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 #include "utils.h"
  33
  34 #ifndef NO_GINAC_NAMESPACE
  35 namespace GiNaC {
  36 #endif // ndef NO_GINAC_NAMESPACE
  37
  38 //////////
  39 // default constructor, destructor, copy constructor assignment operator and helpers
  40 //////////
  41
  42 // public
  43
  44 ncmul::ncmul()
  45 {
  46     debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  47     tinfo_key = TINFO_ncmul;
  48 }
  49
  50 ncmul::~ncmul()
  51 {
  52     debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
  53     destroy(0);
  54 }
  55
  56 ncmul::ncmul(ncmul const & other)
  57 {
  58     debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
  59     copy(other);
  60 }
  61
  62 ncmul const & ncmul::operator=(ncmul const & other)
  63 {
  64     debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
  65     if (this != &other) {
  66         destroy(1);
  67         copy(other);
  68     }
  69     return *this;
  70 }
  71
  72 // protected
  73
  74 void ncmul::copy(ncmul const & other)
  75 {
  76     exprseq::copy(other);
  77 }
  78
  79 void ncmul::destroy(bool call_parent)
  80 {
  81     if (call_parent) exprseq::destroy(call_parent);
  82 }
  83
  84 //////////
  85 // other constructors
  86 //////////
  87
  88 // public
  89
  90 ncmul::ncmul(ex const & lh, ex const & rh) :
  91     exprseq(lh,rh)
  92 {
  93     debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  94     tinfo_key = TINFO_ncmul;
  95 }
  96
  97 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
  98     exprseq(f1,f2,f3)
  99 {
 100     debugmsg("ncmul constructor from 3 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) : exprseq(f1,f2,f3,f4)
 106 {
 107     debugmsg("ncmul constructor from 4 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) : exprseq(f1,f2,f3,f4,f5)
 113 {
 114     debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 115     tinfo_key = TINFO_ncmul;
 116 }
 117
 118 ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
 119       ex const & f4, ex const & f5, ex const & f6) :
 120     exprseq(f1,f2,f3,f4,f5,f6)
 121 {
 122     debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 123     tinfo_key = TINFO_ncmul;
 124 }
 125
 126 ncmul::ncmul(exvector const & v, bool discardable) : exprseq(v,discardable)
 127 {
 128     debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 129     tinfo_key = TINFO_ncmul;
 130 }
 131
 132 ncmul::ncmul(exvector * vp) : exprseq(vp)
 133 {
 134     debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 135     tinfo_key = TINFO_ncmul;
 136 }
 137
 138 //////////
 139 // functions overriding virtual functions from bases classes
 140 //////////
 141
 142 // public
 143
 144 basic * ncmul::duplicate() const
 145 {
 146     debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
 147     return new ncmul(*this);
 148 }
 149
 150 void ncmul::print(ostream & os, unsigned upper_precedence) const
 151 {
 152     debugmsg("ncmul print",LOGLEVEL_PRINT);
 153     printseq(os,'(','%',')',precedence,upper_precedence);
 154 }
 155
 156 void ncmul::printraw(ostream & os) const
 157 {
 158     debugmsg("ncmul printraw",LOGLEVEL_PRINT);
 159
 160     os << "%(";
 161     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 162         (*it).bp->printraw(os);
 163         os << ",";
 164     }
 165     os << ",hash=" << hashvalue << ",flags=" << flags;
 166     os << ")";
 167 }
 168
 169 void ncmul::printcsrc(ostream & os, unsigned upper_precedence) const
 170 {
 171     debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 172     exvector::const_iterator it;
 173     exvector::const_iterator itend = seq.end()-1;
 174     os << "ncmul(";
 175     for (it=seq.begin(); it!=itend; ++it) {
 176         (*it).bp->printcsrc(os,precedence);
 177         os << ",";
 178     }
 179     (*it).bp->printcsrc(os,precedence);
 180     os << ")";
 181 }
 182
 183 bool ncmul::info(unsigned inf) const
 184 {
 185     throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 186 }
 187
 188 typedef vector<int> intvector;
 189
 190 ex ncmul::expand(unsigned options) const
 191 {
 192     exvector sub_expanded_seq;
 193     intvector positions_of_adds;
 194     intvector number_of_add_operands;
 195
 196     exvector expanded_seq=expandchildren(options);
 197
 198     positions_of_adds.resize(expanded_seq.size());
 199     number_of_add_operands.resize(expanded_seq.size());
 200
 201     int number_of_adds=0;
 202     int number_of_expanded_terms=1;
 203
 204     unsigned current_position=0;
 205     exvector::const_iterator last=expanded_seq.end();
 206     for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 207         if (is_ex_exactly_of_type((*cit),add)) {
 208             positions_of_adds[number_of_adds]=current_position;
