ginac/ncmul.cpp

   1 /** @file ncmul.cpp
   2  *
   3  *  Implementation of GiNaC's non-commutative products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 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 "archive.h"
  32 #include "debugmsg.h"
  33 #include "utils.h"
  34
  35 #ifndef NO_NAMESPACE_GINAC
  36 namespace GiNaC {
  37 #endif // ndef NO_NAMESPACE_GINAC
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
  40
  41 //////////
  42 // default constructor, destructor, copy constructor assignment operator and helpers
  43 //////////
  44
  45 // public
  46
  47 ncmul::ncmul()
  48 {
  49         debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
  50         tinfo_key = TINFO_ncmul;
  51 }
  52
  53 // protected
  54
  55 void ncmul::copy(const ncmul & other)
  56 {
  57         inherited::copy(other);
  58 }
  59
  60 void ncmul::destroy(bool call_parent)
  61 {
  62         if (call_parent) inherited::destroy(call_parent);
  63 }
  64
  65 //////////
  66 // other constructors
  67 //////////
  68
  69 // public
  70
  71 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
  72 {
  73         debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  74         tinfo_key = TINFO_ncmul;
  75 }
  76
  77 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
  78 {
  79         debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
  80         tinfo_key = TINFO_ncmul;
  81 }
  82
  83 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  84              const ex & f4) : inherited(f1,f2,f3,f4)
  85 {
  86         debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
  87         tinfo_key = TINFO_ncmul;
  88 }
  89
  90 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  91              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
  92 {
  93         debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
  94         tinfo_key = TINFO_ncmul;
  95 }
  96
  97 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
  98              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
  99 {
 100         debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 101         tinfo_key = TINFO_ncmul;
 102 }
 103
 104 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
 105 {
 106         debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 107         tinfo_key = TINFO_ncmul;
 108 }
 109
 110 ncmul::ncmul(exvector * vp) : inherited(vp)
 111 {
 112         debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 113         tinfo_key = TINFO_ncmul;
 114 }
 115
 116 //////////
 117 // archiving
 118 //////////
 119
 120 /** Construct object from archive_node. */
 121 ncmul::ncmul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 122 {
 123         debugmsg("ncmul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 124 }
 125
 126 /** Unarchive the object. */
 127 ex ncmul::unarchive(const archive_node &n, const lst &sym_lst)
 128 {
 129         return (new ncmul(n, sym_lst))->setflag(status_flags::dynallocated);
 130 }
 131
 132 /** Archive the object. */
 133 void ncmul::archive(archive_node &n) const
 134 {
 135         inherited::archive(n);
 136 }
 137
 138
 139 //////////
 140 // functions overriding virtual functions from bases classes
 141 //////////
 142
 143 // public
 144
 145 void ncmul::print(std::ostream & os, unsigned upper_precedence) const
 146 {
 147         debugmsg("ncmul print",LOGLEVEL_PRINT);
 148         printseq(os,'(','%',')',precedence,upper_precedence);
 149 }
 150
 151 void ncmul::printraw(std::ostream & os) const
 152 {
 153         debugmsg("ncmul printraw",LOGLEVEL_PRINT);
 154         os << "%(";
 155         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 156                 (*it).bp->printraw(os);
 157                 os << ",";
 158         }
 159         os << ",hash=" << hashvalue << ",flags=" << flags;
 160         os << ")";
 161 }
 162
 163 void ncmul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
 164 {
 165         debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
 166         exvector::const_iterator it;
 167         exvector::const_iterator itend = seq.end()-1;
 168         os << "ncmul(";
 169         for (it=seq.begin(); it!=itend; ++it) {
 170                 (*it).bp->printcsrc(os,precedence);
 171                 os << ",";
 172         }
 173         (*it).bp->printcsrc(os,precedence);
 174         os << ")";
 175 }
 176
 177 bool ncmul::info(unsigned inf) const
 178 {
 179         throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
 180 }
 181
 182 typedef std::vector<int> intvector;
 183
 184 ex ncmul::expand(unsigned options) const
 185 {
 186         exvector sub_expanded_seq;
 187         intvector positions_of_adds;
 188         intvector number_of_add_operands;
 189
 190         exvector expanded_seq=expandchildren(options);
 191
 192         positions_of_adds.resize(expanded_seq.size());
 193         number_of_add_operands.resize(expanded_seq.size());
 194
 195         int number_of_adds=0;
 196         int number_of_expanded_terms=1;
 197
 198         unsigned current_position=0;
 199         exvector::const_iterator last=expanded_seq.end();
 200         for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 201                 if (is_ex_exactly_of_type((*cit),add)) {
 202                         positions_of_adds[number_of_adds]=current_position;
 203                         const add & expanded_addref=ex_to_add(*cit);
 204                         number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
