ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions.
   4  *
   5  *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
   6  *
   7  *  This program is free software; you can redistribute it and/or modify
   8  *  it under the terms of the GNU General Public License as published by
   9  *  the Free Software Foundation; either version 2 of the License, or
  10  *  (at your option) any later version.
  11  *
  12  *  This program is distributed in the hope that it will be useful,
  13  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  *  GNU General Public License for more details.
  16  *
  17  *  You should have received a copy of the GNU General Public License
  18  *  along with this program; if not, write to the Free Software
  19  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  20  */
  21
  22 #include <algorithm>
  23 #include <iostream>
  24 #include <stdexcept>
  25
  26 #include "ginac.h"
  27
  28 //////////
  29 // default constructor, destructor, copy constructor assignment operator and helpers
  30 //////////
  31
  32 // public
  33
  34 ncmul::ncmul()
  35 {
  36     debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  37     tinfo_key = TINFO_NCMUL;
  38 }
  39
  40 ncmul::~ncmul()
  41 {
  42     debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
  43     destroy(0);
  44 }
  45
  46 ncmul::ncmul(ncmul const & other)
  47 {
  48     debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
  49     copy(other);
  50 }
  51
  52 ncmul const & ncmul::operator=(ncmul const & other)
  53 {
  54     debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
  55     if (this != &other) {
  56         destroy(1);
  57         copy(other);
  58     }
  59     return *this;
  60 }
  61
  62 // protected
  63
  64 void ncmul::copy(ncmul const & other)
  65 {
  66     exprseq::copy(other);
  67 }
  68
  69 void ncmul::destroy(bool call_parent)
  70 {
  71     if (call_parent) exprseq::destroy(call_parent);
  72 }
  73
  74 //////////
  75 // other constructors
  76 //////////
  77
  78 // public
  79
  80 ncmul::ncmul(ex const & lh, ex const & rh) :
  81     exprseq(lh,rh)
  82 {
  83     debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  84     tinfo_key = TINFO_NCMUL;
  85 }
  86
  87 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
  88     exprseq(f1,f2,f3)
  89 {
  90     debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
  91     tinfo_key = TINFO_NCMUL;
  92 }
  93
  94 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
  95       ex const & f4) : exprseq(f1,f2,f3,f4)
  96 {
  97     debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
  98     tinfo_key = TINFO_NCMUL;
  99 }
 100
 101 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 102       ex const & f4, ex const & f5) : exprseq(f1,f2,f3,f4,f5)
 103 {
 104     debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 105     tinfo_key = TINFO_NCMUL;
 106 }
 107
 108 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 109       ex const & f4, ex const & f5, ex const & f6) :
 110     exprseq(f1,f2,f3,f4,f5,f6)
 111 {
 112     debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 113     tinfo_key = TINFO_NCMUL;
 114 }
 115
 116 ncmul::ncmul(exvector const & v, bool discardable) : exprseq(v,discardable)
 117 {
 118     debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 119     tinfo_key = TINFO_NCMUL;
 120 }
 121
 122 ncmul::ncmul(exvector * vp) : exprseq(vp)
 123 {
 124     debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 125     tinfo_key = TINFO_NCMUL;
 126 }
 127
 128 //////////
 129 // functions overriding virtual functions from bases classes
 130 //////////
 131
 132 // public
 133
 134 basic * ncmul::duplicate() const
 135 {
 136     debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 137     return new ncmul(*this);
 138 }
 139
 140 bool ncmul::info(unsigned inf) const
 141 {
 142     throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 143 }
 144
 145 typedef vector<int> intvector;
 146
 147 ex ncmul::expand(unsigned options) const
 148 {
 149     exvector sub_expanded_seq;
 150     intvector positions_of_adds;
 151     intvector number_of_add_operands;
 152
 153     exvector expanded_seq=expandchildren(options);
 154
 155     positions_of_adds.resize(expanded_seq.size());
 156     number_of_add_operands.resize(expanded_seq.size());
 157
 158     int number_of_adds=0;
 159     int number_of_expanded_terms=1;
 160
 161     unsigned current_position=0;
 162     exvector::const_iterator last=expanded_seq.end();
 163     for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 164         if (is_ex_exactly_of_type((*cit),add)) {
 165             positions_of_adds[number_of_adds]=current_position;
