ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 464                (!(ex_to_numeric((*cit).coeff).is_integer())));
 465         ASSERT(!((*cit).is_numeric_with_coeff_1()));
 466         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 467             printtree(cerr,0);
 468         }
 469         ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 470         /* for paranoia */
 471         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 472         ASSERT(p.rest.is_equal((*cit).rest));
 473         ASSERT(p.coeff.is_equal((*cit).coeff));
 474         /* end paranoia */
 475     }
 476 #endif // def DOASSERT
 477
 478     if (flags & status_flags::evaluated) {
 479         ASSERT(seq.size()>0);
 480         ASSERT((seq.size()>1)||!overall_coeff.is_equal(exONE()));
 481         return *this;
 482     }
 483
 484     int seq_size=seq.size();
 485     if (overall_coeff.is_equal(exZERO())) {
 486         // *(...,x;0) -> 0
 487         return exZERO();
 488     } else if (seq_size==0) {
 489         // *(;c) -> c
 490         return overall_coeff;
 491     } else if ((seq_size==1)&&overall_coeff.is_equal(exONE())) {
 492         // *(x;1) -> x
 493         return recombine_pair_to_ex(*(seq.begin()));
 494     } else if ((seq_size==1) &&
 495                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 496                ex_to_numeric((*seq.begin()).coeff).is_equal(numONE())) {
 497         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 498         add const & addref=ex_to_add((*seq.begin()).rest);
 499         epvector distrseq;
 500         distrseq.reserve(addref.seq.size());
 501         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 502             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 503                                    overall_coeff));
 504         }
 505         return (new add(distrseq,
 506                         ex_to_numeric(addref.overall_coeff).
 507                         mul_dyn(ex_to_numeric(overall_coeff))))
 508             ->setflag(status_flags::dynallocated  |
 509                       status_flags::evaluated );
 510     }
 511     return this->hold();
 512 }
 513
 514 /*
 515 ex mul::eval(int level) const
 516 {
 517     // simplifications: *(...,x,c1,c2) -> *(...,x,c1*c2) (c1, c2 numeric())
 518     //                  *(...,(c1,c2)) -> (...,(c1^c2,1)) (normalize)
 519     //                  *(...,x,1) -> +(...,x)
 520     //                  *(...,x,0) -> 0
 521     //                  *(+(x,y,...),c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 522     //                  *(x) -> x
 523     //                  *() -> 1
 524
 525     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 526
 527     epvector newseq=seq;
 528     epvector::iterator it1,it2;
 529
 530     // *(...,x,c1,c2) -> *(...,x,c1*c2) (c1, c2 numeric())
 531     it2=newseq.end()-1;
 532     it1=it2-1;
 533     while ((newseq.size()>=2)&&is_exactly_of_type(*(*it1).rest.bp,numeric)&&
 534                                is_exactly_of_type(*(*it2).rest.bp,numeric)) {
 535         *it1=expair(ex_to_numeric((*it1).rest).power(ex_to_numeric((*it1).coeff))
 536                     .mul(ex_to_numeric((*it2).rest).power(ex_to_numeric((*it2).coeff))),exONE());
 537         newseq.pop_back();
 538         it2=newseq.end()-1;
 539         it1=it2-1;
 540     }
 541
 542     if ((newseq.size()>=1)&&is_exactly_of_type(*(*it2).rest.bp,numeric)) {
 543         // *(...,(c1,c2)) -> (...,(c1^c2,1)) (normalize)
 544         *it2=expair(ex_to_numeric((*it2).rest).power(ex_to_numeric((*it2).coeff)),exONE());
 545         // *(...,x,1) -> *(...,x)
 546         if (static_cast<numeric &>(*(*it2).rest.bp).compare(numONE())==0) {
 547             newseq.pop_back();
 548             it2=newseq.end()-1;
 549         }
 550     }
 551
 552     // *(...,x,0) -> 0
 553     if ((newseq.size()>=1)&&is_exactly_of_type(*(*it2).rest.bp,numeric)) {
 554         if (static_cast<numeric &>(*(*it2).rest.bp).is_zero()==0) {
 555             return exZERO();
 556         }
 557     }
 558
 559     // *(+(x,y,...),c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 560     if ((newseq.size()==2)&&is_ex_exactly_of_type(newseq[0].rest,add)&&
 561         is_ex_exactly_of_type(newseq[1].rest,numeric)&&
 562         (ex_to_numeric(newseq[0].coeff).compare(numONE())==0)) {
 563         add const & addref=ex_to_add(newseq[0].rest);
 564         numeric const & numref=ex_to_numeric(newseq[1].rest);
 565         epvector distrseq;
 566         distrseq.reserve(addref.seq.size());
 567         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 568             distrseq.push_back(expair((*cit).rest,ex_to_numeric((*cit).coeff).mul(numref)));
 569         }
 570         return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
