ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative 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 <algorithm>
  24 #include <iostream>
  25 #include <stdexcept>
  26
  27 #include "ncmul.h"
  28 #include "ex.h"
  29 #include "add.h"
  30 #include "mul.h"
  31 #include "debugmsg.h"
  32
  33 #ifndef NO_GINAC_NAMESPACE
  34 namespace GiNaC {
  35 #endif // ndef NO_GINAC_NAMESPACE
  36
  37 //////////
  38 // default constructor, destructor, copy constructor assignment operator and helpers
  39 //////////
  40
  41 // public
  42
  43 ncmul::ncmul()
  44 {
  45     debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  46     tinfo_key = TINFO_ncmul;
  47 }
  48
  49 ncmul::~ncmul()
  50 {
  51     debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
  52     destroy(0);
  53 }
  54
  55 ncmul::ncmul(ncmul const & other)
  56 {
  57     debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
  58     copy(other);
  59 }
  60
  61 ncmul const & ncmul::operator=(ncmul const & other)
  62 {
  63     debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
  64     if (this != &other) {
  65         destroy(1);
  66         copy(other);
  67     }
  68     return *this;
  69 }
  70
  71 // protected
  72
  73 void ncmul::copy(ncmul const & other)
  74 {
  75     exprseq::copy(other);
  76 }
  77
  78 void ncmul::destroy(bool call_parent)
  79 {
  80     if (call_parent) exprseq::destroy(call_parent);
  81 }
  82
  83 //////////
  84 // other constructors
  85 //////////
  86
  87 // public
  88
  89 ncmul::ncmul(ex const & lh, ex const & rh) :
  90     exprseq(lh,rh)
  91 {
  92     debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  93     tinfo_key = TINFO_ncmul;
  94 }
  95
  96 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
  97     exprseq(f1,f2,f3)
  98 {
  99     debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
 100     tinfo_key = TINFO_ncmul;
 101 }
 102
 103 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 104       ex const & f4) : exprseq(f1,f2,f3,f4)
 105 {
 106     debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
 107     tinfo_key = TINFO_ncmul;
 108 }
 109
 110 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 111       ex const & f4, ex const & f5) : exprseq(f1,f2,f3,f4,f5)
 112 {
 113     debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 114     tinfo_key = TINFO_ncmul;
 115 }
 116
 117 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 118       ex const & f4, ex const & f5, ex const & f6) :
 119     exprseq(f1,f2,f3,f4,f5,f6)
 120 {
 121     debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 122     tinfo_key = TINFO_ncmul;
 123 }
 124
 125 ncmul::ncmul(exvector const & v, bool discardable) : exprseq(v,discardable)
 126 {
 127     debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 128     tinfo_key = TINFO_ncmul;
 129 }
 130
 131 ncmul::ncmul(exvector * vp) : exprseq(vp)
 132 {
 133     debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 134     tinfo_key = TINFO_ncmul;
 135 }
 136
 137 //////////
 138 // functions overriding virtual functions from bases classes
 139 //////////
 140
 141 // public
 142
 143 basic * ncmul::duplicate() const
 144 {
 145     debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 146     return new ncmul(*this);
 147 }
 148
 149 void ncmul::print(ostream & os, unsigned upper_precedence) const
 150 {
 151     debugmsg("ncmul print",LOGLEVEL_PRINT);
 152     printseq(os,'(','%',')',precedence,upper_precedence);
 153 }
 154
 155 void ncmul::printraw(ostream & os) const
 156 {
 157     debugmsg("ncmul printraw",LOGLEVEL_PRINT);
 158
 159     os << "%(";
 160     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 161         (*it).bp->printraw(os);
 162         os << ",";
 163     }
 164     os << ",hash=" << hashvalue << ",flags=" << flags;
 165     os << ")";
 166 }
 167
 168 void ncmul::printcsrc(ostream & os, unsigned upper_precedence) const
 169 {
 170     debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 171     exvector::const_iterator it;
 172     exvector::const_iterator itend = seq.end()-1;
 173     os << "ncmul(";
 174     for (it=seq.begin(); it!=itend; ++it) {
 175         (*it).bp->printcsrc(os,precedence);
 176         os << ",";
 177     }
 178     (*it).bp->printcsrc(os,precedence);
 179     os << ")";
 180 }
 181
 182 bool ncmul::info(unsigned inf) const
 183 {
 184     throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 185 }
 186
 187 typedef vector<int> intvector;
 188
 189 ex ncmul::expand(unsigned options) const
 190 {
 191     exvector sub_expanded_seq;
 192     intvector positions_of_adds;
 193     intvector number_of_add_operands;
 194
 195     exvector expanded_seq=expandchildren(options);
 196
 197     positions_of_adds.resize(expanded_seq.size());
 198     number_of_add_operands.resize(expanded_seq.size());
 199
 200     int number_of_adds=0;
 201     int number_of_expanded_terms=1;
 202
 203     unsigned current_position=0;
