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