 205                         number_of_expanded_terms *= expanded_addref.seq.size();
 206                         number_of_adds++;
 207                 }
 208                 current_position++;
 209         }
 210
 211         if (number_of_adds==0) {
 212                 return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
 213                                                                                                         status_flags::expanded);
 214         }
 215
 216         exvector distrseq;
 217         distrseq.reserve(number_of_expanded_terms);
 218
 219         intvector k;
 220         k.resize(number_of_adds);
 221
 222         int l;
 223         for (l=0; l<number_of_adds; l++) {
 224                 k[l]=0;
 225         }
 226
 227         while (1) {
 228                 exvector term;
 229                 term=expanded_seq;
 230                 for (l=0; l<number_of_adds; l++) {
 231                         GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
 232                         const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]]);
 233                         term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
 234                 }
 235                 distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
 236                                                                                                                 status_flags::expanded));
 237
 238                 // increment k[]
 239                 l=number_of_adds-1;
 240                 while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
 241                         k[l]=0;
 242                         l--;
 243                 }
 244                 if (l<0) break;
 245         }
 246
 247         return (new add(distrseq))->setflag(status_flags::dynallocated |
 248                                                                                 status_flags::expanded);
 249 }
 250
 251 int ncmul::degree(const symbol & s) const
 252 {
 253         int deg_sum=0;
 254         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 255                 deg_sum+=(*cit).degree(s);
 256         }
 257         return deg_sum;
 258 }
 259
 260 int ncmul::ldegree(const symbol & s) const
 261 {
 262         int deg_sum=0;
 263         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 264                 deg_sum+=(*cit).ldegree(s);
 265         }
 266         return deg_sum;
 267 }
 268
 269 ex ncmul::coeff(const symbol & s, int n) const
 270 {
 271         exvector coeffseq;
 272         coeffseq.reserve(seq.size());
 273
 274         if (n==0) {
 275                 // product of individual coeffs
 276                 // if a non-zero power of s is found, the resulting product will be 0
 277                 exvector::const_iterator it=seq.begin();
 278                 while (it!=seq.end()) {
 279                         coeffseq.push_back((*it).coeff(s,n));
 280                         ++it;
 281                 }
 282                 return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 283         }
 284
 285         exvector::const_iterator it=seq.begin();
 286         bool coeff_found=0;
 287         while (it!=seq.end()) {
 288                 ex c=(*it).coeff(s,n);
 289                 if (!c.is_zero()) {
 290                         coeffseq.push_back(c);
 291                         coeff_found=1;
 292                 } else {
 293                         coeffseq.push_back(*it);
 294                 }
 295                 ++it;
 296         }
 297
 298         if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 299
 300         return _ex0();
 301 }
 302
 303 unsigned ncmul::count_factors(const ex & e) const
 304 {
 305         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 306                 (is_ex_exactly_of_type(e,ncmul))) {
 307                 unsigned factors=0;
 308                 for (unsigned i=0; i<e.nops(); i++)
 309                         factors += count_factors(e.op(i));
 310
 311                 return factors;
 312         }
 313         return 1;
 314 }
 315
 316 void ncmul::append_factors(exvector & v, const ex & e) const
 317 {
 318         if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
 319                 (is_ex_exactly_of_type(e,ncmul))) {
 320                 for (unsigned i=0; i<e.nops(); i++)
 321                         append_factors(v,e.op(i));
 322
 323                 return;
 324         }
 325         v.push_back(e);
 326 }
 327
 328 typedef std::vector<unsigned> unsignedvector;
 329 typedef std::vector<exvector> exvectorvector;
 330
 331 ex ncmul::eval(int level) const
 332 {
 333         // simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 334         //                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 335         //                  ncmul(x) -> x
 336         //                  ncmul() -> 1
 337         //                  ncmul(...,c1,...,c2,...)
 338         //                      *(c1,c2,ncmul(...)) (pull out commutative elements)
 339         //                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 340         //                      (collect elements of same type)
 341         //                  ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
 342         // the following rule would be nice, but produces a recursion,
 343         // which must be trapped by introducing a flag that the sub-ncmuls()
 344         // are already evaluated (maybe later...)