 209             add const & expanded_addref=ex_to_add(*cit);
 210             number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 211             number_of_expanded_terms *= expanded_addref.seq.size();
 212             number_of_adds++;
 213         }
 214         current_position++;
 215     }
 216
 217     if (number_of_adds==0) {
 218         return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 219                                                     status_flags::expanded);
 220     }
 221
 222     exvector distrseq;
 223     distrseq.reserve(number_of_expanded_terms);
 224
 225     intvector k;
 226     k.resize(number_of_adds);
 227
 228     int l;
 229     for (l=0; l<number_of_adds; l++) {
 230         k[l]=0;
 231     }
 232
 233     while (1) {
 234         exvector term;
 235         term=expanded_seq;
 236         for (l=0; l<number_of_adds; l++) {
 237             GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 238             add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 239             term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 240         }
 241         distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 242                                                         status_flags::expanded));
 243
 244         // increment k[]
 245         l=number_of_adds-1;
 246         while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 247             k[l]=0;
 248             l--;
 249         }
 250         if (l<0) break;
 251     }
 252
 253     return (new add(distrseq))->setflag(status_flags::dynallocated |
 254                                         status_flags::expanded);
 255 }
 256
 257 int ncmul::degree(symbol const & s) const
 258 {
 259     int deg_sum=0;
 260     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 261         deg_sum+=(*cit).degree(s);
 262     }
 263     return deg_sum;
 264 }
 265
 266 int ncmul::ldegree(symbol const & s) const
 267 {
 268     int deg_sum=0;
 269     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 270         deg_sum+=(*cit).ldegree(s);
 271     }
 272     return deg_sum;
 273 }
 274
 275 ex ncmul::coeff(symbol const & s, int const n) const
 276 {
 277     exvector coeffseq;
 278     coeffseq.reserve(seq.size());
 279
 280     if (n==0) {
 281         // product of individual coeffs
 282         // if a non-zero power of s is found, the resulting product will be 0
 283         exvector::const_iterator it=seq.begin();
 284         while (it!=seq.end()) {
 285             coeffseq.push_back((*it).coeff(s,n));
 286             ++it;
 287         }
 288         return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 289     }
 290
 291     exvector::const_iterator it=seq.begin();
 292     bool coeff_found=0;
 293     while (it!=seq.end()) {
 294         ex c=(*it).coeff(s,n);
 295         if (!c.is_zero()) {
 296             coeffseq.push_back(c);
 297             coeff_found=1;
 298         } else {
 299             coeffseq.push_back(*it);
 300         }
 301         ++it;
 302     }
 303
 304     if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 305
 306     return _ex0();
 307 }
 308
 309 unsigned ncmul::count_factors(ex const & e) const
 310 {
 311     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 312         (is_ex_exactly_of_type(e,ncmul))) {
 313         unsigned factors=0;
 314         for (int i=0; i<e.nops(); i++) {
 315             factors += count_factors(e.op(i));
 316         }
 317         return factors;
 318     }
 319     return 1;
 320 }
 321
 322 void ncmul::append_factors(exvector & v, ex const & e) const
 323 {
 324     if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 325         (is_ex_exactly_of_type(e,ncmul))) {
 326         for (int i=0; i<e.nops(); i++) {
 327             append_factors(v,e.op(i));
 328         }
 329         return;
 330     }
 331     v.push_back(e);
 332 }
 333
 334 typedef vector<unsigned> unsignedvector;
 335 typedef vector<exvector> exvectorvector;
 336
 337 ex ncmul::eval(int level) const
 338 {
 339     // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 340     //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 341     //                  ncmul(x) -> x
 342     //                  ncmul() -> 1
 343     //                  ncmul(...,c1,...,c2,...) ->
 344     //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 345     //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 346     //                      (collect elements of same type)
 347     //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 348     // the following rule would be nice, but produces a recursion,
 349     // which must be trapped by introducing a flag that the sub-ncmuls()
 350     // are already evaluated (maybe later...)