 166             add const & expanded_addref=ex_to_add(*cit);
 167             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 168             number_of_expanded_terms *= expanded_addref.seq.size();
 169             number_of_adds++;
 170         }
 171         current_position++;
 172     }
 173
 174     if (number_of_adds==0) {
 175         return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 176                                                     status_flags::expanded);
 177     }
 178
 179     exvector distrseq;
 180     distrseq.reserve(number_of_expanded_terms);
 181
 182     intvector k;
 183     k.resize(number_of_adds);
 184
 185     int l;
 186     for (l=0; l<number_of_adds; l++) {
 187         k[l]=0;
 188     }
 189
 190     while (1) {
 191         exvector term;
 192         term=expanded_seq;
 193         for (l=0; l<number_of_adds; l++) {
 194             ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 195             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 196             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 197         }
 198         distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 199                                                         status_flags::expanded));
 200
 201         // increment k[]
 202         l=number_of_adds-1;
 203         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 204             k[l]=0;
 205             l--;
 206         }
 207         if (l<0) break;
 208     }
 209
 210     return (new add(distrseq))->setflag(status_flags::dynallocated |
 211                                         status_flags::expanded);
 212 }
 213
 214 int ncmul::degree(symbol const & s) const
 215 {
 216     int deg_sum=0;
 217     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 218         deg_sum+=(*cit).degree(s);
 219     }
 220     return deg_sum;
 221 }
 222
 223 int ncmul::ldegree(symbol const & s) const
 224 {
 225     int deg_sum=0;
 226     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 227         deg_sum+=(*cit).ldegree(s);
 228     }
 229     return deg_sum;
 230 }
 231
 232 ex ncmul::coeff(symbol const & s, int const n) const
 233 {
 234     exvector coeffseq;
 235     coeffseq.reserve(seq.size());
 236
 237     if (n==0) {
 238         // product of individual coeffs
 239         // if a non-zero power of s is found, the resulting product will be 0
 240         exvector::const_iterator it=seq.begin();
 241         while (it!=seq.end()) {
 242             coeffseq.push_back((*it).coeff(s,n));
 243             ++it;
 244         }
 245         return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 246     }
 247
 248     exvector::const_iterator it=seq.begin();
 249     bool coeff_found=0;
 250     while (it!=seq.end()) {
 251         ex c=(*it).coeff(s,n);
 252         if (!c.is_zero()) {
 253             coeffseq.push_back(c);
 254             coeff_found=1;
 255         } else {
 256             coeffseq.push_back(*it);
 257         }
 258         ++it;
 259     }
 260
 261     if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 262
 263     return exZERO();
 264 }
 265
 266 unsigned ncmul::count_factors(ex const & e) const
 267 {
 268     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 269         (is_ex_exactly_of_type(e,ncmul))) {
 270         unsigned factors=0;
 271         for (int i=0; i<e.nops(); i++) {
 272             factors += count_factors(e.op(i));
 273         }
 274         return factors;
 275     }
 276     return 1;
 277 }
 278
 279 void ncmul::append_factors(exvector & v, ex const & e) const
 280 {
 281     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 282         (is_ex_exactly_of_type(e,ncmul))) {
 283         for (int i=0; i<e.nops(); i++) {
 284             append_factors(v,e.op(i));
 285         }
 286         return;
 287     }
 288     v.push_back(e);
 289 }
 290
 291 typedef vector<unsigned> unsignedvector;
 292 typedef vector<exvector> exvectorvector;
 293
 294 ex ncmul::eval(int level) const
 295 {
 296     // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 297     //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 298     //                  ncmul(x) -> x
 299     //                  ncmul() -> 1
 300     //                  ncmul(...,c1,...,c2,...) ->
 301     //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 302     //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 303     //                      (collect elements of same type)
 304     //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 305     // the following rule would be nice, but produces a recursion,
 306     // which must be trapped by introducing a flag that the sub-ncmuls()
 307     // are already evaluated (maybe later...)