 345         //                  ncmul(x1,x2,...,X,y1,y2,...) ->
 346         //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
 347         //                      (X noncommutative_composite)
 348
 349         if ((level==1)&&(flags & status_flags::evaluated)) {
 350                 return *this;
 351         }
 352
 353         exvector evaledseq=evalchildren(level);
 354
 355         // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
 356         //     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
 357         unsigned factors=0;
 358         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 359                 factors += count_factors(*cit);
 360         }
 361
 362         exvector assocseq;
 363         assocseq.reserve(factors);
 364         for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
 365                 append_factors(assocseq,*cit);
 366         }
 367
 368         // ncmul(x) -> x
 369         if (assocseq.size()==1) return *(seq.begin());
 370
 371         // ncmul() -> 1
 372         if (assocseq.size()==0) return _ex1();
 373
 374         // determine return types
 375         unsignedvector rettypes;
 376         rettypes.reserve(assocseq.size());
 377         unsigned i=0;
 378         unsigned count_commutative=0;
 379         unsigned count_noncommutative=0;
 380         unsigned count_noncommutative_composite=0;
 381         for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 382                 switch (rettypes[i]=(*cit).return_type()) {
 383                 case return_types::commutative:
 384                         count_commutative++;
 385                         break;
 386                 case return_types::noncommutative:
 387                         count_noncommutative++;
 388                         break;
 389                 case return_types::noncommutative_composite:
 390                         count_noncommutative_composite++;
 391                         break;
 392                 default:
 393                         throw(std::logic_error("ncmul::eval(): invalid return type"));
 394                 }
 395                 ++i;
 396         }
 397         GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 398
 399         // ncmul(...,c1,...,c2,...) ->
 400         //     *(c1,c2,ncmul(...)) (pull out commutative elements)
 401         if (count_commutative!=0) {
 402                 exvector commutativeseq;
 403                 commutativeseq.reserve(count_commutative+1);
 404                 exvector noncommutativeseq;
 405                 noncommutativeseq.reserve(assocseq.size()-count_commutative);
 406                 for (i=0; i<assocseq.size(); ++i) {
 407                         if (rettypes[i]==return_types::commutative) {
 408                                 commutativeseq.push_back(assocseq[i]);
 409                         } else {
 410                                 noncommutativeseq.push_back(assocseq[i]);
 411                         }
 412                 }
 413                 commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
 414                 return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
 415         }
 416
 417         // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
 418         //     (collect elements of same type)
 419
 420         if (count_noncommutative_composite==0) {
 421                 // there are neither commutative nor noncommutative_composite
 422                 // elements in assocseq
 423                 GINAC_ASSERT(count_commutative==0);
 424
 425                 exvectorvector evv;
 426                 unsignedvector rttinfos;
 427                 evv.reserve(assocseq.size());
 428                 rttinfos.reserve(assocseq.size());
 429
 430                 for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
 431                         unsigned ti=(*cit).return_type_tinfo();
 432                         // search type in vector of known types
 433                         for (i=0; i<rttinfos.size(); ++i) {
 434                                 if (ti==rttinfos[i]) {
 435                                         evv[i].push_back(*cit);
 436                                         break;
 437                                 }
 438                         }
 439                         if (i>=rttinfos.size()) {
 440                                 // new type
 441                                 rttinfos.push_back(ti);
 442                                 evv.push_back(exvector());
 443                                 (*(evv.end()-1)).reserve(assocseq.size());
 444                                 (*(evv.end()-1)).push_back(*cit);
 445                         }
 446                 }
 447
 448 #ifdef DO_GINAC_ASSERT
 449                 GINAC_ASSERT(evv.size()==rttinfos.size());
 450                 GINAC_ASSERT(evv.size()>0);
 451                 unsigned s=0;
 452                 for (i=0; i<evv.size(); ++i) {
 453                         s += evv[i].size();
 454                 }
 455                 GINAC_ASSERT(s==assocseq.size());
 456 #endif // def DO_GINAC_ASSERT
 457
 458                 // if all elements are of same type, simplify the string
 459                 if (evv.size()==1) {
 460                         return evv[0][0].simplify_ncmul(evv[0]);
 461                 }
 462
 463                 exvector splitseq;