 571                                               status_flags::evaluated );
 572     }
 573
 574     if (newseq.size()==0) {
 575         // *() -> 1
 576         return exONE();
 577     } else if (newseq.size()==1) {
 578         // *(x) -> x
 579         return recombine_pair_to_ex(*newseq.begin());
 580     }
 581
 582     return (new mul(newseq,1))->setflag(status_flags::dynallocated  |
 583                                         status_flags::evaluated );
 584 }
 585 */
 586
 587 exvector mul::get_indices(void) const
 588 {
 589     // return union of indices of factors
 590     exvector iv;
 591     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 592         exvector subiv=(*cit).rest.get_indices();
 593         iv.reserve(iv.size()+subiv.size());
 594         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 595             iv.push_back(*cit2);
 596         }
 597     }
 598     return iv;
 599 }
 600
 601 ex mul::simplify_ncmul(exvector const & v) const
 602 {
 603     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 604 }
 605
 606 // protected
 607
 608 int mul::compare_same_type(basic const & other) const
 609 {
 610     return expairseq::compare_same_type(other);
 611 }
 612
 613 bool mul::is_equal_same_type(basic const & other) const
 614 {
 615     return expairseq::is_equal_same_type(other);
 616 }
 617
 618 unsigned mul::return_type(void) const
 619 {
 620     if (seq.size()==0) {
 621         // mul without factors: should not happen, but commutes
 622         return return_types::commutative;
 623     }
 624
 625     bool all_commutative=1;
 626     unsigned rt;
 627     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 628
 629     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 630         rt=(*cit).rest.return_type();
 631         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 632         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 633             // first nc element found, remember position
 634             cit_noncommutative_element=cit;
 635             all_commutative=0;
 636         }
 637         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 638                 // another nc element found, compare type_infos
 639             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 640                 // diffent types -> mul is ncc
 641                 return return_types::noncommutative_composite;
 642             }
 643         }
 644     }
 645     // all factors checked
 646     return all_commutative ? return_types::commutative : return_types::noncommutative;
 647 }
 648
 649 unsigned mul::return_type_tinfo(void) const
 650 {
 651     if (seq.size()==0) {
 652         // mul without factors: should not happen
 653         return tinfo_key;
 654     }
 655     // return type_info of first noncommutative element
 656     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 657         if ((*cit).rest.return_type()==return_types::noncommutative) {
 658             return (*cit).rest.return_type_tinfo();
 659         }
 660     }
 661     // no noncommutative element found, should not happen
 662     return tinfo_key;
 663 }
 664
 665 ex mul::thisexpairseq(epvector const & v, ex const & oc) const
 666 {
 667     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 668 }
 669
 670 ex mul::thisexpairseq(epvector * vp, ex const & oc) const
 671 {
 672     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 673 }
 674
 675 expair mul::split_ex_to_pair(ex const & e) const
 676 {
 677     if (is_ex_exactly_of_type(e,power)) {
 678         power const & powerref=ex_to_power(e);
 679         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 680             return expair(powerref.basis,powerref.exponent);
 681         }
 682     }
 683     return expair(e,exONE());
 684 }
 685
 686 expair mul::combine_ex_with_coeff_to_pair(ex const & e,
 687                                           ex const & c) const
 688 {
 689     // to avoid duplication of power simplification rules,
 690     // we create a temporary power object
 691     // otherwise it would be hard to correctly simplify
 692     // expression like (4^(1/3))^(3/2)
 693     if (are_ex_trivially_equal(c,exONE())) {
 694         return split_ex_to_pair(e);
 695     }
 696     return split_ex_to_pair(power(e,c));
 697 }
 698
 699 expair mul::combine_pair_with_coeff_to_pair(expair const & p,
 700                                             ex const & c) const
 701 {
 702     // to avoid duplication of power simplification rules,
 703     // we create a temporary power object
 704     // otherwise it would be hard to correctly simplify
 705     // expression like (4^(1/3))^(3/2)
 706     if (are_ex_trivially_equal(c,exONE())) {
 707         return p;
 708     }
 709     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 710 }
 711
 712 ex mul::recombine_pair_to_ex(expair const & p) const