 308     //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 309     //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 310     //                      (X noncommutative_composite)
 311
 312     if ((level==1)&&(flags & status_flags::evaluated)) {
 313         return *this;
 314     }
 315
 316     exvector evaledseq=evalchildren(level);
 317
 318     // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 319     //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 320     unsigned factors=0;
 321     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 322         factors += count_factors(*cit);
 323     }
 324
 325     exvector assocseq;
 326     assocseq.reserve(factors);
 327     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 328         append_factors(assocseq,*cit);
 329     }
 330
 331     // ncmul(x) -> x
 332     if (assocseq.size()==1) return *(seq.begin());
 333
 334     // ncmul() -> 1
 335     if (assocseq.size()==0) return exONE();
 336
 337     // determine return types
 338     unsignedvector rettypes;
 339     rettypes.reserve(assocseq.size());
 340     unsigned i=0;
 341     unsigned count_commutative=0;
 342     unsigned count_noncommutative=0;
 343     unsigned count_noncommutative_composite=0;
 344     for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 345         switch (rettypes[i]=(*cit).return_type()) {
 346         case return_types::commutative:
 347             count_commutative++;
 348             break;
 349         case return_types::noncommutative:
 350             count_noncommutative++;
 351             break;
 352         case return_types::noncommutative_composite:
 353             count_noncommutative_composite++;
 354             break;
 355         default:
 356             throw(std::logic_error("ncmul::eval(): invalid return type"));
 357         }
 358         ++i;
 359     }
 360     ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 361
 362     // ncmul(...,c1,...,c2,...) ->
 363     //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 364     if (count_commutative!=0) {
 365         exvector commutativeseq;
 366         commutativeseq.reserve(count_commutative+1);
 367         exvector noncommutativeseq;
 368         noncommutativeseq.reserve(assocseq.size()-count_commutative);
 369         for (i=0; i<assocseq.size(); ++i) {
 370             if (rettypes[i]==return_types::commutative) {
 371                 commutativeseq.push_back(assocseq[i]);
 372             } else {
 373                 noncommutativeseq.push_back(assocseq[i]);
 374             }
 375         }
 376         commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
 377                                   setflag(status_flags::dynallocated));
 378         return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 379     }
 380
 381     // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 382     //     (collect elements of same type)
 383
 384     if (count_noncommutative_composite==0) {
 385         // there are neither commutative nor noncommutative_composite
 386         // elements in assocseq
 387         ASSERT(count_commutative==0);
 388
 389         exvectorvector evv;
 390         unsignedvector rttinfos;
 391         evv.reserve(assocseq.size());
 392         rttinfos.reserve(assocseq.size());
 393
 394         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 395             unsigned ti=(*cit).return_type_tinfo();
 396             // search type in vector of known types
 397             for (i=0; i<rttinfos.size(); ++i) {
 398                 if (ti==rttinfos[i]) {
 399                     evv[i].push_back(*cit);
 400                     break;
 401                 }
 402             }
 403             if (i>=rttinfos.size()) {
 404                 // new type
 405                 rttinfos.push_back(ti);
 406                 evv.push_back(exvector());
 407                 (*(evv.end()-1)).reserve(assocseq.size());
 408                 (*(evv.end()-1)).push_back(*cit);
 409             }
 410         }
 411
 412 #ifdef DOASSERT
 413         ASSERT(evv.size()==rttinfos.size());
 414         ASSERT(evv.size()>0);
 415         unsigned s=0;
 416         for (i=0; i<evv.size(); ++i) {
 417             s += evv[i].size();
 418         }
 419         ASSERT(s==assocseq.size());
 420 #endif // def DOASSERT
 421
 422         // if all elements are of same type, simplify the string
 423         if (evv.size()==1) {
 424             return evv[0][0].simplify_ncmul(evv[0]);
 425         }
 426
 427         exvector splitseq;
 428         splitseq.reserve(evv.size());
 429         for (i=0; i<evv.size(); ++i) {