 204     exvector::const_iterator last=expanded_seq.end();
 205     for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 206         if (is_ex_exactly_of_type((*cit),add)) {
 207             positions_of_adds[number_of_adds]=current_position;
 208             add const & expanded_addref=ex_to_add(*cit);
 209             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 210             number_of_expanded_terms *= expanded_addref.seq.size();
 211             number_of_adds++;
 212         }
 213         current_position++;
 214     }
 215
 216     if (number_of_adds==0) {
 217         return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 218                                                     status_flags::expanded);
 219     }
 220
 221     exvector distrseq;
 222     distrseq.reserve(number_of_expanded_terms);
 223
 224     intvector k;
 225     k.resize(number_of_adds);
 226
 227     int l;
 228     for (l=0; l<number_of_adds; l++) {
 229         k[l]=0;
 230     }
 231
 232     while (1) {
 233         exvector term;
 234         term=expanded_seq;
 235         for (l=0; l<number_of_adds; l++) {
 236             GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 237             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 238             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 239         }
 240         distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 241                                                         status_flags::expanded));
 242
 243         // increment k[]
 244         l=number_of_adds-1;
 245         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 246             k[l]=0;
 247             l--;
 248         }
 249         if (l<0) break;
 250     }
 251
 252     return (new add(distrseq))->setflag(status_flags::dynallocated |
 253                                         status_flags::expanded);
 254 }
 255
 256 int ncmul::degree(symbol const & s) const
 257 {
 258     int deg_sum=0;
 259     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 260         deg_sum+=(*cit).degree(s);
 261     }
 262     return deg_sum;
 263 }
 264
 265 int ncmul::ldegree(symbol const & s) const
 266 {
 267     int deg_sum=0;
 268     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 269         deg_sum+=(*cit).ldegree(s);
 270     }
 271     return deg_sum;
 272 }
 273
 274 ex ncmul::coeff(symbol const & s, int const n) const
 275 {
 276     exvector coeffseq;
 277     coeffseq.reserve(seq.size());
 278
 279     if (n==0) {
 280         // product of individual coeffs
 281         // if a non-zero power of s is found, the resulting product will be 0
 282         exvector::const_iterator it=seq.begin();
 283         while (it!=seq.end()) {
 284             coeffseq.push_back((*it).coeff(s,n));
 285             ++it;
 286         }
 287         return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 288     }
 289
 290     exvector::const_iterator it=seq.begin();
 291     bool coeff_found=0;
 292     while (it!=seq.end()) {
 293         ex c=(*it).coeff(s,n);
 294         if (!c.is_zero()) {
 295             coeffseq.push_back(c);
 296             coeff_found=1;
 297         } else {
 298             coeffseq.push_back(*it);
 299         }
 300         ++it;
 301     }
 302
 303     if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 304
 305     return exZERO();
 306 }
 307
 308 unsigned ncmul::count_factors(ex const & e) const
 309 {
 310     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 311         (is_ex_exactly_of_type(e,ncmul))) {
 312         unsigned factors=0;
 313         for (int i=0; i<e.nops(); i++) {
 314             factors += count_factors(e.op(i));
 315         }
 316         return factors;
 317     }
 318     return 1;
 319 }
 320
 321 void ncmul::append_factors(exvector & v, ex const & e) const
 322 {
 323     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 324         (is_ex_exactly_of_type(e,ncmul))) {
 325         for (int i=0; i<e.nops(); i++) {
 326             append_factors(v,e.op(i));
 327         }
 328         return;
 329     }
 330     v.push_back(e);
 331 }
 332
 333 typedef vector<unsigned> unsignedvector;
 334 typedef vector<exvector> exvectorvector;
 335
 336 ex ncmul::eval(int level) const
 337 {
 338     // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 339     //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 340     //                  ncmul(x) -> x
 341     //                  ncmul() -> 1
 342     //                  ncmul(...,c1,...,c2,...) ->
 343     //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 344     //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 345     //                      (collect elements of same type)
 346     //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 347     // the following rule would be nice, but produces a recursion,
 348     // which must be trapped by introducing a flag that the sub-ncmuls()
 349     // are already evaluated (maybe later...)
