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