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