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 #include "debugmsg.h"
  30
  31 #ifndef NO_GINAC_NAMESPACE
  32 namespace GiNaC {
  33 #endif // ndef NO_GINAC_NAMESPACE
  34
  35 //////////
  36 // default constructor, destructor, copy constructor assignment operator and helpers
  37 //////////
  38
  39 // public
  40
  41 mul::mul()
  42 {
  43     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  44     tinfo_key = TINFO_mul;
  45 }
  46
  47 mul::~mul()
  48 {
  49     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  50     destroy(0);
  51 }
  52
  53 mul::mul(mul const & other)
  54 {
  55     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  56     copy(other);
  57 }
  58
  59 mul const & mul::operator=(mul const & other)
  60 {
  61     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  62     if (this != &other) {
  63         destroy(1);
  64         copy(other);
  65     }
  66     return *this;
  67 }
  68
  69 // protected
  70
  71 void mul::copy(mul const & other)
  72 {
  73     expairseq::copy(other);
  74 }
  75
  76 void mul::destroy(bool call_parent)
  77 {
  78     if (call_parent) expairseq::destroy(call_parent);
  79 }
  80
  81 //////////
  82 // other constructors
  83 //////////
  84
  85 // public
  86
  87 mul::mul(ex const & lh, ex const & rh)
  88 {
  89     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  90     tinfo_key = TINFO_mul;
  91     overall_coeff=exONE();
  92     construct_from_2_ex(lh,rh);
  93     GINAC_ASSERT(is_canonical());
  94 }
  95
  96 mul::mul(exvector const & v)
  97 {
  98     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
  99     tinfo_key = TINFO_mul;
 100     overall_coeff=exONE();
 101     construct_from_exvector(v);
 102     GINAC_ASSERT(is_canonical());
 103 }
 104
 105 /*
 106 mul::mul(epvector const & v, bool do_not_canonicalize)
 107 {
 108     debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
 109     tinfo_key = TINFO_mul;
 110     if (do_not_canonicalize) {
 111         seq=v;
 112 #ifdef EXPAIRSEQ_USE_HASHTAB
 113         combine_same_terms(); // to build hashtab
 114 #endif // def EXPAIRSEQ_USE_HASHTAB
 115     } else {
 116         construct_from_epvector(v);
 117     }
 118     GINAC_ASSERT(is_canonical());
 119 }
 120 */
 121
 122 mul::mul(epvector const & v)
 123 {
 124     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 125     tinfo_key = TINFO_mul;
 126     overall_coeff=exONE();
 127     construct_from_epvector(v);
 128     GINAC_ASSERT(is_canonical());
 129 }
 130
 131 mul::mul(epvector const & v, ex const & oc)
 132 {
 133     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 134     tinfo_key = TINFO_mul;
 135     overall_coeff=oc;
 136     construct_from_epvector(v);
 137     GINAC_ASSERT(is_canonical());
 138 }
 139
 140 mul::mul(epvector * vp, ex const & oc)
 141 {
 142     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 143     tinfo_key = TINFO_mul;
 144     GINAC_ASSERT(vp!=0);
 145     overall_coeff=oc;
 146     construct_from_epvector(*vp);
 147     delete vp;
 148     GINAC_ASSERT(is_canonical());
 149 }
 150
 151 mul::mul(ex const & lh, ex const & mh, ex const & rh)
 152 {
 153     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 154     tinfo_key = TINFO_mul;
 155     exvector factors;
 156     factors.reserve(3);
 157     factors.push_back(lh);
 158     factors.push_back(mh);
 159     factors.push_back(rh);
 160     overall_coeff=exONE();
 161     construct_from_exvector(factors);
 162     GINAC_ASSERT(is_canonical());
 163 }
 164
 165 //////////
 166 // functions overriding virtual functions from bases classes
 167 //////////
 168
 169 // public
 170
 171 basic * mul::duplicate() const
 172 {
 173     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 174     return new mul(*this);
 175 }
 176
 177 bool mul::info(unsigned inf) const
 178 {
 179     // TODO: optimize
 180     if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial || inf==info_flags::rational_function) {
 181         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 182             if (!(recombine_pair_to_ex(*it).info(inf)))
 183                 return false;
 184         }
 185         return true;
 186     } else {
 187         return expairseq::info(inf);
 188     }
 189 }
 190
 191 typedef vector<int> intvector;
 192
 193 int mul::degree(symbol const & s) const