 350     //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 351     //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 352     //                      (X noncommutative_composite)
 353
 354     if ((level==1)&&(flags & status_flags::evaluated)) {
 355         return *this;
 356     }
 357
 358     exvector evaledseq=evalchildren(level);
 359
 360     // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 361     //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 362     unsigned factors=0;
 363     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 364         factors += count_factors(*cit);
 365     }
 366
 367     exvector assocseq;
 368     assocseq.reserve(factors);
 369     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 370         append_factors(assocseq,*cit);
 371     }
 372
 373     // ncmul(x) -> x
 374     if (assocseq.size()==1) return *(seq.begin());
 375
 376     // ncmul() -> 1
 377     if (assocseq.size()==0) return exONE();
 378
 379     // determine return types
 380     unsignedvector rettypes;
 381     rettypes.reserve(assocseq.size());
 382     unsigned i=0;
 383     unsigned count_commutative=0;
 384     unsigned count_noncommutative=0;
 385     unsigned count_noncommutative_composite=0;
 386     for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 387         switch (rettypes[i]=(*cit).return_type()) {
 388         case return_types::commutative:
 389             count_commutative++;
 390             break;
 391         case return_types::noncommutative:
 392             count_noncommutative++;
 393             break;
 394         case return_types::noncommutative_composite:
 395             count_noncommutative_composite++;
 396             break;
 397         default:
 398             throw(std::logic_error("ncmul::eval(): invalid return type"));
 399         }
 400         ++i;
 401     }
 402     GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 403
 404     // ncmul(...,c1,...,c2,...) ->
 405     //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 406     if (count_commutative!=0) {
 407         exvector commutativeseq;
 408         commutativeseq.reserve(count_commutative+1);
 409         exvector noncommutativeseq;
 410         noncommutativeseq.reserve(assocseq.size()-count_commutative);
 411         for (i=0; i<assocseq.size(); ++i) {
 412             if (rettypes[i]==return_types::commutative) {
 413                 commutativeseq.push_back(assocseq[i]);
 414             } else {
 415                 noncommutativeseq.push_back(assocseq[i]);
 416             }
 417         }
 418         commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
 419                                   setflag(status_flags::dynallocated));
 420         return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 421     }
 422
 423     // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 424     //     (collect elements of same type)
 425
 426     if (count_noncommutative_composite==0) {
 427         // there are neither commutative nor noncommutative_composite
 428         // elements in assocseq
 429         GINAC_ASSERT(count_commutative==0);
 430
 431         exvectorvector evv;
 432         unsignedvector rttinfos;
 433         evv.reserve(assocseq.size());
 434         rttinfos.reserve(assocseq.size());
 435
 436         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 437             unsigned ti=(*cit).return_type_tinfo();
 438             // search type in vector of known types
 439             for (i=0; i<rttinfos.size(); ++i) {
 440                 if (ti==rttinfos[i]) {
 441                     evv[i].push_back(*cit);
 442                     break;
 443                 }
 444             }
 445             if (i>=rttinfos.size()) {
 446                 // new type
 447                 rttinfos.push_back(ti);
 448                 evv.push_back(exvector());
 449                 (*(evv.end()-1)).reserve(assocseq.size());
 450                 (*(evv.end()-1)).push_back(*cit);
 451             }
 452         }
 453
 454 #ifdef DO_GINAC_ASSERT
 455         GINAC_ASSERT(evv.size()==rttinfos.size());
 456         GINAC_ASSERT(evv.size()>0);
 457         unsigned s=0;
 458         for (i=0; i<evv.size(); ++i) {
 459             s += evv[i].size();
 460         }
 461         GINAC_ASSERT(s==assocseq.size());
 462 #endif // def DO_GINAC_ASSERT
 463
 464         // if all elements are of same type, simplify the string
 465         if (evv.size()==1) {
 466             return evv[0][0].simplify_ncmul(evv[0]);
 467         }
 468
 469         exvector splitseq;
 470         splitseq.reserve(evv.size());
 471         for (i=0; i<evv.size(); ++i) {