 713 {
 714     // if (p.coeff.compare(exONE())==0) {
 715     // if (are_ex_trivially_equal(p.coeff,exONE())) {
 716     if (ex_to_numeric(p.coeff).is_equal(numONE())) {
 717         return p.rest;
 718     } else {
 719         return power(p.rest,p.coeff);
 720     }
 721 }
 722
 723 bool mul::expair_needs_further_processing(epp it)
 724 {
 725     if (is_ex_exactly_of_type((*it).rest,mul) &&
 726         ex_to_numeric((*it).coeff).is_integer()) {
 727         // combined pair is product with integer power -> expand it
 728         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 729         return true;
 730     }
 731     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 732         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 733         if (!ep.is_equal(*it)) {
 734             // combined pair is a numeric power which can be simplified
 735             *it=ep;
 736             return true;
 737         }
 738         if (ex_to_numeric((*it).coeff).is_equal(numONE())) {
 739             // combined pair has coeff 1 and must be moved to the end
 740             return true;
 741         }
 742     }
 743     return false;
 744 }
 745
 746 ex mul::default_overall_coeff(void) const
 747 {
 748     return exONE();
 749 }
 750
 751 void mul::combine_overall_coeff(ex const & c)
 752 {
 753     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 754     ASSERT(is_ex_exactly_of_type(c,numeric));
 755     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 756 }
 757
 758 void mul::combine_overall_coeff(ex const & c1, ex const & c2)
 759 {
 760     ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 761     ASSERT(is_ex_exactly_of_type(c1,numeric));
 762     ASSERT(is_ex_exactly_of_type(c2,numeric));
 763     overall_coeff = ex_to_numeric(overall_coeff).
 764                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 765 }
 766
 767 bool mul::can_make_flat(expair const & p) const
 768 {
 769     ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 770     // this assertion will probably fail somewhere
 771     // it would require a more careful make_flat, obeying the power laws
 772     // probably should return true only if p.coeff is integer
 773     return ex_to_numeric(p.coeff).is_equal(numONE());
 774 }
 775
 776 ex mul::expand(unsigned options) const
 777 {
 778     exvector sub_expanded_seq;
 779     intvector positions_of_adds;
 780     intvector number_of_add_operands;
 781
 782     epvector * expanded_seqp=expandchildren(options);
 783
 784     epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 785
 786     positions_of_adds.resize(expanded_seq.size());
 787     number_of_add_operands.resize(expanded_seq.size());
 788
 789     int number_of_adds=0;
 790     int number_of_expanded_terms=1;
 791
 792     unsigned current_position=0;
 793     epvector::const_iterator last=expanded_seq.end();
 794     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 795         if (is_ex_exactly_of_type((*cit).rest,add)&&
 796             (ex_to_numeric((*cit).coeff).is_equal(numONE()))) {
 797             positions_of_adds[number_of_adds]=current_position;
 798             add const & expanded_addref=ex_to_add((*cit).rest);
 799             int addref_nops=expanded_addref.nops();
 800             number_of_add_operands[number_of_adds]=addref_nops;
 801             number_of_expanded_terms *= addref_nops;
 802             number_of_adds++;
 803         }
 804         current_position++;
 805     }
 806
 807     if (number_of_adds==0) {
 808         if (expanded_seqp==0) {
 809             return this->setflag(status_flags::expanded);
 810         }
 811         return (new mul(expanded_seqp,overall_coeff))->
 812                      setflag(status_flags::dynallocated ||
 813                              status_flags::expanded);
 814     }
 815
 816     exvector distrseq;
 817     distrseq.reserve(number_of_expanded_terms);
 818
 819     intvector k;
 820     k.resize(number_of_adds);
 821
 822     int l;
 823     for (l=0; l<number_of_adds; l++) {
 824         k[l]=0;
 825     }
 826
 827     while (1) {
 828         epvector term;
 829         term=expanded_seq;
 830         for (l=0; l<number_of_adds; l++) {
 831             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 832             ASSERT(term[positions_of_adds[l]].coeff.compare(exONE())==0);
 833             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 834         }
 835         /*
 836         cout << "mul::expand() term begin" << endl;
 837         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
 838             cout << "rest" << endl;
 839             (*cit).rest.printtree(cout);
 840             cout << "coeff" << endl;
 841             (*cit).coeff.printtree(cout);
 842         }
 843         cout << "mul::expand() term end" << endl;
 844         */