 351     //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 352     //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 353     //                      (X noncommutative_composite)
 354
 355     if ((level==1)&&(flags & status_flags::evaluated)) {
 356         return *this;
 357     }
 358
 359     exvector evaledseq=evalchildren(level);
 360
 361     // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 362     //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 363     unsigned factors=0;
 364     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 365         factors += count_factors(*cit);
 366     }
 367
 368     exvector assocseq;
 369     assocseq.reserve(factors);
 370     for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 371         append_factors(assocseq,*cit);
 372     }
 373
 374     // ncmul(x) -> x
 375     if (assocseq.size()==1) return *(seq.begin());
 376
 377     // ncmul() -> 1
 378     if (assocseq.size()==0) return _ex1();
 379
 380     // determine return types
 381     unsignedvector rettypes;
 382     rettypes.reserve(assocseq.size());
 383     unsigned i=0;
 384     unsigned count_commutative=0;
 385     unsigned count_noncommutative=0;
 386     unsigned count_noncommutative_composite=0;
 387     for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 388         switch (rettypes[i]=(*cit).return_type()) {
 389         case return_types::commutative:
 390             count_commutative++;
 391             break;
 392         case return_types::noncommutative:
 393             count_noncommutative++;
 394             break;
 395         case return_types::noncommutative_composite:
 396             count_noncommutative_composite++;
 397             break;
 398         default:
 399             throw(std::logic_error("ncmul::eval(): invalid return type"));
 400         }
 401         ++i;
 402     }
 403     GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 404
 405     // ncmul(...,c1,...,c2,...) ->
 406     //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 407     if (count_commutative!=0) {
 408         exvector commutativeseq;
 409         commutativeseq.reserve(count_commutative+1);
 410         exvector noncommutativeseq;
 411         noncommutativeseq.reserve(assocseq.size()-count_commutative);
 412         for (i=0; i<assocseq.size(); ++i) {
 413             if (rettypes[i]==return_types::commutative) {
 414                 commutativeseq.push_back(assocseq[i]);
 415             } else {
 416                 noncommutativeseq.push_back(assocseq[i]);
 417             }
 418         }
 419         commutativeseq.push_back((new ncmul(noncommutativeseq,1))->
 420                                   setflag(status_flags::dynallocated));
 421         return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 422     }
 423
 424     // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 425     //     (collect elements of same type)
 426
 427     if (count_noncommutative_composite==0) {
 428         // there are neither commutative nor noncommutative_composite
 429         // elements in assocseq
 430         GINAC_ASSERT(count_commutative==0);
 431
 432         exvectorvector evv;
 433         unsignedvector rttinfos;
 434         evv.reserve(assocseq.size());
 435         rttinfos.reserve(assocseq.size());
 436
 437         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 438             unsigned ti=(*cit).return_type_tinfo();
 439             // search type in vector of known types
 440             for (i=0; i<rttinfos.size(); ++i) {
 441                 if (ti==rttinfos[i]) {
 442                     evv[i].push_back(*cit);
 443                     break;
 444                 }
 445             }
 446             if (i>=rttinfos.size()) {
 447                 // new type
 448                 rttinfos.push_back(ti);
 449                 evv.push_back(exvector());
 450                 (*(evv.end()-1)).reserve(assocseq.size());
 451                 (*(evv.end()-1)).push_back(*cit);
 452             }
 453         }
 454
 455 #ifdef DO_GINAC_ASSERT
 456         GINAC_ASSERT(evv.size()==rttinfos.size());
 457         GINAC_ASSERT(evv.size()>0);
 458         unsigned s=0;
 459         for (i=0; i<evv.size(); ++i) {
 460             s += evv[i].size();
 461         }
 462         GINAC_ASSERT(s==assocseq.size());
 463 #endif // def DO_GINAC_ASSERT
 464
 465         // if all elements are of same type, simplify the string
 466         if (evv.size()==1) {
 467             return evv[0][0].simplify_ncmul(evv[0]);
 468         }
 469
 470         exvector splitseq;
 471         splitseq.reserve(evv.size());
 472         for (i=0; i<evv.size(); ++i) {
 473             splitseq.push_back((new ncmul(evv[i]))->