 430             splitseq.push_back((new ncmul(evv[i]))->
 431                                setflag(status_flags::dynallocated));
 432         }
 433
 434         return (new mul(splitseq))->setflag(status_flags::dynallocated);
 435     }
 436
 437     return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 438                                           status_flags::evaluated);
 439 }
 440
 441 exvector ncmul::get_indices(void) const
 442 {
 443     // return union of indices of factors
 444     exvector iv;
 445     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 446         exvector subiv=(*cit).get_indices();
 447         iv.reserve(iv.size()+subiv.size());
 448         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 449             iv.push_back(*cit2);
 450         }
 451     }
 452     return iv;
 453 }
 454
 455 ex ncmul::subs(lst const & ls, lst const & lr) const
 456 {
 457     return ncmul(subschildren(ls, lr));
 458 }
 459
 460 ex ncmul::thisexprseq(exvector const & v) const
 461 {
 462     return (new ncmul(v))->setflag(status_flags::dynallocated);
 463 }
 464
 465 ex ncmul::thisexprseq(exvector * vp) const
 466 {
 467     return (new ncmul(vp))->setflag(status_flags::dynallocated);
 468 }
 469
 470 // protected
 471
 472 int ncmul::compare_same_type(basic const & other) const
 473 {
 474     return exprseq::compare_same_type(other);
 475 }
 476
 477 unsigned ncmul::return_type(void) const
 478 {
 479     if (seq.size()==0) {
 480         // ncmul without factors: should not happen, but commutes
 481         return return_types::commutative;
 482     }
 483
 484     bool all_commutative=1;
 485     unsigned rt;
 486     exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 487
 488     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 489         rt=(*cit).return_type();
 490         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 491         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 492             // first nc element found, remember position
 493             cit_noncommutative_element=cit;
 494             all_commutative=0;
 495         }
 496         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 497             // another nc element found, compare type_infos
 498             if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 499                 // diffent types -> mul is ncc
 500                 return return_types::noncommutative_composite;
 501             }
 502         }
 503     }
 504     // all factors checked
 505     ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 506     return all_commutative ? return_types::commutative : return_types::noncommutative;
 507 }
 508
 509 unsigned ncmul::return_type_tinfo(void) const
 510 {
 511     if (seq.size()==0) {
 512         // mul without factors: should not happen
 513         return tinfo_key;
 514     }
 515     // return type_info of first noncommutative element
 516     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 517         if ((*cit).return_type()==return_types::noncommutative) {
 518             return (*cit).return_type_tinfo();
 519         }
 520     }
 521     // no noncommutative element found, should not happen
 522     return tinfo_key;
 523 }
 524
 525 //////////
 526 // new virtual functions which can be overridden by derived classes
 527 //////////
 528
 529 // none
 530
 531 //////////
 532 // non-virtual functions in this class
 533 //////////
 534
 535 exvector ncmul::expandchildren(unsigned options) const
 536 {
 537     exvector s;
 538     s.reserve(seq.size());
 539
 540     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 541         s.push_back((*it).expand(options));
 542     }
 543     return s;
 544 }
 545
 546 exvector const & ncmul::get_factors(void) const
 547 {
 548     return seq;
 549 }
 550
 551 //////////
 552 // static member variables
 553 //////////
 554
 555 // protected
 556
 557 unsigned ncmul::precedence=50;
 558
 559
 560 //////////
 561 // global constants
 562 //////////
 563
 564 const ncmul some_ncmul;
 565 type_info const & typeid_ncmul=typeid(some_ncmul);
 566
 567 //////////
 568 // friend functions
 569 //////////
 570
 571 ex nonsimplified_ncmul(exvector const & v)
 572 {
 573     return (new ncmul(v))->setflag(status_flags::dynallocated);
 574 }
 575
 576 ex simplified_ncmul(exvector const & v)
 577 {
 578     if (v.size()==0) {
 579         return exONE();
 580     } else if (v.size()==1) {
 581         return v[0];
 582     }
 583     return (new ncmul(v))->setflag(status_flags::dynallocated |
 584                                    status_flags::evaluated);
 585 }
 586
 587