 845         distrseq.push_back((new mul(term,overall_coeff))->
 846                                 setflag(status_flags::dynallocated |
 847                                         status_flags::expanded));
 848
 849         // increment k[]
 850         l=number_of_adds-1;
 851         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 852             k[l]=0;
 853             l--;
 854         }
 855         if (l<0) break;
 856     }
 857
 858     if (expanded_seqp!=0) {
 859         delete expanded_seqp;
 860     }
 861     /*
 862     cout << "mul::expand() distrseq begin" << endl;
 863     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
 864         (*cit).printtree(cout);
 865     }
 866     cout << "mul::expand() distrseq end" << endl;
 867     */
 868
 869     return (new add(distrseq))->setflag(status_flags::dynallocated |
 870                                         status_flags::expanded);
 871 }
 872
 873 /*
 874 ex mul::expand(unsigned options) const
 875 {
 876     exvector sub_expanded_seq;
 877     intvector positions_of_adds;
 878     intvector number_of_add_operands;
 879
 880     sub_expanded_seq.resize(seq.size());
 881     positions_of_adds.resize(seq.size());
 882     number_of_add_operands.reserve(seq.size());
 883
 884     int number_of_adds=0;
 885     int number_of_expanded_terms=1;
 886     for (unsigned current_position=0; current_position<seq.size(); current_position++) {
 887         ex const & expanded_ex=recombine_pair_to_ex(seq[current_position]).expand(options);
 888         if (is_ex_exactly_of_type(expanded_ex,add)) {
 889             positions_of_adds[number_of_adds]=current_position;
 890             add const & expanded_addref=ex_to_add(expanded_ex);
 891             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 892             number_of_expanded_terms *= expanded_addref.seq.size();
 893             number_of_adds++;
 894         }
 895         sub_expanded_seq.push_back(expanded_ex);
 896     }
 897
 898     exvector distrseq;
 899     distrseq.reserve(number_of_expanded_terms);
 900
 901     intvector k;
 902     k.resize(number_of_adds);
 903
 904     int l;
 905     for (l=0; l<number_of_adds; l++) {
 906         k[l]=0;
 907     }
 908
 909     while (1) {
 910         exvector term;
 911         term=sub_expanded_seq;
 912         for (l=0; l<number_of_adds; l++) {
 913             add const & addref=ex_to_add(sub_expanded_seq[positions_of_adds[l]]);
 914             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 915         }
 916         distrseq.push_back((new mul(term))->setflag(status_flags::dynallocated |
 917                                                     status_flags::expanded));
 918
 919         // increment k[]
 920         l=number_of_adds-1;
 921         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 922             k[l]=0;
 923             l--;
 924         }
 925         if (l<0) break;
 926     }
 927
 928     return (new add(distrseq))->setflag(status_flags::dynallocated |
 929                                         status_flags::expanded);
 930 }
 931 */
 932
 933 //////////
 934 // new virtual functions which can be overridden by derived classes
 935 //////////
 936
 937 // none
 938
 939 //////////
 940 // non-virtual functions in this class
 941 //////////
 942
 943 epvector * mul::expandchildren(unsigned options) const
 944 {
 945     epvector::const_iterator last=seq.end();
 946     epvector::const_iterator cit=seq.begin();
 947     while (cit!=last) {
 948         ex const & factor=recombine_pair_to_ex(*cit);
 949         ex const & expanded_factor=factor.expand(options);
 950         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 951
 952             // something changed, copy seq, eval and return it
 953             epvector *s=new epvector;
 954             s->reserve(seq.size());
 955
 956             // copy parts of seq which are known not to have changed
 957             epvector::const_iterator cit2=seq.begin();
 958             while (cit2!=cit) {
 959                 s->push_back(*cit2);
 960                 ++cit2;
 961             }
 962             // copy first changed element
 963             s->push_back(split_ex_to_pair(expanded_factor));
 964             ++cit2;
 965             // copy rest
 966             while (cit2!=last) {
 967                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 968                 ++cit2;
 969             }
 970             return s;
 971         }
 972         ++cit;
 973     }
 974
 975     return 0; // nothing has changed
 976 }
 977
 978 //////////
 979 // static member variables
 980 //////////
 981
 982 // protected
 983
 984 unsigned mul::precedence=50;
 985
 986
 987 //////////
 988 // global constants
 989 //////////
 990
 991 const mul some_mul;
 992 type_info const & typeid_mul=typeid(some_mul);
 993
 994