 472             splitseq.push_back((new ncmul(evv[i]))->
 473                                setflag(status_flags::dynallocated));
 474         }
 475
 476         return (new mul(splitseq))->setflag(status_flags::dynallocated);
 477     }
 478
 479     return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 480                                           status_flags::evaluated);
 481 }
 482
 483 exvector ncmul::get_indices(void) const
 484 {
 485     // return union of indices of factors
 486     exvector iv;
 487     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 488         exvector subiv=(*cit).get_indices();
 489         iv.reserve(iv.size()+subiv.size());
 490         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 491             iv.push_back(*cit2);
 492         }
 493     }
 494     return iv;
 495 }
 496
 497 ex ncmul::subs(lst const & ls, lst const & lr) const
 498 {
 499     return ncmul(subschildren(ls, lr));
 500 }
 501
 502 ex ncmul::thisexprseq(exvector const & v) const
 503 {
 504     return (new ncmul(v))->setflag(status_flags::dynallocated);
 505 }
 506
 507 ex ncmul::thisexprseq(exvector * vp) const
 508 {
 509     return (new ncmul(vp))->setflag(status_flags::dynallocated);
 510 }
 511
 512 // protected
 513
 514 int ncmul::compare_same_type(basic const & other) const
 515 {
 516     return exprseq::compare_same_type(other);
 517 }
 518
 519 unsigned ncmul::return_type(void) const
 520 {
 521     if (seq.size()==0) {
 522         // ncmul without factors: should not happen, but commutes
 523         return return_types::commutative;
 524     }
 525
 526     bool all_commutative=1;
 527     unsigned rt;
 528     exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 529
 530     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 531         rt=(*cit).return_type();
 532         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 533         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 534             // first nc element found, remember position
 535             cit_noncommutative_element=cit;
 536             all_commutative=0;
 537         }
 538         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 539             // another nc element found, compare type_infos
 540             if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 541                 // diffent types -> mul is ncc
 542                 return return_types::noncommutative_composite;
 543             }
 544         }
 545     }
 546     // all factors checked
 547     GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 548     return all_commutative ? return_types::commutative : return_types::noncommutative;
 549 }
 550
 551 unsigned ncmul::return_type_tinfo(void) const
 552 {
 553     if (seq.size()==0) {
 554         // mul without factors: should not happen
 555         return tinfo_key;
 556     }
 557     // return type_info of first noncommutative element
 558     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 559         if ((*cit).return_type()==return_types::noncommutative) {
 560             return (*cit).return_type_tinfo();
 561         }
 562     }
 563     // no noncommutative element found, should not happen
 564     return tinfo_key;
 565 }
 566
 567 //////////
 568 // new virtual functions which can be overridden by derived classes
 569 //////////
 570
 571 // none
 572
 573 //////////
 574 // non-virtual functions in this class
 575 //////////
 576
 577 exvector ncmul::expandchildren(unsigned options) const
 578 {
 579     exvector s;
 580     s.reserve(seq.size());
 581
 582     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 583         s.push_back((*it).expand(options));
 584     }
 585     return s;
 586 }
 587
 588 exvector const & ncmul::get_factors(void) const
 589 {
 590     return seq;
 591 }
 592
 593 //////////
 594 // static member variables
 595 //////////
 596
 597 // protected
 598
 599 unsigned ncmul::precedence=50;
 600
 601
 602 //////////
 603 // global constants
 604 //////////
 605
 606 const ncmul some_ncmul;
 607 type_info const & typeid_ncmul=typeid(some_ncmul);
 608
 609 //////////
 610 // friend functions
 611 //////////
 612
 613 ex nonsimplified_ncmul(exvector const & v)
 614 {
 615     return (new ncmul(v))->setflag(status_flags::dynallocated);
 616 }
 617
 618 ex simplified_ncmul(exvector const & v)
 619 {
 620     if (v.size()==0) {
 621         return exONE();
 622     } else if (v.size()==1) {
 623         return v[0];
 624     }
 625     return (new ncmul(v))->setflag(status_flags::dynallocated |
 626                                    status_flags::evaluated);
 627 }
 628
 629 #ifndef NO_GINAC_NAMESPACE
 630 } // namespace GiNaC
 631 #endif // ndef NO_GINAC_NAMESPACE