 194 {
 195     int deg_sum=0;
 196     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 197         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 198     }
 199     return deg_sum;
 200 }
 201
 202 int mul::ldegree(symbol const & s) const
 203 {
 204     int deg_sum=0;
 205     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 206         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 207     }
 208     return deg_sum;
 209 }
 210
 211 ex mul::coeff(symbol const & s, int const n) const
 212 {
 213     exvector coeffseq;
 214     coeffseq.reserve(seq.size()+1);
 215
 216     if (n==0) {
 217         // product of individual coeffs
 218         // if a non-zero power of s is found, the resulting product will be 0
 219         epvector::const_iterator it=seq.begin();
 220         while (it!=seq.end()) {
 221             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 222             ++it;
 223         }
 224         coeffseq.push_back(overall_coeff);
 225         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 226     }
 227
 228     epvector::const_iterator it=seq.begin();
 229     bool coeff_found=0;
 230     while (it!=seq.end()) {
 231         ex t=recombine_pair_to_ex(*it);
 232         ex c=t.coeff(s,n);
 233         if (!c.is_zero()) {
 234             coeffseq.push_back(c);
 235             coeff_found=1;
 236         } else {
 237             coeffseq.push_back(t);
 238         }
 239         ++it;
 240     }
 241     if (coeff_found) {
 242         coeffseq.push_back(overall_coeff);
 243         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 244     }
 245
 246     return exZERO();
 247 }
 248
 249 ex mul::eval(int level) const
 250 {
 251     // simplifications  *(...,x;0) -> 0
 252     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 253     //                  *(x;1) -> x
 254     //                  *(;c) -> c
 255
 256     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 257
 258     epvector * evaled_seqp=evalchildren(level);
 259     if (evaled_seqp!=0) {
 260         // do more evaluation later
 261         return (new mul(evaled_seqp,overall_coeff))->
 262                    setflag(status_flags::dynallocated);
 263     }
 264
 265 #ifdef DO_GINAC_ASSERT
 266     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 267         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 268                (!(ex_to_numeric((*cit).coeff).is_integer())));
 269         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 270         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 271             printtree(cerr,0);
 272         }
 273         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 274         /* for paranoia */
 275         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 276         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 277         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 278         /* end paranoia */
 279     }
 280 #endif // def DO_GINAC_ASSERT
 281
 282     if (flags & status_flags::evaluated) {
 283         GINAC_ASSERT(seq.size()>0);
 284         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(exONE()));
 285         return *this;
 286     }
 287
 288     int seq_size=seq.size();
 289     if (overall_coeff.is_equal(exZERO())) {
 290         // *(...,x;0) -> 0
 291         return exZERO();
 292     } else if (seq_size==0) {
 293         // *(;c) -> c
 294         return overall_coeff;
 295     } else if ((seq_size==1)&&overall_coeff.is_equal(exONE())) {
 296         // *(x;1) -> x
 297         return recombine_pair_to_ex(*(seq.begin()));
 298     } else if ((seq_size==1) &&
 299                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 300                ex_to_numeric((*seq.begin()).coeff).is_equal(numONE())) {
 301         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 302         add const & addref=ex_to_add((*seq.begin()).rest);
 303         epvector distrseq;
 304         distrseq.reserve(addref.seq.size());
 305         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 306             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 307                                    overall_coeff));
 308         }
 309         return (new add(distrseq,
 310                         ex_to_numeric(addref.overall_coeff).
