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