 464                 splitseq.reserve(evv.size());
 465                 for (i=0; i<evv.size(); ++i) {
 466                         splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
 467                 }
 468
 469                 return (new mul(splitseq))->setflag(status_flags::dynallocated);
 470         }
 471
 472         return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
 473                                                                                   status_flags::evaluated);
 474 }
 475
 476 exvector ncmul::get_indices(void) const
 477 {
 478         // return union of indices of factors
 479         exvector iv;
 480         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 481                 exvector subiv=(*cit).get_indices();
 482                 iv.reserve(iv.size()+subiv.size());
 483                 for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 484                         iv.push_back(*cit2);
 485                 }
 486         }
 487         return iv;
 488 }
 489
 490 ex ncmul::subs(const lst & ls, const lst & lr) const
 491 {
 492         return ncmul(subschildren(ls, lr));
 493 }
 494
 495 ex ncmul::thisexprseq(const exvector & v) const
 496 {
 497         return (new ncmul(v))->setflag(status_flags::dynallocated);
 498 }
 499
 500 ex ncmul::thisexprseq(exvector * vp) const
 501 {
 502         return (new ncmul(vp))->setflag(status_flags::dynallocated);
 503 }
 504
 505 // protected
 506
 507 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
 508  *  @see ex::diff */
 509 ex ncmul::derivative(const symbol & s) const
 510 {
 511         return _ex0();
 512 }
 513
 514 int ncmul::compare_same_type(const basic & other) const
 515 {
 516         return inherited::compare_same_type(other);
 517 }
 518
 519 unsigned ncmul::return_type(void) const
 520 {
 521         if (seq.size()==0) {
 522                 // ncmul without factors: should not happen, but commutes
 523                 return return_types::commutative;
 524         }
 525
 526         bool all_commutative=1;
 527         unsigned rt;
 528         exvector::const_iterator cit_noncommutative_element; // point to first found nc element
 529
 530         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 531                 rt=(*cit).return_type();
 532                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 533                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 534                         // first nc element found, remember position
 535                         cit_noncommutative_element=cit;
 536                         all_commutative=0;
 537                 }
 538                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 539                         // another nc element found, compare type_infos
 540                         if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
 541                                 // diffent types -> mul is ncc
 542                                 return return_types::noncommutative_composite;
 543                         }
 544                 }
 545         }
 546         // all factors checked
 547         GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 548         return all_commutative ? return_types::commutative : return_types::noncommutative;
 549 }
 550
 551 unsigned ncmul::return_type_tinfo(void) const
 552 {
 553         if (seq.size()==0) {
 554                 // mul without factors: should not happen
 555                 return tinfo_key;
 556         }
 557         // return type_info of first noncommutative element
 558         for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 559                 if ((*cit).return_type()==return_types::noncommutative) {
 560                         return (*cit).return_type_tinfo();
 561                 }
 562         }
 563         // no noncommutative element found, should not happen
 564         return tinfo_key;
 565 }
 566
 567 //////////
 568 // new virtual functions which can be overridden by derived classes
 569 //////////
 570
 571 // none
 572
 573 //////////
 574 // non-virtual functions in this class
 575 //////////
 576
 577 exvector ncmul::expandchildren(unsigned options) const
 578 {
 579         exvector s;
 580         s.reserve(seq.size());
 581
 582         for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 583                 s.push_back((*it).expand(options));
 584         }
 585         return s;
 586 }
 587
 588 const exvector & ncmul::get_factors(void) const
 589 {
 590         return seq;
 591 }
 592
 593 //////////
 594 // static member variables
 595 //////////
 596
 597 // protected
 598
 599 unsigned ncmul::precedence=50;
 600
 601 //////////
 602 // friend functions
 603 //////////
 604
 605 ex nonsimplified_ncmul(const exvector & v)
 606 {
 607         return (new ncmul(v))->setflag(status_flags::dynallocated);
 608 }
 609
 610 ex simplified_ncmul(const exvector & v)
 611 {
 612         if (v.size()==0) {
 613                 return _ex1();
 614         } else if (v.size()==1) {
 615                 return v[0];
 616         }
 617         return (new ncmul(v))->setflag(status_flags::dynallocated |
 618                                        status_flags::evaluated);
 619 }
 620
 621 #ifndef NO_NAMESPACE_GINAC
 622 } // namespace GiNaC
 623 #endif // ndef NO_NAMESPACE_GINAC