 311                         mul_dyn(ex_to_numeric(overall_coeff))))
 312             ->setflag(status_flags::dynallocated  |
 313                       status_flags::evaluated );
 314     }
 315     return this->hold();
 316 }
 317
 318 exvector mul::get_indices(void) const
 319 {
 320     // return union of indices of factors
 321     exvector iv;
 322     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 323         exvector subiv=(*cit).rest.get_indices();
 324         iv.reserve(iv.size()+subiv.size());
 325         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 326             iv.push_back(*cit2);
 327         }
 328     }
 329     return iv;
 330 }
 331
 332 ex mul::simplify_ncmul(exvector const & v) const
 333 {
 334     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 335 }
 336
 337 // protected
 338
 339 int mul::compare_same_type(basic const & other) const
 340 {
 341     return expairseq::compare_same_type(other);
 342 }
 343
 344 bool mul::is_equal_same_type(basic const & other) const
 345 {
 346     return expairseq::is_equal_same_type(other);
 347 }
 348
 349 unsigned mul::return_type(void) const
 350 {
 351     if (seq.size()==0) {
 352         // mul without factors: should not happen, but commutes
 353         return return_types::commutative;
 354     }
 355
 356     bool all_commutative=1;
 357     unsigned rt;
 358     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 359
 360     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 361         rt=(*cit).rest.return_type();
 362         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 363         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 364             // first nc element found, remember position
 365             cit_noncommutative_element=cit;
 366             all_commutative=0;
 367         }
 368         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 369                 // another nc element found, compare type_infos
 370             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 371                 // diffent types -> mul is ncc
 372                 return return_types::noncommutative_composite;
 373             }
 374         }
 375     }
 376     // all factors checked
 377     return all_commutative ? return_types::commutative : return_types::noncommutative;
 378 }
 379
 380 unsigned mul::return_type_tinfo(void) const
 381 {
 382     if (seq.size()==0) {
 383         // mul without factors: should not happen
 384         return tinfo_key;
 385     }
 386     // return type_info of first noncommutative element
 387     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 388         if ((*cit).rest.return_type()==return_types::noncommutative) {
 389             return (*cit).rest.return_type_tinfo();
 390         }
 391     }
 392     // no noncommutative element found, should not happen
 393     return tinfo_key;
 394 }
 395
 396 ex mul::thisexpairseq(epvector const & v, ex const & oc) const
 397 {
 398     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 399 }
 400
 401 ex mul::thisexpairseq(epvector * vp, ex const & oc) const
 402 {
 403     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 404 }
 405
 406 expair mul::split_ex_to_pair(ex const & e) const
 407 {
 408     if (is_ex_exactly_of_type(e,power)) {
 409         power const & powerref=ex_to_power(e);
 410         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 411             return expair(powerref.basis,powerref.exponent);
 412         }
 413     }
 414     return expair(e,exONE());
 415 }
 416
 417 expair mul::combine_ex_with_coeff_to_pair(ex const & e,
 418                                           ex const & c) const
 419 {
 420     // to avoid duplication of power simplification rules,
 421     // we create a temporary power object
 422     // otherwise it would be hard to correctly simplify
 423     // expression like (4^(1/3))^(3/2)
 424     if (are_ex_trivially_equal(c,exONE())) {
 425         return split_ex_to_pair(e);
 426     }
 427     return split_ex_to_pair(power(e,c));
 428 }
 429
 430 expair mul::combine_pair_with_coeff_to_pair(expair const & p,
 431                                             ex const & c) const
 432 {
 433     // to avoid duplication of power simplification rules,
 434     // we create a temporary power object
 435     // otherwise it would be hard to correctly simplify
 436     // expression like (4^(1/3))^(3/2)
 437     if (are_ex_trivially_equal(c,exONE())) {
 438         return p;
 439     }
 440     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 441 }
 442
 443 ex mul::recombine_pair_to_ex(expair const & p) const
 444 {
 445     // if (p.coeff.compare(exONE())==0) {
 446     // if (are_ex_trivially_equal(p.coeff,exONE())) {
 447     if (ex_to_numeric(p.coeff).is_equal(numONE())) {
 448         return p.rest;
 449     } else {
 450         return power(p.rest,p.coeff);
 451     }
 452 }
 453
 454 bool mul::expair_needs_further_processing(epp it)
 455 {
 456     if (is_ex_exactly_of_type((*it).rest,mul) &&
 457         ex_to_numeric((*it).coeff).is_integer()) {
 458         // combined pair is product with integer power -> expand it
 459         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 460         return true;
 461     }
 462     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 463         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 464         if (!ep.is_equal(*it)) {
 465             // combined pair is a numeric power which can be simplified
 466             *it=ep;
 467             return true;
 468         }
 469         if (ex_to_numeric((*it).coeff).is_equal(numONE())) {
 470             // combined pair has coeff 1 and must be moved to the end
 471             return true;
 472         }
 473     }
 474     return false;
 475 }
 476
 477 ex mul::default_overall_coeff(void) const
 478 {
 479     return exONE();
 480 }
 481
 482 void mul::combine_overall_coeff(ex const & c)
 483 {
 484     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 485     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 486     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 487 }
 488
 489 void mul::combine_overall_coeff(ex const & c1, ex const & c2)
 490 {
 491     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 492     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 493     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 494     overall_coeff = ex_to_numeric(overall_coeff).