 474                                setflag(status_flags::dynallocated));
 475         }
 476
 477         return (new mul(splitseq))->setflag(status_flags::dynallocated);
 478     }
 479
 480     return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 481                                           status_flags::evaluated);
 482 }
 483
 484 exvector ncmul::get_indices(void) const
 485 {
 486     // return union of indices of factors
 487     exvector iv;
 488     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 489         exvector subiv=(*cit).get_indices();
 490         iv.reserve(iv.size()+subiv.size());
 491         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 492             iv.push_back(*cit2);
 493         }
 494     }
 495     return iv;
 496 }
 497
 498 ex ncmul::subs(lst const & ls, lst const & lr) const
 499 {
 500     return ncmul(subschildren(ls, lr));
 501 }
 502
 503 ex ncmul::thisexprseq(exvector const & v) const
 504 {
 505     return (new ncmul(v))->setflag(status_flags::dynallocated);
 506 }
 507
 508 ex ncmul::thisexprseq(exvector * vp) const
 509 {
 510     return (new ncmul(vp))->setflag(status_flags::dynallocated);
 511 }
 512
 513 // protected
 514
 515 int ncmul::compare_same_type(basic const & other) const
 516 {
 517     return exprseq::compare_same_type(other);
 518 }
 519
 520 unsigned ncmul::return_type(void) const
 521 {
 522     if (seq.size()==0) {
 523         // ncmul without factors: should not happen, but commutes
 524         return return_types::commutative;
 525     }
 526
 527     bool all_commutative=1;
 528     unsigned rt;
 529     exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 530
 531     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 532         rt=(*cit).return_type();
 533         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 534         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 535             // first nc element found, remember position
 536             cit_noncommutative_element=cit;
 537             all_commutative=0;
 538         }
 539         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 540             // another nc element found, compare type_infos
 541             if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 542                 // diffent types -> mul is ncc
 543                 return return_types::noncommutative_composite;
 544             }
 545         }
 546     }
 547     // all factors checked
 548     GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 549     return all_commutative ? return_types::commutative : return_types::noncommutative;
 550 }
 551
 552 unsigned ncmul::return_type_tinfo(void) const
 553 {
 554     if (seq.size()==0) {
 555         // mul without factors: should not happen
 556         return tinfo_key;
 557     }
 558     // return type_info of first noncommutative element
 559     for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 560         if ((*cit).return_type()==return_types::noncommutative) {
 561             return (*cit).return_type_tinfo();
 562         }
 563     }
 564     // no noncommutative element found, should not happen
 565     return tinfo_key;
 566 }
 567
 568 //////////
 569 // new virtual functions which can be overridden by derived classes
 570 //////////
 571
 572 // none
 573
 574 //////////
 575 // non-virtual functions in this class
 576 //////////
 577
 578 exvector ncmul::expandchildren(unsigned options) const
 579 {
 580     exvector s;
 581     s.reserve(seq.size());
 582
 583     for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 584         s.push_back((*it).expand(options));
 585     }
 586     return s;
 587 }
 588
 589 exvector const & ncmul::get_factors(void) const
 590 {
 591     return seq;
 592 }
 593
 594 //////////
 595 // static member variables
 596 //////////
 597
 598 // protected
 599
 600 unsigned ncmul::precedence=50;
 601
 602
 603 //////////
 604 // global constants
 605 //////////
 606
 607 const ncmul some_ncmul;
 608 type_info const & typeid_ncmul=typeid(some_ncmul);
 609
 610 //////////
 611 // friend functions
 612 //////////
 613
 614 ex nonsimplified_ncmul(exvector const & v)
 615 {
 616     return (new ncmul(v))->setflag(status_flags::dynallocated);
 617 }
 618
 619 ex simplified_ncmul(exvector const & v)
 620 {
 621     if (v.size()==0) {
 622         return _ex1();
 623     } else if (v.size()==1) {
 624         return v[0];
 625     }
 626     return (new ncmul(v))->setflag(status_flags::dynallocated |
 627                                    status_flags::evaluated);
 628 }
 629
 630 #ifndef NO_GINAC_NAMESPACE
 631 } // namespace GiNaC
 632 #endif // ndef NO_GINAC_NAMESPACE