 495                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 496 }
 497
 498 bool mul::can_make_flat(expair const & p) const
 499 {
 500     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 501     // this assertion will probably fail somewhere
 502     // it would require a more careful make_flat, obeying the power laws
 503     // probably should return true only if p.coeff is integer
 504     return ex_to_numeric(p.coeff).is_equal(numONE());
 505 }
 506
 507 ex mul::expand(unsigned options) const
 508 {
 509     exvector sub_expanded_seq;
 510     intvector positions_of_adds;
 511     intvector number_of_add_operands;
 512
 513     epvector * expanded_seqp=expandchildren(options);
 514
 515     epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 516
 517     positions_of_adds.resize(expanded_seq.size());
 518     number_of_add_operands.resize(expanded_seq.size());
 519
 520     int number_of_adds=0;
 521     int number_of_expanded_terms=1;
 522
 523     unsigned current_position=0;
 524     epvector::const_iterator last=expanded_seq.end();
 525     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 526         if (is_ex_exactly_of_type((*cit).rest,add)&&
 527             (ex_to_numeric((*cit).coeff).is_equal(numONE()))) {
 528             positions_of_adds[number_of_adds]=current_position;
 529             add const & expanded_addref=ex_to_add((*cit).rest);
 530             int addref_nops=expanded_addref.nops();
 531             number_of_add_operands[number_of_adds]=addref_nops;
 532             number_of_expanded_terms *= addref_nops;
 533             number_of_adds++;
 534         }
 535         current_position++;
 536     }
 537
 538     if (number_of_adds==0) {
 539         if (expanded_seqp==0) {
 540             return this->setflag(status_flags::expanded);
 541         }
 542         return (new mul(expanded_seqp,overall_coeff))->
 543                      setflag(status_flags::dynallocated ||
 544                              status_flags::expanded);
 545     }
 546
 547     exvector distrseq;
 548     distrseq.reserve(number_of_expanded_terms);
 549
 550     intvector k;
 551     k.resize(number_of_adds);
 552
 553     int l;
 554     for (l=0; l<number_of_adds; l++) {
 555         k[l]=0;
 556     }
 557
 558     while (1) {
 559         epvector term;
 560         term=expanded_seq;
 561         for (l=0; l<number_of_adds; l++) {
 562             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 563             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(exONE())==0);
 564             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 565         }
 566         /*
 567         cout << "mul::expand() term begin" << endl;
 568         for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
 569             cout << "rest" << endl;
 570             (*cit).rest.printtree(cout);
 571             cout << "coeff" << endl;
 572             (*cit).coeff.printtree(cout);
 573         }
 574         cout << "mul::expand() term end" << endl;
 575         */
 576         distrseq.push_back((new mul(term,overall_coeff))->
 577                                 setflag(status_flags::dynallocated |
 578                                         status_flags::expanded));
 579
 580         // increment k[]
 581         l=number_of_adds-1;
 582         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 583             k[l]=0;
 584             l--;
 585         }
 586         if (l<0) break;
 587     }
 588
 589     if (expanded_seqp!=0) {
 590         delete expanded_seqp;
 591     }
 592     /*
 593     cout << "mul::expand() distrseq begin" << endl;
 594     for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
 595         (*cit).printtree(cout);
 596     }
 597     cout << "mul::expand() distrseq end" << endl;
 598     */
 599
 600     return (new add(distrseq))->setflag(status_flags::dynallocated |
 601                                         status_flags::expanded);
 602 }
 603
 604 //////////
 605 // new virtual functions which can be overridden by derived classes
 606 //////////
 607
 608 // none
 609
 610 //////////
 611 // non-virtual functions in this class
 612 //////////
 613
 614 epvector * mul::expandchildren(unsigned options) const
 615 {
 616     epvector::const_iterator last=seq.end();
 617     epvector::const_iterator cit=seq.begin();
 618     while (cit!=last) {
 619         ex const & factor=recombine_pair_to_ex(*cit);
 620         ex const & expanded_factor=factor.expand(options);
 621         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 622
 623             // something changed, copy seq, eval and return it
 624             epvector *s=new epvector;
 625             s->reserve(seq.size());
 626
 627             // copy parts of seq which are known not to have changed
 628             epvector::const_iterator cit2=seq.begin();
 629             while (cit2!=cit) {
 630                 s->push_back(*cit2);
 631                 ++cit2;
 632             }
 633             // copy first changed element
 634             s->push_back(split_ex_to_pair(expanded_factor));
 635             ++cit2;
 636             // copy rest
 637             while (cit2!=last) {
 638                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 639                 ++cit2;
 640             }
 641             return s;
 642         }
 643         ++cit;
 644     }
 645
 646     return 0; // nothing has changed
 647 }
 648
 649 //////////
 650 // static member variables
 651 //////////
 652
 653 // protected
 654
 655 unsigned mul::precedence=50;
 656
 657
 658 //////////
 659 // global constants
 660 //////////
 661
 662 const mul some_mul;
 663 type_info const & typeid_mul=typeid(some_mul);
 664
 665 #ifndef NO_GINAC_NAMESPACE
 666 } // namespace GiNaC
 667 #endif // ndef NO_GINAC_NAMESPACE